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"IF ij is the total internal force acting on mi (due to all other particles), and F i' is the external force on the ith particle. If we sum over all particles of the system, we obtain, by use of Newton's third law, N
L
Fii
=
(2a-24)
0
i=l MOTION OF THE CENTER OF MASS.
The analog of Newton's second law for the
entire system is therefore
MR
r
(2a-25)
N
where M
=
mi is the total mass of the system,
R is the acceleration of the center
i= 1
of mass of the system, and
~iFi'
is the total external force.
MOMENT OF MOMENTUM AND TORQUE. By forming the cross product of both sides of Eq. (2a-23) with ri and summing over all particles we can show that
~
I
[ri X (m;!i)] =
L
Ti'
= T'
(2a-26)
provided that the internal force Fij acts along the straight line connecting the particles i and j in each case. . In particular, if ri, is the position of the ith particle with respect to the center of mass, so that
it follows from Eq. (2a-26) that N
N
#t l
i=l
fi'
X (m;i:i')
L
ri, X F'
i=l
(2a-27)
FUNDAMENTAL CONCEPTS OF MECHANICS.
UNITS
2-9
That is, the time rate of change of the moment of momentum is equal to the total external torque when both are taken with respect to the center of mass. The above equation is also true if the center of mass is replaced by any point moving with the velocity of the center of mass, which may, of course, also be at rest. Conservation of Momentum. It follows from Eqs. (2a-25) and (2a-26) that: 1. If the total external force is zero, the linear momentum of the center of mass is constant. 2. If the total external torque about a fixed point, or one moving with velocity of the center of mass, is zero, the moment of momentum about that point is constant. Conservation of Energy. WORK-ENERGY THEOREM. The total work done by the external and internal forces acting on the system is equal to the change in the total kinetic energy of the system (the sum of the kinetic energies of all particles) N
\' i 1..
", - " L,\'N lei'r
mi(v i
riO
Vi) =
i=l
(F i'
+ Fii). dr;
(2a-28)
1=1
Z H Q
[Jl
2b. Density of Solids H. M. TRENTl
u.s. Naval Research Laboratory D. E. STONE
Vertex Corporation' R. BRUCE LINDSAY
Brown University
For the definition of density p consult Sec. 2a-3. The cgs unit of density is the gram per cubic centimeter and this is used throughout the tables in this subsection. Densities of the elements in solid form are given in Table 2b-1. All data are takeIt from "Smithsonian Physical Tables" (9th revised edition, 1954) unless otherwi~ stated. The values marked * are calculated densities from X-ray crystallographit data at room temperature and are taken from International Critical Tables (1926}. All others are measured values for poly crystalline condition, save when otherwiS( stated. Standard room temperature is understood, unless otherwise stated. TABLE
2b-1.
DENSITY OF THE ELEMENTS IN SOLID FORM;
Element
Physical state
Density, g/cm 3
Temp., °C
Aluminum ............ Aluminum ............ Antimony ............. Antimony ............. Argon ................ Argon ............. Arsenic ............... Arsenic ............... Barium ............... Beryllium ............. Beryllium ............. Bismuth .............. Bismuth .............. Boron ................ Bromine .............. Cadmium ............. Cadmium ............. Calcium .............. Calcium .............. Carbon ...............
Commercial hard-drawn solid Single crystal Vacuo-distilled solid Single crystal Solid Single crystal Crystallized solid Single crystal Solid Solid Single crystal Vacuo-distilled solid Single crystal Crystallized solid Solid Vacuo-distilled solid Single crystal Solid Single crystal Diamond
2.70 2.692* 6.62 6.73* 1.65 1.645* 5.73 5.75* 3.5 1.85 1.83* 9.78 9.86* 2.535 4.2 8.65 8.56* 1.55 1.54* 3.52
20 20 -233 -253 14 20 20 2(]
-273 20 20 20
Deceased . • H. M. Childers of the Vertex Corporation provided valuable consultant service. 1
2-:\1
---
2-20
MECHANICS TABLE
2b-1.
DENSITY OF THE ELEMENTS IN SOLID FORM '.
Element Carbon .......... ···· . Cerium ............ ·· . Cerium ............. · . Cerium ............... Cesium .......... ···· . Chlorine .............. ChrOnllUDl ............ Chromium ............ Cobalt ............ ·.· . Cobalt ................ Columbium ........... Copper ............... Copper ............... Erbium ............ ·· . Fluorine .............. Gallium .............. Germanium ........... GermaniuDl ........... Gold ................. Gold ................. Gold ............ ··.· . Hafnium .............. Hafnium .............. Helium ............... Hydrogen ............. Indium ............... Indium ............... Iodine ................ Iridium ............... Iridium ............... Iron .................. Iron .................. Krypton .............. Lanthanum ........... Lead ................. Lead ................. Lithium .............. Lithium .............. Magnesium ........... Magnesium ........... Manganese ............ Manganese ............ Mercury .............. Molybdenum .......... Molybdenum .......... Neodymium ...........
Physical state Graphite Solid Cubic crystal Hexagonal crystal Solid Solid Solid Crystal Solid Cubic crystal Solid Vacuo-distilled solid Single crystal Solid Solid Solid Solid Single crystal Vacuo-distilled solid Cast Single crystal Solid Single crystal Solid Solid Solid Single crystal Solid Solid Single crystal Pure solid Single crystal Fe-a Solid Solid Vacuo-distilled Single crystal Solid Single crystal Solid Single crystal Solid Single crystal Mn-a Solid Solid Single crystal Solid
-
(iJO':I/,Unued)
Density, g/cm"
Temp., °C
2.25 6.90 6.90* 6.73* 1.873 2.2 7.14 7.22* 8.71 8.67* 8.4 8.933 8.95* 4.77 1.5 5.93 5.46 5.38* 18.88 19.3 19.4* 13.3 11.3* 0.19 0.0763 7.28 7.43* 4.94 22.42 22.8* 7.86 7.92* 3.4 6.15 11.342 11.48* 0.534 0.534* 1.74 1.71* 7.3 7.21* 14.193 9.01 10.20* 7.00
20 20 20 -273 20 21 20 20 -273 23 20 20 20 -273 -260 20 17
-273 20 20 20
-38.8
2-21
DENSITY OF SOLIDS TABLE
2b-1.
DENSITY OF THE ELEMENTS IN SOLID FORM
Element Neon ................. NickeL ............... Nickel ................ Nitrogen .............. Osmium .............. Osmium ............... Oxygen ............... Palladium ............. ......... Palladium Phosphorus ........... Phosphorus ........... Phosphorus ........... Platinum ............. Platinum ............. Potassium ............ Praseodymium ........ Radium .............. Rhenium ............. Rhodium ............. Rubidium ............. Ruthenium ............ Samarium ............. Scandium ............. Selenium .............. Selenium .............. Silicon ................ Silicon ................ Silver ................ Silver ................ Sodium ............... Sodium ............... Strontium ............. Sulfur ................ Sulfur ................ Sulfur ................ Tantalum ............. Tantalum ............. Tellurium ............. Tellurium ............. Thallium ............. Thallium ............. Thorium .............. Thorium .............. Tin .................. Tin .................. Tin ..................
Physical state Solid Solid Single crystal Solid Solid Single crystal Solid Solid Single crystal Solid, white Solid, red Solid, black Solid Single crystal Solid Solid Solid Solid Solid Solid Solid Solid Solid Solid Single crystal Solid crystal Single crystal Vacuo-distilled Single crystal Solid Single crystal Solid Solid, rhombic Solid, monoclinic Single crystal Solid Single crystal Solid, crystal Single crystal Solid Single crystal Solid Single crystal Solid, white tetragonal Solid, white rhombic Solid, gray
(Continued)
Density, g/cm 3
Temp.,
1.204 8.8 9.04* 1.14 22.5 22.8* 1.568 12.16 12.25* 1.83 2.20 2.69 21.37 21. 5* 0.87 6.48 5(?) 20.53 12.44 1. 53 12.1 7.7-7.8 3.02(?) 4.82 4.86* 2.42 2.32* 10.492 10.49* 0.9712 0.954* 2.60 2.07 1. 96 2.02* 16.6 17.1 * 6.25 6.26* 11.86 11. 7* 11.00 12.0* 7.29 6.55 5.75
-245
DC
-273 -273
20 20
20 19
20 20 20
17 20
20
2-22
MECHANICS TABLE
2b-1.
DENSITY OF THE ELEMENTS IN SOLID FORM
Element Tin .................. Titanium ............. Titanium ............. Tungsten ............. Tungsten ............. Uranium .............. Vanadium ............ Vanadium ............ yttrium .............. Zinc .................. Zinc .................. Zinc .................. Zirconium ............. Zirconium .............
Physical state White single crystal Solid Single crystal Solid Single crystal Solid Solid Single crystal Solid Solid, vacuo-distilled Solid Single crystal Solid Single crystal
Density, g/cm'
7.30* 4.5 4.58* 19.3 19.3* 18.7 5.87 5.98* 3.8 6.92 4.32 7.04* 6.44 6.47*
(Continued)
Temp.,
DC
18
13 15 20 -273
DENSITY OF SOLIDS
2-23
TABLE 2b-2. DENSITY OF COMMON SOLIDS AT 20°C* Substance Agate .................... . Amber .................. . Anthracite ............... . Aragonite ................ . Asbestos ................. . Basalt ................... . Bee!!wax ................. . Beryl .................... . Bone .................... . Brick .................... . Butter ................... . Calcite ................... . Camphor ................. . Caoutchouc .............. . Celluloid ................. . Cement (set) ............. . Chalk ................... . Charcoal, oak ............. . Charcoal, pine ............ . Cinnabar ................. . Clay ..................... . Coal, soft ................ . Coke .................... . Cork .................... . Cork linoleum ............ . Corundum ............... . Dolomite ................. . Ebonite .................. . Emery ................... . Feldspar ................. . Flint .................... . Fluorite .................. . Garnet .......... : .... .' ... . Gelatin .................. . Glass, common ........ ! • • • • Glass, flint ............ 1• • • • Glue ..................... . Granite ................... . Graphite .............. '... . Gum arabic ........... '... .
Density, g/cm"
2.5-2.7 l.06-1.11 1.4-1.8 2.93 2.0-2.8 2.4-3.1 0.96-0.97 2.69-2.7 1. 7-2.0 1.4-2.2 0.86-0.87 2.71
0.99 0.92-0.99 1.4 2.7-3.0 1.9-2.8 0.57 0.28-0.44 8.12 1.8-2.6 1.2-1.5 1.0-1.7 0.22-0.26 0.55 3.9-4.0 2.84 1.15 4.0 2.55-2.75 2.63 3.18 3.15-4.3 1.27 2.4-2.8 2.9-5.9 1.27 2.64-2.76 2.30-2.72 1.3-1.4
Substance
Density, g/cm"
Gypsum ................. . Hematite ................ . Hornblende .............. . Ice ...................... . Ivory .................... . Lava, basaltic ............ . Lava, trachytic ........... . Leather, dry .............. . Leather, greased .......... . Lime, mortar ............. . Lime, slaked .............. . Limestone ................ . Magnetite ................ . Malachite ................ . Marble .................. . Mica .................... . Olivine .................. . OpaL .................... . Paper .................... . Paraffin .................. . Pitch .................... . Porcelain ................. . Pyrite ................... . Quartz ................... . Resin .................... . Rock salt ............... , . Rubber, hard ........ " ... . Rubber, soft .............. . Rutile ................... . Sandstone ................ . Slate .................... . Soapstone ................ . Starch ................... . Sugar .................... . Talc ..................... . Tallow ................... . Tar .. '................... . Topaz ................... . Tourmaline ............... . Wax, sE')aling .............. .
2.31-2.33 4.9-5.3 3.0 0.917 1.83-1.92 2.8-3.0 2.0-2.7 0.86 1.02 1.65-1. 78 1.3-1.4 2.68-2.76 4.9-5.2 3.7-4.1 2.6-2.84 2.6-3.2 3.27-3.37 2.2 0.7-1.15 0.87-0.91 1.07 2.3-2.5 4.95-5.1 2.65 1.07 2.18 1.19 1.1 4.2 2.19-2.36 2.6-3.3 2.6-2.8 1.53 1.61 2.7-2.8 0.91-0.91 1.02 3.5-3.6 3.0-3.2 1.8
'" The density varies with the state and previous treatment of the solids. The figures quoted may be considered reasonable limits (taken largely from" Smithsonian Physical Tables, .. 9th ed.).
2--24
MECHANICS
2b-3. DENSITY OF STEELS· (At room temperature)
TABLE
Composition Type of steel
p,
Condition
g/em' %C
%Si
%Mn
%Cr
-- -- -0.06 0.23 0.435 1.22 0.31 0.315 0.35 1.73 0.80 0.62 0.98 0.20 0.22 0.21 0.30 0.35
0.01 0.11 0.20 0.16 . ... . ... . ... . ... . ... . ... . ... .... . ... .... ....
0.38 . ............... AlInealed at 1700°F 0.635 . ............... Annealed at 1700°F 0.69 . ............... Annealed at 1580°F 0.35 . ............... Annealed at 1470°F Oil-quenched at 1650"F, tempered at 1350°F 0.74 1.00 Annealed at 1580°F 0.69 1.09 0.24 1.56 Annealed at 1580°F 0.30 1.65 Annealed at 1580°F 0.28 1.67 Annealed at 1580°F 0.22 Annealed at 1580°F 1.67 0.28 1.68 Annealed at 1580°F 0.14 Oil-quenched at 1650"F, tempered at 1380°F 1.85 0.10 2.80 Oil-quenched at 1650°F, tempered at 1380°F 0.19 Oij..quenched at 1650°F, tempered at 1380°F 3.88 0.08 Oil-quenched at 1650°F, tempered at 1380°F 5.54 0.59 0.88+0.20Mo Annealed at 1580°F, tempered at 1185°F
Low-alloy Ni-Cr steel. .. 7.85
0.33
....
0.53
0.80
3.38
Low-alloy Ni-Cr steel ... 7.85
0.325
....
0.55
0.71
3 ..41
1.28 1. 28 0.325 0.51 0.34
.... .... .... .... ....
0.24 0.24 0.55 0.22 0.55
1.80 1.80 0.17 1.72 0.78
3.46 3.46 3.47 3.52 3.53 +
%C
%Cr
%Ni %Mo %Zr
Carhon steel. .......... Carhon steel. .......... Carhon steel. .......... Carbon steel. .......... Low-Or steel. .......... Low-Cr steel ........... Low-Or steel ........... Low-Cr steel. .......... Low-Cr steel. .......... Low-Cr steel. .......... Low-Cr steel. .......... Low-Or steel. .......... Low-Cr steel. .......... Low-Cr steel. .. , ....... Low-Cr steel. .......... Low-Cr steel. .. , .......
7.871 7.859 7.844 7.830 7.84 7.84 7.83 7.80 7.82 7.82 7.81 7.84 7.82 7.81 7.79 7.845
. ...
%Ni
Low-alloy Ni-Or steel ... Low-alloy Ni-Cr steel. .. Low-alloy Ni-Or steel. .. Low-alloy Ni-Cr steel. .. Low-alloy Ni-Cr steel ...
7.92 7.82 7.855 7.835 7.86
p,
g/cm'
- - ---
Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainle.. and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels . ..
Annealed at 1580°F, tempered at 1185°F Annealed at 1580°F, tempered at 1185°F Brine quenched at 2190°F Annealed at 1435°F Annealed at 1580°F Annealed at 1435°F 0.39 Mo Annealed at 1580°F, tempered at 1185°F
%Ti %Cu %Mn
-- ---- ---- - -
7.93
0.10
18
9
7.93
....
18
9
7.98
....
23
13
7.98
....
25
20.5
7.98
....
17
12
8.02
....
18
10.5
7.75
....
12.5
7.73
....
13
0.5
2.25
. ..... 0.5
• .. Metals Handhook," 48th ed., American Society for Metals.
Condition
2-25
DENSITY OF SOLIDS TABLE
2b-3.
DENSITY OF STEELS
(Continued)
Composition Type of steel
p,
Condition
g/cm' %C
% Cr
% Ni % Mo % Zr
% Ti % Cn % Mn
------- - - - - ----- - - - - - - -- --·1-------Wronght stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ... Wrought stainless and heat-resisting steels ...
7.70
I
13
7.70
16
7.68
17
7.60
25
7.77
17.88
8.26
7.76
17.55
10.48
7.91
18.40
4.07
7.90
18.50
4.06
6.79
7.78
18.04
2.06
7.90
7.77
17.70
p,
glcm'
......
%W
0.6
0.78
0.68
%Cr
%v
%Mo
%Co
5.33
9.40
%C
Condition
---------1-- - - ---- - - - - ---1-------Toolsteel. ................... Tool steel. ................... Tool steel. ................... Tool steel. ................... Tool steel .................... Tool steel. . ................. Tool steel. ................... Tool steel. ................... Tool steel. ...................
8.67 8.67 7.925 7.93 7.76 8.89 8.68 8.16 7.88
18 18 1.64 5.20 20 18 6 1.5
4 4 3.68 4.60 4.39 4 4
2 1.00 4.00 4.10 2 1 2 1
8.24 4.11 7.75 12 5 5 8
0.80 Quenched at 2200'F 1. 32 Hardened 1. 20 Hardened Annealed Annealed Annealed
---- ---- --%Ni
%Al
20 17 25 28 14 18
12 10 12 12 8 6
%Co
%Cu
---- - --- --Permanent-magnet alloys ....... Permanent-magnet alloys .. _- •.. Permanent-magnet alloys ....... Permanent-magnet alloys ....... Permanent-magnet alloys ....... Permanent-magnet alloys_ ......
6.892 7.086 6.892 7.003 7.307 7.197
Alnico 12.5 5 24 35
- -- - --%Ni
%C
Cast Alnico
...........
8% Ti
%Mn
--- - - --Miscellaneous ferrous alloys ..... Miscellaneous ferrous alloys ..... Miscellaneous ferrous alloys ..... Miscellaneous ferrous alloys ..... Miscellaneous ferrous alloys .....
8.16 8.00 8.3 8.25 7.87
28.37 36 45 50 1.2
13
Quenched at 1740°F lnvar Radio metal ffipernik Austenitic manganese steel. Air-cooled at 1920°F
2-26
MECHANICS TABLE
2b-4.
DENSITY OF ALUMINUM ALLOYS*
(At 20°0) P.
Material
g/cm'
% Al
% Mn
% Cu % Pb
% Bi
% Mg
% Si
% Ni
--------------.---------~
Wrought alloys; Pure aluminum .. (Commercially pure AI) 2S ... 3S ............. l1S ....... ..... R-317 ....... ... 14S ......... ... R-30I (clad) ..... 17S ........ .. 18S ........ '" . 24S ............ 25S ........ .... 32S ........... AS1S ........... 52S ............ 53S ............ 568 ............. 61S ............ 758 ............ R-303 ..........
Material
*
II
% Zn
2.6989 99.996 2.71 2.73 2.82 2.81 2.80 2.78 2.19 2.80 2.77 2.79 2.69 2.69 2.68 2.69 2.64 2.70 2.80 2.82
P.
g/cm'
99.0+ 1.2 98.8 93.5 93.8 0.6 93.6 0.8 93.3 0.8 0.5 95.0 93.5 93.4 0.6 0.8 93.9 84.7 98.15 97.25 97.75 94.6 0.1 97.9 0.20 90.0 89.9
% Al
5.5 4.0 4.4 4.5 4.0 4.0 4.5 4.5 0.9
0.5 0.5
2.66 2.69 2.78 2.79 2.76 2.79 2.91 2.91 2.95 2.68 2.7 2.81 2.81 2.78 2.65 2.65 2.53 2.58 2.77 2.70 2.68 2.73 2.68 2.76 2.89 2.81
88 95 91 93 92 90 89.3 89.5 89.8 83.5 85.1 92.5 95.5 93.0 96.2 94.4 92.0 90.0 90.5 93.2 92.7 89.9 90.0 88.0 91.5 93.2
0.2 1.2 0.7 1.5
4 4 3 4.5 7 1 10 0.8 1.5 4 4.5 4.5
3.8 3.8 8 10
0.3
0.6 0.4 0.4 0.5 0.5 1.5
0.25 1.5 1.2
%Mn % Mg % Cu
0.7
0.5 0.5
0.5 0.3 0.3 0.5
% Zn - -
0.8 12.5 1.0
% Cr
0.9 0.25 0.25 0.25 0.10 0.25 0.30
0.7 0.6
% Si
5.5 6.4
%Ni % Bi % 8n % Ti
-- ---- -- ---12 5 5 3 5.5 2 3.5
1.7
12 12
2.5 2
2.5 1.8
3.5 1.3
6 5 7 8 9.5 8.5
1.5 3.5 1.0
0.6
0.8 1.0
1.0 0.6 2.5 1.3 5.2 1.0 2 5 2.5
-- ---- --
Casting alloys; 13 alloy ..... 43 alloy .... 85 alloy ...... 108 alloy .... Allcast ... A10S alloy .... 113 alloy ... C113 alloy .... 122 alloy. A132 alloy .... Red X-13 ..... 142 alloy ... 195 alloy. B195 alloy .... 214 alloy. A214 alloy. 218 alloy .. ' 220 alloy. 319 alloy ... 355 alloy .. 356 alloy .... Red X-S .... 360 alloy. 380 alloy ... 750 alloy. 40E alloy .....
% Cr
----
1.0 5
0.5
Metals Handbook," 48th ed., American Society for Metals.
6.5
0.2
DENSITY OF SOLIDS TABLE
Material Pure cobalt ........... 61 alloy (cast) ......... Vitallium ............. X-40 alloy ............ 422-19 alloy ........... 8-816 alloy ........... 6059 .................
2b-5.
2-27
DENSITY OF COBALT ALLOYS*
p,
g/cm! % Co %W % Ni % Cr % Mo % Cb % Fe - - - - - - - - - - -- - - - 100 8.9 70.0 5.0 2.0 23.0 8.54 65.0 2.0 27.0 8.30 ... 6.0 8.61 60.0 7.0 10.0 23.0 16.0 23.0 8.31 55.0 ... 6.0 50.0 4.0 20.0 19.0 ... 4.0 8.59 3.0 8.21 39.0 ... 32.0 23.0 6.0
* "Metals Handbook," 48th ed., American Society for Metals.
,
TABJ"E
Material
p,
g/cm 3
:lb-6.
DENSITY OF COPPER ALLOYS*
% Ou %0
%P
% Zn % Pb % 8n % F
---- - --- --- --- --
w rought
alloys: Pure copper .................... 8.96 100 Electrolytic tough-pitch copper ... 8.89-8.94 99.92 Deoxidized copper .............. 8.94 99.94 Gilding metal. ................. 8.86 95.0 Commercial bronze ............. 8.80 90.0 Red brass ...................... 8.75 35.0 Low brass ...................... 8.67 80.0 Cartridge brass ................. 8.53 70.0 YeIlow brass ................... 8.47 65.0 Muntz metal. .................. 8.39 60.0 Leaded commercial bronze ....... 8.83 89.0 Low-leaded brass ............... 8.47 64.5 Low-leaded brass (tube) ......... 8.50 67.0 Medium-leaded brass ............ 8.47 64.5 High-leaded brass ............... 8.47 625 Extra-high-leaded brass ......... 8.50 62.5 Free-cutting brass .............. 8.50 6l.5 Leaded muntz metal. ........... 8.41 60.0 Free-cutting muntz metal ....... 8.41 60.5 Forging brass .................. 8.44 60.0 Architectural bronze ............ 8.47 57.0 Admiralty metal. ............... 8.53 71.0 Naval brass ..... , .............. 8.41 60.0 Leaded naval brass ............. 8.44 60.0 Manganese bronze .............. 8.53 58.5
0.04 .... .. .
.... ....
.... .. .
.... .... ... .... ., .. ....
.... ., .. ... . ....
.... .... ....
... . . ... . ...
... .
0.02 .... . ... . ... . ... .... . ... ..' . . ... . ... . ... . ... . ... . ... .... . ... . ... . ... . ... . ... ... . ....
... .
5.0 10.0 15.0 20.0 30.0 35.0 40.0 9.25 1.75 35.0 0.5 32.5 0.5 34.5 1.0 35.75 1.75 35.0 2.5 35.5 3.0 39.5 0.5 38.4 1.1 38.0 2.0 40.0 3.0 28.0 ...... 39.25 ...... 37.5 1. 75 39.0 •
G
••
~
..
l.00 0.75 0.75 1.00 1.4
8.33 Aluminum brass ................ Aluminum brass ................ 8.33 8.86 Phosphor bronze ................ 8.80 Phosphor bronze 8 % grade C .... 8.78 Phosphor bronze 10 % grade D ... 8.89 Phosphor bronze 1.25% grade E .. 8.94 Cupronickel, 30% .............. Nickel silver, 18% alloy A ....... 8.73 8.70 :Ni-Ag, 18%, alloy B ............ 8.53 Silicon bronze, type A ........... 8.75 Silicon bronze, type B ........... 8.17 5 % aluminum bronze ........... ? 8 % aluminum bronze ........... 10 % aluminum bronze .......... 7.58 7.58 Aluminum bronze .............. 8.9 Constantan .................... Beryllium copper ............... 8.23 ± 0.02 Caating alloys (room temp.): 8.7 Leaded tin bronze .............. 8.80 Leaded tin bearing bronze ....... 8.87 High-leaded tin bronze .......... 8.93 High-leaded tin bronze .......... 8.80 High-leaded tin bronze .......... 9.25 High-leaded tin bronze .......... 9.30 High-leaded tin bronze .......... 8.80 85-5-5-5 ....................... 8.6 Leaded red brass ............... 8.70 Leaded semired brass ............ 8.6 Leaded semired brass ............ 8.50 Leaded yellow brass ............. 8.4 Leaded yellow brass .............
76.0 95.0 92.0 90.0 98.75 70.0 65.0 55.0 97.0 98.5 95.0 92.0 90.0 82.5 55.0 97.65
22.0
88.0 87.0 85.0 83.0 80.0 78.0 70.0 85.0 83.0 81.0 76.0 71.0 66.0
4.5 4.0 1.0 3.0
'" "Metals Handbook," 48th ed., American Society for Metals.
. . . . . . 1 ....
5.0 8.0 10.0 1.25 17.0 27.0
2.50
5.0 7.0 9.0 15.0 25.0 30.0
1.5 1.0 9.0 7.0 10.0 15.0 25.0 5.0 6.0 7.0 6.0 3.0 3.0
6.0 8.0 5.0 7.0 10.0 7.0 5.0 5.0 4.0 3.0 3.0 1.0 1.0
TABLE
Material Leaded yellow brass. . .......... High-strength yellow brass ...... High-strength yellow brass ...... Leaded manganese brass ..... Nickel silver ................... Nickel silver ................... Nickel silver ................... Leaded nickel brass ............. Aluminum bronze ............... Aluminum bronze ............... Aluminum bronze .............. Aluminum bronze ...............
p,
g/cm 3
8.40 7.9 8.2 8.2 8.8-8.9 8.85 8.95 8.95 ?
7.4 7.5 ?
2b-6.
DENSI'l'Y OF COPPER ALLOYS"
% Cu I % 0
I
% P
I%
(Continu.ed)
Zn I % Pb I % Sn
I%
Fe
,---,---,---,---,---,---,--60.0 38.0 I 1.0 1.0 26.0 62.0 3.0 58.0 39.25 1.25 59.0 37.0 0.75 1.25 66.0 2.0 1.5 5.0 64.0 8.0 4.0 4.0 57.0 20.0 9.0 2.0 60.0 16.0 5.0 3.0 89.0 1.0 87.5 3.5 4.0 86.0 79.0 5.0
* "Metals Handbook," 48th ed .• American Society for Metals.
2-31
DENSITY OF SOLIDS
TABLE 2b-7. DENSITY OF LEAD ALLOYS* p,
Material Pure lead .............. Chemically pure lead .... Cable-sheath alloy ...... 1 % antimonial lead ..... Hard lead .............. Hard lead .............. 8 % antimonial lead ..... Grid metaL ............ ASTM-12 bearing metal. ASTM-11 bearing metal. Lead-base babbitt ....... G lead-base babbitt ..... S lead-base babbitt ..... ASTM-lO bearing metal. Lead-base babbitt ...... Lead-base babbitt ...... ASTM-6 bearing metal .. Tin-lead solder ......... Tin-lead solder ......... 50-50 half and half ......
g/cm 3 11.34 11.34 11.34 11.27 11.04 10.88 10.74 10.66 10.67 10.28 iO.24 10.1 10.1 10.07 10.04 9.73 9.33 11.0 10.2 8.89
, %Pb 99.73 99.8 99.0 96.0 94.0 92.0 91.0 90.0 85.0 85.0 83.0 83.0 83.0 80.0 75.0 63.5 95.0 80.0 50.0
% Ca
% Sb
% Sn
% As % Co
---- - - - - - - --- - 0.028
..... ..... .....
1.0 4.0 6.0 8.0 9.0 10.0 15.0 10.0 12.75 15.0 15.0 15.0 15.0 15.0
.....
..... .....
..... .....
..... ..... .....
..... ..... .... . .... . .....
.....
..... . ....
5.0 0.75 1.0 2.0 5.0 10.0 20.0 5.0 20.0 50.0
3.0 1.0
. ..
1.5
* "Metals Handbook," 48th ed., American Society for Metal•. TABLE 2b-8. DENSITY OF MAGNESIUM ALLOYS* Material
p,
% Mg %Al %Mn %Zn % Sn Remarks g/cm 3 --- --- --- -----Magnesium ... 1.74 99.8 AW alloy ..... 1.81 89,9 10.0 0.1 .. . ... Wrought, sand cast, and permanent-mold cast ... Die cast AZ91 alloy .... 1.81 ... . 9.0 0.2 0.7 2.0 AZ92 alloy .. , . 1.82 ... . 9.0 0.1 ... Sand cast and permanent-mold cast 8.0 0.2 A8 alloy ...... 1.80 ... . .. . ... Sand cast . .. Wrought AZ61X alloy .. 1.80 .... 6.0 0.2 1.0 4.0 0.2 ... Sand cast AM244 alloy .. 1.76 ... . .. . 1.25 1 ... Die cast AM11 alloy ... 1.70 ... . .. . 8.5 0.15 0.5 AZ80X alloy .. 1.80 ... . " . Wrought 6.0 0.2 3.0 ... Sand cast AZ63 alloy .... 1.84 ... . 5.0 0.25 1.0 ... Wrought AZ51X alloy .. 1.79 ... . 3.0 0.3 AZ31X alloy .. 1.78 ' " . 1.0 ... Wrought MI .......... 1.76 ... . . .... 1.5 .. . . .. Wrought 3.0 TA54 ........ 1.84 .... 0.5 . .. 5.0 Wrought Mg-Al alloy ... 1.75 98.0 2.0 Mg-Al alloy ... 1. 77 96.0 4.0 Mg-Al alloy ... 1.78 94.0 6.0 Mg-Al alloy ... 1.80 92.0 8.0 Mg-Al alloy ... 1.81 90.0 10.0 I Mg-Al alloy ... 1.82 88.0 I 12.0 I
I
*" Metals Handbook," 48th ed., American Society for Metals.
MECHANICS TABLE
Material
------
2b-9.
DENSITY OF NICKEL ALLOYS'"
p, 3 % Ni % Co % Si % Mn g ( cm -- ---- ----
Nickel. .................. . A nickeL ............. . Cast nickel. .............. . D nickel. ................ . Z nickel.. Monel Cast moneL .. Kmonel. .... S monel.. ............... . HasteUoy A.............. . HasteUoy B .............. . HasteUoy C .............. . HasteUoy D .............. . IlliumG ................. . Inconel .................. . Cast Inconel. ............ . Chromel A ............... . Nichrome ................ . Chromax ............... . Constantan (wrought) ..... . Ni-Fe aUoys .... . Ni-Fe aUoys .............. . Ni-Fe aUoys ............ .. Ni-Fe aUoys ............. . PermaUoy .............. .. Numetal.. .............. .
8.902 8.885 8.34 8.78 8.75 8.84 8.63 8.47 8.36 8.80 9.24 8.94 7.8 8.58 8.51 8.3 8.4 8.25 7.95 8.9 8.8 8.6 8.5 8.35 8.6 8.6
99.95 99.4 97.0 95.2 94 67 63 66 63 60 65 58 85 58 80 77.5 80 60 35 45 90 80 70 60 78 76
1.5
%C
0.5 4.5
0.5
1.0
0.15 0.2
% Al % Cu % Fe
% Mo
% Cr
%W
4.5 1:6
30 32 29 30
1.4
2 20
20 30 17
15
8-11 fl
0.2
24 50
22 14 13.5 20 16 15
55 10 20 30 40 22 16
... Metals Handbook," 48th ed., American Society for Metals. TABLE
2b-10.
DENSITY OF ZINC ALLOYS*
p,
Material
glcm'
% Zn % Al % Cu % Mg % Pb % Cd --- ---
Zinc ........................ Zamak (2) ................ " Zamak (3) .................. Zamak (5) .................. SAE 63, T-ll (cast) .......... Commercial rolled zinc ....... Commercial rolled zinc ....... Commercial rolled zinc ....... Zilloy 40 (rolled) ............. Zilloy 15 (rolled) .............
* UMetals Handbook,"
7.133 6.7 6.6 6.7 6.9 7.14 7.14 7.14 7.18 7.18
100 92 95 94 86 99 99 99 98 98
4 4 4 4
·. ·. ·. ·. ·.
48th ed., American Society for Metals.
--- --- --- --3
·. 1 10
·. ·. ·. 1 1
0.03 0.04 0.04
.... .... . ... . ... 0.01
0.08 0.06 0.3 0.08 0.1
0.06 0.3
2-33
DENSITY· OF SOLIDS TABLE
2b-11.
DENSITY OF WOODS (OVEN-DRY)*
Common name Applewood or wild apple. . . . . . . . .. Aih, black... . . . . . . . . . . . . . . . . . . .. Ash, blue. . . . . . . . . . . . . . . . . . . . . . .. Ash, green. . . . . . . . . . . . . . . . . . . . . .. Ash, white. . . . . . . . . . . . . . . . . . . . . .. Aspen. . . . . . . . . . . . . . . . . . . . . . . . . .. Aspen, large-toothed. . . . . . . . . . . . .. Balsa, tropical American. . . . . . . . .. Basswood. . . . . . . . . . . . . . . . . . .. .. Beech ........................... Beech, blue. . . . . . . . . . . . . . . . . . . . .. Birch, gray. . . . . . . . . . . . . . . . . . . . .. Birch, paper. . . . . . . . . . . . . . . . . . . .. Birch, sweet. . . . . . . . . . . . . . . . . . . .. Birch, yellow. . . . . . . . . . . . . . . . . . .. Buckeye, yellow ................. , Butternut ....................... Cedar, eastern red ................ Cedar, northern white. . . . . . . . . . .. Cedar, southern white. . . . . . . . . . .. Cedar, tropical American .......... Cedar, western red ............... Cherry, black .................... Cherry, wild red. . . . . . . . . . . . . . . .. Chestnut ........................ Corkwood. . . . . . . . . . . . . . . . . . . . . .. Cottonwood, eastern. . . . . . . . . . . . .. Cypress, southern. . . . . . . . . . . . . . .. Dogwood (flowering). . . . . . . . . . . . .. Douglas fir (coast type) ........... Douglas fir (mountain type) ....... Ebony, Andaman marblewood (India) ........................ Ebony, Ebene marbre (Mauritius, East Africa). . . . . . . . . . . . . . . . . .. Elm, American ......... , . . . . . . . .. Elm, rock. . . . . . . . . . . . . . . . . . . . . .. Elm, slippery. . . . . . . . . . . . . . . . . . .. Eucalyptus, Karri (west Australia). Eucalyptm, mahogany (New South Wales). . . . . . . . . . . . . . . . . . . . . . .. Eucalyptus, west Australian mahogany. . . . . . . . . . . . . . . . . . . . . . .. Fir, balsam ...................... Fir, silver ....... '................ Greenheart (British Guiana). . . . . .. See page 2-35 for footnotes.
Botanical name
p,
glcm'
Pyrus malus Fraxinus nigra Fraxinus quadrangulata Fraxinus pennsylvanica lanceolata Fraxinus americana Populus tremuloides Populus grandidentata Ochroma Tilia glabra or Tilia americanus Fagus grandifolia or Fagus americana Carpinus caroliniana Betula populifolia Betula papyrifera Betula lenta Betula lutea Aesculus octandra Juglans cinera Juniperus virginiana ThuJa occidentalis Chamaecyparis thyoides Cedrela odorata ThuJa plicata Prunus serotine Prunus pennsylvanica Castanea dentata Leitneria floridana Populus deltoides Taxodium distichum Comus florida Pseudotsuga taxifolia Pseudotsuga taxifolia
0.717 0.552 0.600 0.714 0.668 0.383 0.404 0.492 0.315 0.352 0.37-0.701' 0.344 0.534 0.425 0.454 0.207 0.433 0.482 0.796 0.512 0.446
Diospyros Kurzii
0.978t
Diospyros melanida Ulmus americana Ulmus racemosa or Ulmus thomasi Ulmus fulva or Ulmus pubescens Eucalyptus diversicolor
0.768t 0.554 0.658 0.568 0.829t
Eucalyptus hemilampra
1. 058t
Eucalyptus marginata Abies balsamea Abies amabilis N ectandra rodioci
0.787t 0.414 0.415 1. 06-1. 2:3t
0.745 0.526 0.603 0.610 0.638 0.401 0.412 0.12-0.20t 0.398 0.655
2-34
MECHANICS TABLE 2b~U. DENSITY OF WOODS (OVEN-DRY)
Common name Gum, black ........................ Gum, blue ....................... Gum, red ........................ Gum, tupelo ..................... Hemlock, eastern ................. Hemlock, mountain ............... Hemlock, western ............. , ... Hickory, bigleaf shagbark ......... Hickory, mockernut .............. Hickory, pignut .................. Hickory, shagbark ................ Hornbeam .................... ·· . Ironwood, black .................. Jacaranda, Brazilian rosewood ..... Larch, western ................... Locust, black or yellow ........... Locust, honey ............ '........ ~agnolia, cucumber .............. ~ahogany (West Africa) .......... ~ahogany (East India) ........... Mahogany (East India) ........... Maple, black .................... Maple, red ...................... Maple, silver .................... Maple, sugar .................... Oak, black ...................... Oak, bur ........................ Oak, canyon live ................. Oak, chestnut .................... Oak, laurel. ..................... Oak, live ........................ Oak, pin ........................ Oak, post ....................... Oak, red ........................ Oak, scarlet ..................... Oak, swamp chestnut ............. Oak, swamp white ................ Oak, white ...................... Persimmon ...................... Pine, eastern white ............... Pine, jack ....................... Pine, Pine, Pine, Pine,
loblolly .................... longleaf .................... pitch ...•.................. red .....•..................
See page 2-35 for footnotes.
*
(Oontinued)
Botanical name Nyssa sylvatica Eucalyptu8 globulu8 Liquidambar styracijlua N ussa aquatica Tsuga canadensis T suga martensiana Tsuga heterophylla Hicoria laciniosa H icoria alba Hicoria glabra H icoria ovata Ostryra virginiana Rhamnidium jerreum Dalbergia nigra Larix occidentalis Robinia pseudacacia Gleditsia triacanthos Magnolia acuminata Khaya ivorensis Swietenia macrophylla Swietenia mahogani Acer nigrum Acer rubrum Acer saccharinum Acer saccharum Quercus velutina Quercus macrocarpa Quercus chrysolepsis Quercus montana Quercus laurijolia Quercus virginiana Quercus palustris Quercus siellata or Quercus minor Quercus borealis Quercus coccinea Quercus prinus Quercus bicolor or Quercus platanoides Quercus alba Diospyro8 virginiana Pinus strobus Pinus banksiana or Pinus divaricata Pinus taeda Pinus palustri8 Pinus rigida Pinus resinosa
p,
g/cm 3
0.552 0.796 0.530 0.524 0.431 0.480 0.43;2 0.809 0.820 0.820 0.836 0.762 1.077 0.85t 0.587 0.708 0.666 0.516 0.668t 0.54t 0.54t 0.620 0.546 0.506 0.676 0.669 0.671 0.838 0.674 0.703 0.977 0.677 0.738 0.657 0.709 0.756 0.792 0.710 0.776 0.373 0.461 0.593 0.638 0.542 0.507
~
2-35
DENSITY OF SOLIDS TABLE
2b-ll.
DENSITY OF WOODS (OVEN-DRY)*
Common name
(Continued)
Botanical name
Pine, shortleaf. . . . . . . . . . . . . . . . . .. Pinus echinata Poplar, balsam ................. " Populus balsamifera or Populus candicans Poplar, yellow ................... Liriodendron tulipifera Redwood. . . . . . . . . . . . . . . . . . . . . . .. Sequoia sempervivens Sassafras. . . . . . . . . . . . . . . . . . . . . . .. Sassafras variafolium Satinwood (Ceylon). . . . . . . . . . . . .. Chloroxylon swietenia Sourwood. . . . . . . . . . . . . . . . . . . . . .. Qxydendrum arboreum Spruce, black. . . . . . . . . . . . . . . . . . .. Picea mariana Spruce, red. . . . . . . . . . . . . . . . . . . . .. Picea T1lbra or Picea rub ens Spruce, white. . . . . . . . . . . . . . . . . . .. Picea glauca Sycamore. . . . . . . . . . . . . . . . . . . . . .. Platanus occidentalis Tamarack. . . . . . . . . . . . . . . . . . . . . .. Larix laricina or Larix americana Teak (India) ..................... Tectona grandis Walnut, black ................... Juglans nigra Willow, black. . . . . . . . . . . . . . . . . . .. Salix nigra
* t
II Handbook of Chemistry and Physics, H 30th ed. Air-dry.
p,
glcm'
0.584 0.331 0.427 0.436 0.473 1. 031 t 0.593 0.428 0.413 0.431 0.539 0.558 0.582t 0.562 0.408
2-36
MECHANICS TABLE 2b-12. DENSITY
0'
OF
PLASTICS* p,
Resin group and subgroup'
Trade names
g/cm l
Lower limit
Upper limit
--- --Acrylate and ~ethacrylate .......... Lucite, Crystalite, Plexiglas Casein ....... ,.... ' ................. Ameroid Cellulose acetate (sheet) ..... " ...... Bakelite, Lumarith, Plastecele, Protectoid "'f Cellulose acetate (molded) .......... Fibestos, Hercules, Nixonite, Tenite '" Cellulose ac~tobutyrate ............. Tenite II Cellulose nitrate ................... Celluloid, Nitron, Nixonoid, Pyralin Ethyl cellulose ..................... Ditzler, Ethocel, Ethofoil, Lumarith, Nixon, Hercules Phenol-formaldehyde compounds: Wood-flour-filled (molded) ........ Bakelite, Durez, Durite, Micarta, Catalin, Haveg, Indur, Makalot, Resinox, Textolite, Formica Mineral-filled (molded) ........... Bakelite, Durez, Durite, Micarta, Catalin, Haveg, Indur, Makalot, Resinox, Textolite, Formica Macerated-fabric-filled (molded) ... Bakelite, Durez, Durite, Micarta, Catalin, Haveg, Indur, Makalot, Resinox, Textolite, Formica Paper-base (laminated) ........... Bakelite, Durez, Durite, Micarta, Catalin, Haveg, Indur, Makalot, Resinox, Textolite, Formica Fabric base (laminated) .......... Bakelite, Durez, Durite, Micarta, Catalin, Haveg, Indur, Makalot, Resinox, Textolite, Formica Cast (unfilled) ................... Bakelite, Catalin, Gemstone, Marblette, Opalon, Prystal Phenolic furfural (filled) ............ Durite Polyvinyl acetals (unfilled) .......... Alvar, Formvar, Saflex, Butacite, Vinylite X, etc. Polyvinyl acetate .................. Gelva, Vinylite A, etc. Copolyvinyl chloride acetate ........ Vinylite V, etc. Polyvinyl chloride (and copolymer) plasticized ...................... Koroseal, Vinylite Polystyrene ....................... Bakelite, Loalin, Lustron, Styron
1.16 1.34 1.27
1.20 1.35 1.60
1.27
1.6()
1.14 1.35
1.23 1.60
1.05
1.25
1.25
1.52
1.59
2.09
1.36
1.47
1.30
1.40
1.30
1.40
1.20
1.10
1.3 1.05
2.0 1.23
1.19 1.34
(?) 1.37
1.2 1.054
1.7 1.070
)
..,
,
* .. Handbook of Chemistry and Physics," 30th ed., p. 1282.
2-37
DENSITY OF SOLIDS
T ABLE 2b-12. DENSITY
OF
PLASTICS (Continued) p,
Resin group and subgroup
Trade names
g/ cm 3
Lower limit
Upper li mit
--- Modified isomerized rubber . ... ... . . Chlorinated rubber .. ... . ...... . .. .. Urea formaldehyde. .. . ..... . . . . . . . . Melamine formaldehyde filled .. .. . .. Vinylidene chloride ..... .... . ... ....
Plioform, P liolite T orneseit, Parlon Bakelite, Beetle, Plascon Catalin, Melmac, P laskon Saran, Velon
TABLE 2b-13. DENSITY ______R_u_b_b_e_r_;_ra_'_v_p_O_I_y_m_e_r_____
OF
I__T_ra_d_e_ N_a_I_n_e_ _
30th ed. , p. 1282.
-
-
( 7)
(7) 1. 55 1. 86 1. 75
RUBBERS*
Natural rubber. . ........... . H evea Butadienestyrene copolyrr.cr . . ..... . .. . . Butadieneacrylonitrile copolymer . . Polychloroprene (neoprene) ... . . . Isobutylenediolefin copolymer (butyl). . . . . . . . . . . . . . . . . . . . . .. . . . .. .. . .. . . . . . . . . . . . . . Alkylene polysulfide . . ..... .
* "Handbook of Chemistry and Physics, "
1.06 1. 64 1.45 1.49 1. 68
___A_t_2_5_ 0C _ I
0 .92 0 . 94 1. 00 1.25 0 .9 1 1.35
__
2c. Centers of Mass and Moments of Inertia R. BRUCE LINDSAY
Brown University
1. 2. 3. 4.
5.
6.
7.
8.
9.
10.
11.
TABLE 2c-1. CENTERS OF MASS * Body Center of Mass Uniform circular wire of radius R, On axis of symmetry distant (R sin e)/e from center sub tending angle 2e at center At intersection of the medians Uniform triangular sheet At intersection of the diagonals Uniform rectangular sheet Uniform quadrilateral sheet From each vertex layoff segments equal to t the length of the corresponding sides meeting at this vertex. Draw extended lines through the ends of the segments associated with each vertex, respectively. These intersect to form a parallelogram. The intersection of the diagonals of this parallelogram is the center of mass of the quadrilateral Uniform circular sector sheet of radius On axis of symmetry distant (2R sin e)/ 38 from center R sub tending angle 2e at center of circular arc Uniform circular segment sheet of On axis of symmetry distant 1'/12A from center, where A = area of segment radius R, subtending angle 2e at R2(2e - sin 2e) center of circular arc and length of 2 chord equal to I = 2R sin e Uniform semielliptical sheet, major On axis of symmetry distant 4a/3rr from center of equivalent ellipse if the semiand minor axes of equivalent ellipse ellipse is bounded by minor axis. The equal to 2a and 2b, respectively distance is 4b /3rr if the semiellipse is bounded by the major axis Uniform quarter-elliptical sheet, major At point 4b/3rr above major axis and and minor axes of equivalent ellipse 4a/3rr above minor axis equal to 2a and 2b, respectively Uniform parabolic sheet segment. On axis of symmetry distant 3h/5 from Chord = 2l perpendicular to axis of vertex symmetry distant h from vertex Right rectangular pyramid (rectan- On axis of symmetry distant h/4 from gular base with sides a and b and with base height h) Pyramid (general) On line joining apex with center of symmetry of base at distance three-quarters of its length from apex
* For definition see Sec. 2a-4.
All bodies cited are homogeneous rigid bodies.
2-38
CENTERS OF MASS AND MOMENTS OF INERTIA
2-39
TABLE 2c-1. CENTERS OF MASS (Continued) Body Center of Mass 12. Frustum of pyramid with area of On line joining apex of corresponding larger base S and smaller base s, and pyramid with center of symmetry of altitude h larger base and distant h(S + 2 VSs + 3s)
13. Right circular cone (height h) 14. Frustum of right circular cone (altitude h, radii of larger and smaller bases Rand r, respectively) 15. Cone (general)
16. Frustum of cone with altitude hand radii of larger and smaller bases R and r, respectively 17. Spherical sector of radius R, with plane vertex angle eqllal to 21i 18. Solid hemisphere of radius R 19. Spherical segment of radius Rand maximum height from base equal to h 20. Octant of ellipsoid with semiaxes a, b, c, respectively, and center of corresponding ellipsoid at origin of system of rectangular coordinates 21. Paraboloid of revolution with altitude h and radius of circular base equal to R 22. Uniform hemispherical shell of radius R (excluding base) 'Z3. Conical shell (excluding base)
4(S + VSs +s) from the larger base On axis of symmetry distant h/4 from base On axis of symmetry distant h[(R 4[(R
+ r)2 + 2r 2] + r)2 - Rr]
from the base On line joining apex with centroid of base at distance three-quarters of its length from apex On line joining apex of corresponding cone with centroid of larger base and distant h[(R 4[(R
+ r)2 + 2r 2] + r)2 - Rr]
from the larger base On axis of symmetry distant 3R ""8 (1 + cos Ii) from the vertex On axis of symmetry distant 3R/8 from center of corresponding sphere . f d' t t h(4R - h) On axIS 0 symmetry IS an 4(3R _ h) above the base of the segment Point with coordinates _ 3c _ 3a _ 3b z =x=g y=S 8 On axis of symmetry distant h/3 from the base On axis of symmetry distant R/2 from center of corresponding sphere On line joining the apex with the center of symmetry of the base at distance twothirds its length from the apex
2-40
MECHANICS TABLE
Body
2c-2.
MOMENTS OF INERTIA*
Axis
Moment of inertia
Uniform rectangular sheet of Through the center parallel to b sides a and b Uniform rectangular sheet of Through the center perpendicular to the sides a and b sheet Uniform circular sheet of Normal to the plate through the center radius T Uniform circular sheet of Along any diameter radius T Uniform circular ring, radii Through center normal rl and r, to plane of ring Uniform circular ring, radii A diameter TI and T, Uniform thin spherical shell, A diameter mean radius T Uniform cylindrical shell, Longitudinal axis radius r, length 1 Right circular cylinder of Longitudinal axis radius r, length 1 Right circular cone, altitude Axis of the figure h, radius of base r Spheroid of revolution, equa- Polar axis torial radius r Ellipsoid, axes 2a, 2b, 2c . ... Axis 2a
a' m 12 a' + b' m~ r'
m
"2
r' m4 rl' + r2' m~-2~m
rl'
+ T2' 4
2r'
m""3 mr'
r'
m'2 m
3 , 10 r 2r'
mS m
(b'
+ c') 5
Uniform thin rod ......... . Normal to the length, l' m3 at one end Uniform thin rod ......... . Normal to the length, l' m 12 at the center Rectangular prism, dimen- Axis 2a (b' + c') m 3 sions 2a, 2b, 2c Sphere, radius r . ......... . A diameter m ~r' 5 Rectangular parallelepiped, Through center pera' + b' edges a, b, and c pendicular to face ab m~ (parallel to edge c) Right circular cylinder of Through center perradius r, length 1 pendicular to the axis of the figure Spherical shell, external ra- A diameter dius rl, internal radius r, Hollow circular cylinder, Longitudinal axis length l, external radius TI, internal radius T, Hollow circular cylinder, Transverse diameter rl' + r,' m ( 4 length l, radii rl and T2
* For definitions see Sec. 2a-5; m
= mass of body.
+ ~)
AI! bodies are homogeneous.
12
2-41
CENTERS OF MASS AND MOMENTS OF INERTIA TABLE
2c-2.
Body Hollow circular cylinder, length l, very thin, mean radius r Right elliptical cylinder, length 2a, transverse axes 2b,2c Right elliptical cylinder, length 2a, transverse axes 2b,2c Frustum of right circular cone with radii of larger and smaller bases, equal to Rand r, respectively Right circular cone, radius of base r, altitude h Solid hemisphere of radius r Spherical sector of radius r, with plane angle at vertex = 28 Spherical segment of radius r and maximum height h Torus or anchor ring mean radius R, radius of circular cross section r Torus mean radius R, radius of circular cross section r
MOMENTS OF INERTIA
Axis
(Continued)
Moment of inertia
Transverse diameter Longitudinal axis 2a (b 2 + c2 ) through center of m 4 mass Transverse axis 2b through center of mass Axis of symmetry 3m(R6 - r 6) lO(RS - r S)
Perpendicular to axis 3m(2+!!!.) 4 of symmetry, through 20 r center of mass 2mr2 Axis of symmetry -5Axis of symmetry through vertex
mr2(1 - cos 8)(2 5
+ cos 9)
Axis of symmetry per( 2 _ 3rh + 3h 2 ) ~ pendicular to base m r 4 20 3r - h Axis of symmetry per- m(4R 2 + 3r2) pendicular to plane of, 4 ring Axis of symmetry in m(4R2 + 5r l ) plane of ring 8
2d. Coefficients of Friction DUDLEY D. FULLER
Columbia University
Symbols
fK fR fs
P r
W
coefficient of kinetic or sliding friction coefficient of rolling friction coefficient of static friction frictional resistance to rolling radius of roller load
2d-1. Static and Sliding Friction. All surfaces encountered in experience are more or less rough in the sense that as bodies move on them they exert forces parallel to the surface and in such direction as to resist motion. Such forces aTe termed "frictional." Frictional force is proportional to the normal thrust between body and surface; however, the coefficient of proportionality, known as the coefficient of friction, can for the same body and surface vary a great deal depending on the nature of the contact and the motion. It is customary to define
f - magnitude of maximum frictional force , -
(2d-l)
magnitude of normal thrust
as the coefficient of static friction if motion is just on the point of starting. On the other hand, fK, called the coefficient of kinetic or sliding friction, is the value of the ratio in Eq. (2d-l), when motion has once been established. In generalfK < fs for the same body and surface or the same two surfaces. The friction between surfaces is dependent upon many variables. These include the nature of the materials themselves, surface finish and surface condition, atmospheric dust, humidity, oxide and other surface films, velocity of sliding, temperature, vibration, and extent of contamination. In many instances the degree of contamination is perhaps the most important single variable. For example, Table 2d-llists values for the static coefficient of friction fs for steel on steel under various test conditions. TABLE
2d-1.
COEFFICIENTS OF STATIC FRICTION FOR STEEL ON STEEL
Test condition
f.
Degassed at elevated temp. in high vacuum ............ . Weld on contact Grease-free in vacuum ............................... . 0.78 Grease-free in air .................................... . 0.39 Clean and coated with oleic acid ...................... . 0.11 Clel1n and coated with solution of stearic acid ........... . 0.Oi3 • Ref crenees follow Tab)e ~(l-4.
2-42
IRef. * 20 1 8 1 21
2-43
COEFFICIENTS OF FRICTION
The' most effective lubricants for nonfluid lubrication are generally those which react chemically with the solid surface and form an adhering film that is attached to the surface with a chemical bond .. This action depends upon the nature of the lubricant and upon the reactivity of the solid surface. Table 2d-2 indicates that a fatty acid such as those found in animal, vegetable, and marine oils reduces the coefficient TABLE
2d-2.
COEFFICIENTS OF STATIC FRICTION AT ROOM TEMFERATURE
Surfaces
NickeL ............. Chromium .......... , Platinum ............ Silver ............... Glass ............... Copper .............. Cadmium ........... Zinc ................ Magnesium .......... Iron ................ Aluminum ...........
Clean
0.7 0.4 1.2 1.4 0.9 1.4 0.5 0.6 0.6 1.0 1.4
Paraffin oil
Paraffin oil
+ 1% lauric
0.3 0.3 0.28 0.8
0.28 0.3 0.25 0.7 0.4 0.08 0.05 0.04 0.08 0.2 0.3
....
0.3 0.45 0.2 0.5 0.3 0.7
acid
Degree of . reactivity of solid Low Low Low Low Low High High High High Mild Mild
of friction markedly only if it can react effectively with the solid surface. Paraffin oil is almost completely nonreactive. The data are taken from ref. 22. It is generally recognized that coefficients of friction reduce on dry surfaces as sliding velocity increases. Dokos (ref. 4) has measured this for steel on steel. It is difficult to screen out the effect of temperature, however, which also increases with sliding velocity so that frequently, under these conditions, both variables are present. Table 2d-3 gives values which are the average of four tests at high contact pressures. TABLE
2d-3.
COEFFICIENTS OF FRICTION, STEEL ON STEEL, UNLUBRICATED
Velocity, in./sec ......... 0.0001 Coefficient of friction/x .. 0.53
I 0.48 0.001 I 0.01 0.39
0.1 0.31
1 110 1100 0.23 0.19 0.18
2-44
MECHANICS
Table 2d-4 presents typical values of the coefficients of static and sliding friction for various materials under a variety of conditions. TABLE 2d-4. COEFFICIENTS OF STATIC AND SLIDING FRICTION* Static friction
Sliding friction
Materials Dry Hard steel on hard steel. .......... 0..78(1)
Mild steel on mild steel. .......... 0..74(19)
Greasy
Dry
Greasy
o..11(l,a) 0..42(2) ....... o..23(1,b) 0. .15(1,c) ....... ....... o..11(l,d) o..o.o.75(18,p) ....... o..o.o.52(18,h) .......
•••••••
0
••••
Hard steel on graphite ............ 0..21(1) o..o.9(1,a) Hard steel on babbitt (ASTM 1) ... 0..70.(11) o..23(1,b) 0. .15(1,c) o..o.8(1,d) o..o.85(1,e) Hard steel on babbitt (ASTM 8) ... 0..42(11) o..17(1,b) o..11(l,c) o..o.9(1,d) o..o.8(1,e) Hard steel on babbitt (ASTM 10.) .. ....... o..25(1,b) o..12(1,c) o..lO(l,d) Mild steel on cadmium silver ...... ....... ........... . Mild steel on phosphor bronze ..... ....... ........... . Mild steel on copper lead .......... ....... ........... . Mild steel on cast iron ............ ....... 0. .183(15,c) Mild steel on lead ................ 1 0..95(11) lo.·5(1,f) Nickel on mild steel. ............. ....... ........... . Aluminum on mild steel. .......... 0..61 (8) ............ Magnesium on mild steel. ......... ....... ........... . Magnesium on magnesium ......... 0..6(22) o..o.8(22,y)
0..57(3)
0..33(6)
....... •
••
00
••
o..o.29(5,h) o..o.81(5,c) o..o.80(5,i) o..o.58(5,j) o..o.84(5,d) o..105(5,k) 0..0.96(5,1) o..108(5,m) o..12(5,a) O.o.9(3,a) o..19(3,u) o..16(1,b) o..o.6(1,c) o..11(l,d)
0. . 14(1,b) o..o.65(1,c) ....... o..07(1,d) ....... o..o.8(11,h) . ...... o..13(1,b) ....... o..o.6(1,c) ....... o..o.55(1,d) . ...... o..o.97(2,f) 0..34(3) 0. . 173 (2,f) . ...... 0. . 145 (2,f) 0..23(6) o..133(2,f) 0..95(11) o..3(11,f) 0..64(3) o..178(3,x) 0..47(3) 0..42(3)
0..35(11) •
0
•••••
* Numbers in parentbeses indicate references to data sources; letters identify lubricant in following
list.
2-45
COEFFICIENTS OF FRICTION
TABLE 2d-4. COEFFICIENTS OF STATIC AND SLIDING FRICTION (Continued) Static friction .Dry Greasy
Materials Cadmium on mild steel. .......... Copper on mild steel. ............ Nickel on nickel. ................ Brass on mild steel. ............. Brass on cast iron ............... Zinc on cast iron ................ Magnesium on cast iron .......... Copper on cast iron .............. Tin on cast iron ................. Lead on cast iron ................ Aluminum on aluminum .......... Glass on glass ...................
.. . . . . .
•••
0
••••••••
0.53(8) ...........'. 1.10(16) 0.28(22,y) 0.51(8) 0.11(22,c)
...... . ............
0.85(16) . ...........
...... . ........... .
.. ........... . ............
1.05(16) ........
....... ...... .
'.,
1. 05(16) 0.30(22,y) 0.94(8) O.35(22,y) 0.1(22,q)
Sliding friction Dry Greasy 0.46(3) 0.36(3) O.18(17,a) 0.53(3) O.12(3,w) 0.44(6) 0.30(6) 0.21(7) 0.25(7) 0.29(7) 0.32(7) 0.43(7) 1.4(3) 0.4(3) O.09(3,a)
........... . ....... ........... . 0.78(8) . ...........
Carbon on glass ................. Garnet on mild steel. ............ Glass on nickel. ................. Copper on glass ................. Cast iron on cast iron ............ Bronze on cast iron .............. Oak on oak (parallel to grain) ....
0.18(3) 0.39(3) 0.56(3) 0.68(8) . . . . . . . . . . . . 0.53(3) 1.10(16) 0.2(22,y) 0.15(9) ....... ........... . 0.22(9) 0.62(9) ............ 0.48(9)
Oak on oak (perpendicular) ....... Leather on oak (parallel) ......... Cast iron on oak ................ Leather on cast iron ............. Teflon on Teflon ................ Teflon on steel. ................. Fluted rubber bearing on steel. ... Laminated plastic on steel ........ Tungsten carbide on tungsten carbide ......................... Tungsten carbide on stee! ........
0.54(9) 0.61(9)
••••
0
••
........... . ............ ....... ........... . ....... ........... .
O.070(9,d) 0.077(9,n) 0.164(9,r) 0.067(9,s) 0.072(9,s)
0.32(9) 0.52(9) 0.49(9) 0.075(9,n) 0.56(9) 0.36(9,t) 0.04(22) ............ 0.04(22,£) 0.04(22) ............ 0.04(22,f) ...... . .......... . ....... 0.05(13,t) ...... . ............ 0.35(12) 0.05(12,t) ~
0.2(22) 0.5(22)
.
0.12(22,a) 0.08(22,a)
Materials
Sliding friction, dry
Nylon 6.6 on mild steel (no fibers) .......................... Nylon 6.6 on mild steel (30% by wt. carbon fibers) ........... Copper-graphite (high copper) on hard steel. ................ Copper-graphite (low copper) on hard steel. ................. ·Carbon-graphite(low graphite) on hard steel. ................ Carbon-graphite (high graphite) on hard steel. ............... Carbon-Teflon on hard steel. .............................. Carbon-copper-Teflon on hard steel. " ......................
0.40(23) 0.35(23) 0.40(23) 0.25(23) 0.50(23) 0.25(23) 0.30(23) 0.29(23)
2-46
MECHANICS
Lubricant References for Table 2d-4 a. - b; c. d. e. f.
g. h. i. j.
k. 1..
Oleic acid Atlan:tic spindle oil (light mineral) Castor oil Lard oil Atlantic spindle oil plus 2 per cent oleic acid Medium mineral oil Medium mineral oil plus -i per cent oleic acid Stearic f!,cid Grease (zinc oxide base) Graphite Turbine oil plus 1 per cent graphite Turbine oil plus 1 per cent stearie acid
Thrbiiie -oil (mediurii- inineralf Olive oil Palmitic acid Ricinoleic acid Dry soap Lard Water Rape oil 3-in-l oil w. Octyl alcohol x. Triolein y. 1 pet cent lauric aCid in paraffin oil
m. n. p. q. r. s. t. u. v.
References for Table 2d-4 1. Campbell, W. E.: Studies in Boundary Lubrication, Trans. ASME 61 (7), 633-641 (1939). 2. Clark, G. L., B. H. Lincoln, and R. R. Sterrett: Fundamental Physical and Chemical Forces in Lubrication, Proc. API 16, 68-80 (1935). 3. Beare, W. G., and F. P. Bowden: Physical Properties of Surfaces. 1, Kinetic Friction, Trans. Roy. Soc. (London), ser. A, 234, 329-354 (June 6, 1935). 4. Dokos, S. J.: Sliding Friction under Extreme Pressures-I, J. Appl. Mech. 13, A-148156 (1946). 5. Boyd, J., and B. P. Robertson: The Friction Properties of Various Lubricants at High Pressures, Trans. ASME 67 (1), 51-56 (January, 1945). 6. Sachs, G.: Versuche nber die Reibung fester Korper .(Experiments about the Friction of Solid Bodies), Z. angew. Math. Mech. 4, 1-32 (February, 1924). 7. Honda, K., and R. Yamada: Some Experiments on the Abrasion of Metals, J.Inst. Metals 33 (1), 49-69 (1925). 8. Tomlinson, G. A.: A Molecular Theory of Friction, Phil. Mag., ser. 7, 7 (46), 905-939 (suppl., June, 1929). 9. Morin, A.: Nouvelles experiences sur Ie frottement (New Experiments on Friction) Acad. roy. 8ci., Paris (a) 57, 128 (1832); (b) 59, 104 (1834); (c) 60, 143 (1835); (d) 63, 99 (1838). 10. Claypoole, W.: Static Friction, Trans. ASME 65, 317-324 (May, 1943). 11. Tabor, D.: The Frictional Properties of Some White-metal Bearing Alloys: The Role of the Matrix and Hard Particles, J. Appl. Phys. 16 (6), 325-337 (June, 1945). 12. Eyssen, G. R.: Properties and Performance of Bearing Materials Bonded with Synthetic Resin, General Discussion on Lubrication and Lubricants, Inst. Mech. Engrs., J. 1, 84-92 (1937). 13: Brazier, S. A., and W. Holland-BowYet:-Ru1515eras a Material for Beatings, General Discussion on Lubrication and Lubricants, Inst. Mech. Engr8., J. 1, 30-37 (1937); India-Rubber J. 94 (22), 636-638 (Nov. 27, 1937). 14. Burwell, J. T.: The Role of Surface Chemistry and Profile in Boundary Lubrication, J. SAE 50 (10), 450-457 (1942). 15. Stanton, T. E.: "Friction," Longmans, Green & Co., Ltd., London, 1923. 16. Ernst, H., and M. E. Merchant: Surface Friction of Clean Metals-A Basic Factor in Metal Cutting Process, Proc. Conf. Friction and Surface Finish (MIT), June, 1940, pp.76-101. 17. Gongwer, C. A.: Proc. Conf. Friction and Surface Finish (MIT), June, 1940,pp. 239244. 18. Hardy, W., and 1. Bircumshaw: Boundary Lubrication-Plane Surfaces and theLimitations of Amontons' Law, Proc. Roy. Soc. (London), ser.A, 108 (A 745), 1-27 (May, 1925). 19. Hardy, W. R., and J. K. Hardy: Note on Static Friction and on the Lubricating Properties of Certain Chemical Substances, Phil. Mag., ser. 6, 38 (233), 32-48 (1919).
COEFFICIENTS OF FRICTION
2-47
20. Bowden, F. P., and J. E. Young: Friction of Clean Metals and Influence of Adsorbed Films, Proc. Roy. Soc. (London), ser. A, 208 (A 1094), 311-325 (September, 1951). 21. Hardy, W. B., and 1. Doubleday: Boundary Lubrication-The Latent Period and' Mixtures of Two Lubricants, Proc. Roy. Soc. (London), ser. A, 104 (A 724), 25-38 (August, 1923). 22. Bowden, F. P., and D. Tabor: "The Friction and Lubrication of Solids," Oxford University Press, New York, 1950. 23. Lancaster, J. K.: Composite Self-lubricating Bearing l\([aterials, Proc. I nst. M echo Engrs. (London) 182,33-54 (1967-1968).
2d-2. Rolling Friction. Rolling is frequently substituted for sliding friction. The resistance to motion is substantially smaller than for sliding under nonfluid film conditions. The frictional resistance to rolling under the action of load W may be designated as P in Fig. 2d-1. The coefficient of rolling friction is then defined as
JE
=
P W
(2d-2)
The frictional resistance P to the rolling of a cylinder under load is applied at the center of the roller and is inversely proportional to the radius r of the roller and proportional to a factor k, a function of the material and its surface condition. Thus
P =~W
..
(2d-3)
If r is in inches, values of k may be taken as follows: hardwood on hardwood, 0.02; iron on iron, steel on steel, 0.002; hard polished steel on hard polished steel, 0.0002 to 0.0004. Noonan and Strange suggest, for steel rollers on steel plates: surfaces well
w
FIG. 2d-1. Rolling friction.
FIG. 2d-2. Load carried on rollers.
finished and clean, 0.005 to 0.001; surfaces well oiled, 0.001 to 0.002; surfaces covered with silt, 0.003 to 0.005; surfaces rusty, 0.00:3 to 0.01. If the load is carried on rollers as in Fig. 2d-2, and k and k' are the respective factors
2-48
MECHANICS
for lower and upper surfaces, the force P is
P
= (k
+ k')W d
(2d-4)
A comprehensive survey of rolling friction may be found in the following references presented at the annual meeting of the American Society of Mechanical Engineers, December 1 to 5, 1968. Hersey, M. D.: Rolling Friction: I, Historical Introduction, Paper 68-LUB-B. Hersey, lVi. D., and M. S. Downes: Rolling Friction: II, Cast Iron Car Wheels, Paper 68-LUB-C. Hersey, M. D.: Rolling Friction: III, Review of Later Investigations. Paper 68-LUB-D.
2e. Elastic Constants, Hardness, Strength, Elastic Limits, and Diffusion Coefficients of Solids H. M. TRENTl
U.S. Naval Research Laboratory D. E. STONE
Vertex Corporation 2 L. A. BEA DBIEN
U.S. Naval Research Laboratory
2e-1. Introduction. For the fundamental ideas connected with elasticity and for the definition of the elastic constants see Sec. 2a-6. For other definitions see Sec. 2e-3. The symbols and abbreviations used in this section are presented below.
E G p
Cj;
So;
T.S. Y.S. Y.P. S.S. El. R.A. Bhn R Vdh, Vhn D v p
Young's modulus modulus of rigidity Poisson's ratio density elastic constant (cf. Sec. 2a-6) elastic coefficient (cf. Sec. 2a-6) tensile strength yield strength yield point shear strength elongation reduction in area Brinell hardness number Rockwell hardness number (often used with sUbscripts) Vickers hardness number diffusion coefficient specific volume pressure
2e-2. Elastic Constants and Coefficients of Crystals. Tables 2e-1 through 2e-6 contain tabulations of the elastic constants Cij and coefficients Si; of cubic, hexagonal, tetragonal, trigonal, orthorhombic, and monoclinic crystals (cf. Sec. 9a for X-ray crystallographic data). All temperatures are room temperatures unless otherwise specified. However, the original sources often contain values for a wide range of temperatures. The two electrical boundary conditions for piezoelectric crystals are as follows: D = 0 denotes ali electric field, generated piezoelectrically, parallel to the direction of wave propagation; E = 0 denotes a field perpendicular to this direction. Boundary 1
2
Deceased. H. M. Childers of the Vertex Corporation provided valuable consultant service.
2-49
2-50
MECHANICS
conditions are given only for those materials for which a change in boundary conditions produces a substantial change in one or more measured values. References for these tables will be found immediately following Table 2e-6. References 1, 2, and 3 are published compilations from which the original sources can be obtained as well as references for values differing slightly from those given in these tables. In those cases in which two references are given, the first is for Gi; and the second for Si;. 2e-3. Elastic Constants, Hardness, Strength, and Elastic Limits of Polycrystalline Solids. Tables 2e-7 through 2e-16 contain data on the Young's modulus, modulus of rigidity, hardness, etc., of various solids, metals, and alloys. The elastic constants, tensile strength, yield strength, shear strength, and all other quantities having the dimensions of stress are expressed in dynes per square centimeter. The definitions of these and other tabulated quantities are given in the following list. 1. Tensile Strength. I "The maximum tensile stress which a material is capable of developing." Note: In practice, it is considered to be the maximum stress developed by a specimen representing the material in a tension test carried to rupture, under definite prescribed conditions. Tensile strength is calculated from the maximum load P carried during a tension test and the original cross-sectional area of the specimen Ao from the formula Tensile strength =
~o
2. Yield Strength. l "The stress at which a material exhibits a specified permanent set." The yield strength is conventionally determined in either of two ways. In the first method, a specimen of the material is repeatedly loaded and unloaded with the load oeing increased at each cycle, the process being continued until a specified permanent set is obtained after one of the unloadings. The stress which produces this specified permanent set is called the yield strength. In the second method, known as the offset method, a load-elongation curve is determined experimentally, the elongation being measured in 'units of extension 'per unit length of the undeformed specimen. A straight line is then drawn having a slope equal to the initial slope of the load-elongation curve and an intercept on the elongation axis equal to the specified offset, which is usually given in units of per cent elongation. The yield strength is taken to be that load defined by the interaction of the added straight line with the load-elongation curve. Further discussion of yield strength can bfl found in ASTM E6-36. 3. Yield Point.' The stress at which a marked increase in deformation takes place without increase in the load. 4. Shear Strength.' "The stress, usually expressed in pounds per square inch, required to produce fracture when impressed perpendicularly upon the cross-section of a material." 5. Elongation.' "In tensile testing the elongation of a specimen is the increase in gage length, after rupture, referred to the original gage length. It is reported as percentage elongation." 6. Reduction in Area.' "In tensile testing the reduction in area of a specimen is the ratio of the difference between the original cross-sectional area of the specimen and the cross-sectional area after rupture, to the original cross-sectional 'area. It is reported as the percentage reduction of area." Standard Definitions of Terms Relating to Methods of Testing, ASTM E6-36. "Metals Handbook," 1948 ed., American Society fOT Metals. 'J. G. Henderson, "Metallurgical Dictionary." 'Nail. Bur. Standards (U.S.) Cire. 0447. 1
2
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS
2":"'51
TABLE 2e-1. ELASTIC CONSTANTS AND COEFFICIENTS OF CUBIC CRYSTALS (C.; in units of 1011 dynes/cm2; 8;j in units of 1O-1s cm 2/dyne) Material
Cll C12 ------
8 11
C44
8 12
- - ---
Ag (silver) .............. 12.40 9.34 4.61 22.9 Ag, 25% Au ............. ....... . . . . . . . ...... 20.7 Ag, 50% Au ............. · . . . . . . ....... 19.7 Ag, 75% Au ............. · . . . . . . ....... ....... 20.5 3.3 0.720 31.3 AgBr ................... .. 5.63 AgCl. .................. 6.01 3.62 0.625 30.4 9.25 4.61 23.07 Ag, 1.34% Cd ........... 12.28 Ag, 1.92 % Cd ........... 12.16 9.13 4.59 23.10 8.90 4.50 25.30 Ag, 8.36% In ............ 11.66 Ag, 3.07% Mg ........... 11.98 8.98 .4.60 23.37 Ag, 7.33% Mg ........... 11.59 8.66 4.52 23.94 9.58 4.81 21.93 Ag, 6.22% Pd ........... 12.77 9.22 4.58 24.29 Ag, 3.17% Sn ........... 12.10 9.16 4.58 23.89 Ag, 2.40% Zn ........... 12.09 9.33 4.61 23.54 Ag, 3.53% Zn ........... 12.30 1.07 0.85 52 Alum ................... 2.56 Aluminum .............. 11.2 6.6 2.79 15.7 Al, 5% Cu .............. · . . . . . . ....... ..... . 15 Ammonium alum ........ 2.50 1.06 0.80 53.5 0.59 0.53 36.2 Ammonium bromide ..... 2.96 0.72 0.68 27.2 Ammonium chloride ...... 3.90 Au (gold) ............... 18.6 15.7 4.20 23.3 1.86 1.22 19.4 Barium nitrate .......... 6.04 CaF2 (fluorspar) ......... 16.44 5.02 3.47 7.10 14.4 11.7 4.27 Chromite ............... 32.3 Chromium alum ......... ...... . ...... . ...... 54.2 6.49 Cobalt zinc ferrite ....... 26.6 15.3 7.8 Copper ................. 16.8 12.1 .7.54 15.0 CusAu .................. 19.07 13.83 6.63 13.4 Cu, 4.1% Zn (a-brass) ... 16.33 11.77 7.44 ....... Cu, 9.1 % Zn (a-brass) ... 15.71 11.37 7.23 ...... . Cu, 17.1% Zn (a-brass) .. 14.99 10.97 7.15 ....... Cu, 22.7% Zn (a-brass) .. 14.47 10.71 7.13 ...... . Cu, 47% Zn (a-brass) .... 15.22 11.62 7.19 ....... 10.2 7.44 41.05 Cu, 44.9% Zn «(3-brass) ... 11. 9 Cu, 48.3% Zn «(3-brass) ... 12.91 10.97 8.24 35.3 Cu, 48.9% Zn «(3-brass) ... 12.79 10.91 8.22 36.4 Cu, 4.81 % AI ........... 16.58 12.16 7.49 15.9 Cu, 9.98% AI. .......... 15.95 . 11.76 7.66 16.75 Cu, 1.58% Ga ........... 16.50 .11.92 7.43 . 15.38 Cu, 4.15% Ga ........... 16.5.2 . 12.10 7.41 15.91 Cu, 1.03% Ge .... : ...... 16 ..66 12.10 7.50 15.44 Cu, 1.71% Ge ........... , 16.31 . 11.82 7.50 15.72 Cu, 4.17% Si ....... '" .... 16 .7~r 12.42 7.48 16.10 Cu, 5.16% Si. ........... 16.08 11.88 7.49 16.71 Cu, 7.69%Si............ 16.58 12.64 7.41 17.72 Cu, 4.59% Zn .... " " .. , 16.34 11.92 7.42 15.91 0"
••••
'
8 44
Ref.
--9.83 -8.91 -8.52 -9.09 -11.7 -11.4 -9.91 -9.91 -10.95 -10.01 -10.24 -9.40 -10.51 -10.30 -10.16 -15 -5.8 -6.9 -15.9 -6.0 -4.2 -10.65 -4.6 -1.66 -1.31 -15.3 -2.37 -6.3 -5.65 ........ .
21.7 2 20.5 4 19.7 4 20.6 4 139 2 160 2 21.69 5 21.77 5 22.20 5 21.74 5 22.10 5 20.79 5 21.83 5 21.85 5 21.68 5 118 1 35.9 1 37 6 125 7,3 189 1 147 1 23.8 2 82.0 1 28.8 2 8.56 2 130 3 12.8 1 13.26 1 15.1 2 ..... . 8 ......... ..... . 8 ........ . . ..... 8 ........ . ...... 8 .. ... " ....... 9 -19.0 13.4 2 -16.2 12.2 2 12.2 1 -16.8 -6.73 13 .. 35 10 -7.11 13.05 10 -,6.45 13.46 10 -6.73 13.50 10 -6.50 13.33 10 -6.60 13.33 10 -6.85 .13.37 10 -7.10 13.35 10 -7.66 13.50 10 -6.71 13.48 10 ,
,
2-52
MECHANICS
TA~LE 2e-1. ELASTIC CONSTANTS AND COEFFICIENTS OF CUBIC CRYSTALS (Continued)
C 12 C44 Cl l 8 11 ------- Cu, 28% Zn ............. ....... ...... . ..... . 19.4
Material
Diamond ............... Diamond ............... Fe ............... ··.·· . Garnet 21.8 % FeO ....... Garnet 22.7% FeO ....... Garnet 23.0% FeO ....... Garnet 23.6% FeO ....... Garnet 26.2 % FeO ...... Garnet 28.7% FeO ....... Garnet 33.5 % FeO ....... Fe,04 (magnetite) ....... FeSz (pyrite) ............ GaAs ................... GaSb ................... Germanium ............. Hexamethylene tetramine Lead nitrate ............. Indium antimonide ....... Potassium alum ......... K (potassium) ........... KBr .................... KC!. ................... KF .................... KI.. ................... Li (195°K) .............. LiBr ................... LiC!. ................... LiF .................... LiI ..................... MgO ................... Magnetite .............. Molybdenum ............ Na (sodium) ............ NaBr ................... NaBrO' ................. NaC!. .................. NaClO, ................. NaF ................... NaI. ................... Ammonium alum ........ NH4Br ................. NH4C!. ................ NickeL ................. Palladium ............... Pb (lead) ............... Pb ..................... PbS (galena) ............
107.6 95 23.7 19.7 19.2 22.2 21.0 22.6 27.3 32.7 27.3 36.2 1.192 8.85 12.89 1.5 4.56 6.72 2.54 0.459 3.46 3.98 6.58 2.67 1.320 3.94 4.94 11.12 2.85 28.6 27.5 46 0.945 3.87 5.73 4.87 4.99 9.71 3.035 2.50 2.96 3.90 24.65 22.71 5.03 4.66 10.2
12.50 57.58 0.953 43 1.38 39 7.72 14.1 11.6 9.0 5.7 7.11 8.02 9.9 5.9 10.4 7.0 6.42 10.3 6.7 7.03 12.6 6.2 7.36 15.7 6.8 6.32 12.4 8.9 3.87 9.7 4.7 10.6 -4.4 10.4 2.85 0.599 0.538 126.4 4.04 4.33 15.8 9.78 4.83 6.71 0.3 0.7 70 3.09 1.37 48.5 3.67 3.02 24.2 1.07 0.84 52.5 0.372 0.263 833 0.58 0.505 30.4 0.62 0.625 26.2 1.49 1.28 ....... 0.43 0.421 39.2 1.102 0.960 316.4 1.88 1. 91 ...... . 2.26 2.49 ....... 4.20 6.28 11.35 1.40 1.35 ...... . 8.7 14.8 4.08 10.4 9.55 4.59 17.6 11.0 2.8 0.779 0.618 420 0.97 0.97 28.7 1.76 1.52 20.4 1.24 1.26 22.9 1.41 1.17 22.9 2.43 2.80 ...... . 0.90 0.72 ...... . 1.06 0.8 53.5 0.59 0.53 36.2 0.72 0.68 27.2 14.73 12.47 7.34 17.60 7.173 . . . . . . . 3.93 1.40 63.2 3.92 1.44 92.8 12 3.8 2.5
8 12
Ref. 8 44 ----
-8.4 -0.099 -0.40 -2.85 -2.2 -2.7 -2.1 -2.3 -2.6 -2.3 -1.1 -1.31 0.39 -42.34 -4.96 -2.66 -12 -19.6 -8.55 -15.6 -370 -4.35 -3.5
13.9 11 1. 74 12 2.3 13 9.02 9, 14 17.5 15 15 16.9 14.3 15 14.9 15 16.1 15 14.7 15 11.2 15 2 10.3 9.6 2 2 186 2 23.1 2 14.90 140 1 1 73.0 2 33.1 2 119 380 9,16 2 198 2 160 . ..... 17 2 238 104 18 ...... 17 ..... . 17 2 15.9 . ..... 17 2 6.76 1 10.47 2 9.1 2 162 2 103 2 65.7 2 79.4 2 85.4 ..... . 17 ...... 17 125 '"" 2 189 2 147 2 8.02 ..... . 19 71.4 20 2 69.4 1 40
........ . -5.4 -144
........ . ........ . -3.1
......... -0.95 -1.26 -0.78 -190 -5.8 -4.8 -4.65 -5.05
......... ........ . -15.9 -6.0 -4.2 -2.74
........ . -27.7 -42.4 -3
2-53
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS TABLE
2e-1.
ELASTIC CONSTANTS AND COEFFICIENTS OF CUBIC CRYSTALS
Material
C 11
PbS ... ... . ........... . .. . . . . . .. . . .. . RbBr. RbCl. .. ............... . RbF ..... . . . . . . . . . . . . . . RbI. ................... Silicon .................. Strontium ni tra te ........ Thallium bromide ....... Thallium chloride ........ Thallium alum .......... Thallium bromide chloride Thallium bromide iodide .. Thorium ................ W (tungsten) ............ Zinc blende .•........... Zinc sulfide .............
TABLE
2e-2.
12.70 3.185 3.645 5.7 2.585 16.57 4.73 3.78 4.01
...... . 3.85 3.6 7.53 50.1 10.0 10.79
8 11
C 12
C••
---
---
2.98 0.48 0.61 1.25 0.375 6.39 2.18 1.48 1.53
2.48 0.385 0.475 0.91 0.281 7.96 1.46 0.756 0.760
8 12
(Continued)
8 ••
Ref.
--8.7
...... ...... . ....... ...... . .
7.68 29.8 33.9 31.6 . . . . . . . ...... 49.0 1.49 0.737 33.1 1.5 0.555 37 4.89 4.78 27.2 19.8 15.14 2.57 6.5 3.4 20.5 7.22 4.12 20
-1.64
40.3
........ . . . . . . . . ........ ... ... ......... ..... . ........ . ,,",., . '
-2.14 -9.4 -9.5 -8.7 -15.5 -9.2 -11 -10.7 -0.729 -8.1 -8.02
12.56 68.5 132 132
115 136 180 20.9 6.60 29.4 24.3
1 17 17 17 17 2 1 2 2 3 1 1 2 2 1 2
ELASTIC CONSTANTS AND COEFFICIENTS OF HEXAGONAL CRYSTALS
(Cij in units of 10" dynes/cm 2 ; 8 ij in units of 10-13 cm 2 /dyne) Material
C11
C"
C"
C12
C13
811
8"
8"
812
8"
Ref.
-- -- --' - - --- - --- - --- --- -Apatite .............. 16.67 BaTi03 (D = 0) ...... 16.8 BaTi03 (E = 0) ...... 16.6 BaTi03 5 % CaTi03 by wt. (E= 0) ........ 17.41 Beryllium ............ 30.8 Beryl r .............. 27.81 Beryl II .......... '" 29.71 Cadmiulll ............ 11.0 CdS ................. 8.1 Cobalt .............. .30.7 Ice (-16°C) ......... 1.33 rViagnesium .. ........ 5.97 SiG, (600°C) (,,-quartz) 11.66 Yttrium .... " ....... 7.79 Zinc .. - ............. 16.1
13.96 6.63 18.9 5.46 16.2 4.29 16.88 35.7 24.8 26.5 4.69 8.0 35.81 1.42 6.17 11. 04 7.69 6.10
4.74 11.0 6.61 7.54 1.56 1.43 7.53 0.306 1.64 3.606 2.431 3.83
1.31 6.55 7.82 7.10 7.66 7.75 7.93 -5.8 10.01 10.26 4.04 4.9 16.5 0.63 2.62 1.67 2.85 3.42
8.00 8.7 6.77 7.39 3.83 4.8 10.3 0.46 2.17 3.28 2.1 5.01
-4.0 -1.95 -2.85
23 2 2
21.1 -2.45 -2.65 9.09 1.04 -1.17 -1.35 -0.80 15.1 -1.17 -0.78 13.3 -9.3 64.0 -1.5 -8.0 -8.7 70 13.24 -2.31 -0.69 326.5 -41.6 -19.3 -7.85 -5.0 61 27.73 -0.60 -2.62 ....... ... '" ..... 26.1 0.53 -7.31
2 1
7.49 10.9 15.1 8.18 6.76 18.3 8.55 8.93 23.3 8.42 3.37 4.47 4.21 36.9 21. 9 3.19 82.8 19.7 10.62 . . . . . .. , ' . 8.38 28.38
8.05 3.77 4.27 3.97 12.9 22.2 4.72 101.3 22.0 9.41
.
0.97 -2.98 -2.61
"
1 1 2 21 2 22 2 2 24 2
2-54 TABLE
MECHANICS
2e-3.
ELASTIC CONSTANTS AND COEFFICIENTS OF TETRAGONAL CRYSTALS
(C.; in units of
1011
Cl l
Material
dynes/cm 2 )
Caa
C44
C66
C13
C12
Ref.
-- -- - ---- --- ----Ammonium dihydrogen phosphate ... Ammonium dihydrogen phosphate ... Ammonium dihydrogen phosphate (D = 0) ........................ Ammonium dihydrogen phosphate (E = 0) ........................ Ammonium dihydrogen phosphate (deuterated) ..................... Barium titanate (D = 0) ........... Barium titanate (E = 0) ........... Indium ........................... Nickel sulfate ..................... Potassium dihydrogen arsenate ...... Potassium dihydrogen phosphate .... Potassium dihydrogen phosphate (DOC) ........................... Sn (tin) ........................... Sn ............................... Sn ............................... Zircon ............................ TABLE
2e-3A.
6.17 3.28 0.85 7.58 2.96 0.87
0.59 0.72 0.614 -2.43
1.94 1.30
2 2
6.76 3.38 0.867 0.687
0.59
2.0
2
6.76 3.38 0.867 0.608
0.59
2.0
2
6.2 28.3 27.5 4.45 3.21 5.3 7.14
3.0 0.91 17.8 8.05 16.5 5.43 4.44 0.655 2.93 1.16 3.7 1.2 5.62 1.27
8.14 7.85 1.29 8.6 13.3 4.9 7.35 8.7 2.2 8.39 9.67 1. 75 7.35 4.60 1.38
0.61 11.3 11.3 1.22 1.78 0.7 0.628
-0.5 1.4 18.7 14.2 17.9 15.1 3.95 4.05 2.31 0.21 -0.6 -0.2 -0.49 1.29
2 2 2 2 1 1 2
0.63 5.3 2.265 0.741 1.60
3.49 4.07 3.5 3.0 2.34 2.8 4.87 2.81 0.90 -0.54
1 1 2 2 2
ELASTIC CONSTANTS AND COEFFICIENTS
(Continued) (8;; in units of 10-13 cm 2/dyne)
OF TETRAGONAL CRYSTALS
8 11 8 33 8 4 , 8 66 8 12 Ref. 813 ---- -- - --------- - Ammonium dihydrogen arsenate .. 16.9 44.5 152.9 124.0 -17.3 -11.1 3 Ammonium dihydrogen phosphate 20 45.7 117 169 1.7 -12.9 2 Ammonium dihydrogen phosphate 17.5 43.5 114 163 2 7.5 -11 Material
Ammonium dihydrogen phosphate (D = 0) ..................... Ammonium dihydrogen phosphate (E = 0) ..................... Ammonium dihydrogen phosphate (deuterated) .................. Barium titanate (D = 0) ........ Barium titanate (E = 0) ......... Indium ........................ Nickel sulfate .................. Potassium dihydrogen arsenate ... Potassium dihydrogen phosphate. Potassium dihydrogen phosphate (O°C) ........................ Sn (tin) ........................ Sn ............................ Sn ............................ Zircon .........................
18.1
43.5 115.3 145.5
1.9 -11.8
2
18.1
43.5 115.3 164.6
1.9 -11.8
2
44 110 164 19 7.25 10.8 12.4 8.84 8.05 15.7 18.4 .8.84 149.4 187 152.7 82 34.3 86.5 56.2 65 19 27 86.0 152 14.8 19.5 78.7 159.2 17.5 14.6 16.3 18.5 13.9
20 8.5 14.1 11.8 22.1
77.5 159 20.6 19.0 45.4 44.2 57.0 135 72 62
2 -3.15 -2.35 -50.6 -46.8 2 1.7
-11 -3.26 -5.24 -90.2 -1.3 1 -3.79
2 2 2 2 1 1 2
-4 -5.3 -3.6 -9.9 -1.6
-7 -2.07 -4.1 -2.5 -1.4
1 1 2 2 2
2-55
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS
TABLE 2e-4. ELASTIC CONSTANTS AND COEFFICIENTS OF TRIGONAL CRYSTALS (Cij in units of 1011 dynes/cm 2 ) Material
C 11
C 33
C 44
C 12
C '3
C 14
11.7 2.61 2.11 4.50 0.79 0.75 0.49 1.6 3.03 1.191 1. 51 4.8 1.60 2.31 3.5 4.9 3.5
10.1 1.05 -0.42 -2.03 0.03 -0.03 -0.03 -1.3 0.5 -1. 791 1.72 3.8 0.82
Ref.
--- -- ------ ------
Alumina (corundum) ... ... . ..... 46.5 56.3 23.3 12.4 Antimony ............. ......... 7.92 4.27 2.85 2.48 Bismuth ....................... 6.28 4.40 1.08 3.50 Calespar (calcite) ............... 13.74 8.01 3.42 4.40 Dextrose sodium bromide ........ 2.06 2.40 0.634 0.53 Dextrose sodium chloride ....... '1 2.20 1. 77 0.771 1.09 Dextrose sodium iodide .......... 2.58 2.06 0.771 1.52 Haematite .......... " ......... 24.2 22.8 8.5 5.5 Mercury ( -190°C) ............. 3.60 5.05 1.29 2.89 a-Quartz ....................... 8.674 10.72 5.79 0.699 a-Quartz ....................... 8.75 10.77 5.73 0.762 Sapphire ........................ 49 . 6 50.2 20.6 10.9 Sodium nitrate ................. 8.67 3.74 2.13 1.63 Tellurium ......... ,. " ......... ..... . 7.00 ...... ..... . Tourmaline .................... 27.2 16.5 6.5 4.0 Tourmaline I ................... 26.3 15.1 5.95 6.1 8.8 Tourmaline II .................. 30.4 17.6 6.5
. ...... -0.68 -0.9 -0.4
-2 2 2 2 1 1 1 2 2 2 2 25 2 2 1 1 1
TABLE 2e-4A. ELASTIC CONSTANTS AND COEFFICIENTS OF TRIGONAL CRYSTALS (Continued) (8ij in units of 10-13 cm 2 /dyne) Material
8 11
8"
--- -2.90 1. 94 16.1 16.1 17.7 33.8 26.9 28.7 11.0 17.3 56.9 52.3 63.8 70.2 60.2 51.6 4.42 4.44 78.7 35.0
Alumina (corundum) ........ Aluminum phosphate ........ Antimony .................. Bismuth ................... Calespar (calcite) ........... Dextrose sodium bromide .... Dextrose sodium chloride .... Dextrose sodium iodide ...... Haematite ................. Lithium trisodium chromate .. Lithium trisodium molybdate ............... 29.5 27.1 Mercury ( -190°C) ......... 154 45 a-Quartz ................... 12.77 9.6 a-Quartz ........... '" ..... 12.69 9.71 Sapphire ................... 2.18 2.02 Sodium nitrate ............. 13.4 30.8 Tellurium ....... " ......... 48.7 23.4 Tourmaline ................ 3.85 6.36 Tourmaline I ............... 4.22 7.34 Tourmaline II ............. '1 3.64 5.89
8 44
8 ,2
8"
8 ,4
5.78 -1.05 -0.38 -0.1 -8.3 53.0 41.0 -3.8 -8.5 104.8 -14.0 -6.2 -3.4 -4.3 39.4 158 -8.6 -16.0 130 -26.1 -16 130 -34.3 -6.2 11.92 -1.02 -0.23
-1.71 8.9 -8.0 16.0 8.6 -3.4 3.6 3.8 0.80
...... . . . . . . . . ...... . ........
...... ........ . . . . . . . . . . . . . . . -119 151 20.04 -1.79 20.05 -1.69 5.04 -0.50 -2.2 51.5 58.1 -6.9 15.4 -0.48 17.1 -0.80 15.4 -1.00
Ref.
--
---
-21 -100 4.50 -1.22 -4.31 -1.54 -0.49 -0.16 -4.8 -6.0 -13.8 ........ 0.45 -0.71 -1.11 0.76 0.29 -0.53 1
2 3 2 2 2 1 1 1 2 3 3 2 2 2 25 2 2 1 1 1
2-56
MECHANICS
'fABLE 2e-5. ELASTIC CONSTANTS AND COEFFICIENTS OF ORTHORHOMBIC CRYSTALS (C'i in units of 1011 dynes/cm 2 ) Material
Cl l
C2 2
CBB
C44
C55
C66
C12
---- ---- -- -- --
Aragonite ........ 16.0 8.7 8.5 Baryte .......... 8.62 9.17 10.84 Celestite ......... 10.44 10.61 12.86 Iodic acid ........ 3.03 5.45 4.36 Lithium ammonium. tartrate .. 3.86 5.39 3.63 Magnesium sulfate ........ 6.98 5.29 8.22 Potassium pentaborate ... 5.82 3.59 2.55 Rochelle salt (D = 0) ....... 2.55 3.81 3.71 Rochelle salt (E = 0) ..... ' . 2.55 3.81 3.71 Rochelle salt (D = 0) ....... 4.25 5.15 6.29 Rochelle salt (E = 0) ....... 4.25 5.15 6.29 Sodium ammonium tartrate .. 3.68 5.09 5.54 Sodium tartrate .. 4.61 5.47 6.65 Staurolite ........ 34.3 18.5 14.7 Strontium formate ....... 4.39 3.48 3.74 Sulfur ........... 2.40 2.05 4.83 Topaz ........... 28.2 34.9 29.5 a-Uranium ....... 21.47 19.86 26.71 Zinc sulfate ...... 4.00 3.22 5.45
4.12 1.20 1.35 1.84
C'3 -~
C2a
Ref.
----
2.56 2.87 2.79 2.19
4.27 2.74 2.66 1.74
3.73 5.23 7.73 1.19
0.17 3.41 6.05 1.17
1. 57 3.56 6.19 0.55
2 1 2 1
1.19 0.67
2.33
1.65
0.87
2.01
1
1.07 2.33
2.22
3.90
2.82
2.83
1
1.64 0.463 0.57
2.29
1. 74
2.31
2
1.34 0.321 0.979 1.41
1.16
1.46
2
..... 0.286 0.960 1.41
1.16
1.46
2
1.25 0.304 0.996 2.96
3.57
3.42
2
0.58 0.278 0.974 2.96
3.57
3.42
2
3.08 3.47 3.20 3.52 6.1 12.8
1 1 26
1.04 -1.49 -0.14 1.33 1.71 1.59 8.8 12.6 8.5 4.65 2.18 10.76 1.32 1.80 1.19
1 2 2 27 1
1.06 0.303 0.87 1.24 0.31 0.98 4.6 7.0 9.2 1.54 1.07 0.43 0.87 10.8 13.3 12.44 7.342 0.50 1. 70
1.72 0.76 13.1 7.433 1. 81
2.72 2.86 6.7
2-57
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS TABLE
2e-5A. OF
ELASTIC CONSTANTS AND COEFFICIENTS
(Continued) (8i; in units of 10-13 CIll 2 / dyne)
ORTHORHOMBIC CRYSTALS
8 ..
Material
8"
8"
8"
813
8"
Ref.
- - - - - - - - ---- -- - - - - - - --- --- ----Aragonite ................. Baryte ................... Barium formate .......... . Celestite .................. lodic acid ................. Lithium ammonium tartrate Magnesium sulfate ......... Potassium pentabol'ate ..... Rochelle salt CD = 0) ...... Rochelle salt CE = 0) ...... Rochelle salt CD = 0) ...... Rochelle salt CE = 0) ...... Sodium ammonium tartrate. Sodium tartrate ........... Strontium formate ... ...... Sulfur .................... Topaz .................... a-Uranium. ,. , ............ Zinc sulfate ...............
6.95 18.4 ..... 22.0 39.8 30 24.5 23.2 52.4 52.4 51.8 51.8 57.0 37.1 28.4 71 4.43 4.91 29.5
13.2 17.36 ..... 21. 9 20.1 25.6 34.1 73.6 35.4 35.4 34.9 34.9 38.5 31.6 31 83 3.53 6.73 37.7
12.2 10.96 ..... 11.4 25.6 35 15.0 98.3 33.7 33.7 33.4 33.4 40 26.4 31 30 3.84 4.79 20.4
24.3 83.33 78.5 74.1 54.5 84 93.5 61 74.7 ...... 79.8 174 94.5 80.6 65 232 9.23 8.04 200
39.0 34.84 60.0 35.8 45.6 150 42.9 215 311 350 328 360 330 323 93 115 7.53 13.62 58.8
23.4 36.50 82.5 37.6 57.6 43 45.0 175 102 104 101 103 115 102 58 132 7.63 13.45 55.3
-3.0 -9.45 . ...... -13.9 -7.75 -8.2 -16.6 -10.6 -15.4 -15.4 -15.3 -15.3 -15.5 -12.0
0.4 -2.68 ....... -3.7 -9.7 -2.7 -2.68 -6.1 '-10.3 -10.3
-2.4 -2.73
-4.0 -0.45 -12.2 -6.05 -60 -9.1 -9.1 ~21.1 -10.3 -21.1 -10.3 -22 -15.5 -11.5 -10.9 -2 -8 11 -15 -36 -13 -1.38 -0.86 -0.06 -1.19 0.08 -2.61 -10.8 -3.49 -6.10
2 1 3 2 1
2 2 2 2 2 1
2 2 27 1
TABLE
Material
C ll
2e-6. ELASTIC CONSTANTS AND COEFFICIENTS OF MONOCLINIC (C,; in units of 1011 dynes/em 2 ; 8,j in units of 10-13 em 2 /dyne) C 22
C 33
C 44
C' 5
C 66
C 12
C 13
C 23
C1
---- ------ -- ----------Dipotassium tartrate* ... Ethylene diamine tartrate* ............. Lithium sulfate* ........ Sodium thiosulfate* ..... Tartaric acid* ..........
6.9
3.5
4.4
0.84
1.3
0.96
1.2
3.2
1.4
0
13.4 5.7 3.31 9.30
3.5 7.1 3.02 1.93
6.04 4.9 4..57 4.65
0.53 2.7 0.57 0.81
0.83 2.9 1.11 0.82
0.57 1.4 0.60 1.1
2.7 2.7 1.83 2.0
8.1 1.6 1.84 3.7
2.2 1 1.6 -0 1.68 0 1.4 -1
---- -- ------ ----------811
8 22
8 33
8 44
8"
--------- ----- --- --- --:Dipotassium tartrate* ... "Ethylene diamine tartrate* ............. Lithiumsulfate* ........ Sodium thiosulfate* ..... Tartaric acid* .......... Dipotassiumtartrate** .. Ethylene diamine tartrate .............. Lithium sulfate** ... ~ ...
22.4
33.7
38.8 37 23.9 21.3 50.2 156 21.6 77 47.5 35.3
38.6 119 98 23.1 67.4 38.5 24.0
188 36.9 223 130 113.5
8 66 --~
81.5 104.1 172 41 327 180 102
812
813
-0.8 -16.4 -10.5
174 4.0 -52 74 -9.5 -5 212 -32.3 -6.21 96 -6.1 -15 122.5 -17.4 -8
33.4 36.5 100 192 117 191 22.9 __22.5 !-22.8 _7!.! 64.0 ~6.1
J
81
-19 -3.6 -71.9 -18 -6.2
-6
-7 7 15 28 -7
-3 -30 -18 -17 -5.4 -7.5 -4.6 -2
* The single-starred values of the 8i; correspond to the single-starred values of the O'i; that is, (0*)-1
** The doubJe-starred values are referled to a differently oriented sot of axes.
8 23
---------
= (8*).
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS
References for Tables 2e-1 through 2e-6 1. Hearmon: Advances in Phys. 5,323 (1956). 2. Huntington: "Solid State Physics," vol. 7, p. 213, Academic Press, Inc., New York, 1958. 3. Sundara Rao, Vedan, and Krishnan: "Progress in Crystal Physics," vol. 1, p. 73, S. Viswanathan, Madras, India, 1958. 4. Rohl: Ann. Phys. 16,887 (1933). 5. Bacon: Dept. Phys., Case Inst. Technol., Tech. Rept. 15, 1955. 6. Karnop and Sachs: Z. Physik 53, 605 (1929). 7. Sundara Rao: Current Sci. (India) 17,50 (1948). 8. Rayne: Phys. Rev. 112, 1125 (1958). 9. Jones: Physica Hi, 13 (1949). 10. Neighbors and Smith: .Acta Met. 2, 591 (1954). 11. Sundara Rao and Balakrishnan: Proc. Indian Acad. Sci. 28A, 475 (1948). 12. McSkimmin and Bond: Phys. Rev. 105, 116 (1957). 13. Bhagavantam and Bhimasenachar: Proc. Roy. Soc., ser. A, 187,381 (1946). 14. Kimura: Proc. Ph1}s.-Math. Soc. Japan 21, 686, 786 (1939); 22,45, 219 (1940). 15. Ramachandra Rao: Proc. Indian Acad. Sci. 22A, 194 (1945). 16. Seitz: J. Appl. Phys. 12, 100 (1941). 17. Spangenberg and Haussuhl: Z. Krist. ill!), 422 (1957). 18. Nash and Smith:Phys. Chem. Solids 9,113 (1959). 19. Rayne: Phys. Re;. 118, 1545 (1960). 20. Prasad and Wooster: Acta Cryst. 9,38 (1956). 21. Gutsche: Naturwissenschaften 45, 566 (1958). 22. Bass, Rossberg, and Ziegler: Z. Physik 149, 199 (1957). 23. Bhimasenachar: Proc. Indian Acad. Sci. 22 (sec. A), 209 (1945). 24. Smith and Gjevre: J. Appl. Phys. 31,647 (1960). 25. Mayer and Heidemann: J. Acoust. Soc. Am. SO, 756 (1958). 26. Bhimasenachar and Venkata Rao: J. Acoust. Soc. Am. 29, 343 (1957). 27. Fisher and McSkimmin: J. Appl. Phys. 29, 1473 (1958).
AbbTeviations in Tables 2e-7 through 2e-16 Abbreviation H.R ................ C.R.. . . . . . . . . . . . . .. W.Q ................ O.Q ................ A.Q.. . . . . . . . . . . . . .. A.C ................ F.C ................ h-t. . . . . . . . . . . . . . . .. WT .. , . . . . . . . . . . . . . .
ann. . . . . . . . . . . . . . .. art. aged. . . . . . . . . . .. nat. aged ........... spec.. . . . . . . . . . . . .. G.S .................
Definition Hot Tolled Cold rolled Water quenched Oil quenched Air quenched Air cooled Furnace cooled Heat-treated Wrought Annealed Artificially aged Naturally aged Specimen Grain size
TABLE 2e-7. ELASTIC AND STRENGTH CONSTANTS FOR SILVER, GOLD, PLATINUM,
Material
Condition
Ag ..................... 1 Strained 5 %, heated 5 hr ·at 350°C Ag .................... . Ann. Ag + 80 Mo ............ . Ag + 40 Mo ............ . Ag + 20 Mo ............ . Ag +20W ............. . Ag +40W ............. . Ag+80W ............. . Ag + 40 Ni ............ . Ann. Ag + 20 Ni ........... . Ann. Ag + 1 graphite ........ . Ag + 5 graphite ....... . Ag + 10 graphite ....... . Ag+5Cd ............. . Ag + 10 Cd ............ . Ag+20Cd ............ . 33 Ag, 52 Hg, 12.5 Sn, 2 Cu, 0.5 Zn ............ . Au 99.99% ............. . Cast Au 99.99% ............ . Wrought, ann. 58.3 Au, 4.9 Ag, 31.6 Cu, Air cooled 5.2 Ni
E
u
Tensile strength
Yield strength at 0.2% offset
El t
7.1-7.8 X 1011
0.37 55 41 24 34 41 55 26 21
X 10' X 10' X 10' X 10' X 10' X 10' X 10' X 10'
16 X 10' 19 X lOB 20 X 10' 1.0 X 1011 2.8-5.9 X lOB 7.44 X 1011 10.42 12.4 X 10'1 ........ . 8.00 X 1011 0.42 13. 1 X lOB Nil 56.9 X 10' 33. 1 X lOB at 0.1% offset
3 4 4
TAllLE 2e-7. ELASTIC AND STRENGTH CONSTANTS FOR SILVER, GOLD, PLATINUM, PAL
Material
H.6 Au, 4.6 Ag, 43.4 Cu, [ Air cooled 5.0 Ni, 5.4 Zn 69 Au, 25 Ag, 6 Pt ....... Pt 99.99% .............. Pt+5Ir ............... Pt+lOIr .............. Pt + 25 Ir .............. Pt + 3.5 Rh ............. Pt + 5.0 Rh ............. Pt + 10.0 Rh ............ Pt + 20.0 Rho ........... Pt + 5 Ru .. o. Pt + 10 Ru ............. Pt + 1 Ni. .............. Pt + 2 Ni. ..... Pt + 5 Ni. .............. 84 Pt, 10 Pd, 6 Ru ....... 96 Pt, 4 W .............. Pd (pure) ............... 60 Pd, 40 Ag ............ 60 Pd, 40 Cu ............ 95Pd, 4 Ru, 1 Rh ........ 0
•••••
0
0
0
0"
•••
0
•••
* References are on p. 2-76.
Ann. Ann. Ann.
I
E
Condition
[
0
••••••••••••
14.7 X 1011 0.39
............. 0·.·.·.·.·.· .
Ann.
.............
Ann. Ann. Ann.
0·.· ... ·.· ...
Ann.
0·.·.· .......
Ann. Ann.
.............
Ann. Ann. Ann. and rolled
Ann. Ann. Ann.
I
............. [ .... [
Ann.
Ann. Ann. Ann.
(J"
0
••••••••••••
0
••
0
••
•••••••••
•
•
•••••••••
0_.·.·.· . . . · .
............. 0·······.··· . 0·····.····· . 0
••
•••••••••
•
12.1 X 1011
............ . 0
••••••••••••
0
••••••••••••
Tensile strength
Yield strength at 0.2% offset
46.8 X 10 8 [26.7 X 10 8 at 0.1% offset 37.6 X 108 . ........ 12-13 X 10 8 ......... 27 X 10 8 . ......... 38 X 10 8 . ........ 86 X 10 8 . ........ 17 X 10 8 . ........ 21 X 10 8 . ........ 31 X 10 8 . ........ 48 X 10 8 . ........ 41 X 10 8 . ........ 59 X 10 8 . ........ 21 X 10 8 . ........ 28 X 10 8 . ........ 45 X 10 8 ......... 55 X 108 . ........ 48-52 X 10 8 ......... 2::15 X 10 8 ......... 35 X 10 8 ......... . 52 X 10 8 38~1'X 10 8
••
00-
......
TABLE
Alloys Cast alloys: AI, 12 Si. ........................ AI, 5 Si. ......................... AI, 5 Si. ......................... AI, 5 Si, 4 Cu ..................... AI, 4 Cu, 3 Si. .................... AI, 5 Si, 3 Cu ..................... AI, 5 Si, 3 Cu ..................... AI, 5 Si, 3 Cu ........ ............ AI, 5.5 Si, 4.5 Cu .................. AI, 7 Cu, 2 Si, 1.7 Zn .............. AI, 7 Cu, 3.5 Si ..... . .. . . . . . . . AI, 10 Cu, 0.2 Mg ................. AI, 10 Cu, 0.2 Mg ................. AI, 12 Si, 2.5 Ni, 1.2 lVlg, 0.8 Cu .... AI, 12 Si, 1.5 Cu, 0.7 Mn, 0.7 Mg ... AI, AI, AI, AI, AI, AI, AI, AI, AI, AI,
4 Cu, 2 Ni, 1.5 Mg ............. 4.5 Cu ....................... 4.5 Cu, 2.5 Si .................. 3.8 Mg ............ .......... SMg ......................... 10 Mg ........................ 6 Si, 3.5 Cu ..... .......... 6 Si, 3.5 Cu ..... .......... 5 Si, 1.3 Cu, 0.5 Mg ............ 5 Si, 1.3 Cu, 0.5 Mg ............
AI, 7 Si, 0.3 Mg. . . . . . .. _.. _...... AI, 7 Si, 0.3 Mg .................. AI, AI, AI, AI, AI, AI,
S Si, 1.5 Cu, 0.3 Mg, 0.3 Mn .... S Si, 1.5 Cu, 0.3 Mg, 0.3 Mn ... 9.5 Si, 0.5 Mg .................. 8.5 Si, 3.5 Cu .................. 6.5 Sn, 1 Cu, 1 Ni. ............. 5.5 Zn, 0.6 Mg, 0.5 Cr, 0.2 Ti. ..
2e-8.
ELASTIC AND STRENGTH CONSTANTS FOR ALUMINUM A
Condition Die cast Die cast Sand cast Die cast Sand cast Sand cast Sand cast, h-t, aged Perm. mold cast, h-t, aged Perm. mold cast, h-t, aged Sand cast Perm. mold cast Sand cast (ann.) H-t, artificially aged Perm. mold cast, art. aged Perm. mold cast (stress relieved) Ann. (sand cast) H-t, nat. aged H-t, nat. aged Perm. mold cast Die cast Sand cast, h-t, nat. aged H-t, art. aged As cast H-t, art. aged (sand cast) H-t, art. aged (perm. mold cast) H-t, art. aged (sand cast) H-t, art. aged (perm. mold cast) Sand cast (stress relieved) Perm. mold (stress relieved) Die cast Die cast (Perm. mold cast) art. aged Sand cast
E
G
q
Tensile strength
s
7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10
X X X X X X X X X X X X X X X
1011 1011 1011 1011 10" 1011 1011 1011 1011 1011 1011 1011 1011 1011 10"
2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65
X X X X X X X X X X X X X X X
1011 1011 1011 1011 10" 1011 1011 1011 1011 1011 1011 1011 1011 1011 1011
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
25.5 20.7 13.1 27.6 14.5 18.6 24.1 2S.9 19.3 16.5 20.7 18.6 27.6 24.8 24.S
X X X X X X X X X X X X X X X
10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
12 9. 6. 15 9. 9. 13 15 11 10 16 13 20 19
7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10 7.10
X X X X X X X X X X
1011 1011 1011 10" 1011 1011 1011 1011 1011 10"
2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65
X X X X X X X X X X
1011 1011 1011 1011 1011 1011 1011 1011 1011 1011
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
18.6 22.0 27.6 18.6 2S.9 31. 7 24.S lS.6 24.1 29.6
X X X X X X X X X X
10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
12 11 1 11 1 17 16 1 1 lS
7.10 X 1011 7.10 X 10"
2.65 X 1011 0.33 22.7 X 10' 1 2.65 X 10 11 0.33 27.6 X 10' IS
7.10 7.10 7.10 7.10 7.10 7.10
2.65 2.65 2.65 2.65 2.65 2.65
X X X X X X
10" 10" 10" 10 11 10" 1011
X X X X X X
10" 1011 10" 1011 10" 10 11
0.33 0.33 0.33 0.33 0.33 0.33
20.7 24.S 28.9 31.0 15.2 24.1
X X X X X X
10' 14 10' 10' 15 10' 1 10' 6. 10' 17
W:rought alloys:
Aluminum 99.996 AI. .... " ........ Aluminum 99.996 AI. .............. Aluminum 99.0+ AI. ............... Aluminum 99.0+ AI. ............... AI, 1.2 Mn ....................... ........... AI, 1.2 Mn ... AI, 5.5 Cu, 0.5 Pb, 0.5 Bi. AI, 5.5 Cu, 0.5 Pb, 0.5 Bi. ......... AI, 4 Cu, 0.6 Mn, 0.6 Mg, 0.5 Pb, 0.5 Bi ............. AI, 4.4 Cu, 0.8 Si, 0.8 Mn, 0.4 Mg .. AI, 4.4 Cu, 0.8 Si, 0.8 Mn, 0.4 Mg .. AI, 4 Cu, 0.5 Mg, 0.5 Mn .......... AI, 4 Cu, 0.5 Mg, 0.5 Mn .......... AI, 4 Cu, 2 Ni, 0.5 Mg ............ AI, 4 Cu, 2 Ni, 1.5 Mg ......... AI, 4.5 Cu, 1.5 Mg, 0.6 Mn ........ AI, 4.5 Cu, 1.5 Mg, 0.6 Mn ........ AI, 4.5 Cu, 0.8 Mn, 0.8 Si. ......... AI, 12.5 Si, 1.0 Mg, 0.9 Cu, 0.9 Ni .. AI, 1.0 Si, 0.6 Mg, 0.25 Cr. AI, 2.5 Mg, 0.25 Cr ....... AI, 2.5 Mg, 0.25 Cr ............... AI, 1.3 Mg, 0.7 Si, 0.25 Cr. AI, 1.3 Mg, 0.7 Si, 0.25 Cr ......... AI, 5.2 Mg, 0.1 Mn, 0.1 Cr ......... AI, 5.2 Mg, 0.1 Mn, 0.1 Cr ......... AI, 1.0 Mg, 0.6 Si, 0.25 Cu, 0.25 Cr. AI, 1.0 Mg, 0.6 Si, 0.25 Cu, 0.25 Cr. AI, 5.5 Zn, 2.5 Mg, 1.5 Cu, 0.3 Cr, ~2Mn .................... Al, 5.5 Zn, 2.5 Mg, 1.5 Cu, 0.3 Cr, 0.2 Mn ........................ AI, 6.4 Zn, 2.5 Mg, 1.2 Gu ......... References are on p. 2·-76. 7~-in. round specimen. : ;l1-in. round specimen. 10)::
t
1011 10" 1011 10" 1011 1011 10" 1011
2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65
X X X X X X X X
1011 1011 1011 1011 1011 1011 1011 1011
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
4.74XlO' 11.2 X 10' 8.96 X 10' 16.6 X 10' 11.0 X 10' 20.0 X 10' 36.5 X 10' 39.3 X 10'
1.2 10. 3.4 14. 4.1 17 32. 30.
H-t, nat. aged Forged, h-t, aged Sand cast Ann. H-t, nat. aged H-t, art. aged H-t, art. aged H-t, art. aged Ann. Strain hardened (H) Ann. H-t, nat. aged Ann. Hard HI! Ann. H-t, nat. aged
7.10 X 1011 7.31 X 10" 7.31X1011 7.17 X 1011 7.17 X 1011 7.10 X 10" 7.10 X 10" 7.31 X 1011 7.31X1011 7.17 X 1011 7.10 X 1011 7.03 X 10" 7.03 X 1011 7.03 X 1011 6.89 X 1011 6.89 X 1011 7.10 X 1011 7.10 X 1011 6.89 X 1011 6.89 X 1011
2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65 2.65
X X X X X X X X X X X X X X X X X X X X
1011 1011 1011 1011 1011 1011 1011 1011 1011 1011 10" 1011 1011 1011 10" 1011 1011 10" 1011 1011
0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33
42.1 18.6 48.3 17.9 42.7 43.4 19.3 18.6 46.9 39.3 38.6 32.4 20.0 28.3 11.0 22.8 29.0 40.0 12.4 24.1
24. 9.6 41. 6.8 27. 32. 16. 7.5 31. 24. 31. 27. 9.6 24. 4.8 13. 13. 33. 5.5 14.
Ann.
7.17 X 1011
2.65 X 1011 0.33 22.8 X 10' 10.
H -t, art. aged Ann. (0.064 sheet)
7.17 X 1011 7.17 X 1011
2.65 X 1011 0.33 56.5 X 10' 49. 2.69 X 1011 0.33 20.7 X 10' 10.
Ann. Cold rolled 75% Ann.
Hard HI! Ann. Hard HI! H-t, then cold-worked H-t, then cold-worked, then art. aged Quenched (h-t) Ann.
H-t, art. aged Ann.
6.89 6.89 6.89 6.89 6.89 6.89 7.10 7.10
X X X X X X X X
X X X X X X X X X X X X X X X X X X X X
10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
'\[ 10-mm ball, 500-kg load. § 7:i 6-in. sheet specimen. /I H-strain hardened to a prescribed ha
TABLE
Alloy
99.997 Cu, 0.0016 S .................. 99.996 Cu, 0.002 S, 0.002 Fe .......... 99.950 Cu, 0.043 02, 0.002 Fe, 0.002 S 99.92 Cu, 0.04 02 .................... 99.94 Cu, 0.02 P ..................... 95 Cu, 5 Zn ......................... 95 Cu, 5 Zn ......................... 90 Cu, 10 Zn ........................ 90 Cu, 10 Zn ........................ 85 Cu, 15 Zn ...................... 85Cu,15Zn ........................ 80 Cu, 20 Zn ........................ 80 Cu, 20 Zn ........................ 10 Cu, 30 Zn ........................ 70 Cu, 30 Zn ........................ 70 Cu, 30 Zn ............ 65 Cu, 35 Zn ....................... 65 Cu, 35 Zn ....................... 60 Cu, 40 Zn ............... 89 Cu, 9.25 Zn, 1.75 Pb .............. 64.5 Cu, 35 Zn, 0.5 Pb ............... 67 Cu, 32.5 Zn, 0.5 Pb ...... 64.5 Cu, 34.5 Zn, 1.0 Pb .. 62.5 Cu, 35.75 Zn, 1.75 Pb .. 62.5 Cu, 35 Zn, 2.5 Pb ............... 61.5 Cu, 35.5 Zn, 3 Pb ............... 60 Cu, 39.5 Zn, 0.5 Ph ............... 60.5 Cu, 38.4 Zn, 1.1 Pb ............. 60 Cu, 38 Zn, 2 Pb .................. 57 Cu, 40 Zn, 3 Pb .................. 71 Cu, 28 Zn, 1 Sn .............. 60 Cu, 39.25 Zn, 0.75 Sn .............
2e-9.
ELASTIC AND STRENGTH CONSTANTS FOR COPPER ALLO
Condition
}'-in. rod, cold drawn Ann., %-in. rod
Ann., %-in. rod H.R. (0.040-in. flat) 0.040 in. flat spec. (G.S. 0.050 mm) Rolled strip 0.040 in. (G.S. 0.050 rom) Rolled strip 0.040 in. (spring) Flat, 0.040 in. (spring) Flat, 0.040 in. a. H.R. Flat, 0.040 in. (G.S. 0.050 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (G.S. 0.050 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (G.S. 0.070 mm) Flat, 0.040 in. (spring temper) Flat, 0.040 in. (extra epring temper) Flat, 0.040 in., ann.
Flat, 0.040 in. (spring temper) Flat, 0.040 in., ann. Rod, ann. Flat specimen, ann.
Tubular specimen, ann. Rolled, flat spec., ann. Rolled, flat spec., ann. Rolled, flat spec., anD.
Rod, ann. H.R. I-in. plate Light ann. 1.5-in. OD tubing Extruded I-in. rod Extruded 1-in. section All H.R. (I-in. plate) Ae H.R. (I-in. plate)
E
G
12.77 X 1011 11.2 X 1011 10.9 X 1011 11.7X1011 11.7 X 1011 1l.7XlO11 11.7X1011 11.7 X 1011 11.7 X 1011 11. 7 X 1011 11.7 X 1011 11.7X1011 11.0 X 1011 11.0 X 1011 11.0X1011 11.0 X 1011 10.3 X 1011 10.3 X 1011 10.3X1011 11. 7 X 1011 10.3 X 1011 10.3X1011 10.3XlOll 10.3XlOll 9.65XlO11 9.65 X 1011 10.3 X 1011 10.3 X 1011 10.3 X 1011 9.65 X 10" 10.3X10" 10.3 X 10"
4 A .. GS.X.1~11
< 8.96 X 8.96 X 9.65>< 10.7 X
Sand caSt
10.3
XlQ1i
·. .. .. . . .. .
Sand caSt Sand cast Sand caSt Sand casi Sand cast Sand cast, cooled in sand Sand cast Sand .cast, cooled in sand Sand.cast
X wi . ... . . . . . . .
. .......... . .......... . .........,. . . . . . .. .. . . ..........
1011 1011 1011 101i 101i
10.3
........... '~
........... 11. 7 X 1011 12.4 X 1011 1l.7 X 1011
48.2 X 10' 19.3 X
44.8 X 34.4 X 27.6 X 23.4 X ,26.2 X ........... 46.2 X ........... 51.7 X ........... 51. 7 X ........... 65.5 X
·
........ ... ...........
........... 22.0>< 10' 10.3 X ........... 24.1 X 10' 8:27 X · . . . . . . . . . . 2~. 4>< 10' 8.96 >< ............; 2~.6X10· 9.65 X ...........!.. . ;79.2 X 10' 48.2 X
..........
' ~ At 0.01 % offset. § to-nun ball, 3,OOO-kg load.
10' 10' 10' 10' 10' 10' 103 10' 10'
20.7 X 16.5 X 17.,2 X 10.3 X 11.7 X 22.0 X 18.6 X 24.1 X 31'.0 X
TABLE 2e-10., ELASTIC AND STRENGTH CONSTANTS FOR VARIOUS
Material
Condition
Iridium ......... Ann. Osmium ........ Ann. Rhodium ....... Ann. Ruthenium ...... As cast .Antimony ....... ............................... Beryllium ....... Vacuum cast Cadmium ....... Chill cast I-in. section Calcium ........ Cast slab Chromium ...... As cast Cobalt .......... Cast Columbium ..... Sheet, ann. O.Ol-in. section Columbium ..... Sheet, worked O.Ol-in. section Lithium ........................................ Manganese ...... Molybdenum .... Silicon .......... Sodium ......... Tantalum ....... Tantalum ....... Titanium ....... Titanium ....... Tungsten ....... Zirconium .......
Quenched Pressed + sintered (sheet) Chill cast 3.55 X 0.97 X 0.97 in.
~
52 X 10" 56 X 1011 o
•
•
•
•
•
•
•
•
•
•
•
•
41 X 10 11 7.78 X 10 11 29 X 10" 5.5 X 1011t 2-3 X 1011 ............. 21 X 10 11
G
Tensile strength
·....... . . · . . . . . .. . . .......... .......... ·... . . ... .
. ......... . .........
........
'.'
.......... .......... ......... . .......... . . . . . . . . . . . . . ......... . ............ . ......... . ............. ......... . .............
34 X 1011 11.26 X 1011
.........
. ..........
.......... ............................... ............ . ......... . Ann. O.OIO-in. sheet Worked O.OlO-in. sheet Ann. Hard, 60 % reduction
50 X 10 8
... .. ... .. 1.1 X 10 8 12-15 X 10 8 7.1 X 10 8 5.5 X 10 8 . ......... 23.7 X 10 8 34 X 10 8 69 X 10 8
.. . . . . . . . .
50 X 10 8 69 X 10 8 . ......... . .........
34 X 10 8 76 )< 10 8 11.6 X 1011 .......... 54 X 10 8 ............. ......... . 76.82 X 10 8 34 X 1011 13.5 X 1011 . ......... .............................. . 9.99 X 1011 .......... Hard drawn 84 X 10 8
'* References are on p.
t Sand cast. t 3.2-kg load,
E
2-76.
lO-mm ball. Per cent in 4 in.
.............
.............
......... . ......... .
TABLE
%CI
0.03 0.02 0.02 0.02 0.02 0.02 0.02 0.05 0.07 0.05 0.06 0.054 0.025 0.08 0.07 0.03 0.08 0.08 0.10 0.10 0.10 0.10 0.11 0.12 0.15 0.15 0.16 0.15 0.17 0.18 0.18 0.18
0.20
2e-ll.
Alloy
Iron: 2.50 C, 0.79 Si, 0.09 S, 0.04 P 3.52 C, 2.55 Si, 1.01 Mn, 0.215 P, 0.086 S 3.52 C, 2.55 Si, 1.01 Mn, 0.215 P, 0.086 S 1.11>-2.30 C, 0.81>-1.20 Si, 0040 Mn, 0.020P, 0.012 S 2.25-2.70 C, 0.80-1.10 Si Steel: 0.12 Mn, 0.005 Si, 0045 Cu, 0.07 Mo 0.5 Cu 1.0 Cu 1.5 Cu 2.0 Cu 2.5 Cu 3.0 Cu 0.39 Si, 0.25 Mn,'0.014 P, 0.049 S 1.17 Si, 0.32 Mn, 0.013 P, 0.034 S 1.73 Si, 0.35 Mn, 0.014 P, 0.030 S 2.39 Si, 0.16 Mn, 0.010 P, 0.016 S 0.42 Mn, 0.025 Si, 0.031 AI, 0.265 Ti 0.30 Mn, O.OIOY, 0.023 S, 0.09 Ni, 0.09 Cu, 0.26 V 1.01 Cr, 0.41 Cu, 0.80 Si, 27 Mn, 0.145 P, 0.020 S 18.95 Cr, 7.69 Ni 13047 Cr, 0.27 V, 0.04 P, 0.01 S 1.07 Cu, 0.54 Ni, 0043 Mn, 0.16 Si, 0.104 P, 0.022 S 1.46 Si, 0.102 Mn 0.45 Mn, 3.71 Ni, 0.10 S 0.5 Cr, 0.3 Mo, 2.5 Ni 0.6 Cr, 0.3 Mo, 3.3 Ni 0.Q7 Si, 0.69 Mn, 0.092 P, 0.027 S, 0.16 AI, 1.09 Cu, 0.15 Mo, 0.63 Ni 0.6 Mn, 1.4 Cr, 0.17 Mo, 1.0 Ni 0.84 Mn, 0.12 S, 0.099 P, 0.01 Si 0.75 Mn, 0.30 Si, 1.75 Ni, 0.25 Mo 0.75 Mn, 0.30 Si, 3.50 Ni 004 Mn, 1.2 Cr, 0.25 Mo, 4.1 Ni 13.50 Cr, 0.11 Si 0.5 Mn, 0.25 Mo, 1.8 Ni 0.55 Mn, 0.25 Si 2.50 Cr,O.55 Mn, 0.40 Si, 0.40 Mo, 0.20 V 0.92 Mn, 0.115 P, 0.12 S, 0.02 Si 16.17 Cr, 1.06 Mn, 0.30 Si
ELASTIC AND STRENGTH CONSTANTS FOR IRON AND STEEL
Condition
Cast
~s-in. cast, ann. bar 2-in. bar Malleable, cast, ann.
............................ R.R. at 540°C As normalized As normalized As normalized As normalized All normalized As normalized As rolled, All rolled All rolled All rolled R.R., 5 %~Btrained, aged Annealed R.R. %-in. bar C.R. %-in. bar R.R. 3%-ill. bar H.R. %·in. bar W.Q. from 1830°F A.C. from 1550°F O.Q. from 820°C (carburized) O.Q. from 820°C (carburized) R.R. 4 hr at 540°C W.Q. from 900°C (carburized) IJ.jj-in. diam C.R. bar Cast Cast O.Q. from 780 to 180° O.Q. from 1740°F, T at llWOF P.(O.Q.)(carburized)
E
13.8 X 12.1 X 8.27 X 17.2 X
G
Tensile strength
1011 . . . . . . . . . . . . ..... 32.8XI0' 1011 5.IOXI011 ..... 23.5XI0' 1011 43.4 X 1011 ..... 15.5 X 10' 1011 8.61 X 1011 0.17 39.3 X 10'
17.2 X 1011
8.61 X 1011 0.17
· . . . . . . . . . . . ............ ............ ............ ............ ............ ............ ............ ............ ............ · . . . . . . . . . . . ............ ............ ............ ............ ............ .......... ... ......... '"
... .........
... .......... 20.7 X 1011
34.3 34 39 48 .. 55 ..... 56 ..... 56 40.0 46.5 50.0 52.7 48.9 29.2
8.20 X 1011
..... ..... ..... 20.9XI011 ............ ..... ............ ............ . ... ............ ............ .... ............ ............ ..... ............ ........... .......... .... ·20:9'X' iOii ............ ............ ............ .... ............ ............ ....
'2iXx'ioi,
............ ............ . ........... ............ 20.5XlOll ............ 22.6 X 1011
34.4 X 10'
..... ..... ..... ....
17.2 X 10" ............ 18.2 X 1011 8.54 X 10" 20.5 X 1011 7.92 X 1011
............ ·C;.,;t"· ..................•... · . . . . . . . . . . . ............ C.R. O.Q. from 1740°F, T at 840°F
I " I
.... ..... ................
X X X X X X X X X X X X X
I
Yield strength
. ......... . ......... 25."8 x'io"
22.4 X lO't
10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
24.0 X lO't 27 X 10' 31 X 10' 43 X lO' 50 X 10' 52 X lO' 52 X lO' 27.9 X lO' 32.7 X lO' 37.6 X lO' 36.9 X lOs 46.9 X 10' 15.8XlO'
54.0 X lOs
41.3 X 10'11
98.5 X 10' 56.8 X 10' 48.8 X lOs
. . . .. . .. .. 38."7 x·io. .
63.7 X 60.4 X 93.1 X 122 X 52.8 X
10' 10' 10' 10' 10'
47.1 X 10' 34.4 X lO't 78.4 X lO't 108 X lO't 39.2XIO't
85.8 57.4 68.9 68.9 135 90.9 83.8 45 96.5 67.6 130
10' 10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
60.8 52.4 44.8 44.8 120 75.8 66.8 25 82.7 45.5 61.2
X X X X X X X X X X X
X X X X X X X X X X X
lO't 10' 10' lO't lO't 10' 10' lO't 10' 10' 10'
o.19 o.20 o.25 o.25 o.15 o. 15 o. 27 o.27 o.19 o.19
o. 10 o. 10
.30 . 34 .38 .91 .04 .37 .60 .45 .33 .33 .34 .37 .31 .43 .40 .32 .32 .27 . 78
1:35 Mn, 0.10 S W.Q. from 1550°F 0.45 Cr, 1.19 Mn, 0.67 Si, 0.033 P, 0.019 S Rolled 0.45 Mn, 0.40 S, 0.03 Si, 0.012 P Rolled, %-in. plate to 0.35 ............................ to 0.25; 0.3-D.6 Mn, 0.045 P, 0.05 S H.R. to 0.25; 0.3-D.6 Mn, 0.045 P, 0.05 S C.R . 0.72 Mn, 0.21 Si, 0.0248, 0.014 P Wr., ann. at 1450°F, F.C. 0.72 Mn, 0.21 Si, 0.024 S, 0.014 P Wr. W.Q. from 1600°F, T at 1l00°F 0.85 Mn, 0.05 (max) S, 0.045 (max) P H.R. (trans. prop.) H.R. (long. prop.) 0.85 Mn, 0.05 (max)S, 0.045 (max) P 0.75 Mn, 0.20 S, 0.10 P H.R. (trans. prop.) 0.75 Mn, 0.20 S, 0.10 P H.R. (long. prop.) 0.70 Mn. 3.5 Ni Ann. 0.88 Mn, 0.35 Si, 0.035 S, 0.019 P lRolled %-in. plate 0.65 Mn, 0.22 Si Wr., ann. at 1450°F; F.O. 0.38 Mn, 0.16 Si, 0.036 P O.Q. from 1575°F, T at 940°F 0.36 Mn, 0.16 Si, 0.018 S, 0.015 P ~i hr at 1550°F, O.Q. from 120°F, T ~, hr at 800°F 0.50 Cr, 1.14 Mn, 0.84 Si, 0.033 S, 0.021 P n.R. %-in. bar 0.56 Cr, 0.62 Mn, 0.26 Si O.Q. from 1470°F, T at 750°F 1.14 Cr, 0.69 Mn, 0.12 Si Nat 1525°F 0.78 Cr, 0.24 Mo, 0.54 Mn, 0.21,Si, 0.025'p, W., F.C. from 1450°F 0.029 S 0.78 Cr, 0.24 Mo, 0.54 Mn, 0.21 Si, 0.025 P, Wr., O.Q. from 1600°F, T at 0.029 S 1l00°F 0.46 Mn, 21.39 Cr, 10.95 Ni, 3.16 W, 1.39 A.C. from 1740°F Si 1.18 Cr, 0.16 V, 0.71 Mn, 0.33 Si, 0.037 S, Wr., F.C. from 1450°F 0.024 P 1.66 Mn, 0.25 Si, 0.024 S, 0.015 P Wr. F.C. from 1450°F 3.47 Ni, 0.64 Mn, 0.20 Si, 0.023 S, 0.015 P Wr. F.C. from 1450°F 1.65 Ni, 0.99 Cr, 0.51 Mn, 0.20 Si, 0.028 S, Wr., F.C. from 1450°F 0.019 P 1.92 Ni, 0.86 Cr, 0.30 Mo, 0.60 Mn, 0.16 Si, Wr., F.C. from 1450°F 0.019 S, 0.014 P 2.42 Ni, 0.49 Cr, 0.38 Mo, 0.88 Mn, 0.23 Si, Cast ann. at 1575°F, 6-in. bar, 0.13 Cu, 0.04 S, 0.03 P Tat 1200°F 12.69 Mn, 0.12 Si W.Q. from 1830°F O.10Mn Ann. at 1472°F
* References are on p. 2-76. t At yield point. tAt 0.2 % offset. 41 % in 70 mm. § %in8in.
............ ................. 89.6)(10 8t 60.8)(10 20.9X10 11 82.0 X 1011 0.276 59.0 X 108 37.4 X 1 20.4 X 1011 ............ 0.306 43.5X10 8 22.3 X 1 20.3 X 1011 78.5 X 1011 0.297 . ......... ........ 20.53 X 1011 78.06 X 1011 0.313 ....... , .. .. . . .. . 20.12 X 1011 78.20 X 1011 0.286 .......... .... .
.
18.9 X 1011 20.4 X 1011
81.3 X 1011 0.316 46.4 X 10 8 82.7 X 1011 0.310 62.8 X 108
.. ... .. . . .. . ............ ..... ............ . . . . . . .. . . . . .....
42.6X10' 44.1 X 108 43.1 X 108 46.1 X 10' 54.7 X 10' 59.5X10 8 8.06 X 1011 0.287 52.2X108 7.44 X 1011 ..... 155 X 10 8 7.44 X 1011 ..... 163 X 108
............ ............ ..... ............ ............ ..... . . '20.'5 X'io,i ............ ............ 0.291 19.8 X 1011 20.8 X 1011 20.5 X 1011 21 X 21.1 X 21 X 19.7'X
1011 ............ ..... 86.1X108 1011 8.27X1011 , , - 0 , . 164 X 108 1011 ............ ... 83.4 X 108 1011 8.27 X 1011 0.288 52.8 X 108
19.8 X 1011
25.8 X 1 37.9 X 1 22.5 25.0 24.7 27.5 39.3
X1 X 1 X 1 X 1 X 1
28.6 24.1 X 110 99.2 X 1 99.2 X 1 55.6 X
10
6i."7 x'ir 29.3 X 1
8.13 X 1011 0.272 86.8 X 108
62.4 X 1
20.1 X 1011 ............ ..... 88.2 X 108
30.9 X 1
20.3 X 1011
8.13 X 1011 0.289 61.1 X 10 8
33.9 X 1
19.2 X 10" 21 X 10" 19.8 X 10"
8.27X1011 0.295 58.5 X 10 8 8.34X10 11 0.308 65.0 X 108 7.78 X 1011 0.299 61. 9 X 108
29.8 X 1 36.5 X 1 30.2 X 1
19.8 X 10"
7.92 X 1011 0.288 66.2 X 108
34.2 X 1
20.2 X 1011
7.92 X 1011 ..... 81.3 X 10'
67.5 X 1
............ . . . . . . . . . . . . . . .. 102 X 108 ............ ............ ..... 68.2 X 108
II At 0.005 % permanent set. •• At 0.05 % permanent set. tt % in 1.5 in. H % in 3.94 in. 'If'lf % in 1.97 in.
~
53.2 X lO 65.4 )( 1
§§ % in 0.7 At 0.001
1111
*** At 0.1 %
ttt m, in 4
,TABLE
Alloy
99.90 Pb ......................... 99.73 Pb ......................... 99.73 Pb ......................... 0.023-{).033 Ca, 0.02-0.1 Cu, 0.0020.02 Ag ....................... 1 Sb ........................... 4Sb ........................... 6 Sb ........................... dSb ........................... 6Sb ...........................
2e-12.
ELASTIC AND STRENGTH CONSTANTS FOR LEAD AND LEAD
E
Condition
Rolled, aged Sand cast Chill cast
~
* References are on p. 2-76.
t M 6-in. ball, 9.85-kg load for 30 seo.
Yield strength at 0.5% offset
Tensile strength
.......... 1. 77 X 10' 0.95 X 10' 1.38 X 1011 1.1-1.3 X 10' 0.55 X 10' .......... 0.40-0.45 1.4 X 10'
.......... Extruded Extruded and aged 1.38 X 10" Rolled, 95 % reduction .......... Chill cast .......... Extruded .......... Cold rolled, 95 % reduc- .......... tion .......... 8 Sb., ........................... Rolled, 95 % reduction .......... 9Sb ........................... Chill cast .......... 4.5-5.5 Sn ...................... .................... 20 Sn .......................... .................... ........... 50Sn .......................... .................... .......... 2.89 X 1011 4.50-5.50 Sn, 9.25-10.75 Sb ...... Chill cast 4.50 5.50 Sn, 14-16 Sb . . . . . . . . . Chill cast 2.89 X 1011 9.3-10.7 Sn, 14-16 Sb . . . . . . . . . . Cast 2.89 X 10" 0.75-1.25 Sn, 0.3-1.4 As, 14.5-17.5 Sb Chill cast 2.89 X 1011 0.6-1.0 Sn, 1.5-3.0 As, 12.0-13.5 Sb Chill cast 2.89 X 10"
+
f1
.......
I ~lo tio in
2 3 4
2.1XlO' 2.1 X 10' 2.77 X 10' 4i.71XlO' 2.27 X 10' 2.82 X 10'
4 5 4 2 6 4
3.20 5.2 2.3 4.0 4.2 6.9 6.9 7.2 7.1 6.8
3 1 5 1 6
X X X X X X X X X X
10' 10' 10' 1.0 X 10' 10' 2.51 X 10' 10' 3.3 X 10' 10' 10' 10' 10' 10'
TABLE
Alloy
99.9+ Mg ............. , .............. 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, ~0.3 Si, ~0.05 Cu, ~0.01 Ni, 0.3 other 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, ~0.3 Si, ~0.05 Cu, ~0.01 Ni, 0.3 other 8.3-9.7 AI, 0.10 Mn, 1.7-2.3 Zn, :;:0.3 Si, :;:0.05 Cu, :;:0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5-3.5 Zn, :;:0.3 Si, ~0.05 Cu, :;:0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5-3.5 Zn, :;:0.3 Si, :;:0.05 Cu, :;:0.01 Ni, 0.3 other 5.3-6.7 AI, ~0.15 Mn, 2.5·-3.5 Zn, :;:0.3 Si, :;:0.05 Cu, :;:0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, :;:0.5 Si, ~0.1O Cu, ~0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ~0.5 Si, :;:0.10 Cu, :;:0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, :;:0.5 Si, :;:0.10 Cu, :;:0.01 Ni, 0.3 other 8.3-9.7 AI, ~0.13 Mn, 0.4-1.0 Zn, ~0.5 Si, 0.10 Cu, :;:0.01 Ni, 0.3 other .......... 8.3-9.7 AI, ~0.10 Mn, 0.4-1.0 Zn, ~0.5 Si, :;:0.3 Cu, ~0.01 Ni, 0.3 other ......... 2.5-3.5 AI, ~0.20 Mn, 0.6-1.4 Zn, 0.080.30 Ca, :;:0.3 Si, ~0.05 Cu, :;:0.005 Fe, :;:0.005 Ni, 0.3 other ................. 2.5-3.5 AI, ~0.20 Mn, 0.6-1.4 Zn, 0.080.30 Ca, ~0.3 Si, :;:0.05 Cu, :;:0.005 Fe, :;:0.005 Ni, 0.3 other. . ..............
2e-13.
ELASTIC AND STRENGTH CONSTANTS FOR MAGNESIUM
Condition
E
........................ 4.48 Sand and permanent cast 4.48 molds, as fabricated Sand and permanent cast 4.48 molds, cast and stabilized Sand and permanent cast, 4.48 solution h-t Sand and permanent cast 4.48 molds, as fabricated Sand and permanent cast 4.48 molds, cast and stabilized Sand and permanent cast 4.48 molds, solution h-t Sand and permanent cast 4.48 molds, as fabricated Sand and permanent cast 4.48 molds, solution h-t Sand and permanent cast, 4.48 solution h-t, aged
G
( 10- 7 6.52 X 10- 6 1. 23 >( 10- 5 4.85 X 10- 5 1. 52 X 10- 5 1.68 X 10- 5 1.79 X 10- 5 1.88 X 10- 5 1.98 X 10- 5 2.24 X 10- 5 2.57 X 10- 5 0.72 X 10- 5 6.5 X 10- 5 0.66 0.16 X 10- 5
1 11 11
sec
2 2 2 1 3 4 1 3 3 3 3 5 5 5 5 5 1 7 7 7 6 6 6 1 9 9 9 9 9 9 1 8 8 8 8 8 8 B
1 1
MECHANICS
TABLE 2e-17. DIFFUSION COEFFICIENTS FOR METALS (Continued) Metal
Test temp.
Room Pt into Cu ............................. . Room Pb into Pb ............................. . Room Sb into Ag ............................. . Si into ferrite ........................... . 1435 ± 5°C Si into Cu ............................. . Room Sn into Ag ............................. . Room Room Sn into Cu ............................. . Room Sn into Pb ............................. . 49.27°C Ti into In .............................. . 74: 19°C Ti into In ............................... . Ti.into In .............................. . 101.55°C Ti into In .............................. . 139. 16°C 155. 60°C Ti into In ...•........................... Ti into In .............................. . 155.91°C Ti into In .............................. . 157.80°C Room Ti intd Pb ............................. . N. B. of H.
D
(Cm2) sec
1.02 X 10- 4 6.6 5.31 X 10-6 1.1 X 10- 7 3.7 X 10- 2 7.82 X 10-6 1.13 3.96 1.4 X 10-12 9.2 X 10-12 4.6-4.8 X 10-11 2.8-3.2 X 10-10 2.17 X 10- 9 1.87 X 10-7 2.27 X 10-6 0.025
The values quoted from ref. 1 are for Do in the equation D = Doe-H1BT •
1
1 1 10 1 1 1 1 9 9 9 9 9 9 9 1
Cf. ref. 1 for value.
References for Table 2e-17 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
Ref.
No:wick, A. S.: J. Appl. Phys. 22, 1182 (1951). Slifkin, L., D. Lazarus, and T. Tomizuka: J. Appl. Phys. 23, 1032 (1952). Smithells, C. J.: "Metals Reference Book." Martin, A. B., and F. Asaro: Phys. Rev. 80, 123A (1950). Chemla, Marius: Compt. rend. 234, 2601 (1952). Moore, W. J., and Bernard Selikson: J. Chem. Phys. 19, 1539 (1951). Cohen, G., and G. C. Kuczynski: J. Appl. Phys. 21, 1339L (1950). Hoffman, R. E.: J. Chem. Phys. 20,1567 (1951). Eckert, R. E., and H. G. Drickamer: J. Chem. Phys. 20, 13 (1951). Bradshaw, F. J., G. Hoyle, and K. Speight: Nature 171,488 (1953). Kuczynski, G. C.: J. Appl. Phys. 21. 632 (1950).
ELASTICITY, HARDNESS, AND STRENGTH OF SOLIDS
2-79
7. Rockwell Hardness Number.l itA hardness value indicated on a direct-reading dial when a designated load is imposed on a metallic material in the Rockwell hardness testing machine using a steel ball or a diamond penetrator. The value must be qualified by reference to the load and penetrator used. Severllil scales are in common use: Rockwell A hardness is determined with a minor load of 10 kg and a major load of 60 kg using the diamond cone (brale); Rockwell B hardness is determined with a minor load of 10 kg and a major load of 100 kg using a f-1rin. steel ball; Rockwell C hardness is determined with a minor load of 10 kg and a majorload of 150 kg using the diamond cone"; Rockwell D hardness is determined with a minor load of 10 kg and a major load of 100 kg using a diamond cone indenter; Rockwell E hardness is determined with a minor load of 10 kg and a major load of 1QO kg using a -§-in. steel ball indenter; Rockwell F hardness is determined with a minor load of 10 kg and a major load of 60 kg using a ftin. steel ball; Rockwell G hardness is determined with a minor load of 10 kg and a major load of 150 kg, using a -h-in. steel ball indenter. A second set of Rockwell hardness numbers are the Rockwell superficial hardness numbers. One of these is the Rockwell 15T hardness, which is determined with a minor load of 3 kg and a major load of 15 kg, using a y\-in. steel ball. Note: The methods of determining the hardness values can be found in Standard Methods of Test for Rockwell Hardness and Rockwell Superficial Hardness of Metallic Materials, ASTM E18--42.
8. Brinell Hardness Number.2 itA hard spherical indenter of diameter D mm is pressed into the metal surface under a load W kg and the mean chordal diameter of the resultant indentation measured (d mm). The Brinell hardness number (Bhn) is defined as W Bhn = curved area of indentation 2W .~-~---- 7rD(D - VD2 - d2) and is expressed in kg/min 2." 9. Vickers Hardness Number.2 itA pyramidal diamond indenter is pressed into the surface of a metal under a load of W kg and the mean diagonal of the resultant~ind~ta tion measured (d mm). The Vickers hardness number (Vhn), or Vickers diamond hardness (Vdh), is defined as Vdh (or Vhn) =
. W. . pyramldal area of mdentatlOn
The indenter has an angle of 136 0 between opposite faces and 146 0 between opposite edges. From simple geometry, this means that the pyramidal area of the indentation is greater than the projected area of the indentation by the ratio 1:0.9272. Hence Vdh =
0.9272W projected area of indentation = 1.8544W /d 2
The value is expressed in kg/mm 2 ." 10. Diffusion Coefficient. If the concentration (mass of solid per unit volume of solution) at one surface of a layer of liquid is d 1, and at the other surface d 2, the thickness of the layer is h, the area under consideration is A, and the mass of a given substance which diffuses through the cross section A in time t is m, then the diffusion coefficient is defined as
1 2
J. G. Henderson, "Metallurgical Dictionary." D. Tabor, "The Hardness of Metals."
2-80
MECHANICS
2e-4. Effect of High Pressure on the Specific Volume of Solids. Tables 2e-18 to 2e-22 present data on the change of specific volume of certain solids as a result of the imposition of very high pressure. The general reference in this field is P. W. Bridgman, "The Physics of High Pressure," G. Bell & Sons, Ltd, London, 1949. Specific references are attached to each table. TABLE 2e-18. VOLUME OF SOLID HELIUM AT OOK* Pressure, kg/em"
Volume, ml/mole
Compressibility (l/v) (avjap)T
52 91 141 207 305 475 718 1,105 1,715 2,240
19.0 18.0 17.0 16.0 15.0 14.0 13.0 12.0 11.0 10.5
184 X 10- 6 135 100 73 52 37 25 16 12 10
"'J. S. Dugdale and F. E. Simon, Proc. Roy. Soc. (London) 218, 291 (1953);
TABLE 2e-19. FRACTIONAL CHANGE OF VOLUME AT 25°0 OF RELATIVELY INCOMPRESSIBLE METALS* ~
c-'~~
Pressure, kg/em' 5,000 10,000 15,000 20,000 25,000 30,000 >I
de/>
(~/2)
- 6 sin ~
d~
+1 -
5 cos if; - 3 cos if; In (sin ~
+ sin
2
*)
This formula holds if the mass of the earth equals the mass of the reference ellipsoid and if both centers of mass coincide. if; is the spherical distance between the fixed point where To is computed and the variable point at the surface of the sphere with radius R on which the anomalies 6.g are assumed to be given. Hence, by means of gravity anomalies the earth's gravitational potential can be computed. The value of T/'YH! where T is the value of the disturbing potential at the earth's surface, approximately equals the geoid undulation, i.e., the distance between the surface of the reference ellipsoid and the equipotential surface vV 0 = const at mean sea level, the geoid (cf. Sec. 2h-1). The deflection of the vert'cal is found by differentiating the disturbing potential T in the horizontal direction. The horizontal derivative of Stokes' formula is known as Vening Meinesz' formula. Thus, by means of gravity anomalies we are able to compute geoid undulations and deflections of the vertical with respect to an ellipsoid whose mass is identical with the mass of the earth and whose center coincides with the mass center of the earth. By knowing the undulations and the deflections of the vertical for the different datums of the world, all datums can be shifted into one common system. To determine the earth's potential from the solution of the geodetic boundary-value problem requires that the earth's surface be covered with gravity measurements. At present, huge parts of the earth, especially the oceans, are without gravity anomalies. Hence, the gravity measurements have to be combined with the results of satellite observations to improve the knowledge about the earth's gravity field. Either given gravity anomalies are expanded into spherical harmonics and compared 1 M. S. Molodenskii, V. F. Eremeev, and M. r. Yurkina, "Methods for Study of the External Gravitational Field and Figure of the Earth," Israel Program for Scientific Translations, Jerusalem, 1962. 2 M. Hotine, "Mathematical Geodesy," ESSA Monograph 2, Government Printing Office, October, 1969.
2-99
GEODETIC DATA
TABLE 2h-4. NORMAL GRAVITY FROM THE EQUATOR TO THE POLE: COMPUTED FROM THE INTERNATIONAL GRAVITY FORMULA h = 978.0490(1 + 0.0052884 sin 2 B - 0.0000059 sin 2 2B) cm/sec 2• Unit 1 milligal] B,
deg
Gravity
B, Difference deg
Gravity'
DifB, ference deg
--
--- --
978,049.00 978,050.57 978,055.27 978,063.10 978,074.06 978,088.12 978,105.26 978,125.48 978,148.74 978,175.02
Gravity
Difference
---
1.57 4.70 7.83 10.96 14.06 17.14 20.22 23.26 26.28
31 32 33 34 35 36 37 38 39 40
979,416.53 979,496.80 979,578.46 979,661.40 979,745.54 979,830.77 979,916.98 980,004.08 980,091.94 980,180.48
78.78 80.27 81.66 82.94 84.14 85.23 86.21 87.10 87.86 88.54
61 62 63 64 65 66 67 68 69 70
982,001.46 982,077.35 982,151.49 982,223.77 982,294.12 982,362.45 982,428.67 982,492.70 982,554.46 982,613.88
77.55 75.89 74.14 72.28 70.35 68.33 66.22 64.03 61.76 59.42
12 13 14 15 16 17 18 19
978,204.29 978,236.50 978,271.63 978,309.63 978,350.44 978,394.04 978,440.35 978,489.33 978,540.92 978,595.05
29.27 32.21 35.13 38.00 40.81 43.60 46.31 48.98 51.59 54.13
41 42 43 44 45 46 47 48 49 50
980,269.47 980,359.12 980,449.01 980,539.14 980,629.39 980,719.65 980,809.82 980,899.78 980,989.42 981,078.64
88.99 89.65 89.89 90.13 90.25 90.26 90.. 17 89.96 89.64 89.22
71 72 73 74 75 76 77 78 79 80
982,670.89 982,725.41 982,777.37 982,826.72 982,873.39 982,917.33 982,958.47 982,996.77 983,032.19 983,064.67
57.01 54.52 51.96 49.35 46.67 43.94 41.14 38.30 35.42 32.48
20 21 22 23 24 25 26 27 28 29 30
978,651. 66 978,710.68 978,772.05 978,835.68 978,901.49 978,969.42 979,039.38 979,111.28 979,185.03 979,260.55 979,337.75
56.61 59.02 61.37 63.63 65.81 67.93 69.96 71.90 73.75 75.52 77.20
51 52 53 54 55 56 57 58 59 60
981,167.33 981,255.37 981,342.67 981,429.10 981,514.58 981,598.99 981,682.23 981,764.19 981,844.79 981,923.91
88.69 88.04 87.30 86.43 85.48 84.41 83.24 81.96 80.60 79.12
81 82 83 84 85 86 87 88 89
983,094.19 983,120.69 983,144.16 983,164.55 983,181.85 983,196.03 983,207.08 983,214.99 983,219.73 983,221. 31
29.52 26.50 23.47 20.39 17.30 14.18 11.05 7.91 4.74 1.58
°12 3 4 5 6 7 8 9 10 11
90
with the harmonic coefficients found by satellite observations, or gravity anomalies are computed, using the harmonic coefficients obtained from satellites, and compared with given gravity anomalies, in order to compute corrected harmonic coefficients. The geoid map of Fig. 2h-l and the gravity anomalies for 5° by 50 surface elements of Tables 2h-5 and2h-6 were obtained by such a combination. Combination methods, using instead of the expansion into spherical harmonics the solution of the geodetic boundary-value problem to express the earth's potential, are under investigation.1,2 1 K. Arnold, An Attempt to Determine the Unknown Parts of the Earth's Gravity Field by Successive Satellite Passages, Bull. Geod. no. 87, p. 97, Paris, 1968. 2 Koch, K. R.: Alternate Representation of the Earth's Gravitational Field for Satellite Geodesy, Boll. Geofisica teorica ed applicata 10 (40) (1968).
TABLE 2h-5. 50 BY 50 MEAN GRAVITY ANOMALIES FROM A COMBINATION OF SATELLI D.-I.TA REFERRED TO THE INTERNATIONAL GRAVITY FORMULA:
EASTERN
(Units milligals)
o·
300
60'
120'
90'
90'
60'
30"
....f
8
00
-30'
_600
6 19 21 10 55 24
7 14 25 17 67 25
5 18 -3 11 9 23 20 22 23 23 20 -14
3 13 39 20 12 9
3 15 36 20 22 4
2 8 32 17 19 10
10 -4 -6 3 1 16 8 8 22 8 26 31 18 16 16 17 38 57 46 8 22 -5 -9 21 15 2 -1 -35 -15 18
12
2 -1 -1 -30 -35 -21 -20 -8 16 13 3 4 11 18 17 20 13 5 -13 -21 -2 -3 -27 -19 -15 -0 -0 -3 3 8 10 13 8 11 1 10 -6 -6 -5 -9 -9 -15 -22 -18 -1 9 10 1 -5 8 0 1 -8 -28 -24 -11 -8 -0 -25 -26 -23 -10 -8 -3 43 -11 4 4 2 31 25 -5-14 -25 -20 14 14 -10 -16 -1 18 -37 -15 -6-11 9 11 20 16 21 22 -45 25 5 62 39 39 16 -17 -26 -3 6
2 3 3 2 11 22 20 7 20 27 18 12 32 19 8 8 -2 -15
-7 -24 -26 20 13 ..,.2 12 10 -15 1 4 31 16 7 11 -20 4 1 -11 -10 -14 -1 7 14
-1 -28 -25 3 8 -1
8 5 4 8 25 11
13 7 10 7 16 8
14
5 1 32 38
3 16 28 17 7 14
3 16 11 4 3 5
3 -2 -3 15 14 13 21 18 16 7 12 8 6 la 1 21 33 10
7 -2 -24 -7 -1 2 4 5 -12 -3 -3 13 19 -19 -'-24 17 3 -3 -4 4 29 -11 -9 5 4 7 9 10 6 -5 -6-11 -14 3 13 -0 3 -51 -7 3 -20 3 -3 -1 -34 -26 -28 -19
3 2 2 3 4 2 8 5 4 7 15 15 16 16 15 2 -12 2 -0 4 3 -4 -10 -6 -2 3 -5 -5 -10 -11
5 5 5 5 5 5 o -2 -4 -5 -6 5 3 5 3 4 . 14 11 8 -4 -14 -4 o -2 6 -2 -2 -1 -5 5 8 1 -9 -7 -6 -7 -9 -6
14 -18 -12 -15 -14 -21
.,..3 -3 -2 -29 -28 -34
1 4 -20 -31 -45 -42
-31 -49 -6 6 -4 -8 -22 1 -30 -21 -8 -32 -20 -8 -23 -47 -50 -36
-58 -21 -11 -16 -30 -16
-17 -27 -38 7 -4 22 -29 -22 -13 -16 -23 -8 -12 -6 -3 -2 1 -6 -16 0-31 -22 -7 9 -12 -10 2 -10 -14 -15 1 -22 -21 -2 -0 -4 -0 9 4' 16 -14 7 -8 12 5 -10 -5 8 17 -7 4 13 -3 11 25 3 -4 -16 1 12 3 23 8 26 17 1
-30 -10 -4 ·-4 35 13
-42 -9 -8 -13 19 31
-49 -50 -30 -28 -25 -9 -12 -34 -4 -6 3 -1
-14 -1 -13 2 -11 5 -25-34 -3 -34 -9 -11
14 10 11 8 14 7
8 -5 -10 -6 -6 -14
3 11 19 9 7 0
12 13 9 11 22 9
30 12 15 11 24 13
18 13 17 9 20 15
2 7 19 23 25 IV
21
21
17 14 8 16 20 19
3 5 6 8 12 16 19 17 14 13 -6 -8 -10 -12 -12 -10 -5 36 15 29 50 58 62 60 54 45 37 33 32 34 3 -1 -4 -5 -4 -2 7 15 14 11 -4 -6 -6 -5 -3 0 5 10 16 22 -8 5 5 5 5 5 6 6 6 6
11 38 34 2 28 6
8 37 32 6 32 6
13 21 19 16 21 17
5 2 15 21
9 3 20 21
24
23
20
11 9 18 18 23
2 14 16 29 19 18
15 20 23 26 28 24
32 13 10 35 32 33
2 -1 28 15 25 16 9 12 27 22 6 6
1 10 11 14 36 5
-51 -11 2 -25 -5 -4
-6 -14 -17 -14 -8 -16 -4 -5 3 3 9 14
-5 -7 -11 1 -10 7 -1 16 7 -1 18 19
1 3 13 15 16 27
1 13 41 32 31 28
5 9 15 34 5
6 23 11 37 31 4
6 5 21 13 12 23 21 17 27 23 4 -8
1 2
1
1
22 32 29 28 4 1 -3 12 18 11 -2 -1 2 - 9-14 -7 8 -10 -14 -4 11 9 2 -28 -17 2 12 -6 -1 -18 -32 4 -1 4 10
7 -2 -3 -1 -25 -27 -a2 -31 -3 -45 3 -7 5 -6 -12 -24 -42 -15 -12 -22 19 17 15 11 -0 -4 -6 -10 -12 -12 4 -4 -9-11 -11 30 21 18 17 12 3 -2 4 3 30 20 11 11 13 9 4 33 23 13 12 13 11 5 7 6 14
1
-2 -2 -
4 -1 -4 5 6 6 28 26 25 21 23 20 1 14 11 10 -37 7 6 17 -45 1 11 7 4 7 -25 -2 18 14 11 8 4 4 -10 5 6 7
-90' • R. H. Rapp, Comparison of Two Methods lor the Combination of Satellite and Gravimetric Data, Ohio Btate Uni•• Depl. Good. Sci. Repl. 113
TABLE
2h-6. 5°
BY
5°
MEAN GRAVITY ANOMALIES FROM A COMBINATION OF SATELL
DATA REFERRED TO THE INTERNATIONAL GRAVITY FORMULA: WESTERN H
(Units milligals)
210' 2400 270' 300' 180' 90' 1--------------------',--------------------,--------------------,-------------------,----4 13 2 2 2 3 -0 -3 -3 6 0 6 4 8 10 13 15 14 12 10 9 8 13 16 12 14 11 6 7 10 7 11 12 12 11 9 11 34 3,5 18 21 24 26 28 16 15 M 6 ~ ~ 9 16 22 13 27 33 33 33 29 34 34 32 29 13 10 39 33 15 16 -6 11 9 6 3 2 5 9 15 5 6 25 9 15 10 0 -3 1 4 20 24 6 9 11 -3 7 2 8 17 3 12 -5 -2 1 -9 2 -10 3 22 19 3 -1 18 23 24 26 10 -1 -6 2 1 2 5 9 4 1 2 4 -17 o -3 -7 -10 -5 -7 -7 -2 -4. -17 19 8 7 19 24 16 42 59 17 5 -10 -13 -13 -11 4 4
n
eo' 1 - - - - - - - - - - - - - - - - - - , - - - - - - - - - - - - - - - - - - - - - -
4 9 1 -0 2 3 -9 0 -11 -4 1 3 -33 -22 -5 11 -2 -2 7 14 18 42 29 29 12 10 8 6 -1 -7 -36 3 27 6 11 19 7 3 -10 -15 -9 -6 17 0 -22 2 -18 -20 3 -16 -3 16 8 6 13 15 9 12 o -5 -9 -5 -8 15 3 22 18 22 11 11 -8 -5 -10 -11 -6 3 11 1 -7 -11 -8 -2 3 1 -3 -14 -15 -5 -6 22 14 24 27 13 4 -3 -5 -2 -7 10 10 -15 -20 -6 -9 -13 -12 -6 -6 -5 -13 -18 -25 -21 -8 6 5 22 -1 -6 -3 1 -0 6 -16 -15 -10 -8 -7 o -8 -5 -12 -15 -20 -12 -10 7 -0 -1 2 -0 11 -6 -31 -18 -2 -9 -7 -6 -7 -37 -11 7 2 3D' 1 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -13 -1 2 12 23 -27 -28 -24 -18 -28 -19 2 0 10 10 -7 -21 -25 -26 -15 -19 2 26 -4 8 9 7 22 -2 -5 --58 -27 -23 -28 -13 3 -7 -8 -12 -15 -18 -19 -21 -11 -12 17 -4 -5 2 11 36 26 2 -7 -2 -14 -14 -29 -19 --23 -15 -10 -5 1 23 5 15 -7 -20 4 -49 -16 -27 -26 -7 -4 -8 -3 9 -16 -3 -2 -5 -8 -18 10 -22 2-3 -4 0 4 18 22 -11 -28 -36 -18 -.50 -29 17 -12 -·1 1 1 12 17 31 12 18 -8 -17 -22 -23 -8 -2 22 21 -12 -14 -10 -5 -4 -11 -12 -14 -1 -12 -1 0 >-' o 6 9 5 31 24 23 11 -1 -4 1 -8 -8 -6 -2 -2 -3 -7 -7 -3 -6 -2 -3 5 -7 -7 21 >-' 0' 2 -5 21 9 3 11 24 19 4 -9 -6 -1 -7 -5 -8 -0 -2 -6 -8 -6 -5 -1 -4 -6 -8 -5 7 12 10 -1 -1 -7 -5 -7 -4 -5 -1 -3 -4 1 -0 -9 -6 13 3 -7 2 -7 -10 -2 -6 -7 2 -4 2 1 0 2 o -8 26 18 13 5 -11 11 2-6 6 3 14-2 -3 -13 -3 -3 2 -7 2 1 -0 -3Q -6 -20 ~5 44 21 7 -2 7 4-1 9 13 6 8 -3 -5 -8 -1 -3 0 -4 1 -5 4-2 8 -12 21 -12 -2 48 -8 -7 -18 4 -2 -8 -6 -1 -10 -16 0 6-10 13 -4 21 27 16 10 -6 -2 -4 -1 5 1 8-4 -3 -2 -0 -6 -4 10 9 4 _30' 1 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
if'
-"I
4 -2 -3 -6 -3 -3 -1 -.5 -3 7 7 7 -1 -2 -2 -1 -2 -1 10 8 6 3 4 0 -5 -1 3 84M 2 1 1 -1 1 6 -7 -8 -6 -4 -6 -3 3 4 2 5 6 8 1 -1 -1 8 10 11 -12 -10 -10 -Ie -7 -2
-20 -2
-60'
4 4
8 9
11 9
9 9 3 -0
7 0
8 7
6 8
4 -2 9
10
9
U
8 8
5 8 5
5 10
9
14 U
16
7
9
6
9
11
8
9 4
o 3 1 5
5 5 7
o
29 6
2
13
10
Ie
11
7
28 6
5 2 9
7
15 9
11 -0 10
3
6 -4
14 -1 -5 6 -1 1 2 0
1 - - - - - - - - - - - - - - --------,-----------1 -2 -6 -7 -6 -4 -6 -7 -6 -2
-18 -13 -18 -19 -9
-18 -19 -18 -18 20
-17 -24 -22 -15 20
-15 -28 -28 -19 20
_90' • Rapp, op. cit., p, 27.
-14 -31 -12 -14 -11
-15 -32 -15 -12 20
-16 -2D -8 -10 21
I
-16 -24 -22 -7 20
-13 -16 -16 --5 20
o
1
-10 -8 -7 4 -8 -1 5 -5 13 -19 -2 -22 20 20 -6
2 4 8 11 12 9 6 7 8 -2 5 17 -6 -3 3 -1 7 8 10 11 -6 27 20 12 15 40 1 -9 -18 -11 -12 13 16 11 15 22 -2 -23 -1 17 17 13 7 -9 -6 -4 20 20 20 20 20 -23 -9 19 18 18
14 H W H 31 21 30 1 40 32 21 13 -10 8 18 -10 -22 -9 13 6 -1
2-102
MECHANICS
2h-7. Geodetic Reference System: 1967. In 1967 the General Assembly of the International Union of Geodesy and Geophysics recommended replacing the International Ellipsoid and the International Gravity Formula with the Geodetic Reference System 1967 defined byl a = 6378160m GM = 398603 km 3 /sec 2 J 2 = 10827 X 10- 7 with J 2 = - V5 020 • This set of parameters is identical with the parameters adopted by the International Astronomical Union in 1964 as part of a system of new
+90 0
+80· ..... y .. " ...... ...... '.
• ~ ~9I
. .' . . .... ~. '. ::... . . . . ..... "-1-'-'-'.~.1-''-"'-"-1-'---l---1 /1U.-1Q.,t.;;:;:; ~>I\': .···.l40 .....·)~ ."': ·b.~.~.::~:~ :::.~. ~.·20~0.)."""' ..... / ....... ···20,.:--:- ". 'J-.. \.~..p ';. r. JI': ..... .. .••••••••••• "
. ' "',). . . . .
FIG. 2h-1. Geoid obtained by combining satellite and gravimetric data. Units: meters. (W. Kohnlein, Smithsonian Astrophysical Observatory Special Report 264, p. 57, 1967.)
astronomical constants. The values for a, GM, and J 2 , together with the value for the earth's rotational velocity, define an equipotential ellipsoid of revolution completely, so that the shape of the ellipsoid and its external gravity field are determined by the four constants. Only preliminary numerical values for the shape of the ellipsoid and the gravity formula of the Geodetic Reference System 1967 have been published until now. 2 ,3 Bull. Geod. no. 86, p. 367, Paris, 1967. A. H. Cook, The Polar Flattening and Gravity Formula in the Geodetic Reference System 1967, Geophys. J. 15, p. 431, Oxford, 1968. 3 H. Moritz, "The Geodetic Reference System 1967," Allgem. Vermes8., p. 2, Karlsruhe, 1968. 1
2
2i. Seismological and Related Data B. GUTENBERG l
California Institute of Technology J. E. WHITE
Globe Universal Sciences, Inc.
2i-l.List of
~ymbols ,
V v P
,velocity- of longitudinal wave P velocity of transvers.e wave S symbol denoting longitudinal wave S symbol denoting transverse wave k bulk modulus or volume elasticity p. rigidity or shear modulus p density, T Poisson's ratio A 'ratio t temperature in degrees centigrade, time p pressure in bars h depth in the earth T period of seismic disturbance G symbol denoting surface shear waves Ra symbol denoting Rayleigh waves Ll. epicentral distance SH symbol denoting component of S wave in horizontal plane SV symbol denoting component of S wave in vertical plane i actual IJ.ngle of incidence at a discontinuity, 'i apparent angle of iIlicidence at a discontinuity, , u ratio of horizontal ground displacement to incident amplitu~e
VYv
:::
"
2i-2. Fundamental Equations for Elasti~ Consta~ts and Wave Velocities. In purely elastic, isotropic, homogeneous media; the velocity V of longitudinal waves P, v of transverse waves S, the bulk modulus k, the rigidity p., the 'density p, and Poisson's ratio II are connected by the following equations: p
= k
+ -tp.
v2 = ~
(2i-1)
A=Iv
(2i-2)
p
P II
=
iA2 -1 A' - 1
k = p(P 1
-tv') .
Deceased.
2-103
p.
= v2 p
(2i-3)
2-104
MECHANICS
2i-3. Elastic Constants and Wave Velocities in Rocks (Laboratory Experiments). In rocks the elastic constants and the wave velocities usually increase with increasing pressure p (Tables 2i-2 and 2i-3) and decrease with increasing temperature t and with porosity. Phase changes affect all elastic quantities. Many sedimentary rocks show significant anisotropy, with an axis of symmetry. Table 2i-4 gives an example of velocity differences for vertical and horizontal traveP and for shear polarization. TABLE 2i-1. CORRESPONDING V~LUES OF POISSON'S RATIO (]' AND V Iv (]' 1°.0°1°.10 10.20 10.22
0.241°.251°.261°.281°.3°1°.40 1°·50
Vlv 1.414 1.500 1.633 1.670 1.710 1.732 1.756 1.809 1.871 2.449
co
TABLE 2i-2. ELASTIC CONSTANTS AND WAVE VELOCITIES IN ROCKS AT ROOM TEMPERATUREt
I
-
---.---
k, 1011 dynes/cm 2 1011 dynes/cm2 1-',
(]'
1atm
4,000 atm
4,000 atm
1 atm
-----Dunite ............ 4!--6 Gabbro ............ 3-4 Granite ............ 1-}-2j. Obsidian glass ...... 2i-3 1 1 Ice ................ rlI
6-}-7 4-5 3i-3j. ? ?
? 6± 2i-3j.
3i± : 1
V, v, km/sec kID/sec
---
~
12± si±
5i± 3i-4
?
0.25-0.30 0.2-0.3 0.20-0.26 0.l-o.2? 0.3-0.4
7-}-8j. 5-7
5-6i 5±
3i-3!
4-1-4 3-}-4 2-3j. 3j.± 1-}-2
t F. Birch, ed., Handbook of Physical Constants, Geol. Soc. Am., Spec. Paper 36 (1942); L. H. Adams, Elastic Properties of Materials of the Earth's Crust, in "Internal Constitution of the Earth," 2d ed., pp. 50-80, 1951. See also S. P. Clark, Jr., ed., Handbook of Physical Constants, rev. ed., Geol. Soc. Am., Mem. 97 (1966).
TABLE 2i-3. LONGITUDINAL VELOCITIES, KM/SEC, AT PRESSURES P AND TEMPERATURES t CORRESPONDING TO THE DEPTH h IN THE EARTH AF~~R LABORATORY MEASUREMENTt p,
t,
bars
°C
260 1,300 2,600 3,900 6,700
45 135 225 290 400
h, kIn 1
5 10 15 25
Dunite 7.55 7.50 7.22
.... ....
San Marcos gabbro 6.70 6.90 6.96 6.95 6.S0
Texas gray Woodbury granite granite 5.90 6.02 6.02 6.01
5.90 6.15 6.14 6.04
t D. S. Hughes and C. Maurette, Variation of Elastic Wave Velocities in Basic Igneous Rocks with Pressure and Temperature, Geophysics 22, 23-31 (1957).
2i-4. Periods and Amplitudes of Seismic Waves. Seismological instrumentation great advances in fidelity of observation, geographic distribution of stations, and machine data reduction. Strain seismometers have uniform sensitivity from periods of many hours dowIl to a few seconds. Tilt meters and gravimeters also ~as;llfade
1 J. E. White and R. L. Sengbush, Velocity Measurements in Near-surface Formations, GeophY8ic8 18, 54 (1963). -
2-105
SEISMOLOGICAL AND RELATED DATA
~dicate earth motion down to "dc," i.e., periods much greater than the tidal period. A worldwide net of 125 stations has been established, recording three-component motion in 0.1-to-1-sec range and 10-to-100-sec range. A few array stations exist at which signals from dozens of seismometers in an array can be combined. This improved instrumentation gives an improved portrayal of earthquakes and more accurate knowledge of the structure of the earth. Earthquakes create permanent displacements, which may be observed at great distances. 1 Great earthquakes excite the free oscillations of the earth to measurable amplitudes,2 at periods of 3 to 54 min. Love waves and Rayleigh waves in the period range 10 to 100 sec are governed by velocity contrasts in the crust and mantle. Body waves display periods of 0.1 to 10 sec, depending on range, with shear waves tending to longer periods than compressional waves.
TABLE 2i-4. VELOCITIES
Chalk ........... Shale ............
IN
SHALLOW SEDIMENTS, KM/SEC
V vert.
V horiz.
2.6 1.8
3.0 2.4
Vsv
vert.
1.1 0.4
VSH
horiz.
1.2 0.6
Periods of natural microseisms (continuous motion from meteorological sources and ocean waves) range from a fraction of a second to a minute or more. The largest amplitudes of the most frequent types of micrDseisms (periods 4 to 10 sec) are a few microns at inland stations on rock and between 10 and 100 microns at stations near oceans during heavy storms. Mter great earthquakes, waves through the earth's interior may reach the surface at great distances with amplitudes of over 10 microns and periods of the order of 5 sec, while the largest surface waves may have ground amplitudes of 10 mm with periods of 20 sec. Much greater amplitudes occur near the source. In motion from not too close artificial explosions, longitudinal waves usually carry the largest amplitudes; even waves through the earth's core have been identified on such records.' 2i-5. Travel Times of Earthquake Waves. Examples of travel times are given in Table 2i-5. Surface waves traveling a few times around the earth have travel times of several hours. No dispersion has been established for waves through the earth's body except for waves through the transition zone from the liquid outer core to the probably solid inner core. 4 However, the prevailing increase in the velocity of longitudinal and transverse waves with depth results in a prevailing increase in wave velocity of surface waves as their length (depth of energy penetration) increases. Surface waves of first, second, and third modes have been observed. The group velocity of surface waves of first mode has a minimum. for periods of several seconds, depending on the crustal structure. 1 C. J. Wideman and M. W. Major, Strain Steps Associated with Earthquakes, Bull. Seis. Soc. Am. 67, 1429 (1967). 2 L. E. Alsop, Spheroidal Free Periods of the Earth Observed at Eight Stations around the World, Bull. Seis. Soc. Am. 54,755 (1964). 3 B. Gutenberg, Travel Times of Longitudinal Waves from Surface Foci, Proc. Natl. Acad. Sci. U.S. 39, 849 (1953). 4 B. Gutenberg, Wave Velocities in the Earth's Core, Bull. Seis. Soc. Am. 48, 301-314 (1958). • M. Ewing and F. Press, Crustal Structure and Surface-wave Dispersion, Bull. Seis. Soc, Am. 40, 271-280 (1950); 42, 315-325 (1952); 43, 137-144 (1953). Surface Waves and Guided Waves, "Encyclopedia of Physics," vol. 47, pp. 119-139, Springer-Verlag, Berlin,' 1956.
i
2-106
MECHANICS
2i-6. Reflection· arid Refra'ction of Waves. If a longitudinal wave P or a transverse wave S arrives at a discontinuity, one P and one S wave are reflected and one of each type is refracted if the velocity ratioVrlVi of the reflected or refracted (r) and incident (i) wave permits.' " Vr •• (2i-4) . sm ~r = Vi sm ti where ii is the angle of incidence. Examples are given in Table 2i-6. Amplitudes of transverse waves (vibrations .perpendicular to the ray) are frequently resolved into two components, SH in the horizontal plane, and SV (with a vertical component) perpendicular to SH. If an SH wave is incident, the reflected Wave and the refracted wave (if it exists) are always of the SH type. TABLE
2i-5.
TRAVEL TIMES
AND TRANSVERSE WAVES
t
(MIN: SEC) OF DIRECT LONGIT.UDINAL. WAVES
S
THROUGH THE EARTH STARTING AT DEPTH
AND OF SURFACE SHEAR WAVES PERIODS OF ABOUT
G
AND RAYLEIGH WAVES
h
= 25km
P
S
0 2 4 10 20 40 70 100 120 150 180
0:04 0:32 0:59 2:28 4:34 7:36 11:12 13:46 18:54 19:46 20:10
R a,
G, min
min
0:07 0:55 1:56
... .
....
.. , .
. ...
.....
4.1 8.3 16.5 28.9 41.3 49.5 61.9 74.2
4.5 9.0 17.9 31.4 44.8 53.8 67.2 80.6
8:16 13:42 20:20 25:14 28:00 ••
00.
.0 , 0 '
WITH
1 MIN (INDEPENDENT OF FOCAL DEPTH)
(c. = epicentral distance, deg; P waves arriving at C.
tl
Ra
P h,
....
.0.0
h
> 100 deg enter the earth's core)
= 300km
h
= 700 km
P
S
P
S
0:39 0:46 1:07 2:17 4:15 7:11 10:44 13:15 18:19 19:11 19:35
1:08 1:24 1:51 4:03 7:39' 12:52 19:21 24:23 27:09
1:20 1:24 1:32 2:20 3:55 6:44 10:11 12:37 17:38 18:31 18:54
2:24 2:30 2:48 4:12 7:02 12:01' 18:20 23:14 26:01
. .... .0 ...
t B. Gutenberg, Travel Times of"Longitudinal Waves from Surface Foci, Proc. Nat!. Acad. Sci, U.S. ·39, 849 (1953); H. Jeffreys and K.· E .. Bullen, "Seismological Tables," British Associat,ion for the Advancement of Science, 1940; B. Gutenberg, and C. F. Richter, On Seismic Waves, GeTland. Boilr. Geophy •. 4S, 56-133 (1934); 54,94"':136 ( 1 9 3 9 ) . ' . .
If a wave arrives at the earth's surface (actual angle of incidence i) a wave of the same type is reflected (angle i), and one of the other type may be reflected [Eq. (2i4)] (see Table 2i-7). As a consequence of these three waves, the apparent angle of incidence ~ calculated from records of horizontal H and vertical V instruments (tan ~ = H IV) differs from i. In case of incident 'transverse waves the particles move in ellipses,2 if (V sin i) Iv > 1. If an SH wave is incident, the reflected wave has the same amplitude as the incident wave, the' ground displacement is twice the incident amplitude, and ~ = i.' For energy ratios of waves reflected and refracted at the boundary of the earth's core, see Table 2i-8. An SH wave incident upon the core is totally reflected . . 1 M. Ewing,. W. S. Jardetzky, and F. Press, "Elastic Waves in Layered Media," pp.,74-93, : McGraw-Hill Bo.o.k Co.mpany, New Yo.rk, 1957; B. Gutenberg, Energy Ratio. o.f Reflected and Refracted Seismic Waves, Bull. Seis. Soc. Am. 34,85-102 (1944). 2 B. Gutenberg, SV and SR, Trans. Am. Geophys. Union 33,573-584 (1952).
2-107
SEISMOLOGICAL AND RELATED DATA
TABLE 2i-6. SQUARE ROOT OF ENERGY REFLECTED OR TRANSMITTED AT A DISCONTINUITY WITH DENSITY RATIO (UPPER LAYER TO LOWER) 1.103,CORRESPONDING VELOCITY RATIO 1.286 FOR l! AND FOR S, POISSONJS RATIO 0.25 IN BOTH LAYERS (Incident energy taken as unity. Based on Slichter-Gabriel. t 1- indicates values between 0.95 and 1.0. i = angle of incidence. P = longitudinal, SV= component of transverse wave in plane of ray) Refracted waves Pfrom
SVfrom
Pfrom
SVfrom
--------~------_I-------~-------I-------._-------I------_.-------
iO
Above
P
W
0.0 0.1 0.1 0.2 ... 0.3 ... 0.4 .. . 0".0
11-
0.0 0.1 0.1 0.1 0.2 0.3 0.0
1110.5
0 15 30 45 60 75 90
Below
W
P
t
Reflected waves
10.9 0.9 0.8 0.0
Above
Below
W
P
W
P
Above P
0.0 -0.2 0.0 0.1 0.1 0.1 ... 0.2 0.2 ... 0.4 0.3
1- 0.2 1- 0.2 1- - 0.1 1- 0.2 . .. 1- 0.9 . .. 0.8 0.9 . .. 0.0 1.0
.. . .. . .. . .. . .. . ., .
Below
Above
W
P
W
P
0.0 0.1 0.1 0.0 0.1 0.1 0.0
0.2 0.2 0.1 0.1 0.2 0.4 1.0
0.0 0.1 0.1 0.1 0.1 0.1 0.0
1.0 10.9 0.9
W
Below P
W
0.0 0.0 0.2 0.1 0.1 0.1 0.2 0.1 0.0 0.3 . .. 0.2 . .. .. . . , . 0.3 .. . . .. . .. 0.5 .. . . .. . .. 1.0
B. Gutenl:erg, Bull. Seis. Soc. Am. 34,85 (1944).
TABLE 2i-7. SQUARE ROOTS OF RATIO OF REFLECTED TO INCIDENT ENERGY a AT EARTH's SURFACE "AS "FUNCTION OF ANGLE OF INCIDENCE i AND RATIO OF HORIZONTAL" U AND VERTICAL W GROUND DISPLACEMENTS TO INCIDENT AMPLITUDE FOR CONTINUOUS SINUSOIDAL WAVES IF POISSON'S RATIO Is 0.25; i = APPARENT ANGLE OF INCIDENCE CALCULATED FROM OBSERVED HORIZONTAL AND VERTICAL COMPONENTS (Elliptic motion of ground is indicated by *, and corresponding values for 'i are calculated on the assumption that the vertical and horizontal component reach their maximum simultaneously, t = cO:rnponent of transverse wave in plane of ray)
sv
-----
Longitudinal wave P incident
SVincident
i
a of P
a of SV
0° 20 30 35.3 40 45 60 80 90 tB.
1.0 0.8 0.6 0.5 0.4 0.3 0.0 0.1 1.0
U
w
'i, deg a of P
aof SV
U
- - - - - - -----
----- ------
0.0 0.6 0.8 0.9 0.9 0.9 1.0 1.0 0.0
0.0 2.0 0.8 1.9 1.2 1.7 1.3 1.5 1.4 1.4 1.5 1.3 1.7 1.0 1.3 " 0.5 0.0 0.0
0 23 34 39 44 48 60 69
71
0.0 0.9 1.0 0.0
... ... ... ... ...
w
'i, deg
- - - ----1.0 0.4 0.0 1.0 1.0 1.0 1.0 1.0 1.0
2.0 1.8 1.7 4.9 0.7* 0.0 0.5* 0.3* 0.0*
Gutenberg, SV and SH, T,·ans. Am. Geophys. Union' 33, 573-584 (1952).
0.0 0.8 1.0 0.0 1.6* 1.4 1.1* 0.5* 0.0*
0 23 30 ±O -64* ±90 66* 59* 60:"
2-108
MECHANICS
2i-7. Wave Types and Their Symbols. The main discontinuities of the earth (Fig. 2i-1) are its surface, the "Mohorovicic discontinuity" (depth 10 ± km below the surface in the deeper parts of the major oceans, 30 ± km under the lower parts of continents, up to about 70 km under high mountain ranges, e.g. North Pamir 1 ), and the boundary of the earth's core at a depth of 2,900 ± 10 km (radius r = 3,470 km). The transition from the outer to the inner core is probably gradual. At a distance of about 1,500 km from the earth's center, the velocity of longitudinal waves begins to increase more rapidly with depth than in the outer core but becomes approximately constant about 300 km deeper. This transition zone between the outer and the inner core may correspond to a transition from the liquid to the solid state. TABLE 2i-8. SQUARE ROOTS OF ENERGY RATIOS FOR WAVES REFRACTED (REFR.) AND REFLECTED (REFL.) AT THE BOUNDARY OF THE EARTH's COREt [Assumed at the core boundary: densities 5.4 (mantle), 10.1 (core); longitudinal velocities 13.7 and 8.0 km/sec, respectively; transverse velocity in the mantle 7.25 km/sec, 0 in core. i = angle of incidence of the arriving wave]
P incident in mantle i
Refr. P
Refl. P
Refl. S
P incident in core i
Refr. P
Refr. S
Refl. P
SV incident in mantle i
Refr. P
- ---- --- --- - ---- --- --- - ---0 20 40 60 80 83.8 85 89 90
0.999 0.96 0.87 0.79 0.84 0.85 0.85 0.60 0.00
0.04 0.12 0.29 0.42 0.20 0.00 0.10 0.71 1.00
0.00 0.24 0.39 0.44 0.51 0.52 0.52 0.36 0.00
0 20 33-fr 35 35.7 37 50 80 90
0.999 0.90 0.79 0.83 0.00
..... ..... .....
.....
0.00 0.44 0.62 0.55 0.00 0.85 0.92 0.62 0.00
0.04 0.08 0.00 0.10 1.00 0.53 0.40 0.78 1.00
0 20 30 31 32.0 33 40 64 65.0
0.00 0.50 0.61 0.58 0.00 0.84 0.92 0.55
... .
Refl. P
Refl. S --- --0.00 1.00 0.39 0.78 0.47 0.64 0.49 0.65 0.00 1.00 '" . 0.54 . ... 0.40 .., . 0.84 ... 1.00
.
t After S. Dana, The Partition of Energy among Seismic Waves Reflected and Refracted at the Earth's Core, Bull. Bei8. Soc. Am. 34, 189-197 (1944). By international agreement longitudinal waves in the mantle are indicated by P (starting downward at the source) or p (starting upWard), transverse waves by S or s, longitudinal waves through the outer core by K, through the inner core by I, and (hypothetical) transverse waves through the inner core by J (Fig. 2i-2). Some authors use P' == PKP, P" == PKIKP. For a source below the surface, there is one reflection at the surface near the epicenter, another about halfway between source and station. The symbols for these waves are, respectively, pP and PP, sP and SP, pS and PS, sS and SS. Similarly, for twice-reflected waves pPP, PPP, etc., are used. Time differences pP - P, sP - P, 8S - S, etc., give a good indication for the focal depth (Table 2i-9).2 Among observed waves through the core reflected at the 1 I. P. Kominskaya, G. G. Mikhota, and Yu. V. Tulina, Crustal Structure of the PamirAlai Zone from Seismic Depth-sounding Data, Izvest., Geophys. 8er., trans. by Am. Geophys. Un., 1959, p. 673. . . 2 B. Gutenberg and C. F. Richter, Materials for the Study of Deep-focus Earthquakes, Bull. Seis. 80S. Am. 26, 341-390 (1936); see also H. Jeffreys and K. E. Bullen, "Seismological Tables," p. 24, British Association for the Advancement of Science, 1940.
2-109
SEISMOLOGICAL AND RELATED DATA
surface of the earth are pPKP, sPKP, P'P' == PKPPKP, P'P'P', P'P'P'P' (with a travel time of about Ii hr). Waves in the mantle with a reflection at the core surface permit accurate determination of the radius of the core. They are indicated bye, e.g., PcP, PeS, SeS; pPeP, SeSSeS, etc., are in addition, reflected at the surface. All these waves usually have
-E--I---OUTER CORE
- 15°, M 8
MECHANICS
is found from ground amplitudes b (in microns) of surface waves with periods of 20 sec in shallow earthquakes. The magnitude M is based on amplitudes a of P, PP, and S waves in shocks (focal depth h) recorded at the epicentral distance t;.: Ms
M
+ F(t;.) M = log a - log T + f(t;.,h) Ms - 0.37(Ms - 6.74) (approximately)
(2i-12)
= log b =
For F(t;.) and f(t;.,h) , see Table 2i-12; small station corrections are to be added. The amplitudes b of surface waves of length L decrease with increasing focal depth h
TABLE 2i-12. VALUES OF f(t;.,h) IN EQ. (2i-12) FOR VERTICAL COMPONENTS Z OFP "', AND PP, HORIZONTAL COMPONENT SH OF S, AND F(t;.) FOR HORIZONTAL COMPONENT OF MAXIMUM (MAX) (h = focal depth; t;. = epicentral distance, deg*)
I
h = 25 km t;.
PZ 20 30 50 80 100 160
PPZ
SH
Max
...
5.8 6.3 6.6 6.7 7.4
4.0 4.3 4.6 5.0 5.1 5.4
I
h = 300 km
h = 600km
PZ
PPZ
SH
PZ
6.1 6.3 6.1 6.6 7.2 ., .
..
6.4 6.6 6.9 6.8 6.6
5.8 6.1 6.7 6.4 6.7
6.4 6.4 6.3 6.2 7.2
.. .
.
PPZ
SH
. ..
5.9 6.0 6.4 6.5 6.7
--- - - - - - - - - - - - - - - -
6.0 6.6 6.7 6.7 7.4
.. .
6.7 6.7 6.9 7.2 6.9
...
.
..
6.3 6.5 6.8 7.0 6.7
*
B. Gutenberg, Amplitudes of Surface "Waves and Magnitudes of Shallow Earthquakes, Bull. Se;s. Soc. Am. 35, 3-12 (1945); Magnitude Determination for Deep-focus Earthquakes, Bull. Seis. Soc. Am. 35, 117-130 (1945). B. Gutenberg and C. F. Richter, Magnitude and Energy of Earthquakes. Ann. Geofts. Rome, 9, 1-15 (1956).
TABLE 2i-13. INTENSITY I AT THE EPICENTER, CORRESPONDING MAXIMUM ACCELERATION a, CM/SEC', MEAN RADIUS Tp OF AREA OF PERCEPTIBILITY, KM, FOR A GIVEN MAGNITUDE M IN AVERAGE SHOCKS IN SOUTHERN CALIFORNIA (h = 16 ± KM) (Values for I, a, T are based on empirical equationst)
M
2.2
3
4
I
5
6
-----I a Tp
1.5 1 0
2.8 3 25
4.5 10 55
6.2 36 110
8
8.1. 2
11.2 1,670 740
12.0 3,160 1,000
7
--~
---"
7.8 130 200
9.5 460 390
t B. Gutenberg and C. F. Richter, Earthquake Magnitude, Intensity, Energy, and Acceleration, BUll. Sei •. Soc. Am. 32, 163-191 (1942).
corresponding to a factor e- qhIL , where q (about 2) depends on crustal structure. The average relationship of intensity to magnitude in California earthquakes is given in Table 2i-13. The energy E corresponding to the magnitude M found from body waves is given to a first approximation' by log E = 12.24 1
+ 1.44M
M. Bath, Earthquake Seismology, Earth-Sci. Revs. 1, 69-86 (1966).
(2i-13)
2-115
SEISMOLOGICAL AND RELA'l'ED DATA
2i-l1. Seismicity of the Earth.
Earthquakes are divided into shallow shocks > 300, maximum 720 ± km). Most shocks occur in narrow belts (Table 2i-14).' Deep and intermediate shocks are limited to the circumpacific belt and the trans-Asiatic (Alpide) belt. For the magnitude of the largest observed shock and the relative frequency of earthquakes in various depth intervals, see Table 2i-15, which also shows examples of regional differences. 2i-12. Energy E of Earthquakes. Most calculations of E depend on Eq. (2i-13). This empirical formula is based on many observations, but is subject to adjustment. (h ::; 60 km), intermediate (60 < h ::; 300), and deep (h
TABLE 2i-14. NUMBER OF SHALLOW, INTERMEDIATE) AND DEEP-FOCUS EARTHQUAKES, % OF ALL EARTHQUAKES IN THE GIVEN DEPTH RANGE, AND CORRESPONDING ENERGY RELEASE (a) IN THE MAJOR UNITS OF THE EARTH AND (b) IN SELECTED AREAS (Averages 1904-1957) Number, % Region Shallow
IInt~me .
Energy, %
Deep
Shallow
--- ---
--- ---
(a) Circumpacific belt ............ Trans-Asiatic belt ............. Atlantic and Indian Oceans .... All others .................... Total ...................... (b) Pacific region, Alaska to U.S ... North and Central America, West Coast ................ South America, western part ... Kermadec-Tonga Is ........... New Hebrides and Solomon Is .. Marianas Is .................. Japan-Kamchatka ............ Philippine Is ................. Celebes-Sunda Is ............. Hindu Kush ................. Asia Minor to Italy ........... TotaL .....................
82 10 5 3 100 2 12 10 3 12 2 15 5 8 0 2 71
91 9 0 0 --100 --0
100 ::;;>_U
~ ~~
w~
300
~ ::E~
~ ~~
~~
I
11
1 1
I
I
LEVELS OF AIRGLOW EMISSION
400
l
W
t>J
>-3
I
300
ffi
iE
~
T ---.--l--
kgn0
k< 1250(7) A Nz+hv-N+N
200
t>J
o ~ o t< o
~
H Q
~
t< k-3 trl
P--
t' H
100
Z
":j
o
50
40 30 20
~
P->-3
H
o
Z
10
(
;i\L~
S:,~:_
L I11l77Z7Z7z ::J
//-//."'"
'-,
'0
I>::
(Prepared in collaboration with W. W. Kellogg and A. Kochanski.)
I
f-' ~
CD
2:-140
MECHANICS \000
\
\
\MAXIMUM OF SUNSPOT
\
]
\ CYCLE
'\
gf
~~~~p~¥ g~CLE
E 500
\
'\ "\
tr1
\ \
'\.
,)....... pF2
/5'Fl '[)
103
105
104
106
ELECTRON CONCENTRATION, ELECTRONS Icm 3 (0)
1,000
\
\MAXIMUM OF SUNSPOT
\ CYCLE
1\
Mk'tl~s~~~of\ CYCLE
\
1\
\
""- t'-."\)F I-"
C 0102
E
104
103
105
106
ELECTRON CONCENTRATION, . ELECTRONS/cm 3 (b)
FIG.. 2k-3. Diurnal and solar-cycle variations in the structure of the ionosphere. Daytime . . (b) Nighttime. (After Henson, ref. 18.)
(a)
On a surface of constant pressure, the equation for the speed of the geostrophic wind V. is given by
v
= ~
a fan
•
(2k-6)
where -a/an is the gradient of geopotential on the constant-pressure surface normal to the direction of the geostrophic wind. On a consta~t-level surface,
v
=
•
1. ap fp
an
(2k-7)
where p is the density of the air and - ap / an is the horizontal pressure gradient normal to the geostrophic wind component. Gradient Wind. To improve the approximation of the geostrophic wind to the true wind in the free atmosphere, other terms may be included in the equation of motion. The most common additional term is that which expresses the acceleration arising from the curvature of the path of the moving air parcel. The addition of this term to the expression for the geostrophic wind speed gives the gradient wind speed V. (2k-8)
METEOROLOGICAL INFORMATION
2-141
where r is the radius of curvature of the trajectory of the air parcel and the following sign convention is used: for cyclonic curvature 1'f > 0, for anticyclonic curvaturerf < O. Zonal Motion. The average motion of the atmosphere is predominantly geostrophic and zonal. The zonal motion between sea level and 50 mb, for s.ummer and winter, Northern and Southern Hemispheres, is shown in Fig. 2k-4, from Mintz [25]. cb
11m
15
°lgi,
w 20 a::
~40 g: sO
10 w
!5
80 101
!;{z
~~ ~~
it", '"
SL
m p
3l0d 'S
310d 'S
FIG. 2k-4_ Zonal circulation of the atmosphere, m sec-I, averaged over all longitudes. represents motion from the west, E is motion from the east. (Frorn Mintz, ref. 25.)
W
For levels above 35 km, see Murgatroyd in ref. [2]. A pronounced 26-month oscillation of the zonal wind in the equatorial stratosphere has been observed (see, e.g., Reed [29]). Eddy Motion. Superimposed on the average zonal motion of the atmosphere are eddy circulations covering a wide spectrum, including cyclones and anticyclones in the lower troposphere and planetary or Rossby waves in the middle troposphere. Under barotropic conditions frequently observed in the middle troposphere, the speed c of planetary waves is given by (2k-9)
2-142
MECHANICS
where U is the west wind speed, {3 the northward change of the Coriolis parameter, and X the wavelength. For an introduction to current numerical techniques of modeling and predicting atmospheric processes, especially atmospheric motions, see . Thompson [31]. Energy Conversions. Figure 2k-5, from Oort [26], shows an est~mate of the generation G dissipation D, and conversion C rates for energy processes m the atmosphere. In the a~erage, the energy cycle proceeds from mean available potential energy PM via eddy available potential energy PE and eddy kinetic energy KE to the mean kinetic energy (KM). 2k-l0. Radiation. Solar Constan:t. The solar constant, the mean value of the total solar radiation, at normal incidence, outside the atmosphere at the mean solar distance = 0.140 w cm- 2 (p.e. = 2%) [18].
FIG. 2k-5. Tentative flow diagram of the atmospheric energy in the space domain. Values are averages over a year for the Northern Hemisphere. Energy units are in 10& joules m- 2 (= 108 ergs cm- 2); energy transformation· units are in watts m- 2 (= 10 3 ergs cm- 2 sec-I). (From Oort, ref. 26.) ! !
Insolation. Figure 2k-6 shows the average daily solar radiation received on a square centimeter of horizontal surface at the ground during January and July on cloudless days [11] (SOlid lines) and on days with average cloudines~ [13] (dotted lines). The units are gram-calories per square centimeter per day. Albedo. Table 2k-6 gives a range of albedo measurements 1 observed for various type of surface. Heat Balance of the Atmosphere. Taking the incident solar radiation as 100 units, Byers [5] has computed the heat budget of the atmosphere as shown in Table 2k-8. 2k-l1. Clouds. 2 The drop-size spectra of typical cloud types are given in Fig. 2k-7.
i
i
2k·12. Climatology. Space limitations preclude the presentation of climatological I data. In addition to standard climatological texts, see [17], [32], [7], [8], [9], and [35];. the reports of World Data Center A, especially the sub centers on Meteorology, Upper Atmosphere Geophysics, and Rockets and Satellites; and various numbers in the key' to Meteorological Records Documentation series, especially No. 4.11 [10].
For a more complete list, including sources, see List, op. cit., Pl). 442-444. Dat,a furnished by Dr. H. J. aufm Kampe, Si~twJ. OQI"P~ ~~!I;i.:q~ering Laboratories, Ft. Monmouth, N.J. I
2
2-143
METEOROLOGICAL INFORMATION
~
...
,
JANUARY
JULY FIG. 2k-6. Average daily solar insolation (g-cal cm- 2 day-I) at the ground on cloudless days (solid lines) and on days of average cloudiness (dotted lines). (After Fritz and MacDonald [11, 13].)
MECHANICS TABLE
2k-6.
ALBEDO MEASUREME])jTS
Forest .............................................. . Fields, grass, etc ..................................... . Bare ground ......................................... . Snow, fresh ......................................... '.. Snow, old .. ,.' ........................................ '. Whole earth, visible spectrum .......................... . Whole earth, total spectrum, .......................... : " Clouds* ............................................ , . Water (reflectivity values are given in the following tablelt ElevatIon of sun ...... 1900 1700 1500 1400 1300 Reflectivity, %... . . . . 2.0 2.1 2.5 3.4 6.0
I
0
20 13.4
I
% 3-10 3-37 3-30 80-90 45-70 39 35 5-85
50 58.4
I
0° 100.0
*
For clouds in the absenee of absorption the albedo is a function of the drop-size distribution, liquid water content, and cloud thickness. See S. Fritz [12]. t The reflectivity of a wat~r surface for solar radiation is a function of the sun's elevation angle. The values given have been computed for a plane surface; however, the observed reflection from diaturbed surfaces shows only small deviation froID these values.
I
3000
" l"\
\
1000 500
:
'.
\ \...
ft>0:
IU
m
100
:::!:
I~
1\.'\ -.:;;:
--
-
STRATUS STRATOCUMULUS
-
ALTOCUMULUS
---FAIRWEATHER CUMULUS_
~I\
I-
, - CUMULUS CONGESTUS -
CUMULONI \1BUS
,:::I
Z
50
'IU
i,2= '
\
.ii
.... 2: H (')
U2
2-195
VISCOSITY OF LIQUIDS TABLE
2m-3.,
VISCOSITIES OF GLYCEROL-WATER SOLUTIONS*
T-m 't: lp eratur e °C ,
Glycerol, wt. %
0
I
40
20
60
I
I
I
80
I
100
Viscosity, centipoise !
10 50 90 98 99 100
* From
I
2.43 14.6 1,310 7,350 9,390 12,000
,
!
I
1. 31 5.98 218 936 1.150 1,410
0.824 3.09 59.8 194 234 283
I I
0.573 1.85 22.43 59.6 68.9, 81.1
I
1. 25 11.0 24.7 27.7 31.8
0.907 5.98 12.2 1:1.2
I
14.8
J, B. Segur and H. E. Oberstar, Ind. Eng. Chem. 43(9), 2117 (September, 1951). Values from original reduced by 0.3 per cent (to adjust basis used to 1.002 for water at 20°0) and rounded to three significant figures. Original tabulation gives values every 10°C fcir 24 compositions.
Dampler,Lakshminarayanan, Lorenz, and Tomkins.! The authors have examined the data up to December, 1966, for 174 single-salt melts, selected the best data in each c~se, and presented these both as tabulations and empirical viscosity-temperature relations. For each compound a concise statement is given, citing the measurements on which the tabulated values are based, and comparing these with other measurements available. A measure of the precision with which each empirical equation represents the data is given, as is an estimated accuracy of the measurements themselves. , This latter estimate is based on an evaluation of the measurement technique, purity of material, and agreement with other values. 2m-7. Viscosity at Elevated Pressure. Absolute measurements of viscosity at elevated pressure depend on factors like variations in dimensions of the instrument which are often not known with certainty. Most measurements have been made with falling-weight or rolling-lt>all viscometers, calibrated at atmospheric pressure. Such instruments can measure a wide range of viscosities with ,a precision of about one per cent, but uncertainties of several per qent may arise in introducing corrections to the calibration constant owing to increased pressure. With the exception of water between 0 and 33°C, the viscosity of liquids increases monoto'nically with increasing pressure. Typically, the log~rithm of viscosity versuS pressure at constant temperature is concave toward the pressure axis at low pressures, becomes almost linear over an appreciable pressure range, and finally, if the sample does not freeze first, reverses curvature and shows an increasing slope at high pressure. The viscosity, especially at elevated pressure, is remarkably sensitive to molecular structure, in contrast to, equilibrium properties such as density or compressibility which tend to follow a rather uniform pattern at high pressure. Water. The lower-temperature isotherms for the viscosity of water versus pressure show minima. At 2°C the minimum value occurs at about 1,000 bars, where the 1 G. J. Janz, F. W. Dampier, G. R. Lakshminarayanan, P., K. Lorenz, and R. P. T. Tomkins, Molten Salts, vol. I, Electrical Conductance, Densit3c and Viscosity Data, Nat!. Bur. Standards Ref. DataSer. 15, October, 1968. See also G. J. Janz, "Molten Salts Handbook," Academic Press, Inc., New York, 1967. (Less detailed, but includes some mixtures.)
If
i-L ~
TABLE
T,K '7, cp
1060 l.149
1070 l.10.
I
1080 l.071
1090 l.03.
Best equation:
I
1100 l.00.
TJ =
2m-4.
I
1110 0.975
Potassium Chloride 1120 1130 1140 0.94. 0.92. 0.901
I
I
55.5632 - 0.127847T
Temperature range, K: 1056.5-1202.0
T,
KI I I
TJ,CP
780 4.41
790 4.17
800 3.95
I
810 3.75
I
820 3.56
I I 830 3.39
840 3.23
I
1070 l.245
1080 l.210
I
1090 l.17.
I
Best equation:
1100 l.149 TJ
=
I
+ 9.99580
I
1110 l.12,
I
860 2.94
I I 870 2.81
I
1150 0.881
1160 0.86,
I
I
1170 118(} 0.847·.0.83.
8,
880 2.69
Uncertainty estimate, %: 1.5
I
890 2.57
I I I 900 2.47
910 920 2.36 ·2.27
I I 930 2.18
I
1120 l.09.
1130 l.07.
64.3240 - 0.152525T 8,
I
1140 l.05.
I
+ 1.23215 X
centipoise: 0.0040
1150 l.03.
I
1160 l.02 2
I
1170 l.00.
I
950 2.02
I
960 l.95
1O- 4 T2 - 3.34241 X lO-.T'
Uncertainty estimate, %: 1.0
~KI~I~I~I~I~I~'I~I~I~ cp 2.53 2.35 2.19 2.04 l.91 l.79 l.68 l.58 l.49 = 8,
4.00 X 10- 2 exp (4531/RT)
centipoise: 0.0367
o
~o >-
1
o
"'l t"'
H
ID
q
H
t:I
UJ.
• I~(X, - X,), ~ n-p
where Xe and Xe are experimental and calculated values, n is the number of experimental values used, and p is the number of coefficients in "Best equation." t Original tabulation gives values every 10 K. :t In 80me cases, as here, the information available was considered insufficient to warrant a quantitative estimate of uncertainty. It is stated that H • • • the data can be considered reliable."
if
'"-"
CO
-..:t
2-198
MECHANICS
viscosity is about 93 or 94 per cent of its value at one atmosphere. This minimum ratio rises and shifts to lower pressures as the temperature is raised. Between 30 and 40°C the minimum disappears; at higher temperatures the isotherms show the normal monotonic increase with pressure. Between about 2 and 20°C, various measurements disagree by as much as 3 per cent, an amount significantly greater than their precision, though within their possible systematic error. References 1. 2. 3. 4.
Horne, R. A. and D. S. Johnson: J. Phys. Chem. 70(7), 2182 (1966). Bett, K. Eo, and J. B. Cappi: Nature :007, 620 (Aug. 7, 1965). Wonham, J.: Nature 215,1053 (Sept. 2, 19(7). Bruges, E. A., B. Latto, and A. K. Ray: Int. J. Heat Mass Transfer 9,465(1966).
Other Liquids. All other liquids for which measurements are available show a monotonic increase in viscosity with pressure. In Table 2m-5 we list values for a few liquids selected from the measurements by Bridgmanl (falling-weight viscometer) and by several investigators at The Pennsylvania State University' (rolling-ball viscometers). These two collections of data are the most extensive that are available on pure compounds. Bridgman obtained his liquids from various sources. Some were the purest available commercial liquids ; some specially purified by various other workers. The Penn State measurements utilized the API-42 compounds mentioned earlier.' There are nO objective grounds for assigning uncertainties to most of these
TABLE 2m-5A. VISCOSITY OF LIQUIDS UNDER ELEVATED PRESSURE a P
{kg/em', .. (atm) ressure bars* ..... (atm) Temperature, °C
500 490
1,000 980
2,000 1,960
6,000 5,880
4,000 3,920
8,000 7,850
10,000 9,810
12,000 11,770
Viscosity in centipoises n-Pentane: b 7J at 30°C, 1 atm = 0.215 cp, from API-44 tables
I
30 75
0.2151°.3261°.4441°.71911.51 0.139 0.222 0.313 0.516 1.02
30 75
0.5191°.724]°.97511.6314.09110.0 125.9178.0 0.324 0.451 0.602 0.959 2.05 4.08 7.96 16.6
30 75
0.991 11. 27 6.68110.4 2 29 4 10 . 1 1.93 . 1 2. 04 4. 27 0.450 0.59 11.57 0.74 1 1.10
8.86 115.1 78 4. 94 1 4.42 2. 1. 74 1 2.83 6.69
Toluene: 7J at 30°C, 1 atm = 0.5187 cp, from API-44 tables 1 35 . 2
Ethyl alcohol: 7J at 30°C, 1 atm = 0.991 cpc
* 1 bar
= 0.9807 kg/em 2 •
1
16 . 1 5 . 94
I
24.3 8.22
Values rounded to closest 10 bars.
1 P. W. Bridgman, in Proc. Am. Acad. Arts Sci. 61, 57 (1926); "The Physics of High Pressure," G. Bell & Sons, Ltd., London, 1952. 2 D. L. Hogenboom, W. Webb, and J. A. Dixon, J. Chem. Phys. 46(7), 258G (1967); D. A. Lowitz, J. W. Spencer, W. Webb, and R. W. Schiessler, J. Chem. Phys. 30(1), 73 (1959); E. M. Griest, W. Webb, and R. W. Schiessler, J. Chem. Phys. 30(1), 73 (1958); results summarized in "Properties of Hydrocarbons of High Molecular Weight Synthesized by Research Project 42 of the American Petroleum Institute," op. cit. 'R. W. Schiessler and F. C. Whitmore, Ind. EnO. Chem. 47(8), 1660 (August, 1955).
TABLE
Pressure, bars ....................
Compound
~-n-Octylheptadecane· ..
C(-C8),
Perhydrochrysene ......
~ S S
l-a-Decalylpentadecane CIS
®tl l-a-N aphthyl-
pentadecane g-C15 , I.
(atm)
2m-5B.
I
200
VISCOSITY OF LIQUIDS UNDER ELEVATED PRESSUREd
I
400
I
600
Temperature, °C
37.78 60.00 79.44 98.89 115.00 37.78 60.00 79.44 98.89 115.00 135.00 60.00 79.44 98.89 115.00 135.00 60.00 79.44 98.89 115.00 4.35.00
I
1,000
I
1,400
I
1,800
I
2,200
I
2,600
I
3,000
I
3,400
Viscosity in centipoises
7.06 3.91 2.60 1.87 1.48 25.6 10.4 5.86 3.80 2.77 2.09 8.56 5.24 3.55 2.64 1.99 8.41 5.05 3.41 2.52 1.90
9.40 5.13 3.35 2.37 1.85 46.8 15.6 8.36 5.15 3.78 2.74 11.8 7.18 4.76 3.57 2.64 10.9 6.49 4.24 3.15 2.36
12.5 6.65 4.26 2.96 2.31 87.5 24.5 12.1 7.05 5.07 3.56 16.1 9.46 6.19 4.63 3.37 14.2 8.18 5.22 3.90 2.89
16.2 8.45 5.34 3.65 2.83 177 40.1 17.9 9.73 6.73 4.60 21.4 12.2 7.89 5.85 4.17 18.2 10.3 6.43 4.75 3.47
26.3 13.1 8.07 5.38 4.17 951 121 41.6 19.1 12.2 7.67 36.6 19.8 12.2 8.75 6.15 29.6 15.8 9.48 6.84 4.83
41.3 63.0 19.5 28.1 11.6 16.2 7.58 10.3 5.80 7.80 9,080 464 2,510 110 345 41.2 95.9 23.0 46.1 13.1 23.5
92.3 39.7 22.6 13.7 10.2
131 55.0 30.7 18.2 13.2
1,450 255 102 43.6
8,650 832 252 87.5
;:1
187 75.5 41.2 23.7 16.7
Ul
o
o
Ul
~
"'1
o
I:z;j
3,670 778 194
2,720 488
E q 8
31.0 18.3 12.8 8.75
47.6 27.0 18.3 12.1
71.8 39.4 25.9 16.7
56.0 36.3 22.6
79.2 49.9 30.3
111 67.9 40.3
23.9 13.7 9.59 6.64
35.3 19.5 13.2 8.87
27.4 18.1 11.7
38.1 24.7 15.3
33.0 20.0
43.8 25.9
Ul
-
If
I-'
c:o c:o
t:Y
~
TABLE
2m-50.
Pressure, bars ..............................
(atm)
400
800
1
Compound
n-Dodecane .. " ................. n-C12
n-Pentadecane. . . . . . .. , ......... n-C15
cis-Decahydronaphthalene ........
~ trans-Decahydronaphthalene ......
~
1,200 1
Temperature, °C
37.78 60.00 79.44 98.89 115.00 135.00 37.78 60.00 79.44 98.89 115.00 135.00 15.56 37.78 60.00 79.44 98.89 15.56 37.78 60.00 79.44 98.89 115.00
o o
VISCOSITY OF LIQUIDS UNDER ELEVATED PRESSURE'
1,600
1
2,400
2,000
1
2,800
I·
3,600
3,200
1
1
1
Viscosity in centipoises
1.102" 0.8026" 0.63 0.5156" 0.41 0.34 1.953" 1.335 1.01 0.7960" 0.67 0.54 3.71 2.310" 1.569" 1.17 0.9162" 2.30 1.546" 1.114" 0.86 0.6960" 0.59
1. 70 1. 23 0.98 0.80 0.69 0.58 3.20 2.10 1.56 1. 24 1.06 0.87 6.59 3.76 2.57 1. 93 1.50 3.76 2.45 1. 76 1. 35 1.08 0.90
2.50 1. 75 1.36 1.11 0.97 0.82 4.85 3.11 2.27 1. 75 1.48 1. 22 10.7 5.81 3.95 2.84 2.19 5.84 3.70 2.58 1. 94 1.53 1. 30
3.52 2.39 1.82 1.46 1. 26 1.07 7.00 4.37 3.14 2.37 1. 98 1. 60 17.3 8.81 5.89 4.05 3.06 8.81 5.38 3.63 2.70 2.12 1. 78
4.78 3.19 2.37 1. 87 1.59 1.34
6.35 4.16 3 05 2.36 1. 99 1. 64
5.29 3.86 2.95 2.45 1. 98
5.93 4.19 3.13 2.58 2.05 27.9 13.3 8.60 5.69 4.17 13.2 7.73 5.06 3.70 2.84 2.36
7.89 5.47 4.02 3.27 2.59 45.3 20.2 12.5 7.93 5.67
10.43 7.02 5.09 4.09 3.22 73.0 30.3 18.2 10.9 7.59
45.5 26.6 15.1 10.2
68.7 38.7 20.9 13.6
11.0 6.89 4.98 3.75 3.09
15.5 9.38 6.58 4.90 3.99
12.7 8.64 6.31 5.07
17.3 11.4 8.11 6.44
6.67 4.47 3.62 2.98 2.39
8.41 5.83 4.38 3.59 2.86
8.90 6.33 5.05 3.93
11.16 7.78 6.20 4.73
7.13 5.23 4.26 3.36
is: t:J
()
::c:
po..
!Z H ()
U2
106 56.5 28.8 18.1
15.0 10.4 8.15
Footnotes to Tables 2m-GA, 2m-5B, 2m-5C a P. W. Bridgman, Proc. Am. Acad. Arts Sci. 61, 57 (1926); "The Physics of High Pressure," G. Bell & Sons, Ltd., London, 1952' G. E. Babb and G. J. Scott [J. Chem. Phys. 40,3666 (1964)] report results which deviate by 4 per cent or less up to 8,000 bars. e T. Titani, as quoted in J. Timmermans, "Physico-chemical Constants of Pure Organic Compounds," vol. 1 American Elsevier Publishing Company, Inc., New York, 1950. d D. A. Lowitz, J. W. Spencer, W. Webb, and R. W. Schiessler, J. Chem. Phys. 30(1),73 (1959). Original also includes data for 7-n ..hexyltridecane, 11-n-decylheneicosane, 13-n-dodecylhexacosane, 1, 1-dipheny lethane, 1, I-diphenylheptane, 1, I-diphenyltetradecane, 9 (2-cYclohexylethyl)heptadecane, 9 (2-phenylethyl) heptadecane, 1,2,3,4,5,6,7,8,13,14,15, 16-dodecahydrochrysene, 1, I-di (a-decaly I) hendecane. e Confirmed measurements of E. M. Griest, W. Webb, and R. W. Schiessler. J. Chem. Phys. 29(4), 711 (1958). Original also includes data for I-phenyl-3 (2-pheny lethyl) hendecane; 1-cyclohexyl-3 (2-cyclohexylethyl) hendecane, 9 (3-cyclopentylpropyl) heptadecane, 1-cyclopentylpropyl)heptadecane, 1·-cyc!opentyl-4(3-cyclopentylpropyl) dodecane, 1,7 -dicyclopentyl-4(3-cyclopentylpropyl) heptane, 9-n-octyl(1 ,2,3 ,4-tetrahydro)naphthacene. Original also includes data for spiro(4,5)decane, spiro(5,5)f D. L. Hogenboom, W. Webb, and J. A. Dixon, J. Chem. Phys. 46(7), 2586 (1967). undecane, cis-octahydroindene, and trans-octahydroindene. g Obtained with Cannon-Fenske capillary viscometers by American Petroleum Institute Research Project 42. "Properties of Hydrocarbons of High Molecular Weight Synthesized by Research Project 42 of the American Petroleum Institute," op. cit., ineludes smoothed data from references d, e, and f for pressures in psi and temperatures in OF. b
;:1 [J2
C':l
o
[J2
>-
2.0
w
Covilolion Incepr,on
1
ll..
G~
:
>
]
Q{:165
"
0.0
0
CD
::
Tempcrolure; 72Q Dc' C:X, ~ 1.2
ID
1&'·
n.
n.
/.0
(J)
1
-'1)
Temperolure. 76°
ex
..
Ie
OI's.Q,96
0 00
(J)
0
W 0::
n. -2.0
p
0
0::
0
n. -3.0 -4.0
~
z
~
w -5.0 0:: => (J)
0.:
(JI
rt
(J)
u
0
~
0 v
(b
(b
0
IV ()
(
t> f'
(J)
w -6.0
I () C:II!~ 9
0::
n.
...J
\
-7.0
w i:':J w
Note. When the last significant digit is shown in boldface type, the conversion factor represents a conventional factor which is accurate by definition and involves no approximation.
~
CI:l CJ.;J
2-234
MECHANICS
2r-1. Definitions. The viscosity of a fluid is defined in relation to a macroscopic system which is assumed to possess the properties of a continuum. To obtain an elementary definition of viscosity (Fig. 2r-l) consider two infinite flat plates, a at rest and b moving at a constant velocity u, the space between them being filled with the fluid under y consideration. In the resulting shear flow the velocity distribution is linear with a constant transverse gradient /I du/dy. It is assumed (Newton's law of fluid friction) that the shearing stress TO at either wall is proportional to the velocity gradient
-
du
TO
a
(2r-l)
= p, dy
FIG. 2r-1. Illustration of Newton's law of fluid friction.
The coefficient of proportionality p, is known as the viscosity, or more precisely, as the dynamic or absolute viscosity of the fluid. The various units of viscosity and their conversion factors are given in Table 2r-1. The ratio v
= !':
(2r-2)
p
is known as the kinematic viscosity; the respective units and conversion factors are given in Table 2r-2.
TABLE 2r-2. KINEMATIC VISCOSITY v; UNITS AND CONVERSION FACTORS Units
m 2/sec
m'/hr
cm 2/sec (stokes)
ft'/hr
ft'/sec
m 2/sec ............ . 1 3,600 1 X 10' 10.7639 299.0 X 10- 5 m'/hr .............. 277.8 X 10-' 2.778 1 cm'/sec (stokes) .... 1 X 10-' 1 10.7639 X 10-' 0.36 ft'/sec ....... ...... 929.03 0.092903 334.45 1 ft2/hr .............. 25.806 X 10- 6 0.092903 0.25806 277.8 X 10- 6
From British Standard Code B.S. 1042: 1943 amended March, 1946.
3.875 X 10' 10.7639 3.875 3,600 1
See Note to Table 2r-1.
In a general field of flow, Ul, U2, u, of a homogeneous Newtonian incompressible fluid, the shearing stresses are proportional to the respective rates of change of strain (Stokes'law). The symmetric stress tensor tii is assumed to be a linear function of the rate of strain tensor eii. Taking into account that in a fluid at rest the stress is an isotropic tensor, we put
where Oii is the Kronecker symbol (0 = 1 for i = j and a = 0 for i trary. Since tii = 0 for ei; = 0, we have tii = -3p and 3" hypothesis). Consequently
~
j) and p is arbi= 0 (Stokes'
+ 2p,
(2r-3)
VISCOSITY OF GASES
2-235
where now p denotes the hydrostatic pressure. The scalar I-' is defined as the absolute viscosity of the fluid. The viscosity is assumed to be a function of the thermodynamic state of the fluid and independent of the velocity field. For a homogeneous fluid I-' is a function of two properties. It is customary to use either of the following two alternative representations: or I-' = l-'(p,T) I-' = l-'(p,T) (2r-4) where T is the absolute temperature, p is the pressure, and p is the density of the fluid. Numerical values of viscosity cannot be calculated with the aid of the equations of thermodynamics. They must be measured directly, the measurement being usually very difficult, particularly at higher pressures and temperatures. In principle, values of viscosity can be calculated by the methods of the kinetic theory of gases and statistical mechanics with quantum corrections where necessary. In relation to a microscopically defined system the viscosity of a gas is assumed to be due to a transfer of momentum effected by molecules, their velocity being composed of the molecular (random) velocity and the macroscopic (ordered) velocity. In shear How (Fig. 2r-2), the shearing stress acting on a small element of area aa is equal to the integral of the change in momentum effected by the particles moving across, both from above and from below it, the integral extending over all --------~~~------~x particles crossing. 2r-2. Variation of Viscosity with Temperature and Pressure. The calculation of the viscosity of gases has so far met with only limited success, extensive experimental determinations still forming the basis for practical applications. The calculation of the viscosity of gases must make FIG. 2r-2. Kinetic interpretation use of a molecular model for the gas, increasing of viscosity. refinements being possible. On the simplest assumption of infinitely small, perfectly elastic molecules with zero fields of force (Maxwell) it is found that the absolute viscosity of a gas is independent of pressure and that it increases in proportion to Tt:
(au) ap
= T
0
(2r-5)
p = const
where Kl and K2 are empirical constants. On the assumption of hard elastic spheres with a weak attraction force (Sutherland), it is found that KT! 1 1-'=-(2r-6) 7=lji C +1' where K and C are empirical constants. Sutherland's equation (2r-6), as well as experimental results, show the increase with temperature to be faster than that in Maxwell's equation (2r-5). The fact that the viscosity of a gas increases with temperature can be understood if it is realized that in gases the effects of molecular motion dominate over those due to intermolecular forces. In liquids cohesion forces are more important, and since the molecular bonds in a liquid are loosened as the temperature is increased, the absolute viscosity of a liquid decreases with temperature; that for a gas increases with
2-236
MECHANICS
temperature. Sutherland's equation (21'-6) is inadequate for the correlation of experimental data over large temperature intervals. In problems of compressible fluid flow it is customary to use the empirical relation /10
;;; =
(T)'" To
(21'-7)
where /100 is the value of /10 at a reference temperature To and w is an empirical constant ranging from 0.6 to 1.5. This correlation is less precise than those given later. All preceding formulas relate to gases at low pressures (say atmospheric). Experimental results (which are still very scarce) show that the viscosity of gases at constant temperature increases with pressure, the increase being of the order of 20 to 40 per cent per 1,000 atm. For moderate pressure ranges it is possible to use a linear interpolation formula (21'-8) where /100 is the viscosity at temperature T, but at zero density, and k is an empirical constant. More precisely;, the viscosity of a gas increases as its density is increased. Since the viscosity of a gas consisting of molecules which exert no forces upon one another (Maxwell) is independent of density, this behavior is talcen as evidence of the existence of intermolecular fields of forces. However, exceptions exist to this rule, notably steam and hydrocarbons, whose viscosity at constant temperature dec/'eases with pressure, and therefore density, in certain ranges of states. In turn this is taken as evidence of the existence of some form of molecular association whose precise nature is not understood. 2r-3. Variation of Viscosity with Temperature and Pressure According to Kinetic Theory. There: exists a rigorous kinetic theory of the equilibrium and transport properties of gases which is based on Boltzmann's equation. Thus, in particular, and in principle, the viscosity, thermal conductivity (see Sec. 4g) and virial coefficients of gases (see Sec. 4i) are calculated in a consistent and unified way. This theory is due to Chapman and Enskog (S. Chapman and T. G. Cowling, "Mathematical Theory of Non-uniform Gases," Cambridge University Press, New York, 1970; J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, "Molecular Theory of Gases and Liquids," John Wiley & Sons, Inc., New York, 1964.) The calculations are made on the basis of assumed semiempirical force potentials. For nonpolar gases the most widely used potentials have been the Lennard-Jones twelve-six potential and the modified Buckingham exp-six potential; that used for polar gases is the Stockmayer potential. The viscosity at zero density is then calculated from the equation
VmkT fl'(n) (T*) 161ff u 2{}(2,2)*(T*)
5 /100 =
. (21'-9)
or, with the values of the universal constants substituted
!!'..)t fl'(n) (T*)
•
/100.
mlCropOlse
=
M . ( 26.694 gig-mole K
(cr2/.A2) {}(2,2)*(T*)
(21'-10)
Here cr is the molecular distance at which the potential vanishes, M is the molecular weight, k is Boltzmann's constant, and T* = kT IE is a dimensionless temperature with E denoting the depth of the potential well. The collision integral {}(2,2)* and the factor fl'(n), both of which are unique functions of the dimensionless temperature T*, are given in terms of the intermolecular force potential and must be tabulated
2-237
VISCOSITY OF GASES
for each one of them separately. Such tabulations for the more general m - 6 potential can be found in "Tables of Collision Integrals for the (m - 6) Potential for Ten Values of m" by M. Klein and F. J. Smith (Arnold Engineering Development Center Rept.) AEDC-TR-68-!J2, May, 1968, Arnold Air Force Station, Tenn.), with m taking the values m = 9, 12, 15, 18, 21, 24, 30, 40, 50, and 75. Tables for the exp-six potential can be found in "Transport Properties of Gases Obeying a Modified Buckingham (Exp-Six) Potential" by E. A. Mason [J. CAem. Phys. 22, 169 (1954)J. The factor j,,(n) with n = 1, 2, . . . represents successive approximations and it is usual to confine it to the third approximation, j/3), at most. In principle, the form of and the constants in a potential can be determined by quantum mechanics from a knowledge of the structure of the molecule. However, the attendant mathematical difficulties preclude us from doing so, and potentials must be determined by fitting experimental data on a variety of properties to expressions like the one in Eq. (2r-9). The efforts to associate definite potentials and physically meaningful constants with even the simplest molecules have not yet met with complete success. One of the difficulties is connected with the fact that often several alternative potentials give equally good fits to a set of experimental data of a definite property of a gas, but none seems to reproduce all properties to within the experimental error. Thus, there exists no preferred or universal form of the potential, but, as a matter of experience, it can be stated that the viscosity of the simpler gases, except that of helium, is reproduced reasonably well by the potential family
me
E(r) = m - 6
[m]S/(m-S) 6
[(,,)m r - (,,)sJ r
(2r-ll)
in which IT, e, and m are treated as adjustable constants. The viscosity of helium is best reproduced by the exp-six potential with rm = 3.135 A, elk = 9.16 K, and a = 12.4 [E. A. Mason and W. E. Rice, J. Chem. Phys. 22, 522, 843 (1954)J. Average, and to a certain extent preliminary, values of" and € for the Lennard-Jones potential are listed in Table 2r-3. A better representation is obtained with the aid of the 1.5 I I semiempirical formula '.\
Fp.
= 1.0 _
1~0
\
+ o~~
(2r-12)
where
Fp.
0.5
S2p,
=
-
26.694 VMT
a
(2r-12a)
and () =
1.0.
/
'1/ ,
1/
0.,2
gT
A ,
0..4
(2r-12b)
'-
--- -----
0..6 I/T*
0.,8
----
1.0
12
FIG. 2r-3. Dimensionless second virial The optimum values of the constants a, g, coefficient for viscosity b* as a function of and s are listed in Table 2r-4 for several reduced inverse temperature, according gases. to Kim and Ross. [J. Chem. PhY8. 42, Except for the neighborhood of the 263 (1965) J. critical point, the effect of density (i.e., pressure) on the viscosity of gases, even up to pressures of the order of several hundred atmospheres, can be accounted for with the aid of the virial expansion
p,(p,T)
=
p,o(T)
+ b(T)p + C(T)p2 + ...
(2r-13)
containing three or four terms. Kim and Ross [J. Chem. Phys. 42, 263 (1965)J provided a theory for the virial beT). The diagram in Fig. 2r-3 represents the universally valid relation between b*
=
(T*)-lQrei(T*)Bo o(T*)/fI,(2,2)*(T*)
(2r-14)
2-238
MECHANICS
and l/T*.
For the Lennard-Jones model, the expression reduces to
(1) (~)t ( M )t fT E/k gig-mole
b* _ _ 1 (_b ) - 15.20 g/cm'
(2r-15)
In the range where l/T* exceeds 0.2 (T* < 5 approximately), the virial coefficient b is nearly.a constant with b* "" 1. Consequently, Eq. (2r~14) can be simplified.to J,L(p,T) - J,Lo(O,T) =
15.20~ em'
(i) (Eir,kr (g/g~lOler + O(p2)
(2r~16)
This form leads to an approximate equation for the excess viscosity J,L(p,T)- J,Lo(O,T) which has often been used for correlations. This form is (2r-17)
J,L(p,T) - J,Lo(O,T) "" f(p)
in which f(p) is a unique '(empirical) function for each gas. TABLE
2r-3.
MOLECULAR-FORCE CONSTANTS FOR THE
LENNARD-JONES
E(r)
=
4E
(12-6)
[(n
12
-
POTENTIAL
(n
6
]
Symbol
Gas Acetylene .................................... .
Air .......................................... . Argon ....................................... .
Ar
Bromine ..................................... . Carbon dioxide ............................... . Carbon monoxide ............. ' ......•......... Chlorine...... . ....................... . Deuterium ................................... . Ethylene .................................... .
Br. CO. CO
Helium ...................................... .
He
Hydrogen .................................... Iodine .............. , ........................ Krypton ...................................... Methane .....................................
. . . .
H.
Neon ........................................ .
Ne
Nitric oxide .................................. .
NO
C1,
D. C.H.
I. Kr CH.
Nitrogen .................................... .
N,
Oxygen ...................................... . Propane ..................................... . Xenon ....................................... .
0, C,H. Xe
Elk, K
fT,!
Ref.
185 { 84.0} 117.5 { 124.0} 152.8 520 261.1 110.3 257 39.3 205 { 1O.22} 86.20 38.0 550 206.4 144 { 35.7} 60.9 119 { 91. 5} 113.5 113 254 229
4.221 { 3.689} 3.512 { 3.418 } 3.292 4.268 3.705 3.590 4.40 2.948 4.232 { 2. 576} 2.158 2.915 4.982 3.522 3.796 { 2.789} 2.648 3.470 { 3.68l } 3.566 3.433 5.061 4.055
1 1
2 1
2 1
2 3 1 1 1 1 2 1 1 2 1 1
2 1 1
2 1 1 1
Not. 1. Differences in the values in this table and the table in Sec. 4i are a measure of the uncertainties which still exist, as well as of the fact that the best fits to experimental values of virial coefficients and viscosity .are obtained with slightly different values of the constants. Not. 2. In the case of helium the best form of potential function is.that of the modified Buckingham exponential-six with parameters as quoted in the text. Consequently, the values of the parameters shown in the table may not be physically meaningful, especially in tb,e case of those quoted from ref. 2.
References for Table 2r-3 1. Hirschfelder, J. 0., C. F. Curtiss, and R. B. Bird: "Molecular Theory of Gases and Liquids," Table I-A, p. 1110, John Wiley & Sons, ·Inc., New York, corrected edition,
1964. 2. DiPippo, R., and J. Kestin: Viscosity of Seven Gases up to 500°C and Its Statistical Interpretation, Proc. 4th Symp. on Thermophys. Properties, ASME, New York, 1968. 3. Nat!. Bur. Standards Cire. 564, 1955.
2-239
VISCOSITY OF GASES
TilLE 2r-4. PARAMETERS IN VISCOSITY CORRELATION, EQ. (2r-12) Gas
Symbol
Air ...................... Argon ................... Butane .................. Carbon dioxide ........... Ethane .................. Ethylene ................. Helium .................. Krypton ................. Methane ................. Neon .................... Nitrogen .................
Ar C.HIO CO. C,Hs C.H. He Kr CH. Ne N.
....
.
I' g X 10',
a
. (K)-I
1.3034 1.0300 0.91040 0.94147 0.92669 0.71342 1.5779 0.83447 1.0532 1.6602 1. 3127
6.0906 7.5793 5.5145 5.3316 6.2093 3.3598 4.0302 8.4746 5.2434 6.6667 6.2232
8,
A
3.484 2.970 4.730 3.230 3.820 2.235 2.250 2.935 3.208 2.895 3.548
Temp. range, K
298-773 298-573 311-511 298-773 294-511 303-368 298-673 298-473 283-411 298-453 298-773
Unpublisbed correlation prepared by authors of this article.
2r-4. Viscosity in the Neighborhood of the Critical Point. Contrary to earlier views, it has now become accepted that the viscosity of a gas does not increase anomalously in the neighborhood of the critical point, even though the representation in the form of Eq. (2r-13) breaks down there. The viscosity in the neighborhood of the critical point has been measured (rather sketchily) for a very small number of substances only. A qualitative idea of the resulting behavior can be obtained from the diagram for CO 2, given as Fig. 2r-4 [J. Kestin, J. H. Whitelaw and T. F. Zien, Physica SO, 161 (1964)]. 2r-6. Law of Corresponding States. Attempts have also been made to correlate the viscosity of gases with the aid of the law of corresponding states. The most promising correlation [J. M. J. Coremans and J. J. M. Beenakker, Physica 26, 653 (1960)] makes use of molecular constants for the formation of reduced variables. The reference temperature is chosen as T* = kT IE, the reference density being chosen as the fraction of volume occupied by the molecular core p* = ¥ ...n(-~o-)3· where n is the number density. The viscosity p. is referred to iJ.O measured at zero density, so that P.r = p.1P.o and (2r-18) P.r = J(T*,p*) where f is an approximately universal function. series P.r
= 1
+
0.55p*
It can be represented by the power
+ 0.96p*2 + 0.61p*3 T*0.69
(2r-19)
from which it is seen that the relative excess viscosity !ir - 1 is a unique function of relative density p* at constant relative temperature T* according to Eq. (2r-17). Equation (2r-18) reproduces the experimental values for nonpolar or only slightly polar gases, with an error of the order of ±3 per cent over a fairly large range of· temperatures and densities. The error is negligible up to densities of approximately 200 amagat units, and the equation can be used up to about 500 amagat units. 2r-6. Mixtures of Gases. The viscosity of a gaseous mixture cannot be deduced from the knowledge of its composition and of the viscosities of its components by macroscopic methods, and methods of statistical mechanics must be used. In any case it should be noted that the viscosity of a mixture is not equal to the weighted mean of the viscosity of its components, it being possible for the viscosity of a mixture to be higher than that of its components. For example, a mixture of argon (P.Ar = 222 X 10-6 poise) and helium (P.He = 195 X lO- s poise) containing 40 per cent He
2-240
MECHANICS 450~----~------~------~-----r------'------'
400~----~----~~----~----~------~~~~
'"~
.~ 350 e-----~-----+---_+---+--+_I+_--__l
e
.~
:i.
>iii
I-
§ 300 :; o
~
15
250~-----+------~----~~---+------~--~
'"E ~ '" 200~----+------~~~--~----+---~ ".
'i?
"-
I
150'~~---O~.1------~QL2------0L.3------0~A~----~O.L5-----0~.6 DENSITY p, g/cm 3
FIG. 2r-4. Viscosity of carbon dioxide as a function of density in the near-critical region according to Kestin, Whitelaw, and Zein [Physica 30,161 (1964)].
and 60 per cent Ar has a viscosity of '" = 230 X 10- 6 poise. Thus for a given pressure and temperature, the viscosity of a mixture can pass through a maximum when plotted as a function of composition. Maxima are also exhibited by the binary mixtures H 2-Xe, He-Xe, H 2 -S0 2 , H 2 -CaH s, H 2-C0 2 , H 2-CaH., H 2-C 2 H., H 2-NO, H 2-C 2 H 4, He-Ar, H 2 -NHa, H 2-CH4, NHa-C 2 H4, HCI-C0 2, CH.-NH" and possibly many others. Even in the case of binary mixtures,the relation among the viscosity of the mixture, the viscosities of the pure components, and the composition is quite complex. At present the quality of the statistical approximation obtained by the methods of statistical mechanics is somewhat uncertain, and it is necessary to refer the reader to the treatise by J. O. Hirschfelder et al. (see footnote to Table 2r-3) for further details. Table 2r-5 gives sources of data on the viscosity of gaseous mixtures.
2-241
VISCOSITY OF GASES TABLE
2r-5.
REFERENCES TO DATA ON BINARY GASEOUS MIXTURES
Mixture
Air-H.O He-AI' He-Ne He-Kr He-H. He-N. He-O. He-CO. Ne-Ar Ne-N. Ne-CO. Ar-NHa Ar-N. Ar-CO. Kr-CO. N.-H. N.-CO. CO.-CH. CH.-C.HlO
Pressure range, atm
Temperature range, °C
Reference
1 1-50 1-35 1-25 1-25 1-25 1-25 { 1-25 1-70 1-35 1-25 1-25 1-25 1-25 1-25 1-25 1-25 1-25 1-25 1-25
25-75 20-30 20-30 20-30 20-30 20-30 20-30 20-30 20 20-30 20-30 20-30 20-30 20-30 20-30 20-30 20-30 20-30 20-30 20-30
1 2 3 4 5 4 5 6 9 3 6 7 8 6 4 5 5 4 5 5
References for Table 2r-5 1. Kestin, J., and J. H. Whitelaw: Measurement of the Viscosity of Dry and Humid Air,
2. 3. 4. 5. 6 .. 7. 8. 9.
p. 301 in "Humidity and Moisture," vol. III, p: 301, Reinhold Book Corporation, New York,1965. Iwasaki, H., and J. Kestin: Physica 29, 1345 (1963). Kestin, J., and A. Nagashima: J. Chem. Phys. 40, 3648 (1964). Kestin, J., Y. Kobayashi, and R. T. Wood: Physica 32, 1065 (1966). Kestin, J., and J. Yata: J. Chem. Phys. 49, 4780 (1968). DiPippo, R., J. Kestin, .and K. Oguchi: J. Chem. Phys. 46,4758 (1967). Breetveld, J. D., R. DiPippo, and J. Kestin: J. Chem. Phys. 45, 124 (1966). Iwasaki, H., J. Kestin, and A. Nagashima: J. Chem. Phys. 40,2988 (1964). Richardson, H. P., D. Cummins, and R. A. Guereca: Absolute Viscosity Determinations by Means of a Coiled-capillary Viscosimeter: Data for Helium, Carbon Dioxide Mixtures, Proc. 4th Symp. Thermophys. Properties, ASME, New York, 1968.
2r-7. Tables of Viscosity. The variation of the viscosity of several gases, all extrapolated to zero density (but accurate enough at atmospheric pressure), can be obtained from the correlation in Eq. (2r-12) and the data in Table 2r-4. Table 2r-6 contains the best available data on the absolute viscosity p. of gases at 20°0 and atmospheric pressure together with the temperature increment (tJ.p.) T and the pressure increment (tJ.p.)p at that point. Table 2r-7 lists the same values for the kinematic viscosity p. The values have been carefully selected in each case, either mean values or preferred values having been chosen depending on the merits of the available experimental material. The estimated uncertainties are also based on a critical assessment of available data and are, to a certain extent, arbitrary. Experimental results for both high pressures and temperatures are, for all intents and purposes, nonexistent.
~fI:>-
TABLE 2r-6. ABSOLUTE VISCOSITY p. OF GASES IN MWROPOISES (10- 6 glom sec = 10- 6 dyne sec/cm2; at 20°C and 1 atm)
I>:)
Gas
Symbol
p., p.poises
Estimated Temp. uncertainty increment ±Llp.,
p.poises Acetylene ............ Air ................. Ammonia ............ Argon ............... Bromine ............. iso-Butane ........... n-Butane ............
C2H 2 ......
NH. Ar Br2 C 4H 1o C 4H 1o
93.5 (at O°C) 181.92 97.4 222.86 149.5 74.8 84.8
Carbon dioxide ....... CO2 Carbon monoxide ..... CO Chlorine ............. Clz
146.63 175.3 133.0
Chloroform .......... Cyanogen ............ Deuterium ........... Deuteromethane ...... Ethane .............. Ethylene ......•.....
CHCla C 2N 2 D2 CD 4 C2H 6 C 2H 4
100.0 100.2 124.68 129.0 91.0 100.0
Helium .............. Hydrogen ............ Hydrogen bromide .... Hydrogen chloride .... Hydrogen deuteride ...
He H2 HBr HCI HD
196.14 88.73 184.3 142.5 111.8
- -
--~~
--~
.... . 0.006 3 0.1 ••• 0.
.... . .... . 0.07 0.1
..... .0 ...
..... 0.07 .0 . . •
0.8 . . • 0.
0.1 0.05 .....
.... . 0.3
Pressure increment (Llp.)p,
(Ll/L)T,
Source
p.poises ;oC p.poises/atm 00
•••
0.536 0.425 0.704 0.500 0.237 0.300 0.450 0.474 0.451 0.340 0.360 0.284 0.580 0.277 0.320 0.464 0.200 0.680 0.500
.....
........ 0.1224
........
0.1753
........ ........ ........
0.0046
........ . .......
. ....... .
....... 0.0082
. ....... ••
0
•••
•
•
........ -0.0093 0.0118
. .......
........ . .......
"International Critical Tables" Bearden, Phys. Rev. 56, 1023 (1939) Wtd. mean of 2 values Ref. 1 Ref. 2 Ishida, Phys. Rev. 21 (1923) Kuenen and Visser, Amsterdam Acad. Sci. 22, 336 (1913) Ref. 1 Wtd. mean of 4 values Rankine, Proc. Roy. Soc. (London), ser. A, 86,162 (1912) Ref. 2 Ref. 2 Ref. 1 Ref. 2 Wtd. mean of 2 values Van Cleave and Maass, Can. J. Research 13B, 140 (1935) Ref. 1 Ref. 1 Ref. 2 Ref. 2 Kestin and Nagashima, Phys. Fluids 7,730 (1964)
~
toJ
Q
~
H
Q
Ul
TABLE 2r-6. ABSOLUTE VISCOSITY p. OF GASES IN MICROPOISES (Continued)
Gas
Symbol
/I,
p.poises
Hydrogen iodide ...... Krypton ............. Mercury ............. Methane .............
HI Rr
Methyl bromide ...... Methyl chloride ...... Neon ............... Nitric oxide .......... Nitrogen ............ Nitrous oxide ........
CHaBr CHaCI Ne NO N2 N,O
132.7 107.0 313.81 189.8 175.69 145.6
Oxygen ............... Propane ............. Sulfur dioxide ........ Xenon ..............
0, CaHs S02 Xe
203.31 80.0 125.0 227.40
Hg CH 4
183.0 249.55 450.0 (200°C) 109.8
Estimated Temp. Pressure uncertainty increment increment (L'.,u}T, ±L'.,u, (L'.,u)Pl ,upoises p.poises;oC ,upoises / atm .....
0.15
0.640 0.735
. ....... 0.2816
.....
.
....
. .......
0.1
0.330
0.016
.....
0.460 0.425 0.697 0.538 0.454 0.475
. ....... . .......
..... 0.15 0.1 0.09
..... 0.1
..... .... .
0.14
0.616 0.22 0.400 0.725
--
0.0354 ........
0.1234
.. . . . . . .
0.1205
... . . ... ........ 0.2624
Source
Ref. 2 Ref. 1 Ref. 2 j Restin and Leidenfrost, "Thermodynamic Prop- w. erties of Gases, Liquids, Solids," p. 321, ASME (') o 1958 W. H Ref. 2 f-3 ~ Breitenbach, Ann. Phys. 5, 166 (1901) o Ref. 1 ":J Wtd. mean of 3 values o Ref. 1 ~ Johnston and McCloskey, J. Phys. Chern. 44, 1038 w. trJ w. (1940) Ref. 1 Ref. 2 Ref. 2 Ref. 1 _._.-
References 1. Kestin, J., and W. Leidenfrost: Physica 25, 1033 (1959). 2. Golubev, I. F.: "Viaz'kost' gazov i gazovykh smesei," Moscow, 1959. difficult to assess.
This reference contains extensive data whose accuracy, however, it is
~
ioI'-
~
~fI:>.
TABLE 2r-7. KINEMATIC VISCOSITY V OF GASES (10- 3 em 2/see; at 20°0 and 1 atm)
fI:>.
Gas
Symbol
v, 10- 3 cm 2jsec
Acetylene ........................... Air ................................. Ammonia ........................... Argon .................. , ........... Bromine ............................ iso-Butane .......................... n-Butane ............................ Oarbon dioxide ...................... Carbon monoxide .................... Chlorine ............................ Chloroform .......................... Cyanogen ........................... Deuterium ........................... Deuteromethane ..................... Ethane ............................. Ethylene ............................ Helium ............................. Hydrogen bromide ................... Hydrogen chloride ................... Hydrogen deuteride .................. Hydrogen ........................... Hydrogen iodide ..................... Krypton ............................ Mercury ............................ Methane ............................
02H2
80.6 (at 0°0) 151.1 138 134.3 22.50 31.0 35.1 80.09 150.6 45.11 20.16 46.35 744.2 154.7 72.9 85.84 1,179 54.79 93.99 889.4 1,059 34.42 72.44 87.12 (at 200°C) 164.8
...... NH, Ax Br2 04H 1O 04H 1O 002 CO Cl, CHCI, C,N, D2 CD 4 02Hs C 2H 4 He HBr HCI HD H2
HI Kr Hg CH4
Estimated uncertainty ±L'>.v, 10- 3 cm 2/sec
0.08 4 0.06
.....
..... ..... 0.04 0.09
..... ..... .....
0.4
.....
0.6
.....
0.6
..... ..... 2.4 0.6
Temp. increment (L'>.v)T, 10-' em 2/ (sec WO)
0.960 1.07 0.882 0.152 0.204 0.244 0.516 0.921 0.307 0.137 0.325 4.24 1.22 0.471 0.997 6.81 0.389 0.651
0.044
6.01 0.237 0.460
0.2
1.06
.....
Pressure increment (L'>.v)p, 10-' cm2j(sec) (atm)
-150.9 -134.1
-80
~
t'j Q
t:ci il> Z H Q
U1
-740
-1,200
-1,060 -72.20 -160
TABLE
Gas
2r-7.
Symbol
KINEMATIC VISCOSITY
v, 10-' cm'/sec
V
OF GASES
(Continued)
Estimated uncertainty ±/lv, 10-' cm'/sec
Temp. increment (/lv h, 10-' cm'/(sec)(OC)
Pressure increment (/lv)p, 10-' cm'/(sec)(atm)
;:S
m C)
Methyl bromide ...................... Methyl chloride ...................... Neon ............................... Nitric oxide ......................... Nitrogen ............................ Nitrous oxide ........................ Oxygen ............................. Propane ............................. Sulfur dioxide ........................ Xenon ..............................
-
CR,Br CH,CI Ne NO N, N,O
0, C,Rs SO, Xe
33.64 50.97 374.1 152.1 150.9 79.57 152.8 43.7 46.94 42.02
..... ..... 0.18 0.08 0.08 ..... 0.08 ..... ..... 0.026
o
m
0.232 0.376 2.11
0.950 0.905 0.531 0.984 0.269 0.310 0.278
~
>
-374
o
-150.8
Cl
":J
-152.6
~
m t<J
m
-42.38
% ~
c.n
%
TABLE 2r-8. VISCOSITY OF COMPRESSED WATER AND SUPERHEATED STEAM (MICROPOISES) Of each pair of figures the upper represents the adopted value and the lower the tolerance (±)
-
-
Pressure, bars
H'>-
Ol
-
Temperature, °C
0
50
100
150
200
250
300
350
375
400
425
450
475
500
550
600
- -- - - - - - --- - - - - - -
17,500 400 -
5,440 140
5
17,.500 400
5,440 140
2,790 70
10
17,500 400
5,440 140
2,790 70
I
121.1 1.2
141.5 1.4
253
264 8
274 8
284
8
8
304 9
325 10
345 10
365 11
202.3 2.0
234 9
244 10
254 10
264 11
274 11
284 11
305 12
325 13
345 14
366 15
202.2 2.0
234 9
244 10
255 10
265
275 11
285
305 12
326 13
346 14
366 15
202.5 2.0
1,810 50
160.2 1.6
181.4 1.8
1,810 50
158.5 1.6
180.6 1.8
223 7
11
307 12
327 13
347 14
367 15
289 12
309 12
329 13
349 14
369 15
292 12
312 12
332 13
352 14
372 15
11
295 12
315 13
334 13
354 14
374 15
280 11
289 12
299 12
318 13
337 14
357 14
376 15
276 11
285 11
294 12
302 12
321 13
340 14
359 14
379 15
276 11
282 11
290 12
298 12
307 12
324 13
343 14
362 14
381 15
286 11
289 12
296 12
303 12
311 12
328 13
346 14
365 15
384 15
236 9
246
256 10
266 11
276
10
1,070 30
200.6 2.0
240 10
250 10
259 10
269
279
11
11
1,350 30
1,080 30
199.2 2.0
244 10
253 10
263 10
273
282
11
11
1,830 50
1,360 30
1,080 30
905 23
249 10
258 10
267 11
276
286
11
2,810 70
1,840 50
1,360 30
1,090 30
911 23
254 10
263 10
271 11
5,460 140
2,820 70
1,840 50
1,370 30
1,100 30
917 23
262
269
11
11
17,400 400
5,460 140
2,820 70
1,850 50
1,380 30
1,100 30
924 23
273 11
17,400 400
5,460 140
2,830 70
1,860 50
1,380 40
1,110 30
930 23
291 12
1,820 50
1,340 30
17,500 400
5,450 140
2.800 70
1,820 50
1,350 30
75
17,500 400
5,450 140
2,800 70
1,830 50
100
17,500 400
5,450 140
2,810 70
125
17,500 400
5,460 140
150
17,400 400
175 200
177.8 l.8
--
735 29
11
287 12
201.6 2.0
2,800 70
50
243 7
182.2 1.8
5,440 140
700 --
233 7
161.8 1.6
17,500 400
25
650 ----
11
~ EI
o
p::
i>
Z H
o
1]2
225
17,400 400
5,460 140
2,830 70
1,860 50
1,390 . 40
1,120 30
936 23
747 30
491 20
299 12
298 12
302 12
309 12
316 13
332 13
350 14
368 15
386 15
250
17,400 400
5,470 140
2,840 70
1,870 50
1,390 40
1,120 30
943 24
760 30
597 24
321 13
309 12
310 12
315 13
321 13
336 13
353 14
371 15
389 16
275
17,400 400
5,470 140
2,840 70
1,870 50
1,400 40
1,130 30
949 24
772 31
633 .367 15 25
324 13
320 13
322 13
327 13
341 14
357 14
374 15
392 16
300
17,400 400
5,470 140
2,850 70
1,880 50
1,400 40
1,130 30
955 24
785 31
657 26
.458 18
345 14
331 13
330 13
334 13
346 14
361 14
377 15
395 16
:350
17,300 400
(>,480 140
2,860 70
1,890 50
1,420 40
1,150 30
968 24
805 32
693 28
573 23
416 17
363 14
351 14
349 14
357 14
369 15
385 15
401 16
400
17,300 700
5,480 200
2,870 120
1,900 80
1,430 60
1,160 50
981 39
825, 33
721 29
628 25
503 20
411 16
379 15
369 15
369 15
379 15
392 16
408 16
450
17,300 700
5,490 220
2,880 120
1,910 80
1,440 60
1,170 50
993 40
837 33
743 30
664 27
565 23
468 19
415 17
393 16
383 15
389 16
401 16
415 17
17,200 700
5,490 220
2,890 120
1,920 80
1,450 60
1,180 50
1,010 40
850 34
762 30
693 28
609 24
521 21
456 18
421 17
400 16
401 16
410 16
423 17
550
17,200 700
5,500 220
2,900 120
1,930 80
1,460 60
1,200 50
1,020 40
860 34
780 31
716 29
643 26
564 23
497 20
453 18
418 17
414 16
420 17
431 17
600
17,200 700
5,500 220
2,910 120
1,940 80
1,480 60
1,210 50
1,030 40
870 35
795 32
736 29
670 27
600 24
534 21
485 19
439 18
428 17
430 17
439 18
650
17,200 700
5,510 220
2,920 120
1,960 80
1,490 60
1,220 50
1,040 40
882 35
809 32
754 30
698 28
629 25
567 23
516 21
460 18
442 18
441 18
448 18
700
17,100 700
5,510 220
2,930 120
1,970 80
1,500 60
1,230 50
1,060 40
895 36
822 33
770 31
713 28
654 26
596 24
545 22
482 19
458 18
453 18
458 18
750
17,100 700
5,520 220
2,940 120
1,980 80
1,510 60
1,240 50
1,070 40
905 36
835 33
784 31
732 29
676 27
621 25
572 23
504 20
474 19
466 19
468 19
800
17,100 700
5,520 220
2,950 120
1,990 80
1,520 60
1,260 50
1,080 40
915 37
846 34
798 32
748 30
695
644 26
596 24
526 21
491 20
478 19
478 19
~ o
111
o
111 H
500
28
8
~
o";j
~
111 [:oj 111
I
Note 1. The entry shown for ODe and 1 bar relates to a metastable liquid state. The stable state is here solid. Note 2. The values and the tolerances in the region of the critical point do not take into account the possibility of an anomalous behavior of the viscosity in the immediate neighborhood of the critical point. .
~ t-.:)
~
2-248
MECHANICS
2r-B. Steam. The dynamic and kinematic viscosity of steam has been settled (subject to future amendment) by international agreement ["Supplementary Release on Transport Properties of the Sixth International Conference on the Properties of Steam," New York, 1963; obtainable from the Secretariat of the International Conference on the Properties of Steam, ASME, United Engineering Center, New York. See also E. Schmidt, "VDI-Wasserdampftafeln" (VDI-Steam Tables), 7th ed., Springer Verlag, 1968]. According to this internationally recognized correlation, the viscosity of steam and water can be represented empirically by the following equations, depending on the range of states under consideration: Superheated steam at 1 bar pressure in temperature range 100°C JLl
=
micropoise Tolerance for
80.4
< t < 700°C:
+ 0.407 o~ t
(2r-20)
±l%,
100
/ax a 2 cf>/ax 2 a 2 cf>/ax ay
similarity parameter stream function 2t.1. Basic Equations in Rectangular Coordinates. The basic equations of motion for a compressible inviscid gas may be written as follows. Momentum Equation. By applying Newton's laws of motion the Euler momentum equation may be derived in the form
+ u au + v au + w au = ax ay az ~ + u av + v av + w~ = at ax ay az aw + u aw + v aw + w aw = au at
at
ax
ay
az
2-253
+X -1 ap + y p ay -1 ap + Z -1 ap p ax
paz
(2t-l)
2-254
MECHANICS
where x, y, z = rectangular coordinates t = time u, v, w = velocity components in direction of x, y, and z axes, respectively p = pressure p = density X, Y, Z = rectangular components of external body force Continuity Equation. The assumption that the gas is a continuous medium expressed by the equation
tf + y;; (pu) + :y (pv) + ;. (pw)
=
0
IS
(2t-2)
Energy Equation. The relationship between the kinetic and internal energy and the work done on the fluid by pressure and external forces is expressed by the equation p DE -I- p D Dt ' Dt
(!2 q2)
= pQ
+ p(uX + vY + wZ)
-
~ax
(pu) -
~ ay
(pv) -
~ az
(pw) (2t-3)
where D == ~ + u ~ + v -.i + w ,i Dt at ax ay az E = internal energy per unit mass = f Cv dT q2 = u2 + v2 + w2 Q = external-heat-production rate per unit mass Cv = specific heat at constant volume Equation of State. For a complete specification of a flow it is necessary to give an equation of state. This commonly takes the form p = f(p,T.)
Many gases obey the equation of state of a perfect gas p
=
pRT
under a great variety of conditions. In this equation R is a constant which depends on the particular gas. If the specific heat can be assumed constant, the gas is said to be calorically perfect and E = cvT where T is the temperature on the absolute scale. A specific case of great importance is that of isentropic flow. If the entropy is constant throughout the flow, the equation of state can be written as
where K is a constant and l' is the ratio of the specific heat at constant pressure Cp to that at constant volume Cv• Now the flow is completely determined by the momentum equations, the continuity equation, and the equation of state. Many practical flow problems are essentially cases of isentropic flow. 2t-2. Dynamic Similarity and Definition of Basic Flow Parameters. In the testing of models it is necessary to maintain a proper scaling of certain dynamic parameters in addition to the geometric scaling. For compressible inviscid flow with no heat sources and in which body forces are neglected, the only dynamic dimensionless parameter is the Mach number_ Definition of Mach Number. Thelocal Mach number.is defined as the ratio of the local flow velocity q to the local sound velocity a; i.e., (2t-4)
COMPRESSIBLE FLOW OF GASES
2-255
Thus in a nonuniform flow the Mach number will vary from point to point. The size of the Mach number indicates whether the flow is subsonic, M < 1; transonic, M ~ 1; or· supersonic, M· > 1. The term hypersonic is often used to describe flows where
M >5. Dynamic Similarity. If the same gas flows around two geometrically similar bodies, it might be expected that under the right conditions the streamline pattern would be similar. This is true if the Mach numbers of the two flows are equal. It then follows that all other dimensionless coefficients such as drag coefficient, lift coefficient, pressure coefficient, etc., are also equal. In determining the Mach number in a flow it is necessary to know not only the flow velocity but the sound velocity as well. For a perfect gas the sound velocity is proportional to the square root of the temperature; i.e.,
a
=
v''YRT
Table 2t-1 is based on this relationship. 2t-3. Basic Idea of One-dimensional Flow. In many cases, as in a pipe of slowly varying cross section, it is possible to make the assumption of constant flow properties across any cross section perpendicular to the pipe axis. Although strictly speaking there are no one-dimensional flows, because of viscous effects on the boundaries, it is still possible to get much valuable information of a practical nature from the assumptions. TABLE
2t-1.
Basic Equations.
VARIATION OF VELOCITY OF SOUND WITH TEMPERATURE
T, oK
a, fps
a, m/sec
150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350
805 832 857 882 907 930 953 975 997 1,019 1,040 1,060 1,081 1,100 1,120 1,139 1,158 1,176 1,195 1,213 1,230
246 254 261 269 276 283 290 297 304 311 317 323 329 335 341 347 353 359 364 370 375
On the assumption of isentropic flow the equations of motion are (momentum)
(2t-5)
(continuity)
(2t-6)
2-256
MECHANICS
where A is the cross-sectional area. For unsteady one-dimensional flow in general and in particular for an excellent treatment of flow in pipes of constant area see ref. 3. The above equations also cover the case of cylindrical and spherically symmetric flow; i.e., 1 iiA 1 (for cylindrical flow)
x Aax = x
Aiix = 1iiA 2
(for spherically symmetric flow)
In the important case of steady flow the equations can be integrated to give _'Y_l!. ~ u' = const 'Y-1p 2 puA = m = const
+
(2t-7)
(2t-8)
where m is the mass flow. By taking logarithmic derivatives and remembering the definition of the Mach number M, the continuity equation may be written du (1 _ M') u
+ dA A
= 0
(2t-9)
Thus, if du T" 0 and M = 1, we see that dA = O. In other words, the Mach number becomes equal to unity only in a section of the pipe where the area is a minimum. This fact is of prime importance in the design of supersonic wind tunnels. The dependence of the various flow variables on the Mach number for steady onedimensional isentropic flow is given in Table 2t-2. 2t-4. Two-dimensional and Axially Symmetric Flow. Many important types of flow belong to the class of two-dimensional or axially symmetric flows. These include flows past wedges, cones, bodies of revolution, etc. The important distinctions to be made are those between subsonic and supersonic flow. Purely subsonic flow is qualitatively quite similar to incompressible flow, while supersonic flow exhibits many startlingly different properties. Among these are the appearance of shock waves (see Sec. 2v) and the existence of wavefronts. A general discussion of the above topics can be found in refs. 2, 3, and 6. The greater bulk of the literature on two-dimensional and axially symmetric flow is concerned with steady flow. The unsteady cases are usually extremely difficult to solve. Velocity Potential and Stream Function. In cases ofirrotational or steady flow it is convenient to introduce the velocity potential or the stream function. This reduces the number of equations to one. The velocity potential exists whenever there is a state of steady or unsteady irrotational flow; i.e., the velocity components satisfy the equations
Then the velocity components u, v, w can be expressed as the components of the gradient of the velocity potential cf>. Thus iicf>
U=-
iix
v
iicf>
=-
iiy
w
=
iicf>
iiz
(2t-1O)
For steady isentropic flow the equations of motion reduce to the single equation for cf>,
ar
cf>zz ( 1- cf>z·)
+cf>UY (cf>u') 1-(i2 +cf>•• (cf>l) 1- ar (2t-ll)
where
2-257
COMPRESSIBLE FLOW OF GASES
TABLE2t-2. DEPENDENCE OF FLOW VARIABLES ON MACH NUMBER FOR ONl!:-DIMl!:NflWNAL ISEN'l'lWPIC FUlIY*
pu'/2po
pu/poao
pip~
T/To
a/ao
5.822 2.9635 2.0351 1. 5901
0.00000 0.00695 0.02723 0.05919 0.10031
0.00000 0.09940 0.19528 0.28437 0.36393
1.00000 0.99502 0.98028 0.95638 0.92427
1.00000 0.99800 0.99206 0.98232 0.96899
1.00000 0.99900 0.99602 0.99112 0.98437
0.48795 0.57950 0.66803 0.75324 0.83491
1. 3398 1.1882 1.0944 1.0382 1.0089
0.14753 0.19757 0.24728 0.29390 0.33524
0.43192 0.48704 0.52880 0.55739 0.57362
0.88517 0.84045 0.79161 0.73999 0.68704
0.95238 0.1)3284 0.91075 0.88652 0.86059
0.97590 0.96583 0.95433 0.94155 0.92768
0.52828 0.46835 0.41238 0.36091 0.31424
0.91287 0.98703 1.0574 1.1239 1.1866
1.00000 1.0079 1.0304 1.0663 1.1149
0.39670 0.41568 0.42696 0.43114
0.57870 0.57415 0.56161 0.54272 0.51905
0.63394 0.58170 0.53114 0.48290 0.43742
0.83333 0.80515 0.77640 0.74738 0.71839
0.91287 0.89730 0.88113 0.86451 0.84758
1.5 1.6 1.7 1.8 1.9
0.27240 0.23527 0.20259 0.17404 0.14924
1.2457 1. 3012 1.3533 1.4023 1.4479
1.1762 1.2502 1.3376 1.4390 1.5553
0.42903 0.42161 0.40985 0.39476 0.37713
0.49203 0.46288 0.43264 0.40216 0.37210
0.39484 0.35573 0.31969 0.28684 0.25699
0.68966 0.66138 0.63371 0.60680 0.58072
0.83045 0.81325 0.79606 0.77904 0.76205
2.0 2.1 2.2 2.3 2.4
0.12780 0.10935 0.09352 0.07997 0.06840
1.4907 1. 5308 1.5682 1.6033 1.6360
1.6875 1. 8369 2.0050 2.1931 2.4031
0.35785 0.33757 0.31685 0.29614 0.27579
0.34294 0.31504 0.28863 0.26387 0.24082
0.23005 0.20580 0.18405 0.16458 0.14719
0.55556 0.53135 0.50813 0.48591 0.46468
0.74535 0.72894 0.71283 0.69707 0.68168
2.5 2.6 2.7 2.8 2.9
0.05853 0.05012 0.04295 0.03685 0.03165
1.6667 1. 6953 1.7222 1. 7473 1.7708
2.6367 2.8960 3.1830 3.5001 3.8498
0.25606 0.23715 0.21917 0.20222 0.18633
0.21948 0.19983 0.18181 0.16534 0.15032
0.13169 0.11788 0.10557 0.09463 0.08489
0.44444 0.42517 0.40683 0.38941 0.37286
0.66667 0.65205 0.63784 0.62403 0.61062
3.0 3.1 3.2 3.3 3.4
0.02722 0.02345 0.02023 0.01748 0.01512
1.7925 1.8135 1.8329 1. 8511 1.8682
4.2346 4.6573 5.1210 5.6287 6.184
0.17151 0.15774 0.14499 0.13322 0.12239
0.13666 0.12426 0.11301 0.10281 0.09359
0.07623 0.06852 0.06165 0.05554 0.05009
0.35714 0.34223 0.32808 0.31466 0.30193
0.59761 0.58501 0.57279 0.56095 0.54948
3.5 3.6 3.7 3.8 3.9
0.01311 0.01138 0.00990 0.00863 0.00753
1.8843 1.8995 1. 9137 1.9272 1.9398
6.790 7.450 8.169 8.951 9.799
0.11243 0.10328 0.09490 0.08722 6.08019
0.08523 0.07768 0.07084 0.06466 0.05906
0.04523 0.04089 0.03702 0.03355 0.03044
0.28986 0.27840 0.26752 0.25720 0.24740
0.53838 0.52763 0.51723 0.50715 0.49740
4.0 4.1 4.2 4.3 4.4
0.00659 0.00577 0.00506 0.00445 0.00392
1. 9518 1. 9631 1.9738 1. 9839 1.9934
10.72 11.71 12.79 13.95 15.21
0.07379 0.06788 0.06250 0.05759 0.05309
0.05399 0.04940 0.04524 0.04147 0.03805
0.02766 0.02516 0.02292 0.02090 0.01909
0.23810 0.22925 0.22084 0.21286 0.20525
0.48795 0.47880 0.46994 0.46136 0.45305
4.5 4.6 4.7 4.8 4.9
I
0.00346 0.00305 0.00270 0.00239 0.00213
2.0025 2.0111 2.0192 2.0269 2.0343
16.56 18.02 19.58 21.26 23.07
0.04898 0.04521 0.04177 0.03862
0.01745 0.01597 0.01464 0.01343 0.01233
0.19802 0.19113 0.18457 0.17832
0.44499 0.43719 0.42962 0.42228
0.03572
0.03494 0.03212 0.02955 0.02722 0.02509
5.0
I 0.00189
2.0412
25.00
0.03308
0.02315
0.01134
M
p/po
0.0 0.1 0.2 0.3 0.4
1.00000 0.99303 0.97250 0.93947 0.89561
0.00000 0.09990 0.19920 0.29734 0.39375
0.5 0.6 0.7 0.8 0.9
0.84302 0.78400 0.72093 0.65602 0.59126
1.0 1.1 1.2 1.3 1.4
u/ao
I
A/A*
00
I 0.36980
I
* A more complete table may be found in refs.
4, 5, and 7.
I
0.17235 0.16667
I
0.41516 0.40825
2-258
MECHANICS
and qmax is the velocity with which the gas flows into a vacuum. Other forms of this equation in different numbers of dimensions and for unsteady flow can be found in ref. 2. - - TRANSONIC THEORY 0.6
0.4
10.0'
Cp 0.2
1'
7.5 0
o~
4.5 0
1.2
1.0
0.8
0.6
1.6
1.4
M", fa) M 2-1
~:1;!1lf
4
o
\
\
2 WEDGE SEMI-ANGLE
c
X= [(r+l)r;!(t!c)]%
\
08:P~~
3
4.5 0 7.5" 10.00
\
Cp
LJNEA~',
THEORY _
CPo
- .......
[(r+])M~]llJ (tlc)%
CP
----
(I
o X (b) FIG. 2t-1. Comparison of the extended transonic similarity law with experiment. (a) Plotted in conventional coordinates. (b) Plotted in transonic similarity coordinates. (After J. R. Spreiter, NACA; taken from ref. 6.)
In compressible flow a stream function if; exists only for steady two-dimensional or axially symmetric flow. The introduction of the function if; causes the continuity equation to be satisfied identically. In two dimensions u If cylindrical coordinates (x, function if; may be defined by
T,
=
1
pif;y
v
=
-
1
- if;x p
(2t-12)
e) are used and the flow is independent of e, then the v
-
1
-if;x
pf
(2t-13)
COMPRESSIBLE FLOW OF GASES
2-259
Note that u and v are now the velocity components in the x and r directions and y2 + Z2. Further details are given in ref. 2. Eq1wtions of Small-pertw'bation Them·y. For many slender or flat two- and threedimensional bodies it may be assumed that the flow is disturbed very little from uniform flow. Thus if the free-stream velocity U is parallel to the x coordinate and M ro is the free-stream Mach number, the velocity components can be written in the form r =
-vi
u
=
U
+ B(S) constant in the Tait equation for water n unit vector normal to surface u velocity vector 1I1R Mach number of reflected shock = '/l'2R/C2 u p
Subscripts 1, 2, and 3 on any quantity (e.g., 1Il, P2, ps) mean that the quantity is measured in front of an incident shock, behind the incident shock, or behind a reflected shock, respectively. Primed and double-primed quantities (e.g., p', 11/') are measured, respectively, on the two sides of a boundary between two media. Subscript R on any quantity means that that quantity is measured in,a coordinate syAtem moving with a reflected s h o c k . ' "
2-274
MECHANICS
2v-2. Introduction. Sound waves of infinitesimal amplitude in fluids always propagate without change of form (neglecting the effects of viscosity, thermal conductivity, and relaxation). For waves of finite amplitude this is no longer true. The denser regions move faster than the less dense, and hence the denser regions are always catching up with less dense ones in front of them, but since the velocity increases with density, the effect becomes more and more pronounced, the front of the wave becoming steeper and steeper until the density, temperature, and pressure changes across it are virtually discontinuous-a shock wave is formed. Mathematically, a shock wave is an actual discontinuity propagating with a velocity greater than the local sound velocity. Physically, although a shock transition is extremely abrupt (of the order of 10 mean free paths for a typical shock in a gas), it nevertheless is continuous, because of the action of dissipative forces. In what follows, attention will be focused exclusively on the regions behind or in front of the shock front. The relations that will be given are of general validity (except as noted) and are in any case independent of the actual course of events within the front itself. It might be imagined that there could be a flow in which a shock moves from a dense region to a rarefied one. However, it can be shown from the energy-conservation law that steady-state flows of this type cannot exist in any fluid having an adiabat that is concave upward, the almost universally prevailing situation. Another type of discontinuity occurring in gas flows is called a "contact discontinuity." It differs from a shock in that there is no mass flow across it, as there is in the case of a shock. Contact discontinuities cannot occur in steady-state flows and will not be further considered. 2v-3. Steady-state One-dimensional Flow. General Relations. Consider a shock propagating steadily in a fluid. Relative to a coordinate system moving with the shock, the equations of steady compressible flow are ap au u-+p-=O ax ax u au ax
+
1 ap p ax
=
(2v-la)
0
(2v-lb)
Equation (2v-la) leads to (2v-2) From Eqs. (2v-l) and (2v-2) we have (2v-3) Also, from (2v-lb),
~ u' +
J d:
=
(2v-4a)
canst
From the energy-conservation equation, it can be shown that
fU2'
+ H2
=
fU,2
+ H,
(2v-4b)
These equations lead at once to the Rankine-Hugoniot relations:
E, - E, =t:,.E
=
..!2 (p, + p,) (~ \Pl
H2 - H, = t:,.H = and
U, =
~
2
(P2 - p,)
~)
(2v-5a)
P2
(.!PI + P'.!)
)!
1 ( p, - PI ~ liP! - lip,.
-
(2v-5b) (2v-5c)
Equations (2v-5a), (2v-5b), and (2v-5c) are based solely upon hydrodynamics and
2-275
SHOCK WAVES
thermodynamics and are valid for all fluids. Further progress can now be made only when they are supplemented by an equation of state for the fluid. Special Cases. THE IDEAL GAS P
pR*T
=
From Eqs. (2v-5a), (2v-5b), and (2v-5c) and the equation of state it can be shown that P2('Y PI('Y P2('Y PI('Y P2Pl T, = PIP2
P!:.
PI P2 PI T2
and
+ 1) - PI('Y + 1) - P2('Y + 1) + PI('Y + 1) + P2('Y -
1) 1) 1) 1)
(2v-6a) (2v-6b) (2v-6c)
In terms of the Mach number of the incident shock JIll "
P!:. PI P2 PI
and LIQUIDS.
equation.
2M ,''Y - l' + 1 1'+1 M ,'( l' + 1) M,'('Y - 1)
(2v-7a) (2v-7b)
+2
An often-used equation of state for liquids, especially water, is the Tait A convenient form of it is P = B(S) [
G~~:~~r
B
Approximately
p,C,'
=
-
1]
(2v-8a) (2v-8b)
n
It is a good approximation in liquids to assume that the initial and final states are connected by an adiabatic compression. With this assumption,
u, where
=
c, ( 1
+1 ) + n~u
(2v-9a)
u= n~ [(~)(n-I)/' - 1J - 1 PI
(2v-9b)
Systems Subject to Chemical Reaction. The Rankine-Hugoniot relation, Eq. (2v-5a), is plotted in the (p, lip) plane in Fig. 2v-l with an adiabat for comparison. This relation is of course valid when the system reacts chemically, if the chemical energy is included in tJ.E. In this case the point (PI,PI) does not lie on the Rankine-Hugoniot curve, but either above or below it, depending on whether the chemical reaction is endothermic or exothermic. An especially interesting case, detonation, occurs when there is enough chemical energy alone to sustain the shock wave. Since the wave velocity is measured by the slope of the line through (PI,PI) which intersects the Rankine-Hugoniot curve [see Eqs. (2v-5)], there are usually an infinite number of possible velocities. However, in a steady-state detonation the lowest possible velocity, which corresponds to a line through (PI,PI) just tangent to the Rankine-Hugoniot curve, is the one that occurs. This is the Chapman-J ouguet condition: 1-3 ......
o
~
t"'
t?
t;j
"'J
10' 10 10' 10 5 10'
(lb per sq ft) per (cu ft per sec) (lb per sq ft) per (ft per sec) slug per (ft to the fourth power) (sl ug per ft to the fourth power) per sq sec (ft to the fifth power) per lb
59.61
Z H
6.366 X 10-' 59.16
>-3 ,.....
o
Z
[f1
59.16 1. 690 X 10-'
--
* Multiply a magnitude expressed in ega units by the tabulated conversion factor to obtain magnitude in mks units.
t Multiply a magnitude expressed in ega units by the tabulated conversion factor to obtain magnitude in British units. on the basis of standard acceleration due to gravity. Note: M, L, T represent mass, length, and time, respectively, in the sense of the theory of dimensions. mks rayl are proposed terms. Alternate terms and units are in square brackets.
These conversion factors were calculated
Mks mech,mical ohm, and mks acoustical ohm, rayl, and
cr' tv ~
3-30
ACOUSTICS
Note:.It is recommended that tuning and retuning of musical instruments be within an accuracy of plus or minus 0.5 Hz at the standard tuning frequency when the instruments are played where the ambient temperature is 22°0 (71.6°F).
Tone. (1) A tone is a sound wave capable of exciting an auditory sensation having pitch. (2) A tone is a sound sensation having pitch. Vibrato. The vibrato is a.family of tonal effects in music that depend upon periodic variations of one or more characteristics of the sound wave. Note: When the particular characteristics are known, the term "vibrato" should be modified accordingly: e.g., frequency vibrato, amplitude vibrato, phase vibrato, and so forth.
3a-12. Acoustical Units
Acoustical Units. In different sections of acoustics at least three systems of units are in common use: the centimeter-gram-second (cgs), the meter-kilo gram-second (mks) , and the British. Table 3a-3 is provided to facilitate conversion from one system of units to another.
3b. Standard Letter Symbols and Conversion Factors for Acoustical Quantities LEO L. BERANEK
Bolt Beranek and Newman Inc.
Symbols T a
w
p, a
a
absolute temperature, degrees Kelvin absorption, energy, acoustic, total in a room absorption coefficient, energy absorption coefficient, energy, average acoustic admittance (complex) acoustic compliance acoustic conductance acoustic impedance (complex) acoustic mass (inertance) acoustic power acoustic reactance acoustic resistance acoustic susceptance admittance, acoustic (complex) admittance, electric (complex) admittance, mechanical (complex) admittance, rotational (complex) admittance, specific acoustic (complex) amplitude of velocity potential angle, solid angular displacement angular frequency (2 ...f) angular wave number antiresonance frequency area (diaphragm, tube, room, or radiator) atmospheric (static) pressure attenuation constant (coefficient) average absorption coefficient, energy Boltzmann constant capacitance, electrical characteristic impedance charge, electrical circular wave number coefficient of absorption compliance, acoustic compliance, specific acoustic
3-(11
3-32
ACOUSTICS
OM OR ~, 7/.
k'j b,
~y, ~.
U, V, W; U z , U y , U z 8
GA
GE GM GR Gs K
i q; U Il
dB
E,w P
PO ~
Di R8 ~r,
x
~
X Il
r 8
compliance, mechanical compliance, rotational components of the particle displacement in the x, y, z directions components of the particle velocity in x, y, z directions condensation conductance, acoustic conductance, electric conductance, mechanical conductance, rotational conductance, specific acoustic conductivity, thermal current, electric current, volume (volume per second) (volume velocity) decay constant (damping coefficient) decibel density, energy density of the medium (instantaneous) density of the medium (static) dielectric coefficient dilatation directivity index directivity ratio displacement, angular displacement, linear displacement, particle displacement, volume dissipation (damping) coefficient (energy) distance from source distance, linear elasticity, shear electric admittance (complex) electric capacitance .
Q
GE i
ZE PE
XE RE P
BE e J
E,w T,EK
V,E p H
m B 1M, F
electric charge electric conductance electric current electric impedance (complex) electric power electric reactance electric resistance electric resistivity electric susceptance electromotive force, voltage_ energy energy density energy, kinetic energy, potential field strength, magnetic flare coefficient ina horn flux density, magnetirforl/e
STANDARD LETTER SYMBOLS
frequency frequency,angular (21rf) frequency, resonanee
f
'" fR ZA
impedance, acoustic (complex) impedance, characteristic acoustic impedance, electric (complex) impedance, mechanical (complex) impedance, rotational (complex) impedance, specific acoustic (complex) index of refraction inductance inertance, (acoustic mass) inertia, moment o'f intensity, sound intensity level, decibels
PoC
ZE ZM ZR Zs n L
MA I I,J L/
kinematic viscosity kinetic energy (inductive energy)
v
T,EK
leakage coefficient, magnetic length of a vibrating string, pipe, or rod level in' decibels, general linear displacement linear distance logarithmic decrement loudness, sones loudness level, decibels or phons
a-
l
L x,
~
8
A
N
LN H
magnetic field strength magnetic flux magnetic flux density magnetic leakage coefficient magnetomotive force magnetostriction constant, mass mass, acoustic mass, specific acoustic mechanical admittance mechanical compliance mechanical conductance mechanical impedance (complex) mechanical power. mechanical reactance mechanical resistance mechanical susceptance modulus of elasticity moment of inertia
B a5'
K
m,MM MA Ms YM eM GM ZM PM XM RM BM Y,E I
LNR
noise reduction, decibels number of turns
N ~ ~, 7],
Ua
3-33
1;;
~x, ~y, ~z
particle displacement particle-displacement components in the x, y, z directions particle velocity (average)
3-34
ACOUSTICS
u, v,
W; U:l:1 U Y1 U z
U, U'" Up U
P T ()
P fi;,
d'i
(Ji;,
tT
Y,P V,Ep cf>
P PA, WA
PE PM PR p. pa p, pm pp p 'Y = a
+ jp
particle-velocity components in the x, y, z directions particle velocity (instantaneous) particle velocity (maximum) particle velocity (peak) particle velocity (rms) perimeter period T = 11f phase angle phase constant (coefficient) piezoeiectric constants Poisson's ratio porosity (of an acoustical material) potential energy (capacitive energy) potential velocity power power, acoustic power, electric power, mechanical power, rotational pressure, atmospheric (static) pressure, sound (average) pressure, sound (instantaneous) pressure, sound (maximum) pressure, sound (peak) pressure, sound (rms) propagation constant (coefficient)
Q
quality factor
a
radius of a diaphragm, tube, or radiator ratio of reactance to resistance ratio of specific heats reactance, acoustic reactance, electric reactance, mechanical reactance, rotational reactance, specific acoustic· reflection coefficient, energy refraction, index of relaxation time reluctance resistance, acoustic resistance, electric resistance, mechanical resistance, rotational resistance, specific acoustic resistivity, electrical resonance frequency reverberation time room constant aSI(l - a) rotational admittance rotational compliance rotational conductance
Q 'Y
XA XE
XM XR Xs r n T
(R
RA RE RM RR Rs P
fR
T R
YR Otf.·
GR
STANDARD LETTER SYMBOLS
rotational rotational rotational rotational rotational
Ls /L
A {2
I,J Lp, LTV
pa Pi
PM pp P
Lp
A r
Ys Cs Gs
Zs Ms Xs
Rs 'Y C
s A, U o
BA BE BM BR Bs T
F K
T
T T a
'U
C
impedance (complex) power reactance resistance susceptance
sensation level, decibels shear elasticity, shear modulus (modulus of rigidity) simple source strength solid angle sound intensity sound power level, decibels sound pressure (average) sound pressure (instantaneous) sound pressure (maximum) sound pressure (peak) sound pressure (rms) sound pressure level, decibels source, simple, strength of source, distance from specific acoustic admittance specific acoustic compliance specific acoustic conductance specific acoustic impedance (complex) specific acoustic mass specific acoustic reactance specific acoustic resistance specific heats, ratio of speed of sound stiffness strength of a simple source susceptance, acoustic susceptance, electric susceptance, mechanical susceptance, rotational susceptance, specific acoustic temperature, absolute, kelvins tension (force) in a membrane or string thermal conductivity thickness time time, relaxation time, reverberation torque total acoustical (energy) absorption in a room transmission coefficient, energy, barriers transmission loss transmission loss of building structures, decibels turns, number of velocity velocity of sound
3-35
3-36
ACOUSTICS
velocity, angular velocity, particle (average) velocity, particle (instantaneous) velocity, particle (maximum) velocity, particle (peak) velocity, particle (rms) velocity potential . velocity potential amplitude velocity, volume viscosity, dissipative or frictional viscosity, kinematic voltage, electromotive force volume volume current; volume velocity volume displacement volume velocity; volume current
fJ)
Ua
u; Um 'Up 'U
.p A q, U 'f/
e" V q, U X q, U
k
wavelength wave number (phase constant),
w J
width work
Y,E
Young's modulus
A
TABLE
3b-1.
Multiply the number of
CONVERSION FACTORS FOR ACOUSTICAL QUANTITIES
To obtain the number of
By
.Acoustic ohms ........... 10 5 Atmospheres ............ 406.80 Centimeters ............. 10-' Cubic centimeters ........ 10- 6 Dynes .................. 10- 5 Dynes/cm' .............. 1(}-1 Ergs ................. : .. 10- 7 Ergs per second .......... 10- 7 Ergs per second/cm' ..... 10- 3 Gauss .................. 10- 4 Kilograms .............. 10 3 Mechanical ohms ........ 10- 3 Meters ................. 10' Microbars ............... 10-1 Newtons ................ 10 5 Newtons per square meter 10 Pounds per square foot ... 0.4882 Rayls .................. 10 10- 4 Watts per square meter .. Webers per square centimeter ................ 10 4
Conversely multiply by
Mks acoustic ohms Inches of water at 4°C Meters Cubic meters Newtons Newtons per square meter Joules Watts Watts per square meter Webers per square meter Grams Mks mechanical ohms Centimeters Newtons per square meter Dynes Dynes per square centimeter Grams per square centimeter Mks rayls Watts per square centimeter
10- 5 2.458 X 10-' 10' 10 6 10 6 10 10 7 10 7 10 3 10 4 10- 8 10 3 10-1 10 10- 6 10-1 2.0482 10-1 10 4
Gauss
10- 4
3c. Propagation of Sound in Fluids FREDERICK V. HUNT
Harvard University
3c-1. Glossary of Symbols'
B
c'
Cp ,
c.
d;i
D E,F,G,H E,Ek, E 1 ; E di•• f, f., f(
), f(h)
Af.
F;, F
g(h) h i, j, k I j
J k, ko K; K" K o, KT L M
nv N O( 1
)
material coordinate (31); surface element (12) surface (12), attenuation per wavelength (76), Avogadro's number (95); first order vector potential coefficient relating Vp and vp (58) speed of sound, reference speed (25); low- and high-frequency limit speeds (84) speed of thermal wave (78b) specific heats at constant pressure, constant volume (14) rate of deformation tensor (9) material differential operator (2) algebraic abbreviations (74) energy densities per unit mass (60), (12); degraded component of internal energy (66) frequency, sum of viscosity terms (62), "function of" (45), special tabulated function (75) critical bandwidth (98) vector body force per unit mass (6) tabulated function (75) material mass coordinate (37), argument of tabulated function (75), Planck's constant (89) coordinate indexes (1) average sound-energy-flux density = sound intensity (64) designation of imaginary axis, [e+ i ""] (69) sound-energy flux vector (54) phase constant = wlc = '27r/"A, Boltzmann's constant (89), ko = wlco = '27r/"Ao (47) elastic modulus = - V(DPIDV) (25), material constant = colc'" (84); isentropic modulus, reference modulus, isothermal modulus mean free path (86), a sum of linear dimensions (90) peak particle-velocity Mach number = w~olco (49), molecular weight (95) total number of molecules per unit volume (95) number of modes of vibration (90) additive terms of indicated order of magnitude (76)
Numbers indicate equation number in or near which quantity is defined. 8-37
3-38
ACOUSTICS
q, qi; q
q; qE, qL
R, R; R " R2 S, 81
S; S';
Sirr
incremental, or sound, pressure; first- and second-order sound pressures (25) total pressure (7), equilibrium or reference pressure (25); mean pressure (7), thermodynamic pressure (14) rms fundamental and second-harmonic pressure (49a); Prandtl number (72) heat flux vector (12); Stokes radiation coefficient (21b) exemplar of state or condition variable (39); superscript indicates function of spatial (E) variables, or material (L) variables (32b) vorticity = ~V X U (lld), real part of complex impedance; first- and second-order components of vorticity (57) specific entropy per unit mass (14), first-order condensation = pdPo (59) Stokes number = w'Il poco2 (72), total interior surface (90); frequency number for radiation = wlq (72); entropy generated irreversibly (15a)
u,
Ul; 'Ut, U20 U3
U" U2
V; V 'D
V; Vi; Xl, X2, Xa
XiX' y z, Z a; ax, Ole
time (2); stress tensor (6) absolute temperature (14) particle velocity (1); velocity components first- and second-order components of particle velocity (25) specific volume = p-l (1); mean molecular velocity (86) viscosity number = 2 + '1'1'1 (10) volume (1); residual stress tensor (7) cartesian coordinates (1) frequency number = W'l'D I poco 2 (72), specific acoustic reactance (69); frequency number for relaxation (84) thermoviscous number = KI'I'DC p (72) specific acoustic impedance ratio (87), and impedance (69) attenuation constant (69); "Kirchhoff" and "classical" attenuation (79a,b)
[3; [3noiee 'Y
0; iii;; A 'I, 'I',
'IB
0 Ih " K
A; Ao
,
P, 11 ,
JIB
~; ~t
TT, Tv, Tk
'Pe;
cf>~,
cf>k
x if; W; Wn Wv, Wk
V,V·,V X
< )
coefficient of thermal expansion = p(avlaT)p (22); spectrum level 10 109,o [d(p2 Ipo2) Idfl (98) ratio of specific heats = CpIC. (14) finite increment (32); Kronecker delta (7); dilatation rate = V . U (4) specific internal energy per unit mass (13) coefficient of shear viscosity (10), "second" or dilatational viscosity (10), bulk viscosity (10) first- and second-order variational components of temperature (25) thermal conductivity (21a) wavelength = clf (47); AO = coif kinematic viscosity coefficients (10) = 'II p, etc. displacement of particle from equilibrium (31); partial derivative with respect to subscript variable (41b) densities: total, equilibrium; first- and second-order variational components relaxation times (83, 85) scalar velocity potential (55); viscous and thermal dissipation functions (16, 18) complex propagation constant = '" jk (69) functional relation (71) angular frequency = 2",/; relaxation angular frequencies (84) gradient, divergence, and curl operators time average
+
PROPAGATION OF SOUND IN FLUIDS
3c-2. The Motion of Viscous Fluids. The motions of a fluid medium that comprise sound waves are governed by equations that include (1) a continuity equation expressing the conservation of mass, (2) a force equation expressing the conservation of momentum, (3) a heat-exchange equation expressing the conservation of energy, and (4) one or more defining equations expressing the constitutive relations that characterize the medium and its response to thermal or mechanical stress. These equations will first be presented in their complete exact form in order to provide a rigorous point of departure for the approximations that must ultimately be made in formulating the linearized, or small-signal, acoustic equations. The transformation properties of these equations can be indicated by writing them in either vectorial or tensorial form, and both forms will be exhibited in order to facilitate contacts with the rich literature dealing with the motion of fluids. 1 Cartesian spatial coordinates will be designated Xl, X2, X3, and the vector velocity of a material particle will be identified as u with components Ul, U2, U3' These will also be written as Xi and Ui, where it is implied that the subscript i, j, or k takes on successively the values 1, 2, 3. The term "material particle" denotes a finite mass element of the medium small enough for the values assumed by the state variables at every interior point of the particle not to differ significantly from the values they have at the interior reference point whose coordinates "locate" the particle. Equation of Continuity. The conservation of mass requires that pV = poV o, where Po and Va are initial and p and V are subsequent values assumed by the density and volume of a particular material element of the medium. It follows that
pDV
+ VDp
= 0
DV
--y=
Dp p
(3c-I)
If pa Va is set equal to 1, Va becomes the specific volume, v == lip; whence the relation between the total logarithmic time derivatives of v and p is 1 Dv
vDt =
1 Dp
- PDt =
D log v
-----nt
=
D log p
----nt
(3c-2)
where D( )IDt denotes the "material" derivative, i.e., one that follows the motion of a material "particle" of the medium relative to a fixed spatial coordinate system, and is defined by
~ ==~ Dt at
+u'grad (
)==~+U,~ at ax,
~3c-3)
Analysis of the rate of deformation of a volume element yields the kinematical relation
! Dv
v Dt
=
div u == ~
=
au,
ax,
(3c-4)
where ~ is the dilatation rate. Note that in the last terms of (3c-3) and (3c-4) summation is implied over all the allowable values of the subscript index. Equations (3c-2), (3c-3), and (3c-4) can be combined to yield the following equivalent forms of Euler's continuity equation: 1 A definitive restatement of the classical-continuum point of view, with critical comments on more than 800 bibliographical references, has been given by C. Truesdell, The Mechanical Foundations of Elasticity and Fluid Dynamics, J. Rational M echanic8 and Analysis 1, 125-300 (January and April, 1952), and Corrections and Additions . . . , J. Rational Mechanic8 and Analysi8 2, 593-616 (July, 1953). See also Lamb, "Hydrodynamics," 6th ed., Dover Publications, New York, 1945; Rayleigh, "Theory of Sound," 2d ed., rev., Dover Publications, New York, 1945; and L. Howarth, ed., "Modern Developments in Fluid Dynamics," voL I, chap. III, Oxford University Press, New York, 1953.
ACOUSTICS
ap
ap
aUt
Dp.
.
at + u, ax, + p ax, = Dt + p dlv U. = 1 Dp ap . = -pDt - + A = -at + u . grad p + p dlv U
=
=
ap at
+ u· vp + pV' U
=
ap at
+ V· (pu)
0
(3c-5)
In the last line of (3c-5), the Gibbs-Hamilton notation has been used for the differential vector operators, V "" grad; V . "" div j V X "" curl. Force Equation. The linear-momentum principle can be stated in terms o( Cauchy's first law of motion, (3c-6) where the vector F, is an extraneous body force per unit mass, and where tit is a secondrank stress tensor that represents the net mechanical action of contiguous material on . a volume element of the medium due to the actual forces of material continuity. For l1n isotropic medium in which the stress is a linear function of the rate of deformation, as here assumed, the stress tensor can be resolved arbitrarily as the sum of a scalar, or hydrostatic, pressure function P and a residual stress tensor V,; defined by tit = -Po,;
+ V,;
tit
=
t;;
(3c-7)
where 0,; is the Kronecker delta which equals unity if i = j, but is zero otherwise. Unless Vii vanishes, P is not identical with the mean pressure, Pm = -itii. The resolution given by (3c-7) is both unique and useful, however, if P is made equal to the thermodynamic pressure P th defined below. Then the residual stress tensor is given, to a first approximation, by the linear. terms of an expansion in powers of the viscosity coefficients, (3c-8) V'i = Vi' in which d,; is the rate of deformation tensor defined by di ;
=
~ (aui 2
ax;
i) + aU ax,
(3c-9)
and where", is the "first," or conventional shear, viscosity coefficient. In accordance with current proposals for standardization, ",' replaces A, the symbol used by Stokes, Rayleigh, Lamb, et al., to designate the "second," or dilatational, viscosity coefficient. The term "bulk" viscosity is reserved for (A + i.u) ---+ (",' + i",), the linear combination of coefficients that vanishes when the Stokes relation holds. Thus, '1 "" first, or shear, viscosity j r/ "" second, or dilatational, viscosity j '1B "" ",' + i'1 = bulk viscosity; l' "" '1/p; p'"" '1 ' /pj VB"" rlB/p (kinematic viscosities); (A
G
+ 21') --> '1' + 2'1 = '1B + : '1 = '1 + '::) = '1'0 '0 "" 3~ + '1B = 2 + :L "" viscosity number '1 ",
(3c-1O)
Putting (3c-7), (3c-8), (3c-9) into (3c-6) yields the vector force equation in the following equivalent forms: au,
aUi
Pat: +pu; ax; =pFi =
pF, (3c c lla)
PROPAGATION OF SOUND IN FLUIDS p
~~
p
~~
=
=
+ (-'I' + 1]) grad (div u) + 1]V2(U) + (div u) grad 1]' + 2 (grad 1] - grad) u + grad 1] X curl u p(u . V)u - vp + (1]' + 21])V(V . u) - 1]V X (v X u) + (V' u)V1]' + 2(V1] . V)u + V1] X (v X u)
3-:-41
pF - grad P
pF -
(3c-lIb)
(3c-He)
The vorticity, defined by R = j curl u = j(v X u), and the dilatation rate, ,:; == V . u, can be introduced as useful abbreviations. A somewhat more symmetrical expression in terms of the mass transport velocity pU is obtained if the last form of the continuity equation (3c-5) is multiplied by u and added to (3c-lIe), giving
a~~) + u(V' pU) + (pu' v)u
=
pF - vP
+ 1]'OV':; - 2~v X R + ,:;V1]' + 2(V1] . v)u + 2V1] X R
(3c-lId)
These equations reduce to the so-called Navier-Stokes equations when it is assumed that 1] and 1]' are constant (V1] = V1]' = 0) and that the Stokes relation holds (1]B = 0, '0 = ~); and still further simplification follows if the motion is assumed irrotational so that R = O. If the viscosity coefficients are to be regarded as functions of one or more of the state variables, however, the gradients of the ~'s must be retiLinEid so that the implicit functional dependence can be introduced by writing, for example, V1] = (a1]/aT)vT + .... Energy Relations and Equations ofllState. The conservation of energy requires that the following power equation be sati"Sfied:
+
D(EkDt Er) =
r pFiUi dV + lv
f
it tiiui dai -
1 A
qi da;
(3c-12)
where Ek is the kinetic energy associated with the material velocity, Er is the total internal energy, V is a volume bounded by the surface A, da; is the projection of a surface element of A on the plane normal to the +Xi axis, F, is the extraneous body force (per unit mass), and qi is the total heat flux vector (mechanical units). After the surface integrals are converted to volume integrals by using the divergence theorem, and with the help of (3c-6), this equation reduces to the Fourier-Kirchhoff-C. Neumann' energy equation, D. 'aqi p Dt = tiidii - ax,
(3c-13)
where. is the local value of the specific internal energy (per unit mass) defined through Er =
Iv
P€
dV.
It is now postulated that the state of the fluid is completely specified
by • and two other local state variables, which can be taken as the specific entropy s (per unit mass) and the specific volume v = in terms of which the thermodynamic pressure and temperature, and the specific heats can be defined by
p-"
• = .(s/v)
p (:;)p
(3'c-14)
C == T
The second law of thermodynamics can be introduced in the form of an equality, which replaces the classical Clausius-Duhem inequality, through the expedient of accounting explicitly for the creation of entropy Sirr (per unit volume) by irreversible 1
See footnote, p. 3-39.
ACOUSTICS
dissipative processesjl thus D Dt
f
V
psdV = -
f
~da·
AT'
+ Jv ( DBirrdV Dt
(3c-15a)
This relation states that the increase of entropy in a material element is accounted for by the influx of heat and by the irreversible production of entropy within the element. The left-hand side of (3c-15a) can also be written, with the help of the continuity relation, as
Iv
p(Ds/ Dt) dV.
Then, after converting the surface integral to a volume
integral, the second law can be given in differential form as , Ds _ ...!!- ~ + DBirr p- = ox, T Dt De _ 1. oq, + q, oT + DBirr T ox,
T2 ox,
Dt
(3c-15b)
A thermal-dissipation function q,k can be defined by (3c-16) whereupon multiplying (3c-15b) by T yields the second-law equality in the form (3c-15c)
Taking the material derivative of the basic equation of .state (3c-141) (where the subscript added to an equation number indicates the serial number of the equality sign to which reference is made when sev:eral relations are grouped under one marginal identification number), introducing the definitions for P th and T, multiplying by p, and using (3c-4), gives Ds D. (3c-17) pT Dt = p Dt +Pthtl The energy equation (3c-13) can be recast, using (3c-7) an(3cr9), in the form (3c-18) in which V,jd'j, the dissipative component of the stress power t'jd,j, is defined as the viscous dissipation function q,~. The usefulness of specifying the arbitrary scalar in (3c-7) as the thermodynamic pressure, so that P; = P th, becomes apparent when p~l)./Dt-is eliminated between (3c-18) and (3c-17), giving pT Ds = (Pth _ P)tl Dt = ~ _
+ q,~
oq. ox;
_ Oqi
ox;
(3c-19)
The viscous dissipation function (dissipated energy per unit volume) is thus seen to account for either an effiux of heat or an increase of entropy. Subtracting (3c-19) from (3c-15c) then allows the rate of irreversible production of entropy to be evaluated directly in terms of the two dissipation functions,
TD~t
=
~ + q,.
(3c-20)
The total heat:iflux vector q., whose divergence is the energy transferred away from the volume element, must account for energy transport by either conduction or radii Tolman and Fine, Revs. Modern Phys. 20, 51-77 (1948).
37""43
PROPAGATION OF SOUND IN FLUIDS
ation. The part due to conduction is given by the Fourier relation, which serves also to 'define the heat conductivity K,
(3,c-21a) The last term, containing the gradient of K, must be retained if implicit dependence of Kon the state variables is to be represented. On the other hand, if Kis assumed to be constant, (3c-21a) reduces to the more familiar form
The component of heat flux due to radiation can be approximated, for small temperature differences, by Newton's law of cooling,
a(q')r.d = P.q C (T -,,-uXi
- T 0)
= V'qrad .
(:;k-21b)
where (T - To) is the local temperature excess and q is a radiation coefficient introduced by Stokes'! The foregoing thermal relations can be combined with the equations of continuity and momentum more readily if the term T(D8/ Dt) appearing in (3c-19) is expressed in terms of the variables u, v, and T. The defining equations (3c-14) establish that P = P(v,8)'and T = T(V,8) , from which it follows that one may also write 8 = 8(T,v) or B = 8(T,P). Using both of the latter leads; after some, manipulation,' to the identity !:J. pT DB Dt = pC. [ ('Y - 1) ~
+ DT] Dt
(3c-22)
in which # is the coefficient of thermal expansion, # == p(av/aT)p. Mter (3c-22) and (3c-21) are'combined with (3c-19), the energy equation can be written in the alternate, forms, pC.DT + pC. 'Y - 1 au; + aqi _ q", = 0 Dt # ax, aXi
pC~ (~~ + U' VT)
+ p(C p ; ; C.) !:J. - V • (KVT) + pC.q(T - To) -
aT +u'VT + ('Y -1)!:J. __K_V2T _ VT'VK +q(T _ To) at # pC. pC. The viscous dissipation function (3c-9) in the explicit form ~ =
=
_.:hi.... = pC.
0 (3c-23) 0
can be evaluated, with the aid of (3c-8) and
= '1/'d d;; + 2'1/diidi; + i'1/ [(aul)2 + (aU2)2 + (aus)'
Viidii
= '1/B!:J.'
~
~
kk
3
_ aUl aU2 _ aU2 aus _ aus aU1] aXl aX2 axs aXl aX2 aX2 axs axs aXl U + '1/ [(aUl + aU2)2 + (a 2 + aus)2 + (aus + aUl)2] (3c-24a) aX2 aXl axs aX2 aXl axs
The thermal dissipation function . due to heat conduction can be evaluated, with the aid of (3c-16) and (3c-21a), in the form .=
qi aT= -Tax,
(aT)2 +-Tax, K
K • =_(VT)2
T
(3c-24b)
It does not appear explicitly in (3c-23), but it is there implicitly as a consequence of the heat-transfer processes described by (3c-23). lPhil. Mag. (4) 1,305-317 (1851). • See, for example, Zemansky, "Heat and Thermodynamics," 3d ed., pp. 246-255, McGraw-Hill Book Company, New York, H151.
3-"44
ACOUSTICS
Summary of Assumptions. The fluid considered is assumed to be continuous except at boundaries or interfaces, locally homogeneous and isotropic when at rest, viscous, thermally conducting, and chemically inert, and its local thermodynamic condition is assumed to be completely determined by specifying three "state" variables, any two of which determine the third uniquely through an equation of state. No structural or thermal "relaxation" mechanism has been presumed up to this point in the analysis, except to the extent that ordinary heat conduction and viscous losses may be described in such terms. Local thermodynamic reversibility has been assumed in using conventional thermodynamic identities based on the second law, but the irreversible production of entropy by dissipative processes has been accounted for explicitly. It is also assumed that the stress tensor is a linear function of the rate of deformation, and that the tractions due to viscosity can be represented by the linear terms of an expansion in powers of the viscosity coefficients. The viscosity and heat-exchange parameters of the fluid '1], '1]', K, and q. may depend in'any continuous way on the state variables and hence may be implicit functions of time' and the spatial coordinates. Within the scope thus defined the equations given are exact. The functional dependence on time and the spatial coordinates of the condition and motion variables P, T, p, and u can be evaluated, in a formal sense at least, by solving the set of four simultaneous equations connecting these variables [Eqs. (3c-5), (3c-11), (3c-23), and (3c-15) or one of its alternates]. No general solution of these complete equations has been given, however, and one or another of the least important terms is usually omitted in order to render the equations tractable for dealing with specific problems. 3c-3. The Small-signal Acoustic Equations. The physical theory of sound waves deals with systematic motions of a material medium relative to an equilibrium state and thus comprises the variational aspects of elasticity and fluid dynamics. Such perturbations of state can be described by incremental, or acoustic, variables and approximate equations governing them can be obtained by arbitrarily "linearizing" the general equations of motion. These results, as well as higher-order approximations, can be derived in an orderly way by invoking a modified perturbation analysis. 1 This consists of replacing the dependent variables appearing in (3c-5), (3c-11), and (3c-23) by the sum of their equilibrium or zero-order values and their .first- and secondorder variational components, and then forming the separate equations that mus~. be satisfied by the variables of each order. Two of the composite state variables, for example P and T, can be defined arbitrarily, whereupon the third, P, is determined by the functional equation of state. These definitions, some self-evident manipulations, and the subscript notation identifying the orders can be exhibited as follows:
+ + +
+ + + + + + [G~)Jo (T - T~) +
P "" Po Pl P. T "" To 01 02 Vp = VPl VP. VT = VOl VO. P(p,T) "" Po(po,To) PI p.
PI
K=
KT "" P
+ P2
=
(iJP) iJp
[(~~)Tl (p
- po)
Co' ""
T
[(iJP) ] "" (K.)o iJp • PO 0
Co' Co 2 PI = - (PI ~OPOOl) p. = - (P' ~OP002) 7 7 U "" 0 Ul U. V • U "" LI. "" Ll.l LI.. = V • Ul V • U2 pU = [poudl [PlUl poU.]. V' (pU) = [poV • ulh (PIV • Ul UI • VPl poV • U2].
+
+
+
+
1
+
+
Eckart, PhY8. Rev. 73, 68-76 (1948).
+ +
+
+ ... +
+ +
(3c-25)
PROPAGATION OF SOUND IN FLUIDS
3-45
Terms containing Vpo have been omitted in writing out V • (pu), on the assumption that po, To, and Po are constant and Uo = O. The reference state need not be so restricted to one of static equilibrium provided its time and space rates of change are presumed small in comparison with the corresponding change rates of the acoustic variables. The extraneous body force F will also be omitted hereafter; it would become important in cases involving electromagnetic interaction, but it usually derives from a gravitation potential and affects primarily the equilibrium configuration. l Little generality is sacrificed by omitting F and assuming a static reference, moreover, since the basic equations characterize directly the equilibrium condition and since the "cross-modulation" effects brought in by nonlinearity are dealt with adequately through second- or higher-order approximations. Notice that the foregoing represents a mathematical-approximation procedure that is concerned only with the precision achieved in interpreting the content of the basic equations. The accuracy with whioh the basic equations themselves delineate the behavior of a real fluid is an entirely different quesLion that must be considered independently on its own merits. It follows that,while good judgment may restrain the effort, there is no impropriety involved in pursuing higher-order solutions of the acoustic equations, even though the equations themselves may embody first-order approximations to reality such as that represented by assuming linear dependence on the viscosity coefficients and the deformation rate. When the appropriate relations from (3c-25) are substituted in (3c-5), (3c-ll), and (3c-23), the first-order acoustic equations can be separated out in the form apl at + po(V • Ul) co 2 (1V OVPl l ) VPl at + -:y + {3opo
po aUl
poC.
alit at + poCv('Y{30 -
-
=
+ 1) V X (V X Ul) = KOV 20 l + POCvqOl = 0
(1)o'D)V(V' Ul)
1)
(V . Ul) -
(3c-26a)
0 O
0 (3c-26b) (3c-26c)
Inasmuch as the first-order effects of both shear and dilatational viscosity and of heat cOllduction and radiation have been included, these equations comprehend a viscothermal theory of small-signal sound waves. The sound absorption and velocity dispersion predicted by this theory are discussed below. Note especially that taking heat exchange into account explicitly by including (3c-26c) has precluded the conventional adiabatic assumption and denied the simplifying assumption that P = pep). Adiabatic behavior would be assured, on the other hand, if it were assumed at the outset that K = q = 0, but the behavior would not at the same time be strictly isentropic so long as irreversible viscous losses are still present and accounted for. The difference between adiabatic and isentropic behavior in this case is of second order, however, as indicated by the fact that the second-order dissipation functions '" do not appear in the first-order energy equation (3c-26c), which is thereby reduced to yielding just the isentropic relation between dilatation and excess temperature. It is allowable, therefore, in this first-order approximation, to replace the quotient (vedVpl) appearing in (3c-26b) with the isentropic derivative (aT lap). = (I' - 1) I p{3, whereupon the first-order equation of motion for an adiabatic viscous fluid can be written as (3c-27) If the effects of viscosity, as well as of heat exchange, are to be neglected, the divergence of what is left of (3c-27) can be subtracted from the time derivative of (3c-26a) 1 But, for a case in which F and Vpo cannot be neglected, see Haskell, J. Appl. Phys. 22,157-168 (February, 1951).
3-46
ACOUSTICS
to yield the typical small-signal scalar wave equation of classical acoustics,
e:),
a;;'1 =
(3c-28a)
V'P1
and, with the help of the first-order isentropic relation P1 = CO'(P1)" this wave equation becomes, in terms of the sound pressure, (3c-28b) 3c-4. The Second-order Acoustic Equations. The same substitution of composite variables that delivered (3c-26a), (3c-26b), and (3c-26c) will also yield directly the second-order equations of acoustics, which can now be marshaled as follows:
ap. at Po
+ po(V . u.) + V' (P1U1)
=
(3c-29a)
0
au. + --ata(P1ul) at + POU1 (V • u,) + Po (U1 . V) 111 + Co''Y (1 + (3oPo vp, VII,) vp, - '7o'Ov(v . u,) + 2'70(V
X R.)
- (V'7~)(V . U1) - 2(V'71 . V)U1 - 2(V'71) X R1
ao. + 111 • (V01) + 'Y at
-;;
1 (V . 112)
,.,0
The subscripts appended to generic form '7(T,
p, . • • ) =
K
-
=
0
(3c-29b)
KC V'1I 2 O
Po
v
and the '7's imply that each may be expressed in the
'7o(T o, po, . . . )
+ '71
a'7 aT 111
'71 = -
a'7 + -ap P1 + . ..
(3c-30)
No general solution of these complete second-order equations has been given, but they provide a useful point of departure for making approximations and for investigating some second-order phenomena that cannot be predicted by the first-order equations alone. 3c-6. Spatial and Material Coordinates. Equations (3c-26) and (3c-29) are couched in terms of'the local values assumed by the dependent variables p, P, T, and u at places identified by their coordinates Xi in a fixed spatial reference frame, commonly called Eulerian coordinates (in spite of their first use by d' Alembert). As an alternate method of representation, the behavior of the medium can be described-in terms of the sequence of values assumed by the dependent condition and state variables pertaining to identified material particles of the medium no matter how these particles may move with respect to the spatial coordinate system. The independent variables in this case are the identification coordinates ai, rather than the position coordinates; the latter then become dependent variables that describe, as time progresses, the travel history of each particle of the medium. Such a representation in terms of material coordinates is commonly called Lagrangian (in spite of its first introduction and use by Euler). The Wave Equation in Material Coordinates. The use of material coordinates can be demonstrated by deriving the exact equations governing one-dimensional (planewave) propagation in a nonviscous adiabatic fluid. Consider a cylindrical segment of the medium of unit cross section with its axis along +x, the direction of propagation, and let X and x + ilx define the boundaries of a thin laminar "particle" whose undisturbed equilibrium position is given by a and a + aa. The difference x - a = ~ defines the displacement of the a particle from its equilibrium position and provides a convenient incremental, or acoustic, dependent variable in terms of which to describe
PROPAGATION OF SOUND IN FLUIDS
the position, velocity, and acceleration of the particle; thus
x(a,t)
=
a
ax _ L _ a~ at - u (a,t) - at
+ ~(a,t)
(3c-31)
Continuity requires that the mass of the particle remain constant during any dis. placement, which means that (3c-32a) or, for three-dimensional disturbances and in general,
Po a(Xl,X2,XS) pL = a(al,a2,aS)
(3c-32b)
in which the symbolic derivative stands for the Jacobian functional determinant. The superscript L is used here and below as a reminder that the dependent variable so tagged adheres to, or "follows" in the Lagrangian sense, a specific particle, and that it is a function of the independent identification coordinates. When not so tagged, or with superscript E added for emphasis, the state variables p, P, T and the condition variable u are each assumed to be functions of time and the spatial coordinate x. The net force per unit mass acting on the particle at time't is - (pL)-laPL / ax, where pL and pL are the density and pressure at x, the" now" position of the moving particle. However, inasmuch as x is not an independent variable in this case, the pressure gradient must be rewritten as (apL/aa) (aa/ax), from which the second factor can be eliminated by recourse to (3c-32a). The momentum equation then becomes just poa2~
at2
-aPL
=aa
(3c-33)
The adiabatic assumption makes available the simplified equation of state, P = P(p), and this relation, in turn, allows the material gradient, apL / aa, to be written as (3c-34)
aa from which the last factor can be eliminated by using (3c-32a) again; once to the exact wave equation 1 a2~ = (CpL) 2 a2~ = c2
at 2
aa 2
Po
(1 + aaa~)-2 aaa2~2
This leads at
(3c-35)
The pressure-density relation for a perfect adiabatic gas is P = Po(p/ po)'Y, from which it can be deduced that
c2 = (ap) ap.
=
,,(Po Po
(.!!-)' Y-l = Po
co2
(.!!-)' Y-l Po
(3c-36)
No generalization of comparable simplicity is available for liquids. 2 )Vb.en (3c-36) is introduced in (3c-35), the exact "Lagrangian" wave equation fo>; an adiabatic perfect gas becomes a2~ (pL)'Y+1 -a2~ = co 2 ( 1 J.. -a~)-('Y+1) -a2~ (3c-37) = co 2 at 2 Po aa 2 aa aa 2 In the Lagrangian formulation illustrated above, the choice of a, the initial-position coordinate, as the independent variable is useful but any other coordinate that Rayleigh, "Theory of Sound," vol. II, §249; Lamb, "Hydrodynamics," §§13-15, 279-284. But see Courant and Friedrichs, "Supersonic Flow and Shock Waves," p. 8, Interscience Publishers, Inc., New York, 1948. 1
2
3-48
ACOUSTICS
identifies the particles would serve the same purpose. For example, the particle located momentarily at x can be uniquely identified by the material coordinate h ""
fox
p
dx, whcre h represents the mass of fluid contained between the origin and
the particle. Inasmuch as this included mass will not change as the particle moves, the use of h as an independent" mass" variable automatically satisfies the requirements of continuity, with some attendant simplification in the analysis of transient disturbances. In the undisturbed condition, P = PO and x = a, whence the relation a = hiPO allows the independent variables to be interchanged by direct substitution in (3c-37). Material and Spatial Coordinate Transforms. It is useful to have available a systematic procedure for converting a functional expression for one of the state variables from the form involving material coordinates to the corresponding form in spatial coordinates, or the inverse. One should avoid, however, the trap of referring to the state variables themselves as Lagrangian or Eulerian quantities; density and pressure, for example, are scalar point functions that can have only one value at a given place and time. On the other hand, it is of prime importance to distinguish carefully (and to specify!) the independent variables when computing the derivatives of these quantities. The E and L functions are tied together by the displacement variable ~, which provides a single-valued connection between the a particle and its instantaneous position coordinate x and which may therefore be regarded as a function of either of its terminal coordinates a or x. This can be indicated [cf. (3c-31)] by writing x(a,t) = a + Ha,t), or the inverse relation a(x,t) = x - Hx,t) , from which follow the alternate expressions a = x -
Ha,t)
x = a
+ Hx,t)
(3c-38)
The desired coordinate transforms can then be established by means of Taylor series expansions, the two forms following according to whether the expansion is centered on the instantaneous partiCle position or spatial coordinate x, or on the particle's equilibrium position or material coordinate a. Thus, if q is used to represent anyone of the variables p, P, T, or u, one of the expansions can be based on the obvious identity qL(a,t) =
qE(X,t)"~a+~(".t)
= qE (X,t)"~a
+ [Hx,t)
aqE (x,t)] ax "~a
+ 1: [~2(x,t) a2qE (~,t)] 2
ax
"~a
+...
(3c-39)
Note that all terms on the right of (3c-39) are functions of the spatial coordinates and that each is to be evaluated at the equilibrium position coordinate a. This transform yields, therefore, the instantaneous value in material coordinates of the variable represented by q, in terms of the local value of q modified by correction terms (comprising the succeeding terms of the series) based on the spatial rate of change of q and the instantaneous displacement. The inverse transform is derived in a similar way from the identity qE(X,t) =
[qL(a,t)]a~"_i;(a.t)
qE(X,t) =
[qL(a,t)]a~" - [Ha,t) aqL(a,t)] aa
a~"
+1: [~2(a,t) a2qL(~,t)J 2
aa
a~"
-
. . . (3c-40)
In symmetrical contrast with (3c-39), all terms on the right in (3c-40) are functions of the material coordinates and are to be evaluated for a = x. This transform, therefore, yields the instantaneous local value of the variable q at the place x, in terms of the instantaneous value of q for the now-displaced particle whose equilibrium position or material coordinate is a = x, modified by the succeeding terms of the series in accordance with the material-coordinate rate of change of q and the instantaneous displacement.
3-49
PROPAGATION OF SOUND IN FLUIDS
The transforms (3c-39) and (3c-40) indicate that the differences between qL and qE are of second order, which explains why the troublesome distinction between spatial and material coordinates does not intrude when only first-order effects are being considered. It also follows that the first two terms of these transforms are sufficient to deliver all terms of qL or qE through the second order. The use of these transforms can be illustrated by writing them out explicitly for u and p, including all second-order terms, 'ilL ;: ~, u E = 'ilL - ~UaL = ~, - ~~ta (3c-4Ia) pL = Po (I + ~a)-' = po(l - ~a + ~a2 - . • . ) pE = po(l - ~a + ~a2 + Haa) = poll - ~a + (Ha)aJ (3c-4Ib) in which the subscripts indicate partial differentiation with respect to a or t. The product of (3c-4la) and (3c-4Ib) gives at once the relation between the material and spatial coordinate expressions for the mass transport pu; thus, through second order, pEU E = pLu
-
HpLuL)a
+ e(paLU a L )
= po[~t -
(H,)a]
=
po[~ -
Halt
(3c-42)
It is then straightforward to show that, if the particle velocity w is simple harmonic, the time average of the local mass transport pEU E will vanish through the second order, even though the average value of u E is not zero. Note, however, that the displacement velocity ~, is measured from an equilibrium position that is here assumed to be static; the average mass transport may indeed take on nonvanishing values if the wave motion as a whole leads to gross streaming (see Sec. 3c-7). :"c-6. Waves of Finite Amplitude.' A distinguished tradition adheres to the study of .the propagation of unrestricted compressional waves. That the particle velocity is forwarded more rapidly in the condensed portion of the wave was known early (Poisson, 1808; Earnshaw, 1858; Riemann, 1859); and that this should lead eventually to the formation of a discontinuity or shock wave was recognized by Stokes (1848), interpreted by Rayleigh,2 discussed more recently by Fubini,3 and has been reviewed still more recently with heightened interest by modern students of blast-wave transmission. 4 By virtue of the adiabatic assumption underlying P = P(p), the speed of sound is also a function of density alone and may be approximated by the leading terms of its expansion about the equilibrium density: c2 =. co 2 [ 1 -
2~a Po Co
(DC) Dp
0
+ ... ]
(3c-43)
When (3c-43) is introduced in the exact wave equation in material coordinates, (3c-35), the latter can be recast in the following form, using the subscript convention for partial differentiation and retaining only, but all, terms through second order:
~tt
-
C02~aa
= -co 2 [
1
+ ~ (~~)
J (~a2)a
(3c-44)
If it is then assumed that an arbitrary plane displacement HO,t) = f(t) is impressed at the origin, it can be verified by direct substitution that a solution of (3c-44) is
Ha,t) =
f
(t -!::) + ~ [1 + i'.!l (DC) ] [f' (t - !::)J2 Dp CO
2c0 2
Co
0
(3c-45)
Co
The density variations associated with these disphwements are to be found by entering (3c-45) in (3c-32), and the variational pressure can then be evaluated in terms of the adiabatic compressibility of the medium. Relatively more attention has been devoted to the analysis of solutions of (3c-37) for the case of an adiabatic perfect gas. For an arbitrary initial displacement, as 1 For more recent developments see Sec. 3n, Nonlinear Acoustics (Theoretical), pp. 3-183 to 3-205. 2 "Theory of Sound," vol. II, §§249-253. Proc. Roy. Soc. (London) 84, 247-284 (1910). 3 Alta Frequenza 4, 530-581 (1935). 'See also Sec. 2y of this book, Shock Waves, pp. 2-273 to 2-278.
.
3-50
ACOUSTICS
above, the solution of the corresponding wave equation (3c-37), again including all terms through second order, is Ha,t)
=
I
(t -!!.) + ~ 2co' Co
'Y
+ 1 [I' (t 2
- !!.) J'
(3c-46)
Co
Technological interest in this problem centers on the generation of spurious harmonics, which can be studied by assuming the initial displacement to be simple harmonic, viz., I(t) = ~o(l - cos wt) at the origin. The solution then takes the explicit form Ha,t) =
~o[l
- cos (wt - koa)]
+ -1 ko'~o2a[1 + -'Y 8
- cos 2(wt - koa)]
(3c-47)
in which ko is written for the phase constant, ko = w/co = 27r/Ao, The most striking feature of the solutions (3c-45) and (3c-47) is the appearance of the material coordinate a in the coefficient of the second-harmonic term. As a consequence, the condensation wave front becomes progressively steeper as the wave propagates, the energy supplied at fundamental frequency being gradually diverted toward the higher harmonic components. The compensating diminution of the fundamental-frequency component would be exhibited explicitly if third-order terms had been retained in (3c-46) and (3c-47) inasmuch as all odd-order terms include a "contribution" to the fundamental. When such higher terms are retained it is predicted that propagation will always culminate in the formation of a shock wave at a distance from the source given approximately by a == 2~o/ (-y + l)M', where M is the peak value of the particle-velocity Mach number.l On the other hand, when dissipative mechanisms are taken into account, the fact that attenuation increases with frequency for either liquids or gases leads to the result that, except for very large in tial disturbances, the wavefront will achieve a maximum steepness when the propagation distance is such that the rate of energy conversion to higher frequencies by nonlinearity is just compensated by the increase of absorption at higher frequencies. Note, however, that this steepest wave front does not qualify as a "disturbance propagated without change of form." When attention is centered on the fundamental component, the diversion of energy to higher frequencies appears as an attenuation and accounts for the relatively more rapid absorption sometimes observed near a sound source.' The variational or acoustic pressure, in material coordinates, can be expressed generally as a function of the displacement gradients by using the adiabatic pressuredensity relation pL = Po(pL /po)'Y in conjuction with the continuity relation (3c-32); thus, (3c-48) in which the last member identifies the steady-state alteration of the average pressure and the fundamental and second-harmonic components of sound pressure. When the harmonic solution (3c-47) is introduced in (3c-48), the two alternating components of pressure for a' » (A/47r)' can be shown, after some algebraic manipulation, to be
+ V2 P, sin (wt - koa) + 1) sin 2(wt - koa) = V2 P sin 2(wt -
PI L
= +yPoM sin (wt - koa) =
P2 L
=
'YPoM'koa-Hy
2
koa)
(3c-49a) (3c-49b)
in which P, and P 2 are the rms values of the fundamental and second-harmonic sound pressures, and M = ko~o = w~o/co is again the peak value of the particle-velocity Mach number at the origin. The relative magnitude of P 2 :ncreases linearly with distance from the origin and is directly proportional to the peak Mach number, as may be deduced from (3c-49a) and (3c-49b); thus
P2 P,
=
1
4;
('Y
+ l)Mkoa
'Fubini, Alta Frequenza 4, 530-581 (1935). Fox and Wallace, J. Acoust. Soc. Am. 26, 994-1006 (1954). Soc. Am.:36, 534-542 (1964). 2
(3c-50)
Blackstock, J. Acoust.
3-51
PROPAGA'I'IONOF SOUND IN FLUIDS
Various experimental studies of second-harmonic generation have given results in reasonably good agreement with the predictions of (3c-50).1 The sound-induced alteration of mean total pressure, or "average" acoustic pressure, is given by the time-independent terms yielded by the substitution of (3c-47) in (3c-48), viz., (3c-51) Note that this pressure increment is given as a function of the material coordinates, which means that it pertains to a moving element of the fluid. The local value of the pressure change can be found by means of the transform (3c-40), which gives, through second-order terms, the following replacement for (3c-48), (3c-52) When (3c-47) is introduced in (3c-52), the time-independent terms give the local change in mean pressure as (3c-53) and since 'Y is usually less than 2, it follows that the local value of mean pressure will be reduced by the presence of the sound wave, in striking contrast to the increase of mean pressure that would be observed when following the motion of a particle of the medium. Negative pressure increments as large as 10 newtons m- 2 (100 dynes cm- 2) have been reported experimentally, in reasonably good agreement with (3c-53). The mean value of the material particle velocity, u L == ~t, vanishes, as may be seen by differentiating (3c-47). The local particle velocity that would be observed at a fixed spatial position does not similarly vanish, however, and may be shown, by using the transform (3c-40) again, to be UN
= 1;, -
H'a
( E u)
= - -1 C Oll!2 = - pocow2~02 --= 2 2
2poco
(pOC0 2)-1
( )
J
(3c-54)
where (J) is the average sound energy flux, or sound intensity.' Sc-7. Vorticity and Streaming. As suggested above, and with scant respect for the traditional symmetry of simple-harmonic motion, sound waves are found experimentally to exert net time-independent forces on the surfaces on which they impinge, and there is often aroused in the medium a pattern of steady-state flow that includes the formation of streams and eddies. The exact wave equation considered in the preceding section has been solved only for one-parameter waves (i.e., plane or spherical), and these solutions do not embrace some of the gross rotational flow patterns that are observed to occur. It is necessary, therefore, to revert for the study of these phenomena to the perturbation procedures introduced by the first- and second-order equations (3c-26) and (3c-29). It is plausible that vortices and eddies should arise, if there is any net transport at all, inasmuch as material continuity would require that any net flow in the direction of sound propagation must be made good in the steady state by recirculation toward the source. Streaming effects can be studied most usefully, therefore, in terms of the generation and diffusion of circulation, or vorticity. More specifically, the time average of the second-order velocity U2 will be a first-order measure of the streaming 1 Thuras, Jenkins, and O'Neil, J. Acoust. Soc. Am. 6, 173-180 (1935); Fay, J. Acoust. Soc. Am. 3, 222-241 (October, 1931); O. N. Geertsen, unpublished (ONR) Tech. Report no. III, May, 1951, D.C.L.A.; D. T. Blackstock, Report of the Fourth International Congress on Acoustics, Part I, 1962. 2 Westervelt, J. Acoust. Soc. Am. 22, 319-327 (1950).
3-52
ACOUSTICS
velocity. The vector function describing u. can always be resolved into solenoidal and lamellar components defined by V'A. = - (v Xu.)
(3c-55)
The irrotational component that represents the compressible, or acoustic, part of the fluid motion is derived from the scalar potential '1',. The vector potential A. is associated with the rotational component comprising the incompressible circulatory flow that is of primary interest in streaming phenomena. The failure of the first-order equations to predict streaming can be demonstrated by writing directly the curl of the first-order force equation (3c-26b). The gradient terms are eliminated by this operation, since V X v( ) == 0, leaving just (3c-56) Thus the first-order vorticity, RI == i(V X UI), if it has any value other than zero, obeys a typical homogeneous diffusion equation. On the other hand, it would appear to follow that, if RI were ever zero everywhere, its time derivative would also vanish everywhere and RI would be constrained always thereafter to remain zero. This is not a valid proof of the famous Lagrange-Cauchy proposition on the permanence of the irrotational state, but the absence of any source terms on the right-hand side of (3c-56) does indicate correctly I that first-order vorticity cannot be generated in the interior of a fluid even when viscosity and heat conduction are taken into account. Instead, first-order vorticity, if it exists at all, must diffuse inward from the boundaries under control of (3c-56).j A notably different result is obtained when the second-order equations are dealt with in the same way. It is useful, before taking the curl of (3c-29b), to eliminate the second and third terms of this equation by subtracting from it the product of (Pr/ po) and (3c-26b), and the product of UI and (3c-26a). In effect this raises the first-order equations to second order and then combines the information in both sets. The augmented second-order force equation can then be arranged in the form PO a~.
+ 21/o(V
X R.)
-2[(V1/I· V)UI
+ po'llpIV(V . UI)
+ V1/1
X (V X UI)] - Biv
- 2POPI(V X R I) - 2pO(UI X R I)
+ 2(V1/1
(~PI')
X R I)
+ PoV (~UI. UI) + B.vp.
- 1/o'llV(V . U2) -
V1/~ (V· UI)
= 0
(3c-57)
The following abbreviations have been used for the coefficients of VPI in (3c-26b) and of VP2 in (3c-29b): BI
co' [ == -;y 1
+ {jopo (D(h) DPI
0
]
(3c-58)
in which the quotients (VBr/VPI) and (vB./vp,) have been replaced by the corresponding material derivatives DB I Dp, which must be evaluated, of course, for the particular conditions of heat exchange satisfying the energy equations (3c-26c) and (3c-29c). This evaluation can be evaded temporarily (at the cost of neglecting vB I and VB,) by observing that each of the last five terms of (3c-57) contains a gradient. These disappear on taking the curl of (3c-57), whereupon the vorticity equation emerges as
aR. at -
poV'R.
=
aS I )+_ "21 Po'll ( VSI X V at Po IV X (UI . V)V'71
+ po81V'RI
-- POVSI X (V X R I) - V X (UI X RI)"+ PO-IV X (V1/1 X R I) I
St. Venant, Compt. rend. 68, 221-237 (1869).
(3c-59)
PROPAGATION OF SOUND IN FLUIDS
in which
·3-53
has been introduced as an abbreviation for the first-order condensation, This inhomogeneous diffusion equation puts in evidence various secondorder sources of vorticity: four vanish if the first-order motion is irrotational (R l = 0), and two drop out when the shear viscosity is constant (V7)l = 0). It is notable that the dilatational viscosity 7)' does not appear in any of these source terms except through the ratio 7)'/7) that forms part of the dimensionless viscosity number '0 "" 2 + (7)'/7). Except for the third source term, which (3c-56) shows to be one order smaller than the change rate of R l , all the vorticity sources would vanish -and the streaming would "stall"-if the wave front were strictly plane with Ul, 81, and 7) functions of only one space coordinate. Wave fronts cannot remain strictly plane at grazing incidence, however,' and rapid changes in the direction and magnitude of Ul will occur near reflecting surfaces, in the neighborhood of sound-scattering obstacles, and in thill viscous boundary layers. As a consequence, the "surfa,ce" source terms containing Rl become relatively more important in these cases. 2 In other circumstances, when the sound field is spatially restricted by source directionality, the first source term in (3c-59) dominates and leads to a steady-state streaming velocity proportional to the ratio of the dilatational and shear viscosity coefficients-and hence to a unique independent method of measuring this moot ratio. s Both the force that drives the fluid circulation and the viscous drag that opposes it are proportional to the kinematic viscosity, which does not therefore control the final value of streaming velocity but only the time constant of the motion, i.e., the time required to establish the steady state. 4 Evaluating the second-order vorticity source terms in any specific case requires that the first-order velocity field be known, and this calls in the usual way for solutions that satisfy the experimental boundary conditions and the wave equation. Unusual requirements of exactness are imposed on such solutions, moreover, by the fact that even the second-order acoustic equations yield only a first approximation to the mean particle velocity. The analysis of vorticity can be recast, by skillful abbreviation and judicious regrouping of the elements of (3c-57), in such a way as to yield a general law of rotational motion, according to which the average rate of increase of the moment of momentum of a fluid element responds to the difference between the sound-induced torque and a viscous torque arising from the induced flow. 5 A close relation has also been shown to exist in some cases between the streaming potential and the attenuation of sound by the medium without regard for whether the attenuation is caused by viscosity, heat conduction, or by some relaxation process; in effect the average momentum of the stream "conserves" the momentum diverted from the sound wave by absorption. 6 This principle has so far been established rigorously only for the adiabatic assumption under which P = P(p), and under restrictive assumptions on the variability of 7) and '0, but its prospective importance would appear to justify efforts to extend the generalization. 3c-8. Acoustical Energetics and Radiation Pressure. If the kinetic energy density that appeared briefly in (3c-12) is restored to (3c-18), the change rate of the specific 81
81
= PI! PO.
1 Morse, "Vibration and Sound," 2d ed., pp. 368-371, McGraw-Hill Book CompanY4 New York, 1948. 2 Medwin and Rudnick, J. Acoust. Soc. Am. 25, 538-540 (1953). 3 Liebermann, Phys. Rev. 15,1415-1422 (1949); Medwin, J. Aco",,;8t. Soc. Am. 25, 332-341 (1954). 4 Eckart, PhY8. Rev. '13, 68-76 (1948). 5 Nyborg, J. Acoust. Soc. Am. 25, 938-944 (1953); Vvestervelt, J. Acoust. Soc. Am. 25, 60-67 and errata, 799 (1953). 6 Nyborg, J. Acoust. Soc. A.m. 25, 68--75 (1953); Doak, Proc. Roy. Soc. (London), ser. A, 226, 7-16 (1954); Piercy and Lamb, Proc. Roy. Soc. (London), ser. A, 226, 43-50 (1954).
3-54:
AconSTICS
total energy density (per unit mass), E/p, can be formulated in terms of D(E/p) _ D(ju u) p -----nt - p Dt 0
+
D(iu u)
D. p Dt
Dv
0
=p
Dt
(3c-60)
-pPDt-Voq+cfJ>J
Material derivatives are used here so that the energy balance reckoned for a particular volume element will continue to hold as the derivatives "follow" the motion of the material particles. The mechanical work term on the right in (3c-60) can be resolved into two components by writing P = Po + p, where the excess, or sound, pressure p' now represents the sum of the variational components of all orders (p = Pi
+ P2 + ...)
Thus D(E/p) D(ju u) Dv Dt - pp Dt p -----nt = p 0
Dv
+ PP o Dt
- V
0
q
+
0.03
z
12.5 kHz
ILl I-
!;;: O.Og
10.0
------~8.0
~~] 4.0 ~%-[~~~~§~§~~~g~i~~~i~~~~6.3 w- w ~ ~- wro ro ~ ro m
0.01
-2.0
RELATIVE HUMIDITY, % FIG. 3d-6. Values of the total attenuation coefficient m (in meters-I) versus percent relative humidity for air at 20°C and normal atmospheric pressure for frequencies between 2,000 and 12,500 Hz at one-third-octave intervals. To convert to decibels per meter, mUltiply ordinate by 4.343. (After Harris.)
attenuation coefficient per meter as expressed in the equation 1 = loe- m., where 10 is the sound intensity (in watts/m') at x = 0, and I is that at x. To convert from m to decibels per meter, multiply by 4.343. Hatris 4 has also presented data on the absorption of sound in air at pressures in the range from 0.2 to 0.9 atm at 20°0. The results show that, at a given frequency, 1 L. J. Bivian, High Frequency Absorption in Air and in Other Gases, J. ACoUBt. Soc. Am. 19,914-916 (1947). , P. E. Krasnooshkin, On Supersonic Waves in Cylindrical Tubes and the Theory of the Acoustical Interferometer, Phys. Rev. 65, 190 (1944). See also W. H. Pielemeier, Observed Classical Sound Absorption in Air, J. Aco.ust. Soc. Am. 17, 24-28 (1945). 3 C. M. Harris, Absorption of Sound in Air versus Humidity and Temperature, Acoust. J. Soc. Am. 40, 148-159 (1966). 4 C. M, Harris, On the Absorption of Sound in Humid Air at Reduced Pressures, J. Acoust. Soc. Am. 43, 530-532 (1968).
3·~·-80
ACOUSTICS· Q20~------------------------------~
125 Hz
OJ
--------------0.0
~
0
5
m
ffi
ro
~
~
TEMPERATURE, ·C
(0) FIG. 3d-7. Attentiatio':' of sound in air vs. temperature, at atmospheric pressure, for various values of relative humiditY"llnd frequency; The CO. content is. 0.03 percent; (After Harri8.)
40% 50 70 90%
~J~0~~-~5UU~O~~~5LU~JOLW~J5~~20~~25~.~ro TEMPERATURE, ·C
(b)
l!'IG. 3d-7. Continued.
ACOUSTIC PROPERTIES OF GASES lOr-------------------------------~
500 Hz
o
o
;a-c 0.4
----------
TEMPERATURE, 0(; (c 1
FIG. 3d-7. Continued.
f!
iiE o o
::::: en -c
0.2
TEMPERATURE, @C (If) FIG. 3d-7. Continued.
3-81
3-82
ACOUSTICS
-10
-5
o
;)
10
TEMPERATURE,
15
25
20
'c
30
leI FIG. 3d-7 (Continued)
12.-'---------------...., 11 4,000 Hz 10
'\ \15
9
\
\ \
8
\
\
\
\
\
\\ '\.
---------
-5
o
5 10 15 TEMPERATURE, ·C
If) FIG. 3d-7 (Continued)
20
25
30
ACOUSTIC PROPERTIES OF GASES
3-83
a plot of molecular absorption versus humidity has a maximum value that is independent of pressure. Lowering the pressure shifts- the peaks in the curves of absorption versus humidity to lower values of relative humidity. The relations among frequency of maximum absorption, relative humidity, and frequency are given in Fig.3d-S. Other studies of the molecular absorption process are reported by Monk,! Shields and Faughn,2 Henderson and Herzfeld,3 and Connelly.4
FREQUENCY, fmox,kHz FIG. 3d-8. Frequency of maximum total absorption, Imax, as a funCtion of relative humidity. The parameter is atmospheric pressure. The temperature is 20°C.
Below 1,000 Hz the attenuation of sound in air is much less than above 1,500 Hz. Harris and Tempest 6 have measured attenuation coefficients for air in this frequency range. Their data for a range of moisture contents, temperatures, and barometric pressures are given in Fig. 3d~9a through 'e. ' , 1 R. G. Monk, Thermal Relaxation in Humid Air, .J. AcouBt. Soc. Am. 46, 580-586 (1969). 2 F. D. Shields and J. Fa'ughn, Sound Velocity and Absorptions in Low-pressure Gases Confined to Tubes of Circular Cross Sections, J. AcouBt. Soc. Am. 46, 158-163 (1968). 8 M. C. Henderson and K. P. Herzfeld, Effect of Wat!)r Vapor on the Napier Frequency of Oxygen and Air, J. AcouBt. Soc. Am. 37, 986-988 (1965). 4 J. H. Connolly, Combined Effect of Shear Viscosity, Thermal Conduction, and Thermal Relaxation on Acoustic Propagation in Linear-molecular Ideal Gases, J. Acoust. Soc. Am. 36,2374-2381 (1964). 6 C. M. Harris and W. Tempest, Absorption of Sound below.clOOO Hz, J. Acoust. Soc. Am. 36, 2390-2394 (1964). -
+ 5.03358T - 5.79506 X 1O-2T2 + 3.31636 X 1O-4T3 - 1.45262 X 1O-6T4 + 3.0449 X 1O-9T5 mlsec 1
2
J. R. Lovett, J. Acoust. Soc. Am. 45, 1051 (1969). M. Greenspan and C. E. Tschiegg, J. Research NBS 59C, 249 (1957).
(3e-2)
'3~94
ACOUSTICS
TABLE 3e-17.
SPEED OF SOUND IN FOUR ALCOHOLS AT .p= 1 ATM* c, m/sec
T,oC Methyl
Ethyl
1,232.1 1,189.2 1,196.7 1,154.9 1,161. 8 1,121. 2 1,088.2 . 1,127 ..6 1,094.1 1,055.9 1,024.0 1,061. 2
0 10 20 30 40 50
n-Propyl
n-Butyl
1,295.0 1,258.6 1,223.2 1,188.7 1,154.7 1,121. 0
1,327.0 1,292.5 1,257.7 1,223.6 1,190.3 1,157.2
'" W. D. Wilson, J. Aco",t. Soc. Am. 36, 333 (1964).
TABLE3e-18.
SPElilD OF SOUND IN FOUR ALCOHOLS AT T = 20°C* c, m/see
p, psi
14.7 2,000 4,000 6,000 8,000 10,000 12,000 14,000
* W.
Methyl
Ethyl
1,121. 2 1,197.5 1,264.7 1,324.8 1,379.5 1,430.2 1,477.5 1,521. 6
1,161. 8 1,241. 8 1,311.8 1,374.1 1,430.8 1,483.3 1,532.4 1,577.9
n-Propyl
1,223.2 1,299.3 1,367.1 1,428.0 1,483.8 1,535.7 1,584.3 1,629.7 .
n-Butyl
1,257.7 1,331. 1 1,397.0 1,456.5 1,511. 1 1,562.1 1,610.0 1,655.2
D. Wilson, J. Acoust. Soc. Am. 36, 333 (1964).
ATTENUATION OF SOUND IN FOUR ALCOHOLS AT T
TABLE 3e-19.
=
30°0*
10 16 ",/!"sec 2 /m p, kg/em'
Methyl
Ethyl
n-Propyl
30:2 18.2 13.5 11.2 9.9
48.5 31. 2 24.5 21.4 19.9
64.5 48.5 41. 5 39.2 39.0
n-Butyl
f = 45 MHz f = 45 MHz f = 25 MHz f = 25MH", 1
500 1,000 1,500 2,000
74.3 60.5 55.8 54.0 53.5
• E. H. Carnevale and T. A. Litovitz, J. Acoust. Soc. Am. 2'1,547 (1955).
for T in °C. The values for H 20 in Table 3e-21 were calculated from !!:q.(3e-2). Some results at very high pressures, up to 10,000 kg/em', with reduced accuracy, are also available. 1,' 1 G. Holton et aI., J. Acons;. Soc. Am. 43, 102 (1968). 'W. H. Johnson, Jr., and G. Holton, Rev. Sci. Instr. 39, 1247 (1968),
3-95
ACOUSTIC PROPERTIES OF LIQUIDS
3e-20.
TABLE
ATTENUATION OF SOUND IN n-BUTYL P = 2,000 KG/CM 2
*
ALCOHOL AT
(f = 25 MHz) T, °C ................ ,
10"01./1", sec'/m.......
30 53.5
0 '15 124.0 79.6
45 39.0
* E. H. Carnevale and T. A. Litovitz, J. Acoust. Soc. Am., 27, 547 (1955). 3e-21. SPEED OF SOUND 99.82 MOLE % D 20t AT p
TABLE
IN =
H 20* 1 ATM
AND
c, m/sec T,OC H 2O
D 20
20 30
1,402.3 1,421. 6 1,447.2 1,482.3 1,509.0
1,320.9 1,347.5 1,384.2 1,412.3
40 50 60 70
1,528.8 1,542.5 1,550.9 1,554.7
1,433.1 1,447.4 1,456.3 1;460.5
74 80 90 100
1,555.1 1,554.4 1,550.4 1,543.0
1,460.8 1,457.8 1,452.0
0 4
10
* J. R. Lovett, J. Acoust. Soc. Am. 46, 1052 (1969). M. Greenspan and C. E. Tschieg.g, J. ReBearch NBS 69C, 249 (1957). t W. D. Wilson, J. Acoust. Soc. Am. 33, 374 (1961). TABLE
99.82
3e-22. SPEED OF SOUND IN H 20* AND % D 20t NEAR ROOM TEMPERATURE
MOLE
c, m/sec p, psi
H20 at 30.68° C 14.7 1,450 2,000 2,901 4,000
1,510.6 1,527.8
4,351 5,802 6,000 7,252 8,000
1,561.6 1,578.4
8,702 10,000 10,150 11,600 12,000 14,000
1,611.8
* A. J. Barlow and E. Yazgan, Brit. J.
D20 at 30°C 1,412.3 1,433.3
1,544.5 1,454.7
1,476.3 1,595.3 1,498.0 1,519.8 1,628.8 1,645.4 1,541.5 1,563.0 App. PhY8. 18,645 (1967).
t W. D. Wilson, J. ACO'ust. Soc. Am. 33,374 (1961).
3-96
ACOUSTICS
Sea Water. Wilson' has measured the speed of sound in sea water from the Bermuda-Key West area of the Atlantic over the following range: temperature -3 < T < 30 0 0, pressure 1.033 < p < 1,000 kg/cm 2, and salinity 3.3 < S < 3.7 percent. Typical results are given in Tables 3e-25 and 3e-26. There is some reason to believe that these values are high. LovetV recommends that they be reduced by 0.65 m/sec.
TABLE 3e-23. ATTENUATION OF SOUND IN H 20 AT P (f varied from 8 to 67 MHz) T, DC 10 15",//2, sec'/m
o
56.9
44.1
5 10 15 20 30 40 50 60 70 80 90
* J. M. M.
36.1 29.6 25.3
19.1 14.6 12.0 10.2 8.7 7.9 7.2
Pinkerton, Nature 150, 128 (1947).
TABLE 3e-24. ATTENUATION OF SOUND IN H 20 AT T 0 18.5
p, atm ...............
10 15",/1', sec 2 /m ......
* T.
1 ATM*
500 15.4
1,000 12.7
1,500 11.1
30°0*
=
I
2,000 9.9
A. Litovitz and E. H. Carnevale, J. Appl. Phys. 26, 816 (1955).
TABLE 3e-25. SPEED OF SOUND IN SEA WATER AT P
1 ATM*
c, m/sec
T, DC
8 -3 0 5
10 15 20 25 30
= 3.3%
1,431.9 1,446.3 1,468.2 1,487.6 1,504.6 1,519.6 1,531.9 1,443.8
8
= 3.5%
1,435.0 1,449.4 1;471. 2 1,490.4 1,507.4 1,522.2 1,535.1 1,546.2
8
= 3.7%
1,437.6 1,451. 9 1,473.5 1,492.7 1,509.5 1,524.2 1,536.9 1,547.9
• W. D. Wilson, J. Acoust. Soc. Am. 32,641 (1960).
Electrolytes. Monovalent ions in most cases affect the attenuation only slightly and increase the speed of sound to an extent depending on the concentration. Polyvalent ions introduce dispersion. References are given in Sec.3e-7. 1 2
W. D. Wilson, J. Acoust. 80c. Am. 32, 641 (1960). J. R. Lovett, J. Aco1l3t. 80c. Am. 45, 1051 (1969).
3-97
ACOUSTIC PROPERTIES OF LIQUIDS
3e-6, Mixtures. The behavior ofliquid mixtures is varied. If the two constituents are both Kneser liquids, then c and", are in most cases intermediate to those of the constituents themselves. A mixture of two associated liquids will generally have a maximum in '" at some composition and also, especially if one component is water, a maximum in c at some other composition. A mixture of one Kneser and one associated liquid may behave like a mixture of two Kneser liquids or in even a more complex fashion than a mixture of two associated liquids. The literature is extensive; references are given in Sec. 3e~7. 3e-7. Sources of Other Data. By far the best single source of data is Schaafs' book [1]. The coverage is through 1963. Data are given on inorganic, organic, and silico-organic liquids; on supercooled liquids; crystalline liquids; fatty acids; and molten metals and salts. Also treated are binary (and some ternary) mixtures, and aqueous and some nonaqueous solutions of electrolytes. Bergmann's book [2] is a good source for miscellaneous substances, as is a recent report by Turk and Hunter TABLE 3e-26. SPEED OF. SOUND IN SEA WATER AT T
=
20°0 *
c, m/sec p, kg/em'
1.033 100 200 300 400 500 600 700 800 900
* W.
S = 3.3%
S = 3.5%
1,519.6 1,535.4 1,551.5 1,567.7 1,584.0 1,602.0 1,616.8 1,633.1 1,649 .. 4 1,665.5
1,522.2 1,537.1 1,554.2 1,571.5 1,586.8 1,603.1 1,619.5 1,635.8 1,652.1 1,668.2
S
= 3.7% 1,524.1 1,540.1 1,556.3 1,572.5 1,588.9 1,605;2 1,621. 6 1,637.9 1,654.2 1,670.3
D. Wilson, J. Acoust. Soc. Am. 32, 641 (1960).
[16]. Sette has published four compilations, treating absorption [3, 6] and velocity . [5, 7] in pure liquids [3, 7] and in mixtures [5, 6]. Velocity as related to molecular constitution is treated by Markham et aI. [4], Herzfeld and Litovitz [15], Schaafs [17], and Nozdrev [1$]. Del Grosso and Smura [8] give the speed of sound in and impedances of liquids suitable for certain applications; liquids simulating sea water and liquids having unusually low or high speeds of sound are· included. Weissler ana coworkers present considerable data in connection with their work on molecular structure, especially for alcohols [9], linear polymethyl siloxanes [10], cyclic compounds [11], inorganic halides [12], acetylene derivatives [13J, and polyethylene glycols [14]. The acoustic and some other properties of many alcohols are given by Marks [19]. 1. Schaafs, W.: Landolt-Bornstein New Series, Group II, "Atomic and Molecular Physics," vol. 5, "Molecular Acoustics," Springer-Verlag New York Inc., New York, 1967. _2. Bergmann, L.: "Der Ultraschall und seine Anwendung in Wissenschaft und Technik," 6th ed., S. Hirzel Verlag KG, Leipzig, 1954 . . 3. Sette, D.: Nuovo Cimento (Supple) 6, 1 (1949). 4. Markham, J. J., R. T. Beyer, and R. B. Lindsay: Rev. Mod. Phys. 23, 353 (1951). 5. Sette, D.: Ricerca Sci. 19, 1338 (1949). 6. Sette, D.: Nuovo Cimento (Suppl. 2) 7,318 (1950). 7. Sette, D.: Ri",erca Sci. 20, 102 (1950). 8. Dd Grosso, V. A., and E. J. Smma: NRL Rept. 4193, 1953.
3-98 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
ACOUSTICS
Weissler, A. J. Am. Chem. Soc. 70, 1634 (1948). Weissler, A. J. Am. Chem. Soc. 71, 93 (1949). Weissler, A. J. Am. Chem. Soc. 71, 419 (1949). Weissler, A. J. Am. Chem. Soc. 71, 1272 (1949). Weissler, A., and V. A. Del Grosso: J. Am. Chem. Soc. 72,4209 (1950). Weissler, A., J. W. Fitzgerald, and I. Resnick: J. Appl. Phys. 18,434 (1947). Herzfeld, K. F., and T. A. Litovitz: "Absorption and Dispersion of Ultrasonic Waves," Academic Press, Inc., New York, 1959. Turk, R. A., and J. L. Hunter: The Velocity and Absorption of Sound in Various Liquids, ONR Tech. Rept. 8, Contract NONR 2577(01) (AD) 651978), Department A, Clearinghouse, Springfield, Va. Schaafs, W.: "Molekularakustik," Springer-Verlag OHG, Berlin, 1963. Nozdrev, V. F.: "Application of Ultrasonics in Molecular Physics," Gordon and Breach, Science Publishers, Inc., New York, 1963. Marks, G. W., J. Acoust. Soc. Am. 41, 104 (1967).
3f. Acoustic Properties of Solids W. P. MASON
Columbia University
Sf-1. Elastic Constants, Densities, Velocities, and Impedances. Solids are used for conducting acoustic waves in such devices as delay lines useful for storing information and as resonating devices for controlling and selecting frequencies. Acousticwave propagation in solids has been used to determine the elastic constants of single crystals and poly crystalline materials. Changes in velocity with frequency and changes in attenuation with frequency have been used to analyze various intergrain, interdomain, and imperfection motions as discussed in Sec. 3£-2. In an infinite isotropic solid and also in a finite solid for which the wavefront is a large number of wavelengths, plane and nearly plane longitudinal and shear waves can exist which have the velocities Vlon.
= ~A + 2/L p
Vsh•••
=
~p
(3f-l)
where /L and A are the two Lame elastic moduli, /L is the shearing modulus, and A + 2/t has been called the plate modulus. For a rod whose diameter is a small fraction of a wavelength, extensional and torsional waves can be propagated with velocities
where
(3f-2)
For anisotropic media, three waves will, in general, be propagated, but it is only in special cases that the particle motions will be normal and perpendicular to the direction
3-99
ACOUSTIC PROPERTIES OF SOLIDS
of propagation.
The three velocities satisfy an equation 1 All AI2 Au
A12
pv 2
I
A22 -
=0
pv 2
(3£-3)
A23
where p is the density, v the velocity, and the A's are related to the elastic constants of the crystal by the formulas
+ m 2c66 + n 2c55 + 2mnc56 + 2nlc15 + 21mc16 + m 2c26 + n 2c45 + mn(c46 + C25) + nl(c14 + C56) + lm(cl2 + C66) + m 2c46 + n'c35 + mn(c45 + C36) + nl(cl3 + C5S) + lm(c14 + CS6) 12c", + m2c24 + n 2c34 + mn(c44 + C23) + nl(c36 + C'15) + lm(c2S + e'6) 12c66 + m 2c22 + n 2c44 + 2mnc24 + 2nlc46 + 21mc" l'c55 + m 2c44 + n'c33 + 2mnc34 + 2nlc35 + 21mc45
All = PCll AI2 = ['CI6 AI3 = i 2cl5 A23 =
A22 = Aoo =
(3f-4)
In these formulas CII to C66 are the 21 elastic constants and i, m, n the direction cosines of the direction of propagation with respect to the crystallographic x, y, and z axes which are related to thea, b, c crystallographic axes as discussed in an IRE publication. 2 In Eq. (3f-3), we solve for the quantity pv 2• It was shown by ChristoffeP that the direction cosines for the particle motion ~, i.e., o!, (3, ,)" are related to the A constants and a solution of pv 2 by the equations o!AII
+ {3A12 + ')'A13
= O!PVi2;
"'AI2
+ {3A22 + ')'A23
= {3PVi2;
+ {3A23 + ')'Aaa =
o!AIS
')'PVi2
(3£-5) where i = 1, 2, 3. Hence, solutions of Eq. (3£-3) are related to particle motions by the equations of (3£-5). Most metals crystallize in the cubic and hexagonal systems. Furthermore, when a metal is produced by rolling, an alignment of grains occurs such that the rolling direction is a unique axis. This type of symmetry, known as transverse isotropy, results in the same set of constants as that for hexagonal symmetry. For cubic crysta~s, the resulting elastic constants are CII =
C22
=
C"
(3f-6)
CI2 = CI8 = C"
while for hexagonal symmetry or transverse isotropy, the resulting elastic constants are Cts =
C23,
ell -
Caa,
C66=
2
CI2
(3£-7)
For cubic symmetry, the waves transmitted along the [100J direction and the [110J direction have purely longitudinal and shear components with the elastic-constant values and particle direction ~. given by [lOOJ direction Vlong
= ~
~-Cllp
~
along [100J
Vsbe.,
= "\.JC44 -p
along any direction in the [lOOJ plane
I Love, "Theory of Elasticity," 4th ed., p.298,. CambTidge UniveTsity Press, New York, 1934. 2 Standards on Piezoelectric Crystals, Proc. IRE 3'1 (12), 1378-1395 (December, 1949),
3-100
ACOUSTICS
[110] direction
+ C'22 p + 2C44
• /cu
Vl ong =
~\j
~
~
along [110]
along [001] ~ along [lID]
[111] direction
v, =
+ 2c12 + 4C44 3p
• /cu
Viano
= "\/
=
V,hear
~
along [111]
• /c-,-,---C-'-2-+-'-C-4-4 V2
=
V,
= -"
3p
~
can be in any direction in the (111) plane. For hexagonal or transverse isotropy, waves transmitted along the unique axis and any axis perpendicular to this will have the values [001] direction
=
Viano
~
./c" '1p
~
along [001]
V,hear
.Ie..
= "\1p
along any direction in the [001] plane
[100] direction -
= • /cu Vlong
~
."
~
p
along [100]
VI shear =
~
along [001]
~-C44 p
along [010]
The fifth constant is measured by transmitting a wave 45 deg between the [100] and [001] directions; i.e., I = n = 1/V2; m = O. For this case A
-
11 -
Cu
+2 C44
A
_
C'3
I, -
C44
+ C4' 2
Cu -
C'2
+ 2C44
4
+ c"
(3f-8)
2 The three solutions of Eq. (3f-3) are
PV2,3
2
=
[(cu
+ c" + 2C(4)/2] + V[(cu 2
- c,,)/2)2
+ (C13 + C..)2
(3f-9)
For these three velocities, the particle velocities have the direction cosines For
V"
For
V2,
For
V"
{3 = 1 a
a
= 'Y
{ ell 2(c13
C33
(3f-1O)
+ C(4)
= __ { Caa - eu
-I-
y 2(C13
"
+ C(4)
11
-I- [ '
(eu - caal"]} :l(C13
+ C(4)
Hence, unless C11 is nearly equal to c", a longitudinal or shear crystal will generate both J;ypes of waves. Experimentally, however, it is found that a good discrimination can 3e obtained against the type of wave that is not primarily generated and a single v.elocity can be measured. A resonance technique can also be used to evaluate all the elastic constants of a crystalline material.
3-101
ACOUSTIC PROPERTIES OF SOLIDS TABLE
3f-1.
DENSITIES OF GLASSES, PLASTICS, AND METALS IN
POLYCRYSTALLINE AND CRYSTALLINE FORM (X-RAY DENSITIES FOR CRYSTALS)*
Materials
Composition
Aluminum Hard-drawn ........... . CrystaL .............. . -',', ...... '.'-, .... ' , ' " ._, ..... . Aluminum and copper ... ,.. 10 AI, 90 Cu .5 Al, 95 Cu .3 AI, 97 Cu Beryllium............... . CrystaL .............•.. Brass: yellow ............... . 70 Cu, 30 Zn Red .................. . 90 Cu, 10 Zn White ................ . 50 Cu, 50 Zn Bronze ................. . 90 Cu, 10 Sn 85 Cu, 15 Sn 80 Cu, 20 Sn 75 Cu, 25 Sn Chromium .............. . CrystaL .............. . Cobalt .................. . Crystal. .............. . Constantan ........... " . 60 Cu, 40 Ni Copper ................. . CrystaL .............. . Duralumin .............. . 17ST = 4Cu,0.5Mg,0.5Mn Germanium ............. . CrystaL .............. . German silver ........... . 26.3 Cu, 36.6 Zn, 36.8 Ni 52 Cu, 26 Zn, 22 Ni 59 Cu, 30 Zn, 11 Ni 63 Cu, 30 Zn, 6 Ni Gold ................... . CrystaL .............. . Indium ................. . CrystaL .............. . Invar ................... . 63.8 Fe, 36 Ni, 0.20 C Iron .................... . Crystal. .............. . Lead ................... . CrystaL .............. . Lead and tin ............ . 87.5 Pb, 12.5 Sn 84 Pb, 16 Sn 72.8 Pb, 22.2 Sn 63.7 Pb, 36.3 Sn 46.7 Pb, 53.3 Sn 30.5 Pb, 69.5 Sn
Temp.,
DC
2.0 25
20 18
20
18 21
18 20
20
20 20 20
18
Density, 10 3 kg/rna or g/cm a 2.695 2.697 7.69 8.37 8.69 1.87
1.871 8.5-8.7 8.6 8.2 8.78 8.89 8.74 8.83 6.92-7.1 7.193
8.71 8.788 8.88 8.3-8.. 93 8.936 2.79 5.3 5.322 8.30 8.45 8.34 8.30 18.9-19.3 19.32 7.28 7.31 8.0 7.6-7.85 7.87 11.36 11.34 10.6 10.33 10.05 9.43 8.73 8.24
--------~-'-.:..:...:..-=-=~~~------------.--..:-..---
3-102
ACOUSTICS T1...BLE
3f-1.
DENSITIES OF GLASSES, PLASTICS, AND METALS IN
POLYCRYSTALLINE AND CRYSTALLINE FORM (X-RAY DENSITIES FOR CRYSTALS)*
Materials
(Continued)
Composition
Magnesium ............... . Crystal. ................ . Manganese ............... . Crystal. ................ . Mercury .................. . 71 Ni, 27 Ou, 2 Fe Monel metal ............ . Molybdenum. . . . . . . . . .. .. CrystaL ................ . Nickel ................... . Crystal ................. . Nickel silver .............. . Phosphor bronze .......... . 79.7 Cu, 10 Sn, 9.5 Sb, 0.8 P Platinum ................. . CrystaL ................ . Silicon ................... . CrystaL ................ . Silver. . . . . ......... . Crystal. ................ . Steel K9 .................. . 347 stainless steel. ......... . Tin ...................... . CrystaL ................ . Titanium ................. . Tungsten ................. . CrystaL ................ . Tungsten carbide .......... . Zinc ...................... . Crystal. ................ . Fused silica ............... . Pyrex glass (702) .......... . Heavy silicate flint ........ . Light borate crown ........ . Lucite .................... . Nylon 6-6 ................ . Polyethylene .............. . Polystyrene ............... .
Temp.,
DC
25
20
25 25 20
18 15 25 25
25 25
Density, 10' kg/m' or g/cm'
l.74 1.748 7.42 7.517 13.546 8.90 10.1 10.19 8.6-8.9 8.905 8.4 8.8 21.37 21.62 2.33 2.332 10.4 10.49 7.84 7.91 7-7.3 7.3 4.50 18.6-19.1 19.2 13.8 7.04-7.18 7.18 2.2
2.32 3.879
2.243 1.182 1.11
0.90 1.056
* See also Tables 2b-l through 2b-13. When a longitudinal or shear wave is reflected at an angle from a plane surface, both a longitudinal and a shear wave will in general be refle'Jted from the surface, the angles of reflection and refraction satisfying Snell's law sin {3
sin a
Vs
VZ
(3£-11)
ACOUSTIC PROPERTIES OF SOLIDS
3-103
where a and (3 are the angles of incidence and refraction with respect to a normal to the reflecting surface. Exceptions to this rule occur if a shear wave has its direction of particle displacement parallel to the reflecting surface, in which case only a pure shear wave is reflected, with the angle of reflection being equal to the angle of incidence. Use is made of this result in constructing delay lines which can be contained in a small volume. When the direction of transmission is normal to the surface, the incident wave is reflected without change of mode. If the transmitting medium is connected to another medium with different properties, the transmission and reflection factors are determined by the relative impedances of the two media. The impedance is given by the formula (3£-12)
where E is the appropriate elastic stiffness and p the density. The aflection and transmission coefficients between medium 1 and medium 2 are given by the equations
T
= 1 -
R
2Z2
- = Z!
+ Z2
(3f-13)
Tables 3f-1 to 3f-4 list the densities, elastic constants, velocities, and impedances for a number of materials used in acoustic-wave propagation. Sf-2. Attenuation Due to Thermal Effects, Relaxations, and Scattering. When sound is propagated through a solid, it suffers a conversion of mechanical energy into heat. While all the causes of conversion are not known, a number of them are, and tables for these effects are given in this section. Sf-S. Loss Due to Heat Flow. When a sound wave is sent through a body, a compression or rarefaction occurs which heats or cools the body. This heat causes thermal expansions which alter slightly the elastic constants of the material. Since the compressions and rarefactions occur very rapidly, there is not time for much heat. to flow and the elastic constants measured by sound propagation are the adiabatic constants. For an isotropic material, the adiabatic constants are related to the isothermal constants by the formulas!
where the superscripts u and () indicate adiabatic and isothermal constants, a is the linear temperature coefficient of expansion, B the bulk modulus (B = A + ilL), e the absolute temperature in kelvins, p the density, and Cv the specific heat at constant volume. Table 3f-5 shows these quantities for a number of materials. The difference between AU and AB should be taken account of when one compares the elastic constants measured by ultrasonic means with those measured by static means. From the data given in Table 3f-5, it is evident that this effect can produce errors as high as 10 percent in the case of zinc. Adiabatic elastic constants are measured from frequencies somewhat less than those for which thermal equilibrium is established during the cycle up to a frequency! f == (uCvv 2 /27rE) for which wave propagation takes place isothermally. This latter frequency is approximately 10!2 Hz for most metals. When account is taken of the energy lost by heat flow betwee:', \he hot and cool parts, this adds an attenuation for longitudinal Ylaves equal to nepers/m
(3f-15)
1 W. P Mason, "Piezoelectric Crystals and Thei,: Application to Ultrasonics," pp. 480481, D. Yan Nostrand Company, Inc., Princeton, N.J., 191)0.
TABLE
3f-2.
ELASTIC CONSTANTS, WAVE VELOCITIES, AND CHARACTERISTIC IMPEDANCES OF METALS, GLASSES, AND PLASTICS
Materials
Aluminum, rolled .......... Beryllium ................. Brass, yellow, 70 Cu, 30 Zn C onstantan ............... Copper, rolled ............. Duralumin 17S ............ Gold, hard-drawn .......... Iron, cast ......... ........ Iron electrolytic ........... Armco .................. Lead, rolled ............... Magnesium, drawn, annealed ................ Monel metal. ............. Nickel. ................... Nickel silver .............. Platinum ................. Silver .................... Steel, K9 ................. 347 stainless steel. ......... Tin, rolled ................ Titanium ................. Tungsten, drawn . ......... Tungsten carbide .......... Zinc, rolled ............... Fused silica ............... Pyrex glass ............... Heavy silicate flint ......... Light borate crown ......... Lucite .................... Nylon 6-j) ........ " ...... Polyethylene .............. Polystyrene ...............
}.. X 10-10 newton/m'
Yo X newton/m'
I' X newton/m'
6.8-7.1 30.8 10.4 16.1 12.1-12.8 7.15 8.12 15.2 20.6 21.2 1. 5-1. 7
2.4-2.6 14.7 3.8 6.09 4.6 2.67 2.85 5.99 8.2 8.24 0.54
6.1 1.6 11.3 11.4 13.1 5.44 15.0 6.92 11.3 11.35 3.3
4.24 16.5-18 21.4 10.7 16.7 7.5 21.6 19.6 5.5 11. 6 36.2 53.4 10.5 7.29 6.2 5.35 4;61 0.40 0.355 0.076 0.360
1.62 6.18-6.86 8.0 3.92 6.4 2.7 8.29 7.57 2.08 4.40 13.4 21.95 4.2 3.12 2.5 2.18 1.81 0.143 0.122 0.026 0.133
2.56 12.4 16.4 11.2 9.9 8.55 10.02 11.3 4.04 7.79 31.3 ' 17.1 4.2 1.61 2.3 1.77 2.2 0.562 0.511 0.288 0.319
10-10
10-10
Poisson's V. ratio, 0'
I
= v'(}.. + 21')/p,
V.
= v;;;"
Vext ""
..,;-y;jp, z. = v' p(}..
+
21'), 10' kg/sec m'
I-'
~
Z. = .,,;;, 10' kg/sec m'
m/sec
m/sec
0.355 0.05 0.374 0.327 0.37 0.335 0.42 0.27 0.29 0.29 0.43
6,420 12,890 4,700 5,177 5,010 6,320 3,240 4,994 5,950 5,960 1,960
3,040 8,880 2,110 2,625 2,270 3,130 1,200 2,809 3,240 3,240 690
5,000 12,870 3,480 4,270 3,750 5,150 2,030 4,480 5,120 5,200 1,210
17.3 24.1 40.6 45.7 44.6 17.1 62.5 37.8 46.4 46.5 22.4
8.2 16.6 18.3 23.2 20.2 8.5 23.2 21.35 25.3 25.3 7.85
0.306 0.327 0.336 0.37 0.303 0.38 0:276 0.30 0.34 0.32 0.35 0.22 0.25 0.17 0.24 0.224 0.274 0.4 0.4 0.458 0.353
5,770 5,350 6,040 4,760 3,260 3,650 5,941 5,790 3,320 6,070 5,410 6,655 4,210 5,968 5,640 3,980 5,100 2,680 2,620 1,950 2,350
3,050 2,720 3,000 2,160 1,730 1,610 3,251 3,100 1,670 3,125 2,640 3,984 2,440 3,764 3,280 2,380 2,840 1,100 1,070 540 1,120
4,940 4,400 4,900 3,575 2,800 2,680 5,250 5,000 2,730 5,090 4,320 6,240 3,850 5,760 5,170 3,720 4,540 1,840 1,800 920 1,840
10.0 47.5 53.5 40.0 69.7 38.0 46.5 45.7 24.6 27.3 103 91.8 30 13.1 13.1 15.4 11.4 3.16 2.86 1.75 2.49
5.3 24.2 26.6 18.1 37;0 16.7 25.4 24.5 11.8 14.1 50.5 55.0 17.3 8.29 7.6 9.22 6.35 1.3 1.18 0.48 1.19
m/sec
Cf
~
o o q
~ H
Q
Ul
TABLE (8
3f-3.
ELASTIC CONSTANTS OF CUBIC SINGLE CRYSTALS"
= compliance lhodulus, m 2/newton; c = stiffness modulus, newtons/m 2; for cgs units of dynes/cm 2, multiply the c tabular entries by 10; divide the Crystal
8ll
X
lOll
812
X 1011
8
tabular entries by 10 to obtain cm 2 /dyne)
844
X 1011
C11 X 10-10
C12 X 10-10
CH
B
X 10- 10
=
[(C11
+ 2C12)/3]
X 10- 10
Anisotropy 2044/(C11 -
C12)
--.......... Ag ............. Al.. ......................... .......... Au .......... ........ Cu ............ Fe .............. ... - .... Ge ................. '" . K ........ . . . . . . . . . . . . . . . . . Na ............. ... , ....... Ni (sat.) ..................... Ph ............... ... -. Si ......... ................ W ...................
.....
Diamondt ............ · .. · .... NaCl.. ......... '" .. KEr ......................... KC!. ......... ........... -. Alloy
2.32 1. 59 2.33 1.49 0.757 0.9134 83.3 48.3 0.80 9.30 0.768 0.257 0.0958 2.4 4.0 2.7
-0.993 -0.58 -1.07 -0.625 -0.282 -0.260 -37.0 -20.9 -0.312 -4.26 -0.214 -0.073 -0.01 -0.50 -1.2 -0.3
2.29 3.52 2.38 1.33 0.862 1.49 38.0 16.85 0.844 6.94 1.26 0.66 0.174 7.8 7.5 15.6
I ofAtom % second
11.9 10,82 19.13 17.02 23.7 12.92 0.416 0.615 25.0 4.85 16.57 50.2 107.6 4.9 3.5 4.0
8.94 6.13 16.45 12.3 14.1 4.79 0.333 0.469 16.0 4.09 6.39
19.9 12.5 1.24 0.58 0.62
4.37 2.85 4.20 7.51 11.6 6.70 0.263 0.592 11. 85 1.44 7.956 15.15 57.6 l.26 0.50 0.62
9.93 7.69 17.5 13.9 17.3 7.50 0.361 0.518 19.0 4.34 9.783 30.0 44.2 2.5 1.6 1.7
2.95 1.24 2.137 3.18 2.37 1.65 6.34 8.11 2.63 3.79 l.56 l.0 l.:n 0.688 0.342 0.361
CuG:1 ...... , ......
CuSi. .............
CuGe .............
* See
4.53 4.81 9.98 l.58 4.15 4.17 5.16 7.69 l.03 l.71
q
CQ
>-3 (") '""""
>u
!:d
o
>u ~
!:d
'"'3 EI
)-f
U1
o>:;j
Elastic Constants of Copper Alloyst
component
CuZu ............. CuAI. ...........
> (") o
U1
1.59 1.59 l.67 l.55 l.59 l.61 l.67 l.73 l.52 l. 57
-0.671 -0.674 -0.711 -0.65 -0.672 -0.685 -0.709 -0.745 -0.637 -0.663 -------
also Tables 2e-l through 2e-6.
-rRecent data by W. L. Bond and H. J. McSkimin. t Data from C. S. Smith.
1.348
1.335 l.305 l.346 l.349 l.336 l.335 l.350 l.333 l.333
16.34 16.58 15.95 16.49 16.51 16.78 16.09 16.64 16.66 16.30 ----
11.92 12.16 11.77 11.93 12.10 12.42 11.88 12.60 12.00 11.83
.-.---~---
7.42 7.49 7.66 7.43 7.41 7.48 7.49 7.41 7.50 7.50
I I
I
13.39 13.63 13.16 13.45 13.57 13.87 13.28 13.95 13.62 13.32
3.36 3.39 3.66 3.25 3.36 3.43 3.56 3.-
l.l
o
c::j U1 t-3 l.l U1
....
Cll
Cd ............... Mg ............... Zn ............... Co ............... --
X 10-10 12.12 5.86 16.35 30.71
C12
X 10-10 4.81 2.49 2.64 16.5
C13
X 10-10 4.42 2.08 5.17 10.27
C33
X 10-10
C44
4.45 6.60 5.31 35.81
X 10-10
B
=
1 2(811 + 812) +
1.85 1.65 3.78 7.55 ------
-
---
833
5.03 3.46 8.26 / 19.01 - - - _ .. _-
---
..
_-
+ 4813
X 10-10
TABLE
Material
3f-5.
ADIABATIC AND ISOT.HERMAL ELASTIC CONSTANTS AND ATTENUATION DUE TO HEAT FLOW
a.,
lO-'Xdensity, kg/m'
joules/kg/oC X 10-'
a X 10'
l/oC
K X 10-' watts/m'/mfOC
).8 X 10-10 newtons/m'
P. X 10-10 newtons/m'
2.699 1.82 8.96 19.32 7.87 11.4 1.74 8.90 10.49 7.3 19.3 7.1 2.2
0.9 2.17 0.384 0.13 0.46 0.128 1.04 0.44 0.234 0.225 0.134 0.382 0.92
23.9 12.4 16.5 14.2 11. 7 29.4 26 13.3 19.7 23 4.3 29.7 0.5
2.22 1.58 3.93 2.97 0.75 0.344 1.59 0.92 4.18 0.67 2.0 1.12 0.01
6.1 1.6 13.1 15.0 11.3 3.3 2.56 16..4 8.55 4.04 31.3 4.2 1.61
2.5
()." _ ).8)
X 10-' newtons/m'
y o8) X 10-' newtons/m'
(Yo" -
A//', nepers/m
t;
Aluminum ... ',' .......
Beryllium ......... ',' .. Copper ............... Gold .................. Iron .......... ', ........
Lead ................. l:\'Iagnesium ...........
NickeL ............... Silver ................ Tin ................... Tungsten .......... ,.... Zinc ..................
Fusedsi1ica ...........
-
- - - _.. -
- - -- - -
14.7 4.. 6 2.85 8.2 0.54 1.62 8.0 2.7 2.08 13.4 4.2 3.12
3.8 1..4 5.5 6.1 2.7 2.12 1.3 5.7 4.5 3.5 3.1 4.3 0.00045
3.2 11.4 3.7 1.5 4.8 0.36 2.1 6.1 ~.6
4.0 2.8 10.7 0.002
2.3 X 10-16 2.1 X 10-18 4.45 X 10-10 1.95 X 10- 16 1.88 X 10-" 2.95 X 10-15 2.0 X 10-" 3.8 X 10-17 1.95 X 10-15 9.7 X 10-10 5,0 X 10-17 3.8 X 10-18 2.6 X 10-".
o q
~ H
o
>Tj
5 ~ ~
t;;J
"(J).
o
I:;J
-
"(J).
TABLE
Metal
3f-6.
o
FACTORS GOVERNING INTERGRAIN HEAT FLOW IN METALS
Pb
R ................................. 0.065 (C p - C.)/C•.. .................... 0.067 Product .........., .................... 4.4 X 10-3
Ag
Cu
Au
Fe
0.031 0.040 1.2 X 10-3
0.031 0.028 8.7 X 10-4
0.014 0.038 5.3 X 10-4
0.022 0.016 3.5 X 10-4
~
AI
0.0009 0.046 4 X 10-5
W
t::1
"(J).
10-1 0.006 6 X 10-9
<j" o'""'
-..J
ACOUSTICS
where fis the frequency, v the velocity, K the heat conductivity, and E the appropriate elastic constant for the mode of propagation considered. Since Q = B/2A, it becomes pC.v' (3f-16) Q = 2fK[(E" - E9)/E8] where Q is the ratio of 271" times the energy stored to energy dissipated per cycle and B is the phase shift per unit length. Table 3f-5 shows the attenuation for a number of solids due to thermoelastic loss. The thermoelastic effect produces about half the thermal attenuation for metals but only about 4 percent for dielectric crystals. The largest source of loss for these crystals is the Akhieser effect which results from an instantaneous separation of the phonon modes, followed by an equilibration of these temperatures which occurs with a relaxation time 7'. This effect produces a loss of about 40 times the thermoelastic loss for insulators. According to a recent theoryl this loss is 3K
7'
=
C.v'
(3f-17)
where the ratio of the total thermal energy Eo to the specific heat C. is proportional to a factor F times the absolute temperature T. F varies from 0.25 at very low temperatures to unity above the Debye temperature. D is a nonlinear constant which can be calculated when the third-order moduli of the material are known, K is the thermal conductivity, p the crystal density, v is the sound velocity, and v the Debye average velocity. A number of third-order moduli have been measured for at least six crystals, and the agreement with Eq. (3f-17) is good. Figure 3f-1 shows typical measurements of the attenuation of the two -shear waves and the longitudinal wave in a single crystal of aluminum oxide AhOa. Below 20 to 30 K the attenuation is independent of the temperature. This region is assumed to be controlled by scattering losses due to imperfections in the crystal and transducers. This loss is a good measure of the imperfections in the crystal. Above this region the attenuation for the slow shear wave increases as the fourth power of the temperature from 20 to 80 K. This is in agreement with the theory of Landau and Rumer (1937),' which considers the direct interactions of the acoustic waves with the thermal phonons. This formula can be put into the form a =
60')"!(£ Mv'
('!.) a 271"A (J
(3f-18)
where a is the attenuation in nepers per cm, ')' the Grueneisen constant, k the Boltzmann constant, M the average atomic mass, v an average sound velocity, T the absolute temperature, (J the Debye temperature, and A the acoustic wavelength. The agreement with the formula is quite good. The fast shear wave and the longitudinal wave hehave in a different manner with slopes proportional to T7 and TO, respectiveiy. Explanations for these values have not yet been obtained. For higher temperatures when the product of the angular frequency w times the thermal relaxation time 7' is much less than unity, individual interactions between sound waves and phonons can no longer be followed. In this region the two effects causing the thermal attenuation are the thermoelastic effect and the Akhieser effect, discussed above. 3f-4. Loss Due to Intergrain Heat Flow. A related .thermal loss that occurs in polycrystalline material is the thermoelastic relaxation loss which arises from heat flow 1 See W. P. Mason, "Physical Acoustics," vol. HIB, chap. 6, Academic Press, Inc., New York, 1965. . 2 L. Landau and G. Rumer, Physik. Z. Sowjetunion 11, 18 (1937).
ACOUSTIC PROPERTIES OF SOLIDS
from grains that have received more compression or extension in the course of the wave motion than do adjacent grains. The Q from this source has been shown to bel
..!:
Q
= Cp
-
C.
C.
R~ fo2
(3f-19)
+ f2
where R is that fraction of the total strain energy which is associated with the fluctuations of dilations, and fo, the relaxation frequency, is approximately D fo = L c 2 =
K P
(3f-20)
Cp L c 2
where L, is the mean diameter of the crystallites and D the diffusion constant. 3.0~----------.-----.-----~
(01
(b)
2.0
1.0
AI 20 3 - LINDE #8 a-AXIS PROPAGATION I GHz ZnS TRANSDUCERS
0.5 0.4 u ...... In 0.3 "'Z" 0 0.2 E
j::::
Z
w
I: c:t
0.10
SLOW SHEAR WAVES (T2)
0.05 0.04 0.03
. FAST SHEAR WAVES
0.02
(Tl)
COMPRESSIONAL WAVES
(U
FIG. 3f-1. Attenuation of plane waves in aluminum oxide.
For most materials, the relaxation frequencies are under 100 kHz. Table 3£-6 gives the product [(Cp - Cv)/Cv]R for a number of metals. 3f-6. Loss Due to Grain Rotation. Another source of loss due to grain structure in metals is the loss due to the viscosity of the boundary layer between grains. This allows a relative rotation of grains provided the relaxation time is comparable to the time of the applied force. Figure 3f-1 shows the elastic modulus and the associated Q of a polycrystalline aluminum rod in torsional vibration at a frequency of 0.8 Hz 9,S compared with similar measurements for a single crystal. The relaxation time for grain-boundary rotation is a function of temperature according to the equation 7"
= 7"oe HIkT
(3f-21)
C. Zener, "Elasticity and An elasticity of Metals," p. 84, University of Chicago Press Chicago, 1948. 1
ACOUSTICS
where H, the activation energy, is of the same order as that found for creep and self-diffusion. Sf-S. Loss Due to Grain Scattering of Sound. Another effect of grain structure in solids is a loss of energy from the main wave due to the scattering of sound when the sound wavelength is of the same order as the grain size. This scattering occurs because adjacent grains have different orientations, and a reflection of sound occurs because of the resulting impedance difference between grains. An approximate formula' holding when the wavelength is larger than three times the grain size, and multiple scattering is neglected, is nepers/m
(3f-22)
where L, is the average grain diameter, f the frequency, v the velocity, and S a scattering factor related to the anisotropy of the metal. The scattering factor taking account of mode conversion has been calculated for cubic and hexagonal crystals. 2 Since thf! formulas are complicated, the reader is referred LO a recent review article. 3 The formula (3f-22) is valid in the Rayleigh scattering region when the wavelength is three times or larger than the grain diameter. For higher frequencies the attenuation increases proportional to the square of the frequency and finally becomes independent of the frequency for high frequencies.
I-
z
~
0.75
(/)
z 0.70
...........
0 0 0
0.65
~ .....
(/)
;;i
>
~-
0::
I.!..
...
~
\\.
/
0::
0.04 a. 0.35
~/
0::
0 I-
0
____ SINGLE CRYSTAL- I - -
~-, k
j:::
0 , where S is the cross-sectional area, i!? the total flux through the magnetostrictive transducer, and 4> the time rate of change of this flux. Hence all the fundamental quantities and coupling factors can be expressed in terms of the analogous quantities as shown by Table 3g-3. These hold for materials having a closed magnetic circuit such as a ring or a rod with closing magnetic circuit having a reluctance small compared with that for the rod. If this is not true, demagnetizing factors and additional reluctance values have to be taken account of and the value of i!? is the average value determined by all these factors. In a transducer, however, it is not U and 4> that we deal with, but rather the input voltage and current. These quantities are related by equations of the type E
=
Ndif> dt
U
=
Ni
(3g-25)
where N is the number of turns and the voltage, current, flux, and magnetomotive forces are directed as shown by Fig. 3g-6. These are the equations of a gyrator, shown 1 W, P. Mason, "Piezoelectric Crystals and Their Application to Ultrasonics," chap. XII, D. Van Nostrand Company, Inc., Princeton, N.J., 1950.
1"
3g-3. MAGNETOSTRICTIVE PROPERTIES OF METALS AND FERRITES Data from C. M. Van der Burgt, Phillips Research Repts. 8,91-132, 1953
TABLE
d" X 10 9 I du X 10 9 webers/newton webers/newton
Material
99.9 nickel. . . . . .......... . 50 Co; 0.5 Cr; 49.5 Fe ... . 35 Co; 0.5 Cr; 64.5 Fe .......... . NiO (15 %); ZnO (35 %); Fe,O, (50%) ...................... . NiO (18%); ZnO (32%); Fe,O, (50%) ...................... . NiO (25 %); ZnO (25 %); Fe,O, (50%) ...................... . NiO (32%); ZnO (18%); Fe,O, (50%) .................... . NiO (40%) ZnO (10%); Fe,O, (50%) ..................... . NiO (50%) Fe,O, (50%) ....... .
-5.3 12.3 13.4
Rev. per. long. /LT(PO)
X 10 4 henrys/m
Rev. per shear /LT(Po) X 10' henrys/m
YOB =
Jc SH
X 10-11
I,,,,
newtons/m2
2.84 8.3 19.2
2.0 2.2 2.1
0.14 0.20 0.14
Shear stiff-
ness GE X 10-11 newton/m 2
I-'
l'Y 00 Torsional coupling leT
Energy stored
Hd,,'/ /L T) X 10 12 joules-m/newton'
Density, kg/m' X 10-'
0.05 0.09 0.047
8.9 8.2 8.1
-11.1
-28.5
1.8
0.034
139
0.68
0.063
0.003
5.06
-16.0
-39.5
77.5
1.62
0.073
74
0.62
0.115
0.0165
4.9
-9.8
-20.3
22.0
1.53
0.082
20
0.59
0.110
0.022
4.85
-8.7
-15.8
13.4
1.5
0.093
13.2
0.58
0.105
0.0282
4.85
-5.9 -4.4
-13.0
5.5 2.8
1.37 0.93
0.112
0.54 0.36
0.13 0.09
0.0315 0.0344
4.76 4.20
190
O.OS
5.35 2.4
>
()
o q
UJ.
>-3
H
Data from R. M. Bozarth, E. A. Nesbit, and H. J. Williams
()
UJ.
Material
Flux density B, webers/m'
Long. rev. per /LT(Po) X 10'
henrys/m
Young's modulus YoA X 10-11 newtons/m ll,
Longitudinal coupling
k"
Energy stored
d" X 10 9 webers/newton
Hd33'//LT) X 10 12
joules-m/newton'
Density, kg/m.' X 10-'
99.9 % nickeL ...................................
0.4 0.5 0.55
0.98 0.515 0.317
2.1
0.232 0.208 0.177
-5.0 -3.26 -2.18
0.127 0.103 0.075
8.9
45% Ni, 55% Fe, i.e., 45% Permalloy ..............
0.722 0.965 1.2 1.4
8.94 7.36 4.45 1.97
1.6
0.154 0.179 0.178 0.15
11.5 12.2 9.4 5.3
0.074 0.101 0.099 0.071
8.17
2V Permindur, 2%V, 50% Co, 4il% Fe .............
1.5 1.6 1.8 2,0
3.54 2.61 2.23
2.3
0.238 0.222 0.202 0.18
0.123 0.108 0.089 0.07
S.3
1.14
... ...
... ... ... ...
... ...
9.35 7.5 6.3 4.0
PROPERTIES OF TRANSDUCER MATERIALS
by the symbol of Fig. 3g-6, which does not satisfy the reciprocity relationship. call ZM the magnetic impedance defined by U
ZM = dif!/dt
3-129 If we
(3g-26)
it is evident that the electrical impedance at the terminals of the transducer is equal to ZE
E
N2
Z
ZM
(3g-27)
=--;- = -
Hence the effect· of the gyrator coupling is to invert all the elements of the equivalent
-+-1
N TO I
D~ tr
=
VYo H
;
P
FIG. 3g-6. Equivalent circuit of a magnetostrictive rod.
circuit. Hence one should determine the element values of Fig. 3g-6 for the appropriate terminating conditions and then invert the values in accordance with Eq. (3g-27) to determine the elements of a magnetostrictive transducer. The values given in Fig. 3~-6 are for a longitudinally vibrating rod where S is the cross-sectional area and I the length. Jl-s is the average value of the permeability in the equations for the reluctance R (3g-28) where
P.s
is for the constant stress condition.
3h. Frequencies of Simple Vibrators.
Musical Scales
ROBERT W. YOUNG
U.S. Naval Undersea Research and Development Center
3h-1. Strings.
The fundamental frequency of vibration of an ideal string is (3h-1)
where 10 is the frequency, l is the free length, F is the force (tension) stretching the string, and m is the mass per unit length. Values of m for steel and gut strings are given in Table 3h-1. In addition to the vibration in a single loop which gives rise to the fundamental frequency, the ideal string may vibrate in harmonics whose frequencies are
In
= nlo
(3h-2)
where n is the integer denoting the particular mode of vibration. The length of each vibration loop is lin. These successive lengths and the corresponding periods of vibration (i.e., the reciprocals of the frequencies) constitute a harmonic series according to the strict mathematical definition; nowadays, however, the frequencies themselves are usually said to make up a harmonic series. The frequencies of actual strings depart somewhat from the frequencies computed from the simple formula because actual strings are stiff, they may be partially clamped at the ends, they are not infinitely thin, the tension increases with amplitude of vibration, the mass per unit length is not exactly uniform, there is internal damping and damping due to the surrounding air and supports, and the supports are not infinitely rigid. In the formulas which follow damping has been neglected. For an actual string set (3h-3) 1= nlo(l + G) where the factor (1 + G) is a measure of the departure (Le., the inharmonicity) from the ideal harmonic values. Table 3h-2 lists values of G for various small perturbations. The approximations are valid only when G is small. For musical purposes it is often convenient to give the inharmonicity in cents (hundredths of an equally tempered semitone) by setting 1
+G
=
20/ 1,200
= eO/ 1,7S1
(3h-4)
1,731G. where 8 is the inharmonicity. To a usually acceptable approximation, Ii If the stiff string listed in Table 3h-2 is of steel music wire, Yip = 25 ..5 X 10 6 m2jsec 2 , Y being Young's modulus and p the density. The tension is very nearly F = l'pJo 27rd 2. Thus for steel wire, and by virtue of the stiffness formula, the inharmonicity in cents is 0 = 3.4 X 101sd2n2IJ02l4, provided that the diameter and length are in centimeters. 3-130
FREQUENCIES OF SIMPLE VIBRATORS. TABLE
Diaro mID
in.
3h-1. Steel, giro
MUSICAL SCALES
3-131
MASS PER UNIT LENGTH OF STEEL AND GUT STRINGS*
Gut, giro
-- - - - -- -
Diaro mID ~-
in.
Steel, giro
Gut, giro
Diaro mm
in.
Steel, giro
Gut, giro
- - - - - - - -- - - -- -
0.20 0.22 0.24 0.26 0.28
0.0079 0.0087 0.0094 0.0102 0.0110
0.25 0.30 0.35 0.42 0.48
0.04 0.05 0.06 0.07 0.09
1.00 1.02 1.04 1.06 1.08
0.0394 0.0402 0.0409 0.0417 0.0425
6.15 6.40 6.65 6.91 7.17
1.10 1.14 1.19 1.24 1.28
1.80 1.82 1.84 1.86 1.88
0.0709 0.0717 0.0724 0.0732 0.0740
19.9 20.4 20.8 21.3 21.7
3.56 3.64 3.72 3.80 3.88
0.30 0.32 0.34 0.36 0.38
0.0118 0.0126 0.0134 0.0142 0.0150
0.55 0.63 0.71 0.80 0.89
0.10 0.11 0.13 0.14 0.16
1.10 1.12 1.14 1.16 1.18
0.0433 0.0441 0.0449 0.0457 0.0465
7.44 7.71 7.99 8.27 8.56
1.33 1.38 1.43 1.48 1.53
1.90 1.92 1.94 1.96 1.98
0.0748 0.0756 0.0764 0.0772 0.0780
22.2 22.7 23.1 23.6 24.1
3.97 4.05 4.14 4.22 4.31
0.40 0.42 0.44 0.46 0.48
0.0157 0.0165 0.0173 0.0181 0.0189
0.98 1.08 1.19 1.30 1.42
0.18 0.19 0.21 0.23 0.25
1.20 1.22 1.24 1.26 1.28
0.0472 0.0480 0.0488 0.0496 0.0504
8.86 9.15 9.46 9.76 10.1
1. 58 1.64 1.69 1.75 1.80
2.00 2.02 2.04 2.06 2.08
0.0787 0.0795 0.0803 0.0811 0.0819
24.6 25.1 25.6 26.1 26.6
4.40 4.49 4.58 4.67 4 . 76
0.50 0.52 0.54 0.56 0.58
0.0197 0.0205 0.0213 0.0220 0.0228
1.54 1.66 1.79 1.93 2.07
0.27 0.30 0.32 0.34 0.37
1.30 1.32 1.34 1.36 1.38
0.0512 0.0520 0.0528 0.0535 0.0543
10.4 10.7 11.1 11.4 11.7
1.86 1.92 1.97 2.03 2.09
2.10 2.12 2.14 2.16 2.18
0.0827 0.0835 0.0843 0.0850 0.0858
27.1 27.6 28.2 28.7 29.2
4.85 4.94 5.04 5.13 5.23
0.60 0.62 0.64 0.66 0.68
0.0236 0.0244 0.0252 0.0260 0.0268
2.21 2.36 2.52 2.68 2.84
0.40 0.42 0.45 0.48 0.51
1.40 1.42 1.44 1.46 1.48
0.0551 0.0559 0.0567 0.0575 0.0583
12.1 12.4 12.8 13,1 13.5
2.16 2.22 2.28 2.34 2.41
2.20 2.22 2.24 2.26 2.28
0.0866 0.0874 0.0882 0.0890 0.0898
29.8 30.3 30.9 31.4 32.0
5.32 5.42 5.52 5.62 5.72
0.70 0.72 0.74 0.76 0.78
0.0276 0.0283 0.0291 0.0299 0.0307
3.01 3.19 3.37 3.55 3.74
0.54 0.57 0.60 0.64 0.67
1.50 1.52 1.54 1.56 1.58
0.0591 0.0598 0.0606 0.0614 0.0622
13.8 14.2 14.6 15.0 15.4
2.47 2.54 2.61 2.68 2.74
2.30 2.32 2.34 2.36 2.38
0.0906 0.0913 0.0921 0.0929 0.0937
32.5 33.1 33.7 34.3 34.8
5.82 5.92 6.02 6.12 6.23
0.80 0.82 0.84 0.86 0.88
0.0315 0.0323 0.0331 0.0339 0.0346
3.94 4.14 4.34 4.55 4.76
0.70 0.74 0.78 0.81 0.85
1.60 1.62 1.64 1.66 1.68
0.0630 0.0638 0.0646 0.0654 0.0661
15.7 16.1 16.5 16.9 17.4
2.81 2.89 2.96 3.03 3.10
2.40 2.42 2.44 2.46 2.48
0.0945 0.0953 0.0961 0.0968 0.0976
35.4 36.0 36.6 37.2 37.8
6.33 6.44 6.55 6.65 6.76
0.90 0.92 0.94 0.96 0.98
0.0354 0.0362 0.0370 0.0378 0.0386
4.98 5.20 5.43 5.67 5.91
0.89 1.70 0.0669 17.8 0.93 1.72 0.0677 18.2 0.97 1.74 0.0685 18.6 1.01 1.76 0.0693 19.0 1.06 1.78 0.0701 19.5
3.18 3.25 3.33 3.41 3.48
2.50 2.52 2.54 2.56 2.58
0.0984 0.0992 0.1000 0.1008 0.1016
38.4 39.1 39.7 40.3 40.9
6.87 6.98 7.09 7.21 7.32
* This table is based on a density of steel of 7.83 glom'. Density of gut is assumed to be 1.4 g/cm', about one-sixth that of steel. This is only approximate, since the density of gut varies from sample to sample, and increases markedly with humidity. Brass wire has a density of 8.7 glcm', about 1.1 times that of steel.
ACOUSTICS
Sh-2. Air Columns and Rods. The air within a simple tube of oonsta:nt cross section, open at both ends or closed at both ends, vibrat,es freely at a ~requency near
f
=
nc
(3h-5)
2l
where n is an integer (mode of vibration number), c is the speed of sound in the contained,air, and l is the length of the tube. (See Sec. 3d for speed of sound in air and its dependence oil temperature.) Th!J diameter of the tube mus~ be relatively small; TABLE
3h-2.
PERTURBATION IN FREQUENCY OF
A STRING ,
Explanation
G
Cause
.
Stiffness Yielding support
Variable density
n'7I" 3d'Y 128l'F 4ml
. 7I"nx - ~1fl (J(x) sm'-· - dx l 0 . l
.'
,
'
.
Y is Young's: modulus, dis the diameter of the string . The support consists of a mass M Oll a spring of transverse for.ce constant K. Multiply by 2 if there are two such supports The mass per .unit length is m = mo[l + (J(X) 1 where mo is the mean value over the string and :D is the distance Jrom one end of the string; the function (J(x) must be small in cOll1parison with unity
plane sound waves propagated longitudinally are assumed. The same formula applies to thin rods vibrating longitudinally and suitably supported (say, at distances l/2n fromt1te ends) so that the v'ibration is not inhibited .. (See Sec. 3f for speed of sound . in SJlids.) . . An open organ pipe is an' example of a doubly open tjIbe of constant cross section. To .calculate its frequency adequately it must be recognized, however, that the .air beyond the physical ends of the tube partakes of the vibration and adds inertia to the vibrating system. (This does not mean, however, that there is a velocity antinode beyond the end of the tube.) The necessary corrections to the simple formula are usually introduced as empirical "end corrections" to be added to the geometrical length; thus (3h-6) where Xl = O.3d is the correction for the unimpeded end (d being the inside diameter of the pipe) and X2 = lAd is the correction for the mouth of the pipe. These are rough approximations; the literature on the end correctibn is extensive. 1 The air inside a cylindrical tube that is closed at one end and open at the other vibrates at frequency . ' nc (3h-7)
f
= 4(l
+ x)
where x = O.3d if the open end is unimpeded. In the case of the "closed" organ pipe . (meaning closed at one end only), for the mouth x = lAd. 1 E. G. Richardson, ed , "The Technical Aspects of Sound," vol. I, pp. 493-496, 578, Elsevier Publishing Company, Amsterdam, 1953; Harold Levine, J. Acoust. Soc. Am. 26, 200-211 (1954).
FREQUENCIES OF SIMPLE VIBRATORS.
3-133
MUSICAL SCALES
The speed of sound c. (and thus the frequency of vibration) in a gas contained within it tube is reduced somewhat from its value Co in free space, as a consequence of friction
and loss of heat to the wall of the tube. If the frequency of vibration f and the tube diameter d are such that dft > 2v t , v being the kinematic viscosity of the gas, the speed of sound (longitudinal phase velocity) within the tube isl
where y is the ratio of specific heats, and P r the Prandtl number for the gas. For air at 20°C, and when dft > 0.8 with d in cm andfin hertz, with slight approximation the Helmholtz-Kirchhoff correction for the speed of sound is c = Co
( 1 - 0.33) dft
Correspondingly the interval by which the frequency of vibration is lowered owing to friction and heat conduction is 572/dft cents. As df! becomes less than 2vt a transi~ tion 1 occurs to an even more marked reduction in the speed of sound propagation in the tube. The air in a conical tube is resonant in some cases at the same frequencies as a doubly open cylindrical tube of the same length, but there is the important difference that the contained sound waves are spherical rather than plane. Table 3h-3 gives equations 2 to be solved for each combination of end conditions; k = 27fj/c. "Closedopen," for example, means that the smaller end of the truncated cone is closed while the larger end is open; Tl is the slant distance from the extrapolated apex of the cone to the smaller end and T2 is the slant distance to the larger end. The slant length of the resonator is thus T2 - Tl. When Tl = 0, the length is T2 and the cone is complete to the apex. Formulas for computing frequency when the cone is complete are shown at the right of Table 3h-3. As in the case of cylindrical tubes, the length should be TABLE 3h-3. FREQUENCIES OF CONICAL RESONATORS Ends
Equation
Closed-closed Closed-open
tan le(r, - TI)
= -
Open-closed
tan le(r, - TI)
=
Open-open
len
ler, _~n.::...c_
f =
2(r, - n)
Forrt.= 0 tan ler,= leT, nc
it
= 2r2
tan len = leT2
f = nc 2r2
slightly modified by end corrections. As the angle of the cone increases the correction decreases and .may even become negative. 3 3h-3. Volume Resonators. The Helmholtz resonator consists of a nearly closed cavity of volume V with an opening of acoustical conductance C. If the opening is 1 A. H. Benade, J. Acoust. Soc. Am. 44, 616~623 (1968). Multiplication by the correction term is erroneously shown there in eq. (13e), instead of division. 2 Eric .J. Irons, Phil. Mag. 9, 346~360 (1930). 3 A. E. Bate and E. T. Wilson, Phil. ,Ma(7.J,3
H
o
Ul
ARCHITECTURAL ACOUSTICS
3-151
frequency in the range from 125 to 4,000 Hz) as a function of weight of the partition in pounds per square foot of surface area. The straight line repres~nts an average of the experimental data showing that the average transmission loss increases approximately 4.4 dB for each doubling of mass per unit area of a homogeneous partition. The transmission loss for a partition is not constant with frequency, increasing usually 3 to 6 dB/octave. A single number which represents the sound transmission loss of a partition averaged over frequency may correlate rather poorly with the subjective assessment of the insulation value of the partition. Therefore another rating is frequently employed to represent the sound insulation value of a partition by a single number; "sound transmission class" (STC). The STC value of a partition is determined by comparing the curve of transmission loss vs. frequency for the partition with a set of standardized transmission loss vs. frequency contours.! Sound insulation values for various types of walls and floors employed in ordinary building construction are given in Table 3j-3. Note that a compound-wall construction can yield relatively high sound insulation with relatively low mass per unit wall area. The double-wall construction is one such example. It is important that the separation between the walls be as complete as possible-structural ties will greatly reduce the effectiveness of such a structure. 3j-S. Noise Level within a Room. The sound level of noise which is transmitted into a room from the outside depends on (1) the noise-insulating properties of its bounding surfaces, (2) the total absorption in the room, and (3) the characteristics of the noise source. The following formula gives a rating of the overall noise reduction provided by the enclosure. It represents, approximately, the difference between the noise level outside a room and the noise level inside a room. Level difference
=
10 log ~
dB
(3j-6)
where a represents the total absorption in the room in sabins defined by Eq. (3j-4), and T represents the total transmittance of the enclosure given by (3j-7) where 7"1 is equal to the transmission coefficient of area Sl, etc. H a source of noise is within a room, then at distances near to the source the sound pressure decreases inversely with increasing distance from the source; there is a decrease in sound pressure level of 6 dB for each doubling of the distance from the source, just as if the source were in the open air. However, at every point in the room there will be an additional contribution to the total pressure as a result of reflections from the walls. As one recedes from the source, the reflected contributions become more and more important until direct sound from the source becomes negligible by comparison. Then if the sound field is diffuse (perfect diffusion is said to exist if the sound pressure everywhere in the room is the same, and it is equally probable that the waves are traveling in every direction), the sound pressure level in the room will be given approxi mately by
Lp = 10 log
aW + 136.4
dB
(3j-8)
1 R. D. Berendt, G. E. Winzer, and C. B. Burroughs, "A Guide to Airborne, Impact, and Structure Borne Noise-Control in Multifamily Dwellings," U.S. Department of Housing and Urban Development, Washington, D.C., September, 1967. See also ASTM Rept. E90-66T, Tentative Recommended Practice for Laboratory Measurement of Airborne Sound Transmission Loss of Building Partitions.
Cf
I-'
Cl
~
TABLE
3j-3.
INSULATION VALUES FOR VARIOUS TYPES OF WALL AND FLOOR CONSTRUCTION'"
Transmission Loss, dB Type of construction
Weight, lb/ft'
STC rating, dB
39 80 34 34
47 53 43 45
125 Hz
175 Hz
--Solid concrete, 3 in. thick .............................. Solid concrete, 6 in. thick, both sides plastered ........... Hollow concrete block, 6 in. thick ...................... Same as above except painted .......................... Hollow gypsum block, 3 in. thick, one side plastered, other side plaster on resilient clips ......................... Double brick wall, 6 in. cavity. Overall thickness 18 in ... Wood stud, gypsum wallboard ......................... Wood stud, gypsum lath and plaster .................... Same as above but with perforated lath ................. Staggered wood stud, gypsum board and insulation ....... Wood stud, plastered gypsum lath on resilient clips ....... Metal channel stud, gypsum board ..................... Metal channel stud, 2 layers of gypsum board ............ -
35 39 32 37
37 42 33 35
250 Hz
350 Hz
500 Hz
700 Hz
1,000 2,000 Hz Hz
4,000 Hz
--- - - - - - - - - - --- --- --40 42 33 36
41 47 37 39
44 50 40 42
49 55 43 47
52 58 47 49
59 64 51 55
64 48 58
o q
U2
27 120 6 15 14 14 13 5 9
45 62 38 46 44 46 52 39 47
48 48 20 32 42 39 46 20 31
43 54 21 34 34 38 44 24 35
41 54 27 37 32 40 46 30 38
43 56 33 40 38 41 53 33 41
47 56 37 42 42 42 54 37 45
48 60 38 46 47 44 56 43 51
44 64 43 48 49 48 57 47 53
55 69 48 48 50 56 50 48 54
62 43 63 62 51 62 44 54
-
* Values based on data taken from R.
> l.l
D. Berendt, G. E. Winzer, and C. B. Burroughs, "A Guide to Airborne, Impact, and Structure Borne Noise-Control in Multifamily Dwellings," U.S. Department of Housing and Urban DeVelopment, Washington, D.C., September, 1967. For average values for other types of construction including doors and windowpane materials, see Fig. 3i-6. For the definition of STC used to obtain the ratings (above), see ASTM Rept. E90-66T, Tentathe Reoommended Practice for Laboratory Measurement of Airborne Sound Transmission Loss of Building Walia and Floors.
1-:3 H
l.l
U2
ARCHITECTURAL ACOUSTICS
8-153
if a value of pC = 40.8 rayls is assumed for air; W = power of the sound source in watts, and a = total absorption of the room in sabins. A consideration of the above formula shows that, if the acoustic-power output of the noise source remains constant, and if the total absorption in the room is increased from al to a2, the reduction in noise level is given by Noise reduction = 10 log ~
5
within the external meatus. The values in Table 3k-2 are representative but arp. subject to wide variations among individuals. 1 Sk-S. Minimum Audible Sound. Table 3k-3lists the minimum audible (threshoiu, sound pressures of pure tones measured at the entrance to the external meatus. The pressure measurements were made when the subject heard the tone one-half the time it was presented via an earphone applied to his ear with a standard static force. Observations were made on young persons, eighteen to twenty-five years of age, with no record of hearing impairment. Sound pressures were determined with a probe-tube microphone a:i:J.~d are given in decibels relative to 2 X 10-4 dyne/cm 2 • The results of such measurements made in various laboratories show a considerable amount of variation. The pressures in Table 3k-3 are based on measurements made in two indep~endent laboratories; see the first footnote for details. The variance in the threshold sound pressures measured at the entrance to the meatus has :been so great that such pressures cannot serve usefully as standards for audiometry. Experience has shown that the most accurate method for storing audiometric standard threshold information is as follows. Measurements of threshold voltages on an earphone applied to a number of young persons at the various audiometric frequencies are the primary data. The sound pressures which are produced by these voltages when the earphone is applied to an artificial ear (coupler) then serve as the standard thresholds for that particular earphone-coupler combination. This method of measuring and storing standard threshold sound pressures is now in use in several countries. A comparison of the standard thresholds was completed under the auspices of Technical Committee 43 on Acoustics of the International Organization for Standardization (ISO). An internationally agreed-upon standard threshold has been issued by ISO in its Recommendation R389, Standard Reference Zero for the Calibration of Pure Tone Audiometers. The standard data in it are sound pressures corresponding to the threshold of hearing for five earphone-coupler combinations now in use in several countries. 2 Sk-4. Threshold of Feeling or Discomfort. The upper limit for a tolerable intensity of sound rises substantially with increasing habituation. Moreover, a variety of subjective effects are reported, such as discomfort, tickle, pressure, and pain, each at a -alightly different level. As a simple engineering estimate it can be said that naIve listeners reach a limit at about 125 dB SPL and experienced listeners at 135 to 140 dB. These are overall measures of sound falling within the audible range and are roughly independent of frequency. 3k-5. Differential Thresholds for Pure Tones and Noise. A differential threshold represents a cl),reful determination by laboratory methods of the ability of a subject to just detect, and report, a difference in any specific property of a sound, all other factors presumably being held constant. The method for determining the differential threshold for intensity of pure tones employed one tone beating with a second tone at 3 beats per second. 3 Much evidence is available to support what should be kept always in mind, that thresholds determined by other methods are a function of numerous psychological parameters and will differ systematically from the values in Table 3k-4. A more conventional method was used to determine the thresholds for white noise, with the results given in the last column. 4 1 E. Waetzmann and L. Keibs, Horschwellenbestimmungen mit dem Thermophon und Messungen am Trommelfell, ~ Ann. Physik 26, 141-144 (1936); O. Metz, The Acoustic Impedance Measured on Normal and Pathological Ears, Acta Oto-Laryngol., Suppl. 63, 1-254 (1946); A. H. Inglis, C. H. G. Gray, and R. T. Jenkins, A Voice and Ear for Telephone Measurements, Bell System Tech. J. 11,293--317 (1932). 2 P. G. Weissler, International Standard Reference Zero for Audiometers, J. Aco"st. Soc. Am. 44, 264-275 (1968). 'R. R. Reisz, Differential Intensity Sensitivity of the Ear for Pure Tones, Phys. ReI'. 31,867-875 (1928). 4 G. A. Miller, Sensitivity to Changes in the Intensity of White Noise and Its Relation to MasKing and Loudness, J. Acoust. Soc. Am. 19, 609-619 (1947).
3-156
ACOUSTICS
The ability to distinguish pitch is subject to a greater range of individual variability than other functions reported here. The data given are for three trained listeners and have been smoothed in both directions. Untrained listeners usually require a greater TABLE 3k-2. ACOUSTIC IMPEDANCE OF THE EAR IN ACOUSTIC OHMS, MEASURED JUST WITHIN THE 11EATUS Frequency
Total impedance
Resistive component
250 350 500 700 1,000
200 150 125 70 55
50 40 35 25 25
Reactive component -190 -145 -1l5 -65 -50
Above 1,000 Hz measurements depend increasingly on the method of measurement.
TABLE 3k-3. MINIMUM AUDIBLE (THRESHOLD) PRESSURE AT ENTRANCE TO EXTERNAL EAR OANAL (MAO) * (In dB re 2 X 10- 4 dyne/cm 2 ) Frequency, Hz 125
250
500
1,000
1,500 2,000
- - ---- ----MAO
22
35
14
8
3,000
4,000
6,000 8,000
10,000
------ --- --- --- ---
9
9
10
9
14
17
16
The following quantities are to be added in order to obtain threshold pressures for other conditions: a. MAO to Threshold Pressure at Tympanic Membranet
Frequency, Hz 125
250
500
1,000
2,000
4,000
6,000
8,000
--- --- --------- ------ --Add ...........
0.0
0.0
-0.5
-1.0
-4.5
-10.5
-4.0
-2.5
b. MAO to Free Field (MAF) (plane wave, 0 0 azimuth in absence of head)t Frequency, Hz 125
250
500
1,000
2,000
--- ------ ------ ---
Add ....
*
+1.0
+0.5
-2.0
-4.0
4,000
6,000
8,000
10,000
--- --- --- ---
-11.0 -12.5
-7.0
-3.0
-3.0
J. P. Albnte, R. E. Shutts, M. B. Whitlock, R. K. Cook, E. L. R. Corliss, and M. D. Burkhard, Research III Normal Threshold of Hearing, AMA Arch. Otolaryngol. 68, 194-198 (1958). t F. M. Wiener and D. A. Ross, The Pressure Distribution in the Auditory Canal in a Progressive Sound Field, J. Acoust. Soc. Am. 18, 401--408 (1946). :t: L. J. Sivian and S, D. White, On Minimum Audible Sound Fields, J. Acoust. Soc. Am. 4, 288-321 (1933).
SPEECH AND HEARING TABLE
3k-3.
3-157
MINIMUM AUDIBLE (THRESHOLD) PRESSURE AT ENTRANCE TO EXTERNAL EAR CANAL (MAC)
(Continued)
c. Mean Monaural to Mean Binaural Listening § Frequency, Hz 125-2,000
4,000
6,000
8,000
10,000
-2.0
-3.0
-4.0
-5.0
-6.0
Add ...................
d. Reference Age Group (18-25) to Older Age Groups 'if
Frequency, Hz
Add for: Men 3D-39 ......... Men 40-49 ......... Men 50-59 ......... Women 30-39 ...... Women 40-49 ...... Women 50-59 ......
125-1,000
2,000
4,000
6,000
8,000
10,000
+1.0 +2.0 +5.0 +1.0 +3.0 +5.0
+2.0 +5.0 +13.0 +2.0 +5.0 +9.0
+5.0 +13.0 +27.0 +3.0 +6.0 +13.0
+6.0 +13.0 +32.0 +4.0 +8.0 +18.0
+6.0 +11.0 +35.0 +4.0 +9.0 +20.0
+7.0 +13.0 +35.0 +4.0 +9.0 +22.0
§ H. Fletcher, "Speech and Hearing in Communication," p. 131, D. Van Nostrand Company, Inc., Princeton, N.J., 1953. ~ J. C. Steinberg, H. C. Montgomery, and M. B. Gardner, Results of the World's Fair Hearing Tests, J. Acoust. Soc. Am. 12,291-301 (1940); J. C. Webster, H. W. Himes, and M. Lichtenstein, San Diego County Fair Hearing Survey, J. Acoust. Soc. Am. 22,473-483 (1950).
TABLE
3k-4.
DIFFERENTIAL THRESHOLD FOR INTENSITY, IN DECIBE.LS
Sensation level, dB above absolute threshold 5 10 20 30 40 50 60 70 80 90 100 110
Pure tones, frequency in 35
.... 7.24 4.31 2.72 1. 76
.... .... .... .... ... . ... . ... .
70
200
Hz
1,000 4,000 7,000 10,000
------------ --. ... 4.75 3.03 2.48 4.05 4.72 4.22 2.38 1.52 1.04 0.75 0.61 0.57
. ...
.... ... . ... .
3.44 1.93 1.24 0.86 0.68 0.53 0.45 0.41 0.41
.... ....
2.35 1.46 1.00 0.72 0.53 0.41 0.33 0.29 0.29 0.25 0.25
1.70 0.97 0.68 0.49 0.41 0.29 0.25 0.25 0.21 0.21
2.83 1.49 0.90 0.68 0.61 0.53 0.49 0.45 0.41
3.34 1.70 1.10 0.86 0.75 0.68 0.61 0.57
White noise 1.80 1.20 0.47 0.44 0.42 0.41 0.41
ACOUSTICS
3-158
frequency difference than that reported here. Note also that individual listeners commonly show idiosyncrasies at particular frequencies. TABLE 3k-5.
DIF~'ERENTIAL
Pure tones, frequency in Hz
Sensation level, dB above absolute threshold
125
50 0.0252 0.0140 0.0092 0.0073
5 10 15 20 30 I.
* J.
THRESHOLD FOR FREQUENCY, IN f1F IF"
0.0110 0.0060 0.0040 0.0032 II 0.0032
250
500
0.0097 0.0053 0.0035 0.0028 0.0028
0.0065 0.0035 0.0024 0.0019 0.0019
1,000
2,000
0.0049 0.0027 0.0018 0.0014 0.0014 I
0.0040 0.0022 0.0014 0.0012 0.0011
I
4,000 0.0077 0 .0042 0.0028 0.0022 0.0022
I
I
D. Harris, Pitch Discrimination, J. Aco".t. Soc. Am. 24, 750-755 (1952).
Sir-5. Masking. M:asking reff)m to OUI' inability to hear a weak sound ill the presence of a louder sound. It is usually measured by t.he amount of change in the threshold of the weaker sound, i.e., how much more intense the weak sound must be made in order to be heard over the masking sound than it needed to be when the masking sound was not present. The masking of one pure tone by another is a complex function of the particular frequencies and of the absolute level of the respective tones. See any standard text on hearing for the curves describing this relationship. The masking of a pure tone by a noise with a reasonably flat and continuous spectl'UlIl is a linear function (except at levels below 10 dB) of the total intensity within a "critical band" centered on the masked tone. The width of the critical band of frequencies whose total energy is just equal to the energy of the masked tone is given by Table 3Ic-5.
TABLE 3k-5. WIDTH OF "CRI'l'ICAL BAND" f1F AS A FUNC1'ION OF CENTER FREQUENCY F (10 log f."F)* Frequency, Hz 100
M, dB
~II~
1,000
2,000
4,000
8,000 10,000
19.417.117.118.019.923.127.729.2
* N. R. French and J. C. Steinberg, Factors Governing the Intelligibility of Speech Sounds, J. Acoust. Soc. Am. 19, 90-119 (1947). The III asking of a narrow-band noise by two tones, one higher and one lower than the noise, shows a similar relationship. The masking produced by the two tones overlaps unless the tones are separated by more than a "critical band," at which point the masking begins to fall off sharply. The critical band measured in this way is 3 to 4 dB wider than the values given in Table 3k-6. 1 The masking of one continuous noise by another can be thought of as a case of differential sensitivity to change in the intensity of a noise (see last column of Table 3k-4). Thus, above 40 dB SPL, if a weak noise is more than 10 dB less intense than a very similar masking noise, the weak noise will not be heard; its presence or absence 1 E. Zwicker, G. Flottorp, and S. S. Stevens, Critical Band Width in Loudness Summation, J. Acoust. Soc. Am. 29, 548-557 (1957). See especially the summary of the concept of critical bands, pp. 554-557.
3-159
SPEECH AND HEARING
does not produce a discriminable difference in intensity. If the spectral compositions of the two noises, masking and masked, are quite different, then the critica;I-band concept must be employed. Sk-7. Sounds of Short Duration. AcolLstic disturbances of very short duration, i.e., less than 0.0001 sec, are heard only to the extent that they transmit energy to the ear. Short pulses at ultrasonic frequencies are generally not heard unless they are rectified. Impulse or step functions excite the ear, but not efficiently. At the opposite extreme, tones, or continuous noise, of duration greater than from 0.2 to 0.5 sec are generally heard independently of duration. Between these limits relatively complex relations are found.! As a first approximation for both tones and noise, the effective intensity of short sounds is a function of total energy integrated over the duration of the sound. More accurately, the threshold is defined by2 It = kItO.8
(3k-1)
For some short tones and for many types of impulse noise, account must be taken of the frequency distribution of energy. Inasmuch as the ear varies in sensitivity as a function of frequency, any change in the shape or duration of a short acoustic pulse will also change its effectiveness because of the altered spectral composition. 3k-S. Loudness. Loudness and pitch are ways in which a listener reacts to sounds. Furthermore, within limits, a listener can use numbers to describe how much of a response he makes to the sound. These numbers usefully describe how loud or how high in pitch a sound seems to be. It is then necessary to relate how loud it is (subjective response) to how intense it is in physical terms. The loudness of a pure tone of 1,.100 Hz is described by the following relationship: log L = 0.0301N - 1.204
1
(3k-2)
in which L is the loudness measured in sones and N is the loudness level in phons (equal to the sound pressure level of the tone in decibels above 0.0002 dyne/cm 2).' Another way of putting this is to say that loudness doubles for each 10-dB change in sound pressure level. There is some evidence that the loudness of a noise grows more rapidly than that of a tone with an increase in sound pressure level, especially at low levels. The exact relations are less well known than those for a tone. The loudness of tones at other frequencies than 1,000 Hz is given by determining the loudness level in the manner described below and converting to sones by Eq. (3k-2). The loudness of noises can be measured by direct subjective comparison with a standard, such as a tone of 1,000 Hz, but such comparisons are difficult and need to be repeated by a number of judges. An approximation to the loudness of a noise can be calculated from measurements of the sound pressure level in a series of bands, usually a third-octave, a half-octave, or an octave in width, covering the audible spectrum. The total loudness of the noise is given by the formula i
Lt = 8m
+ F (18i
- 8m)
(3k-3)
! S. S. Stevens, ed., "Handbook of Experimental Psychology," pp. 1020-1021, John Wiley & Sons, Inc., New York, 1951. 2 D. B. Yntema, "The Probability of Hearing a Short Tone Near Threshold," Ph.D. Dissertation, Harvard University, 1954, 43 pp. 3 S. S. Stevens. The Measurement of Loudness, J. AcouBt. Soc. Am. 27, 815-82\1 (1955).
3-160
ACOUSTICS
The calculated loudness It should be qualified by the width of the bands used for its calculation. The terms 8 are empirical values of a loudness index shown as the parameter of the curves in Fig. 3k-1. The figure is entered with the geometric mean frequency of each band and the band pressure level as arguments. The loudness index 8 i is estimated for each of the i bands. The band having the greatesi , index 8 m is determined by inspection.
0.5 0.3 0.2 0.1 1OL.L":'5...Ll.L.Lf-j-""2!:-L.J.-!-1...J..lJt+--~.L...J+L.I..l..!..!---l j 1 5 2 5
100
1,000
10,000
FREQUENCY, Hz FIG. 3k-1. Loudness index S, as a function of geometric mean frequency of band measured and band pressure level (sound pressure level in third-octave, half-octave, or octave band under measurement). (Taken from S. S. Stevens, "Procedure for Calculating Loudness," Mark VI, Psycho-Acoustic Laboratory Report PNR-253, Mar. 1, 1961.)
As the formula indicates, total loudness is linearly additive except for a constant factor F that represents the reduction due to mutual masking of all bands except the loudest. The value of F depends on the width of the bands used. It has the value of 0.15 for third-octave, 0.2 for half-octave, and 0.3 for octave ba,nds. The loudness L t can be converted to loudness level by Eq. (3k-2).
SPEECH AND
3-161
HEARING
3k~9. Loudness L e v e l The loudness level of a tone of 1,000 Hz, expressed in phons, is denned as the sound pressure level in decibels above the reference level of 0.0002 d y n e / c m . T h e loudness level of tones of other frequencies is given b y the empirical relations in Table 3k-7. 2
TABLE
3k-7.
LOUDNESS L E V E L
AS A F U N C T I O N
AND
Sound pressure level
10 20 30 40 50 60 70 80 90 100 110
OP S O U N D
PRESSURE
LEVEL
FREQUENCY*
Frequency, Hz 125
250
500
1,000
2,000
4,000
8,000
10,000
4.0 17.0 34.0 52.0 70.0 86.0 98.0 108.0 118.0
6.3 18.0 31.0 45.5 59.5 72.5 84,5 95.5 105.5 115.5
16.0 26.5 38.5 52.0 64.5 76.0 86.0 96.0 105.0 113.0
10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0
18.0 28.0 37.0 45.5 55.0 64.0 73.5 84.5 95.0 106.0 117.0
18.0 28.0 36.5 45.0 54.0 63.5 72.5 83,0 94.5 106.0 117.5
11.0 20.5 29.5 38.0 47.0 56.0 66.0 77.0 88.0 101.5
17.0 26.0 35.0 43.5 53.5 63.5 73.5 85.5 98.0
* A m e r i c a n S t a n d a r d f o r N o i s e M e a s u r e m e n t , A S A Z24.2—1942.
N o t e that this table is based on the A S A standard and presumes the ' 'free-field" measurement of sound pressure. This requires a measurement of a plane progressive w a v e at the listener's position before the listener is placed in the field. M o r e meaningful measurements w o u l d doubtless be obtained from pressure measurements at the ear. For this purpose, apply the corrections contained in Table 3k-36 to the ear canal pressures before entering Table 3k-7. T o enter the table with sound pressure levels measured under other conditions, first add the corrections in Table 3k-36, then subtract rather than add corrections in Tables 3k-3a and 3k-3c. N o t e , however, that corrections given for presbycusis in Table 3k-3d m a y give quite misleading results because of recruitment at high frequencies in some elderly people. 3k-10. Pitch. The relation between frequency and the subjective magnitude of perceived pitch is shown b y Table 3k-8. B y definition, the pitch of a tone of 1,000 Hz at 40 d B SPL is 1,000 m e l s . 3 k - l l . Localization of Sound. T h e localization of complex sounds is primarily a function of time differences of arrival at the t w o ears, and t o a first approximation, such differences can be calculated b y assuming the ears on either end of the diameter of a sphere of 7.5 c m radius. T h e localization of tones of low frequency (below 1,500 H z ) is possible on the basis of phase differences, which m a y b e interpreted in terms of time differences. 1
T h e localization of tones of high frequency is possible on the basis of intensity differences resulting from the sound shadow of the head. Exact measurements here are difficult at best. S. S. Stevens and J. Volkmann, The Relation of Pitch to Frequency: A Revised Scale, Am. J. Psychol. 53, 329-353 (1940). 1
3-162
ACO U STICS
TAB LE 3k -8. PITCH OF A P URE T ONE, IN ME LS, Frequency
Mels
Frequency
AS A
F UNC'l'ION OF F l1 EQUE NCY
Frequency
Mels
Mels
"
20 30 40 60 80 100 150 200 250 300
0 24 46 87 126 161 237 301 358 409
350 400
460 508 602 690 775 854 929 1 , 000 1 , 154 1 , 296
.~OO
600 700 800 900 1 , 000 1 , 250 1 , 500
1, 750 2 , 000 2 , 500 3 , 000 3 , 500 4 , 000 5 , 000 6 , 000 7 , 000 10 , 000
1, 428 1 , 545 1 , 771 1 , 962 2 , 116 2 , 250 2 , 478 2 , 657 2 , 800 3,075
Sound loca lization is great ly aided when the head or body can be rotated or moved abou t in the sou nd field while t he observer hears t he appropriate sequence of so und s. ! Sound localiza t ion in reverberan t rooms or with so-ca lled " stereop honic-sound sources" depends critically upon a "precedence effect," by which t he localization determ ined by t he primary sound or sound from t he nearer of two sound sources is overriding in its effect .2 In experimen ts where tim e differences are used t o balance out intensity differences in the opposite direction, 1.0 X 10- 5 sec priority offsets a 6-dB difference in intensity ; 2.3 X 10 - 5 sec offsets a 14-dB difference in intensit y between t he two ears.3 Sk-12. Speech Power. The total radiated speech po wer , averaged over a 15-sec interval for a sample including bo th m en and women at con versational levels used fo r telephone ta lking, has been estima ted as 32 m icrowatts. When m easured a t t he face of a telephone t ransmitter, t his power produces t he sound pressure levels given in T able 3k-9 for different distances from t he mouth of the speaker .4 T ABLE 3k-9. AVERAGE SOUND PRESSURE LEVEL PRODUCED BY CONYER ATIO NAL SPEECH AS A FUNCTION OF D ISTA CE FROM LrPS TO MICROPHO E Dist ance, cm T ouching
0.5
1.0
2.5
5.0
-- -- -- Sound pressure level , . ' . ,
104
102
99
95
90
10.0 -
85
25.0
- 78
50.0 100.0 -
-
--
72
66
A second source of variability lies in the essen tially st at istical distribution of speech power in time. If speech power is m easured in successive -§--sec in tervals (a tim e slightly shor ter than a syllable and slightly longer t han a phoneme ), a distribu t ion is obtained wit h t he mean values given in T ab le 3k-9 and va riability t hat can be ! H . Wallach , U eber die Wahrnehmu ng d er Sch allricht ung, P sychol. Fo!'sch. 22, 238-266 (1938) . 2 H. Wallach, E. B. Newman, an d M. R . R osenzweig, T he Precedence Effect in Sound Lo ~ali zat i on , Am. J . P sychol. 62, 313-336 (1949). • J . H . Shaxby and F. H. Gage , St udies in the Localization of Sound. A. T he L ocalization of Soun ds in t h e M edian P lan e: An Experiment al I nvestigat ion of t h e Physical Processes Concerned, M ed. R esearch Council (Brit.) S pec. R ept. S er . n o. 166 (1932), 32 pp. , , 4 M . H . A b rams, S. J. Goffard, J. M iller, F. H. Sanford, a nd S. S. Stev ens , The Effect of Microphone P osition on the Intelligi bility of Speech in Noise, OS RD Rept. 4023 (1944) . 16 pp.
3-163
SPEECH AND HEARING
attributed to time sampling equalto a standard deviation of 7.0 dB.1 The distribution is badly skewed, so that the value 7.0 dB indicates only a rough order of magnitude. The variability is also greater when particular frequency bands are measured. A third source of variability is the variation in effort expended by the person who is talking. As a rough approximation, a raised voice level is 6 dB above conversational level, the loudest level that can be maintained is 12 dB above conversational level, and the loudest shout .is 18 dB above conversational level. In the other direction, a whisper may be 20 dB below conversational level. 3k-13. Speech Sounds TABLE
Symbol
3k-l0.
CHARACTERISTICS OF SOUNDS IN GENERAL AMERICAN SPEECH
Example
Power, * dB re long time averaget
Relative frequency of sound, %~
Formant frequencies for men and women 'If First
Second
--M W M
-
-
~-
W
Third M
W
- -- - --
cool cook cone talk
+0.6 +2.3 +2.5 +4.1
1.60 0.69 0.33 1.26
300 370 870 950 2,240 2,670 440 470 1,020 1,160 2,240 2,680 500 ... 820 570 590 840 920 2,410 2,710
D
cI~th}
Q
calm
+3.7
{2.81} 0.49
730 850 1,090 1,220 2,440 2,810
a
~Sk}
+2.5
3.95
660 860 1,720 2,050 2,410 2,850
+1.6 +1.4 0.0 0.0 -0.5
3.44 1.84 8.53 2.12 0.53 4.63 2.33
530 610 1,840 2,330 2,480 2,990
u U
0 0
III
e e I i (J'
a A
eI aI ju ou au 01
bat bet tape bit beet bird sofa bun laid bite you soap about boil -
..... +2.9 +1.4 +2.5 +0.6 +2.5 +2.3 +3.0
390 430 1,990 2,480 2,550 3,070 270 310 2,290 2,790 3,010 3,310 490 500 1,350 1,640 1,690 1,960 640 760 1,190 1,400 2,390 2,780
see e
1.59 0.31 1.30 0.59 0.09
* The power measurements do not represent the peak instantaneous power but the average over the ""stained portion of the phoneme where such a period can be defined. In this ca.se, as with the formant frequencies, the absolute values are highly variable, but intercomparisons among the vanous soun9.B are generally more reliable. I t H. Fletcher, "Speech and Hearing in Communication," p. 86, D. Van Nostrand Company. nc .. Princeton, N.J., 1953. ., C b 'd t G. Dewey, "Relative Frequency of English Speech Sounds." Harvard Umverslty Press, am n ge, Mass., 1923. . In N Y k '\[ E. G. Richardson, ed., "Technical Aspects of Sound," pp. 215-217, ElseVler Press, c., ew or. 1953. 1
H. K. Dunn and S. D. White, Statistical Measurements on ConversatiQn!l1' ~:PElElQ~ •.
J. Acoust. Soc. Am. 11,278-288 (1940).
3-164
ACODSTICS TABLE
3k-1O.
CHARACTERISTICS OF SOUNDS IN GENERAL
AMERICAN SPEECH
Symbol
Power, * dB Example re long time averaget
w
lip me nip sing we
r
~p
1 m n 1]
j
-
:res
p
~ie
t
tie 'key by die [uy
k b d g
v f
e ti s z
S :5
h tS dS
VIe
-
foe thin then ~ip
isshy measure hit
-
~op
Joe
-
-3.0 -5.8 -7.4 -4.4 0.0 -l.0 0.0 -15.2 -11.2 -11.9 -14.6 -14.6 -11.2 -12.2 -16.0 -23.0 -12.6 -11.0 -11.0 -4.0 -10.0 -13.0
-6.8 -9.4
(Continued)
Relative frequency of sound, %t
3.74 2.78 7.24 0.96 2.08 6.35 0.60 2.04 7.13 2.71 l.81 4.31 0.74 2.28 l.84 0.37 3.43 4.55 2.97 0.82 0.05 l. 81 0.52 0.44
"B'ormant frequencies for men and women ~ First
Second
~~-.
-----
450 140 140 140
1,000 1,250 1,450 2,350
2,550 2,950 2,250 2,750 2,300 2,750 2,750
500 270
1,350 2,040 800 1,700 Variable 800 1,700 Vl1riable 1,150 1,150 1,450 1,450 2,000 2,000 2,150 2,150
1,850 3,500
...
... ...
140 140 140 140
... ... 140 ...
140
... 140
Third Fourth ~--
~~-
1,350 2,450 1,350 2,450 2,500 3,650 2,500 3,650 2,550 2,550 2,700 2,700 2,650 2,650
* The power measurements do not represent the peak instantaneous power but the average over the sustained portion of the phoneme where such a period can be defined. In this case, as with the formant frequencies, the absolute values are highly variable, but intercomparisons among the various sounds are generally more reliable. t H. Fletcher, "Speech and Hearing in Communication," p. 86, D., Van Nostrand Company, Inc" Princeton, N.J., 1953. :t G. Dewey, ,"Relative Frequency of English Spee-ch Sounds," Harvard University Press, Cambridge, Mass., 1923. 'If E. O. Richardson, ed., "Technical Aspects of Sound," pp. 215~217, Elsevier Press, Inc., New York, 1953. ' , ' Sk-14. Articulation Index. The articulation index is a set of numbers that makes possible the prediction of the efficiency of some types of voice-communication systems by the addition of suitably chosen values. The operations involve (1) dividing the speech spectrum into a series of bands having an equal possible contribution L'>.A to the total efficiency, and (2) determining what proportion of the L'>.A each band will contribute under the particular noise and speech conditions being tested. Under (1) it is customary to use no more than 20 such bands. The frequeney limits of 20 such bands are given in Table 3k-ll.
3-165
SPEECH AND HEARING TABLE
3k-l1.
TWENTY FREQUENCY BANDS CONTRIBUTING EQUALLY TO EFFICIENCY OF SPEECH COMMUNICATION*
Band No.
Frequency range
1 2 3 4 5 6 7
395 395-540 540-675 675-810 810-950 950-1,095 1,095-1,250
,~
Band No.
Frequency range
Band No.
Frequency range
8 9 10
1,250-1,425 1,425-1,620 1,620-1,735 1,735-2,075 2,075-2,335 2,335-2,620 2,620-2,930
15 16 17 18 19 20
2,930-3,285 3,285-3,700 3,700-4,200 4,200-4,845 4,845-5,790 5,790
11
12 13 14
* H. Fletcher, "Speech and Hearing in Communication," D. Van Nostrand Company, Inc., Princeton, N.J., 1953. For conditions where substantial wide-band noise is present, the second requirement may be approximated by the formula
(3k-4) in which Wi is a weight having a maximum value of 1.0, Si is the signal level in band i in decibels, Ni is the noise level in the same band i in decibels referred to the same base as Si. 1 TABLE
3k-12.
ARTICULATION SCORES AS A FUNCTION OF ARTICULATION INDEX*
Articulation index
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00
Monosyllabic CVC syllables, % words (PB lists), %
7 22
38 55 68 79 87 93 96 98
7 22 40 61 77 87 93 96 98 99
* E. G. Richardson, ed., "Technical Aspects of Sound/' Elsevier Press, Inc., New York, 1953. "ove syllables are estimated from sets of words that vary the initial consonants, the vowel, and the final consonant separately. PB words are lists of monosyllables phonetically balanced so that the proportion of phonemes roughly equals that in general speech. ll
The articulation index A is then described by the summation
(3k-5) Articulation scores are related to the articulation index according to the Table 3k-12. 1 N. R. French and J. C. Steinberg, Factors Governing the Intelligibility of Speech Sounds, J. Acoust. Soc. Am. 19, 90-119 (1947).
31, Classical Dynamical Analogies HARRY F. OLSON
RCA Laboratories
Analogies are useful when it is desired to compare an unfamiliar system with one that is better known. The relations and actions are more easily visualized, the mathematics more readily applied, and the analytical solutions more readily obtained in the familiar system. Analogies make it possible to extend the line of reasoning into unexplored fields. In view of the tremendous amount of study which has been directed toward the solution of circuits, particularly electric circuits, and the engineer's familiarity with electric circuits, it is logical to apply this knowledge to the solutions of vibration problems in.other fields by the same theory as that used in the solution of electric circuits. The objective in this section is the establishment of analogies between electrical, mechanical, and acoustical systems. 31-1. Resistance. Electric Resistance. Electric energy is changed into heat by the passage of an electric current through an electric resistance. Electric resistance RE, in abohms, is defined as e (31-1) =-;: t
where e = voltage across the electric resistance, abvolts i = current through the electric resistance, abamp Mechanical Rectilineal Resistance. Mechanical rectilineal energy is changed into heat by a rectilinear motion which is opposed by mechanical rectilineal resistance (friction), Mechanical rectilineal resistance (termed mechanical resistance when there is no ambiguity) RM, in mechanical ohms, is defined as fM RM = -
(31-2)
U
where fM = applied mechanical force, dynes u = velocity at the point of application of the force, em/sec Mechanical Rotational Resistance. Mechanical rotational energy is changed into heat by a rotational motion which is opposed by a rotational resistance (rotational friction). Mechanical rotational resistance (termed rotational resistance when there is no ambiguity) R a, in rotational ohms, is defined as (31-3)
where fa = applied torque, dyne-em n = angular velocity about the axis at the point of the torque, radians/sec Acoustic Resistance. . Acoustic energy is changed into heat either by a motion in a fluid which is opposed by acoustic resistance due to a fluid resistance incurred b'y viscosity or by the radiation of sound. Acoustic resistance RA, in acoustical ohms, 1S defined as
3-166
CLASSICAL DYNAMICAL ANALOGIES
R.a
=
E.. U
3-167 (31-4)
where p = pressure, dynes/cm' U = volume velocity, cm 3/sec 31-2. Inductance, Mass, Moment of Inertia, Inertance. Inductance. Electromagnetic energy is associated with inductance. Inductance is the electrio-cirouit element that opposes a change in current. Inductance L, in abhenrys, is defined as di
e=L Iit
(31-5)
where e = voltage, emf, or driving force, abvolts di di = rate of change of current, abamp/sec Mass. Mechanical rectilineal inertial energy is associated with mass in the mechanical rectilineal system. Mass is the mechanical element which opposes a change in velocity. Mass m, in grams, is defined as
1M
=
du dt
m-
t(31-6)
' where du dt = accel eratlOn, cm / sec 2
1M = driving force, dynes Moment of Inertia. Mechanical rotational energy is associated with moment of inertia in the mechanical rotational system. Moment of inertia is the rotational element which opposes a change in angular velocity. Moment of inertia I, in gram (centimeter)2, is defined as (31-7)
dn
where dt
=
angular acceleration, radians /sec'
fR = torque, dyne-cm
Inertance. Acoustic inertial energy is associated with inertance in the acoustic system. Inertance is the acoustic element which opposes a change in volume velocity. Inertance M, in grams per (centimeter)', is defined as p
where
~~
dU
=
Mdt
(31-8)
= rate of change of volume velocity, cm 3/sec 2
p = driving pressure, dynes/em' 31-3. Electric Capacitance, Rectilineal
Compliance, Rotational COpJ.pli@,nce, Acoustic Capacitance. Electric Capacitance. Electric capacitance is associated with capacitance. Electric capacitance is the electric-circuit element which opposes a change in voltage. Electric capacitance CE , in abfarads, is defined as (31-9) (31-10)
where Q = charge on the electrical capacitance, abcoulombs e = emf, abvolts Rectilineal Compliance. Mechanical rectilineal potential energy is associated with the compression of a spring or compliant element. Rectilineal compliance is the
3-168
ACOUSTICS
mechanical element which opposes a change in the applied force. Rectilineal compliance (termed compliance when there is no ambiguity) CM , in centimeters per dyne, is defined as (31-11)
where x = displacement, om f M = applied)orce, dynes Rotational Compliance. Mechanical rotational potential energy is associated with the twisting of a spring or compliant element. Rotational compliance is the mechanical element that opposes a change in the applied torque. Rotational compliance CR , in radians per centimeter per dyne, is defined as fR =
where
-'GtR-
(31-12)
angular displacement, radians applied torque, dyne~cm Acoustic Capacitance. Acoustic potential energy is associated with the compression of a· fluid or a gas. Acoustic capacitance is the acoustic element which opposes a change in the applied pressure. The acoustic capacitance CA , in (centimeters)5 per dyne, is defined as cf> =
JR
=
x
(31-13)
p = CA
where X = volume displacement, cm 3 p = pressure, dynes/cm 2 31~4. Representation of Electrical, Mechanical Rectilineal, Mechanical Rotational, and Acoustical Elements. Electrical, mechanical rectilineal, mechanical rotational, RR
RE
-'\Nv--
RA ~
ezZZZzz! l
---'000'-CE
-If-
= =
~
m
M
D CA
CM
:J fA,
RM
/
:W I
W CR
~
~
RECflLlNEAL
ROTATIONAL
MECHANICAL ELECTRICAL ACOUSTICAL FIG. 31-1. Graphical representation of the three basic elements in electrical, mechanical rectilineal, mechanical rotational, and acoustical systems.
and acoustical elements have been defined in the preceding sections. Figure 31-1 illustrates schematically the three elements in each of the four systems. The electrical elements, electric resistance, inductance, and electric capacitance, are represented by the conventional symbols . . Mechanical rectilineal resistance is represented by sliding friction which causes dissipation. Mechanical rotational resistance is represented by a wheel with a sliding-
CLASSICAL DYNAMICAL ANALOGIES
3-169
friction brake which C8,uses dissipation. Acoustic resistance is represented by narrow slits which cause dissipation due to viscosity when fluid is forced through the slits. These elements are analogous to electric resistance in the electrical system. Inertia in the mechanical rectilineal system is represented by a mass. Moment of inertia in the mechanical rotational system is represented by a flywheel. Inertance in the acoustical system is represented as the fluid contained in a tube in which all the particles move with the same phase when actuated by a force due to pressure. These elements are analogous to inductance in the electrical system. Compliance in the mechan1cal rectilineal system is represented as a spring. Rotational compliance in the mechanical rotational system is represented as a spring. Acoustic capacitance in the acoustical system is represented as a volume which acts as a stiffness or spring element. These elements are analogous to electric capacitance in the electrical system. Table 31-1 shows the quantities, units, and symbols in the four systems. :n-5. Description of Systems of One Degree of Freedom. Electrical, mechanical rectilineal, mechanical rotational, and acoustical systems of one degree of freedom are shown in Fig. 31-2. In one degree of freedom the activity in every element of the
'M:[~I ACOUSTICAL
f~~Rd ~
:;dJ
RR
'-"
FREQUENCY
ROTATIONAL MeCHANICAL
FIG. 31-2. Electrical, mechanical rectilineal, mechanical rotational, and acoustical systems
of one degree of freedom and the current, velocity, angular velocity and volume velocity response characteristics. system can be expressed in terms of one variabie.In the electrical system an electromotive force e acts upon an inductance L, an electric resistance R E , and an electric capacitance CE connected in series. In the mechanical rectilineal system a driving force iM acts upon a particle of mass m fastened to a spring of compliance eM and sliding upon a plate with a frictional force which is proportional to the velocity and designated as the mechanical rectilineal resistance RM. In the mechanical rotational system a driving torque iR acts upon a flywheel of moment of inertia I connected to a spring or rotational compliance CR and the periphery of the wheel sliding against a brake with a frictional force which is proportional to the velocity and designated as the mechanical rotational resistance RR. In the acoustical system, an impinging sound wave of pressure p acts upon an inertance M and an acoustic resistance RA comprising the air in the tubular opening which is connected to the volume or acoustical capacitance CA. The acoustic resistance RA is due to viscosity. The differential equations describing the four systems of Fig. 31-2 are as follows: Electrical (31-14)
3-170
ACOUSTICS
Mechanical rectilineal (31-15) Mechanical rotational (31-16) Acoustical (31-17) E, F M, FR, and P are the amplitudes of the driving forces in the four systems. EE;"'t = e, FME;"'t = JM, FRE;"'t = JR and PE;"" = p. The steady-state solutions of Eqs. (31-14) to (31-17) are: Electrical e (31-18) ZE
Mechanical rectilineal i;
= RM
FE;"" JM - (i/v)C M) = ZM
(31-19)
FE;"" JR - (j/wC R) = ZR
(31-20)
+ jwm
Mechanical rotational c/>
= RR
+ jwI
Acoustical (31-21) The vector electric impedance is
~ WCE
(31-22)
RM +jwm - - j wCM
(31-23)
ZE = RE
+ jwL
-
The vector mechanical rectilineal impedance is
ZM
=
The vector mechanical rotational impedance is
ZR = RR
+ jwI
-
~
(31-24)
~c·
(31-25)
WCR
The vector acoustic impedance is
ZA = RA,+ jwM -
w A
CLASSICAL DYNAMICAL ANALOGIES
3-1'71
:U-6. Applications of Classical Electrodynamical Analogies. The fundamental principles relating to electrical, mechanical rectilineal, mechanical rotational, and acoustical analogies have been established in the preceding sections. Employing these fundamental principles, the vibrations produced in mechanical and acoustical systems owing to impressed forces can be solved as follows: Draw the electrical network which is analogous to the problem to be solved; solve the electrical network by conventional electrical circuit theory; convert the electrical answer into the original system. In this procedure any problem involving vibrating systems is reduced to the solution of an electrical network. In the illustrations in the preceding sections, the elements in the electrical network have been labeled rE.L and CEo However, when analogies are used in actual practice, the conventional procedure is to label the elements in the analogous electrical network with rM, IV, and CM for a
TO ENGINE Ml
CROSS-SECTIONAL VIEW
ACOUSTICAL NETWORK
31-3. Cross-sectional view and acoustical network of an automobile muffler. In the acoustical network: 111" M2, M s, and M 4, the inertances of the series elements; TAl, ,'A2, and r Aa, the acoustical resistances of the shunt elements; M 5, M 6, and M 7, the inertances of the shunt elements; CAl, CA2, and CAa, the acoustical capacitances of the shunt elements. FIG.
(After Olson, "Dynamical Analogies," D. Van Nostrand Company, Inc., Princeton, N.J., 1959.)
mechanical rectilineal system; with rR, I, and CR for a mechanical rotational system; and with r A, M, and CA for an acoustical system. This procedure will be followed in this section in labeling the elements in the analogous electrical network. The customary procedure is to label the network with the caption mechanical network or rotational network or acoustical network as the case ma.y be. When there is only one path, the term circuit will be used instead of network. A complete treatment of the examples of the use of analogies in the solution of problems in mechanical and acoust.ical systems is beyond the scope of this section. However, a few typical examples will serve to illustrate the principles and method. Acoustical-Automobile ]}!'uf!lm·. The sound output from the exhaust of an automobile engine contains all audible frequencies in addition to frequencies below and above the audible range. The purpose of a muffler is to reduce the sound output in the audible frequency range without increasing the exhaust back pressure. By the application of acoustical principles employing analogies improved mufflers have been developed in which the following advantages have been obtained: smaller size, higher attenuation in the audible frequency range, and reduction of bad, pressure at the engine. A cross-sectional view of the improved muffler is shown in Fig. 31-3. The acoustical network shows that the system is essentially a low-pass acoustical filter. The main channel is of the same diameter as the exhaust pipe. Therefore, there is no increase in the direct flow of exhaust gases as compared with a plain pipe. In order not to impair the efficiency of the engine, the muffler should not increase the acoustical impedance to subaudible frequencies. The system of Fig. 31-3 can be designed so that the subaudible frequencies are not attenuated and at the same time high attenuation is introduced in the audible frequency range.
3-172
ACOUSTICS
T h e terminations at the two ends of the network are not ideal. Therefore, it is necessary to use shunt arms tuned to different frequencies in the low-frequency range. Acoustical resistance is obtained b y employing slit-type openings into the side chambers. In a development of this kind, the frequency spectrum of the sound which issues from the exhaust is usually determined. F r o m these data the amount of suppression required for each part of the audible frequency range can b e ascertained. The acoustical network can b e determined from these data and the terminating acoustical
*M—|
ZMF FLOOR
Z
M
MECHANICAL RECTILINEAL SYSTEM
MACHINE
ZMFH
F
MECHANICAL CIRCUIT
F I G . 31-4. Schematic view, mechanical rectilineal system, and mechanical circuit of a machine mounted directly upon the floor. In the mechanical circuit: /M, the vibrating force developed by the machine; m, the mass of the machine; ZMF, the mechanical impedance of the floor. (After Olson, "Dynamical Analogies," D. Van Nostrand Company, Inc., Princeton, N.J.,
1959.)
— f|| —
•KM CM
DAMPED SPRING
^Hflff FLOOR MACHINE
Z
M
F
-MF MECHANICAL RECTILINEAL SYSTEM
MECHANICAL NETWORK
F I G . 31-5. Schematic view, mechanical rectilineal system, and mechanical network of a machine mounted upon a vibration isolating system. In the mechanical network: fu, the vibrating force developed by the machine; m, the mass of the machine; CM, the compliance of one of the four spring mounts; RM, the mechanical rectilineal resistance of one of the spring mounts. (After Olson, "Dynamical Analogies," D. Van Nostrand Company, Inc., Princeton,
N.J.,
1959.)
networks. In general, changes are required to compensate for the approximations. In this empirical w o r k the acoustical network serves as the guide in directing the appropriate changes. Mechanical Rectilineal—Machine Vibration Isolator. T h e vibration of a machine is transmitted from its supports to all parts of the surrounding building structure. I n m a n y cases, the vibrations are so intense as to b e intolerable. T h e reduction of the transmission of machinery vibrations is one of the most c o m m o n problems in noise control. For these conditions, the solution of the problem is to provide suitable vibrational isolation between the machine and the floor u p o n which it is placed. A machine m o u n t e d directly on the floor is shown in Fig. 31-4. T h e mechanical rectilineal system and the mechanical circuit for vertical vibrations are shown in Fig. 31-4. T h e driving force / M is due to the vibrations of the machine. The
CLASSICAL DYNAMICAL ANA LO GIES
3-173
m echanical circuit shows that t he only isolation in the system of Fig. 31-4 is due to the mass of t he machine. In the simple isolating system of Fig. 31-5 t he machine is mounted on springs with mechanical resistance added to serve as damping. The com pliance and mechanical resistance of each support are C M a nd rM . Since there are foUl' supports, these values become Cl>d 4 and 4rM in t he mechanical rec tilineal system and the mechanical network for vertical vibrations. The mechanical network depicts t he act ion of the shunt circuit CMrM in reducing the force of the vibra tion transmitted to t he floor ZM F . llfechanical Rotational-Vibration Damper. In recipro cating engines and ot her rotat ing machinery, ro tational vibrations of large amplitudes occur at certain speeds. These rotational vibrations are sometimes of such 'high amplitude that t.he shaHs MOMENT OF INERTIA 12
FLYWHEEL II
SHAFT
END VIEW
SIDE VIEW
ROTATIONAL NET WORK
FIG. 31-6. End and side views and the rotational network of a vibration damper. I n t he rot ational n etwork: h , t he moment of inertia of t he flywheel; 1 2, the moment of inertia of the damper ; CR, the rotation al complia n ce of t he damper ; rR, the mech anical rotation al resist ance between the damper and the sh aft. (A.fter Olson, " D ynamical A.nalogies," D. Van Nostrand Company, Inc., Princeton, N .J., 1959. )
will fail after a few hours of opera ting. A number of various rotational dampers have been developed for reducing these ro tational vibrat ions. A typical example of a vibration damper used to control the vibra tions of t he flywheel is hown in Fig. 31-6. The damper consists of a rotational element having a moment of inertia I , rotating on a shaft with a mechanical ro tational resistance rR b etween t he inertia element and shaft. The inert ial element is coupled to the flywh eel by means of a spring of compliance CM. The ro tational compliance is C R = CM/ a', where a is the radius at t he point of attachment of the spring with respect to the center line of t he shaft. Referring to the rotational network it will be seen that the rotational damp er forms a shunt mechanical ro tational system. The shun t ro tational circuit CRTR I , is tuned to t he frequ ency of t he vibration. Since t he mechanical ro tat.ional im pedance of the shunt resonant rotational circuit is very high at the resonant frequency, the angular velocity (or amplitud e) of vibration of t he flywheel will be reduced. A considera t ion of the rotational network illustrates t he principle of t he device. Electrical jy[echanical-Direct Radiator Dynamic Loudspeaker. The direct radiator dynamic loudspeaker shown in Fig. 31-7 is almost universally used for radio, phonograph, television , and other small-scale sound reprodu ctions. The mechanical circuit of t he loudspeaker is shown in Fig. 31-7. T he mechanical reetilineal impedance at the voice coil, where a forc e f M is applied, can be determined from the constants of the elements of the mechanical circuit . The mass m, and t he mechanical resistance rM2 of t he air load can be obtained from Sec. 3i-2 on the acoustic impedan ce of vibrating pistons. The elect rical circuit of the loudspeaker is also shown in Fig. 31-7. The motional
3-174
ACOUSTICS
ELECTRICAL CIRCUIT
MECHANICAL CIRCUIT
CROSS-SECTIONAL VIEW
FIG. 31-7. Cross-sectional view, electrical circuit. and mechanical circuit of a direct radiator loudspeaker. In the electrical circuit: e, the open-circuit voltage of the generator or vacuum tube; rEG, the electrical resistance of the voice coil; L, the inductance of the voice coil; ZEM, the motional electrical impedance of the driving system. In the mechanical circuit: m" the mass of the cone; rMI, the mechanical resistance of the suspension system; eM, the compliance of the suspension system; m2, the mass of the air load; r M2, the mechanical rectilineal resistance of the air load. (After Olson, "Dynamical Analogies," D. Van Nostrand Company, Inc., Princeton, N.J., 1959.)
electrical impedance in the electrical circuit is given by (Bl) ,
(31-26)
ZEM = - ZJ.ldT
where
ZEM =
motional electrical impedance, abohms
B = flux density in air, gauss l = length of conductor in voice coil ZMT = mechanical impedance at location 1M in mechanical circuit, mechanical
ohms The mechanical driving force is given by 1M =
Bli
(31-27)
where 1M = driving force, dynes i = current in voice coil, abamp The velocity can be determined from the mechanical circuit of Fig. 31-7 and th6' following equation:
x= where
1M ZMT
x is the velocity in centimeters per second. P = rMx 2
where P
(31-28)
The sound output is given by (31-293
sound power output, ergs/sec mechanical ohms x = velocity of cone from Eq. (31-28) The object is to select the constants so that the power output as given by Eq. (31-29) is practically independent of the frequency over the desired frequency range. =
rM =
3-175
CLASSICAL DYNAMICAL ANALOGIES TABLE
31-1.
QUANTITIES, UNITS, AND SYMBOLS FOR ELECTRICAL, MECHANICAL
RECTILINEAL, MECHANICAL ROTATIONAL, AND ACOUSTICAL ELEMENTS
Electrical Quantiy
Unit
Mechanical rectilineal Symbol
Electromotive force ........ Volts X 10 8 e Coulombs X 10- 1 Q Charge or quantity Current ........ Amperes X 10- 1 i Electric imped-' ance Electric resistance Electric reactance Inductance .... Electric capacitance Power .........
Ohms X 10 9
ZE
Ohms X 10 9
RE
Ohms X 10 9
XE
Henrys X 10 9 Farads X 10- 9
L
Ergs per second
PE
CE
Quantity
Force Dynes Linear disCentimeters placement Linear velocity Centimeters per second Mechanical Mechanical impedance ohms Mechanical Mechanical resistance ohms Mechanical Mechanical reactance ohms Mass Grams Centimeters Compliance per dyne Ergs per second Power
Unit
x i;
or u
I ZM RM XM m
CM PM
Acoustical Symbol
Torque ........ Dyne-centimeters JR
Quantity Pressure
q,
Angular Radians displacement Radians per Angular velocity second
Volume displacement ¢ or r.l Volume velocity
Rotational impedance Rotational resistance Rotational reactance Moment of inertia Rotational compliance Power .........
Rotational ohms
ZR
Rotational ohms
RR
Rotational ohms
XR
---
JM
I
Mechanical rotational Quantity
Symbol
Unit
(Gram) (centiI meter) 2 Radians per dyne CR per centimeter Ergs per second PR
Acoustic impedance Acoustic resistance Acoustic reactance Inertance Acoustic capacitance Power
Symbol
Unit Dynes per square centimeter Cubic centimeters Cubic centi'[ meters per second Acoustic ohms
p
X kor U
,
ZA
Acoustic ohms RA Acoustic ohms XA Grams per M (centimeter) 4 (Centimeter) 5 CA per dyne Ergs per second PA
,
3m. Mobility Analogy HARRY F. OLSON
RCA Laboratories
The analogies that have been presented and considered in Sec. 31 have been formal ones owing to the similarity of the differential equations of electrical, mechanical and acoustical vibrating systems. For this reason these analogies have been termed the classical impedance analogies; they are, however, not the only ones possible of development for useful applications. For example, mechanical impedance has been defined by some authors-in addition to the ratio of force to velocity as developed in Sec. 31as the ratio of pressure to velocity, the ratio of force to displacement, and the ratio of pressure to displacement. During the past three decades the developments in the field of analogies have been reported in publications" by many investigators. In this connection a useful analogy, developed by Firestone and designated by him as the "mobility analogy," has been employed on a wide scale to solve problems in mechanical vibrating systems. In the mobility analogy mechanical mobility is defined as the complex ratio of velocity to force. Although the mobility analogy can be applied and used with all types of vibrating systems, its most direct and useful application is in the field of mechanical vibrating systems. Therefore, in order to make the subiect of analogies complete in this handbook, it seems logical to include the mobility analogy. Accordingly, it is the purpose of this chapter to develop the mobility analogy, particularly as applied to mechanical rectilineal systems. 2 3m-1. Mechanical Rectilineal Mobility. Mechanical rectilineal mobility is the inverse of mechanical rectilineal impedance. Nlechanical rectilineal mobility ZI, in mechanical mhos, is defined as the complex ratio of linear velocity to linear force as follows: Zj
V
=-
JM
(3m-I)
where v = velocity, em/sec JM = force, dynes It will be evident that a mechanical element in the mechanical mobility sense is analogous to the electric element if velocity difierence across the mechanical element is analogous to the voltage difference across the electric element and if the force through the mechanical element is analogous to the electric current through the electric element. See the end of Section 3 for a list of references. The considerations in this section will be confined to mechanical rec'cilineal systems. The mobility analogy is equally applicable to mechanical rotational systems. In this connection mechanical rectilineal and mech,mical rotational systems are not sufficiently different to warrant a separate treatment for the mechanical rotational system, particularly in view of the faet that fundamental aspects of the two systems have been considered from the classical impedance analogy viewpoint in this book. 1
2
8-176
MOBILITY ANALOGY
Mechanical rectilineal mobility may be written as follows:
ZI,
3-177
in mechanical mhos, is a complex quantity and (3m-2)
where rI = responsivity, mechanical mhos XI = excitability, mechanical mhos 3m-2. Responsivity (Mobility Resistance). In the mechanical rectilineal mobility system mechanical rectilineal responsivity (mobility resistance) rI, in mechanical mhos, is defined as v 1 rr = - = (3m-3) 1M
rM
w here v = velocity, cm/sec 1M = force, dynes rM = mechanical impedance, mechanical ohms Sm-S. Mass (Mobility Capacitance). In the mechanical rectilineal mobility system the mass (mobility capacitance) mI, in grams, is analogous to electric capacitance CEo The mechanical rectilineal excitability Xl of mass (mobility capacitance), in mechanical mhos, is defined as
a
(3m-4) where w =
27r1
I = frequency, hertz Equation (3m-4) shows that the mass (mobility capacitance) mI in the mechanical rectilineal mobility system is analogous to electric capacitance CE in the electric system. Mass (mobility capacitance) mI in the mechanical rectilineal mobility system may also be defined as follows: (3m-5) (3m-6) In the electric system electric capacitance CE may be defined as follows:
.
z=
C de
Edt
(3m-7)
where i = electric current, abamp CE = electric capacitance, abfarads e = electromotive force, abvolts t = time, sec (3m-8) where i = current in abamperes. It will be seen that Eqs. (3m-5) and (3m-6) in the mechanical rectilineal mobility system are analogous to Eqs. (3m-7) and (3m-8) in the electric system. 3m-4. Compliance (Mobility Inertia). In the mechanical rectilineal mobility system the compliance (mobility inertia) CI , in centimeters per dyne, is analogous to electric inductance L. The mechanical rectilineal excitability XI of a compliance (mobility inertia), in mechanical mhos, is defined as (3m-9) where w = 27rJ I = frequency, Hz Equation (3m-9) shows that compliance (mobility inertia) CI, in centimeters per dyne, is analogous to inductance.
3-178
ACOUSTICS
Compliance (mobility inertia) C[ in the mechanical rectilineal mobility system may also be defined as v = C J dilk[
(3m-IO)
dt
In the electric system inductance may be defined as
e=Lr!i
(3m-H)
dt
where L = inductance in abhenrys. It will be seen that Eq. (3m-IO) in the mechanical rectilineal mobility system is analogous to Eq. (3m-H) in the electric system. 3m-Ii. Representation of Electrical and Mechanical Rectilineal Mobility Elements. Electric elements have been defined in Sec. 31. Elements in the mechanical rectilineal mobility system have been described in this sep,t.ion.
m
D MECHANICAL ELEMENTS
mr
CE
II
--II
MOBILITY ELEMENTS
ELECTRICAL ELEMENTS
FIG. 3m-I. Graphical representation of the three basic elements in mechanical rectilineal, mobility, and electric systems. rlk[ = mechanical rectilineal T[ = responsivity rE = electrical resistance resistance Clk[ = compliance C[ = mobility inertia L = inductance m = mass m[ = mobility capacitance CE = electric capacitance (After Olson, "Solutions of Engineering Problems by Dynamical Analogies," D. Van Nostrand Co., Princeton, N.J., 1966.)
Figure 3m-1 illustrates schematically the mechanical elements and the analogous elements in the electric and mechanical rectilineal mobility systems. Mechanical rectilineal resistance rlk[ in the mechanical rectilineal system is represented as sliding or viscous friction. Mechanical rectilineal responsivity (mobility resistance) r[ in the mechanical rectilineal mobility system is the reciprocal of mechanical rectilineal resistance Tlk[ and is analogous to electrical resistance rEo Compliance Clk[ in the mechanical rectilineal system is represented as a spring. Compliance (mobility inertia) C[ in the mechanical rectilineal mobility system is analogous to inductance L in the electric system. Mass m in the mechanical rectilineal system is represented as a mass or weight. Mass (mobility capacitance) m[ in the mechanical rectilineal mobility system is analogous to electric capacitance CE in the electric system.
3-179
MOBILITY ANALOGY
The electrical and the mechanical rectilineal quantities in the mobility system are shown in Table 3m-I. The units and the analogous elements and symbols also are shown in Table 3m-I. 3m-5. Mechanical Vibrating System Consisting of a Mass, Compliance, and Mechanical Resistance. The vibrating system! of one degree of freedom consisting of a mass, compliance, and mechanical resistance has been considered from the standpoint of the classical mechanical impedance analogy in Sec. 31. It is the purpose of this section to consider the same mechanical vibrating system from the standpoint of the mechanical mobility analogy.2 TABLE 3m-I. CORRESPONDENCE BETWEEN ELECTRICAL AND MECHANICAL QUANTITIES IN THE MOBILITY SYSTEM Electrical
Quantity
Electromotive force
Unit
Symbol
Volts X 10-8
e
Velocity
q
Impulse or mo- Gram-centimeter mentum per second
i
Force
Dynes
Charge or quanCoulombs X 10- 1 tity Current
Mechanical rectilineal mobility
Amperes X 10- 1
---
Quantity
Unit
Symbol
Centimeters per second
x or v Q
1M
Electrical impedance
Ohms X 10'
ZE
Mechanical mobility
Mechanical mhos
itl
Electrical resistance
Ohms X 10'
TE
Responsivity
Mechanical mhos
T[
Electrical reactance
Ohms X 10'
XE
Excitability
Mechanical mhos
Inductance Electrical capacitance Power
XI
---. Henrys X 10' Farads X 10' Joules per second
L CE PE
Compliance or mobility inertia
Centimeters per dyne
Mass or mobility Grams capacitance Power
Ergs per second
CI
--m[
---PI
The mechanical system consisting of a mass, compliance, and mechanical resistance is shown in Fig. 3m-2A. The mechanical vibrating system may be rearranged to form the equivalent as shown in Fig. 3m-2B. From the mechanical vibrating system of Fig. 3m-2B it is a relatively simple matter to develop the mobility analogy of Fig.3m-20. 1 The preceding paragraphs have been concerned with fundamental considerations. Therefore, the modifier rectilineal has been employed for the sake of accuracy. Since the remainder of this section will be concerned with applications of the mechanical rectilineal mobility, the modifier rectilineal will be dropped. 2 In view of the fact that this section is concerned with mechanical systems, the modifier mechanical in relation to the mechanical mobility analogy is also superfluous and need not be used.
3-180
ACOUSTICS
~mr MECHANICAL SYSTEM
B
C
~ i~
rr
fMl
mr
v
i
fM3 Cr
i
MOBILITY ELECTRIC NETWORK NETWORK FIG. 3m-2. A mechanical vibrating system consisting of a mass, compliance, and mechanical resistance. A. Mechanical sys_tem. B. Mechanical system equivalent to the mechanical system of A. C. Mobility network of the mechanical system. D. Electric network analog of the mobility system. (Ajter Olson, "Solution oj Engineering Problems by Dynamical Analogies,"' D. Van Noctrand Company, Princeton, N.J., 1966.) MECHANICAL SYSTEM
The sum of the forces through the three branches of the mobility network' of Fig. 3m-2C is (3rn-12) 1M = 1M' + 1M2 + 1M3 V
where
(3m-13)
rI
dv
1M2
=
m[
Iii
(3m-14)
1M3
=
~I
J v dt
(3m-IS)
From the sum of Eqs. (3m-13) to (3m-IS) the differential equation of the mobility network of Fig. 3m-2C is
1M
= mr -dv
dt
+ -v + -C[I r[
J
v
dt
(3m··Hi)
The sum of the electric currents of the electric network of Fig. 3m-2D is
where
i = i, + i2 . e 2,
+ i3
= -
rE
(3m-17) (3m-IS)
.
C de
Iii
(3m-19)
is =
LJedt
(3m-20)
22 =
E
'In establishing analogies between electric and mechanical systems the elements in the electric. network have been labeled rE, L, and CEo However, in using analogies in actual practice, the conventional procedure is to label the elements in the analogous electric network as rM, m, and CM for the classical mechanical rectilineal system and as fl, CI, and mI for the mobility mechanical rectilinear system. This procedure will he followed in this section in labeling the elements of the analogous electric network. It is literally accurate to label the network with the caption "Analogous electric network of the mechanical rectilineal system" (or, of the mobility mechanical rectilineal system). For the sake of brevity, these networks will be labeled "mechanical network" and "mohility network." vVhere there is only one path, "circuit" will be used instead of "network."
3-181
MOBILITY ANALOGY
From the sum of Eqs. (3m-IS) to (3m-20) the differential equation of the electric network of Fig. 3m-2D is . de e I f edt ~=CE-+-+(3m-2I) dt TE L Oomparing the variables and coefficients of the mobility and electric networks in the differential equations (3m-I6) and (3m-2I) establishes the analogous variables and quantities in the two systems as given in Table 3m-I. The classical mechanical impedance analogy of the mechanical system of Fig. 3m-2 has been considered in Sec. 31 and will not be repeated here.
A
e MECHANICAL ,SYSTEM SCHEMATIC VIE'W OF THE ELECTRIC AND MECHANICAL SYSTEMS
C
L:j"I
rII
_ _ _ _ _...1
L
ELECTRIC AND MOBILITY NETWORKS
D
:..'!!L B2t 2
L e2t 2
e
8pa2
~ 3B2 t 2
ELECTRIC NETWORK FIG. 3m-3. Cross-sectional view, the mechanical system, the electric and mobility networks, and the electric network of a direct radiator dynamic loudspeaker. In the electric and mechanical networks: e, the electromotive force of the electric generator. rEG, the electrical resistance of the electric generator. L, the inductance of the voice coil. REl, the electrical resistance of the voice coil. ml, the mass of the cone. CM, and rMl, the compliance and mechanical resistance of the suspension. m. and rM', the mass and mechanical resistance of the air load. m{, the mobility capacitance of the cone. C[ and r /1, the mobility inertia and responsivity of the suspension. m12 and r12, the mobility capacitance and responsivity of the air load. B, the flux density in the air gap. l, the length of the voice coil conductor. a, the radius of the cone. p, the qensity of !'Iir. (After Olson, "Solutions of Engineering Problems by Dynamical Analogies," D. Van Nostrand Company, Princeton, N,J" 1966.)
3-182
ACOUSTICS
Sm-7. Direct Radiator Loudspeaker. The direct radiator dynamic loudspeaker shown in Fig. 3m-3 is almost universally used for radio, phonograph, television, and other small-scale sound reproduction. The electric and mechanical systems of the complete loudspeaker are shown in Fig. 3m-3A. The mechanical vibrating system consisting of the voice coil, cone, suspension, and air load is presented in Fig. 3m-3B. The mass ml of the cone and voice coil, and the compliance CM and mechanical resistance of the suspension system, can be obtained from measurements of the vibrating system. The mechanical system of the air load-namely, the mechanical resistance TM2 and masS m2 of the air load upon the front of the cone-is depicted in Fig. 3m-4A and A r==~-
rill .~
0
Iml '-----'
MECHANICAL SYSTEM
MECHANICAL SYSTEM
B
E
I"
fill
~~ '---I fr
mI
~~
,m
MECHANICAL NETWORK
I
MOBILITY CIRCUIT
C
_1_
tpa
Spa2
~J
2
MECHANICAL
MOBILITY CIRCUIT FIG. 3m-4. Air load upon a loudspeaker cone. A. Mechanical system: m, the mass of the air load. rM, the mechanical resistance of the air load. B. Mechanical network of the air load upon a loudspeaker cone. C. Mechanical network of the air load upon a loudspeaker cone: a, the radius of the cone. p, the density of air. c, the velocity of sound. D. Mechanical system same as A. E. Mobility circuit of the air load upon a loudspeaker cone: mI, the mobility capacitance of the air load. rl, the responsivity of the air load. F. Mobility circuit of the "ir load upon a loudspeaker cone: a, the radius of the cone. p, the density of air. c, the velocity of sound. (After Olson, "Solution of Engineering Problems by Dynamical Analogies." D. Van Nostrand Company, Princeton, N.J., 1966.) r~ETWOFII
nce and mass of the air load upon the front of the cone are shown in the mechanical network of Fig. 3m-4C. The mobility circuit of the air load upon the front of the cone appears in Fig. 3m-4E. The constants of the responsivity and compliance are given in the mobility circuit of Fig. 3m-4F. The electric and mobility networks with the ideal transformer connecting the electric and mobility sections are shown in Fig. 3m-3. In Fig. 3m-3D the ideal transformer has been eliminated, and the entire vibrating system reduced to an electric network. The electrical impedance due to the mechanical system is given by Eq. (31-26) as follows: ZEM
(El)2 =-ZM
(3m·22)
NONLINEAR ACOUSTICS (THEORETICAL)
where
ZEM
3-183
= electrical impedance due to the mechanical system, abohms
mechanical impedance of the mechanical system, mechanical ohms flux density in the air gap, gauss l = length of the voice coil conductor, em Since IjzM = ZI, Eq. (3m-22) may be written as ZM =
B
=
ZEM =
(3m-23)
(BI)2Z1
where ZI = mobility in mechanical mhos. By means of Eq. (3m-23) it is possible to convert the combined electric and mobility networks to the electric network, as shown in Fig. 3m-3. The process employing the mobility analysis of this section may be compared with the classical impedance analysis of Sec. 31. References 1. Olson, H. F.: "Dynamical Analogies" 2d ed., D. Van Nostrand Company, Inc., Prince-
ton, N.J., 1958. 2. Olson, H. F.: "Solution of Engineering Problems by Dynamical Analogies," Van Nostrand Reinhold Co" New York, N.Y., 1968.
3u. N onliuear Acoustics (Theoretical) DAVID T. BLACKSTOCK
University of Texas
Until the early 1950s most of what was known about sound waves of finiteamplitucle was confined to propagation, and to a lesser extent reflection, of plane waves in lossless gases. Since that time a great deal has been learned about propagation in other media, about nonplanar propagation (still chiefly in one dimension), about the effect of losses, and about standing waves. Inroads have been made on problems of refraction. Diffraction is still relatively untouched. In this section the exact equations of motion· for thermoviscous fluids will first be stated. Various retreats from the full generality of these equations will then be discussed. No attempt will be made to cover streaming and radiation pressure. See Sees. 3c-7 and 3c-8 for a discussion of those topics. GENERAL EQUATIONS FOR FLUIDS The basic conservation equations will be stated briefly for viscous fluids with heat flow. Other compressible media, such as solids and relaxing fluids, are discussed later in the section. 3n-1. Conservation of Mass, Momentum, and Energy. In Eulerian (spatial) coordinates the continuity and momentum equatiJns are respectively Dp Dt p -Du,
Dt
+ ap -
ax,
+ a?t, =
= 0
Pax, - a (' 'Y/ dkkO" aXi
.,
(3n-l)
+ 2'Y/ d0'•. )
3-184
ACOUSTICS
An entropy equation is stated here in place of the usual energy equation: (3n-3) Here P is the density, Ui is the ith (cartesian) component of particle velocity, p is pressure, Oi; is the Kronecker delta, eli; = t(auilaxj + aU;/aXi) is the rate-of-deformation tensor, YJ and r/ are the shear and dilatational coefficients of viscosity, Cvand Cp are the specific heats at constant volume and pressure, 3 is absolute temperature, S is entropy per unit mass, 'Y = CpIC" is the ratio of specific heats, (3, = -p- 1 (apla3)p is the coefficient of thermal expansion, 1/;(;1) = 2YJel i ;el;i + YJ'elk/,elii is the viscous energy dissipation function, and Qi is the ith component of the total heat flux. The material derivative D ( ) I Dt stands for a ( ) I at Uia ( ) I aXi. If the flow of heat is due to conduction, a3 (3n-4) Qi = aXi
+
-/C~
where K is the coefficient of thermal conduction. For heat radiation the relation between q and 3 is generally quite complicated; see, for example, Vincenti and Baldwin (ref. 1). The model used by Stokes (ref. 2) amounts to Newton's law of cooling and may be expressed by aQi
pC vq(3 - J o)
:;- = UXi
(3n-5)
where J o is the ambient temperature, and q is the radiation coefficient. Although too simple to describe radiant heat transfer in a fluid adequately, this equation is worth considering because of (1) its analytical simplicity and (2) its application as a convenient model for relaxation processes. 3n-2. Equation of State. To the conservation equations must be added an equation of state. Perfect Gas. The gas law for a perfect gas is (3n-6)
p = RpJ
where R is the gas constant. An approximate form of this equation will now be derived. For a perfect gas the small-signal sound speed Co is given by co 2 = 'YRJo = 'YPol Po, where po and PO are the ambient values of p and p. Let J = (3,0(1 + e), p = po + poc0 2P, and p = po(l + 8), where (3,0 is the ambient value of (3, (for perfect gases (3'°30 = 1). Assume that 0, P, and 8 are small quantities of first order. Expansion of Eq. (3n-6) to second order yields
e=
'YP -
8
+
82 -
'YP8
(3n-7)
First-order relations are now defined to be those that hold in linear, lossless acoustic theory; examples are Pt = -poll' U and p - po = co 2 (p - po). At this point we assert that any factor in a second-order term in Eq. (3n-7) may be replaced by its first-order equivalent. The justification is that any more precise substitution would result in the appearance of third- or higher-order terms, and such terms have already been excluded from Eq. (3n-7). Thus in the l&st second-order term in Eq. (3n-7) P may be replaced by 8 to give () =
COlTect to second order.
'YP - 8 -
(1' - 1)8 2
(3n-8)
This is a useful approximate form of the perfect gas law.
NONLINEAR ACOUSTICS (THEORETICAL)
3-185
One of the most fruitful special cases to consider is the isentropic perfect gas. When a perfect gas is inviscid and there is no heat flow, Eq. (3n-3) can be used to reduce the gas law, Eq. (3n-6), to P (3n-9) po = Po
(p)7
The square of the sound speed, which by definition is,
OJ "" becomes cfi = 'YP = p
(aapp ) s co" (E-) (7-1)1'11 po
(3n-1O) (3n-ll)
An expanded form of Eq. (3n-9) is aR follows:
= 8 + t('Y
P
- l)s'
+
(3n-12)
Other Fluids. For liquids and for gases that are not perfect, one can start with a general equation of state J = J(p,p). Recognizing that (B'J/ap)p = 'Y(pc 2i3.)-t, one obtains the exact expression Ot = ; :
+ 8)-1 [I' (~r P t -
(1
(3n-13)
8tJ
In order to obtain an approximation analogous to Eq. (3n-8), it is first necessary to set down a general isentropic equation of state, p -
po = poCo 2
(8 + 2A ~ 82+ 3A !Z. S3 + . . .)
(3n-14)
where the coefficients B/A, CIA, etc., are to be determined experimentally (see Sec. 30). With the help of this expression and some elementary thermodynamic relations, one invokes the approximation procedure described following Eq. (3n-7) and reduces Eq. (3n-13) to (ref. 3)
o=
'YP - s - (h - 1)8 2
(3n-15)
correct to second order, where
h = 1
+
;! +
2~)
!(-y - 1) (1 -
- (I' -
1)2(4i3,oJ)-1
(3n-16)
If Egs. (3n-14) and (3n-12) are compared, it will be seen that B/A replaces the quantity I' - 1 in describing second-order nonlinearity of the p - p relation. For a perfect gas, therefore, replace B/A by I' - 1 and i3 is given by x - X(cf»
cf> =
t - u ± co(l
+ c,U +
C
2U2 . . . )
(3n-51)
where U is to be interpreted as co-Ix,(cf». Solids. The mathematical formalism for plane, longitudinal elastic waves in solids, either crystalline or isotropic, is very similar to that for liquids and gases (refs. 11-13). The wave equation is given in Lagrangian coordinates as ~tt = co2G(~aHaa
G(~a)
where
=
1
+ C:~:) ~a + C:~:) ~aa
(3n-52) ...
(3n-53)
Here a represents the rest position of a particle; ~ is partical displacement; and M 2 , M 3, M 4, etc., are quantities involving the second-, third-, fourth-, and higher-order elastic coefficients (ref. 12). The quantity co 2G plays the same role that (pc/ PO)2 does for fluids (ref. 14). By the Lagrangian equation of continuity, po/p = 1 + ~a; thus replace Eq. (3n-1S) by A= =
- Co
!o
-Co[~a
1;.
-
[G(~a')Jt d~a' tm3~a2
+ (t -
(3n-54) tm4)m32~aS . . . J
(3n-55)
where ms = -JYI 3/M 2, m4 = 1 - M4/M2m32, etc. Riemann invariants are defined as before by Eq. (3n-24). Note that u = ~, in Lagrangian coordinates. Simple-wave fields are again specified by Eq. (3n-21), which when combined with Eq. (3n-5) leads to (3n-56) ~a = + U + tm3U2 + tm4m32Us The propagation speed for simple waves is
_ ±coG! (da) cit u~con't-
(3n-57)
The factor u, which appears in Eq. (3n-23), is absent here because the coordinate system is Lagrangian. Equation (3n-57) expanded in series form is (3n-58)
3-192
ACOUSTICS
Therefore, the solution of the piston problem, given u(O,t) =
t
+ 1
=
a/co
±
~maU
+ ima'(l
- 2m.) U'
X,(t), is
(3n-59)
where U is to be interpreted, as in Eq. (3n-S1), as co-1X,( Ao) is equivalent to a plane wave in a medium in which the dissipation increases with distance. Conversely, for a converging wave (A < Ao) the dissipation seems to decrease with distance (refs. 17, 18). gn-lS. Equations for Other Forms of Dissipation. If dissipation is due to an agency other than the thermoviscous effects discussed in the last section, it may still be possible to derive an approximate unidirectional-wave equation similar to Burgers'. Relaxing Fluids. An elementary example of a relaxing fluid is one that radiates heat in accordance with Eq. (3n-.5)(ref. 38). For simplicity take the fluid to be a perfect gas, and let it be inviscid and thermally nonconducting. At very low frequencies infinitesimal waves travel at the isothermal speed of sound, given by bo2 = 'Pol po. At very high frequencies the speed is the adiabatic value, given by boo' =
3-201
NONLINEAR ACOUSTICS (THEORETICAL)
'YPo/ Po (the notation boo is used here in place of Co to emphasize the role played by frequency). The dispersion m, defined by
(3n-99) is equal to 'Y - 1 for the radiating gas. If the dispersion is very smail, i.e., m « 1 (which in this case implies 'Y == 1), the following approximate equation for plane waves can be derived:
(q
+ a~/) u x -
bo- 2 (!3iq +!3a
a~/) uu; = ± 2~o u""
(3n-l00)
where t' = t =+= x/boo It is seen that the radiation coefficient q [see Eq. (3n-5)] is the reciprocal of a relaxi1tion time. Subscripts a and 1: used with (3 indicate adiabatic and isothermal values, respectively; that is, !3a = ('Y 1)/2 and (3i = (1 1)/2 = 1. The two values are essentially the same, since it has been assumed that 'Y == 1. At either very low frequencies (wq-l « 1) or very high frequencies (wq-l » 1) the lefthand side of the equation takes on the same form as Eq. (3n-47). If the equation is linearized, a dispersion relation can be found that gives the expected behavior for a relaxation process (the actual formulas for the attenuation and phase velocity agree with the exact ones for a radiating gas only for m « 1). Polyakova, Soluyan, and Khokhlov considered a relaxation process directly and obtained a pair of equations that can be merged to form a single equation exactly like Eq. (3n-lOO) except that {Ji and!3a are equal (ref. 39). Some solutions (refs. 39,40) have been found. One represents a steady shock wave. The shock profile is singlevalued for very weak shocks. But when the shock is strong enough that its propagation speed [see Eq. (3n-72)] exceeds boo, the solution breaks down (a triple-valued waveform is predicted). This illustrates an important fact about the role of relaxation in nonlinear propagation: Relaxation absorption can stand off weak nonlinear effects, but not strong ones. In frequency terms, relaxation offers high attenuation to a broad mid-range of frequencies. If the wave is quite weak, the distortion components are easily absorbed because their frequencies fall in the range of high attenuation. But if the wave is strong, many more very high frequency components are produced, and these are not attenuated efficiently by the relaxation process. To keep the waveform from becoming triple valued, it is necessary to include a viscosity term in the approximate wave equation. In ref. 40 the problem of an originally sinusoidal wave is treated. Quantitative approximate solutions are obtained for cases in which the source frequency is either very low or very high, and a qualitative discussion is given for source frequencies in between. Marsh, Mellen, and Konrad (ref. 30) postulated a "Burgers-like" equation for spherical waves. It is similar to Eq. (3n-100) but is corrected to take account of spherical divergence. A viscosity term is added, and {Ji and !3a are the same. At either very low or very high frequencies the equation takes on the form of Eq. (3n-98) [for spherical waves (A/Ao)! = r/ro = ez1ro ], and some initial attempts at solving this equation were described. Boundary-layer Effects. Consider the propagation of a plane wave in a thermoviscous fluid contained in a tube. The wave can never be truly plane because the phase fronts curve a great deal as they pass through the viscous and thermal boundary layers at the wall of the tube. If the boundary-layer thicknesses are small compared with the tube radius, however, the curvature of the phase fronts is restricted to very narrow regions, and the wave may be considered quasi-plane. The boundary layers still affect the wave, causing an attenuation that is proportional to V;;; and a comparable dispersion. If the frequency is low, the attenuation from this source is much
+
+
3-202
ACOUSTICS
more important than that due to thermoviscous effects in the mainstream (central core of the fluid), and so it makes sense to find a Burgers-like equation for this case. A one-dimensional model of time-harmonic wave propagation in ducts with boundary-layer effects treated as a body force has been given by Lamb (ref. 41). Chester (ref. 42) has generalized this model and applied it to compound flow in a closed tube. His method can be used to obtain the following equation for simple-wave flow:
u. -l!...uu,. co'
=
=+=
1
+ (I'
-
1)/VPr
coD /2
(!:..)t 10('" u,.(x,t' 7r
,,).!£..v;.
(3n-101)
where D is the hydraulic diameter-ef the duct (four times the cross-sectional area divided by the circumference). No solutions are presently available. But the equation does have proper limiting forms. If the effect of the boundary layers (right-hand side) is neglected, the result is Eq. (3n-47). If the nonlinear term is dropped, the time-harmonic solution can be found, and this solution yields the correct attenuation and dispersion. Because of the relative weakness of boundary-layer attenuation (the dimensionless attenuation all. varies as 1lVw), the higher spectral components generated as a manifestation of steepening of the waveform are not efficiently absorbed. Thus discontinuous solutions, modified somewhat by the attenuation and dispersion, are to be expected.
REFLECTION, STANDING WAVES, AND REFRACTION 3n-14. Reflection and Standing Waves. For plane interacting waves in lossless fluids we return to Eqs. (3n-24) to (3n-26). For perfect gases the Riemann invariants are given by t=_c_+~
(3n-102a)
ll=_c_+~
(3n-102b)
1'-1
1'-1
2
2
Equations (3n-26) tell us that the quantity t is forwarded unchanged with speed u + c = t('Y + 1)r - i(3 - 1')6. Similarly, the speed for the invariant 6 is u c = t(3 - 'Y)r - t('Y + 1)6. The roles of independent and dependent variables can be reversed to give the following differential equation for the flow: (3n-103) where N = t('Y + 1)/(1' - 1). For monatomic and diatomic gases N = 2 and N = 3, respectively. An exact solution of this equation in terms of arbitrary functions f(r) and g(13) is known, but it is usually difficult to determine f and g from the initial conditions (ref. 4). Reflection. Certain valuable information about reflection can be obtained without solving for the entire flow field. Consider the problem of reflection from a rigid wall. For the moment we need not be specific about the equation of state. Let the incident wave be an outgoing simple wave. The Riemann invariant t for a particular signal in this wave is, by Eqs. (3n-21) and (3n-24), 2r =
"i +
Ui = 2"i
But rcan also be evaluated at the wall during the interaction of the incident and reflected waves: i.e., 2t = "wall + Uwall = "wall Elimination of r between these two expressions gives
"wall
= 2"i
NONLINEAR ACOUSTICS (THEORETICAL)
3-203
This is an exact statement of the law of reflection for continuous finite-amplitude waves at a rigid wall: The quantity A doubles, not the acoustic pressure. To see what happens to the pressure, we must specify an equation of state. Take the case of a perfect gas, for which A = 2(c - co)/(1' - l)(thus c - Co doubles at a rigid wall). Using Eq. (3n-ll), we obtain p) ( po wall
where
p. =
21'/(1' - 1).
=
[(Pi)l/~ 2. Po
- 1
JIL
(3n-105)
Now define a, wall amplification factor a by <X
=
Po Pi - po
pwall -
Substitution from Eq. (3n-105) gives <X
= r2(p;/po) iilL
-
ll~
p;/Po - 1
- 1
(3n-106)
An analogous result in terms of the source that generated the incident simple wave is given in ref. 43; Eq. (3n-106) was first obtained by Pfriem (ref. 44). For weak waves (pi - Po «Po) <X = 2, in agreement with linear theory. The limiting value for very strong waves is <X = 21L (= 27 for air), a quite startling result. It is only of passing interest, however, because a wave this strong would already have deformed into a shock by the time it reached the wall [for shocks the expression for <X is entirely different; the limiting value for strong shocks is <X = 2 + (1' + 1) 1(1' - 1) = 8 for air (ref. 4)]. In fact, the deviation from pressure doubling is small even for fairly strong waves. For an originally sinusoidal W2"ve of sound pressure level 174 dB, the maximum deviation is about 6 percent (ref. 43). For a pressure release surface the law of reflection for finite-amplitude waves is the same as for infinitesimal waves. To see this, evaluate r as before, first in the incident wave (2t' = Ai + Ui = 2Ui) and then at the pressure-release surface (2r = Asur/ace + U,urface = U,urfaoe, since A = 0 when P = Po, P = po). The result is Usurface
=
2Ui
that is, the particle velocity doubles at the surface. The reflection has an interesting effect on the wave, however. Consider a finite wave train so that after interaction the reflected signal is a simple wave. Toa good approximation, the acoustic pressure wave suffers phase inversion as a result of the reflection. A wave that distorts as it travels toward the surface therefore tends to "undistort" after reflection. This effect has been observed experimentally (ref. 45). Reflection from and transmission through other types of surfaces, such as gaseous interfaces, are considered in ref. 43. Oblique reflection of continuous waves from a plane surface has not been solved in any general way; see ref. 46 for a perturbation treatment. Standing Waves. First consider finite-amplitude wave motion in a tube closed at one end and containing a vibrating piston in the other end. This problem is one of the few in which much experimental evidence is available (refs. 47,48, 50). At resonance, if the piston amplitude is sufficiently high, shocks occur traveling to and fro between the piston and the closed end, Slightly off resonance, again for high enough amplitude, the waveform exhibits cusps. Below resonance the cusps occur at the troughs of the waveform, above resonance at the peaks. It would seem that such rich phenomena would have stimulated intensive theoretical treatments of the problem. In fact, the theoretical problem has proved a difficult nut to crack. The Riemann solution [01 Eq. (3n-103)] is of no avail because of the presence of shocks. There is no well-developed weak-shock theory for compound waves as there is for simple
3-204
ACOUSTICS
waves. For weak waves perturbation treatments have been used (ref. 4"8). For strong waves one approach has been to assume the existence of shocks at the outset. The Rankine-Hugoniot relations are used to provide boundary conditions for the continuous-wave flow in between shocks (refs. 47, 49). A more fundamental approach has been taken by Chester (ref. 42). His treatment is of general interest because of the way the effect of the boundary layer is assimilated in the one-dimensional model [see Eq. (3n-101) for an adaptation to simple waves]. An "inviscid solution" is first obtained; it contains discontinuities at and near resonance, and cusps at one point on either side of resonance. General agreement with experimental observation is thus good (ref. 50). Improved solutions are then considered in which thermoviscous effects, first in the mainstream and then in the boundary layers, are taken into account. an-lll. Refraction. Treatments of oblique reflection and refraction at interfaces have mainly been confined to sheck waves in v;hich the flow behind the shock is basically steady. Slow, continuous refraction, such as that caused by gradual changes in the medium or by gradual variations along the phase fronts of the wave, has been treated, however (refs. 26, 51, 52). The basis of the method is ordinary ray acoustics. The propagation speed along each ray tube and the cross-sectional area of the tube are modified to take account of nonlinear effects. The approach is similar to that given in Sec. 3n-7 except that the cross-sectional area of the horn varies in a manner that depends on the wave motion. Acknowledgment. Support for the preparation of this review came from the Aeromechanics Division, Air Force Office of Scientific Research. References 1. Vincenti, W. G., and B. S. Baldwin, Jr.: J. Fluid Mech. 12,449-477 (1962). 2. Stokes, G. G.: Phil. Mag., ser. 4,1,305-317 (1851). 3. Blackstock, D. T.: Approximate Equations Governing Finite-amplitude Sound in Thermoviscous Fluids, Suppl. Tech. Rept. AFOSR-5223 (AD 415 442), May, 1963. 4. Courant, R., and K. O. Friedrichs: "Supersonic Flow and Shock Waves" Interscience Publishers, Inc., New York, 1948. 5. Earnshaw, S.: Trans. Roy. Soc. (London) 150, 133-148 (1860). 6. Riemann, B.: Abhandl. Ges. Wigs. Gottingen, Math.-Physik. Kl. 8, 43 (1860), or "Gesammelte Mathematische Werke," 2d ed., pp. 156-175, H. Weber, ed., Dover Publications, Inc., New York, 1953. 7. Poisson, S. D.: J. Ecole Poly tech. (Paris) 7, 364-370 (1808). However, Poisson's solution is for the special case of a constant-temperature gas, which in our notation corresponds to fJ = 1. 8. Blackstock, D. T.: J. Acoust. Soc. Am. 34,9-30 (1962). 9. Stokes, G. G.: Phil. Mag., ser. 3, 33, 349-356 (1848). 10. Fubini, E.: Alta Frequenza 4, 530-581 (1935). Fubini was the first to render the Fourier coefficients in terms of Bessel functions. He used Lagrangian coordinates, not Eulerian as in the derivation here, and attempted to calculate some of the higherorder terms. The mathematical similarity of this problem to Kepler's problem in astronomy is discussed in ref. 8. 11. Gol'dberg, Z. A.: Akust. Zh. 6, 307-310 (1960); English translation: Soviet PhY8.Acoust. 6, 306-310 (1961). 12. Thurston, R. N., and M. J. Shapiro: J. Acoust. Soc. Am. 41, 1112-1125 (1967). 13. Breazeale, M. A., and Joseph Ford: J. Appl. Phys. 36, 3486-3490 (1965). 14. Compare Eq. (3n-51) with Eq. (1), p. 481 in H. Lamb, "Hydrodynamics" 6th ed., Dover Publications, Inc., New York, 1945. 15. Laird, D. T., E. Ackerman, J. B. Randels, and H. L. Oestreicher: Spherical Waves of Finite Amplitude, W ADC Tech. Rept. 57-463 (AD 130949), July, 1957. 16. Blackstock, D. T.: J. Acoust. Soc. Am. 36, 217-219 (1964). 17. Naugol'nykh, K. A., S. I. Soluyan, and R. V. Khokhlov: Vestn. Mask. Univ. Fiz. Astron. 4, 65-71 (1962) (in Russian). 18. Naugol'nykh, K. A., S. 1. Soluyan, and R. V. Khokhlov: AkuBt. Zh. 9, 54-60 (1963); English translation: Soviet Phys.-Acoust. 9, 42-46 (1963). 19. Akulichev, V. A., Yu. Ya. Boguslavskii, A. I. Ioffe, and K. A. Naugol'nykh: AkuBt. Zh. 13, 321-328 (1967); English translation: Soviet Phys.-Acou8t. 13, 281-285 (1968)
NONLINEAR ACOUSTICS
(THEORETICAL)
3-205
20. Cole, R. H.: "Underwater Explosions," Dover Publications, Inc., New York, 1965. 21. Taylor, G. I.: Proc. Roy. Soc. (London), ser. A, 186,273-292 (1946). 22. Naugol'nykh, K. A.: Akust. Zh. 11, 351-358 (1965) English translation: Soviet Phys.Acoust. 11, 296-301 (1966). 23. This solution has been derived by G. B. Whitham, J. Fluid Mech. 1,290-318, (1956), on a somewhat different basis. 24. Landau, L. D.: J. Phys. U.S.S.R. 9, 496-500 (1945). 25. Friedrichs, K. 0.: Commun. Pure Appl. Math. 1,211-245 (1948). 26. Whitham, G. B.: Commun. Pure Appl. Math. 5, 301-348 (1952). 27. Blackstock, D. T.: J. Acoust. Soc. Am. 39, 1019-1026 (1966). 28. Rudnick, 1.: J. Acoust. Soc. Am. 30, 339-342 (1958). 29. Lighthill, M. J.: In "Surveys in Mechanics," pp. 250-351, edited by G. K. Batchelor and R. M. Davies, eds., Cambridge University Press, Cambridge, England, 1956. 30. See, for example, H. W. Marsh, R. H. Mellen, and W. L. Konrad, J. Acoust. Soc. Am. 38,326-338 (1965). 31. Mendousse, J. S.: J. Acoust. Soc. Am. 25, 51-54 (1953). 32. Hayes, W. D.: "Fundamentals of Gas Dynamics," chap. D, H. W. Emmons, ed., Princeton University Press, Princeton, N.J., 19fi8. 33. Pospelov, L. A.: Akust. Zh. 11, 359-362 (1965); English translation: Soviet Phys.Acoust. 11, 302-304 (1966). 34. Soluyan, S. I., and R. V. Khokhlov: Vestn. Mosk. Univ. Fiz. Astron. 3, 52-61 (1961) (in Russian). 35. Blackstock, D. T.: J. Acoust. Soc. Am. 36, 534-542 (1964). 36. Gol'dberg, Z. A.: Aku8t. Zh. 2, 325-328 (1956); 3, 322--328 (1957); English translation: Soviet Phys.-Acoust. 2, 346-350 (1956); 3, 340-347 (1957). 37. Fay, R. D.: J. Acoust. Soc. Am. 3, 222-241 (1931). Fay was concerned with a viscous gas. 38. Truesdell, C. A.: J. Math. Mech. 2, 643-741 (1953). 39. Polykova, A. L., S. I. Soluyan, and R. V. Khokhlov: Akust. Zh. 8, 107-112 (1962); English translation: Soviet Phys.-Acoust. 8,78-82 (1962). 40. Soluyan, S. I., and R. V. Khokhlov: Akust. Zh. 8, 220-227 (1962); English translation SovietPhys.-Acoust. 8, 170-175 (1962). 41. Ref. 14, art. 360b. 42. Chester, W.: J. Fluid Mech. 18,44-64 (1964). 43. Blackstock, D. T.: Propagation and Reflection of Plane Sound Waves of Finite Amplitude in Gases, Harvard Univ. Acoust. Res. Lab. Tech. Mem. 43 (AD 242 729), June, 1960. 44. Pfriem, H.: Forsch. Gebeite I ngenieurw. B12, 244-256 (1941). 45. See, for example, R. H. Mellen and D. G. Browning: J. Acoust. Soc. Am. 44, 646-647 (1968). 46. Shao-sung, F.: Akust. Zh. 6, 491-493 (1960): English translation: Soviet Phys.-Acoust. 6, 488-490 (1961). 47. Saenger, R. A., and G. E. Hudson: J. Acous!. Soc. Am. 32, 961-970 (1960). 48. Coppens, A. B., and J. V. Sanders: J. Acoust. Soc. Am. 43, 516-529 (1968). 49. Betchov, R.: Phys. Fluids 1, 205-212 (1958). 50. Cruikshank, D. B.: An Experimental Investigation of Finite-amplitude Oscillations in a Closed Tube at Resonance, Univ. Rochester Acoust. Phys. Lab. Tech. Rept. AFOSR 69-1869 (AD 693635), July 31, 1969. 51. Whitham, G. B.: J. Fluid Mech. 2, 145-171 (1957). 52. Friedman, M. P., E. J. Kane, and A. Sigalla: AIAA Journal 1, 1327-1335 (1963). 53. Westervelt, P. J.: J. Acou8t. Soc. Am. 35, 535-537 (1963). 54. Thuras, A. L., R. T. Jenkins, and H. T. O'Neil: J. Acoust. Soc. Am. 6, 173-180 (1935). 55. Muir, T. G.: "An analysis of the parametric acoustic array for spherical wave fields," Ph.D. dissertation, University of Texas at Austin, Texas (1971). 56. Bellin, J. L. S. and R. T. Beyer: J. Acoust. Soc. Am. 34, 1051-1054 (1962). 57. See, for example, Berktay, H. 0.: J. Sound Vib. 5, 155-163 (1967). 58. Lester, W. W.: J. Acoust. Soc. Am. 40, 847-851 (1966).
30. Nonlinear Acoustics (Experimental) ROBERT T. BEYER
Brown University
. 30-1. Fluids. In the experimental study of nonlinear acoustics, three types of quantities have been measured. These are the effective sound absorption for waves of finite amplitude, the growth of harmonic content, and the nonlinear variation terms in the isentropic expansion of the pressure in the medium in terms of the density changes. Since the comparison of the first two of these properties with theory depends on the third, it is most effective to consider first the nonlinearity of the equation ofstate. This isentropic equation of state can be expanded in a Taylor series in the condensation s = (p - po)lpo: B C p - po = As 2i S2 3i $3 ·(30-1)
+
+
+ ..
Here po and Po are the equilibrium values of the pressure and the density. Also, A = poco 2 • By application of thermodynamics (ref. 1) the ratio BIA can be written o B_2 + 2c - PoCo (.ac) -TfJ -(ae) -
ap
A
T
aT
Cp
p
(30-2)
fJ
In this equation, is the coefficient of thermal expansion, Cp the specific heat at constant pressure, and the derivatives are evaluated under condition of sound waves of infinitesimal aI:Uplitude. BIA is sometimes known as the parameter of nonlinearity. Evaluation of CIA is more involved. It can be shown that (ref. 2)
Q = 2~
A
(!i) A
2
+ 2p0
2C 03
(aap2C) • 2
(30-3)
At a hydrostatic pressure of one atmosphere, the second term on the right is generally quite small compared with the first, although it is likely to ·become appreciable at higher hydrostatic pressures (ref. 3). . For an ideal gas, we can expand the adiabatic equation of state
p = Po
(for
= Po [ 1
+ I'S + 1'(1'2~ 1) + ... ] 82
(30-4)
where I' is the rlJ,tio of specific heats. By comparing coefficients in Eqs. (30-1) and (30-4) we find
A whence
B A
B
= I'PO = I' -
1
= 1'(1' -
I)po
for an ideal gas
( 30-5)
The ratio B I A has now been measured for a considerable number of liquids at atmospheric pressure and, in some instances, over a modest temperature range. A number 3-206
3-207
NONLINEAR ACOUSTICS (EXPERIMENTAL)
of these experimental values are given in Table 30-1. The error in these measurements is generally of the order of 2 to 3 percent, except for the liquid metals, where the larger uncertainties are listed in the table. The few samples of temperature dependence of B/A shown indicate that B/A can increase or decrease with temperature, depending on the material, but that the temperature variation is usually quite slight. TABLE
Liquid
T, °C
30-1.
BIA
VALUES OF
Referenee
B/A
FOR VARIOUS LIQUIDS
T, °C
Liquid
--
--Aceione ....... Alcohol MethyL .....
20
Ethyl. ....... n-Propyl. ....
9.2
2
9.6
2
20
10.5
2
20
10.7
2
n-Butyl. ... ..
20
10.7
2
Benzene ... , ...
30 40 50 60 70
20
I
9.0 9.2 9.3 9.45 9.5
30 30
10.2 9.3
2 2
Cyclohexane ....
30 40 50 60 70 30 30 30 30 30 30 30
10.1 10.1 10.1 9.85 9.75 10.3 9.7 9.8 10.0 9.9 9.7 8.2
2 2 2 2 2 2 5 5 4 4 2 5
Diethylamine ... Ethylene glycol. Ethyl formate .. Heptane ....... Hexane ........ Methyl acetate. Methy] iodide ..
--
Referenee
Estimated error, %
9.5
6
0 10 20 30 40 50 60 80
4.1 4.6 5.0 5.2 5.5 5.55 5.6 5.7
3 1 1 3 3 3 3 3
0 10 20 30
4.9 5.1 5.2 5.4
2 2 2 2
Liquid Metal. Bismuth ........ . . . . . . . . 66 Bi (wt %),34 In
318 125
7.1 6.1
8 8
15
52 In 48 Bi 34 Bi 76 In 83 In 17 Bi Indium. ...... , ......... l\1ercury ................ Potassium ...... , ....... . Sodium ......... ..... ... Tin ................... .
125 125 125 160 30 100 110 240
5.1 5.1 4.9 4.55 2.9 2.9 2.7 4.4
8 8 8 8 8 7 8 8
5 5 5 5 3 15 2 11
Sulfur ........
I Water (distilled) .........
2 2 2 2 2
Benzyl alcohoL. Chlorobenzene ..
..........I 121
BIA
Water (sea, 33 % salinity).
5
The dependence of B / A on hydrostatic pressure is shown in Table 30-2· for several liquids. Table 30-3 gives the few known values of the third-order ratio, C / A, all under the approximation
The general form of the acoustic wave equation for a fluid satisfying Eq. (30-1) (with neglect of the 8 3 and higher terms) is, in Lagrangian coordinates, a'~
at'
co'
=
(1
a'~
+ auax)2+BIA ax'
(30-6)
where ~ is the particle displacement, and Co is the speed of sound for infinitesimal. 1;. In approximate solutions of this equation [such as Eqs. (3n-40) and (3n-92)], the ratio B / A always appears in the form (30-7)
3-208
ACOUSTICS
Hence distortions of the wave form of an initial sinusoid can be used to determine the ratio BIA. Finally, the effective absorption coefficient for a finite-amplitude wave can be written for a nonrelaxing medium as -aeff =
a
3w'~o ( 1 + -B) e+ -4ac' 2A
1
2az
(1 - e-,az),
. + hIgher-order terms
(30-8)
where a is the absorption coefficient for infinitesimal displacement amplitude ~o. The ratio BIA could therefore be obtained from this equation, although with reduced accuracy. TABLE 30-2. VALUES OF
BIA
AT VARIOUS PRESSURES
Pressure p, kg/em' Temperature T, °c
1
250
500
1,000
2,000
4,000
8,000
4.08 5.49 5.74
4.90 5.59 5.79
5.58 5.69 5.84
6.35 5.84 5.86
6.78 6.00 5.82
6.60 6.06 5.64
5.79 5.50
....
8.9
8.0
7.3
6.4
5.7
... .
... .
....
7.84
7.37
7.01
Water [3]
0 40 80 I-Propyl alcohol [9]
10.4
30 Mercury [9]
8.33
40.5
TABLE 30-3. VALUES OF
Pressure at 30°C
CIA
iCE/A)'
2po'co 3 ca'c/ap')T at 30°C
CIA
40.7 55.5 57.5 52.7
-8.7 -16.9 -25.0 -26.7
32.0 38.6 32.5 26.0
162 49
-87 -24
75 25
Water [3]
1 atm 2,000 kg/em' 4,000 kg/em' 8,000 kg/em' I-Propyl alcohol [9]
1 kg/em' 8,000 kg/em'
+
30-2. Solids. Equation (3n-BOc) indicates that the coefficient {'J = 1 BI2A for liquids must be replaced by {'J = -M3/2M, for solids, where M, and M3 are elasticconstant combinations that appear in the partial differential equation for purely longitudinal waves in solids (ref. 10), a'u -at'
= -
1 a'u (
Po
-a' X
ll[,
+M
+ hIgher-order terms )
au.
3 -
ax
(30-9)
where u is the displacement velocity. The constants ly[, and M3 are often written in terms of other so-called second- and third-order elastic coefficients K, and K3:
M3
=
Ka +2K,
The coefficients K2 and Ka are in turn related to the more familiar second- and thirdorder elastic constants Cij and Ci,'k. The connections for the [100J, [110], and [111]
NONLINEAR ACOUSTICS (EXPERIMENTAL)
directions are shown in Table 30-4. More detailed relations of this sort are given in ref. 12. By measurement of the distortion of an initially sinusoidal longitudinal wave through a solid, it is therefore possible to determine the third-order elastic constants. A number of these constants have been determined. Their values are given in Table 30-5 (ref. 13). 30-4. K2
TABLE
AND
Ka
[100], [110],
FOR THE
AND
Direction
DIRECTIONS
[I1J
Ka
011 011
[100]
0111
+ 012 + 20 .. 2 011 + 2012 + 404,
[110] [111]
TABLE
[111]
0111
4 Cm + 60112 + 120", + 240166 + 2C123 + 160456 9
3
30-5.
+ 30112 + 120166
MEASURED THIRD-ORDER ELASTIC CONSTANTS OF SOME CUBIC CRYSTALS AT ROOM TEMPERATURE
[13]
(x 10 12 dynes/em 2) Crystal
Ge Si GaAs GaAsInSb Cu Cu Ge Ge MgO NaCI KCI NaCl KCl BaF2 Approx. accuracy, %
0111
-7.10 -8.25 -6.22 -6.72 -3.14 -15.0 -12.71 -7.32 -7.16 -48.9 -8.3 -7.1 -8.80 -7.01 -5.84 ±5
012a
0,44
-3.89 -4.51 -3.87 -4.02 -2.10 -8.5 -8.14 -2.90 -4.03 -0.95
-0.18 -0.64 +0.57 -0.04 -0.48 -2.5 -0.50 -2.2 -0.18 -0.69
-0.23 +0.12 +0.02 -0.70 +0.09 -1.35 -0.03 -0.08 -0.53 +1.13
-2.92 -3.10 -2.69 -3.20 -1.18 -6.45 -7.80 -3.03 -3.15 -6.6
-0.57 -0.224 -2.99
0.284 0.133 -2.06
0.257 0.127 -1.21
-0.611 -0.245 -0.889
±10
±50
±50
±3
0112
0166
0456
Ref.
-0.53 -0.64 -0.39 -0.69 +0.002 -0.16 -0.95 -0.41 -0.47 +1.47
14 14 15 16 17 18 19 20 21 21 22 22 23 23 24
0.271 0.118 0.271 ±15
References' 1. Beyer, R. T.: J. Acoust. Soc. Am. 32,719-721 (1960). 2. Coppens, A. B., R. T. Beyer, M. B. Seiden, J. Donohue, F. Guepin, R. D. Hodson and C. Townsend: J. Acoust. Soc. Am. 38, 797-804 (1963). 3. Hagelberg, M. P., G. Holton, and S. Kao: J. Acoust. Soc. Am. 41, 564-567 (1967). 4. Maki, W. C.: M.A.T. thesis, Brown University, Providence, R.I., June, 1966. 5. Freeman, R. A.: M.A.T. thesis, Brown University, Providence, R.I., June, 1966. 6. Dunn, F. W.: M.A.T. thesis, Brown University, Providence, R.I., June, 1967. 7. Sander, C. F.: M.A.T. thesis, Brown University, Providence, R.I., June, 1969. 8. Coppens, A. B., R. T. Beyer, and J. Ballou: J. Acoust. Soc. Am. 41, 1443-1448 (1967). 9. Hagelberg, M. P.: J. Acoust. Soc. Am. 47, 158-162 (1970). 10. Thurston"R. N., and M. J. Shapiro: J. Acoust. Soc. Am. 41, 11.12-1125 (1967), 11. Breazeale, M. A., and Joseph Ford: J. Appl. PhY8. 36, 3486, 3490 (1965).
3-210
ACOUSTICS
12. Thurston, R. N., and K. Brugger: Phys. Rev. 133A, 1604-1610 (1964); erratum, ibid. 135(AB7), 3 (1964). 13. Beyer, R. T., and S. V. Letcher: "Physical Ultrasonics," p. 255, Academic Press, Inc., New York, 1969. 14. McSkimin, H. J., and P. Andreatch, Jr.: J. Appl. Phys. 35,3312 (1964). 15. McSkimin, H. J., and P. Andreatch, Jr.: J. Appl. Phys. 38, 2610 (1967). 16. Drabble, J. R., and A. J. Brammer: Solid State Commun. 4,467 (1966). 17. Drabble, J. R., and A. J. Brammer: Proc. Phys. Soc. (London) 91,959 (1967). 18. Sslama, K., and G. A. Alers: Phys. Rev. 161, 673 (1967). 19. Hiki, Y., and A. V. Granato: Phys. Rev. 144, 411 (1966). 20. Bateman, T., W. P. Mason, and H. J. McSkimin: J. Appl. Phys. 32, 928 (1961). 21. Bogardus, E. H.: J. Appl. Phys. 36, 2504 (1965). 22. Stanford, A. L., Jr., and S. P. Zehner: Phys. Rev. 153, 1025 (1967). 23. Chang, Z. P.: Phys. Rev. 140A, 1788 (1965). 24. Gerlich, D.: Phys. Rev. 168,947 (1968).
3p. Selected References on Acoustics LEO L. BERANEK
Bolt Beranek and Newman Inc.
Acoustical Materials Association: Sound Absorption Coefficients of Architectural Acoustical Materials, Acoust. Materials Assoc. Bull. XXIX, New York, 1969. Adam, N.: "Akustik," Verlag Paul Haupt, Bern, 1958. Albers, V. M.: "Underwater Acoustics Handbook," 2d ed. Pennsylvania State University Press, University Park, Pa., 1965. Albers, V. M.: "Underwater Acoustics," vols. 1 and 2, Plenum Publishing Corporation, New York, 1963, 1967. ASHRAE: "Guide and Data Book: Systems and Equipment," chap. 31, Sound and Vibration Control, 1967. Babikov, O. 1.: "Ultrasonics and Its Industrial Applications," translated from Russian, Consultants Bureau, Plenum Publishing Corporation, New York, 1960. Bartholomew, W. T.: "Acoustics of Music," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1946. Beranek, L. L.: "Acoustics," McGraw-Hill Book Company, New York, 1954. Beranek, L. L.: "Acoustic Measurements," John Wiley & Sons, Inc., New York, 1960. Beranek, L. L.: "Noise Reduction," McGraw-Hill Book Company, New York, 1960. Beranek, L. L.: "Music, Acoustics and Architecture," John Wiley & Sons, Inc., New York, 1962. Beranek, L. L.: "Noise and Vibration Control," McGraw-Hill Book Company, New York, 1971. Bergmann, L.: "Der Ultraschall und seine Anwendung in Wissenschaft und Technik," 6th ed., S. Hirzel Verlag KG, Stuttgart, 1954. Brekhovskikh, L. M.: "Waves in Layered Media," Academic Press, Inc., New York, 1960. Burris-Meyer, H., and L. S. Goodfriend: "Acoustics for the Architect," Reinhold Publishing Corporation, New York, 1957. Canac, F., ed.: "Acoustique musicale," Editions du Centre National de la Recherche Scientifique, Paris, 1959. Carlin, B.: "Ultrasonics," 2d ed. McGraw-Hill Book Company, New'York, 1960. Chalupnik, J. D.: "Transportation Noises," University of Washington Press, Seattle, Washington, 1970. Orede, O. E.: "Shock and Vibration Concepts in Engineering Design," Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965.
SELECTED REFERENCES ON ACOUSTICS
3-211'
Crede, C. E.: "Vibration and Shock Isolation," John Wiley & Sons, Inc., New York, 1951. Cremer, L.: "Die wissenschaftlichen Grundlagen der Raumakustik," vol. I, S. Hirzel Verlag KG, Stuttgart, 1949. Cremer, L.: "Die wissenschaftlichen Grundlagen der Raumakustik," vol. II, S. Hirzel Verlag KG, Stuttgart, 1961. Cremer, L.: "Die wissenschaitlichen Grundlagen der Raumakustik," vol. III, S. Hirzel Verlag KG, Stuttgart, 1950. Cremer, L., and M. Heckl: "Korperschall," Springer-Verlag OHG, Berlin, 1967. Culver, C. A.: "Musical Acoustics," 4th ed., McGraw-Hill Book Company, New York, 1956. Davis, H. and S. R. Silverman, eds.:' "Hearing and Deafness," rev. ed., Holt, Rinehart and Winston, Inc., New York, 1960. Eckart, C., ed.: "Principles and Applications of Underwater Acoustics." U.S. Government Printing Office, Washington, D.C., 1968. Fant, G.: "On the Acoustics of Speech," 3 vols, Mouton & Co., The Hague, 1960. Fletcher, H.: "Speech and Hearing in Communication," D. Van Nostrand Company, Inc., Princeton, N.J., 1953. Fliigge, S., ed.: "Handbuch der Physik," vol. XI/I, Akustik I; vol. XI/2, Akustik II, Springer-Verlag OHG, Berlin, 1961, 1962. Frayne, J. G., and H. Wolfe: "Sound Recording," John 'Wiley & Sons, Inc.; New York, 1949. Frederick, J. R.: "Ultrasonic Engineering," John Wiley & Sons, Inc., New York, 1965. Furrer, W.: "Room and Building Acoustics and N,oise Abatement," (Butterworths) Plenum Publishing Corporation, New York, 1964. Hansen, H. lVI., and P. F. Chenea: "Mechanics of Vibrations," John 'Wiley & Sons, Inc., New York, 1952. Harris, C. M., ed.: "Handbook of Noise Control," ¥cGraw-Hill Book Company, New York, 1957. Harris, C. M., and E. Crede: "Shock and Vibration Handbook," 3 vols, McGraw-Hill Book Company, New York, 1961. Helmholtz, H. L. F.: "On the Sensations of Tone as a Physiological Basis for the Theory of Music," translated from 3d, German ed. by A. J. Ellis, Longmans, Green & Co., Ltd., London, 1875; 5th rev. ed., 1930. Herzfeld, K. F., and T. A. Litovitz: "Absorption and Dispersion of Ultrasonic Waves," Academic Press, Inc., New York, 1959. Hirsch, I. J.: "The Measurement of Hearing," McGraw-Hill Book Company, New York, 1952. Hueter, T.F., and R. H. Bolt: "Sonics," John Wiley & Sons, Inc., New York, 1955; Hunt, F. V.: "Electroacoustics," Harvard University Press, Cambridge, Mass., and John Wiley & Sons, Inc., New York, 1954. Hunter, J. L.: "Acoustics," Prentice-Hall, Inc., Englewood Cliffs, N;J., 1957. Kacherovich, A. N., and E. E. Khomootov: "Acoustics and Architecture of Cinema Theaters," State Publishing House "Art," Moscow,,1961. Keast, D. N.: "Measurements in Mechanical Dynamics," McGraw-Hill Book Company, New York, 1967. , Kikuchi, Y.: "Ultrasonic Transducers," Corona Publishing Company, Tokyo, 1969. Kinsler, L. E., and A. R. Frey: "Fundamentals of Acoustics," 2d ed., John Wiley & Sons, Inc., New York, 1962; 5th printing, 1967. . Knudsen, V., and C. Harris: "Acoustical Designing in Architecture," John Wiley & Sons, Inc., New York, 1950. Krasil'nikov, V. A.: "Sound and Ultrasound Waves." 3d 'rev. ed., translated from the, Russian by N. Kaner and M. Segal, Israel Program for Scientific Translations Ltd., Jerusalem, 1963. Kryter, K. D.: The Effects of Noise on Man, J. Speech Hearing Disorders, Monograph' Suppl. I, September, 1950. , Kryter, K. D.: "The Effects of lifoise on Man," Academic P:r;ess, :ti!ew York, 11)70. Kurtze, G.: "Physics and Te(,hniques of Noise Control," (in German) Verlag G'. Braun, Karlsruhe, Germany, 1964. Lamb, H.: "The Dynamical Theory of Sound," 2d ed., N.Y., Dover Publications, Inc., New York, 1960. Lamb, H.: "Hydrodynamics," 6th ed., Dover Publications, Inc., New York, 1945. Lindsay, R. B.: "Mechanical Radiation," McGraw~Hill Book Company, New York, 1960,Lyon, R. H.: "Random Noise imd Vibration in Space Vehicles," '(LS. GoverI).IDent Printing Office, Washington, D.C., 1967. , j " , ,;,,' Malecki, I.: "Physical, Foundations of Technical Acoustios,~'PergamonPress, New y(l~k>; 1968. ,'j
3-212
ACOUSTICS
Mason, W. P.: "Electro-mechanical Transducers and Wave Filters," 2d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1948. Mason, W. P.: "Piezoelectric Crystals and Their Application to Ultrasonics," D. Van Nostrand Company, Inc., Princeton, N.J., 1950. MaBon, "V. P.: "Physical Acoustics," 7 vols., Academic Press, Inc., N ew York, 1964-1 97l. Mason, W. P.: "Physical Acoustics and the Properties of Solids," D. Van Nostrand Company, Inc., Princeton, N.J., 1958. Miller, G. A.: "Language and Communication," McGraw-Hill Book Company, New York, 1951. Morse, P. M.: "Vibration and Sound," 2d ed., McGraw-Hill Book Company, New York, 1948. Morse, P. M., and K. U. Ingard: "Theoretical Acoustics," McGraw-Hill Book Company, New York, 1968. Ol'shevskii, V. V.: "Characteristics of Sea Reverberations," translated from Russian, Consultants Bureau, Plenum Publishing Corporation, New York, 1967. Olson, H. F.: "Acoustical Engineering," 3d ed., D. Van Nostrand Company, Inc., Princeton, N.J., 1957. Olson. H. F.: "Solution of Energy Problems by Dynamical Analogies," D. Van Nostrand Co~pany, Inc., Princeton, N.J., 1958. Olson, H. F.: "Musical Engineering," 1\1cGraw-Hill Book Company, New York, 1952. Parkin, P. H., and H. R. Humphreys: "Acoustics, Noise and Buildings," Faber & Faber, Ltd., London, 1958. Parkin, P. H., H. J. Purkis, and W. E. Scholes: "Field Measurements of Sound Insulation Between Dwellings," Her Majesty's Stationery Office, London, 1960. Peterson, A. P. G., and E. E. Gross, Jr.: "Handbook of Noise Measurement," 6th ed., General Radio Company, West Concord, Mass., 1967. Pierce, J. R., and E. E. David Jr.: "Man's World of Sound," Doubleday & Company Inc., Garden City, N.Y., 1958. Purkis, H. J.: "Building Physics: Acoustics," Pergamon Press, New York, 1966. Lord Rayleigh: "The Theory of Sound," 2d ed., vols. 1 and 2, Dover Publications, Inc., New York, 1945. Rettinger, M.: "Acoustics: Room Design and Noise Control," Chemical Publishing Company, Inc., New York, 1968. Reichardt, W.: "Foundations of Technical Acoustics" (in German), Portig K. G., Leipzig, 1968. Richardson, E. G.: "Technical Aspects of Souml," 3 vols., American Elsevier Publishing Company, Inc., New York, 1962. Rschevkin, S. N.: "A Course of Lectures on the Theory of Sound," translated from the Russian by O. M. Blunn, edited by P. E. Doak, Pergamon Press, New York, 1963. Schaafs, W.: "Landolt-Bornstein New Series, Group II," "Atomic and Molecular Physics," vo!. 5, "Molecular Acoustics," Springer-Verlag New York Inc., New York, 1967. Skudrzyk, E.: "Die Grundlagen der Akustik," Springer-Verlag HG, Vienna, 1954. Skudrzyk, E.: "Simple and Complex Vibrating Systems," Pennsylvania State University Press, University Park, Pa., 1968. Stephens, R. W. B., and A. E. Bate: "Acoustics and Vibrational Physics," St. Martin's Press, Inc., New York, 1966. Stevens, S. S., J. G. C. Loring, and D. Cohen: "Bibliography on Hearing," Harvard University Press, Cambridge, Mass., 1955. Stevens, S. S., ed.: "Handbook of Experimental Psychology," John Wiley & Sons, Inc. New York, 1951. Swenson, G. W., Jr.: "Principles of Modern Acoustics," D. Van Nostrand Company, Inc., Princeton, N.J., 1953. Tolstoy,1. and P. S. Clay: "OceanAcoustics," McGraw-Hill Book Company, New York, 1966. Trapp, W. J., and D. M. Forney, Jr., eds.: "Acoustical Fatigue in Aerospace Structures," Syracuse University Press, Syracuse, New York, 1965. Tucker, D. G., and B. Z. Gazey: "Applied Underwater Acoustics," Pergamon Press, New York, 1966. Urick, R. J.: "Principles of Underwater Sound for Engineers," McGraw-Hill Book Company, New York, 1967. Wever, E. G., and M. Lawrence: "Physiological Acoustics," Princeton University Press, Princeton, N.J., 1954. Wiethaup, H.: "Noise Abatement in Western Germany" (in German), Carl Heymanns Verlag KG, Cologne, 1961. Wood, A.: "Acoustics," Dover Publications, Inc., New York, 1966. Zwikker, C., and C. W. Kosten: "Sound Absorbing Materials," American Elsevier Publishing Company, Inc., New York, 1949.
Section 4
HEAT MARK W. ZEMANSKY, Editor The City College of the City University of New York
CONTENTS 4a. 4b. 4c. 4d. 4e. 4£. 4g. 4h. 4i. 4j. 4k. 41.
Temperature Scales, Thermocouples, and Resistance Thermometers. . . . .. Thermodynamic Symbols, Definitions, and Equations ................ " Critical Constants. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Compressibility......... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Heat Capacities .................................................... Thermal Expansion .............................................. " Thermal Conductivity .............................................. Thermodynamic Properties of Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Pressure-Volume-Temperature Relationships of Gases. Virial Coefficients Temperatures, Pressures, and Heats of Transition, Fusion, and Vaporization Vapor Pressure .................................................... Heats of Formation and Heats of Combustion .........•..............•
4-1
4-2 4-22 4-33 4-38 4-105 4-119 4-142 4-162 4-204 4-222 4-261 4-316
4a. Temperature Scales, Thermocouples, and Resistance Thermometers 1 H. H. PLUMB, R. L. POWELL, W. J .. HALL, AND J. F. SWINDELLS
The National Bureau of Standards
The ComiM International des Poids et Mesures (CIPM) in October, 1968, agreed to adopt the International Practical Temperature Scale of 1968 2 (IPTS-68) in accordance with the decision of the 13th General Conference of Weights and Measures, Resolution 8, of October, 1967. IPTS-68 has replaced IPTS-48 (amended edition of 1960). It was formulated in such a way that temperature measured on it closely approximates the thermodynamic temperature, and extends the range of definition down to 13.81 kelvins. (The previous scale, IPTS-48, terminated at -183°C.) The basic temperature is the thermodynamic temperature, symbol T, the unit of which is the kelvin, symbol K. The kelvin is the fraction 1/273.16 of the thermodynamictemper(1ture of the triple point of water. a The Celsius temperature, symbol t, is defined by t = T - To where To = 273.15 K (the ice point). The unit employed to express a Celsius temperature is the degree Celsius, symbol °C, which is equal to the kelvin. A difference of temperature is expressed in kelvins; it may also be expressed in degrees Celsius. The International Practical Temperature Scale of 1968 distinguishes between the International Practical Kelvin Temperature with the symbol T 68 and the International Practical Celsius Temperature with the symbol t68. The relation between T68 and t68 is t68
=
T68 - 273.15 K
The units of T68 and t68 are the kelvin, symbol K, and degree Celsius, symbol °C, as in the case of the thermodynamic temperature T and the Celsius temperature t. The IPTS-68 is based on the assigned values of the temperatures of a number of reproducible equilibrium states (defining fixed points) and on standard instruments calibrated at those temperatures. Interpolation between the fixed-point temperatures is provided by formulas used to establish the relation between indications of the standard instruments and values of the International Practical Temperature. The defining fixed points are given in Table 4a-1. 1 Acknowledgment is made of the previous contributions to this section in the second edition of the Handbook by H. F. Stimson, J. F. Swindells, and R. E. Wilson. Data on optical pyrometry and thermal radiation are given in Sec. 6. 2 The text in French of this scale is published in Compt. rend. 13eme conf. gen. poids mesures, 1967-1968, Annexe 2, and Comite Consultatif de Thermometrie, 8 e session, 1967, Annexe 18. The English text is published in Metrologia 5(2), 35 (1969). a 13th General Conference of Weights and Measures, 1967, Resolutions 3 and 4 .
. ~r-2
4-3
TEMPERATURE SCALES, THERMOCOUPLES TABLE
4a-1.
DEFINING FIXED POINTS OF THE IPTS-68*
Assigned value of International Practical Temperature
Equilibrium state
Equilibrium between the solid, liquid, and vapor phases of equilibrium hydrogen (triple point of equilibrium hydrogen) Equilibrium between the liquid and vapor phases of equilibrium hydrogen at a pressure of 33330.6 N 1m 2 (25/76 standard atmosphere) Equilibrium between the liquid and vapor phases of equilibrmm hydrogen (boiling point of equilibrium hydrogen) Equilibrium between the liquid and vapor phases of neon (boiling point of neon) Equilibrium between the solid, liquid, and vapor phases of oxygen (triple point of oxygen) Equilibrium between the liquid and vapor phases of oxygen (boiling point of oxygen) Equilibrium between the solid, liquid, and vapor phases of water (triple point of waterlt Equilibrium between the liquid and vapor phases of water (boiling point of waterltt Equilibrium between the solid and liquid phases of zinc (freezing point of zinc) Equilibrium between the solid and liquid phases of silver (freezing point of silver) Equilibrium between the solid and liquid phases of gold (freezing point of gold)
I
T",K
t. °C
13.81
-259.34
17.042
-256.108
20.28
-252.87
27.402
-246.048
54.361
-218.789
90.188
-182.962
273.16
0.01
373.15
100
692.73
419.58
1235.08
961. 93
1337.58
1064.43
*
Except for the triple points and one equilibrium hydrogen point (17.042 Ie) the assigned values of temperature are for equilibrium states at a pressure po ~ 1 standard atmosphere (101325 N/m2). In the realization of the fixed points small departures from the assigned temperatures will occur as a result of the differing immersion depths of thermometers or the failure to realize the required pressure exactly. If due allowance is made for these small temperature differences, they will not affect the accuracy of realization of the Scale. t The water used should have the isotopic composition of ocean water. t The equilibrium state between the solid and liquid phases of tin (freezing point of tin) has the assigned value of t68 ~ 231.9681 °C and may be used as an alternative to the boiling point of water.
In the range 13.81 to 273.15 K, the interpolating instrument is a platinum thermometer and T" is defined by the relation (4a-l) where WeT,s) is the resistance ratio of the platinum thermometer as defined by WeT,s)
R(T. s) R(273.15 K)
and Wc cT _,,(T 68 ) is the resistance ratio as given by the reference function in Table 4a-2. The deviations D.W(T,,) at the temperatures of the defining fixed points are the differences between the measured values of WeT,s) and the corresponding values of W ccT-,s(T'8)'
4-1
HEAT
TABLE 4a-2. THE REFERENCE FUNCTION WCCT_68(T68) FOR PLATINUM RESISTANCE THERMOMETERS FOR THE RANGE FROM 13.81 TO 273.15 K* 20
T68 = {Ao
+ L Ai[ln WCCT_68(T68)]i} K i=l
Coefficients Ai:
,
A.
A.
i
--0 1 2 3 4 5 6 7 8 9 10
0.27315 X 10' 0.2508462096788033 0.135 099 869 964 999 7 0.5278567590085172 0.2767685488541052 0.3910532053766837 0.655 613 230 578 069 3 0.808 035 868 559 866 7 o.705 242 118 234 052 0 0.4478475896389657 0.212 525 653 556 057 8
X X X X X X X X X X
10' 10' 10' 10' 10' 10' 10' 10' 10' 10'
11 12 13 14 15 16 17 18 19 20
0.7679763581708458 0.213 689 459 382 850 0 0.459 843 348 928 069 3 0.763 614 629 231 6480 0.969 328 620 373 121 3 0.923 069 154 007 007 5 0.638 116 590 952 653 8 0.3022932378746192 0.877 551 391 303 760 2 0.117 702 613 125 477 4
X 10 X 10 X X X X X X X
10- ' 10-' 10-' 10-' 10-& 10-7 lO- s
*
The reference function WccT-,,(T,,) is continuous at T" = 273.15 K in its first and second derivatives with the function Wet,,) given by Eqs. (4a-6) and (4a-7) for a = 3.9259668 X 10-'(°0) -1 and o = 1.496334°0. A tabulation of this reference function .. sufficiently detailed to allow interpolation to an accuracy of 0.0001 K, is available from the Bureau International des Poids et Mesures, 92-S.hres, France.
The following interpolation formulas are used to determine Ll W (T 68) at intermediate temperatures: 13.81 to 20.28 K: 20.28 to 54.361 K: 54.361 to 90.188 K: 90.188 to 273.15 K:
LlW(T6S) LlW(Tos) LlW(Tos) LlW(T6S)
+ + + +
+ + +
+ +
= A, B,T6s C , T6S 2 D,Tos8 = .42 B.T6s C.T6S 2 D.T6s8 = A3 B.T6s C,T6S' = A.t6s C.t6S 8(t6S - 100°0)
(4a-2) 1 (4a-3) 2 (4a-4)' (4a-5) 4
In the range 0°0 (273.15 K) to 630.74°0, t6S is defined by t68
=
t'
t' + 0.045 10000
(419.t~800
-
(t' 10000 - 1 )
1) (630.t;400 - 1) °0
(4a-6)
where t' is defined as
t' = ;;;1 [Wet') - 1]
t' ) (t' + 0 ( 10000 10000 -
1
)
(4a-7)
1 Constants for Eq. (4a-2) are determined by the three measured deviations-at the triple point of equilibrium hydrogen, the temperature of 17.042 K, and the boiling point of equilibrium hydrogen-and by the derivative of the deviation function at the boiling point of equilibrium hydrogen as derived from Eq. (4a-3). • Constants for Eq. (4a-3) are determined by the three measured deviations-at the boiling point of equilibrium hydrogen, the boiling point of neon, and the triple point of oxygen-and by the derivative of the deviation function at the triple point of oxygen as derived from Eq. (4a-4). • Constants for Eq. (4a-4) are determined by the two measured deviations-at the triple point and the boiling point of oxygen and by the derivative of the deviation lUnction at the boiling point of oxygen as derived from Eq. (4a-5). 4 Constants for Eq. (4a-5) are determined by the two measured deviations at the boiling point of oxygen and the boiling point of water.
TEMPERATURE SCALES, THERMOCOUPLES
4-5
The resistance ratio Wet') = R(t')/R(OOO) and the constants R(OOO), '" and 15 are determined by measurement of three resistances-at the triple point of water, the boiling point of water (or the freezing point of tin), and the freezing point of zinc. Equation (4a-7) is equivalent to Wet')
when
A
= '"
1
(1 + 1O~00)
From 630.74 to 1064.43°0,
t6S
+ At' + Bt'2
and
B
=
(4a-8)
-10- 4 ",5(°0)-2
is defined by
E (t as)
=
a
+ btss + ct,,2
(4a-9)
where E(t68) is the electromotive force of a standard thermocouple of rhodiumplatinum alloy and platinum, when one junction is at the temperature t68 = 0°0 and the other junction is at temperature t". The constants a, b, and c are calculated from the values of E at 630.74 ± 0.2°0, as determined by a platinum resistance thermometer, and at the freezing points of silver and gold. Above 1337.58 K (1064.43°0) the temperature T" is defined by
LA(T,,(Au»
exp [c2/AT68(Au») - 1 exp [c2/AT,,) - 1
(4a-10)
where LA(T,,) and LA(T68(Au» are the spectral concentrations at temperature T" and at the freezing point of gold, T,,(Au) of the radiance of a black body at the wavelengthl A; C2 = 0.014388 meter kelvin. Table 42r3 (p. 4-6) lists the approximate differences between the IPTS-68 and IPTS-48 and should prove to be a utility for many references to this section. To avoid creating conflicting statements, the preceding description of IPTS-68 has for the most part been taken from the English language version of the International Practical Temperature Scale of 1958 as it appeared in M etrologia. For a more complete description of the IPTS-68 and pertinent supplementary information the reader should refer to the defining text.2 In Tables 4a-4, 4a-5, and 4a-6 which follow, values have been adjusted to agree with IPTS-68. 1 Since T 68 (Au) is close to the thermodynamic temperature of the freezing point of gold, and c, is close to the second radiation constant of the Planck equation, it is not necessary to specify the value of the wavelength to be employed in the measurements [see Metrologia 3,28 (1967)]. 2 Metrologia Ii (2), 35 (1969).
'i O":l TABLE
4a-3.
ApPROXIMATE DIFFERENCES
(t. B
-
t. B), OF
-.
t"OO
0
-100 0
0.022 0.000
t"OO
-10
-20
0.013 0.006
0.003 0.012
0
10
0 100 200 300 400 500 600 700 800 900 1000
0.000 0.000 0.043 0.073 0.076 0.079 0.150 0.39 0.67 0.95 1.24
t"OO 1000 2000 3000
IN KELVINS, BETWEEN THE VALUES OF TEMPERATURE GIVEN BY THE IPTS
1968
AND THE IPTS OF
1948 -70
-80
-90
-100
0.007 0.034
0.012 0.033
0.029
0.022
60
70
80
90
-0.010 0.020 0.061 0.077 0.074 0.100 0.25 0.53 0.81 1.10 1.39
-0.010 0.025 0.064 0.077 0.074 0.108 0.28 0.56 0.84 1.12 1.42
-0.008 0.029 0.067 0.077 0.075 0.116 0.31 0.58 0.87 1.15 1.44
-0.006 0.034 0.069 0.077 0.076 0.126 0.34 0.61 0.89 1.18
-0.003 0.038 0.071 0.076 0.077 0.137 0.36 0.64 0.92 1.21
0.000 0.043 0.073 0.076 0.079 0.150 0.39 0.67 0.95 1.24
400
500
600
700
800
900
1000
2.0 4.2 7.2
2.2 4.5 7.5
2.4 4.8 7.9
2.6 5.0 8.2
2.8 5.3 8.6
3.0 5.6 9.0
3.2 5.9 9.3
-30
-40
-50
-60
-0.006 0.018
-0.013 0.024
-0.013 0.029
-0.005 0.032
20
30
40
50
-0.004 0.004 0.047 0.074 0.075 0.082 0.165 0.42 0.70 0.98 1.27
-0.007 0.007 0.051 0.075 0.075 0.085 0.182 0.45 0.72 1.01 1.30
-0.009 0.012 0.054 0.076 0.075 0.089 0.200 0.47 0.75 1.04 1.33
-0.010 0.016 0.058 0.077 0.074 0.094 0.23 0.50 0.78 1.07 1.36
0
100
200
300
3.2 5.9
1.5 3.5 6.2
1.7 3.7 6.5
1.8 4.0 6.9
100
---~
t?j
po. >-:I
4-7
TEMPERATURE SCALES, THERMOCOUPLES TABLE
4a-4.
THERMAL EMF OF CHEMICAL ELEMENTS RELATIVE TO PLATINUM*
Temp., °C
Lithium, mV
-200 -100 0 +100 200 300
-1.12 -1.00
Sodium, mV
0
+1.00 +0.29 0
+1.82
........
....... . ....... .
..... . •••••
0,
Temp., °C
Magnesium, mV
-200 -100 0 +100 200 300 400 500 600
+0.37 -0.09 0 +0.44 +1.10
Temp. °C
Carbon,' mV
Zinc, mV
-0.07 -0.33 0 +0.76 1.89 3.42 5.29
..... . ....
,
.
..... .
. .....
..... .
','
PotasRubidsium, mV ium, mV
+1.61 +0.78 0
...... .
+1.09 +0.46 0 ..... .
Cesium, mV
+0.22 -0.13 0
. .....
Calcium, mV
Cerium, mV
0 -0.51 -1.13 -1.85
0 +1.14 2.46
. .......
. .....
...... .
.....
Cadmium, mV
Mercury, mV
Indium, mV
.. .... ..... .
. ..... .....
......
0 -0.60 -1.33
0 +0.69
0 +0.58 1.30 2.16
-0.04 -' 0.31 0 +0.90 2.35 4.24
. .... .,. .......
....... .
......'.
Silicon, mV
Germanium, mV
.
...... . .....
...... ......
,
...... . ..... .,
....
..... . , . .....
..... . ..... .
Tin, mV
Lead, mV
Thallium, AlumimY num,mV
.....
,
.
......
. ..... Antimony,
mY
+0.45 +0.06 0 +0.42 1.06 1.88 , 2.84 3.93 5.15
'Bismuth, mY I
-.lOO ..,.100 0 +100 200 300 400 500 600 700 800 900 1000 1100
+63.13 +37.17 0 -41.5.6 -80.57 -110.07
..... .
..... . 0, +0.70 1.54 2.55 3.72 5.15 6.79 8.82 10:98 13.55 16.46 19.46
... , .... ....... . ...... .. ...... ,',
I
-46.00 -26.112 0 +33.9 72.4 91.8 82.3 63.5 43.9 27.9
+0.26 -0.12 0 +0.42 1.07
......
..... . ..... . .....
.
...... i' +12 .. 39 ...... +7.54
+0.24 -0.13 0 +0.44 1.09 1.91
... , .. ... , .. ......
~
0 +4.89 10.14 15:44 20.53 25.10 28.87
0 -7.34 ; -13.57
, ,
4-8 TABLE
HEAT
4a-4.
THERMAL EMF OF CHEMICAL ELEMENTS RELATIVE TO PLATINUM*
(Continued) Temp., °C
Copper, mV
Silver, mV
Gold, mV
Cobalt, mV
Nickel, mV
-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200
-0.19 -0.37 0 +0.76 1.83 3.15 4.68 6.41 8.34 10.47 12.81 15.37 18.16
-0.21 -0.39 0 +0.74 1. 77 3.05 4.57 6.36 8.41 10.73 13.33 16.16
-0.21 -0.39 0 +0.78 1. 84 3.14 4.63 6.29 8.12 10.11 12.26 14.58 17.05 . .....
....... .......
+2.28 +1.22 0 -1.48 -3.10 -4.59 -5.45 -6.16 -7.04 -8.10 -9.33 -10.67 -12.11 -13.60
I
I
.. . .. . ..... .
...... ......
..... .
......
0 -1.33 -3.08 -5.10 -7.24 -9.35 -11.28 -12.87 -13.99 -14.49 -14.21 -13.01 -10.70
I
I
I
Temp., °C
Iridium, mV
Rhodium, mV
Palladium, mV
Molybdenum, mV
Tungsten, mV
Tantalum, mV
-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
-0.25 -0.35 0 +0.65 1.49 2.47 3.55 4.78 6.10 7.55 9.10 10.77 12.57 14.45 16.45 18.45 20.47 22.51
-0.20 -0.34 0 +0.70 1. 61 2.68 3.91 5.28 6.77 8.39 10.14 12.01 14.02 16.15 18.39 20.69 22.99 25.36
+0.81 +0.48 0 -0.57 -1.23 -1.99 -2.82 -3.84 -5.03 -6.40 -7.96 -9.69 -11.61 -13.67 -15.86 -18.11 -20.40 -22.75
...... ......
+0.43 -0.15 0 +1.12 2.62 4.48 6.70 9.30 12.26 15.58 19.25 23.30 27.73 32.53 37.72
+0.21 -0.10 0 +0.33 0.93 1. 79 2.91 4.30 5.95 7.86 10.02 12.45 15.15 18.13 21. 37
*
0 +1.45 3.19 5.23 7.57 10.20 13.13 16.33 19.83 23.63 27.74 32.15 36.86
......
......
......
Thorium, mV
0 -0.13 -0.26 -0.40 -0.50 -0.53 -0.45 -0.21 +0.22 +0.86 +1.72 +2.78 +4.03 +5.41
A positive sign means that in a simple thermoelectric circuit the resultant emf given is in such a direction as to produce a current from the element to the platinum at the reference junction"(O°C). The values below DoC, in most cases, have not been determined on the same samples as the values above O°C. Based upon the original table in American Institute of Physics, "Temperature, Its J\1easurement and Control in Science and Industry," pp. 1309-1310, Reinhold Book Corporation, New York, 1941. Values of the emf hit ve been adjusted to correspond to temperatures expressed on the International Practical Temperature Scale of 1968.
4-9
TEMPERATURE SCALES, THERMOCOUPLES TABLE
4a-5.
THERMAL EMF OF IMPORTANT THERMOCOUPLE MATERIALS RELATIVE TO PLATINUM*
Temp., °C
Chromel P, mV
Alumel, mV
Copper, mV
Iron, mV
Constantan, mV
-200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
-3.36 -2.20 0 +2.81 5.96 9.32 12.75 16.21 19.61 22.94 26.20 29.37 32.47 35.52 38.48 41.38 44.04
+2.39 +1.29 0 -1.29 -2.17 -2.89 -3.64 -4.43 -5.28 -6.18 -7.07 -7.94 -8.78 -9.57 -10.33 -11.06 -11.77
-0.19 -0.37 0 +0.76 1.83 3.15 4.68 6.41 8.34 10.47 12.81 15.37 18.16
-2.92 -1.84 0 +1.89 3.54 4.85 5.88 6.79 7.80 9.11 10.84 12.82 14.28
+5.35 +2.98 0 -3.51 -7.45 -11.71 -16.19 -20.79 -25.46 -30.15 -34.81 -39.39 -43.85
* American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry," p. 1308, Reinhold Book Corporation, New York, 1941. Values of the emf have been adjusted to correspond to temperatures expressed on the Internation ..l Practical Temperature Scale of 1968.
TABLE
Temp., °C
4a-6.
Manganin, mV
THERMAL EMF OF SOME ALLOYS RELATIVE TO PLATINUM*
Goldchromium,
mV 0 +100 200 300 400 500 600
0 +0.61 1.55 2.77 4.25 5.95 7.84
0 -0.17 -0.32 -0.44 -0.55 -0.63 -0.66
Copperberyllium, mV 0 +0.67 1.62 2.81 4.19
...... ......
Yellow brass, mV
Phosphor bronze, mV
0 +0.60 1.49 2.58 3.85 5.30 6.96
0 +0.55 1.34 2.34 3.50 4.81 6.30
Solder 50 Sn50 Pb, mV
Solder 96.5 Sn.,.. 3.5 Ag, mV
0 +0.46
0 +0.45
HEAT
TABLE 4a-6. THERMAL EMF OF SOME ALLOYS RELATIVE TO PLATINUM* (Continued)
Temp., °C
0 +100 200 300 400 500 600 700 800 900 (000
18-8 stainless steel, mV
Spring steel, mV
80 Ni20 Cr, mV
0 +0.44 1.04 1.76 2.60 3.56 4.67 5.92 7.35 8.96
0 +1.32 2.63 3.81 4.84 5.80 6.86
0 +1.14 2.62 4.34 6 .. 25 8.31 10.53 12.89 15 ..41 18.07 20.87
...... ...... ......
......
..... .
60 Ni24 Fe16 Cr, mV
I
0 +0.85 2.01 3.41 5.00 6.76 8.68 10.76 13.03 15.47 18.06
Copper coin (95 Cu4 Sn1 Zn), mV
0 +0.60 1.48 2.60 3.91 5.44 7.14
Nickel
(75 Cu25 Ni), mV
Silver coin (90 Ag10 Cu), mV
0 -2.76 -6.01 -9.71 -13.78 -18.10 -22.59
0 +0.80 1.90 3.25 4.81 6.59 8.64
coin
* American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry, p. 1310, R.einhold Book Corporation, New York, 1941. Values of the emf have been adjusted to. correspond ·to temperatures expressed on the International Practical Temperature Scale of 1968. Thermocouple Reference Tables. Tables 4a-7 through 4a-12 contain abbreviated data on the thermoelectric voltages of six thermocouple combinations, two noblemetal types Sand R and four base-metal types E, J, K, and T. The full tables, functional representations, approximations, and material descriptions appear in NBS Monograph 125, "Thermocouple Reference Tables Based on the IPTS-68" by R. L. Powell, W. J. Hall, O. H. Hyink, L. L. Sparks, G. W. Burns, and H. H. Plumb, U.S. Government Printing,Office, Washington, D.O., 1972. TABLE 4a-7. TYPE S. PLATINUM-10% RHODIUM VS. PLATINUM THERMOCOUPLES .. '(Emf, absolute millIvolts; temp., °0 (IPTS~68); reference junctions atO°C] °C'
0
10
20 •
30
40
50
60
70
80
90
100
--------- --- - - --- --- --- - - --- - ---0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700
0.000 0.055 0.113 0.173 0.. 235 0.299 {}.365 0.432 0.502 0.573 0.645 0.645 0.719 0.795 0;872 0.950 1.'0.2.9. .~.109 1.190 1.273 1.356 1.440 1.440 1.525 1.611 1.698 1.785 1.873 1.962 2.051 2.141 2.232 2.323 2.323 2.414 2.506 2.599 2.692 2.786 2.880 2.974 3.069 3.164 3.260 3.260 3.356 3.452 3.549 3.645 3.743 3.840 3.938 4.036 4.135 4.234 4.234 4.333 4.432 4.532 4.632 4.732 4.832 4.933 5.034 5.136 5.237 5.237 5.339 5.442 5.544 5.648 5.751 5.855 5.960 6.064 6.169 6.274 6.274 6.380 6.486 6.592 6.699 6.805 6.913 7.020 7.128 7.236 7.345 7.345 7.454 7.563 7.672 7.782 7.892 8.003 8.114 8.225 8.336 8.448 8.448 8.560 8.673 8.786 8.899 9.012 9.126 9.240 9.355 9.470 9.585 9.585 9.700 9.816 9.932 10.048 10.165 10.282 10.400 10.517 10.635 10.754 10.754 10.872 10.991 11.110 11.229 11.348 11.467 11.587 11.707 11.827 11.947 11.947 12.067 12.188 12.308 12.429 12.550 12.671 12.792 12.913 13.034 13.155 13.155 13.276 13.397 13.519 13.640 13.761 13.883 14.004 14.125 14.247 14.368 14.368 14.489 14.610 14.731 14.852 14.973 15.094 15.215 15.336 15.456 15.576 15.576 15.697 15.817 15.937 16.057 16.176 16.296 16.415 16.534 16.653 16.771 16.771 16.890 17.008 17.125 17.243 17,360 17.477 17.594 17.711 17.826 17.942 17.942 18.056 18.170,18.282 18.394 18.504 18.612
I
4-11
TEMPERATURE SCALES, THERMOCOUPLES
4a-8. TYPE R. PLATINUM-13% RHODIUM VS. PLATINUM THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at O°C]
TABLE
0
°C
10
20
30
40
50
60
70
80
90
100
--- --- - - - - --- --- - - --- - - - - --- --0 0.00 0.054 0.111 0.171 0.232 0.296 0.363 0.431 0.501 0.573 0.647 100 0.647 0.723 0.800 0.879 0.959 1.041 1.124 1.208 1.294 1.380 1.468 200 1.468 1.557 1.647 1.738 1.830 1.923 2.017 2.111 2.207 2.303 2.400 2.400 2.498 2.596 2.695 2.795 2.896 2.997 3.099 3.201 3.304 3.407 300 3.407 3.511 3.616 3.721 3.826 3.933 4.039 4.146 4.254 4.362 4.471 400 500 4.471 4.580 4.689 4.799 4.910 5.021 5.132 5.244 5.356 5.469 5.582 600 5.582 5.696 5.810 5.925 6.040 6.155 6.272 6.388 6.505 6.623 6.741 700 6.741 6.860 6.979 7.098 7.218 7.339 7.460 7.582 7.703 7.826 7.949 800 8.072 8.196 8.320 8.445 8.570 8.696 8.822 8.949 9.076 9.203 1 900 1 9.331 1 9.460 9.589 9.7181 9.8481 9.978110.109 10.240 10.37110.503 1000 1U.5U3 10.63610.768 10.902 i1 .035 11 . 170 11 .304 11 .439 11.574 11.71011.846 1100 11.846 11.983 12.119 12.257 12.394 12.532 12.669 12.808 12.946 13.085 13.224. 1200 13.224 13.363 13.502 13.642 13.782 13.922 14.062 14.202 14.343 14.483 14.624 1300 14.624 14.765 14.906 15.047 15.188 15.329 15.470 15.611 15.752 15.893 16.035 1400 16.035 16.176 16.317 14.458 16.599 16.741 16.882 17.022 17.163 17.304 17.445 1500 17.445 17.585 17.726 17.866 18.006 18.146 18.286 18.425 18.564 18.703 18.842 1600 18.842 18.981 19.119 19.257 19.395 19.533 19.670 19.807 19.944. 20.080 20.215 1700 20.215 20.350 20.483 20.616 20.748 20.878 21. 006
~:;6~
TABLE 4a-9. TYPE E. CHROMEL VS. CONSTANTAN THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at OOG]
°0
0
10
20
- ---- --- ---
30
40
--- - -
50
60
70
80
90
100
--- --- --- --- - -
---
-9.835 -7.963 -3.811 4,329 11 ,222 18,710 26.549 34,574 42,662 50,713 58,663 66.473 74,104
-8.824 -5.237 6,317 13.419 21.033 28.943 36,999 45.085 53,110 61. 022 68,783 76.358
-200 -8.824 -9.063 -9.274 -9.455 -9.604 -9.719 -100 -5.237 -5.680 -6.167 -6.516 -6.907 -7.279 (-)0 0.00 -0.581 -1.151 -1. 709 -2.254 -2.787 0,591 0.00 1.192 1.801 2.419 3.047 (+)0 6,317 6,996 7,683 8,377 9,078 9,787 100 200 13,419 14,161 14,909 15,661 16.417 17,178 300 21.033 21. 814 22,597 23,383 24.171 24.961 400 28,943 29.744 30,546 31. 350 32,155 32.960 500 36,999 37,808 38.617 39.426 40.236 41. 045 600 45,085 45.891 46,697 47,502 48.306 49.109 700 53,110 53.907 45,703 55,498 56,291 57,083 800 61.022 61. 806 62,588 63,368 64.147 64,924 900 68,783 69.549 70.313 71,075 71,835 72,593 1000 76.358
-9.797 -7.631 -3.306 3,683 10,501 17,942 25,754 33,767 41,853 49,911 57,873 65,700 73.350
-8.273 -4.301 4,983 11,949 19.481 27,345 35,382 43.470 51. 513 59,451 67.245 74,857
-8.561 -4.777 5,646 12,681 20,256 28.143 36,190 44.278 52,312 60,237 68,015 75.608
4-12
HEAT
TABLE 4a-lO. TYPE J. IRON·VS. CONSTANTAN THERMOCOUPLES [Emf, absolute'millivolts; temp., °0 (IPTS-68); reference functions at DoC]
°0
0
10
2D
30
40
------
~I~
70
-200 -7.890 -8.096 -100 -4.632 -5.036 -5.426 -5.801 -6.159 -6.499 -6.821 -7.122 0.00 -0.501 -0.995 -1.481 -1.960 -2.431 -2.892 -3.344 (-)0 0.507 1.019 1.536 2.058 2.585 3.115 3.649 0.00 (+)0 5.268 5.812 6.359 6.907 7.457 8.008 8.560 9.113 100 200 10.777 11.332 11.887 12.442 12.998 13.553 14.108 14.663 300 16.325 16.879 17.432 17.984 18.537 19.089 19.640 20.192 400 21. 846 22.397 22.949 23.501 24.054 24.607 25.161 25.716 500 27.388 27.949 28.511 29.075 29.642 30.210 30.782 31. 356 600 33.096 33.683 34.273 34.867 35.464 36.066 36.671 37.280 700 39.130 39.754 40.382 41.013 41.647 42.283 42.922
80
90
100
-7.402 -3.785 4.186 9.667 15.217 20.743 26.272 31'.933 37.893
-7.659 -4.215 4.725 10.222 15.771 21.295 26.829 32.513 38.510
-7.890 -4.632 5.268 10.777 16.325 21.1~46
27.388 33.096 39.130
TABLE 4a-ll. TYPE K. CHROMEL VS. ALUMEL THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at DOC]
°0
0
10
20
30
40
50
60
70
80
90
100
--- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -200 -5.891 -6.035 -6.158 -6.262 -6.344 -6.404 -6.441 -6.458 -100 -3.553 -3.852 -4.138 -4.410 -4.669 -4.912 -5.141 -5.354 -5.550 -5.730 -5.891 (-)0 0.00 -0.392 -0.777 -1.156 -1.527 -1.889 -2.243 -2.586 -2.920 -3.242 -3.553 0.397 0.798 1.203 1.611 2.022 2.436 2.850 3.266 3.681 4.095 0.00 (+)0 4.095 4.508 4.919 5.327 5.733 6.137 6.539 6.939 7.338 7.737 8.137 100 8.137 8.537 8.938 9.341 9.745 10.151 10.560 10.969 11.381 11. 793 12.207 200 300 12.207 12.623 13.039 13.456 13.874 14.292 14.712 15.132 15.552 15.974 16.395 400 16.395 16.818 17.241 17.664 18.088 18.513 18.938 19.363 19.788 20.214 20.640 500 20.640 21.066 21.493 21.919 22.346 22.772 23.198 23.624 24.050 24.476 24.902 600 24.902 25.327 25.7i;1 26.176 26.599 27.022 27.445 27.867 28.288 28.709 29.128 700 29.128 29.547 29.965 30.383 30.799 31.214 31.629 32.042 32.455 32.866 33.277 800 33.277 33.686 34.095 34.502 34.909 35.314 35.718 36.121 36.524 36.925 37.325 900 37.325 37.724 38.122 38.519 38.915 39.310 39.703 40.096 40.488 40.879 41.269 1000 41.269 41.657 42.045 42.432 42.817 43.202 43.585 43.968 44.349 44.729 45.108 1100 45.108 45.486 45.863 46.238 46.612 46.985 47.356 47.726 48.095 48.462 48.828 1200 48.828 49.192 49.555 49.916 50.276 50.633 50.990 51. 344 51.697 52.049 52.398 1300 52.398 52.747 53.093 53.439 53.782 54.125 54.466 54.807
4-13
TEMPERATURE SCALES, THEMOCOUPLES
TABLE 4a-12. TYPE T. COPPER VS. CONSTANTAN THERMOCOUPLES [Emf, absolute millivolts; temp., °C (IPTS-68); reference junctions at O°C] °C
0
10
20
30
40
50
- - - - - - ---- -- -200 -5.603 -5.753 -5.889 -6.007 -6.105 -100 -3.378 -3.656 -3.923 -4.177 -4.419 (-)0 0.00 -0.383 -0.757 -1.121 -1.475 0.00 0.391 0.789 1.196 1.611 (+)0 4.277 4.749 5.227 5.712 6.204 100 9.286 9.820 10.360 10.905 11.456 200 300 14.860 15.443 16.030 16.621 17.217 400 20.869
60
70
80
90
100
- - - - - - - - - - ---6.181 -4.648 -1.819 2.035 6.702 12.011 17.816
-6.232 -4.865 -2.152 2.467 7.207 12.572 18.420
-6.258 -5.069 -2.475 2.908 7.718 13.137 19.027
-5.261 -2.788 3.357 8.235 13.707 19.638
-5.439 -3.089 3.813 8.757 14.281 20.252'
-5.603 -3.378 4.277 9.286 14.860 20.869
TABLE 4a-13. ELECTRICAL RESISTIVITY OF SOME ELEMENTS AND ALLOYS AS A FUNCTION OF TE¥pERATURE* [At O°C both the relative R./Ro and actual resistivity (microhm em) are given] Temp., Platinum °C (R./Ro) -200 -100 0 +100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500
0.177 0.599 1.000 (9.83) 1.392 1.773 2.142 2.499 2.844 3.178 3.499 3.809 4.108 4.395 4.672 4.937 5.190 5.431 5.660
Copper
Nickel
Iron
Silver
(R./Ro)
(R./Ro)
(R./Ro)
(R./Ro)
.....
. .....
0.176 0.596 1.000 (1.50) 1.408 1.827 2.256 2.698 3.150 3.616 4.093 4.584 5.089 ..... . .... . .... ..... . .... .....
0.117 0.557 1.000 (1. 56) 1.431 1.862 2.299 2.747 3.210 3.695 4.207 4.750 5.332 5.959 .... . .... . .... . .... .
.... .
.... . 1.000 (6.38) 1.663 2.501 3.611 4.847 5.398 5.882 6.326 6.749 7.154 7.541 . .... .....
. .... .... . .... .
......
1.000 (8.57) 1.650 2.464 3.485 4.716 6.162 7.839 9.785 12.003 12.788 13.070 ...... ..... . ..... .
...... ..... .
90 Pt10 Rh
87 Pt13 Rh
(R./Ro)
(R./Ro)
1.000 (18.4) 1.166 1.330 1.490 1.646 1.798 1.947 2.093 2.233 2.369 2.503 2.633 2.762 2.888 3.013 3.136
1.000 (19.0) 1.156 1.308 1.456 1.601 1.744 1.885 2.023 2.156 2.286 2.414 2.538 2.661 2.781 2.900 3.017
* American Institute of Physics, uTemperature, Its Measurement and Control in Science and IndusThe values below O°C, in most cases, were not determined on the same samples as the values above O°C.
try," p. 1312, Reinhold Book Corporation, New York, 1941.
4-14
HEAT
TABLE 4a-14. ELECTRICAL RESISTIVITY OF SOME ALLOYS AS A FUNCTION OF TEMPERATURE* [At 0 0 0 both the relative (Rt/R o) and actual resistivity (microhm em) arEl given] Alumel Ohromel (95 Ni80 Ni-20 60 Ni-24 50 Fe-30 P (90 NiFe-16 Or Ni-20 Or bal. AI, Si, Or 10 Or) and Mn) (Rt/R o) (Rt/R o) (Rt/Ro) (RtlRo) (RtlRo)
Temp.,
00
0 100 200 300 400 500 600 700 800 900 1000 1100 1200
I
I
1.000 (107.6) 1.021 1.041 1.056 1.068 1.073 1.071 1.067 1.066 1.071 1.077 1.083
.....
I
1.000 (111. 6) 1.025 1.048 1.071 1.092 1.108 1.115 1.119 1.127 1.138 1.149
1.000 (99.0) 1.037 1.073 1.107 1.137 1.163 1.185 1.204 1.221 1.237 1.251
.... . .... .
..... . ....
I
1.000 (70.0) 1.041 1.086 1.134 1.187 1.222 1.248 1.275 1.304 1.334 1.365 1.397 1.430
1.000 (28.1) 1.239 1.428 1.537 1.637 1.726 1.814 1.899 1.982 2.066 2.150 2.234 2.318
OonstanMangatan (55 nin Ou-45 Ni) (RtlRo) (RtlRo) 1.000 (48.9) 0.999 0.996 0.994 0.994 1.007 1.024 1.040 1.056 1.074 1.092 1.110
I
1.000 (48.2) 1.002 0.996 0.991 0.983
* American Institute of Physics, "Temperature, Its Measurement and Control in Science and Industry," p. 1312, Reinhold Book Corporation, New York, 1941. The values below DoC, in most cases, were not determined on the same samples as the values above O°C.
4-15
TEMPERATURE SCALES, THERMOCOUPLES
Tables 4a-15, 4a-16, arid 4a-17 give the thermoelectric voltage E and Seebeck coefficient dE / dT, for the three thermocouple combinations that ate most useful between liquid helium temperatures and the ice point: ANSI types E, T, and EP vs. Au-0.07 at.% Fe (often referred to as Ohromel vs. constantan, qopper vs. constantan, and Ohromel vs. Au-0.07 at.% Fe, respectively). Type E thermocouples are recommended for general use above the normal boiling point 6f hydrogen (20 K). Both components of this thermocouple combination have low thermal conductivity and reasonably good homogeneity. For operation below 20 K, the combination EP vs. Au-0.07 at. % Fe is the most sensitive combination commonly available for which there is a standard table. The values given for the last combination are interim: the gold-iron material is not yet standardized. Additional details and discussion for these three types of thermocouples have been published. I,' Seebeck coefficients for each type are shown in Fig. 4a-1. ~
~ 60 ::t ...: z ILl
o
40
.ii:
Il.. ILl
820
:.:: (,) ILl
m
ILl ILl
CJ)
100 200 TEMPERATURE,'K
300
FIG. 4a-1. Seebeck coefficients for USASI thermocouple types E, T, and EP vs. Au-O.07 at. % Fe. I For standardized thermocouples: NBS Mon_ograph 124, "Reference Tables for Low Temperature Thermocouples," by L. L. Sparks, R. L. Powell, imd W. J. :Hall, U.S. Government Printing Office, Washington, D.C., 1972 . • For nonstandardized combinations: L.L. Sparks and R. L. Powell, J. Res. Nat. Bur. Stand. (U.S.) 76 A, No.3, 1972.
HEAT
4--16 TABLE
T,K
4a-15.
E,I'V
TYPE
E
I dE/dT, I I'V/K
THERMOCOUPLES (CHROMEL VS. CONSTANTAN)
T, K
E,I'V
I dE/dT,
T, K
I'V/K
E,I'V
dE/dT, I'V/K
1 2 3 4 5
0.41 1.31 2.70 4.56 6.87
0.660 1.149 1.623 2.085 2.535
51 52 53 54 55
522.68 541.83 561.28 581. 04 601.08
19.001 19.303 19.603 19.900 20.194
101 102 103 104 105
1,806.73 1,838.49 1,870.46 1,902.65 1,935.05
31. 648 31. 865 32.081 32.295 32.509
6 7 8 9 10
9.62 12.81 16.43 20.47 24.92
2.975 3.406 3.829 4.244 4.653
56 57 58 59 60
621.42 642.05 662.97 684.18 705.67
20.486 20.776 21. 063 21. 348 21. 630
106 107 108 109 110
1,967.67 2,000.50 2,033.54 2,066.79 2,100.25
32.722 32.934 33.145 33.355 33.565
11
12 13 14 15
29.77 35.03 40.68 46.72 53.15
5.057 5.455 5.848 6.238 6.623
61 62 63 64 65
727.44 749.49 771.82 794.42 817.29
21.911 22.188 22.464 22.737 23.008
111 112 113 114 ll5
2,133.92 2,167.79 2,201.88 2,236.17 2,270.66
33.773 33.981 34.187 34.393 34.598
16 17 18 19 20
59.97 67.16 84.74 82.69 91.01
7.005 7.385 7.761 8.135 8.506
66 67 68 69 70
840.43 863.84 887.52 9ll.46 935.66
23.277 23.544 23.809 24.072 24.333
ll6 ll7 ll8 ll9 120
2,305.36 2,340.27 2,375.37 2,410.68 2,446.19
34.802 35.005 35.207 35.408 35.609
21 22 23 24 25
99.70 108.76 118.18 127.97 138.12
8.876 9.243 9.608 9.971 10.332
71 72 73 74 75
960.13 984.85 1,009.82 1,035.05 1,060.54
24.592 24.849 25.104 25.357 25.608
121 122 123 124 125
2,481.90 2,517.81 2,553.91 2,590.22 2,626.72
35.809 36.007 36.205 36.402 36.599
26 27 28 29 30
148.64 159.51 170.73 182.31 194.25
10.691 11.049 11.404 11.758 12.110
76 77 78 79 80
1,086.27 1,112.25 1,138.48 1,164.96 1,191. 68
25.858 26.106 26.353 26.598 26.841
126 127 128 129 130
2,663.41 2,700.30 2,737.39 2,774.67 2,812.14
36.794 36.989 37.182 37.375 37.567
31 32 33 34 35
206.53 219.17 232.15 245.47 259.14
12.460 12.808 13.154 13.498 13.840
81 82 83 84 85
1,218.64 1,245.84 1,273.28 1,300.96 1,328.88
27.083 27.323 27.562 27.799 28.035
131 132 133 134 135
2,859.80 2,887.66 2,925.70 2,963.94 3,002.36
37.759 37.949 38.139 38.328 38.516
36 37 38 39 40
273.15 287.50 302.19 317.20 332.56
14.179 14.517 14.853 15.186 15.517
86 87 88 89 90
1,357.03 1,385.42 1,414.04 1,442.89 1,471.97
28.270 28.503 28.735 28.966 29.196
136 137 138 139 140
3,040.97 3,079.76 3,ll8.75 3,157.91 3,197.27
38.703 38.890 39.075 39.260 39.445
41 42 43 44 45
348.24 364.25 380.58 397.24 414.22
15.846 16.172 16.496 16.818 17.137
91 92 93 94 95
1,501. 28 1,530.82 1,560.59 1,590.58 1,620.79
29.424 29.652 29.878 30.103 30.327
141 142 143 144 145
3,236.80 3,276.52 3,316.42 3,356.51 3,396.77
39.628 39.811 39.993 40.174 40.355
46 47 48 49 50
431. 51 449.13 467.05 485.29 503.83
17.454 17.769 18.081 18.390 18.697
96 97 98 99 100
1,651. 23 1. 68 l. 89 1,712.77 1,743.87 1,775.19
30.549 30.771 30.992 31.212 31. 430
146 147 148 149 150
3,437.22 3,477.84 3,518.64 3,559.62 3,600.78
40.534 40.713 40.892 41.070 4l.247
II
I
I
I I
4-17
TEMPERATURE SCALES, THERMOCOUPLES TABLE
4a-15.
TYPE
E
THERMOCOUPLES (CHROMEL VS. CONSTANTAN)
(Continued)
E, pV
dE/dT, 'pV/K
T,K
E, pV
dE/dT,; pV/K
T,K
E, pV
dE/dT, pV/K
151 152 153 154 155
3,642.12 3,683.63 3,725.31 3,767.18 3,809.21
41.423. ,41.599 41. 774 41.948 42.122
196 197 198 199 200
5,675.23 5,724.05 5,773.02 5,822.13 5,871.40
48.743 48.893 ,49.041 49.189 49.336
241 242 243 244 245
; 8,010.92
8,065.87 8,120.95 8,176.15 8,231.48
54.888 '55.014 ;55.140 ,55.265 55.390
156 157 158 159 160
' 3,851.42 ' 3,893.80 3,936.35 , 3,979.08 4,021.97
42.295 42.467 42.639" ,42.811 42.981
201 202 203 204 205
5,920.81 5,970.36 6,020.06 6,059.91 6,119.90
'49.485 49.629 49.775 '49.919: 50.064
246 247 248 249 250
8,286.93 8,342.51 8,398.21 8,454.04 , 8,509.99
55.515 ;55.639 55.763 '55.887 56.010
161 162 163 164 165
4,065.04 4,108.28 4,151.68 4,195.26 4,239.00
43.151 43.321 43.490 43.658 43.825
206 207 208 209 210
6,170.04 6,220.32 6,270.74 6,321.30 6,372.01
50.207 50.350 ·50.492 50.634 50.775
251 252 253 254 255
8,566.06 8,622.25 8,678.57 8,735.01 8,791. 56
56.133 56.255 56.377 56.498 ,56.619
166 167 168 169 170
' 4,282.91 4,326.98 4,371.22 4,415.63 4,460.21
43.993 44.159 44.325 44.591 44.655
211 212 213 214 215
6,422.85 6,473.84 6,524.96 6,576.22 6,627.63
50.915 51.055 51.194 ,51.333 51.471
256 257 258 259 260
8,848.24 8,905.04 8,961. 96 9,019.00 9,076.15
56.739 56.858 56.977 '57.095 '57.212
171 172 173 174 175
, 4,504.94 4,549.84 4,594.91 4,640.14 4,685.53
44.820 44.984 45.147 45.309 45.471
216 217 218 219 220
6,679.17 6,730.84 6,782.66 6,834.61 6,886.69
51.608 '51. 745: 51.882 52.017 52.152
261 262 263 264 265
9,133.42 9,190.81 9,248.31 9,305.93 9,363.66
:57.329 ,57..445 57.559 :57.673 ,57.786
176 177 178 179 180
4,731. 08 4,776.79 4,822.67 4,868.70 4,914.90
45.633 .45.794 45.954 46.114 46.274
221 222 223 224 225
6,938.91 6,991.27 7,043.75 7,096.38 7,149.13
52.287 52.421 52.555 52.688 52.821
266 267 268 269 270
9,421.50 9,479.45 9,537.51 9,595.69 9,653.97
,57.898 ,58.009 58.119 58.227 158.335
181 182 183 184 185
4,961.25 5,007.76 5,054.43 5,101.26 5,148.24
46.432 46.590 46.748 46.905 47.061
226 227 228 229 230
7,202.02 7,255.04 7,308.19 7,361.47 7,414.88
52.953 53.085 53.216 53,347 53.477
271 272 273 274 275
9,712.36 9,770.85 9,829.45 9,888.15 9,946.96
58.442 58.547 58.651 58.755 58.857
186 187 188 189 190
5,195.38 5,242.67 5,290.12 5,337.73 5,385.49
47.217 47.373 47.527 47.681 47.835
231 232 233 234 235
7,468.42 7,522.09 7,575.89 7,629.83 7,683.88
53.607 53.737 53.866 53.995 54.125
276 277 278 279 280
10,005.87 10,064.88 10,123.98 10,183.19 10,242.50
,58.958 59.059 59.159 59.258 59.356
191 192 193 194 195
5,433.40 5,481.46 5,529.68 5,578.05 5,626.56
47.988 48.140 48.292 48.443 48.593
236 237 238 239 240
7,738.07 7,792.39 7,846.83 7,901.40 7,956.10
54.252 54.380 54.507 54.634 54.761
T,K
--
4-18
HEAT TABLE
T,R
4a-16.
E, ltV
TYPE T
dE/dT,
THERMOCOUPLES (COPPER VS. CONSTANTAN)
T, K
MV/K
E, MV
dE/dT, ",V/K
T,K
E, MV
dE/dT,
19.498 19.629 19.758 19.888 20.017
. MV/K
1 2 3 4 5
-0.09 0.28 1.07 2.24 3.76
0.147 0.586 0.985 1.351 1.690
51 52 53 54 55
343.30 355.73 368.33 381.11 394.05
12.345 12.519 12.690 12.859 13.025
101 102 103 104 105
1,147.25 1,166.81 1,186.51 1,206.33 1,226.28
6 7 8 9 10
5.61 7.77 10.21 12.94 15.93
2.006 2.304 2.587 2.859 3.121
56 57 58 59 60
407.16 420.43 433.86 447.44 461.19
13.189 13.350 13.510 13.668 13.824
106 107 108 109 110
1,246.37 20.147 1,266.58 20.275 1,286.92 20.404 1,307.38 20.532 1,327.98 120.660
11 12 13 14 15
19.18 22.68 26.43 30.43 34.67
3.377 3.628 3.876 4.120 4.364
61 62 63 64 65
475.09 489.15 503.35 517.71 532.21
13.978 14 .130 14.281 14.431 14.579
111 112 113 114 115
1,348.71 1,369.56 1,390.54 1,411.64 1,432.88
20.788 20.916 21.043 21.170 21.297
16
17 18 19 20
39.16 43.89 48.85 54.07 59.52
4.606 4.848 5.091 5.333 5.576
66 67 68 69 70
546.86 561. 66 576.61 591. 70 606.93
14.726 14.872 15.017 15.160 15.303
116 117 118 119 120
1,454.24 1,475.73 1,497.34 1,519.08 1,540.95
21.424 21. 551 21.677 21. 803 21. 929
21 22 23 24 25
65.22 71.16 77.34 83.77 90.44
5.818 6.062 6.305 6.548 6.791
71 72 73 74 75
622.30 637.82 653.48 669.27 685.21
15.445 15.587 15.727 15.868 16.007
121 122 123 124 125
1,562.94 1,585.06 1,607.30 1,629.67 1,652.16
22.055 22.181 22.306 22.431 22.557
26 27 28 29 30
97.35 104.50 111.90 119.53 127.40
7.033 7.274 7.515 7.7.54 7.991
76 77 78 79 80
701.29 717.50 733.86 750.35 766.97
16.146 16.284 16.422 16.559 16.696
126 127 128 129 130
1,674.78 1,697.53 1,720.39 1,743.39 1,766.51
22.682 22.807 22.932 23.056 23.181
31 32 33 34 35
135.51 143.86 152.43 161. 24 170.27
8.227 8.461 8.692 8.921 9.147
81 82 83 84 85
783.74 800.6V/K
E,
M
(Continued)
dE/dT,
V
241 242 243 244 245
5,061 5,097 5,132 5,168 5,204
31 05 89 82 86
35.688 35.787 35.886 35.986 36.084
246 247 248 249 250
5,240 : 5,277 5,313 5,349 5,386
99 22 55 99 51
36.183 36,282 36.381 36.480 36.579
32 291 32 399 32 506
251 252 253 254 255
5,423 5,459 5,496 5,533 5,570
15 87 69 62 64
36.677 36.776 36.874 36.972 37.070
4,036 12 ; 4,068 78 : 4,101 56 4,134 44 4,167 43
32 32 32 32 33
614 721 828 934 040
256 257 258 259 260
5,607 5,644 5,682 5,719 5,757
75 97 28 69 20
37.167 37.264 37.360 37.456 37.551
4,200 4,233 4,267 4,300 4,333
52 72 02 43 95
33 33 33 33 33
146 252 357 462 566 :
261 262 263 264 265
5,794 5,832 5,870 5,908 5,946
79 49 27 15 12
37.645 37.739 37.831 37.923 38.014
221 222 223 224 225
4,367 4,401 4,435 4,469 4,503
56 29 11 04 07
33 33 33 33 34
670 774 | 877 980 083
266 267 268 269 270
: 5,984 6,022 6,060 6,098 6,137
17 32 56 88 30
38.103 38.193 38.281 38.368 38.455
226 227 228 229 230
4,537 4,571 4,605 4,640 4,674
21 44 78 22 76
34 34 34 34 34
185 287,. 388 490 591:
271 272 273 274 275
6,175 6,214 6,253 6,291 6,330
79 37 05 80 65
'38.541 38.627 38.714 38.802 38.891
858 971 083 195'' 307
231 232 233 234 235
4,709 4,744 4,778 4,813 4,848
40 14 98 93 97
34 34 34 34 35
691 792 892 992 092;
276 277 278 279 280
6,369 6,408 ! 6,447 ; 6,486 6,526
59 62 74 97 31
38.983 39.078 39.178 39.283 39.397
419 531 642 ^ 753;: 864
236 237 238 239 240
4,884 11 4,919 35 4,954 .69 4,990 13 5,025 .67
35 35 35 35 35
192 291 391, 490 589
151 152 153 154 155
2,280.58 2,306.40 2,332.35 i 2,358.42 2,384.61
25 25 26 26 26
767 889 010 130 251
196 197 198 199 200
3,559 3,590 , 3,621 : 3,652 3,683
13 16 30 56 92
30 31 31 31 31
975 086 197 307 417
156 157 158 159 160
2,410.93 2,437.36 2,463.91 2,490.58 2,517.37
26 26 26 26 26
371 491 611 ; 731 850 ;
201 202 203 204 205
; 3,715 3,746 ' 3,778 3,810 ; 3,842
39 97 66 46 38
&i 31 31 31 31
527 637 746 856 965
161 162 163 164 165
2,544.28 2,571.31 2,598.46 2,625.72 I 2,653.10
26 27 27 27 27
969 088 206 325 442
206 207 208 209 210
3,874 3,906 3,938 3,971 4,003
39 52 76 10 56
166 167 168 169 170
2,680.61 2,708.22 2,735.96 i 2,763.81 2,791.78
27 27 27 27 28
560 677 795 • 911 028
211 212 213 214 215
171 172 173 174 175
i 2,819.87 : 2,848.07 ; 2,876.39 2,904.82 2,933.37
28 28 28 28 28
144 260 376 491 606
216 217 218 219 220
176 177 178 179 180
2,962.04 ! 2,990.81 3,019.71 3,048.71 3,077.84
28 £8 28 29 29
721 836 950 065 179
181 182 183 184 185
3,107.07 3,136.42 3,165.88 3,195.46 3,225.15
29 29 29 29 29
292 406 519 632 745
186 187 188 189 190
3,254.95 3,284.86 3,314.89 3,345.03 3,375.28
29 29 30 30 30
191 192 193 194 195
3,405.64 3,436.12 3,466.71 3,497.40 3,528.21
30 30 30 30 30
;
;
:
:
:
!
:
1
32 074 3 2 182 :
;
1
!
;
4-20 TABLE
HEAT 4a-17. T Y P E E P V S . ATJ-0.07 F E ( C H R O M E L V S . A U - 0 . 0 7 A T . % F E ) (INTERIM
T/K
E,
M
dE/dT,
V
T, K
VALUES)
E, pN
dE/dT, uY/K
T, K
E, /zV
dE/dT, II.V-/K-
1 2 3 4 5
7 17 27 39 52
86 21 86 59 26
8 10 11 12 13
645 035 220 226 073
51 52 53 54 55
785 801 817 834 850
00 42 89 42 99
16 16 16 16 16
402 450 498 548 598
101 102 103 104 105
1,665 1,684 1,703 ; 1,722 1,740
72 47 26 09 95
18 18 18 18 18
731 770 809 848 886
6 7 8 9 10
65 79 94 109 124
69 .78 .40 45 86
13 14 14 15 15
782 369 852 243 555
56 57 58 59 60
867 884 901 917 934
61 29 01 79 61
16 16 16 16 16
648 699 750 801 852
106 107 108 109 110
1,759 1,778 1,797 1,816 1,835
86 80 78 80 85
18 18 18 19 19
924 961 998 035 071
11 12 13 14 15
140 156 172 188 204
54 44 50 68 94
15 15 16 16 16
801 989 128 228 293
61 62 63 64 65
951 968 985 1,002 1,019
49 42 40 43 51
16 16 17 17 17
903 953 004 055 105
111 112 113 114 115
1,854 94 •• 1,87406 1,893 .22 1,912 42 1,931 65
19 19 19 19 19
107 143 178 213 247
16 17 18 19 20
221 237 253 270 286
26 60 95 29 60
16 16 16 16 16
331 347 346 330 305
66 67 68 ' 69 70
1,036 1,053 1,071 1,088 1,105
64 82 05 33 66
17 17 17 17 17
155 205 255 304 354
116 117 118 119 120
1,950 1,970 1,989 2,008 2,028
91 21 54 91 31
19 19 19 19 19
281 315 349 382 415
21 22 23 24 25
302 319 335 351 367
89 15 36 54 67
16 16 16 16 16
272 235 195 154 114
71 72 73 74 75
1,123 1,140 1,157 1,175 1,193
03 46 94 46 03
17 17 17 17 17
402 451 499 547 595
121 122 123 124 125
2,047 2,067 2,086 2,106 2,125
74 20 70 23 78
19 19 19 19 19
447 480 512 543 575
26 27 28 29 30
383 399 415 431 447
77 82 85 84 81
16 16 16 15 15
076 040 008 980 957
76 77 78 79 80
1,210 1,228 1,246 1,263 1,281
65 31 03 79 59
17 17 17 17 17
642 689 736 783 829
126 - 127 128 129 130
2,145 2,165 2,184 2,204 2,224
37 00 65 33 04
19 19 19 19 19
606 637 668 698 728
31 32 33 34 35
463 479 495 511 527
76 69 61 52 43
15 15 15 15 .15
938 924 915 911 912
81 82 83 84 85
1,299 1,317 1,335 1,353 1,371
44 34 29 28 31
17 17 17 18 18
875 921 966 Oil 056
131 132 133 134 135
2,243 2,263 2,283 2,303 2,323
79 56 36 20 06
19 19 19 19 19
758 788 818 847 876
36 37 38 39 40
543 559 575 591 607
35 27 20 15 12
15 15 15 15 15
917 927 941 960 982
86 87 88 89 90
1,389 1,407 1,425 1,443 1,462
39 51 68 89 14
18 18 18 18 18
101 145 189 233 276
136 137 138 139 140
2,342 2,362 2,382 2,402 2,422
95 87 82 80 80
19 19 19 19 20
905 834 963 991 020
41 42 43 44 45
623 639 655 671 687
12 14 19 28 40
16 16 16 16 16
007 036 068 103 140
91 92 93 94 95
1,480 1,498 1,517 1,535 1,554
44 78 16 59 06
18 18 18 18 18
319 362 404 446 488
141 142 143 144 145
2,442 2,462 2,482 2,503 2,523
83 90 99 10 25
20 20 20 20 20
048 076 104 131 159
46 47 48 49 50
703 719 736 752 768
56 76 00 29 62
16 16 16 16 16
180 221 264 309 355
96 97 98 99 100
1,572 1,591 1,609 1,628 1,647
56 11 70 34 01
18 18 18 18 18
529 570 611 651 691
146 137 148 149 150
2,543 2,563 2,583 2,604 2,624
42 62 85 10 38
20 20 20 20 20
186 213 240 267 293
i
4-21
TEMPERATURE SCALES, THERMOCOUPLES TABLE
4a-17.
TYPE
EP vs. Au-O.07
FE (CHROMEL VS.
Au-O.07
AT.
%
FE)
(INTERIM VALUES)
(Continued) E, p.V
dE/dT, p.V/K
T, K
E, p.V
dE/dT, p.V/K
T, K
E, .uV
dE/dT, p.V/K
151 152 153 154 155
2,644.69 2,665.02 2,685.38 2,705.76 2,726.18
20.320 20.346 20.372 20.398 20.423
196 197 198 199 200
3,582.42 3,603.72 3,625.03 3,646.36 3,667.71
21. 288 21.305 21.322 21.340 21. 357
241 242 243 244 245
4,556.11 4,578.05 4,600.00 4,621. 96 4,643.94
21.933 21. 944 21. 955 21. 966 21.977
156 157 158 159 160
2,746.61 2,767.07 2,787.56 2,808.07 2,828.61
20.449 20.474 20.499 20.524 20.548
201 202 203 204 205
3,689.08 3,710.46 3,731.86 3,753.27 3,774.71
21.374 21.391 21.408 21.424 21.441
246 247 248 249 250
4,665.92 4,687.91 4,709.91 4,731.93 4,7.~3. 95
21. 987 21. 998 22.009 22.019 22.030
161 162 163 164 165
2,849.17 2,869.75 2,890.36 2,910.99 2,931. 65
20 .. 573 20.597 20.621 20.644 20.668
206 207 208 209 210
3,796.16 3,817.62 3,839.10 3,860.60 3,882.12
21.457 21.474 21.490 21.506 21. 522
251 252 253 254 255
4,775.99 4,798.03 4,820.09 4,842.15 4,864.23
22.040 22.050 22.060 22.071 22.081
166 167 168 169 170
2,952.33 2,973.03 2,993.76 3,014.50 3,035.27
20.691 20.714 20.736 20.759 20.781
211 212 213 214 215
3,903.65 3,925.19 3,946.75 3,968.33 3,989.92
21.538 21. 554 21.569 21. 585 21.600
256 257 258 259 260
4,886.31 4,908.41 4,930.51 4,952.63 4,974.75
22.090 22.100 22.109 22.118 22.127
171 172 173 174 175
3,056.06 3,076.88 3,097.71 3,118.57 3,139.45
20.803 20.825 20.846 20.867 20.888
216 217 218 219 220
4,011.53 4,033.15 4,054.79 4,076.44 4,098.11
21.615 21.630 21.645 21.659 21. 674
261 262 263 264 265
4,996.88 5,019.03 5,041.17 5,063.32 5,085.48
22.135 22.143 22.150 22.157 22.164
176 177 178 179 180
3,160.35 3,181.27 3,202.21 3,223.17 3,244.15
20.909 20.930 20.950 20.970 20.990
221 222 233 224 225
4,119.70 4,141.49 4,163.19 4,184.92 4,206.65
21.688 21.702 21.716 21. 729 21. 743
266 267 268 269 270
5.107.64 5,129.82 5,152.00 5,174.18 5,196.37
22.170 22.175 22.180 22.185 22.190
181 182 183 184 185
3,265.15 3,286.17 3,307.21 3,328.27 3,349.34
21.010 21. 030 21. 049 21.068 21.088
226 227 228 229 230
4,228.40 4,250.17 4,271.94 4,293.73 4,315.53
21.756 21. 769 21. 782 21.794 21.807
271 272 273 274 275
5,218.56 5,240.75 5,262.96 5,285.16 5,307.37
22.194 22.198 22.203 22.209 22.216
186 187 188 189 190
3,370.44 3,391.56 3,412.69 3,433.85 3,455.02
21.106 21.125 21.144 21.162 21.180
231 232 233 232 235
4,337.34 4,359.17 4,381. 00 4,402.85 4,424.71
21.819 21.831 21.843 21.855 21.866
276 277 278 279 280
5,329.59 5,351. 83 5,374.06 5,396.32 5,418.60
22.224 22.235 22.248 22.266 22.290
191 192 193 194 195
3,476.21 3,497.41 3,518.64 3,539.88 3,561.14
21.199 21. 217 21.235 21.252 21.270
236 237 238 239 . 240
4,446.59 4,468.47 4,490.36 4,512.27 4,534.19
21.878 21.889 21. 900 21. 911 21. 922
T,K
--
4b. Thermodynamic Symbols, Definitions,and Equations MARK W. ZEMANSKY
The City College of the City Univer8ity of New York
4b-1. Simple Systems. A simple system is defined as one of constant mass whose equilibrium states are described with the aid of only three thermodynamic coordinates, one of which is the kelvin temperature. The simple systems most often used are listed in Tables 4b-l and 4b-2, and the rules for converting any equation holding for a hydrostatic system into the analogous equation for another simple system are given in Table 4b-7. Tables 4b-3 to 4b-6 contain the most useful thermodynamic equations involving first derivatives only. Table 4b-8 refers to phase transitions.
TABLE
4b-1.
THERMODYNAMIC SYSTEMS AND COORDINATES
System
Intensive coordinate
Extensive coordinate
Hydrostatic system ........ Stretched wire ............ Surface film .............. Electric cell ............... Capacitor ...... , ......... Magnetic substance ........
Pressure P Tension .7 Surface tension ..! Emf 8 Electric intensity E Magnetic intensity ?rC
Volume V Length L Area A Z Charge Polarization pI Magnetization M
TABLE
4b-2.
WORK DONE BY THERMODYNAMIC SYSTEMS
System
Intensive quantity (generalized force)
Hydrostatic system .......... Stretched wire ............... Surface film ................. Electric cell ................. Capacitor ................... Magnetic substance ..........
Pin N/m2 .:Tin N ..! in dynes/em 8in V E in N/C ?rCin A/m
4-22
Extensive quantity (generalized displacement)
Work
P dV in J Vinm 3 -.7dL in J Linm -..! dA in ergs A in cm 2 -8 dZ in J Zin C pI in C'm -EdP ' in J MinWb·m -?rCdM in J
4-23
THERMODYNAMIC SYMBOLS, DEFINITIONS TABLE
4b-3.
DEFINITIONS AND SYMBOLS FOR 'lHERMAL QUANTITIES
Thermal quantity
Symbol
Heat .......................................... . Internal energy ............................. '.... . Entropy ....................................... . Enthalpy (also called heat content, heat function, total heat) ................................... . Helmholtz function (also called free energy and work function, with symbol A used) .................. . Gibbs function (also called free energy, free enthalpy, thermodynamic potential,·wltb. symbol Fused) ....
Q
U S
H
U+PV
F
U - TS
iI -TS 1
Volume expansivity (coefficient of volume expansion) . Isothermal bulk modulus .......... '.' ............. .
Definition.
V B
(oV) aT
p
-V (OP) oV _V(OP) oV s 1 (av) V oP
T
Adiabatic bulk modulus .......................... .
Bs
Isothermal compressibility ....................... .
k
T
Adiabatic compressibility ........................ . Heat capacity at constant volume ................. .
ks Cv
..
Heat capacity at constant pressure ................ .
- +-
e;)8
dQ) _ T(aS) (clT v aT v Q )· .:.... T (aS) d (clT aT p
Ratio of 'heat capacities .......................... .
p
Cp . 'Y
Cv
Joule coefficient ....... " ......................... .
G~)u
Joule-Thomson (Kelvin) coefficient ............... .
,(aT) oP
Linear expansivity .......... , ................... .
a
Isothermal Young's modulus ..................... .
y
II
(oL) L aT..7 L (oJ) A aL L (oJ) A aL 1
7'
Adiabatic Young's modulus ...................... .
.
Y8
8
4-24
HEAT TABLE
4b-4.
THERMODYNAMIC EQUATIONS FOR A HYDROSTATIC SYSTEM OF CONSTANT MASS
First law of thermodynamics:
Q dQ
=
U2
=
dU
U +W + dW
-
1
(4b-l)
Second law of thermodynamics:
dQ
T dS
=
(4b-2)
Third law of thermodynamics: ( 4b-3)
lim !:l.ST = 0 T-->O
dU dH dF dG
T dS - P dV T dS + VdP - S dT - P dV - S dT + V dP
= =
= =
( 4b-4) ( 4b-5) (4b-6) ( 4b-7)
Maxwell's equations: (4b-8) (4b-9) (4b-1O) (4b-ll)
Basic thermodynamic equations:
v= (:~)v = T G~)v = -T G~)v (:0)s
T dS
C
(4b-12)
aH) (. as' (av)' (aF) Cp = ( aT p = T aT) p = T aT p aT s
(4b-13)
=
v
C dT
+ T G~)v dV
=
v
C dT
+ {3[ dV
(4b-14)
TdS = CpdT - T(:0)pdP = CpdT - V{3TdP T dS
=
Cv (aT) aP v dP
+C
(~C;;) Ca~;)T
p
(aT) aV p dV
=
TG';.)v
=
-T
=
Qv {3 k dP
(4b-15)
+ {3V C dV P
(4b-17)
Gi.)p
(4b-18)
l'
Cv = T (ap) (av) = -T (aV)2 (ap) = TV{32 aT v aT p aT p aV T k CP (aP laV)s k = Cv = (aPlaVlT = ks
p.
= (aT)
CP
"I
_
aP
= (aT) aV
H
r
= ~ T (av)' - V] = ~ ({3T - 1) CP L aT p Cp
u=
_ ~ [T (ap) C
v
aT
v-
(4b-16)
p] = _ ~ ({3T _ p) C k
v
(4b-19) (4b-20) (4b-21) (4b-22)
4-2'5
THERMODYNAMIC SYMBOLS, DEFINITIONS TABLE
4b"5.
FIRST DERIVATIVES OF
T, P, V,
AND
S
TABLE
Internal energy
CU) CU)
aT p
aT v
4b-6.
U, H, F,
FIRST DERIVATIVES OF
U C
H aT ) p
=
Cp
=
C v
(aH) - v aT
=
Cv
C )= ::-8 F aT p ,
VfJ +k
__
"-
PVfJ 'Y - 1
t-:) 0)'
Gibbs function G
(aH) aT
s=
=-8•
CGY aT v
=-8+ ,,'
VfJ k
0 ~f'
. ,- 1- 8 +PV,- -
aF
CT),s =',
CP fJT
C
G aT ) p
PVfJ '
G~)v =-8 ,'-
=
t
8
AND
Helmholtz function F
1
,CTJ,g=
1
-8 + -8 +
fJT
G~t =
CU)
=
aP v
CU) s= aP
-
VfJT
=
Cvk fJ
+
VkP
VfJT 'Y-1
PVk 'Y
(aH) aP T
=
V(l - fJT)
(aH) aP v
=
V
Cs H aP )
+
=
-CPJL
C C
G~)T = PVk
aF
.!
Cp)s =
=V
SV'T
-~
_
8k('Y
CU)
aV T
=
fJT k
_p
eH) av T
=
fJT k
C
_.!.
F ) =-P av T
k
\.
PVk +-:;--
iJ:l
~-
>-:3
G aP ) T
=
G) aP v
= _
V
8k fJ
. 1Cp)s aG
-1) + PVk
'YfJ
V'YfJ l)k
('Y -
CF} = _ 8k aP v fJ
Cvk fJ
~
fJT
=
_
+
V
8V,T
'YfJ
'Y
G~)T =-~
+V
.
CP 8('Y -l)k+ V ,
TABLE
4b-6.
FIRST DERIVATIVES OF
U, H, F,
(aU) CP p I'flT P (aH) CP av P = Vfl = (I' - l)k av P = Vfl
U ) =-P av s
Cs t = C
WITH RESPECT TO
G~)s = - i
T, P, V,
AND
S (Continued)
Helmholtz function F
e F) = av p
Gibbs function a
-~-P Vfl
ea) - S av p = - V{:l
Cv\ = tT .
Cvk -P S(I' - 1) _ P
of
aa CV)s =
V{:l
U ) = T _ Pk as T {:l
aU
a
Enthalpy H
Internal energy U
e e
AND
t_PV'T
U as ) v = T
.
Cp T _ (I' - l)Pk I'fl
C
CF)
e
I Cst
C
G~)v = - ~~
H) as
T
=
T-~(:l
H as ) p = T
I' - -1 -H ) =T+ as ,. {:l
as
= _ Pk
T
of
fl
ST PV,T c;-
1
fl
~
o
1:;:1
~
....
o
112
~
o
t
atm
Pc> g/cm' V o, cm'/mole
111. 3
0.235 0.842 0.5308 0.720 1.487 1.210 0.90
72.5 271 75.25 252 301.8 261 278
0.59 1.18 0.468 0.850 0.441 0.3010
115 135 94.0 200 173 93.06
....... 48.00
....... .......
....... ....... 38.2 49.2 102 72.85 69 78 34.5 61 130.8 76.1 34.20 59 16.28 16.43 35.54 44.7 55 250 38 1.22 2.26 145 12.77 12.80
. . . . .. .
. .....
...... .
......
0.451 0.573
295 124
...... . . ......
0.0668
...... . ..... 60.33
. . .. . . . ...... .
...... ......
0.515
196
...... . 1. 58
...... . 0.041 0.0693
...... 44.1
...... 97.6 57.76
...... .
......
0.0308 0.03102
65.45 64.99
ReL
1 2 1 2 3 4 1 1 5 1 1 6 1 1 1 7 1 1 1 1 1 1 8 9 10 1
11 1 1 1 1
4-34
HEAT
TABLE
4c-1.
CRITICAL TEMPERATURE, PRESSURE, AND DlDNSITY OF ELEMENTS AND INOItGANIC COMPOUNDS
(Continued)
Element or compound
Hydrogen bromide .............. . Hydrogen chloride ............... . Hydrogen cyanide ............... . Hydrogen deuteride ............. . Hydrogen fluoride ............... . Hydrogen iodide ................ . Hydrogen selenide ............... . Hydrogen sulfide ................ . Iodine .................... . Krypton ....... , ....... , ....... . Lead ........................... . lVIercuric chloride ............... . Monochlorosilane_ .............. . Neon .......................... . Niobium pentabromide .......... . Niobium pentachloride ........... . Nitric oxide .................... . Nitrogen.............. ; ... . Nitrogen dioxide ................ . Nitrogen trifluoride ....... ; ..... ; N itrousoxide ................... . Nitryl fluoride .................. . Oxygen ....................... . Oxygen fluoride ................. . Ozone ......................... . Perchloryl fluoride ............... . Phosgene ....................... . Phosphine ...................... . Phosphonium chloride ........... . Phosphorous .................... . Phosphorous trichloride .......... . Radon .. ' ................. , ,. , , ... . Rubidium ...................... . Silane ......... .- ..... , ......... . Silicon tetrachloride ............. . Silicon tetrafluoride .............. . Silver .......................... . Stannic chloride. . . . .. . ......... . Sulfur ...... ' .........' .. , ....... . Sulfur dioxide ............ , ...... . Sulfur hexafluoride .... ' .......... . Sulfur tetrafluoride ..... , .. , , , ... . Sulfur trioxide ........... , . , , .. , .. . Tantalum pentabromide ......... . Tantalum pentachloride ..... " , .. . Titanium tetrachloride .... , , . , ... . Trichlorofluorosilane ...... , .. , ... . Trichlorosilane ....' .......... , ... . Tritium ......................... . U rallium hexafluoride .... , ....... . Water ......................... . Water (heavy) .................. . Xenon ................ , ........ .
Pc,
362.96 324.7 456.7 35.91 461 423.2 411 373.6 785 209.39 5400 972 409 44.44 1009 807 180.3 126.3 431 233.90 309.59 349.5 154.78 215.2 285.3 368.4 455 324.5 322.3 993.8
,a3
377 .16 2111 270 506.8 259.01 7500 591. 9 1313 430.7 318.71 364.1 491.4 973 767 438.42 495 40.0 503.4 647.4 644.1 289.75
84.00 81. 5 53.2 14.65 64.1 80.8 88 88.9
Ref.
g/cm 3
1
81.0 139 62.99 96.0
0.3488
97.71
0.9085 2.2 1.555 0.444 0.4835 1.05 0.68 0.52 0.3110 0.56
92.24 94.2 174.6 150 41.74 469 397 58 90.10 82.2
47.5 26.86
16
46 64.6 33.54 100 44.72 71.596
0.4525
97.28
0.41 0.553
78.0 ..... . 97.6
18 19 20
50.14 48.9 54.6
53.0 56 64.5 72.7 120.8
0.637 0.52
161 190
36.95 77.808
1 9 1
14 15 8 1
17 1 1 1
1
21 22 23 1
9
0.520
264
2 9
0:334 0.309 0.584
256 104 291
7 8
1.85 0.7419
58.3 351.2
0.525 0.7517
122 194.3
0;633 1.26 0;89
126 461 402
0.533 0.109
254 27.7
29
0.326
55.3
1 1
1.105
118.8
30 1
8,24 1
116 37.11
13 1
1 1
62.0
42.2 37.1 36.66
1 1
1
116
54.27 850
12
0.45 0.195 0.0481 0.29
14 1 1
25 1, 26
27 83.8 45.7 35.33 41.2 45.5 218.3 216 58.0
1
16 17 28 1 8
4-35
CRITICAL CONSTANTS TABLE
4c-2.
CRITICAL TEMPERATURE, PRESSURE, AND DENSITY OF ORGANIC COMPOUNDS
Compound
Acetic acid ....................... . Acetic anhydride .................. . Acetone .......................... . Acetonitrile ....................... . Acetylene ........................ . Aniline ........................... . Benzene .......................... . Bromobenzene .................... . n-Butane ......................... . Butanol. ...................... . I-Butene ......................... . 2-Butene (cis) .................... . 2-Butene (trans) .................. . Carbon tetrachloride .............. . Carbon tetrafluoride ............... . Chloro benzene .................... . Chlorodifluoromethane ............ . Chloroform ....................... . Chlorotrifluoroethylene ........... . Chlorotrifluoromethane ............ . l-Chloro-l, I-difluoroethane ......... . 2-Chloro-l, I-difluoroethylene ....... . Cyclohexane ...................... . Cyclopentane ..................... . Cyclopropane ..................... . Dibromomethane ................. . 1,1-Dichloroethane ................ . 1,2-Dichloroethane ................ . 1,1-Dichloro-l, 2,2,2-tetrafluoroethane Dichlorodifluoromethane ........... . Dichlorofluoromethane ............. . Diethyl ether ..................... . Diethyl ketone .................... . 1,1-Difluoroethane ................. . 1,1-Difluoroethylene ............... . Dimethylamine ................... . 2,2-Dimethylbutane ............... . 2,3-Dimethylbutane ............... . Dimethyl ether ................... . Dimethyl oxalate .................. . Dioxane .......................... . Ethane ......................... . Ethyl acetate ..................... . Ethyl alcohol. .................... . Ethylamine ....................... . Ethyl bromide .................... . Ethyl chloride .................... . Ethyl cyclopentane ................ . Ethyl fluoride. . . . . . . . . . . . . . . .. . .. . Ethyl formate .................... . Ethyl mercaptan. . . . . . . . . . . . .. . .. Ethyl methyl ether. . . . . . . . . . .. . .. . Ethyl methyl ketone ............. . Ethyl propyl ether .............. . Ethyl sulfide ............. . Ethylene ....................... .
594.8 569 508.7 547.9 309.5 698.8 562.7 670.9 425.17 560.11 419.6 428.2 433.2 556.4 227.9 632.4 369.6 536.6 379 302.02 410.3 400.6 554.2 511.8 397.81 583.0 523 561 418.7 384.7 451. 7 467.8 561. 0 386.7 303.3 437.7 489.4 550.3 400.1 628 585 305.43 523.3 516 456.4 503.9 460.4 569.5 375.32 508.5 499 437.9 533.7 500.6 498.7 283.06
Pc,
Po.
atm
g/cm 3
cm 3 /mole
V"
Ref.
57.1 46.2 46.6 47.7 61.6 52.3 48.6 44.6 37.47 48.60 39.7 40.5 41. 5 44.97
0.351
171
0.273 0.237 0.231 0.340 0.300 0.458 0.228 0.270 0.234 0.236 0.240 0.558 0.60 0.365 0.525 0.496 0.55 0.578 0.435 0.499 0.273 0.27
213 173 113 274 260 343 255 275 240 238 234 276 147 308 165 241 212 181 231 197 308 260
1 1 1
44.6 48.48 54 40 38.2 40.7 44.0 40.57 44.55 54.23 70.6 50 53 32.6 oIJ.6
51.0 35.6 36.9 44.4 43.8 52.4 30.67 30.99 52.6 39.3 50.7 48.20 37.8 63.0 55.54 61.5 51. 72 33.53 46.62 46.8 54.2 43.4 39.46 32.1 54.2 50.50
1 1
1 1 1
1 31 1 1
1 1 32 1 1
1 1 1
33 33 1 1
34 1 1 0.44 0.582 0.555 0.522 0.265 0.256 0.365 0.417
225 294
0.240 0.241 0.246
359 358 187
0.36 0.203 0.308 0.276
245 148 286 167
0.507
215
1 1
0.262
268
18 1
0.323 0.300 0.272 0.252 0.260 0.300 0.227
229 207 221 286 339 301 124
1 1 1 1
218 197 280 336 181 154
1
33 1 1 1 35 33 33 1
36 36 1 37 1
1 1 1 1
1 1 1
4-36
HEAT TABLE
4c-2.
CRITICAL TEMPERATURE, PRESSURE, AND DENSITY OF ORGANIC COMPOUNDS
Compound
To, K
Ethylene oxide ..................... Fluorobenzene ..................... Hexafluorobenzene ................. n-Hexane ......................... Iodobenzene ....................... Isobutane ......................... Isopentane ........................ Methane .......................... Methyl acetate .................... Methyl alcohol. .................... Methylamine ...................... Methyl borate ..................... Methyl bromide .................... Methyl butyrate ................... Methyl chloride .................... Methylcyclopentane ................ Methyl fluoride .................... Methyl formate .. '" ............... Methyl iodide ..................... Methyl isobutyl ketone ............. Methyl isopropyl ketone ............ 2-Methylpentane ................... 3-Methylpentane ................... Methyl n-propyl ketone ............ Methyl sulfide ................... . Methylene chloride ................. Neopentane ....................... N itromethane ...................... n-Octane ..........................
469.0 560.08 516.91 507.9 721 408.14 461.0 191.1 506.9 513.2 430.1 501.7 464 554.5 416.28 532.77 317.71 487.2 528 571.5 553.4 497.9 504.4 564.0 503.1 510.2 433.76 588 569 . 4
',"1-Perltalle . . . . . . . . . . . . . . . . . . . . . . . . .
56\).715
Perfluorobutane .................... Perfluorocyclohexane ............... Perfluoro-n-heptane ................ Perfluorohexane .................... Perfiuoromethylcyclohexane ......... Phenol. ........................... Propane ........................... Prop~ne: .. '. : ...................... PrOpIOnIC aCld ..................... Propionitrile ....................... n-Propyl acetate ................... n- Propyl alcohol. .................. Propyl formate .................... Propyne .......................... Pyridine .......................... Toluene ........................... Trichlorotrifluoromethane ........... Trichlorotrifluoroethane ............. 1, 1, 1-Trifiuoroethane ............... Trimethylamine ....................
386.4 457.2 474.8 447.7 486.8 692.4 370.0 365.0 612 564.4 549.4 537.3 538.1 401 617.4 594.0 471.2 487.3 346.3 433.3
(Continued) Pc,
atm
g/cm'
p"
V" cm 3 /mole
Ref.
70.97 44.91
0.32 0.269
137 357
29.94 44.6 36.00 32.9 45.80 46.3 78.47 73.6 35.4
0.234 0.581 0.221 0.234 0.162 0.325 0.272
368 351 263 308 99 228 118
34.3 65.93 37.36 58.0 59.2
0.300 0.353 0.264 0.300 0.349
340 143 212 113 172
32.3 38.0 29.95 30.83 38.4 54.6 59.97 31.57 62.3 24.64 03.31 22.93 24 16.0
.... .
1 39 40 1 1 41 1 1 1 1 1 42 1 1 1 38 1 1 1 35 35 36 36 35 1 1 43 1 1 1 44 45 1 46 45 1 1 1 1
.... .
.... .
.... .
.... .
23 60.5 42.01 45.6 53 41.3 32.9 50.2 40.1 52.8 60.0 41. 6 43.2 33.7 37.1 40.2
. ....
.... . .... . . ....
. ....
...
... ... ...
. ...
"
0.278 0.235 0.235 0.286 0.309
310 367 367 301 201
0.238 0.352 0.235 0.232 0.600
303 173 486 311 397
0.584
664
0.220 0.233 0.32 0.240 0:296 0.273 0.309
200 181 232 230 345 220 285
0.29 0.554 0.576 0.434 0.233
318 189 325 194 254
.... .
.... . . .... .... . .... .
.... . .....
"
.
...
... ... ...
...
1
1 1 1 1 1 1 1 1
33 1
CRITICAL CONSTANTS
4-37
References for Table 4c-l and 4c-2 1. Kobe, K. A., and R. E. Lynn, Jr.: Chem. Revs. 52, 117 (1953). 2. Nisel'son, L. A., U. V. Maguchiva, and T. D. Sokolova: Zhur. Neorg. Khim. 10, 592 (1965) . 3. Johnson, J. W., D. Cubicciotti, and W. J. Silva: J. Phys. Chem. 69, 1989 (1965). 4. Johnson, J. W., and D. Cubicciotti: J. Phys. Chem. 68,2235 (1964). 5. Smith, C. R. F.: U.S. AEC Rept. NAA-SR-5286, 1960. 6. Gattow, G., and M. Draeger: Z. anorg. al/gem. Chem. 343, 11 (1966). 7. Hochman, J. M., and C. F. Bonila: Symp. Thermophys. Prop. Am. Assoc. Mech. Engrs. (Purdue), 122 (1965). 8. Lapidus, I. I., A. L. Seifer, and L. A. Nisel'son: Izvest. Uysshikh Tcheben Zavedenii Tsvetn Met 9, 92 (1966). 9. Gates, D. S., and G. Thodos: A. I. Ch. E. Journal 6, 50 (1960). 10. Nizhenko, V. I., L. I. Sklyarenko, and U. N. Eremenko: Ukrain. Khim. Zhur. 31, 559 (1965) . 11. Peshkov, V. P.: Zhur. Ekspl. i Teoret. Fiz. 33,833 (1957). 12. Frank, E. U., M. Brose, and K. Mangold: Progr. InteTn. Research Thermodyn. Transport Properties Symp., Thermophys. PToperties 2d, p. 159, 1962. 13. Frank, E. U., and W. Spalthoff: Z. ElectTochem. 61, 348 (1957). 14. Grosse, A. V., and A. D. Kirshenbaum: J. Inorg. & Nuclear Chem. 24, 739 (1963). 15. Johnson, J. W., W. J. Silva, and D. Cubicciotti: J. Phys. Chem. 70, 1169 (1966). 16. NiseI' son, L. A., and T. D. Sokolova: Zhur. Neorg. Khim. 9, 2066 (1964;). 17. Nisel' son, L. A., A. I. Pustil'nik, and T. D. Sokolova: Zhur. Neorg. Khim. 9, 1049 (1964). 18. Jarry, R. L., and H. C. Miller: J. Phys. Chem. 60, 1412 (1956). 19. Couch, E. J., and K. A. Kobe: J. Chem. Eng. Data 6, 229 (1961). 20. Hetherington, G., and P. L. Robinson: J. Chem. Soc., 2230 (1955). 21. Anderson, R., J. G. Schnizlein, R. C. Toole, and T. D. O'Brien: J. Phys. Chem .. 56, 473-474 (1952). 22. Jenkins, A. C., and C. N. Birdsall: J. Chem. Phys. 20, 1158 (1952). 23. Engelbrecht, A., and H. Atzwanger: J. Inorg. & Nuclear Chem. 2, 348 (1956), and R. L. Jarry: J. Phys. Chem. 61,498 (1957). 24. Menzer, W.: Natunuissenschaften 45, 126 (1958). 25. Kang, T. L., L. J. Hirth, K. A. Kobe, and J. J. Mcketta: J. Chem. Eng. Data 6, 220 (1960) . 26. Otto, J. and W. Thomas: Z. physik. Chem. (Franlcfurt) 23,84 (1960). 27. Tullock, C. VV., F. S. Fawcett, W-. C. Smith; and D. D. Coffman: J. Ant.. Clwdn. Soc. 82, 539 (1960). 28. Menzer, W.: Naturwissenchaften 45,126 (1958). 29. Rogers, J. D., and F. G. Brickwedde: J. Chem. Phys. 42, 2822 (1965). 30. Oliver, G. D., and J. W. Gisard: J. Am. Chem. Soc. 78,561 (1956). 31. Singh, R., and L. W. Shemilt: J. Chem. Phys. 23, 1370. (1955). 32. McCormack, K. E., and W. G. Schmeider: J. Chem. Phys. 19,849 (1951). 33. Mears, W. H., R. F. Stahl, S. R. Orfes, R. C. Shair, L. F. Kells, W. Thompson, and H. McCann: Ind. Eng. Chem. 47, 1449 (1955). 34. Booth, H. S., and W. C. Monic: J. Phys. Chem. 62, 875 (1958). 35. Kobe, K. A., H. R. Crawford, and R. W. Stephenson: Ind. Eng. Chem. 47, 1767 (1955). 36. Kay, W. B.: J. Am. Chem. Soc. 68, 1136 (1946). 37. Stern, S. A., and W. B. Kay: J. Phys. Chem. 61,374 (1955). 38. Kay, W. B.: J. Am. Chem. Soc. 69, 1273 (1947). 39. Doulsen, D. R., R. T. Moore, J .. P. Dawson, and G. Waddington: J. Am. Chem. Soc. 80, 2031 (1958). 40. Counsell, J. F., J. H. S. Green, J. L. Hales, and J. F. Martin: Trans. Faraday Soc. 51,212 (1965) . 41. Beattie, J. A., D. G. Edwards, and S. Marple: J. Chem. Phys. 17, 576 (1949). 42. Griskev, R. G., W. E. Gorgas, and L. N. Canjar: A. I. Ch. E. Journal 6,128 (1960). 43. Beattie, J. A., D. R. Doulson, and S. W. Levine: J. Chern. Phys. 19, 948 (1951). 44. Brown, J. A., and W. H. Mears: J. Phys. Chem.62, 960 (1958). 45. Rowlenson, J. S., and R. Thacker: Trans. Faraday Soc., 53, 1 (1957). 46. Dunlap, R. D., C. J. Murphy, Jr., and R. G. Bedford: J. Am. Chem. Soc. 80,83 (1958).
4d. Compressibility GEORGE C. KENNEDyl
Institute of Geophysics and Planetary Physics, University of California, Los Angeles R. NORRIS KEELER2
Lawrence Radiation Laboratory, University of California, Livermore
4d-1. Compressibilities below 250 Kilobars.3 The data on the compressibility of solids are widely scattered through the scientific literature. Further, these data are given at various preSSl,l.re intervals and for various pressure units. Bridgman normally published work in units of kilograms per square centimeter, whereas most modern high-pressure data are published in units of bars or kilo bars. Bridgman further examined the compressibility of some substances a number of different times with substantially differing results. Data at the upper end of one pressure range determined with one kind of apparatus do not overlap well with data in another pressure range determined with another kind of apparatus. A large fraction, if not most, of the available data on compressibility of solids, liquids, and gases, where data extends to 10 kb and beyond, has been extracted from the technical literature. All this has been plotted. Where data are in conflict, we have plotted the various results and attempted to fit the hest smoot.h "urV8E through them. From these curves we have read off points and tabulated the results: pressure P in kilobars, and relative volume, the ratio of the volume V to the volume Vo at standard conditions. Many of the results in the following tables are interpolations and smoothed values, so that the tabulated results are not identical in many cases to those found in the source material. A substantial amount of judgment in selection of data has had to be used. In addition, a large amount of data has recently become available from the extensive program of shock-wave research carried out at Los Alamos Laboratory, Lawrence Radiation Laboratory, and various foreign laboratories. Dr. R. N. Keeler has reduced the shock-wave data for a number of selected substances and presented them as a separate set of tables in a following section. The reduction of data from shock-wave experiments is crucially dependent on assumptions of an equation of state. Consequently, these assumptions are set out by R. N. Keeler. It should be emphasized that the assumptions used in the reduction of these data differ from those used by a number of other laboratories. For a number of substances, specifically for such substances as indium and calcium, the shock-wave results are quite different from the static compression results. Where conflicts occur, the shock-wave results are to be preferred. References are given by number after the table titles or underneath the column heads. Temperatures are 25°C, unless otherwise marked. 1 Compressibilities below 250 kilo bars. , High-pressure compressibilities. 3 Unv. Calif. (Los Angeles) Inst. Geophys. and Planetary Phys. Publi. 732. 4--38
4-39
COMPRESSIBILITY TABLE
P,
kilobars
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
4d-1. VIVo
OF ELEMENTS*
H2
H2
He
N2
N,
at 30°C
at 65°C
[1]
[1]
at 65°C [1]
at 23.5°C [7]
at 65°C [1]
. ....
... . ... .
... . ... .
. ... ....
12.17 11.04 10.29 9.72 9.29 8.97 9.71 8.49 8.29 8.13 7.95
5.54 4.76 4.31 4.00 3.74 3.58 3.44 3.31 3.21 3.12 3.04 2.98 2.92
1.24 1.16 1.11 1.06
1.29 1.20 1.14 1.09 1.06 1.03 1.00 0.98 0.96 0.95 0.93 0.92 0.91
.....
.... .
13.89 11.55 10.52 9.81 9.29 8.87 8.55 8.25 8.01 7.78 7.54 7.32
.... . ....
..... .....
.
* For references see p.
4-96.
. '" . '" . .... ... . ... . .... . ... . ... '"
Ar at 25°C [11] 1. 06 0.85 0.77 0.73 0.69
.... . ._-
. ... . ... . ... .... .... . ... . ...
. ...
Ar at 55°C [7]
0.88 0.80 0.75 0.71 0.68 0.66 0.64 0.63 0.62 0.61 0.60 0.59 0.58 0.57
TABLE
4d-1. VIVo
OF ELEMENTS
(Continued)
kilobars
Ag [13]
Al [2]
As [2]
Au [13]
Ba [12]
Be [5]
Bi at 25°C [12]
Bi at -78.5°C [10]
C (graphite) [6, 12]
Ca [12]
Cd [12]
Ce [2,5]
0 5 10
1.000 0.995 0.990
1.000 0.993 0.986
1.000 0.988 0.977
1.000 0.997 0.994
1.000 0.955 0.908
1.000 0.996 0.991
1.000 0.985 0.971
1.000 0.985 0.972
1.000 0.984 0.972
1.000 0.968 0.942
1.000 0.987
0.977
1.000 0.976 0.953
15 20
0.986 0.981
0.980 0.974
0.967 0.960
0.990 0.988
0.872 0.865
D.987 0.982
D.959 0.948
0.960 0.948
0.962 0.954
0.917 0.896
0.966 0.957
0.835 0.813
25
0.977
0.969
0.952
0.985
0.813
0.978
0.848
0.937
0.946
0.877
0.947
0.798
P,
!o
f
b d
30 35 40 45 50 55
0.972
..... ..... ..... ..... .....
0.964 0.960 0.95.5 0.951 0.947 0.943
0.945 0.938 0.933 0.926 0.920 0.915
0.983 . ....
. .... . .... . .... . ....
0.788 0.765 0.744 0.725 0.707 0.691
0.975 0.971 0.967 0.965 0.963 0.960
0.840 0.833 0.825 0.814 0.807 0.800
0.843 0.839 0.835 0.826 0.823
.....
0.939 0.933 0.927 0.923 0.917 0.913
0.860 0.844 0.829 0.815 0.801 0.788
0.938 0.930 0.922 0.915 0.907 0.900
0.787 0.777 0.769 0.762 0.755 0.699
a
60
.....
0.938
0.910
.... .
0.658
0.958
0.794
. ....
0.908
0.778
0.895
0.693
65 70 75 80 85
.....
0.935 0.932 0.929 0.927 0.923
0.906 0.902 0.897 0.895 0.892
. .... . .... . .... . .... . ....
0.647 0.636 0.625 0.615 0.605
0.956 0.953 0.951 0.949 0.947
0.781 0.776 0.771 0.766 0.762
. .... . ....
0.905 0.901 0.897 0.895 0.891
e
0.745 0.737 0.728 0.722
0.887 0.883 0.876 0.871 0.866
0.687 0.682 0.676 0.671 0.667
0.889 0.887 0.884
0.713 0.706 0.699
0.860 0.856 0.851
0.663 0.660 0.657
90 95 100
.....
.... . ..... .... . .... . .... . . . ..
.
0.920 0.917 0.914
0.888 0.886 0.883
. .... . .... . ....
..... . .... .....
c
0.595 0.586 0.576
0.945 0.944 0.943
0.746 0.742 0.737
.....
..... .....
-_... _ - - -
* For references see p.
4-96. a Transition at 5.5.5 kb; volumes 0.682 and 0.633. b Two transitions at 25.4 and 27.0: extreme volumes 0.936 and 0.850. 'Transition at 77.5; volumes 0.760 and 0.748. d At 27.7 the volumes are 0.931 and 0.846. 'Transition at 62.7; volumes 0.771 and 0.758. f Transition at 12.2; volumes 0.926 and 0.850.
----- - - - - - - - - - - - _ .. _
-- - - - - -
~
trJ
P> >-'3
TABLE
kilobars
Co [13]
Cs at 25°C [2,5]
Cs at 50°C (solid) [15]
Cs at 75°C (liquid) [15]
0 5 10 15 20
1.000 0.997 0.994 0.991 0.989
1.000 0.840 0.756 0.700 0.650
1.000 0.813 0.727 0.672
1.000 0.810
P,
4d-1. V /VO
(Continued)
OF ELEMENTS
Fm
Dy [17]
Er [17]
[13]
Ge [2, 13]
Gd [17]
Hg [19]
1.000 0.996 0.993 0.989 0.985
1.000 0.986 0.974 0.963 0.953
1.000 0.987 0.976 0.965 0.955
1.000 0.997 0.994 0.991 0.989
1.000 0.992 0.985 0.980 0.975
1.000 0.987 0.974 0.963 0.953
1.000 0.981 0.966
..
1.000 0.987 0.975 0.965 0.955
0.982 0.979
0.943 0.934 0.925 0.917
0.946 0.937 0.928 0.921
0.987 0.986
. ....
· .... . .... . .... .., ..
0.970 0.965 0.960 0.956
0.943 0.935 0.927 0.920
. .... . ... . . .... . ... -
0.945 0.936 0.928 0.919
.....
.... .
. .... . ....
.....
.....
.. , .. · ....
. .... ., ,
g
25 30 35 40
0.987 0.984
· .... .....
0.606 0.570 0.542 0.519
.... . ..... . .. ,.
. ....
. . ..
,
. .... .....
h
45 50 55 60 65 70 75 80 85 90 95 100
.. •
,.,
••
0.
.. , . · .... ,- ... , .... .... . , .... . - ... ..... .... . .... . ,
0.445 0.428 0.415 0.405 0.397 0.390 0.385 0.380 0.375 0.372 0.370 0.368
l
Cu [13]
.... .
.... . ... , . .... . .... . .. ...
.... . .... . "
..
-" -"
....
.
.... . .... . .... . · ....
.... . .... .
. .... .... . ... , . .... . .....
•
••
0
•
. .... . .... . .... . ....
.....
.
....
. ....
. ....
.....
. ·
..... ••
0
••
..... .....
.... .... 0·.· . · .... · ....
..... . ....
.....
.
.....
.....
. .... . .... .....
. ....
. ....
. ....
.... .. '"
0-
•••
. .... ..... ... . .... . ....
.. ..
'"
. .... . ....
. .... . .... . ...
.
. ....
0.951 0.947 0.943 0.940 0.937 0.934 0.930 0.927 0.924 0.921 0.919 0.917
Ho [17]
Q
o
~ '"0 ~
tol
Ul Ul
blH
t"' >-3
H
>1
*
For references see p. 4-96 . • Transition at 22.6; volumes 0.628 and 0.622. h Discontinuity of volume at 44.7.
!......
t TABLE 4d-1. V /VO
OF
ELEMENTS (Continued)
kilobars
In at 25°C [9J
In at -78.5°C [10J
Ir
K
[13J
[2]
La 12,5J
Li [2J
Lu [17]
Mg [2]
Mn [2J
Mo [13]
Na [2J
Nb [13]
0 5 10 15 20
1.000 0.987 0.975 0.965 0.955
1.000 0.987 0.975 0.965 0.955
1.000 0.998 0.997 0.995 0.994
1.000 0.875 0.810 0.759 0.720
1.000 0.980 0.963 0.947 0.931
LOOO
0.962 0.938 0.899 0.873
1.000 0.988 0.976 0.965 0.955
1.000 0.987 0.975 0.963 0.952
1.000 0.990 0.982 0.974 0.967
1.000 0.997 0.995 0.993 0.991
1.000 0.931 0.883 0.846 0.825
1.000 0.996 0.993 0.990 0.988
25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0.946 0.937 0.928 0.920 0.912 0.904 0.896 0.890 0.882 0.876 0.870 0.865 0.859 0.854 0.845 0.840
0.946 0.937 0.930 0.923 0.917 0.910
0.992 0.991
0.961 0.955 0.950 0.946 0.942 0.938 0.935 0.932 0.929 0.926 0.923 0.921 0.919 0.917 0.916 0.915
0.788 0.767 0.749 0.734 0.718 0.705 0.692 0.680 0.670 0.658 0.648 0.637 0.627 0.620 0.610 0.602
0.985 0.983
.
0.942 0.933 0.926 0.917 0.910 0.902 0.895 0.887 0.881 0.875 0.869 0.864 0.858 0.854 0.850 0.845
0.990 0.989
.....
0.915 0.903 0.890 (1.880 0.870 0.861 0.852 0.844 0.836 0.828 0.821 0.815 0.810 0.806 0.802 0.798
0.946 0.938 0.930 0.922
..... .... .
.. ,",. .. -,' .. , ..... .-.... . .... .-, ...
·0.689 0.663 0.641 0.622 0.605 0.591 0.578 0.565 0.554 0.543 0.534 0.525 0.518 0.511 0.505 0.499
JP,
.
I
I' I
..... ..... .... . ..... .....
..... ......
i
....
. .... . .... ..... . .... . .... . .... . ....
* For references see p. 4-96. i
Transition at 22.9; volumes 0.924 and 0.922.
0.850 0.831 0.815 0.798 0.783 0.769 0.757 0.745 0.732 0.722 0.711 0.700 0.692 0.684 0.676 0.669
. .... .. ..
.
. .... . . .... . .... . .... . .... . .... . .... . .... . .... '-'"
. .... ..... ..... . .... . .... . .... . .... . .... . ....
. .... . .... . .... .
....
..
',"
iI1 t:9 p,. "3
TABLE
4d-L VIVo
(Continued)
OF ELEMENTS
kilobars
Nd [2]
Ni [13]
P (red) [8]
P (black) [2]
P (violet) [2]
Pb 25°0 [9]
Pb at 75°0 [16]
Pd [13]
Pr [2]
Pt [13]
Pu [20]
Rb at 25°0 [5]
Rb at 50°0 [15]
0 5 10 15 20 25 30 35 40 45
1.000 0.984 0.970 0.958 0.946 0.936 0.925 0.915 0.906 0.896
1.000 0.997 0.994 0.991 0.988 0.98/} 0.984
1.000 0.977 0.958
1.000 0.984 0.970 0.957 0.946 0.935 0.92/} 0.917 0.911 0.904
1.000 0.977 0.955 0.935 0.917 0.899 0.883 0.8/}7 0.852 0.837
1.000 0.988 0.977 0.966 0.957 0.948 0.940 0.932 0.924 0.915
1.000 0.988 0.976 0.965 0.955 0.945 0.935
1.000 0.997 0.994 0.992 0.988 0.986 0.984
1.000 0.991 0.983 0.975 0.968 0.961 0.955 0.949 0.943 0.938
1.000 0.877 0.805 0.753 0.710 0.675 0.648 0./}2/} 0.607 0.591
1.000 0.840 0.765 0.718
. .... ..... . ....
1.000 0.998 0.995 0.993 0.992 0.990 0.899
..... . .... .....
1.000 0.982 0.965 0.950 0.937 0.925 0.915 0.905 0.895 0.885
0.826 0.815 0.807 0.799 0.791 0.784 0.777
0.908 0.901 0.899 0.889 0.883 0.877 0.872
. ....
.0.0 .
•••
0.
•
•••
0.
0.933 0.929 0.924 0.920 0.915 0.911 0.907
0.575 0.561 0.548 0.536 0.525 0.515 0.505
0.904 0.901 0.989 0.987
0.496 0.487 0.477 0.470
P,
..... · .. , . '0.0.
•.• 0.
· .0 .•
.... · ....
. . • 0.
• .0'.
.0 . . •
.
• .• 0.
. .... . ....
c
o
~
;g t::J
Ul Ul
j
50 55 60 65 70 75 80
0.887 0.879 0.871 0.863 0.856 0.848 0.842
·
....
. . • 0.
·
....
0
••••
o.
'00
0
••••
0
••••
., '0'
0
••
..... . - ...
. .... . ....
.0 ' 0 '
0.
0.848 0.841 0.835 0.929 0.824 0.818 0.814
.... . .... .
••
0
•
.0.0 . . .0 . . •
••
0
•
.... .
. .... .....
•
•••
0
•
0.876 0.864 0.861 0.853 0.846 0.840 0.834
.0 '0.
. .... • •• 0.
. .... .0.0. .0.0.
. ....
b3 ....
....t"' ~
k
85 90 95 100
0.836 0.830 0.825 0.820
. 0.0.
.. ... · .0 . .
· ....
* For references see p. 4-96.
. .
.... ....
. .... . ....
0.810 0.806 0.802 0.797
0.668 0.665 0.662 0.659
0.867 0.862 0.857 0.852
••
•••
•••
·0
0
•• '0 •
•••
0.
•
. ··0 .
0
•
..... •••
0
•
0.826 0.820 0.815 0.808
.
....
. •• 0. • .• 0. •• "0
I
i Reversible transition in this region . • Irreversible transition at 83.3 from violet to black; volumes 0.773 and 0.670.
!
CI:I
± TABLE
P,
kilobars
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Rh [13]
Ru [13]
1.000 0.997 0.995 0.993 0.991 0.990 0.989
1.000 0.998 0.996 0.994 0.992 0.991 0.989
.... . .....
....
.
.... . .... . .... . .... . .... . .... . .... .
. .... . ....
. .... .... . . .... . .. . . . .... . .... . .... . ....
4d-1. VIVo
S at 25°C [9]
S at -78.5°C [10]
SO at 25°C
1.000 0.950 0.915 0.888 0.869 0.851 0.837 0.822 0.810 0.800 0.791 0.782 0.774 0.766 0.758 0.752 0.745
1.000 0.958 0.925 0.900 0.881 0.864 0.850 0.839 0.831 0.825 0.821
1.000 0.£,86
0.740 0.735 0.730 0.725
. ....
.... .
[1:2]
0.£075
0.963 0.953 0.943 0.934 0.2125 0.816 0.908 0.900 0.894 0.S87 0.880
.... . .... .
0.E:75
. .... .... .
0.869 0.865
.... .
0.S16 0.S15 O. E:14 0.813
I
85 90 95 100
....
.
. ....
.... .
.... .
.... . .. -.,
.....
.... .
.... . .... . .... .
OF ELEMENTS
(Continued)
Sb at -78.5°C [10]
Se at 25°C [12]
Se at -78.5°C [10]
Si [2]
Sm [17]
Sm [12]
Ta [13]
1.000 0.987 0.976 0.965 0.956 0.946 0.937 0.928 0.920 0.913 0.905
1.000 0.952 0.915 0.885 0.860 0.839 0.825 0.811 0.800 0.791
1.000 0.995 0.990 0.985 0.981 0.977 0.975 0.971 0.967 0.964 0.960 0.957 0.955 0.953 0.950 0.948 0.946
1.000 0.982 0.966 0.953 0.940 0.928 0.915 0.910 0.894
.....
1.000 0.991 0.982 0.973 0.965 0.958 0.950 0.942 0.935 0.928 0.921 0.915 0.908 0.902 0.895 0.890 0.884
1.000 0.996 0.994 0.992 0.990 0.988 0.981
.... . .... . .... . .... . .... .
1.000 0.945 0.907 0.876 0.850 0.830 0.813 0.798 0.786 0.776 0.767 0.760 0.751 0.745 0.738 0.731 0.725
.... . .... . .... . .... .
0.719 0.714 0.708 0.702
0.945 0.943 0.942 0.941
..... ..... ..... .....
0.878 0.822 0.816 0.810
...
,
.
.... .
.... . . .... . .... . .... . .... . .... ....
.... . --
* For references see I
p. 4-96.
Transition at 83.3 ;volumes 0.858 and 0.821.
.
.... . .... .
..... .....
..... .....
..... .....
.....
'I
iII
,.. i3j
J-3
TABLE
Te
Te
kilobars
at 25°C [12]
at -78.5°0 [10, 13]
0 5 10 15 20 25 30 35
1.000 0.975 0.955 0.930 0.918 0.902 0.888 0.876
40
P,
4d-1. V /VO
OF ELEMENTS
(Continued)
Th
Ti
U
U
Y
[2,13]
Tl [12]
Tm
[2]
[17]
[2]
[13]
[16]
Yb [17]
Zn [12]
Zr [2]
1.000 0.976 0.958 0.942 0.928 0.915 0.903 0.892
1.000 0.990 0.981 0.972 0.963 0.955 0.947 0.940
1.000 0.994 0.989 0.985 0.980 0.977 0.973 0.968
1.000 0.987 0.975 0.965 0.955 0.946 0.937 0.929
1.000 0.987 0.975 0.965 0.955 0.946 0.937 0.928
1.000 0.995 0.990 0.985 0.981 0.976 0.973 0.969
1.000 0.998 0.996 0.994 0.993 0.992 0.991 .0 ' 0 ,
1.000 0.986 0.973 0.961 0.950 0.940 0.930 0.921
1.000 0.962 0.928 0.889 0.874 0.852 0.832 0.814
1.000 0.992 0.988 0.973 0.967 0.960 0.952 0.944
1.000 0.994 0.987 0.982 0.975 0.970 0.965 0.959
0.865
0.882
0.932
0.965
0.911
0.921
0.966
.....
0.913
0.797
0.937
0.954
m
0
0.791 0.785 0.779 0.774 0.770 n 0.760 0.754 0.748 0.744 0.740 0.735 0.730
0.873 0.869
0.926 0.920 0.916 0.911 0.907
0.962 0.958 0.955 0.953 0.950
0.903 0.895 0.887 0.880 0.872
· .... · ..... .....
0.963 0.960 0.957 0.955 0.952
. ....
• •• 0.
• .• 0.
... ,.
. .... . ....
.... .... . ....
0.930 0.923 0.917 0.910 0.904
0.950 0.945 0.940 0.935 0.931
0.903 0.900 0.896 0.894 0.890 0.888 0.885
0.947 0.945 0,944 0.942 0.940 0.938 0.936
0.865 0.859 0.852 0.846 0.840 0.834 0.829
0.897 0.891 0.886 0.881 0.876 0.872 0.867
0.927 0.924 0.920 0.917 0.915 0.912 0.909
p
45 50 55 60 65 70 75 80 85 90 95 100
••• 0.
..... •
~
••
0-
..... •••
•
0
0
•
•••
..... •
0
..
•••
..
,
. . . 0.
* For references Bee p. 4-96. Transition at 40.1; volumes 0.848 and 0.893 . • Transition at 68.6; volumes 0.766 and 0.759 . • Transition at 40.3; 'volumes 0.881 to 0.837. P Transition at 36.7; volu",.s 0.921 and 0.914.
•
.0
••
..... 00
•
'0'
.0
••
00.0.
•••
0
•
· .... •
.0
.0
••
•••
0.950 0.948 0.945 0.944 0.943 0.942 0.941
. .... . ....
. .... •••
..
0.
"-
···0 . •
••
0.
. .... . .... •• '0'
o
••
,.
. .
. ....
.0 ' 0 '
• •• 0.
... ' 0 '
.....
. .
. .... .. ....
.... .... , .. , . . ....
. .0 . .
••• 0.
••
•
•
••
0
0.
••
••
0
•
Q
o
is::
~
U1 U1
I:d
H
t"'
~
m
:t CTI
TABLE
4d-2. VIVo
OF INORGANIC COMPOUNDS* -
!
~
P,
kilobars
0
AgBr at 25°C [9]
AgBr at -78.5°C [10]
1.000
1.000
AgBrO, [9]
AgCl at 25°C [9]
AgCl "t -78.5°C [10]
1.000
1.000
1.000
AgCN [5]
1.000
AgNO, [9]
1. 000
1.000
1.000
1.000
1.000
c
d
0.985
0.985
0.974 0.963 0.953 0.945 0.937 0.930 0.924 0.918 0.912
0.974 0.963 0.954 0.945 0.937 0.931 0.925 0.920 0.914
0.989
0.985
0.990
0.990
0.955
0.820
0.822
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
0.987 0.968 0.959 0.950 0.941 0.932 0.923 0.915 0.906 0.899 0.892 0.885 0.880 0.875 0.870
0.978 0.968 0.960 0.951 0.943 0.935 0.927 0.920 0.913
0.979 0.969 0.959 0.950 0.941 0.933 0.924 0.915 0.907 0.900 0.893 0.887 0.880 0.874 0.868
0.979 0.970 0.961 0.953 0.945 0.937 0.930 0.923 0.917
0.922 0.895 0.873 0.854 0.787 0.772 0.760
. .. -.
0.810 0.800 0.790 0.779 0.770 0.761 0.752 0.743 0.735 0.727 0.720 0.713 0.706 0.700 0.693
0.812 0.802 0.793 0.785 0.776 0.769 0.762 0.756 0.750
..... .. , ' . .....
0.972 0.959 0.947 0.937 0.928 0.919 0.910 0.902 0.895 0.888 0.881 0.875 0.870 0.865 0.860
. .... . .... . .... . .... . .... . ....
0.983 e 0.955 0.937 0.921 0.907 0.895 0.883 0.872 0.862 0.852 0.843 0.835 0.828 0.822 0.816 0.810
.....
0.856
0.863
. ....
.
....
0.687
. ...
0.805
.... . .. - ..
. .... . .... . ....
0.681 0.675 0.670
. ....
0.800 0.796 0.792
85 90 95 100
0.847 0.841 0.835 0.829
* For references
.....
..... .....
.... . -,.- . . .... .... . . .... . ....
.. .
..... ..... .... .
,-.
••
o.
. .... .. ... . ....
. ....
b
0.852 0.848 0.845
see p. 4-96. Transition at 84.3; volumes 0.859 and 0.848. Transition at 88.2; volumes 0.860 and 0.744. 'Transition at 2.9 kb; volumes 0.989 ± 2.9 and 0.826. d Transition in this region. 'Transition at 9.3; volumes 0.970 and 0.957. b
AgI at -78.5°C [10]
0.989
a
a
AgI at 25°C [9]
5
.....
0.743 0.737 0.732
. ....
BaS at -78.5°C
BaS at 25°C [10]
. .... . ....
[10]
~
l:':i ~
1-:3
TABLE
4d-2. V /VO
OF INORGANIC COMPOUNDS
(Continued) --
,
P,
kilobars
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
1.000 0.985 0.974 0.964 0.954 0.945 0.937 0.930 0.923 0.916 0.910 .
,
...
1.000 0.987 0.976 0.967 0.958 0.950 0.948 0.936 0.930 0.925 0.920 ....
.
.... .
. ....
.... .
. ....
... , .
.... .
0,0
....
•••
0,'"
.
.
. ....
.. ... .. ... .. ',"
... - .
•
.... . . .... . '-'"
....
* For references, J
.---.-
oCaTe CaSe CaSe CaS GaTe CsBr CsBr BaSe BaTeBaSe BaTe ,.1 CaS at 25°C at -78,5°C at 25°C at -78.5°C· at 25°C at -78.5°C at -25°G at -78.5°C at 25.oC at -78,5°0 at 25°C at -78.5°C - [10] [10J [10] [10] [10] [10] [10] [9] [10J [10] [10] [10] ! 1.000 0:983 0.969 0.957 0.945 0.935 0.927 0.918 0.909 0.901
1.000 0.985 0-.973 0.962 0.951 0.943 0.935 0.929 0.923 0.916
.... . .... .
.... . f .... .
....
.. ... .... . . ....
f
.... . .... . .
.... .
.... .
.... . .... .
.... .
.... .
.... . .. .. .
.... . .... .
.... .
.... .
1.000 0.987 0.975 0.966 0.957 0.949 0.943 0.937 0.932 0.929 0.925
1.000 0.988 0.978 0.969 0.961 0.955 0.948 0.943 0.938 0.934 0.930
.... . .... . . ....
..
.... . . .... .... . .... . . .... . .... .. ...
'"
.. ... .. '"
1.000 0.990 0.980 0.972 0.964 0:956 0:950 0.943 0.938 0.932 _ 0.927
1.000 0.991 0.982 0.974 0.967 0.960 0.954 0.949 0.945 0.939 0.935
LOOO 0:988 0.978 0.969 0.961 0:953 0:947 0.940 0:934 0:928 0.922
1.000 0.989 0.980 0.971 0.963 0.956 0-.950 0.943 0.937 0.932 0.926
1.000 . 0.972 0.947 , 0.924 , 0.904 0.885 i 0.868 0.851 0.837 0.823 0.810
.....
. ....
I .....
. .... . .... . .... . .... . .... . .... . .... . .... . ....
.... . . .... . .... . ....
. .... . .... . .... . .... . .... .. - ..
0.799 0.789 : 0.780 0.770 0.762 0.753 0.746 0.738 0.731 0.724
i
.....
..... .... . ..... ..... .... . .....
. ....
.....
.
.... . . .... . .... ... , .
. .... ....
•••
o
•
.... . .... . .... . .... . .... .
. .... . ... ,
. ....
1.000 0.973 0.948 0-.926 0.907 0.890 0-.875 0.862 0.850 0.839 0.830
o
o
~ "d
.~
.t;J TIl TIl
Ea ....
t< ~
t--3
H
>-1
-_ .... __ ... -
---
(")
o
:::;:
--
----
* For references, W
~
see p. 4-96. Very sluggish transition between 9.8 and 14.7. Probably two sluggish transitions in neighborhood of 24.5.
Volume discontinuity of one about 4 times that of other.
t
01
I-'
TABLE
4d-2. V /VO
OF INORGANIC COMPOUNDS*
NH.Br NH.B60S . 4H 2 O at 25°0 [5] [9]
t>:l
NH.Ol at 25°0 [9]
NH.Ol at -78.5°0 [10]
NH.IO. [6J
NH4N03 [9]
1.000 0.973 0.052
1.000 0.978 0.960
1.000 0.980 0.963
1.000 0.972 0.948
0.805 0.794
0.933 0.917
0.045 0.931
0.946 0.931
0.928 0.912
0.885 0.885 0.873 0.862 0.851 0.842
0.773 0.773 0.764 0.754
0.906 0.906 0.895 0.885 0.875 0.867
. .... . .... . ....
. .... . ....
0.888 0.888 0.875 0.864 0.853 0.843
0.897 0.882 0.870 0.857 0.846 0.835
. .... . .... . .... . .... ..... . .... . .... ..... ..... . ....
. .... . .... . .... . .... . . .. . . .... . .... . .... . .... . ....
0.835 0.826 0.S18 0.810 0.803 0.796 0.790 0.783 0.776 0.769
. .... . ....
. .... . ....
. ....
. .... . ....
NH.Br NH.OH0 2 at -78.5°0 [5] [10]
kilobars
NaIO. [6]
NaNH.0.H.06 [21]
NaN03 [9]
0 5 10
1.000 0.981 0.966
1.000 0.974 0.952
1.000 0.982 0.965
1.000 0.964 0.938
1.000 0.973 0.950
1.000 0.973 0.951
1.000 0.965 0.932
15 20
0.953 0.942
0.933 0.917
0.950 0.937
0.917 0.900
0.929 0.910
0.032 0.915
25 30 35 40 45 50
. . .. ..... .....
.... . . .... . .... . .... . ....
0.912 0.912 0.001 0.890 0.881 0.871
0.845 0.845 0.834 0.824
0.878 0.878 0.863 0.850 0.838 0.827
55 60 65 70 75 80 85 90 95 100
.... . .... . .... . .... . .... . .... . ..... .... . .... .
..... . .... . .... ..... .... . . .... . .... .... . . .... . ....
0.852 0.943 0.836 0.830 0.823 0.817 0.812 0.807 0.802 0.797
0.817 0.808 0.800 0.892 0.885 0.878 0.872 0.865 0.859 0.852
P,
!:
(Continued)
aa
.
.....
..... .....
....
.
0.889
z
. .... . ....
. . .... . .... ""
y
* For references, see p. 4-96. "Transition at 53.9; volumes 0.864 and 0.853. , Transition at 22.8; volumes 0.892 and 0.868. aa Transition at 11.2; volumes 0.926 and 0.815.
. .... .....
.....
. .... . .... ..... . .... . .... .... . . ....
. .... ..... . .... . .... . ... . .... .....
. .... . .... . .... ..... . .... . ....
0.826 0.817 0.810 0.804 0.797 0.792 0.787 0.784 0.780 0.777
iIi t'=J
i>-
>-'3
TABLE
P,
kilobars
0
4d-2. V IVa
OF INORGANIC COMPOUNDS*
NH4P0 4 [5J
NiSO. [21]
PbI z [5]
NH2S0aH [21]
NH4010 4 [6]
1.000
1.000
1.000
1.000
1.000
0.979 0.963 0.948 0.935
0.971 0.948 0.927 0.910
NH.I at 25°0 [9]
NH.I at -78.5°0 [10]
NH4IOa [6]
PbS at 25°0 [2]
PbS at -78.5°0 [10]
1.000
1.000
1.000
1.000
1.000
1.000
0.982 0.966 0.952 0.940
0.832 0.807 0.781 0.767
0.967 0.941 0.920 0.901
0.986 0.973 0.961 0.950
0.983 0.969 0.956 0.945
0.989 0.980 0.971 0.962
NH4H,PO. [21]
bb
5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
0.981 0.965 0.951 0.939 0.877 0.867 0.857 0.848
....
. .... . .... . .... .
.... . .... . .... . ..
".,
.... . .... . .... . . ... .
0.983 0.967 0.953 0.940 0.886 0.861
.... . .... . . .... . .... . .... .. -.,
. .... . .... .... . .... . . .... ..
'"
.
.... .
.... .
0.897 0.878 0.863 0.850 0.838 0.827 0.818
. .... . .... . .... . .... ..... . .... . .... . .... .... . . .... .... . . .... .... .
'*' For references, see p. 4-96. bb Transition at 5.0; volumes 0.963 and 0.924. "Transition at 0.5; volumes 0.997 ± and 0.856. ad Volume at 24.2 = 0.958 and at 22.3 = 0.937.
(Continued)
cc
0.923 0.913
..... ..... ..... ..... ..... ..... .... . ..... ..... ..... .... . ..... ..... .0"
•
dd
0.895
..... . .... . .... . .... . .... . .... . .... . .... .... . . .... . .... . .... . .... . ....
.... .
0.929 0.919
. .... . .... . .... . .... . .... . .... ... " . . .... . .... . .... ..... . .... . .... . ....
0.754 0.740 0.728 0.716 0.705 0.695 0.686 0.678 0.670 0.662 0.655 0.648 0.642 0.635 0.628 0.622
0.885 0.870 0.858 0.846 0.837 0.828
. .... . .... . .... . .... . .... . .... . .... . .... . .... . ....
0.940
. .... ..... . .... . .... .....
. .... . .... . .... . .... . .... ..... . .... . .... . .... . ....
0.935 0.928 0.921 0.915 0.909 0.903 0.899 0.896 0.892 0.890 0.887 0.885 0.882 0.880 0.878 0.876
0.933 0.925 0.918 0.913 0.909 0.905
()
o
~
;g trJ m
m
td
>-
~
TABLE
4d-lO. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
Ag-Mn system [37]
Ag-Au alloyst [14] Pressure, kilobars
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
Ag,Al [13]
1.000 0.997 0.995 0.993 0.991 0.989 0.987 0.986 0.984 0.982 0.980 0.979 0.977 0.976 0.974 0.972
tAt 30°.
50 Ag 50 Au
25 Ag 75 Au
1.000 0.998 0.997 0.995 0.994 0.993 0.992
1.000 0.998 0.997 0.996 0.995 0.994 0.993
1.000 0.998 0.997 0.996 0.994 0.993 0.992
.....
· ....
..... ..... .... ,-
. .... ..... . .... .. - .. . .... . ....
..... .....
. .... . ....
.... .... · .... . .... . ....
.... . ..... .....
-
* For references see p. 4-96.
75 Ag 25 Au
- _ .... -
0·
•••
---------
· .0 .•
· .... 0
••••
. .
--
Ag 98.70 Cd 1.30 [13]
Ag 91.40 In 8.60 [37]
Ag 96.92 Mg 3.08 [37]
100 Ag
96.15 Ag 3.85 Mn
85.41 Ag 14.59 Mn
1.000 0.997 0.995 0.993 0.992 0.990 0.988 0.987 0.985 0.983 0.981 0.980 0.978 0.977 0.975 0.974
1.000 0 .. 997 0.995 0.993 0.991 0.990 0.988 0.986 0.985 0.983 0.981 0.980 0.978 0.976 0.975 0.973
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987 0.985 0.983 0.982 0.980 0.978 0.977 0.975 0.973
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987 0.985 0.983 0.982 0.980 0.978 0.976 0.975 0.973
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.986 0.984 0.982 0.980 0.978 0.977 0.975 0.973 0.971
1.000 0.998 0.996 0.993 0.991 0.989 0.987 0.985 0.983 0.981 0.979 0.977 0.975 0.973 0.972 0.970
----
---
~
tol
~
TABLE
4d-IO. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
AgZn [13J
Ag 5Zn s [13J
Ag-96.44 Zn 3.56 [13J
100 Al
85.7 AI 14.3 Mg
1.000 0.998 0.996 0.994 0.992 0.991 0.989 0.987
1.000 0.997 0.994 0.991 0.989 0.986 0.984 0.982
1.000 0.997 0.993 0.990 0.987 0.984 0.981 0.978
100 Ag
79.0 Ag 21.0 Pd
48.9 Ag 51.1 Pd
29.5 Ag 70.5 Pd
100 Pd
100 Ag
92.75 Ag 7.25 Pt
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987
1.000 0.998 0.996 0.995 0.993 0.991 0.989 0.988
1.000 0.999 0.997 0.996 0.994 0.993 0.991 0.990
1.000 0.999 0.997 0.996 0 .. 994 0.993 0.992 0.991
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.987
0.985 0.983 0.982 0.980 0.978
0.985 0.983 0.982 0.980 0.978
0.983 0.981 0.980 0.978 0.976
0.983 0.981 0.979 0.977 0.975
0.985 0.983 0.982 0.980 0.979
0.976 0.975 0.973
0.977 0.975 0.974
0.975 0.973 0.972
0.973 0.972 0.970
0.976 0.975 0.973
16 18 20 22 24
' 0.985 0.933 0.982 0.980 0.978
9.986 0.985 0.983 0.982 0.981
0.988 0.987 0.986 0.984 0.983
0.990 0.988 0.987 0.986 0.985
1.000 0.998 0.997 0.996 0.995 0.994 0.993 0.992 a 0.991 0.990 0.989 0.988 0.987
26 28 30
' 0.976 0.975 0.973
0.979 0.978 0.977
0.982 0.981 0.980
0.984 0.983 0.982
0.986 0.985 0.985
0 2 4 6 8 10 12 14
AI-Mg system [33J
Ag-Pt system [37J
Ag-Pd system [33J Pressure, kilobars
(Continued)
1.000 0.998 0.996 0.993 0.991 0.989 0.987 0.985
1.000 0.998 0.996 0.993 0.992 0.989 0.987 0.985
0.979 0.977 0.974 0.972 0.970
0.975 0.973 0.970 0.967 0.965
0.967 0.965 0.963
0.963 0.961 0.958
a
o
~ IV ~ t;}
Ul U1
~
H
t"' H 8
>.-
I 00· "'F
TABLE
4d-IO. V /VO
OF ALLOYS AND INTERMETALLIC GOMPOUNDS*
t
(Continued)
0;,
00
Bi-Pb system [34) Pressure, kilobars
0 2 4 6 8 10 12 14 16 18 20 22 24
Bi-Te system [34)
Bi-Sb system [34)
Ca-Cd system [36)
25 Bi 75 Pb
100 Pb
100 Bi
80 Bi 20 Sb
50 Bi 50 Sb
20 Bi 80 Sb
100 Sb
100 Bi
99.00 Bi 1.00 Te
100 Ca
95 Ca 5 Cd
100 Cd
1.000 0.995 0.990 0.985 0.980 0.976 0.971 0.967 0.963 0.959 0.955 0.951 0.947
1.000 0.995 0.990 0.985 0.981 0.977 0.972 0.968 0.965 0.961 0.957 0.954 0.951
1.000 0.993 0.987 0.981 0.976 0.970 0.965 0.961 0.956 0.952 0.948 0.944 0.940
1.000 0.995 0.990 0.985 0.980 0.976 0.971 0.967 0.962 0.958 0.954 0.949 0.945
1.000 0.995 0.991 0.987 0.983 0.979 0.975 0.956 0.967 0.964 0.960 " 0.956 0.953
1.000 0.995 0.990 0.985 0.981 0.976 0.972 0.968 0.964 0.960 0.957 0.953 0.949
1.000 0.995 0.989 0.984 0.980 0.975 0.971 0.966 0.962 0.958 0.954 0.951 0.947
1.000 0.993 0.987 0.981 0.976 0.970 0.965 0.961 0.956 0.952 0.948 0.944 0.940
1.000 0.994 0.988 0.983 0.978 0.973 0.968 0.963 0.958 0.953 0.949 0.947 0.942
1.000 0.987 0.974 0.962 0.952 0.941 0.931 0.922 0.913 0.904 0.896 0.888 0.881
1.000 0.987 0.977 0.967 0.958 0.949 0.941 0.932 0.924 0.916 0.909 0.902 0.895
1.000 0.994 0.990 0.986 0.982 0.977 0.973 0.969 0.966 0.962 0.958 0.955 0.951
c
l
c
26 28 30
0.944 0.940 0.937
0.948 0.945 0.942
0.902 0.899 0.896
32 34 36
0.934 0.931 0.928
0.939 0.936 0.933
0.893 0.890 0.887
0.941 0.937 .....
0.949 0.946 0.942
0.945 0.942 0.939
0.943 0.940 0.937
0.902 0.899 0.896
0.849 0.846
0.873 0.867 0.860
0.889 0.882 0.876
0.948 0.944 0.9"41
0.938 0.935 ... ..
0.935 0.932 0.929
..... .....
0.893 0.890 0.887
0.843 0.840 0.838
0.853 0.848 0.842
0.870 0.864 0.859
0.938 0.935 0.932
0.926 0.923
..... .....
0.885 0.882
0.835 0.833
0.836 0.830
0.853 0.848
0.929 0.926
.....
c ... , .
0.887
.....
c, k
38 40
0.925 0.922
0.930 0.928
0.885 0.882
k I
Transition in this region. Volume at 39.2 = 0.913. At 26.0 VI-II = 0.048, and
.... . . ....
-
* For references see p. 4-96. I!
0.877 0.867
VII-III =
0.034.
.
P:!
l;l
~
-
TABLE
I Pressure, kilobars
0 2 4 6 8 10 12 14 16 18 20 22 24
4d-lO. V /VO
~-'---
--- - - -- -
1.000 0.987 0.974 0.962 0.952 0.941 0.931 0.922 0.913 0.904 0.896 0.888 0.881
1.000 0.989 0.980 0.971 0.963 0.955 0.947 0.940 0.933 0.926 0.920 0.914 0.908
0.05C Carboloy 0.09 Mn 0.01 Si 999t 36.0 Ni [13] 63.88 Fe 28.6 Ca 100 Mg [37] 71.4 Mg 1.000 0.990 0.982 0.974 0.968 0.961 0.955 0.948 0.942 0.937 0.932 0.926 0.921
---------- --------------
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
Ca-Mg system [36]
61.9 Ca 100 Ca 38.1 Mg
-----.~
Cd-Bi system [35]
Carbon steel [37]
100 Fe
95.69 Fe 100.00 Cd 75.10 Cd 50.05 Cd 24.40 Cd 100.00 Bi 24.90 Bi 49.95 Bi 75.58 Bi 4.31 C
1.000 0.994 0.988 0.983 0.977 0.972 0.968 0.963 0.958 0.953 0.949 0.945 0.941
1.000 0.999 0.998 0.998 0.997 0.997 0.996 0.996 0.995 0.995 0.995 0.994 0.994
1.000 0.997 0.995 0.993 0.992 0.990 0.988 0.986 0.984 0.983 0.981 0.980 0.978
1.000 0.998 0.997 0.996 0.995 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986
1.000 0.998 0.997 0.996 0.995 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986
1.000 0.995 0.991 0.987 0.983 0.979 0.975 0.972 0.968 0.965 0.962 0.959 0.956
0.976 0.975
0.985 0.984
0.985 0.984
..... .....
0.974
0.983
0.983
.... . -'" .
. .... ..... .. ... . .... .... .
26 28
0.873 0.867
0.902 0.897
0.917 0.912
0.936 0.932
0.993 0.993
30 32 34 36 38 40
0.860 0.853 0.848 0.842 0.836 0.830
0.892 0.887 0.882 0.877 0.873 0.869
0.907 0.903 0.899 0.895 0.891 0.888
0.928
0.992
.... . ..... .... . .. ... .....
· .... · .... · .... ..... ·
....
.... . .. , .. .. ... .... . .....
.....
.. ... .....
(Continued)
.,
••
•••
0
4
•
..... .. , .. ..... .....
1.000 0.994 0.990 0.985 0.980 0.976 0.972 0.968 0.964 0.960 0.956 0.952 0.949 m 0.928 0.925 n 0.905 0.902 0.899 0.897 0.895 0.892
1.000 0.994 0.989 0.983 0.978 0.974 0.970 0.965 0.961 0.957 0.953 0.949 0.946
1.000 0.994 0.988 0.983 0.978 0.973 0.968 0.964 0.959 0.955 0.950 0.946 0.942
1.000 0.993 0.987 0.981 0.976 0.970 0.965 0.961 0.956 0.952 0.948 0.944 0.940
0
q
c
0.910 0.902
0.899 0.897 r 0.863 0.860 0.857 0.854 0.852 0.850
0.902 0.899
p
0.884 0.880 0.877 0.874 0.872 0.870
* For references see p. 4-96. t WC with 3 % Co binder. , Transition in this region. m Volumes at 24.5 = 0.948 and 0.931. n Volumes at 28.4 = 0.925 and 0.910. • Volumes at 24.5 = 0.945 and 0.915. P Volumes at 28.4 = 0.901 and 0.888. • Volumes at 24.5 = 0.941 and 0.901. r Volumes at 28.4 = 0.897 and 0.868.
l.l
o
is:
~
[:I:J U2 U2
tdH
t:>-3 >1
0.896 0.893 0.890 0.887 0.885 0.882
t
~
~
to TABLE
4d-l0. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
100 Cd
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 (J.935
* For references see p. 4-96.
Cd-Zn system [36]
Cd_Sn system [36]
Cd-Pb system [36] Pressure, kilobars
(Continued)
50 Cd 50 Pd
100 Pd
100 Cd
75 Cd 25 Sn
50 Cd 50 Sn
25 Cd 75 Sn
100 Sn
100 Cd
50 Cd 50 Zn
100 Zn
1.000 0.994 0.991 0.987 0.983 0.979 0.975 0.971 0.967 0.963 0.960 0.957 0.953 0.949 0.946 0.943 0.940 0.937 0.934 0.931 0.929 ..
1.000 0.994 0.990 0.986 0.982 0.977 0.973 0.969 0.966 0.962 0.958 0.955 0.951 0.948 0.944 0.941 0.938 0.935 0.932 0.929 0.-926·
1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 0.935
1.000 0.995 0.991 0.987 0.983 0.979 0.976 0.972 0.969 0.965 0.962 0.958 0.955 0.952 0.949 0.946 0.943 0.941 0.939 0.937 0.934
1.000 0.996 0.992 0.988 0.984 0.980 0.977 0.973 0.970 0.966 0.963 0.960 0.957 0.953 0.951 0.948 0.945 0.942 0.940 0.937 0.934
1.000 0.996 0.992 0.988 0.984 0.981 0.977 0.974 0.971 0.968 0.965 0.961 0.958 0.956 0.953 0.950 0.948 0.945 0.942 0.940 0.938
1.000 0.996 0.922 0.988 0.984 0.981 0.977 0.974 0.971 0.967 0.964 0.961 0.958 0.956 0.953 0.950 0.948 0.945 0.943 0.940 0.938
1.000 0.995 0.990 0.987 0.983 0.979 0.976 0.973 0.969 0.965 0.962 0.959 0.956 0.952 0.950 0.947 0.944 0.942 0.939 0.937 0.935
1.000 0.995 0.992 0.988 0.985 0.981 0.978 0.974 0.971 0.968 0.965 0.962 0.959 0.956 0.953 0.950 0.947 0.945 0.942 0.940 0.938
1.000 0.996 0.993 0.990 0.987 0.984 0.981 0.977 0.975 0.972 0.969 0.966 0.964 0.961 0.958 0.956 0.954 0.951 0.949 0.947 0.945
III trJ ;> "'3
TABLE
4d-l0. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
Cu-Ag system [33]
Co-Fe system [33]
(Continued)
Cu-AI system [33]
Cu-Au system [33]
Pressure,
kilo bars 100 Co
59.06 Co 40.94 Fe
100 Fe
100 Cu
96.0 Cu 4.0 Ag
100 Cu
90.02 Cu 9.90 Al
100 Cu
93 Cu 7 Au
0 2 4 6 8
1.000 0.998 0.997 0.996 0.995
1.000 0.998 0.997 0.996 0.995
1.000 0.998 0.997 0.996 0.995
1.000 0.998 0.997 0.995 0.994
1.000 0.998 0.996 0.995 0.993
1.000 0.998 0.997 0.995 0.994
1.000 0.998 0.997 0.995 0.994
1.000 0.998 0.997 0.995 0.994
l.000 0.998 0.996 0.995 0.993
10 12 14 16 18
0.994 0.993 0.992 0.991 0.990
0.994 0.993 0.992 0.991 0.990
0.993 0.992 0.991 0.990 0.989
0.992 0.990 0.989 0.987 0.986
0.992 0.990 0.988 0.987 0.986
0.992 0.990 0.989 0.987 0.986
0.993 0.991 0.990 0.988 0.987
0.992 0.990 0.989 0.987 0.986
0.992 0.991 0.990 0.988 0.987
20 22 24
0.989 0.988 0.987
0.989 0.987 0.986
0.988 0.987 0.986
0.984 0.983 0.982
0.984 0.983 0.982
0.984 0.983 0.982
0.985 0.984 0.983
0.984 0.983 0.982
26 28 30
0.986 0.985 0.984
0.985 0.984 0.983
0.985 0.984 0.983
0.980 0.979 0.978
0.980 0.979 0.978
0.980 0.979 0.978
0.980 0.979 0.978
0.980 0.979 0.978
I
85 Cu 15 Au
75 Cu 25 Au
1.000 0.998 0.997 0.995 0.994
1.000 0.998 0.997 0.995 0.994
b
0.993 0.992 0.990 0.989 0.988
0.993 0.991 0.990 0.989 0.987
0.985 0.984 0.982
0.987 0.985 0.984
0.986 0.985 0.984
0.981 0.980 0.979
0.983 0.982 0.980
0.983 0.981 0.980
b
o
o
:s; '"ti
:r.J ~
m m
tti
H
t:-
-3
>1
c
-
-
* For references see p. b c
4-96. Slight discontinuity here. Transition in this region.
t
'1
i-'
t
--:( ~
TABLE
-
4d-IO. VIVo
I Pressure,
CU3Au
kilo bars
[13]
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
1.000 0.99\) 0.997 0.9\)6 0.995 0.993 0.992 0.990 0.989 0.988 0.986 0.985 0.984 0.983 0.982 0.980
Cu-Cr system [37]
Cu-Ga system [33]
(Continued)
Cu-Ge system [33]
Cu-Mn system' [37]
Cu 5 Cd 8 R.T.
[13]
100 Cu
99.818 eu 0.182 Cr
100 Cu
95.85 Cu 4.15 Ga
100 Cu
98.2\) Cu 1.71 Ge
100 Cu
95.40 Cu 4.60 Mn
90.86 Cu 9.14 Mn
1.000 0.997 0.995 0.992 0.990 0.988 0.985 0.983 0.981 0.978 0.975 0.973 0.971 0.969 0.966 0.964
1.000 0.998 0.997 0.995 0.9\)4 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
1.000 0.998 0.997 0.9\)5 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
1.000 0.998 0.9\)7 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
1.000 0.998 0.997 0.995 0.994 0.992 0.991 0.989 0.988 0.987 0.985 0.984 0.982 0.981 0.980 0.978
1.000 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
1.000 0.998 0.997 0.995 0.993 0.992 0.990 0.989 0.988 0.986 0.985 0.\)84 0.982 0.981 0.980 0.979
1.000 0.998 0.997 0.995 0.994 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
1.000 0.9\)8 0.9\)7 0.\)\)5 0.994 0.992 0.991 0.989 0.988 0.987 0.985 0.984 0.982 0.981 0.980 0.978
1.000 0.998 0.996 0.995 0.993 0.992 0.990 0.989 0.987 0.986 0.984 0.983 0.981 0.980 0.978 0.977
- _ ... _ - - - - - - - - - -
* For references see p. 4-96.
OF ALI,OYS AND INTERMETALLIC COMPOUNDS*
-----
--_ .. _-
~
t9
>-
>-3
TABLE
4d-lO. V IVa
OF ALLOYS AND IN'rERMETALLIC COMPOUNDS*
Cu-Pd system [37]
Cu-Ni system [33]
(Continued)
Cu-Pt system [37]
Cu-Si system [33]
Pressure,
kilobars
100 Cu
100 Cu
89.86 Cu 10.14 Si
1.000 0.998 0.996 0.995 0.994 0.993
1.000 0.998 0.997 0.995 0.994 0.992
1.000 0.998 0.996 0.995 0.993 0.992
1.000 0.998 0.997 0.995 0.994 0.992
1.000 0.998 0.996 0.995 0.994 0.992
1. 000 0.998 0.996 0.994 0.992 0.991
0.990 0.989 0.987 0.986 0.984 0.983 0.982
0.991 0.990 0.988 0.987 0.986 0.985 0.983
0.989 0.987 0.985 0.984 0.983 0.981 0.980
0.980 0.979 0.978
0.982 0.981 0.980
0.978 0.976 0.974
100 Cu
1.000 0.998 0.997 0.995 0.994 0.992
100 Cu
60 Cu 40 Ni
50 Cu 50 Ni
0 2 4 6 8 10
1.000 0.998 0.997 0.995 0.994 0.992
1.000 0.998 0.996 0.995 0.993 0.992
1.000 0.998 0.997 0.996 0.995 0.993
1.000 0.999 0.998 0.996 0.995 0.994
1.000 0.999 0.998 0.997 0.996 0.995
12 14 16 18 20 22 24
0.990 0.989 0.987 0.986 0.984 0.983 0.982
0.991 0.989 0.988 0.987 0.986 0.985 0.984
0.992 0.991 0.990 0.988 0.987 0.986 0.985
0.993 0.991 0.990 0.989 0.988 0.987 0.986
0.993 0.992 0.991 0.990 0.988 0.987 0.986
0.990 0.989 0.987 0.986 0.984 0.983 0.982
0.991 0.990 0.988 0.987 0.986 0.984 0.983
0.990 0.989 0.987 0.986 0.984 0.983 0.982
0.991 0.990 0.989 0.987 0.986 0.985 0.984
26 28 30
0.980 0.979 0.971>
0.983 0.982 0.981
0.984 0.982 0.981
0.985 0.983 0.982
0.985 0.985 0.984
0.980 0.979 0.978
0.982 0.980 0.979
0.980 0.979 0.978
0.982 0.981 0.980
100 Ni
CU31Sn S [13]
98.662 Cu 1.338 Pt
95.91 Cu 4.09 Pd
40 Cu 60 Ni
s
Cl
o
~
>ti ;:0.
t'=J
7Jl 7Jl
t;J
H
t' H >-3
kj
b
* For references see p. 4-96. Slight discontinuity here. , Cusp at 10.1.
b
t ""
C;.j
t TABLE
4d-IO. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
Ou-Zn system [33] Pressure. kilobars
~---
800u 20 Zn
52.7Ou 47.3 Zn
0 2 4 6
1.000 0.998 0.997 0.995
1.000 0.998 0.996 0.995
1.000 0.998 0.996 0.994
1.000 0.997 0.995 0.993
1.000 0.998 0.996 0.994
1.000 0.998 0.996 0.994
8 10
0.994 0.992
0.993 0.992
0.992 0.991
0.992 0.990
0.992 0.990
0.991 0.990
--
* For references see p. 4-96. t U
OU6Zns [13]
900u 10 Zn
0.990 0.989 0.987 0.986 0.984 0.983 0.982 0.980 0.979 0.978
Cusp at 6.8; volume 0.996. Cusp at 1l.0; volume 0.99l.
0.990 0.989 0.988 0.986 0.985 0.983 0.982 0.981 0.980 0.978 -----_.-
0.989 0.988 0.986 0.985 0.983 0.982 0.980 0.979 0.978 0.976
Fe-Si system [33]
Fe-Ni alloys [37] OuZn [13]
1000u
12 14 16 18 20 22 24 26 28 30
"""
(Continued)
0.988 0.986 0.985 0.983 0.982 0.980 0.978 0.977 0.976 0.975
0.989 0.987 0.985 0.984 0.982 0.981 0.979 0.977 0.976 0.974
0.988 0.986 0.984 0.982 0.980 0.978 0.976 0.975 0.973 0.972 -----
85 ..58 Fe 14.42 Ni
76.16 Fe 23.84 Ni
63.0 Fe 37.0 Ni
100 Fe
94.25 Fe 5.75 Si
1.000 0.998 0.997 0.996 t 0.994 0.993
1.000 0.999 0.997 0.996
1.000 0.998 0.996 0.994
1.000 0.998 0.997 0.996
1.000 0.999 0.997 0.996
0.994 0.993
0.993 0.991 u 0.990 0.988 0.986 0.985 0.983 0.982 0.980 0.978 0.977 0.975
0.995 0.994
0.995 0.994
II:
0.993 0.992 0.991 0.900 0.989 0.988 0.987 0.986 0.985 0.984
8
0.992 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983 0.982 --
0.992 0.991 0.990 0.988 0.987 0.986 0.985 0.984 0.983 0.982
t;J
~
0.993 0.992 0.990 0.989 0.988 0.987 0.986 0.985 0.984 0.983 --
TABLE
4d-IO. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
(Continued) ---
Li-Mg system [36]
In-Ph system [36] Pressure, kilohars
75 In 25 Pb
100 In
50 In 50 Ph
25 In 75 Ph
,-
100 Ph
100 Li
80 Li 20 Mg
60 Li 40 Mg
40 Li 60 Mg
20 Li 80 Mg
Martensite [13] 100 Mg •
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
1.000 0.995 0.990 0.985 0.980 0.975 0.971 0.966 0.962 0.958 0.954 0.950 0_947 0.943 0.939 0.936 0_933 0.930 0.927 0.923 0.921
1.000 0.995 0.990 0.985 0_981 0.976 0.972 0.968 0.963 0.959 0.955 0.952 0.948 0.944 0.940 0.937 0.933 0.930 0.927 0.923 0_921
1.000 0_995 0.990 0.985 0.980 0.975 0.971 0.967 0_963 0_959 0.955 0.952 0.948 0.945 0.941 0.938 0.934 0_ 931 0.928 0.925 0.922
1.000 0_995 0.990 0.985 0_981 0.977 0.972 0.968 0.965 0.961 0_957 0.954 0.950 0.947 0.943 0.940 0_937 0.934 0.931 0.928 0.925
1.000 0.995 0.990 0_986 0.982 0.978 0_974 0_970 0.966 0_962 0.958 0.954 0.951 0.947 0.944 0_941 0.937 0.935 0.932 0.929 0.927
1.000 0.982 0.967 0.954 0.940 0.927 0.915 0_904 0.892 0.882 0.872 0.862 0.853 0.845 0.835 0.828 0.820 0.813 0.807 0.800 0.794
1.000 0.987 0_975 0.963 0.952 0.941 0.931 0.921 0.911 0.902 0.893 0.885 0.877 0.869 0.862 0.855 0.848 0.841 0.835 0.830 0.825
1.000 0.990 0.980 0.970 0.961 0.953 0.944 0.936 0.928 0.920 0.914 0.906 0.900 0.894 0.888 0.882 0.877 0.872 0.866 0.861 0.856
1.000 0.992 0.984 0.977 0.969 0.962 0.955 0_948 0.942 0.935 0.929 0.924 0.918 0.913 0.908 0.903 0.899 0.895 0.890 0.887 0.884
1.000 0.993 0.985 0.978 0.971 0.965 0.959 0.953 0.947 0.941 0.935 0.930 0.925 0.920 0.915 0_910 0.906 0.902 0.898 0.894 0.890
1.000 0.994 0.988 0.983 0.977 0.973 0.968 0.963 0.958 0.953 0.949 0.944 0.940 0,936 0.932 0.929
_ _ _ , __
-
1.000 0.998 0.997 0.996 0.995 0.994 0.992 0_991 0.990 0.989 0.987 0.986 0.985 0_984 0.983 0.982
-
>_"H
o
o
~
~
t9
[J2 [J2
td
H
t-
-'3
kj
._-
* For references see p. 4-96.
t
;:I
t
....:t 0:. TABLE
4d-10. VIVo
Ni-Mn system [33] Pressure, kilobars
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 -
OF ALLOYS AND INTERMETALLIC COMPOUNDS* (Continued)
Pb-Sb system [36]
Ni-Si system [33]
35% Ni 65% Fe [13]
100 Ni
71.0 Ni 29.0 Mn
100 Ni
94.2 Ni 5.8 Si
1.000 0.998 0.996 0.994 0.992 0.990 0.988 0.986 0.985 0.983 0.982 0.981 0.979 0.978 0.977 0.975
1.000 0.999 0.998 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.984
1.000 0.998 0.997 0.995 0.994 0.993 0.991 0.990 0.989 0.987 0.986 0.985 0.983 0.982 0.981 0.979
1.000 0.999 0.998 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.984
1.000 0.998 0.997 0.996 0.995 0.994 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.985
1.000 0.998 0.997 0.996 0.994 0.993 0.992 0.991 0.990 0.989 0.988 0.987 0.986 0.985 0.985 0.984
.... . .... . .... . .... . .. .. ,
. .... . .... .... . , .... .....
....
. .... .... . . .... .... . . ....
. .... . ....
..... ..... . .... ..... . ....
---
* For references Bee p. 4-96.
Nirex [13]
,
. .... ..... . .... . ....
. .... . .... .....
100 Pb
80 Pb 20 Sb
60 Pg 40 Sb
40 Pb 60 Sb
20 Pb 80 Sb
100 Sb
1.000 0.995 0.990 0.986 0.982 0.978 0.974 0.970 0.966 0.962 0.958 0.955 0.951 0.948 0.944 0.941 0.938 0.935 0.932 0.929 0.927
1.000 0.995 0.990 0.985 0.980 0.976 0.972 0.968 0.964 0.960 0.956 0.953 0.949 0.946 0.943 0.940 0.937 0.934 0.931 0.928 0.925
1.000 0.995 0.990 0.986 0.982 0.977 0.973 0.969 0.965 0.961 0.957 0.953 0.950 0.946 0.943 0.940 0.936 0.933 0.930 0.927 0.925
1.000 0.995 0.990 0.985 0:980 0.976 0.972 0.968 0.964 0.960 0.957 0.953 0.950 0.947 0.943 0.941 0.938 0.935 0.932 0.929 0.927
1.000 0.995 0.991 0.986 0.982 0.978 0.973 0.969 0.965 0.962 0.958 0.955 0.951 0.948 0.945 0.941 0.938 0.936 0.933 0.930 0.928
1.000 0.995 0.990 0.985 0.980 0.976 0.972 0.967 0.963 0.959 0.955 0.951 0.947 0.944 0.940 0.937 0.933 0.930 0.927 0.925 0.922
~
~
1-:3
TABLE
4d-1O. V /VO Pb~Sn
Pressure, kilobars
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
system [36]
(Continued)
Pb-Zn system [36]
100 Ph
75 Pb 25 Sn
50 Pb 50 Sn
25 Pb 75 Sn
100 Sn
1.000 0.995 0.990 0.986 0.982 0.978 0.974 0.970 0.966 0.962 0.958 0.955 0.951 0.948 0.944 0.941 0.938 0.935 0.932 0.929 0.927
1.000 0.995 0.990 0.986 0.982 0.978 0.975 0.971 0.967 0.964 0.960 0.957 0.953 0.950 0.947 0.943 0.9:10 0.937 0.934 0.932 0.929
1.000 0.996 0.991 0.987 0.983 0.979 0.975 0.972 0.968 0.965 0.962 0.958 0.956 0.953 0.950 0.947 0.944 0.942 0.939 0.937 0.934
1.000 0.996 0.992 0.988 0.984 0.980 0.977 0.973 0.970 0.966 0.963 0.960 0.957 0.953 0.950 0.948 0.945 0.942 . 0.940 0.937 0.935
1.000 0.996 0.992 0.988 0.985 0.981 0.978 0.975 0.972 0.968 0.965 0.962 0.959 0.956 0.953 0.951 0.948 0.945 0.943 0.941 0.939
100 Pb
50 Ph 50 Zn
100 Zn
1.000 0.995 0.990 0.986 0.982 0.978 0.974 0.970 0.966 0.962 0.958 0.955 0.951 0.948 0.944 0.941 0.938 0.935 0.932 0.929 0.927
1.000 0.996 0.992 0.988 0.984 0.980 0.976 0.972 0.969 0.965 0.962 0.959 0.955 0.952 0.949 0.946 0.943 0.941 0.938 0.935 0.933
1.000 0.997 0.993 0.990 0.987 0.985 0.982 0.978 0.976 0.973 0.970 0.967 0.965 0.962 0.959 0.957 0.954 0.952 0.950 0.947 0.945
SbSn [13]
Sb,Th [13]
1.000 0.995 0.991 0.987 0.983 0.979 0.976 0.972 0.969 0.966 0.962 0.959 0.956 0.953 0.950 0.947
1.000 0.994 0.988 0.983 0.978 0.973 0.968 0.964 0.959 0.955 0.951 0.947 0.943 0.939 0.935 0.932
Q
o
ts:
~
Ul Ul
tdH
t"'
H
~
--
'" For references see p. 4-96.
t
--l --l
TABLE
4d-1O. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
Pressure, kilobars
00
,!,l~:Ili sy~tem [38]
Stainless steel. [13] . -
Sn-Zn system [36]
..
t
(Continued)
100 Sn
80 Sn 20 Zn
50 Sn 50 Zn
20 Sn 80 Zn
100 Zn
H26:j:
H29§
100 Tl
80 Tl 20 Bi
50 Tl 50 Bi
20 Tl 80 Bi
100 Bi
8 10 12 14 16 18 20 22 24
1.000 0.996 0.992 0.988 0.984 0.981 0.977 0.974 0.970 0.967 0.964 0.961 0.958
1.000 0.996 0.992 0.989 0.985 0.981 0.978 0.974 0.971 0.968 0.965 0.962 0.958
1.000 0.996 0.993 0.990 0.986 0.983 0.979 0.976 0.973 0.970 0.967 0.963 0.960
1.000 0.996 0.993 0.989 0.986 0.982 0.979 0.976 0.973 0.970 0.967 0.963 0.961
1.000 0.996 0.993 0.990 0.987 0.983 0.980 0.977 0.975 0.972 0.969 0.966 0.963
1.000 0.999 0.997 0.996 0.995 0.994 0.993 0.992 0.990 0.989 0.988 0.987 0.986
1.000 0.999 0.997 0.996 0.995 0.994 0.992 0.991 0.990 0.989 0.988 0.986 0.985
1.000 0.994 0.989 0.984 0.979 0.974 0.969 0.964 0.960 0.955 0.951 0.947 0.943
1.000 0.994 0.989 0.984 0.979 0.974 0.969 0.965 0.960 0.956 0.951 0.947 0.943
1.000 0.994 0.989 0.984 0.979 0.974 0.969 0.965 0.960 0.956 0.952 0.948 0.944
1.000 0.994 0.989 0.983 0.978 0.974 0.968 0.964 0.960 0.955 0.951 0.947 0.942
1.000 0.993 0.987 0.981 0.976 0.970 0.965 0.961 0.956 0.952 0.948 0.944 0.940
v
c
26 28 3.0 32 34 36 38 40
0.955 0.952 0.950 0.947 0.945 0.942 0.940 0.938
0.956 0.953 0.950 0.947 0.945 0.942 0.940 0.938
0.957 0.954 0.952 0.949 0.947 0.944 0.942 0.939
0.958 0.955 0.952 0.950 0.947 0.945 0.942 0.940
0.961 0.958 0.956 0.953 0.951 0.949 0.947 0.945
0.985 0.984 0.983
0.984 0.983 0.982
.... ..... ..... ..... .....
. .... . ....
0.938 0.934 0.930 0.926 0.923 0.919 0.915 0.912
0.939 0.936 0.932 0.928 0.925 0.922 0.918 0.915
0.940 0.936 0.933 0.930 0.926 0.923 0.920 0.917
0.902 0.898 0.895 0.892 0.889 0.886 0.883 0.881
0.902 0.899 0.896 0.893 0.890 0.887 0.885 0.882
0
.2 4 U
* For ~eferences Bee p.
.
. ....
. .... . ....
4-96.
t Stainless steel H26: 0.094 C, 0.36 Mn, 0.023 P, 0.022 S, 0.35 Si, 12.26 Cr, 0.46 Ni, 0.50 Mo, N.D. Cu. § Stainless steel H29: 0.058 C, 0.70 Mn, 0.030 P, 0.013 S, 0.85 Si, 18.51 Cr, 8.95 Ni, N.D. Mo, 0.20 Cu . • Volumes at 24.5: phase I = 0.942, phase II = 0.921, phase III = 0.905. c Transition in this region.
P:i
trJ
~
>-3
TABLE
4d-IO. VIVo
OF ALLOYS AND INTERMETALLIC COMPOUNDS*
(Continued)
Tl-Cd system [38] Pressure, kilo bars
0 2 4 6 8 10
TI-In system [38]
100 Tl
80 Tl 20 Cd
60 Tl 40 Cd
40 Tl 60 Cd
20 Tl 80 Cd
100 Cd
100 Tl
77 Tl 23 In
50 Tl 50 In
20 Tl 80 In
100 In
1.000 0.994 0.989 0.984 0.979 0.974
1.000 0.995 0.990 0.985 0.980 0.975
1.000 0.995 0.990 0.986 0.981 0.977
1.000 0.995 0.990 0.986 0.981 0.977
1.000 0.996 0.991 0.987 0.983 0.979
1.000 0.995 0.991 0.987 0.983 0.979
1.000 0.994 0.989 0.984 0.979 0.974
1.000 0.994 0.988 0.983 0.977 0.973
1.000 0.995 0.990 0.985 0.980 0.975
1.000 0.995 0.990 0.985 0.980 0.975
1.000 0.995 0.990 0.985 0.981 0.976
0.971 0.966 0.962 0.958 0.954 0.950 0.946 0.942 0.938 0.934 0.931 0.927 0.924 0.921 0.918
0.970 0.966 0.961 0.957 0.953 0.949 0.945 0.942 0.938 0.935 0.932 0.928 0.925 0.922 0.919
0.972 0.967 0.963 0.958 0.954 0.950 0.946 0.943 0.939 0.936 0.932 0.929 0.926 0.922 0.920
w
12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.969 0.964 0.960 0.955 0.951 0.947 0.943 0.938 0.934 0.930 0.926 0.923 0.919 0.915 0.912
0.970 0.965 0.960 0.956 0.952 0.948 0.944 0.940 0.936 0.933 0.930 0.926 0.923 0.921 0.918
0.972 0.968 0.963 0.959 0.955 0.951 0.947 0.943 0.940 0.936 0.932 0.929 0.925 0.922 0.919
* For references see p. 4-96 . .. Transition at 11.5: volumes 0.969 and 0.963.
0.972 0.968 0.963 0.960 0.956 0.952 0.948 0.945 0.941 0.938 0.934 0.932 -0.928 0.926 0.923
0.975 0.971 0.967 0.963 0.959 0.956 0.952 0.949 0.946 0.942 0.939 0.936 0.933 0.931 0.928
0.976 0.972 0.969 0.966 0.962 0.959 0.956 0.953 0.950 0.948 0.945 0.942 0.940 0.937 0.935
0.969 0.964 0.960 0.955 0.951 0.947 0.943 0.938 0.934 0.930 0.926 0.923 0.918 0.915 0.912
0.962 0.958 0.954 0.950 0.945 0.941 0.937 0.933 0.930 0.926 0.923 0.920 0.916 0.913 0.910
Q
o
l$: '"d
~
"(fJ "(fJ
b:lH
§
t
~ ~
t00 o
TABLE
4d-1O. V /VO OF ALLOYS AND INTERMETALLIC COMPOUNDS * (Continued)
Tl-Sn system [38]
Tl-Pb system [38] Pressure, kilobars
0 2
4
6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 -
100 Tl
80 Tl 20 Pb
60Tl 40 Pb
40 Tl 60 Pb
20 Tl 80 Pb
100 Pb
100 Tl
80 Tl 20 Sn
60 Tl 40 Sn
40 Tl 60 Sn
20 Tl 80 Sn
100 Sn
1.000 0.994 0.989 0.984 0.979 0.974 0.969 0.964 0.960 0.955 0.951 0.947 0.943 0.938 0.934 0.930 0.926 0.923 0.919 0.915 0.912
1.000 0.994 0.989 0.984 0.979 0.974 0.970 0.965 0.961 0.956 0.952 0.948 0.945 0.940 0.937 0.933 0.929 0.926 0.923 0.920 0.917
1.000 0.995 0.990 0.985 0.981 0.976 0.972 0.967 0.963 0.958 0.954 0.950 0.947 0.942 0.938 0.935 0.931 0.928 0.924 0.921 0.918
1.000 : 0.995 . 0.990 ' 0.986 0.981 .0.977 0.972 0.968 0.963 0.959 0.955 .0.951 ,0.947 0.943 0.939 0.935 0.932 0.928 0.925 0.922 0.919
1.000 0.995 0.990 0.986 0.981 0.977 0.973 0.968 0.964 0.961 0.957 0.953 0.949 0.945 0.942 0.938 0.935 0.931 0.928 0.925 0.922
1.000 0.995 0.990 0.986 0.982 0.977 0.973 0.969 0.965 0.962 0.958 0.954 0.951 0.947 0.944 0.941 0.938 0.935 0.933 0.930 0.927
1.000 0.994 0.989 0.984 0.979 0.974 0.969 0.964 0.960 0.955 0.951 0.947 0.943 0.938 0.934 0.930 0.926 0.923 0.919 0.915 0.912
1.000 0.!i94 0.989 0.984 0.979 0.975 0.970 0.966 0.961 0.957 0.953 0.949 0.945 0.942 0.938 0.935 0.931 0.928 0.925 0.922 0.919
1.000 0.995 0.991 0.987 0.982 0.978 0.973 0.969 0.965 0.961 0.957 0.953 0.950 0.946 0.942 0.939 0.936 0.932 0.929 0.926 0.923
1.000 0.995 0.991 0.986 0.982 0.978 0.973 0.970 0.966 0.962 0.959 0.955 0.952 0.949, 0.946 0.942 0.939 0.936 0.933 0.931 0.928
1.000 i 0.996 . 0.992 i 0.987 0.984 0.980 0.976 i 0.972 0.969 0.966 0.962 0.959 0.956 0.953 0.950 0.947 0.944 0.941 0.938 0.936 0.933
1.000 0.996 0.992 0.988 0.985 0.981 0.977 0.974 0.971 0.968 0.964 0.961 0.958 0.956 0.953 0.950 0.947 0.945 0.943 0.941 0.938
---
* For references Bee p. 4-96.
----
'---
------
tIl t;j
~
TABLE
Pressure, kilo bars
Ethyl acetate
[3]
Acenapathylene
Acetone
[23]
[24]
4d-ll. VIVo
OF ORGANIC COMPOUNDS*
Ethyl alcohol
Methyl alcohol
Propyl alcohol
c-Propyl alcohol
n-Amyl iodide
Amyl alcohol
n-Amyl bromide
n-Amyl chloride
n-Amyl ether
[23]
[23]
[23]
[26]
[25]
[23]
[25]
[25]
[24]
1.000 0.888 0.843 0.810 0.786 0.766 a 0.728 0.719 0.710 0.702 0.695 0.688 0.680 0.674 0.668 0.662 0.657 0.652 0.647 0.643 0.639
1.000 0.975 0.955 0.937 0.923 0.910
1.000 0.885 0.831 0.795 0.768
10
1.000 0.887 0.830 0.795 0.770 0.750
1.000 0.893 0.831 0.795 0.769 0.749
1.000 0.892 0.836 0.797 0.771 0.752
1.000 0.895 0.854 0.825 0.802 0.785
1.000 0.906 0.853 0.820 0.798 0.780
1.000 0.915 0.860 0.830 0.806 0.787
1.000 0.888 0.842 0.816 0.796 0.777
1.000 0.907 0.860 0.828 0.802 0.782
1.000 0.892 0.844 0.815 0.792 0.773
12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.736 0.724 0.713 0.704 0.695 0.687 0.680 0.672 0.666 0.660 0.654 0.649 0.643 0.639 0.635
0.899 0.888 0.879 0.871 0.863 0.856 0.849 0.843 0.838 0.832 0.827 0.822 0.818 0.813 0.808
.... . .... .
0.735
0.737
0.769
.... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .
..... .... . .... . . .... .... . .... . .... . .... . .... . .... . . .... . .... .... . .... . .... .
0.761
. . .. . .... .
. .... ..... ..... ..... .....
0 2 4 6 8
.....
.... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .
.... . .... . .... .
.... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .
.... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .
.... . .... . . . .. . ..... .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .
.... ... . .... . . .... .... . .... . .... . .... . .... . .... . .... . .... . .... . . .... ,
.... . . .... .... . .... . .... . .... . .... . .... .
. ....
.... . . .... . . .. . .....
.....
..... ..... ..... ..... .....
..... ..... . .... . ....
o
o
~ >0
~
U2 U2
ttl>-< t-
'3
>1
* For references see p. 4-96. a
Freezes at 10.8; volumes 0.776 and 0.755.
t
00
i-'
TABLE
Nitroaniline [5] Pressure, kilobars
*
4d-ll. V jVo
OF ORGANIC COMPOUNDS*
t
b:l
(Continued) Diphenylbenzene [5] ortho-
meta-
para-
Hexaethylbenzene [24]
1.000 0.974 0.950 0.930
1.000 0.974 0.950 0.931
1.000 0.974 0.950 0.931
1.000 0.980 0.960 0.940
0.784 0.772 0.759 0.748 0.738 0.730 0.722 0.715 0.708 0.703 0.697
0.912 0.896 0.884 0.872 0.862 0.852 0.845 0.837 0.830 0.823 0.817
0.917 0.905 0.893 0.883 0.874 0.865 0.857 0.849 0.842 0.835 0.829
0.917 0.905 0.894 0.884 0.875 0.867 0.860 0.853 0.846 0.840 0.834
0.692 0.687 0.683 0.679 0.675 0.672
0.812 0.805 0.800 0.796 0.792 0.789
0.824 0.818 0.813 0.808 0.805 0.801
0.830 0.823 0.818 0.814 0.809 0.805
0.923 0.908 0.895 0.883 0.872 0.862 0.853 0.845 0.837 0.830 0.823 c 0.807 0.802 0.798
Anthracene [24]
Anthraquinone [6]
Benzene [24]
Bromobenzene [26]
Chlorobenzene [24]
ortho-
meta-
para-
0 2 4 6
1.000 0.983 0.967 0.952
1.000 0.980 0.964 0.948
1.000 0.977 0.960 0.944
1.000 0.972 0.951 0.935
1.000 0.978 0.961 0.947
1.000 0.857 0.805 0.770
1.000 0.930 · .... .....
1.000 0.895 0.860 0.834
8 10 12 14 16 18 20 22 24 26 28
0.939 0.928 0.917 0.907 0.898 0.890 0.883 0.876 0.870 0.865 0.859
0.935 0.924 0.913 0.903 0.895 0.887 0.880 0.872 0.866 0.860 0.854
0.931 0.920 0.910 0.900 0.892 0.884 0.877 0.869 0.863 0.857 0.851
0.920 0.910 0.898 0.888 0.880 0.872 0.865 0.857 0.851 0.845 0.838
0.935 0.924 0.915 0.906 0.898 0.890 0.883 0.877 0.871
0.745 0.725 0.712 0.700 0.699 0.682 0.675 0.667 0.660 0.654 0.648
..... · .... ..... .. '" , .... · .... ..... · .... · .... ..... · ....
30 32 34 36 38 40
0.853 0.849 0.845 0.840 0.837 0.832
0.848 0.843 0.838 0.833 0.829 0.825
0.845 0.840 0.835 0.830 0.826 0.821
0.832 0.827 0.822 0.817 0.812 0.808
0.644 0.638 0.634 0.630 0.625 0.622
..... ..... ., ... .....
b
For references see p. 4-96. b Freezes at 7.4; volumes 0.817 and 0.788 • • Sluggish transition here, not complete.
....
..
.
'"
•••
0
•
.... . .... . ..... .. ... .. ...
, . '"
.....
II: to! i>
1-3
TABLE
Nitrobromobenzene [5] Pressure, kilobars
4d-ll. VIVo
OF ORGANIC COMPOUNDS*
Nitrochlorobenzene [51
(Continued)
Nitroiodobenzene [5]
Aminobenzenesulfonic acid [5] Benzil ,. [5]
ortho-
meta-
para-
ortho-
para-
ortho-
meta-
para-
ortho-
meta-
para-
0 2
1.000 0.970
1.000 0.980
1.000 0.975
1.000 0.970
1.000 0.970
1.000 0.973
1.000 0.975
1.000 0.975
1.000 0.983
1.000 0.987
4 6
0.950 0.935
0.962 0.946
0.957 0.942
0.944 0.920
0.949 0.930
0.953 0.937
0.957 0.942
0.956 0.940
0.968 0.955
0.976 0.965
1.000 0.985 f 0.949 0.935
e
1.000 0.953 0.925 0.904
d
8 10 12 14 16 18 20 22 24 26 -- .. .28-
30 32 34 36 38 40
0.915 0.898 0.885 0.873 0.863 0.855 0.847 0.840 0.832 0.827 0.821 0.816 0.810 __0.80,.6. ,.. 0.802 0.798 I 0.793_
0.933 0.923
0.928 0.915
0.902 0.888
0.915 0.903
0.923 0.910
0.928 0.916
0.926 0.914
0.943 0.932
0.956 0.947
0.916 0.902
0.911 0.901 0.892 0.885 0.877 0.870 0.864 0.858 0.952 0.846 0.841 Q.837 0.832 0.828 0.825
0.905 0.895 0.886 0.877 0.868 0.862 0.855 0.848 0.-842 0.836 0.831 0.. 825 0.820 0.814 0.810
0.875 0.965 0.855 0.846 0.839 0.832 0.825 0.819 0.813 0.810 0.804 0 .. 799. 0.795 0.792 0.787
0.890 0.880 0.871 0.862 0.853 0.846 0.839 0.831 0:825 0.820 0.814 0.809. 0.804 0.800 0.795
0.899 0.888 0.879 0.870 0.863 0.855 0.848 0.842 0.836 0.831 0.825 0.820. 0.815 0.811 0.807
0.905 0.895 0.887 0.879 0.871 0.864 0.857 0.851 0.845 0.840 0.835 0.830 0.826 0.822 0.818
0.903 0.893 0.885 0.877 0.869 0.862 0.855 0.849 {).843 0.838 0.833 0_827 0.823 0.817 0.814
0.922 0.913 0.905 0.897 0.890 0.883 0.876 0.871 {).865 0.861 0.856 0.852 0.848 0.845 0.841
0.940 0.934 0.928 0.922 0.918 0.913 0.908 0.904 0.900 0.897 0.893 0 •.889 0.886 0.883 0.880
0.885 0.873 0.862 0.852 0.843 0.835 0.828 0.821 0.815 0.810 0.805 0.801 0.797 {).793 0.790
0.888 0.874
fJ
0.865 0.855 0.846 0.838 0.831 0.824 0.818 0.812 0.808 . 0 .. 813 0.800 O.79ti . 0.793 0.790 0.787 "
(")
o
is::
~ rFl
m
5j H
t-' >-3
H
>-'
8
TABLE
4d-l1. V /VO
Pressure, kilobars
Cyanamide [5]
nDec·ane [24]
Dextrin [6]
Dextrose [6]
0
1.000
1.000
1.000
1.000
OF ORGANIC COMPOUNDS*
DiDiphenyl ethylene Diphenyl amine glycol [24] [28] [27]
1.000
1.000
1.000
(Continued)
I
n-Dodecane [24]
Ethyl ether [23]
Ethyl bromide [23]
Ethyl chloride [23]
Ethyl iodide [23]
1.000
1.000
1.000
1.000
1.000
k
2
0.985
0.892
0.980
0.990
0.949
0.964
0.964
0.800
0.859
0.910
0.849
0.877
0.964 0.948 0.935 0.923 0.912 0.903 0.895 0.886 0.879 0.872 0.866 0.860
0 .. 980 0.972 0.964 0.956 0.949 0.942 0.935 0.928 0.922 0.916 0.911
0.915
0.939 0.920 0.905 0.891 0.880 0.869 0.860 0.850 0.842 0.834 0.827 0.820 0.813 0.808 0.802 0.797 0.792 0.788 0.784
0.938 0.920 0.914 0.890 0.878
0.783 0.770 0.758 0.747 0.737 0.727 0.719 0.711 0.703 0.696 0.690 0.684 0.628 0.623 0.618 0.615 0.611 0.607 0.604
0.790 0.761 0.734 0.714 0.695
0.830 0.789 0.766 0.746 0.731
0.793 0.761 0.735 0.715 0.695
0.835 0.805 0.779 0.758 0.740
j
4 6
8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.971 0.959 0.947 0.938 0.928 0.920 0.911 0.904 0.897 0.890 0.882 0.876 0.870 0.865 0.859 0.853 0.848 0.843 0.838
0.766 0.756 0.741 0.728 0.717 0.707 0.699 0.690 0.684 0.677 0.672 0.666 0.662 0.657 0.652 0.649 0.645 0.642 0.638
•••
0.
•
•
•
0·0
0
••
•
•• ,0,
. 0.0. •••
0.
. ....
..
•
o
••••
0
••
•• 0
•• '0'
o. '"
0.
......
.....
..
•. '0.
•••
•• , 0 ,
0.
•••
.... . .0.0 .
.....
..... .....
••
0.
'0'
••••
••
·0
•••
0
•
0
•
• 0'0'
o.
•
.. ...
,
,0,
. .... •
••
0
•
..... ..... .0.0 . .0 •. ' •••
0
•
.0.0 . .0
,",
•
·.·0 . .0.0. .0 ' 0 . •••
0
•
.• 0'.
..... . •• 0.
Q
o
~ 'd
P:I
i?'J
1]). 1]).
Ii) H
to
-3
>1
*
For references see p. 4-96. ; Freezes at 3.0; volumes 0.863 and 0.789 • • Freezes at 1.65; volumes 0.916 and 0.813.
t
00 '-l
TAllLE
Pressure, kilobars
0
vIVo
OF ORGANIC COMPOUNDS*
0.829 0.804
'6 8 10
0.782 0.765 0.751
12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.740 0.727 0.717 0.708 0.700 0.693 0.687 0.682 0.677 0 .. 672 0.668 0.666 0.663 0.661 0.660
2
Fluorene [16]
Glycerin [27]
Guanidine suVate [5]
n-Heptane [24]
1.000
1.000
1.000
1.000
1.000
l.000
1.000
1.000
1.000
1.000
1.000
0.948 0.915
0.989 0.978
0.971 0.950
0.975 0.952
0.964 0.935
.....
0.865 0.816
0.918 0.876
0.914 0.865
0.916 0.873
0.912 0.867
0.967 6.957 0.947
0.931 0.915 0.901
0.933 0.917 0.902
0.912 0.893 0.877
0.799 0.755 0.734
0.846
.....
0.842
0.938 0.930 0.923 0.916 0.910 0.904 0.898 0.893 0.887 0.883 0.878 0.873 0.870 0.866 0.862
0.890 0.879 0.869 0.860 0.852 0.844 0.837 0.830 0.824 0.818 0.813 0.808 0.805 0.801 0.798
0.890 0.879 0.868 0.859 0.850 0.842 0.835 0.829 0.824 0.819 0.815 0.812 0.810 0.809 0.808
0.863
· .0 .•
·
..
,.
•••
0
•
•••
0
•
... , .
.... . .... . .... . .... .
.... . · ·.0. .... . · ....
· .... ..... .... .
.... . ....
.
-
* For references see p. 4-96. Freezes at 0.5; volumes 0.967 and 0.870. Three transitions below 4.9. n Transition at 10.3; volumes 0.803 and 0.797. '. Freezes at 11.2; volumes 0.722 and 0.680. I
m
00
3-Methyl- 2-Methyl- 3-Methyl- 2-Methylhephephepheptanol tanol-5 tanol-3 tanol-1 [25] [25] [25] [25]
Fluoranthene [24]
Z
4
:t
(Continued)
Eugenol [27]
Ethylene Ethylene glycol bromide [5] [27]
1.000
4d-l1.
. ..... ...
,
• • '0 •
.. , .. ... , .
..... .. '" ..... ..... ... , . .. '" ..... .. , .. .....
•••
0
•
m 0.818 0.810 0.803 n 0.792 0.786 0.780 0.775 0.770 0.766 0.762 0.757 0.754 0.750 0.747 0.744 0.741 0.738 0.735
0
0.675 0.665 0.655 0.646 0.638 0.630 0.623 0.616 0.610 0.604 0.591 0.594 0.590 0.586 0.583
i:II t:;j
>-"'3
TABLE
Pressure, kilobars
n-Hexane
[26J
Cyclohexane
[24J
Methylcyclohexane
[24J
4d-ll. V IV(I
n-Hexadecane
[24J
OF ORGANIC COMPOT)"NDS*
Hexamethyletletetramine
n-Hexyl alcohol
(Continued)
Iodoform Isoprene
[26J
[5J
[27J
l.000
1.000
1.000
1.000
0.977 0.955 0.937 0.922 0.908 0.896 0.885 0.875 0.865 0.857 0.848 0.841 0.833 0.827 0.820 0.815 0.809 0.804 0.799 0.794
Levulose
[6J
Ethyl dldibenzyl Limonene malonate
Melamine
[24J
[27J
[5J
1.000
1.000
1.000
l.000
0.860 0.819 0.789
0.990 0.981 0.972
0.896 0.853 0.826
0.929
0.983 0.969 0.953
0.764 0.743 0.725
0.963 0.955 0.947 0.940 0.934 0.927 0.920 0.915 0.909
0.806 0.790 0.775 0.763 0.752 0.742 0.733 0.725 0.717 0.711 0.705 0.700 0.695 0.691 0.687 0.683 0.679
. .... . .... . .... . .... . ....
[5J
---0
1.000
1.000
1.000
2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.876 0.823 0.790
..... .... . ..... .....
.... .
..... .... .
....
. .... .
.... . .... . .... . .... . .... .
.... . .. , .. .... .
0.862 0.825 0.799
1.000 r
p
0.886 0.840 0.810
0.828 0.803 0.783
0.980 0.962 0.947
0.918
0.786 0.767 0.751 0.737 0.725 0.715 0.706 0.698 0.690 0.684 0.677 0.672 0.666 0.660 0.655 0.650 0.646
0.768 0.755 0.744 0.735 0.725 0.717 0.710 0.703 0.697 0.692 0.698 0.682 0.678 0.674 0.670 0.666 0.663
0.935 0.925 0.915 0.906 0.898 0.890 0.883 0.876 0.870 0.863 0.857 0.851 0.845 0.840 0.836 0.831 0.827
. ....
.....
.... .
q
0.747 0.729 0.715 0.704 0.694 0.685 0.678 0.672 0.665 0.660 0.655 0.650 0.645 0.641 0.637 0.633 0.630
..... ..... . .... .....
. .... ..... .....
..... ..... ..... .... . .... . .... . .....
..... .... .
. .... . .... . .... . .... . .... . .... . .... . .... . .... . .... .... . . .... .... . .....
. .... . .... ..... ..... ..... . .... . .... . ....
. .... .....
.
.. ..
. .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . ....
0.947 0.938 0.929 0.921 0.914 0.907 0.900 0.894 0.888 0.882 0.877 0.872 0.867 0.864 0.860 0.856 0.852
o
o
~ >-0 ~
l'OI
U1 U1
td H
t-'
H
f-3
>-
-----
* For references see p.
4-96. P Freezes at 0.3; volumes 0.967 and 0.926. (Volume liquid = 0.977,t 0.2.) q Transition at 7.4; volumes 0.784 and 0.757. r Freezes at 0.4; volumes 0.970 and 0.861.
t
00
CD
TABLE
Pressure, kilobars
Menthol [6]
Mesitylene [24]
Triphenylmethane [24]
4d-l1. V /VO
Methylamine hydrochloride [5]
OF ORGANIC COMPOUNDS*
I
Methylene Morpholine chloride hydrogen [24] tartrate [5]
Naphthalene [24]
(Continued)
I ,3-Methylnaphthalene [24]
I
Tetrahydro- n-Octane 180- n-Octaoctane cosane naphtha[24] [27] [24] lene [24]
!o
--1.000 0.883
1.000 0.893
1.000 0.955
0.835
0.930
0.813 0.800 0.788 0.777
0.828 x 0.750 0.725 0.707 0.695
0.803
0.912 0.896 0.883 0.872
0.856 0.845 0.835 0.826 0.818 0.810
0.768 0.760 0.751 0.744 0.737 0.731
0.683 0.674 0.665 0.658 0.650 0.645
..... .....
0.803 0.797 0.790 0.785 0.779 0.774 0.770 0.765
0.725 0.720 0.715 0.710 0.706 0.702 0.798 0.795
0.639 0.634 0.630 0.625 0.621 0.618 0.615 0.611
1.000 0.974
1.000 0.982
1.000 0.910
1.000 0.985
1.000 0.970
1.000 0.965
1.000 0.926
0.825
0.952
0.860
0.971
0.946
0.937
0.829
0.921 0.905 0.888 0.875
0.802 0.784 0.764 0.756
0.935 0.919 0.906 0.893
0.967 t 0.900 0.890 0.880 0.871
0.959 0.949 0.939 0.930
0.928 0.912 0.899 0.887
0.915 0.896 0.881 0.868
0.861 0.849 0.837 0.826 0.816 0.806
0.745 0.735 0.725 0.717 0.:710 0.702
0.883 0.1l72 0.862 0.854 0 ..845 0.838
0.862 0.853 0.845 0.838 0.830 0.823
0.819 0.787 0.762 0.744 v 0.690 0.678 0.669 0.660 0.652 0.645
0.922 0.914 0.907 0.900 0.893 0.886
0.877 0.867 0.858 0.849 0.841 0.833
0.639 0.633 0.628 0.623 0.619 0.615 0.612 0.609
0.880 0.874 0.869 0.864 0.858 0.854 0.849 0.845
0.826 0.820 0.813 0.807 0.802 0.797 0.792 0.787
0 2
. 1. 000 0.966
1.000 0.909
4
0.941
6 8 10 12 14
w
8
16 18 20 22 24 26 28 30 32 34 36 38 40
*
.. ...
.... .
..... -
.... . .....
.... . .... . .... .
u
0.697 0.691 0.685 0.680 0.676 0.672 0.668 0.665
0.832 0.825 0.819 0.814 0.809 0.804 0.800 0.796
For references see p. 4-96. • Freezes at 3.4; volumes 0.871 and 0.837. u Transition at 24.8; volumes 0.821 and 0.805. ," Freezes at 2.99; volum~s 0.902 and 0.840.
0.801 0.795 0.788 0.782 0.775 0.769 0.763 0.758
• Transition at 5.4; volumes 0.956 and 0.904• • Freezes at 12.2; volumes 0.741 and 0.701. z Freezes at 5.4; volumes 0.741 and 0.701.
... , .
.... . .....
..... ... , .
..... .....
..... ... . ,
.... . ..... ••••
j
.....
..... .....
0.861 0.851 0.842 0.834 0.826 0.818 0.813 0.806 0.800 0.795 0.789 0.784 0.779 0.775
il1 trJ
>-
;.3
TABLE
Pressure, kilobars
n-Octadecane [24]
1.000 0.966 0.935 0.913 0.895 0.880 0.868 0.857 0.846 0.837 0.828 0.820 0.813 0.806 0.800 0.794 0.787 0.782 0.776 0.772 0.767
0 2
-4
'6 '8
10 12 14 16 18 20 :22 :24 :26 :28 30 32 34 36 38 40 --
* For references see
Octanol-3 [25]
1.000 0.916 0.871
..... .....
..... .... . ..... .... . .... . .... . ..... .... . .... . .... . .... . .... . .... . .... . .... . .... .
Octylene [24]
1.000 0.905 0.845 0.805 0.778 0.757 0.742 0.728 0.715 0.705 0.695 0.686 0.678 0.670 0.663 0.657 0.650 0.644 0.638 0.633 0.628
4d-ll. V IV.) Methyl oleate [27]
1.000 0.932
..... . ....
. .... . .... ..... . .... . .... ..
,_
.
..... . .... ..... . .... . .... ..... . .... . .... . ....
..... .... .
OF ORGANIC COMPOUNDS*
Oxalic acid :anhydrous [5]
1.000 0.985 0.971 0.958 0.947 0.937 0.928 0.920 0.912 0.905 0.898 0.892 0.885 0.880 0.874 0.868 0.863 0.858 0.853 0.849 0.845
n-Pentane [26]
1.000 0.852 0.802 0.765 0.738 0.717 . ....
. .... . ....
. .... . .... .... . . .... ..... ..... . .... . . ... ..... . - ...
. .... .....
(Continued)
1sopentane [26]
1.000 0.857 0.802 0.765 . .... .... . . .... ..... . .... . .... . .... .. . . . .... . .... . ....
.
. .... . ....
•
._0, •
.... . .... . ....
.
2-Methyl- 3-Methylpentane pentane [26] [26]
1. 000 0.863 0.816 0.784
. .... . .. . . .... · . .. . . .... . .... . .... · .. . . . .... . .... . .... .... . _
.... .
· . .. ~
. ....
. .... . ....
1.000 0.867 0.813 0.780 0.755 0.736
. .... . .... ..... ""
.
. .... . .... . .... . .... . .... . .... . .... . .... . .... . .... . ....
Phenylenediamine [5] ortho-
meta-
para-
~~-
~~-
1.000 0.978 0.960 0.945 0.932 0.920 0.910 0.900 0.890 0.882 0.874 0.867 0.860 0.854 0.848 0.843 0.838 0.834 0.830 0.826 0.822
1.000 0.977 0.959 0.944 0.930 0.918 0.907 0.897 0.888 0.880 0.873 0.865 0.858 0.852 0.847 0.841 0.836 0.832 0.828 0.824 0.821
1.000 0.977 0.959 0.944 0.930 0.918 0.907 0.897 0.888 0.879 0.871 0.864 0.856 0.850 0.844 0.838 0.833 0.828 0.823 0.819 0.816
C'":l
o
~
"0 ~
trJ
'(f1 '(f1
6j H
t< >-3
H
>1
-
p. 4-96.
t
'-0 f-/o
tCD N
TABLE
Pressure, kilo bars
Phenylenediamine hydrochloride [5]
ortho-
meta-
4d-l1. V /1'0
OF ORGANIC COMPOUNDS*
Aminophenol [5]
2,4-
1.000 0.979 0.962 0.946 0.932 0.919 0.908 0.898 0.888 0.880 0.871 0.863 0.856 0.850 0.844 0.838 0.833 0.829 0.824 0.820 0.816
1.000 0.979 0.962 0.946 0.932 0.919 0.908 0.898 0.890 0.882 0.874 0.867 0.861 0.855 0.849 0.844 0.839 0.835 0.831 0.827 0.823
para-
1.000 0.979 0.962 0.946 0.932 0.919 0.908 0.898 0.890 0.881 0.873 0.866 0.860 0.854 0.848 0.843 0.838 0.834 0.830 0.825 0.821 -
* For references see p. 4-96.
Nitrophenol [5]
Dichlorophenol ortho-
meta-
para-
[5]
--0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
(Continued)
1.000 0.979 0.961 0.945 0.932 0.920 0.911 0.902 0.894 0.886 0.879 0.872 0.866 0.860 0.855 0.849 0.845 0.843 0.836 0.832 0.827
1.000 0.980 0.963 0.950 0.937 0.926 0.916 0.908 0.900 0.892 0.885 0.879 0.873 0.867 0.862 0.857 0.853 0.849 0.845 0.841 0.837
1.000 0.982 0.966 0.952 0.940 0.928 0.917 0.908 0.900 0.891 0.884 0.876 0.869 0.862
0.857 D.851 -).846 0.843 0.836
0.831 0.827
1.000 0.972 0.953 0.936 0.923 0.910 0.899 0.889 0.880 0.871 0.862 0.855 0.847 0.840 0.834 0.828 0.822 0.817 0.812 0.808 0.804
ortho-
meta-
---
---
1.000 0.973 0.950 0.934 0.918 0.905 0.893 0.883 0.873 0.865 0.856 0.849 0.842 0.836 0.830 0.825 0.820 0.816 0.812 0.808 0.804
1.000 0.980 0.961 0.946 0.932 0.920 0.910 0.900 0.892 0.884 0.876 0.870 0.863 0.857 0.851 0.845 0.840 0.835 0.831 0.827 0.823
para-
1.000 0.979 0.960 0.943 0.929 0.916 0.905 0.895 0.885 0.877 0.868 0.861 0.854 0.847 0.841 0.835 0.830 0.825 0.821 0.817 0.813
Tri-ocresyl phosphate
Normal butyl phthalate
[27]
[27]
1.000 0.9478
.....
1.000 0.931 0.892 0.864 0.841
.....
. ....
..... ..... .....
•
0
••
•
n-Propyl bromide
[25]
1.000 0.902 0.850 0.812 0.786 0.766 0.750
P:: to! P>
>-3
1 ~-----.--
-
TABLE
Pressure, kilobars
n-Propyl n-Propyl iodide chloride [25] [25]
Propylene glycol [27]
4d-l1. V jVo
Quinone [3]
OF ORGANIC COMPOUNDS*
Semicarbazide hydrochloride [5]
0 2
1.000 0.878
1.000 0.902
1.000 0.943
1.000 0.978
1.000 0.987
4
0.831
0.854
0.906
0.957
0.977
Styrene [24]
Succinic acid [6]
(Continued) Toluic acid [5] Sucrose [6]
Thymol [6] ortho-
meta-
para-
1.000 0.907 aa 0.821
1.000 0.985
1.000 0.985
1.000 0.966
1.000 0.972
1.000 0.974
1.000 0.972
0.973
0.972
0.942
0.950
0.953
0.950
0.797 0.779
0.960 0.948
0.961 0.950
0.922 0.905
0.932 0.918
0.936 0.922
0.932 0.916
0.764 0.752 0.740 0.731 0.722 0.714 0.707 0.700 0.695 0.689 0.684 0.679 0.674 0.670 0.666 0.662
0.936 0.925 0.915 0.905 0.896 0.888 0.881 0.874
0.940 0.932 0.924 0.916 0.910 0.903 0.897 0.893 0.883 0.854 0.850
0.890 0.877 0.865 0.855 0.846 0.838 0.830 0.823 0.817 0.811 0.806
..
",
.....
..... .. - .. . .... .....
.... - .. . .... .. - ..
0.905 0.894 0.884 0.874 0.865 0.856 0.849 0.841 0.834 0.828 0.822 0.816 0.810 0.806 0.802 0.797
0.910 0.899 0.888 0.878 0.869 0.860 0.852 0.845 0.838 0.832 0.826 0.820 0.815 0.810 0.806 0.801
0.902 0.890 0.878 0.868 0.859 0.851 0.843 0.835 0.829 0.822 0.817 0.810 0.805 0.800 0.795 0.790
y
6 8
0.798 0.771
0.824 0.800
0.877 0.855
0.931 0.915
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
0.750 0.734
0.780 0.762
0.836 0.820
.... . .... . .. ... .. ...
. .... .... .
.....
.....
"
.....
.. -,..... .. -., - , ...
0.900 0.886 0.874 0.862 0.852 0.842 0.833 0.825 0.817 0.810 0.803 0.797 0.791 0.786 0.781 0.777
,-.
. ....
.... . .... . .. ...
.....
,-
, - ... .....
...
. . • 0.
,_
.. ,-. . .... .... .
.... .... . ... - . ,_ ... , - ...
.... . .. ,-.
.
•
0
•••
..
,
.. -., .. - .. .... .
.... . .'., ..
...... .... .
.
0.967 0.959 z 0.946 0.939 0.932 0.925 0.918 0.912 0.907 0.901 0.896 0.891 0.886 0.882 0.877 0.874 0.869 0.866
- - - - - - - - _... _--
-------
..... .. -" .. -, . .....
.... . . .... ..... .. -.,
.
-,
c
o
~ "d
pj. t;j Ul Ul
bj
.... s:: ~
-------
* For references see p. 4-96.
• Transition at 4.4; volumes 0.952 and 0.943. 'Transition at 9.3; volumes 0.953 and 0.950. •• Freezes at 3.1; volumes 0.884 and 0.835.
t
>-3
Q
P>
'"d
P>
Q
>-
-3 trI
>-< lf1
t
f-'
0 ""l
TABLE
4e-2.
l\10LAR HEAT CAPACI1'Y AT CONSTANT PR~JSSURE OF THE CHEMICAL ELEMENTS AT HIGHER THAN ROOM TEMPERATURE, CAL/MOLE'
t
R
i-'
o
Ae revised December, 1967 Element
298.15
400
500
600
700
800
00
1000
1200
7.59(1) 7.50(1) 4.968
7.59(1) 7.50(1) 4.968
1500
2000
2500
3000
---Aluminum AI 26.9815 ................ Antimony Sb 121.75 ................. Argon Ar 39.948 .................... Arsenic As 74.9216 .................. Beryllium Be 9.0122 ................. Bismuth Bi 208.980 ............... , . Boron (crystalline) B 10.811 .......... Boron (amorphous) B 10.811. ....... Bromine Br, 159.818 ................ Cadmium Cd 112.40 ................. Calcium Ca 40.08 ................... Carbon (graphite) C 12.01115 ........ Carbon (diamond) C 12.0115 ........ Cerium Ce 140.12 ................... Chlorine CJ, 70.906 .................. Chromium Cr 51.996 ............... Cobalt Co 58.9332 ................. Copper Cu 63.54 ..•................. Erbium Er 167.26 ................... Europium Eu 151.96 ................ Fluorine F, 37.9968 ................. Germanium Ge 72.59 ................ Gold Au 196.967 .................... Hafnium Hf 178.49 .................. Helium He 4.0026 ................... Holmium Ho 164.930 ................ n-Hydrogen H, 2.01594 .............. n-Deuterium D, 4.02820 ............. Indium In 114.82 ................... Iodine I, 253.8088 ... '" ............. Iridium Ir 192.2 .................... Iron Fe 55.847 ...................... Krypton Kr 83.80 ................... Lanthanum La 138.91. .............. Lead Pb 207.19 .................... Lithium Li 6.939 .................... Lutetium Lu 174.97 ................. Magnesium Mg 24.312 ...............
5.81(e) 6.03(e) 4.968(g) 5.89(a)
3.93(e) 6.20(e) 2.65(e) 2.86(e) 18.09(1) 6.20(e) 6.26(a)
2.04(e) 1. 46(e) 6.44(1/) 8. 11 (g) 5.58(e) 5.93(a)
5.84(e) 6.71(e) 6.48(e) 7.49(g) 5.58(e) 6.06(e) 6.15(a)
4.968(g) 6.49(a)
6.892(g) 6.978(g) 6.39(e) 13.01(e) 6.00(e) 5.97(a)
4.968(g) 6. 65(/l) 6.32(e) 5.78(e) 6.40(e) 5095(c)
6.16 6.22 4.968 6.15 4.73 6.45 3.72 3.78 8.78(g) 6.49 6.62 2.85 2.45 6.76 8.44 6.02 6.34 6.08 6.79 6.68 7.90 5.8.5 6.17 6.34 4.968 6.65 6.975 6.989 6.93(e) 19.28(1) 6.14 6.54 4.968 6.81 6.56 6.62(c) 6.42 6.24
6.45 6.38 4.968 6.32 5.20 6.69(e) 4.49 4.40 8.86 6.78(e) 7.03 3.50 3.24 7.10 8.62 6.41 6.74 6.25 6.87
*
8.21 5.95 6.29 6.52 4.968 6.74 6.993 7.018 7.03(1) 8.95(g) 6.27 7.10 4.968 6.97 6.79 7.20(1) 6.46 6.52
6.72 6.56 4.968 6.50 5.54 7.6(1) 4.99 4.88 8.91 7.10(1) 7.45 4.04 3.85 7.46 8.74 6.73 7.09 6.39 6.97 7.24 8.43 6.03 6.40 6.70 4.968 6.76 7.008 7.078 6.99 8.98 6.41 7.66 4.968 7.13 7.02(c) 7.06 6.50 6.80
7.00 6.88 4.968 6.74 5.82 7.6 5.32 5.26 8.94 7.10 7.87(a)
4.44 4.31 7.84 8.82 7.00 7.42(a)
6.52 7.11 7.52 8.59 6.10 6.51 6.88 4.968 6.80 7.035 7.171 6.96 9.00 6.55 8.27 4.968 7.29 7.25(1) 6.93 6.61 7.08
7.37(e) 7.15(e) 4.968 7.02(a)
6.06 7.6(1) 5.56 5.57 8.97 7.10 7.86(1/) 4.74 4.66 8.25 8.88 7.22 7.7.5(1/) 6.62 7.27 7.88 8.71(g) 6.19 6.65 7.06 4.968 6.95 7.078 7.288 6.93(1) 9.02(g) 6.69 9.07 4.968 7.45(/l) 7.17 6.92 6.79 7.36(e)
6.54(e) 5.95 6.05 9.01(g) 7.10(1) 9.32(1/) 5.15 5.16 9. 14(/l) 8.95 7.66 8.84 6.82 7.67 9.09(e) 6.50 6.89 7.43 4.968 7.61 7.215 7.557 ......... 6.96
4.968
......... ......... 4.971(g: 4.968
4.968
4.968(g:
......... . . . . . . . . . . . . . . . . . . ......... 5.020(g: 6.26 6.39
6.67 6.75
7.12(c) 7.07(e)
4.968(g) 4.968 4.968 4.969(g: 4.968 ........ 7.4(1) 5.008(g) 5.219 5.796(g: 6.06(e) 5.43 5.67 5.97 5.86 5.60(e) 9.35(1) 9.01(g) 9.68(e) 8.48 ......... . . . . . . . . . 7.358(g 9.50(1/) 10.33 7.00(e) 7.5(1) . . . . . . . . . ......... 6.010(g: 8.18 9. 14(e) ......... 5.1O(g) 9.11(1) 5.61 6.74(g) 6.86(e) 7.13(e)
6.60(1) 7.0(1)
7.79(a)
4.968 8.58 7.401 7.824 .........
4.968
7.24 8. 13Cy) 4.968
7.03 6.89 7.24 7.8(1)
6.88(1) 6.87(1) 7.85 7.8(1)
13.01(a)
.........
4.968 1O.69(a) 7.706 8.164 . ........
4.968 8.162(g) 8.568(g) . ........
4.968
4.968(g:
5.709(g) 5.509(g:
7.65(e) 8.73(1')
4.968
4.968
......... ......... 9.09(e) 4.968(g)
4.969
4.968
4.968(g:
6.951(g) 7.925(g; 4.977
5.022(g;
~ ~ ~
>-:3
Manganese Mn 54.9380 .............. Mercury Hg 200.59 .................. Molybdenum Mo 95.94 .............. Neodymium Nd 144.24 ............. Neon Ne 20.183 .................... Nickel Ni 58.71 ..................... Niobium (columbium) Nb(Cb) 92.906 .. Nitrogen N, 28.0134 ................. Osmium Os 190.2 ............... ' ... Oxygen 0, 31.9988 .................. Ozone 0,47.9982 ................... P •. lladium Pd 106.4 ................. Phosphorus (red, trielinie) P 30.9738 .. Phosphorus (white) P 30.9738 ........ Platinum Pt 195.09 .................. Plutonium Pu[239] .................. Potassium K 39.102 ................. Radon Rn [222] ..................... Rhenium Re 186.2 .................. Rhodium Rh 102.905 ................ Ruthenium Ru 101.07 ............... Samarium Sm 150.35 ................ Scandium Se 44,956 ................. Selenium (metallic) Se 78.96 •......... Silicon Si 28.086 .................... SHver Ag 107.870 ................... Sodium Na 22.9898 .................. Sulfur S 32.064 ..................... Tantalum Ta 180.948 ................ Tellurium Te 127.60 ................. Thallium TI 204.37 .................. Thorium Th 232.038 ................. Thulium Tm 168.934 ................ Tin (white) Sn 118.69 ............... Titanium Ti 47.90 ................... Tungsten (wolfram) W 183.85 ........ Uranium U 238.03 .................. Vanadium V 50.942 ................. Xenon Xe 130.30. . ................ Ytterbium Yb 173.04 ................ Yttrium Y 8.905 ...... , ............. Zinc Zn 65.37 ....................... Zirconium Zr 91.22 ..................
6.28(e) 6.76 7.21 6.69(1) 6.54 6.48 5.73(e) 6.05 6.25 6.55(",) 7.24 6.88 4.968(g) 4.968 4.968 6.23(e) 7.37 6.80 5.88(e) 6.18 6.09 6.96(g) 7.07 6.99 5.90(e) 5.99 6.09 7.02(g) 7.20 7.43 9.38(g) 10.46 11.30 6.21(e) 6.35 6.49 5.07(e) 5.54 5.85 6.29(1) 6.29(1) 5.70(1l) 6.18(e) 6.31 6.44 7.64(",) 8.03(tJ) 8.53(')') 0.70(e) 7.53(1) 7.34 4.968(g) 4.968 4.968 6.16(e) 6.22 6.32 5.97(e) 6.21 6.45 5.75(e) 5.82 5.91 7.06(",) 7.93 8.94 6.10(",) 6.29 6.41 6.06(e) 6.65(e) 8.40(1) 4.78(e) 5.30 5.61 6.07(e) 6.18 6.30 7.53(1) 6.72(e) 7.30 5.40(rh) 7.73(1) 9.08 6.06(e) 6.22 6.30 6.14(e) 6.68 7.21 6.29(a) 6.57 7.03(a) 6.53(",) 7.15 6.85 6.51 6.46(e) 6.49 7.32(e) 6.45(e) 6.89 6.31 6.53 5.98(a) 5.81(e) 5.96 6.06 7.65 6.61(a) 7.10 5.95(e) 6.27 6.44 4.968(g) 4.968 4.968 7.41 6.39(a) 6.60 6.34(a) 6.49 6.65 6.31 6.55 6.07(e) 6.06(",) 6.54 6.78
8.35(",) 7.63 8.01 6.48(1) 4.968(g) 4.968 6.38 6.48 6.55 7.66 8.14 8.71 4.968 4.968 4.968 8.31 7.37 7.44 6.28 6.38 6.48 7.20 7.35 7.51 6.18 6.27 6.63 7.67 7.88 8.06 11.92 12.70 12.37 6.62 6.90 6.76 6.16 6.50(e) 6.82 6.70 9.00(0) 8.40(.) 7.13 7.11 7.20 4.968 4.968 4.968 6.69 6.43 6.56 6.69 6.93 7.17 6.04 6.23 6.42 9.75 10.19 10.52 6.57 6.75 6.96 8.40(1) 6.13 5.82 5.99 6.42 6.56 6.72 7.12 7.00 6.92 8.20 7.80(1) 6.45 6.33 6.39 8.26(e) 9.00(1) 7.73 7.2(1) ...... , .. .. .... .. 7.76 8.06 7.45 6.59 6.76 7.08 6.87(1) 6.85 6.85(1) 7.01 6.77 7.25 6.16 6.27 6.37 9.08 9.99(",) 8.31 6.70 6.57 6.85 4.968 4.968 4.968 7.25 7.13 7.37 7.00 7.18 6.82 6.79(e) 7.5(1) 7.5 7.01 7.23 7.45
9.01(1l) 4.968 6.70 10.03(",) 4.968 7.88 6.68 7.82 6.54
8.34 13.15 7.17
6.57
7.08
9.21(f'l) 4.968 6.93 10.65(')') 4.968 8.34 6.88(e) 8.06 6.72 8.53 13.43 7.44
10.99(0)
4.968 7.47 4.968 8.65(e)
4.968 8.63 4.968 10.30(1)
8.33 7.00(e) 8.74 13.68(g) 7.86(e)
8.60
5.039(g) 5.252(g) 4.968 4.968(gJ 1O.46(e) 4.968
4.968(g:
8.76
8.86(g)
4.968
4.968(g·
9.03(g)
7.34
7.72
8.37(e)
4.968 7.22(e)
4.968
4.968
9.00(0)
7.26(1) 4.968 6.95 7.65(e) 6.75 10.82(",) 7.46 6.35 7.15 6.92(1)
'
6.57 9.00(1) . ........ 8.67 7.52 ........ .
7.73(",) 6.59 10. 26(iJ) 7.27 4.968 7.64(a)
7.53 7.5(1) 7.90(,,)
il1 trJ
~
>-:l 7.11 11.22(1l) 8.06 6.49 7.62(e)
7.24(e) 6.06(g)
..........
6.08(g)
9.14(a)
('1
~
~
('1
6.66(e) , .......
4.968(g) 4. 969 (g'
..
H
>-:l
H
trJ
6.69 . ........
6.87 .........
U2
7.17
7.46(e)
5.420(g)
5.830
6. 173 (g'
5.20(g)
5.32(g) 6.266(g:
8.30
9.80(e)
4.968 5.01
4.968(g: 5.16(g)
4.968
4.969(g)
9.28(a)
7.89 ....... - . 7 .10CtJ) 6.80 9.15(')') 7.85 4.968 8.79(1) 7.90 4.968(g) 7. 50 ell)
8.43(e) . ......... 7. 85(tJ) 7.14 7.71 11.45(1) 8.69(e) 4.968 4.968 4.97(g) 4.97 8.43(a)
4.968 7.50(1l)
4.968
t
f-'
o
CO
·4-110
REA'!'
gases). With the exception of B (amorphous), C. (diamond), Se, Te, and the gases R 2, D 2, Eu, Sm, Tm, and Yb, the tabulated values are based on (1) RHultgren, R.L. Orr, P. D. Anderson, and K. K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Alloys," John Wiley & Sons, Inc., New York, 1963 (and later looseleaf supplements); (2) JANAF Thermochemical Tables, Clearinghouse, U.S. Dep~rtment of Commerce, Springfield, Va. (PB Rept. 168370, 1965; PB Rept. H,8370-1, 1966) (and later looseleaf supplements); and (3) J.Hilsenrath, C. G. Messina, lJ.nd W. H. Evans, Ideal Gas Thermodynamic Functions for 73 Atoms and Their First and Second Ions to 10,000K, Air Force Weapons Lab. Rept. TDR-64-44, Kirtland Air Force Base; N.Mex., 1964. TABLE 4e-3. HEAT CAPACITY OF WATER (Osborne, Stimson, and Ginnings, National BUreau of Standards) Temp,oC
--
J g·K
Temp.,oC
--
0 5 10 15 20 25 30 35 40 45 50
4.2177 4.2022 4.1922 4.1858 4.1819 4.1796 4.1785 4.1782 4.1786 4.1795 4.1807
50 55 60 65 70 75 80 85 90 95 100
4.1807 4.1824 4.1844 4.1868 4.1896 4.1928 4.1964 4.2005 4.2051 4.2103 4.2160
J g·K
As a first approximation in explaining the temperature dependence of the heat capacity of solids, Einstein made the assumption that all oscillators in the lattice ~ibratlld with the same frequency /In. If h is Planck's constant and k is Boltzmann's constant; let
and denote the zero-point energy per mole by U o• Then the Einstein theory· of specific heat yields for the molar energy U at the temperature T fE' .) U - U o x ~. mstem 3RT = e" - 1
(4e-l)
where R is the universal gas constant. The Einstein molar heat capacity at constant volume is given .by Cv = dU/dT, or x 2e" .. . . . Cv (4e-2) (Emstem) 3R = (e" - 1)2 The inolarentropy SIs equal to f(Cv/T) dT, whence (Einstein)..Ii 3R
=
_x_. - In (1 - e-") e" - 1
(4e-3)
Numerical values of the quantities in Eqs. (4e-l), (4e-2), and (4e-3) are given in Tables 4e-4, 4e-5 and 4e-6, taken from '~Contributions to the Thermodynamic Functions by a Planck-Einstein Oscillator in One Degree of Freedom," prepared by Herrick L. Johnston, Lydia Savedoff, and Jack Belzer, of the Cryogenic Laboratory of the
4-111
HEAT CAPACITIES TABLE
eE T
0.0
0.1
0.2
4e-4.
0.3
U - Uo 3RT 0.4
(EINSTEIN)
0.5
0.6
0.7
0.8
0.9
- - - - - - - - - - - - - - -- - - - - - - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1.00000 0.95083 0.90333 0.85749 0.81330 0.77075 0.72982 0.69050 0.65277 0.61661 0.58198 0.54886 0.51722 0.48702 0.45824 0.43083 0.40475 0.37998 0.35646 0.33416 0.31304 0.29304 0.27414 0.25629 0.23945 0.22356 0.20861 0.19453 0.18129 0.16886 0.15719 0.14624 0.13598 0.12638 0.11739 0.10898 0.10113 0.09380 0.08695 0.08057 0.07463 0.06909 0.06394 0.05915 0.05469 0.05055 0.04671 0.04314 0.03983 0.03676 0.03392 0.03128 0.02885 0.02658 0.02450 0.02257 0.02079 0.01914 0.01761 0.01621 0.01491 0.01371 0.01261 0.01159 0.01065 0.00979 0.00899 0.00826 0.00758 0.00696 0.00639 0.00586 0.00538 0.00494 0.00453 0.00415 0.00381 0.00349 0.00320 0.00293 0.00269 0.00246 0.00225 0.00206 0.00189 0.00173 0.00158 0.00145 0.00133 0.00121 0.00111 0.00102 0.00093 0.00085 0.00078 0.00071 0.00065 0.00059 0.00054 0.00050 0.00045 0.00042 0.00038 0.00035 0.00032 0.00029 0.00026 0.00024 0.00022 0.00020 0.00018 0.00017 0.00015 0.00014 0.00013 0.00012 0.00011 0.00010 0.00009 0.00008 0.00007 0.00007 0.00006 0.00006 0.00005 0.00005 0.00004 0.00004 0.00004 0.00003 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
TABLE
eE T
0.0
0.1
0.2
0.3
Cv 4e-5. 3R 0.4
(EINSTEIN)
0.5
0.6
0.7
0.8
0.9
----- --- - -- -- -- -- ---- - -- 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
1.00000 0.99917 0.99667 0.99253 0.98677 0.97942 0.97053 0.96015 0.94833 0.93515 0.92067 0.90499 0.88817 0.87031 0.85151 0.83185 0.81143 0.79035 0.76869 0.74657 0.72406 0.70127 0.67827 0.65515 0.63200 0.60889 0.58589 0.56307 0.54049 0.51820 0.49627 0.47473 0.45363 0.43301 0.41289 0.39331 0.37429 0.35584 0.33799 0.32073 0.30409 0.28806 0.27264 0.25783 0.24363 0.23004 0.21704 0.20462 0.19277 0.18149 0.17074 0.16053 0.15083 0.14162 0.13290 0.12464 0.11683 0.10944 0.10247 0.09588 0.08968 0.08383 0.07833 0.07315 0.06828 0.06371 0.05942 0.05539 0.05162 0.04808 0.04476 0.04166 0.03876 0.03605 0.03351 0.03115 0.02894 0.02687 0.02495 0.02316 0.02148 0.01993 0.01848 0.01713 0.01587 0.01471 0.01362 0.01261 0.01168 0.01081 0.01000 0.00925 000855 0.00791 0.00731 0.00676 0.00624 0.00577 0.00533 0.00492 0.00454 0.00419 000387 0.00357 0.00329 0.00304 0.00280 0.00258 0.00238 0.00219 0.00202 0.00186 0.00172 0.00158 0.00145 0.00134 0.00123 0.00114 0.00104 0.00096 0.00088 0.00081 0.00075 0.00069 0.00063 0.00058 0.00054 0.00049 0.00045 0.00042 0.00038 0.00035 0.00032 0.00030 0.00027 0.00025 0.00023 0.00021 0.00019 0.00018 0.00016 0.00015 0.00014 0.00013 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008
-
Ohio State University, under contract between the Office of Naval Research and the Ohio State University Research Foundation, 194.9. Debye assumed that the oscillators occupying the lattice points in a crystalline solid vibrated with a continuous spectrum of frequencies from zero to a maximum value Pm. Defining the "Debye temperature" eD and y by the equations
4-112
HEAT TABLE
eE T
S 4e-6. 3R
(EINSTEIN)
I
0.0
0.1
0.3
0.2
0.4
0.5
0.6
0.7
0.8
0.9
-- - - - - - - - - - - - - -- - - - - - - 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
00 3.30300 2.61110 2.20772 1.92293 1.70350 1.5256~ 1.37684 1.24939 1.13845 1.04066 0.95363 0.87560 0.80521 0.74139 0.68331 0.63027 0.58171 0.53714 0.49617 0.45845 0.42367 0.39158 0.36194 0.33455 0.30921 0.28579 0.26410 0.24403 0.22546 0.20826 0.19234 0.17760 0.16396 0.15133 0.13964 0.12884 0.11883 0.10958 0.10102 0.09312 0.08580 0.07905 0.07281 0.06704 0.06172 0.05681 0.05228 0.04809 0.04423 0.04068 0.03740 0.03438 0.03159 0.02903 0.02666 0.02450 0.02249 0.02064 0.01896 0.01739 0.01596 0.01464 0.01343 0.01232 0.01130 0.01035 0.00949 0.00869 0.00797 0.00730 0.00669 0.00613 0.00562 0.00514 0.00470 0.00431 0.00394 0.00361 0.00330 0.00303 0.00276 0.00252 0.00231 0.00211 0.00193 0.00176 0.00162 0.00148 0.00135 0.00123 0.00113 0.00103 0.00094 0.00086 0.00078 0.00072 0.00065 0.00060 0.00055 0.00050 0.00046 0.00042 0.00038 0.00035 0.00032 0.00028 0.00026 0.00024 0.00022 0.00020 0.00019 0.00016 0.00015 0.00014 0.00013 0.00012 0.00011 0.00010 0.00009 0.00008 0.00008 0.00007 0.00006 0.00005 0.00005 0.00004 0.00004 0.00004 0.00003 0.00003 0.00003 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00001 0.00001 0.00001 O.qOOOl 0.00001 0.00001 0.00001 0.00001 0.00001 O.OOOCI 0.00001 0.00001
TABLE
eD T
0.0
0.1
-
0.2 --
4e-7.
0.3
U - Uo 3RT 0.4
(DEBYE)
0.5
I
0.6
0.7
0.8
0.9
- - - - - - - - - - - -- -
0 1.000000 .963000 .926999 .891995 .857985 .824963 .792923 .761858 .781759 .702615 1 .674416 .647148 .620798 .595351 .570793.. 547107 .524275 .502280 .481103 .460726 2 .441128 .422291 .404194 .386816 .370137 .354136 .338793 .324086 .309995 .296500 3 .283580 .271215 .259385 .248070 .237252 .226911 .217029 .207589 .198571 .189959 4 .181737 .173888 .166396 .159246 .152424 .145914 .139704 .133780 .128129 .122739 5 .117597 .112694 .108016 .103555 .099300 .095241 .091369 .087675 .084152 .080789 6 .077581 .074520 .071598 .068809 .066146 .063604 .061177 .058858 .056644 .054528 7 .052506 .050573 .048726 .046960 .045271 .043655 .042109 .040630 .039214 .037858 8 .036560 .035317 .034126 .032984 .031890 .030840 .029834 .028869 .027942 .027053 9 .026200 .025380 .024593 .023837 .023110 .022411 .021739 .021092 .020470 .019872 10 .019296 .018741 .018207 .017692 .017196 .D16718 .016257 .015812 .015384 .014970 11 .014570 .014185 .013813 .013453 .013106 .012770 .012445 .012131 .011828 .011534 12 .011250 .010975 .010709 .010452 .010202 .009960 .009726 .009499 .009279 .009066 13 .008859 .008658 .008463 .008275 .008091 .007913 .007740 .007572 .007409 .007251 14 .007097 .006947 .006801 .006660 .006522 .006388 .006258 .006132 .006008 .005888
- - - - - - - - - - - - - - - - -- -
eD T
-. 10 20 30 40
0
1
2
3
4
5
6
7
8
9
- -- - - - - - - - - - - -- .019296 .014570 .011250 .008859 .002435 .002104 .001830 .001601 .000722 .000654 .000595 000542 .000304 .000283 .000263 .000245
.007097 .005771 .004756 .003965 .003340 .002840 .001409 .001247 .001108 .000990 :000887 .000799 000496 .000454 .000418 .000385 .000355 .000328 .000229 .000214 .000200 .000188 .000176 .000166
4-113
HEAT CAPACITIES
eD
-
T
0.0
0.1
0.2
TABLE
Cv 4e-S. 3R
0.3
0.4
(DEBYE)
0.5
--- --- --- ---
0.6
0.7
0.8
0.9
--- ------ ---
0 1.000000 .999500 .998003 .915514 .992046 .987611 .982229 .975922 .968717 .960643 1 .951732 .942020 .931545 .920346 .908467 .895950 .882842 .869186 .855031 .840422 2 .825408 .810034 .794347 .778392 .762213 .745853 .729355 .712759 .696103 .679424 3 .662758 .646137 .629593 .613154 .596848 .580700 .564732 .548966 .533421 .518113 4 .503059 .488272 .473763 .459543 .445620 .432002 .418693 .405700 .393024 .380669 5 .368635 .356922 .345529 .334456 .323698 .313255 .303121 .293293 .283767 .274536 6 .265597 .256943 .248568 .240466 .232631 .225056 .217735 .210662 .203828 .197229 7 .190856 .184704 .178766 .173035 .167505 .162169 .157021 .152055 .147264 .142644 8 .138187 .133889 .129744 .125746 .121890 .118172 .114585 .111126 .107790 .104572 9 .101467 .098472 .095583 .092795 .090105 .087509 .085004 082585 .080251 .077997 10 .075821 .073719 .071690 .069729 .067835 .066005 .064236 .062526 .060874 .059276 11 .057731 .056237 .054791 .053393 .052039 .050730 .049462 .048235 .047046 .045895 12 .044780 .043700 .042653 .041639 .040655 .039702 .038777 .037880 .037010 .036166 13 .035347 .034552 .033781 .033031 .032304 .031597 .030910 .030243 .029595 .028964 14 .028352 .027756 .027177 .026613 .026065 .025532 .025013 .024508 .024016 .023537
-
--- ---
eD
-
T
0
1
2
--- --- --- --- --- --4
3
5
6
7
8
9
------ --- ------ --- -----10 20 30 40
.075821 .057731 .044780 .035347 .028352 .023071 .019018 .015859 .009741 .008414 .007318 .006405 .005637 .004987 .004434 .003959 .002886 .002616 .002378 .002168 .001983 .001818 .001670 .001538 .001218 .001131 .001052 .000980 .000915 .000855 .000801 .000751
.013361 .003550 .001420 .000705
.011361 .003195 .001314 .000662
the values of molar energy, molar heat capacity at constant volume and molar entropy were found to be U - Uo 3 (Y Z3 dz (4e-4) (Debye) 3RT = D(y) = Y')o e' - 1 Cv (Debye) 3R
S (Debye) -
3R
=
3y 4D(y) - eY - 1
4
= -
3
D(y) - In (1 - c
(4e-5) Y)
(4e-6)
Values of the quantities in Eqs. (4e-4), (4e-5) and (4e-6) are given in Tables 4e-7, 4e-8 and 4e-9, prepared by John E. Kilpatrick and Robert H. Sherman, of the Los Alamos Scientific Laboratory, under contract with the U.S. Atomic Energy Commission, 1964. To calculate U - U o in joules/mole, and C v and S in joules/mole kelvin, take as the value of R R = 8.3143 joules/mole kelvin To convert to calories, it must be kept in mind that there are three different calories: The 15-degree calorie = 4.1858 joules The International steam table calorie = 4.1868 joules The thermochemical calorie = 4.1840 joules
4-114
HEAT TAllLE
ev
-T
-
0.0
0.1
0.3
0.2
S
4e-9. 3R
0.4
(DEBYE)
0.5
0.6
0.7
0.8
0.9
--- --- --- --- --- --- --- --- --- --0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
'"
1.357896 0.733585 0.429176 0.260801 0.163557 0.105924 0.070920 0.049083 0.035057 0.025773 0.019444 0.015007 0.011814 0.009463
3.636168 1.267635 0.693684 0.407715 0.248562 0.156373 0.101605 0.068257 0.047393 0.033952 0.025029 0.018928 0.014639 0.011546 0.009263
2.943771 1.186113 0.656362 0.387463 0.236970 0.149554 0.097495 0.065715 0.045775 0.032892 0.024313 0.018431 0.014284 0.011286 0.009069
2.539553 1.111987 0.621403 0.368341 0.225990 0.143077 0.093583 0.063289 0.044227 0.031873 0.023623 0.017950 0.013940 0.011034 0.008881
2.253613 1.044212 0.588616 0.350279 0.215585 0.136926 0.089858 0.060972 0.042744 0.030895 0.022959 0.017485 0.013607 0.010790 0.008697
2.032703 0.981958 0.557832 0.333211 0.205724 0.131083 0.086310 0.058760 0.041324 0.029956 0.022318 0.017037 0.013284 0.010552 0.008519
1.853102 0.924550 0.528900 0.317077 0.196375 0.125530 0.082930 0.056646 0.039963 0.029053 0.021701 0.016603 0.012972 0.010321 0.008345
1.702152 0.871435 0.501685 0.301819 0.187510 0.120252 0.079709 0.054626 0.038658 0.028184 0.021106 0.016184 0.012669 0.010097 0.008176
1.572296 0.822152 0.476064 0.287386 0.179103 0.115234 0.076639 0.052695 0.037407 0.027349 0.020532 0.015778 0.012375 0.009880 0.008011
1.458656 0.776313 0.451928 0.273728 0.171126 0.110462 0.073712 0.050849 0.036208 0.026546 0.019978 0.015386 0.012090 0.009669 0.007851
-- --- --- --- --- --- --- --- --- --- --€Iv T
0
1
2
3
4
5
6
7
8
9
--- --- --- --- --- --- --- --- --- ---
10 20 30 40
0.025773 0.003247 0.000962 0.000406
0.019444 0.002805 0.000872 0.000377
0.015007 0.002439 0.000793 0.000351
0.011814 0.002135 0.000723 0.000327
0.009463 0.001879 0.000661 0.000305
0.007695 0.001662 0.000606 0.000285
0.006341 0.001478 0.000557 0.000267
0.005287 0.001320 0.000513 0.000250
0.004454 0.001183 0.000473 0.000235
0.003787 0.001065 0.000438 0.000221
At values of the temperature less than eD/1 00, the Debye theory can be relied upon to give correctly the COllLl'iLutioll Lo the heat capacity attributable to lattice vibrations. In some cases it holds well at temperatures up to e D /50. At these low temperatures the Debye expression for Cv reduces to (4e-7) or
Cv
=
mJI 124.8 moe· K
(T)3 "15>
tYD
(4e-8)
For metals there is a contribution to the heat capacity due to the free electrons equal to "T, where " is known as the electronic constant. The total heat capacity of a metal is therefore
(4e-9) The most reliable values of eD and" are obtained from heat-capacity measurements in the liquid helium region. It is customary in such work to plot Cv /T against Ta. On such a plot a nonmetal gives a straight line through the origin, whereas a metal gives a straight line with a positive intercept. Values of eD and" are given in Table 4e-IO. They were obtained in almost all cases by calorimetric measurements in the liquid helium range or lower. Values of , ElD are given in kelvins, and those of "in millijoules per mole kelvin squared.
4-115'
HEAT CAPACITIES TABLE
4e-10.
VALUES OF
8D
AND 'Y, IN THE HEAT-CAPACITY EQUATION
Substance
Symbol
Aluminum .... · . · . · . .. . .. . Antimony. .. . 0.' • . ..... .. . Argon ....... .. . ., . ·. Arsenic .. " .. ..... ..... . · . Barium. .... .. . · . ... . · . Beryllium. . .. · .', ... ·. Bismuth ...... ... .. . . .. . .. Bismuth telluride ..... · . .. . . .. ... Cadmium. . . ... ',' . · . . .. Calcium .... . .. . .. · . ·. Calcium fluoride .. '" . ' " . Carbon (graphite) . ·.· . ·. Carbon (diamond) .... · . .. . · . .. Cesium ...... · . . .... ... . Chlorine ...... ... .. . .. . Chromium ..... ... " ',' · . Cobalt ... . . ... · . · . Copper ..... .. . . .. . ·.·., . .. Dysprosium. · . ·. . . . Gadolinium ...... · . .. . · . Gallium ..... .. . ... Germanium ..... · .. .... . .. . Germanium telluride .... Gold ....... ... .. .. . · . Hafnium. .. .. · . ·. ·. Helium 4 (hcp) ...... · . ·. 3 Helium (bcc) .. '.. ... . · . · . Hydrogen. .. . ... .. · . · . Hydrogen2 ..... ... . . . ..... ·. Ice. .... . .. Indium ...... ... ·. " Indium antimonide. .. . · . · . · . Iodine. . . .. . .. ' .. ·. ·. Iridium. ... . ..... '," . · . · . Iron. .... · . · . . . . .. . .. Iron oxide .... ... . .. ·. ·. Iron selenide ... · . ... ·.·. Iron sulfide .. . .. .. '.',' · . Krypton. .. ·. .. ·. · Lanthanum ... · .... '.' . .. . · . Lead ....... ... . ... · . · . . .. Lead selenide . ., . · . · . ·. Lead sulfide. · . · . . .. .. . Lead telluride ... . .. ·. Lithium .. . . " . .... · . .. . · . Lithium chloride. ... .. . · . ... . Lithium fluoride .... ·. ·. Magnesium ... ... ·. ·.· . Magnesium cadmide .. " ·.·. Magnesium oxide ..... ·. Manganese. · . · . ·. ·. Mercury . .. . ... ·. · . Molybdenum. ... . ... · . .. . · . Neon. ... . ...... . ..... .. . · . Nickel. . . ...... . .. .. . . .. · . Nickel selenide .... ....... .. . .. . Niobium. ' " . ... . · . .... . '" . · .
Al Sb A As Ba Be Bi Bi,I'e, Cd Ca CaF, C C Cs Cl Cr Co Cu Dy Gd Ga Ge GeTe Au Hf He 4 (hcp) He 3 (bcc) H H2 H 2O In InSb I Ir Fe Fe203 FeSe2 FeS2 Kr La Pb PbSe PbS PbTe Li LiC!; LiF Mg Mg,Cd MgO Mn Hg Mo Ne Ni NiSe2 Nb
•
0,0
'
,
0
•••••
,
mJ
428 211 93 282 110 1440 119 155 209 230 510 420 2230 38 115 630 445 343 210 195 320 370 166 165 252 26.4 16 . 105 97 192 108 200 106 420, 467 660 366 637 72 142 105 135-160 194 124-135, 344 422 732 400 290 946 410 71.9 450 75 450 297 275
(4e-9).
'Y, mole. K2
Refs.
1. 35 0.112
1, 2, 89 3
0.19 2 ..7 0.17 0.021
3, 4 5 6, 7 8, 9 31
0.69 2.. 9
3.2 1.40 4.7 0.688 0.60 1..32 0.69 2.16
10
11, 5 32 12 13, 14, 90 15 16 17, 18, 19 20, 21, 22, 54 23 93 10, 24 25, 26 85 20,27, 91 28 84
1.,6
29, 30 44
.3.J 5.0
59 60, 61, 92 33 66 66
10 3.0
62, 95 56
1..63 1.3 0 .. 8 14 1. 79 2.0 7.1 7.79
15 86 34, 35, 36 63, 64 37 38 48, 49, 50 65, 75 59, 67, 68, 94 45 16, 69 66 52, 58, 94
.
4-116 TABLE
HEAT
4e-lO.
VALUES OF
E>
AND 'Y, IN THE HEAT-C.HACITY EQUATION
(4e-9)
(Continued)
Substance
Niobium-tin. . . . . . . . . .. . . . . . . . . .. Nitrogen ........................ Osmium ......................... Oxygen ........................ Palladium. . . . . . . . . . . . . . . . . . . . . .. Platinum. . . . . . . . . . . . . . . . . . . . . . .. Potassium ............ " .... " ... Potassium bromide. . . . . . . . . . . . . .. Potassium chloride. . . . . . . . . . . . . .. Potassium fluoride .............. " Potassium iodide ............... " Rhenium ........................ Rhodium ........................ Rubidium. . . . . . . . . . . . . . . . . . . . . .. Rubidium bromide. ............. Rubidium chloride.... . . . . . . . . . . .. Rubidium iodide. . . . . . . . . . . . . . . .. Ruthenium ...................... Scandium. ..................... Selenium. . . . . . . . . . . . . . . . . . . . . . .. Silicon .......................... Silicon dioxide. . . . . . . . . . . . . . . . . .. Silver ...................... '.' ... Silver bromide. . . . . . . . . . . . . . . . . .. Silver chloride. ................. Sodium ......................... Sodium bromide.. . . . . . . . . . . . . . . .. Sodium chloride ............... '" Sodium fluoride. . . . . . . . . . . . . . . . .. Sodium iodide .................... Strontium. . . . . . . . ..... .... . . . . . . .. Tantalum. . . . . . . . . . . . . . . . . . . . . .. Tellurium. . . . . . . . . . . . . . . . . . . . . .. Thallium. . . . . . . . . . . . . . . . . . . . . . .. Thorium. . . . . . . . . ... . . . . . . . . . . .. Tin (white) .................... " Tin (gray) ....................... Titanium. . . . . . . . . . . . . . . . . . . . . . .. Titanium dioxide ................. Tungsten. . . . . . . . . . . . .. . . . . . . . . .. Uranium ........................ Uranium dioxide ................. Vanadium ....................... Xenon .......................... yttrium ......................... Yttrium iron garnet. . . . . . . . . . . . .. Zinc. . . . . . . . . . . . . . . . . . . . . . . . . . .. Zinc sulfide. . . . . . . . . . . . . . . . . . . . .. Zirconium. . . . . . . . . . . . . . . . . . . . . ..
mJ
Symbol
Nb,Sn N Os 0 Pd Pt K KBr KCI KF KI Re Rh Rb RbBr RbCI RbI Ru Sc Se Si SiO, Ag AgBr AgCI Na N aBr NaCI N aF NaI Sr Ta Te TI Th Sn Sn Ti Ti0 2 W U U02 V Xe Y YIG Zn ZnS Zr
'Y, mole. K'
228 68 500 91 274 240 91 174 235 336 132 430 480 56 131 165 103 600 360 90 640 470 225 144 183 158 225 321 492 164 147 240 153 78.5 163 199 210 420 760 400 207 160 380 64 280 510 327 315 291
Refs.
13.1
87
2.4
59
9.42 6.8 2.1
53 27 15 39 39,40,41 86 39 59,70, 94 59 15 86 86 86 59 46, 96 71 25,26 42 54
2.3 4.9 2.4
3.3 10.7
0.650 1.4
3.6 5.9 1.47 4.3 1. 78 3.5 1.3 10.0 9.8 10.2 0.65 2.80
5, 72, 73 86 39 86 39 5
59, 68, 74, 94 71 75 76, 97 67,77,78 41 28,79, 80 43 59, 68, 81 57,97 47 45 51,94 24, 82, 83 35 28
HEAT CAPACITIES
4-117
References for Table 4e-l0 1. Phillips, N. E.: Phys. Rev. 114, 676 (1959). 2. Zavaritskii, N. V.: Zhur. Eksp. i. Teoret. Fiz. 84, 1116 (1958) [transl. Soviet Phys. JETP 7, 773 (1958)]. 3. Culbert, H. V.: Phys. Rev. 157, 560 (1967). 4. Taylor, W. A., D. C. McCollum, B. C. Passenheim, and H. W. White: Phys. Rev. 161, 652 (1967). 5. Roberts, L. M.: Proc. Phys. Soc. (London), ser. B, 70, 738 (1957). 6. Ahlers, G.: Phys. Rev. 145,419 (1966). 7. Gmelin, M. E.: Compt. rend. 259,3459 (1964). 8. Kalinkina, 1. N., and P. G. Strelkov: Zhur. Ek8p. i. Teoret. Fiz. 84, 616 (1958) [trans!. Soviet PhY8. JETP 6, 426 (1958)]. 9. Phillips, N. E., PhY8. Rev. 118, 644 (1960). 10. Phillips, N. E.: Phys. Rev. 184, A385 (1964). 11. Griffel, M., R. W. Vest, and J. F. Smith: J. Chem. Phys. 27, 1267 (1957). 12. Flubacher, P., A. J. Leadbetter, and J. A. Morrison: Phys. Chem. Solids 18, 160 (1960). 13. Burk, D. L., and S. A. Friedberg: Phys. Rev. 111, 1275 (1958). 14. Desnoyers, J. E., and J. A. Morrison: Phil. Mag. 8(8), 42 (1958). 15. Martin, D. L.: Phys. Rev. 189, A150 (1965). 16. Rayne, J. A., and W. R. G. Kemp: Phil. Mag. 1(8), 918 (1956). 17. Arp, V., N. Kurti, and R. Petersen: Bull. Am. PhY8. Soc. 2(II), 388 (1957). 18. Duyckaerts, G.: PhY8ica 6, 817 (1939). 19. Heer, C. V., and R. A. Erickson: Phys. Rev. 108,896 (1957). 20. Corak, W. S., M. P. Garfunkel, C. B. Satterthwaite, and A. Wexler: Phys. Rev. 98, 1699 (1955). 21. Phillips, N. E.: Proc. 5th Intern. Con!. Low Temp. Phys. Chem., pp. 414-416, University of Wisconsin Press, Madison, Wis., 1958. 22. Rayne, J. A.: AU8tralian J. Phys. 9, 189 (1956). 23. Dreyfus, B., B. B. Goodman, G. Troillet, and L. Weil: Compt. rend. 253, 1085 (1961). 24. Seidel, G., and P. H. Keesom: Phys. Rev. 112, 1083 (1958). 25. Flubacher, P., A. J. Leadbetter, and J. A. Morrison: Phil. Mag. 4(8), 273 (1959): 26. Keesom, P. H., and G. Seidel: Phys. Rev. 113, 33 (1959). 27. Ramanathan, K. G., and T. M. Srinivasan: Proc. Indian Acad. Sci. 49, 55 (1959). 28. Kneip, G. D., Jr., J. O. Betterton, Jr., and J. O. Scarbrough, PhY8. Rev. 130, 1687 (1963) . 29. Bryant, C. A., and P. H. Keesom: Phys. Rev. Letters 4, 460 (1960). 30. Clement, J. R., and E. H. Quinnell: Phys. Rev. 92, 258 (1953). 31. Itskevich, E. S.: Zhur. Eksp. i. Teoret. Fiz. 38, 351 (1960). 32. Huffman, D. R., and M. H. Norwood: Phys. Rev. 117,709 (1960). 33. Kouvel, J. S.: Phys. Rev. 102, 1489 (1956). 34. Jones, G. 0., and D. L. Martin: Phil. Mag. 45(7), 649 (1954). 35. Martin, D. L.: Phil. Mag. 46(7), 751 (1955). 36. Scales, W. W.: Phys. Rev. 112, 59 (1958). 37. Bergenlid, U. M., R. S. Craig, and W. E. Wallace: J. Am. Chem. Soc. 79,2019 (1957). 38. Barron, T. H. K., W. T. Berg, and J. A. Morrison: Proc. Roy. Soc. (London), ser. A, 250, 70 (1959). 39. Berg, W. T., and J. A. Morrison:Proc. Roy. Soc. (London), ser. A, 242, 467, 478 (1957). 40. Keesom, P. H., and N. Pearlman: Phys. Rev. 91, 1354 (1953). 41. Webb, F. J., and J. Wilks: Proc. Roy. Soc. (London), ser. A, 230, 549 (1955). 42. Jones, G. H. S., and A. C. Hollis-Hallett: Can. J. Phys. 38,696 (1960). 43. Keesom, P. H., and N. Pearlman: Phys. Rev. 112, 800 (1958). 44. Keesom, P. H., and N. Pearlman: Unpublished data. 45. Fenichel, H., and B. Serin: Phys. Rev. 142,490 (1966). 46. Wohlleben, D. (quoted by M. A. Jensen and J. P. Maita: PhY8. Rev. 149,410 (1966). 47. Radebaugh, R., and P. H. Keesom: Phys. Rev. 149, 209 (1966). 48. Guthrie, G. L., S. A. Friedberg, and J. E. Goldman: PhY8. Rev. 139, A1200 (1965). 49. Stetsenko, P. N., and Y. 1. Avsebt'ev: Soviet Phys. JETP 20,539 (1965). 50. Scurlock, R. G., and W. N. R. Stevens: Proc. PhY8. Soc. (London) 86,331 (1965). 51. Heiniger, F., E. Bucher, and J. Muller: Phys. Kond. Jl.laterie, 5,243 (1966). 52. van der Hoeven, B. J. C., and P. H. Keesom: Phys. Rev. 134, A1320 (1964). 53. Veal, B. W., and J. A. Rayne: Phys. Rev. 135, A442 (1964). 54. Martin, D. L.: Phys. Rev. 141,576 (1966). 55. Zimmerman, J. E., A. Arrott, and S. Shinozaki: in Proc. Low Temp. Calorimetry Con!. (Hel8inki), O. V. Lounasmaa, ed., p. 147, 1966. 56. van der Hoeven, B. J. C., and P. H. Keesom, Phys. Rev. 137, Al03 (1965).
~118
HEAT
Ho, J. C., and N. E. Phillips: Phys. Rev. Letters 17, 694 (1966). Leupold, H. A., and H. A. Boorse: Phys. Rev. 134, A1322 (1964). Wolcott, N. M.: Bull. inst. intern. du froid, Annexe 1955-3, PP. 286-289. Duyckaerts, G;: Physica 6, 401 (1939). Keesom, W. H., and B. Kurrelmeyer: Physica 6, 633 (1939). Berman, A., M. W. Zemansky, and H. A. Boorse: Phys. Rev. 109,70 (1958). Logan, J .. K., J. R. Clement, and H. R. Jeffers: Phys. Rev. 105, 1435 (1957). Smith, P. L.: Phil. Mag. 46(7), 744 (1955). Douglass, R. L.,W. H .. Lien, R. G. Peterson, and N. E. Phillips: Proc; 7th Intern. Conf. Low Temp. Phys. Chem., pp. 242-243, University of Toronto Press, 1960. 66. Gr¢nvold, F. C., and E. F. 'Westrum, Department of Chemistry, University of Michigan. 67. Bryant, C. A.: Thesis, Purdue University, 1960 (unpublished). 68. P. H. Keesom and N. Pearlman: in "Encyclopedia.of Physics," S. Flugge, ed., vol. XIV, "Low Temperature Heat Capacity of Solids," Tables 1-13, Springer-Verlag OHG, Berlin, 1956. 69. Keesom, W: H., and C. W. Clark:Physica 6, 513 (1939). 70. Keesom, P. H., and C. A. Bryant: Phys. Rev. Letters 2, 260 (1959). 71. Smith, P. L.: Bull. inst.intern. du froid, Annexe 1955-3, pp. 281-283. 72. Gaumer, R. E., and C. V. Heer: Phys. Rev. 118, 955 (1960). 73. Lien, W. H., and N.E. Phillips: Phys. Rev. 118,958 (1960). 74. Chou, C., D. White, and H. L. Johnston: Phys. Rev. 109,788 (1958). 75. van derHoeven, B. J. C., and P. H. Keesom: Phys. Rev. 135, A631 (1964). 76. Smith, P. L., and N. M. Wolcott: Bull .. inst. intern. du froid, Annexe 1955-3, pp. 283286. 77. Corak, W. S., and C. B. Satterthwaite: Phys. Rev. 102, 662 (1956). 78. Zavaritskii, N. V.: Zhur. Eksp. i. Teoret. Fiz. 33, 1085 (1957) [transl. Soviet Phys. JETP 6, 837 (1958)]. 79. Aven, M. H., R. S. Craig, T. R. 'Waite, and W. E. Wallace: Phys. Rev. 102, 1263 (1956). 80. Wolcott, N. M.: Phil. Mag. 2(8),1246 (1957). 81. Waite, T. R., R. S. Craig, and W. E. Wallace: Phys. Rev. 104, 1240 (1956). 82. Garland, C. W., and J. Silverman: J. Chem. Phys. 34,781 (1961). 83. Martin, D. L.: Phys. Rev. 167, 640 (1968). 84. Edwards, D.O., and R. C. Pandorf: Phys. Rev. 140, A816 (1965). 85. Finegold, L.: Phys. Rev. Letters 13, 233 (1964). 86. Lewis, J. T., A. Lehoczky, and C. V. Briscoe, Phys. Rev. 161,877 (1967). 87. Vieland, L. J., and A. W. Wicklund: Phys. Rev. 166,424 (1968). 88. Rayne, J. A.: Phys. Rev. 95, 1428 (1954). 89. Berg, W. T.: Phys. Rev. 167, 58il (Hllol::I). 90. van der Hoeven, B. J. C., and P. H. Keesom: Phys. Rev. 130, 1318 (1963). 91. Martin, D. L.:Phys. Rev. 170, 650 (1968). 92. Shinozaki, S. S., and A. Arrott: Phys. Rev. 152,611 (1966). 93. Donald, D. K., L. T. Crane, and J. E. Zimmerman, unpublished [quoted by O. V. Lounasmaa and L. J. Sundstrom, Phys. Rev. 150,399 (1966)]. 94. Morin, F. J., and J. P. Maita: Phys.Rev. 129, 1115 (1963). 95. Ohtsuka, T., and T. Satoh: in Proc. Low Temp. Calorimetry Can/. (Helsinki), O. V. Lounasmaa, ed., p. 92, 1966. 96. Flotow, H. E., and D. W. Osborne: Phys. Rev. 160,467 (1967). 97. Gordon, J. E., H. Montgomery, R. J. Noer, G. R. Pickett, and R. Tobon: Phys. Rev. 152, 432 (1966).
57. 58. 59. 60. 61. 62. 63. 64. 65.
4f. Thermal Expansion RICHARD K. KIRBY, THOMAS A. HAHN, AND BRUCE D. ROTHROCK
The National Bureau of Standards
In Table 4f-1, the coefficients of linear thermal expansion, a = (l/L m )dL/dT, are given in units of 10- 6 K-l; and the expansion, E = (LT - L 293 ) /L293, is given in units of 10- 6• When data are given for two or more crystalline forms of the element, the forms are designated (a), (fJ), ('Y), etc. The coefficient of cubical expansion may be computed from the following equations: fJ = 3a
+
fJ = 2aa ac fJ=aa+ab+ac
where aa, ab, and ac are the coefficients of linear expansion in the a, b, and c directions. In Table 4f-2, the coefficients of linear thermal expansion, a = (l/L o)dL/dT, are given in units of 10-8 K-l. The data designated by the symbols II or .L are in directions parallel or perpendicular to the c axis of the crystal. An (S) denotes data for the material in the superconducting state. The data for the material in the normal state in the snperconducting region were measured in a magnetic field high enough to destroy superconductivity. An asterisk (*) denotes a region where large errors may result because of the coefficient changing rapidly. In Table 4£-3, the coefficient of linear thermal expansion, a = (1/L 20 )dL/dt, is given in units of 1O- 6 /K-l; and the expansion, E = (L, - L 20 ) /L 20 is given in units of 10-5 where t stands for the Celsius temperature and L 20 is the length at 20°C. References used in the compilation of these tables and data on or references to publications on the thermal expansion of other materials can be obtained from the National Bureau of Standards. An approximate relation between the coefficient of volume expansion fJ
=
1.V
(aV) aT
p
and the temperature is given by Gruneisen's equation fJ =
Cv Qo[l - k(U /Qo)l'
where Cv is the molar heat capacity at constant volume, U is the energy of the lattice vibrations, and Qo and k are constants. If the Debye temperature ElD is known, both Cv and U may be calculated at any temperature T from the equations* Cv
=3R[12(:!..-)3 {eDIT y 3dy
U =
ElD
loT
10
Cv dT
* This material is concluded on page 4-142. 4-119
e" - 1
-3
ElD/T
eeD1T
-
1
]
4-120 TABLE
Temperature, K
25 50 75 100 150 200 250 293 350 400 500 600 700 800 1000
TABLE
HEAT
4£-1.
COEFFICIENTS OF LINEAR THERMAL EXPANSION,
Antimony
Aluminum
a (lO-a) (K-l),
Antimony a axis
Antimony c axis
a
€
a
€
a
€
a
0.5 3.5 8.1 12.0 17.1 20.2 22.0 23.0 24.1 24.9 26.5 28.2 30.4 33.5
-4160 -4120 -3970 -3720 -2980 -2040 -980 0 1340 2560 5150 7890 10890 14110
..... . ......
..... . ..... .
...... ..... .
..... . ..... .
..... . . .....
8.2 9.3 10.1 10.5 10.8 11.0 11.2 11. 3 11.6 11.8 11.9 12.0
-2220 -2000 -1520 -1000 -470 0 630 1200 2350 3520 4700 5890
4.7 6.0 7.1 7.7 8.1 8.4
-1580 -1440 -1120 -750 -360 0
15.1 15.8 16.1 16.1 16.2 16.2
-3500 -3110 -2310 -1500 -700 0
......
...... ...... . .....
4£-1.
..... . ..... . ..... .
..... .
..... . ..... . ..... .
..... .
. ..... ...... ......
a (lO-a) (K-l),
Bismuth c axis
Bismuth a axis
Bismuth
. ..... ...
..,
. ... . . ..... . ..... . . ..... . .....
COEFFICIENTS OF LINEAR THERMAL EXPANSION,
Beryllium c axis
Tempera-
...... ..... .
..... . ..... .
E
tUTS ,
K a
25 50 75 100 150 200 250 293 350 400 500 600 700 800 1000 1200 1400
I
a
E
'"
.... . .... .
0.1 0.7 2.9 5.2 7.4 8.9 10.2 11.1 12.3 13.4 14.4 15.7
-970 -960 -870 -670 -350 0 550 1080 2260 3540 4940 6440
...
....
.... .
""
'"
. . .
.
.... . .... .
I
4.8 9.2 11.1 11.9 12.6 12.9 13.1 13.2 13.4 13.4 13.5
E
E
a
... . ... .
. ..... . .....
. ... ... .
. ..... ......
9.0 9.9 10.9 11.2 11.5 11.7 11.9 11.9 12.1
-2390 -2150 -1630 -1070 -500 0 680 1270 2470
15.3 15.7 16.1 16.2 16.2 16.2 16.3 16.3 16.4
-3500 -3110 -2320 -1510 -700 0 930 1740 3380
I -3200 -3010 -2760 -2470 -1860 -1220 -570 0 760 1430 2780
... ... ... ...
. . . .
. ..... ..... . ..... . ..... .
...
. .
..... . ..... .
...
a
... . . ... . . ... . ... . "
... .
. ..... ..... . . ..... . ..... ..... . . .....
. ... . ... ... . ... . . ... . ...
I
E
...... ...... ...... ...... . .....
. .....
4-121
THERMAL EXPANSION , AND THE EXPANSION, • (10- 6), OF ELEMENTS
Argon
ex
Arsenic
ex
e
Barium
ex
e
e
--- --- --- ------
220 460 590
.. . .. . ... .. .
.. . .. . .. . .. . ... .. . .. . .. .
1950 10870 24140
.... . . .... .... . ..... ..... ..... ..... .... . ..... .... . . .... .....
.. . . .. .. . .. . .. .
5.6
. ..
.. . .. . .. . . .. .. . . ..
AND THE EXPANSION, •
30.7
31. 3 32.0 33,0 38.4
..
-7370 -7010 -6420 -5760 -4340 -2860 -1330
o
1800 3420 6940
-3.8 +2.7 7.8 10.7 14.4 16.5 18.2 19.8 22.1 24,9 36.7
...
. ... . ... . ... . ... . ...
13 18 21 24
0 880 1850 4110
. .. . ..
. ...
,
,
0 320
. .. ... .. ., . ... .. .
.. . . ..
,
(10- 6),
. ... . ... . ...
OF ELEMENTS
-3340
-3110 -2460 -1690 -820
o
1190 2360 5350
43.5 58.8 60.4 59.9 58.7 57.5 55.8 54.3 51. 7 49.1 41. 9
•
ex
e
0,5 1.3 4,1 7.1 9.6 11.2 12.7 13.7 15.2 16.4 17.7 19,0 21. 6
-1300 -1280 -1150 -870 -450 0 690 1350
0,7 1.6 4,7 8.0 10.7 12.3 13.9 15.0 16.6 18.0 19.3 20.6
-1470 -1440 -1290 -970 -500 0 750 1480 3060 4790 6650 8650
2790 4380
6080 7920 11970
(Continued)
Cadmium c axis
-3460 -3480
ex
---
.. . . .. . .. "
Cadmium a axis
Cadmium
12.0 21.4 25.3 27.1 29.2 30.2
... . .. ... ...
Beryllium a axis
Beryllium
Carbon (diamond)
Calciurn
-15450
-14090 -12580 -11080 -8110 -5200 -2370
o
3020 5550 10120
14.0 16.7 18.9 20.4
21.4 22.1 22.7 23.0 23,5 23.8 24.0
-4260 -3870
-2970 -1990 -940
o
1280 2420 4750 7120 9510
0.05 0.20 0.41 0,70 1.00 1.5 1.8 2.5 3,0 3.4 3.7 4.3 4.7 5,1
-84 -78 -63 -36
o
71 153 369 640 960 1320 2120 3030 4020
4-122 TABLE
Temperature
HEAT
4f-1.
COEFFICIENTS OF LINEAR THERMAL EXPANSION, a
Carbon (graphite) a axis
Carben (graphite)
Carbon (graphite) c axis
.(lO-:-6,)(K-l),
Cerium
K
25 50 75 100 150 200 250 293 350 400 .500 600 700 800 1000 1200 1400 1600 1800 2000
TABLE
Temperature, K
25 50 75 100 150 200 250 293 350 400 500 600 700 800 1000
a
a
E
.... ... .
. .....
....
......
o.
-1300 -1030 -700 -330. 0 460 870 1730 2640 3600 4580 6630 8730 10890 13090 15330 17610
-0.4 -0.6 -0.8 -1.0 -1.2 -1.2 -1.1 -0.7 -0.2 +0.2 0.5 0.8 0.9 1.0 1.1 1.2 1.2
... .
4.9 6.1 7.0 7.6 7.8 8.1 8.4 8.9 9.4 9.8 10.0 10.4 10.6 10.9 11.1 11.3 11.5
4f-1.
0
•••
0.
E
"0 ••
.
,.,
..... ..... ..... 152 127 92 47 0 -68 -128 -226 -276 -278 -246 -118 +52 250 460 690 930
Dysprosium .c axis
a
a
5.5 5.6 5.7 5.9 6.1 6.3 6.7
...
0"
E
•
'"
.
0"
•
15.4 19.5 22.6 24.8 25.9 26.8 27.4 28.2 28.6 28.9 29.1 29.6 30.1 30.6 31.1 31.6 32.1
..0.· . .. 0.· .
. .....
-4220 -3340 -2280 -1090 0 1500 2860 5640 8480 11360 14260 20140 26100 32180 38340 44620 50980
a
E
. .. . .. . .. ... ... .. . ...
E
•••
0'
... .
... . ... . 0 320 600 1170 1770 2390 3040
... .
0
E
••• •
0
•••
.... ....
. ... . ...
. ...
0.' •
14.8 15.8 16.5 18.2 19.6 21. 6 23.5
0 870 1680 3410 5310 7370 9620
'0'
.
... .
... . 8.4 9.0 9.3 9.5 9.7 9.8 10.1 10.5 10.9 11.6 14.8
. ... . ... ,0 ••
·
...
.
'"
. ... 0 310 590 1210 1870 2600 3390 5140
...
.0 .•
...
. ...
(lO-6) (K-l), Erbium .a axis
Erbium
a
..0.
5.2 5.6 5.8 6.4 7.0 7.6 8.2 9.4
COEFFICIENTS OF LINEAR THERMAL EXPANSION, a
Dysprosium a axis
... . .. .. . .. .
a
E
a
. ...
. .. . .. . .. . ..
-1300 -860 -410 0 550 1040 2040 3070 4140 5260 7830
6.0 6.1 6.2 6.4 6.7 7.1
... . ..
E
"0 •
· .,. ·
'0'
..0.
0 340 650 1280 1930 2620
. ... · ...
4--,.123
THERMAL EXPANSION AND THE EXPANSION,
(10- 6),
E
OF ELEMENTS
Chromium
Cesium
(Continued)
Cobalt
Copper
Dysprosium
a
a
E
a
•
a
E
.. . .. . .. . .. .
0.1 0.6 1.5 2.5 4.0 5.1 5.6 5.0 7.1 8.0 9.0 9.7 10.4 10.9 12.0
-980 -980 -950 -900 -740 -510 -240 0 290 670 1530 2470 3470 4530 6830
. .....
..... .....
0.6 3.8 7.6 10.5 13.6 15.2 16.1 16.7 17.3 17.6 18.3 18.9 19.6 20.4 22.4 24.8
-3252 -3214 -3067 -2836 -2218 -1492 -707
.. . · .. .. .
100
... · .. · .. · .. ...
... ... .. .
....
..... . ...... ..... . ..... . 13.7 13.8 13.9 14.2 14.9 18(a)
14.3((3) 14.5 14.7
. ....
AND THE EXPANSION, E
Erbium c axis
. ..... . .....
(10- 6),
Europium
.....
..... . .... ..... .....
0 780 1480 2880 4330 5900 8380 11260 14170
OF ELEMENTS
•
a
.. .
0 310 590 1170 1790 2450 3180
....
E
... .
...
.
'"
... . .. . ..
5.2 6.2
...
.
. ... '" .
-460 -160 +150 350 0 220 530 1270 2080 2940 3850 5890
16.6 16.9 17.1 17.7 18.2 18.7
... . ... .
'"
. .
0 960 1800 3540 5340 7180 '"
'"
. .
... 25
... ... ... ... .. , . .. '"
6.0(a)
-1 -2 +5.5((3) 6.7 7.8 8.4 8.9 9.4 11.7
-1120 -940 -760 -360 0 500 960 1920 2950 4050 5230 7870
Gadolinium c axis
a
a
E
(Continued) GadolinlUm a axis
a
... .
0
970 1840 3640 5500 7420 9420 13700 18410
4.9(a)
1.9 7.7((3) 8.3 8.ti 9.0 9.3 10.0 10.6 11.4 12.3 14.2
Gadolinium
E
a
a
5.5 5.6 6.0 6.4 6.9 7.7
5.4 9.0 11. 5 12.4 12.8 13.0
E
0 40 410 1490 2690 3950 5240
4-124 TABLE
HEAT
4f-1.
COEFFICIEN1.1S OF LINEAR THERMAL EXPANSION, a
Gallium
Temperature,
Gal- Gal- Gallium lium lium a axis b axis c axis
(10- 6) (K-l) ,
Germanium
Gold
K a
a
a
a
--25 50 75 100 150 200 250 293 350 400 500 600 700 800 1000 1200
TABLE
19.2 19.7
4f-1.
-840 0
a
11
34 47 55 65 71 79 87
11.5
a
€
31.0
-0.1 +0.2 1.1 2.4 4.1 4.9 5.6 5.7 6.0 6.2 6.5 6.7 6.9 7.2
-950 -950 -930 -890 -720 -490 -240 0 330 640 1280 1940 . 2620 3320
3.2 7.8 10.5 11.9 13.1 13.6 14.0 14.2 14.5 14.7 15.2 15.8 16.4 17.1 18.8 21.1
-3250 -3120 -2880 -2600 -1970 -1300 -610 0 820 1550 3040 4590 6200 7870 11440 15400
COEFFICIENTS OF LINEAR THERMAL EXPANSION, a
Iodine a axis
Iodine
Temperature, K
25 50 75 100 150 200 250 293 350 400 500 600 700 800 1000 1200 1400 1600 1800
16.6
a
---
a
-16600 -16100 -15000 -13800 -10700 -7300 -3600 0 5360
133
0 7580
(10- 6) (K-l), Iodine c axis
Iodine b axis
a
€
a
94
0 5870
34
0 2560
4-125
THERMAL EXPANSION AND THE EXPANSION, e
(Continued)
OF ELE!y[ENTS
Holmium
:aafnium
a
(10-'),
Indium a axis
Indium
e
a
a
.. . .. . ...
. ..... ...... ..... .
... ...
4.8 5.4 5.7 5.9 6.0 6 ..1 6.2
-1090 -830 -550 -260 0 350 660
10.1 19 .. 3 23 ..0 24.9 26.7 28.2 30.0 32.1 35.9 39,9
. .. ... ... ... ... 10 ...
...
Indium c axis
e
a
e
a
e
-6970 -6580 -6050 -5450 -4150 -2780 -1330 0 1930 3830
4.4 17.7 24.2 28.4 34.0 39.5 46.0 52.9 64.6 77.3
-9130 -8840 -8310 -7650 -6080 -4250 -2120 0 3320 6860
21.4 22.6 20.5 18.0 12.2 5.6 -2.0 -9.6 -21.5 -34.8
-2660 -2090 -1550 -1060 -300 +150 +240 0 -870 -2240
I
I AND THE EXPANSION, e
Iridium
(10-'),
Krypton
Iron
I
-~------~--~--
a
e
a
(Continued)
OF ELEMENTS
E
Lead
Lanthanum
,
I
I
eo
a
e
a
2170 8230 16040 25780
. ..... ..... . ..... . ..... .
.....
14.2 21. 7 24.4 25.4 26.6 27.5 28.2 28.7 29.3 29.8 32.1
ao
e
---
... . ... .
..... . ..... . ..... .
4.4 5.3 5.9 6.2 6.5 6.7 6.8 7.2 7.4 7.7 7.9 8.4 8.8 9.2 9.6 10.1
-1110 -860 -580 -270 0 380 710 1410 2140 2900 3680 5320 7040 8840 10730 12700
... .
0.2 1.3 3.5 5.7 8.4 10.1 11.1 11.8 12.6 13.2 14.3 15.2 16.1 16.5 15.5(= f-
I~
Region of anomalous effecls I kg/cm2 • 9.80665x 104 N/m2
100
:;:
80
:;
6::J 60 0
Z 0
U
-' 40
-3
TABLE
4h-11.
ENTHALPY OF ARGON,
(H - EoO)/RTo
70 atm i 100 atm 40atm 7 atm 10 atm T, K 1 atm 4atm - - - - - - - - - - - -- - - - - - - - - - - 100 200 300 400 500
0.8935 1. 8236 2.7422 3.6590 4.5750
1. 8029 2.7319 3.6532 4.5718
1. 7819 2.7217 3.6476 4.5686
1. 7606 2.7114 3.6418 4.5654
1.53 2.610 3.586 4.535
1.3 2.512 3.533 4.506
600 700 800 900 1000
5.4907 6.4063 7.3218 8.2372 9.1525
5.4891 6.4057 7.3220 8.2380 9.1538
5.4874 6.4052 7.3222 8.2388 9.1551
5.4859 6.4047 7.3226 8.2396 9.1564
5.471 6.400 7.326 8.249 9.170
5.457 6.397 7.330 8.258 9.184
4h-12.
TABLE
T, K
4atm
1 atm
ENTROPY OF ARGON,
7 atm
10 atm
40 atm
SIR 70 atm
100 atm
---- - - - - -- - -- - -- - - - - -- - -
2.42 3.48 4.48
100 200 300 400 500
15.8425 17.6069 18.6245 19.3449 19.9032
16.2012 17.2308 17.9548 18.5146
15.6218 16.6637 17.3913 17.9527
15.245 16.2995 17.0308 17.5937
13.64 14.8389 15.6067 16.1850
12.83 14.2067 15.0118 15.6037
12.2 13.781 14.618 15.2261
5.445 6.395 7.335 8.268 9.198
600 700 800 900 1000
20,3593 20.7449 21.0787 21.3733 21.6368
18.9715 19.3575 19.6917 19.9864 20.2500
18.4104 18.7969 19.1313 19.4263 19.6900
18.0522 18.4391 18.7739 19.0690 19.3328
16.6513 17 .0426 17.3802 17.6772 17.9423
16.0776 16.4732 16.8134 17.1122 17.3785
15.7072 16.1070 16.4498 16.7503 17.0179
1100 1200 1300 1400 1500
10.0679 10.9832 11.8985 12.8138 13.7291
10.0696 10.9852 11.9007 12.8162 13.7316
10.0712 10.9871 11.9029 12.8186 13.7342
10.0729 10.9891 11. 9051 12.8210 13.7367
10.090 11.009 11.927 12.845 13.763
10.107 11.029 11.950 12.869 13.788
10.125 11.049 11.972 12.894 13.815
1100 1200 1300 1400 1500
21. 8751 22.0926 22.2927 22.4780 22.6505
20.4884 20.7060 20.9062 21.0916 21.2640
19.9285 20.1462 20.3464 20.5318 20.7043
19.5715 19.7892 19.9895 20.1749 20.3474
18.1819 18.4003 18.6010 18.7869 18.9597
17.6190 17.8381 18.0394 18.2256 18.3988
17.2592 17.4789 17.6807 17.8673 18.0408
1600 1700 1800 1900 2000
14.6443 15.5595 16.4749 17.3901 18.3053
14.6470 15.5624 16.4778 17.3931 18.3085
14.6497 15.5652 16.4808 17.3962 18.3116
14.6524 15.5680 16.4837 17.3992 18.3147
14.680 15.597 16.513 17.430 18.346
14.707 15.625 16.543 17.460 18.377
14.735 15.654 16.572 17.491 18.409
1600 1700 1800 1900 2000
22.8119 22.9635 23.1064 23.2415 23.3698
21.4254 21. 5771 21. 7200 21. 8551 21. 9834
20.8657 21.0174 21.1603 21.2955 21.4238
20.5089 20.6606 20.8035 20.9387 21.0670
19.1214 19.2733 19.4165 19.5518 19.6802
18.5607 18.7128 18.8561 18.9915 19.1201
18.2029 18.3552 18.4987 18.6343 18.7630
2100 :2200 2300 2400 2500
19.2206 20.1358 21.0510 21. 9662 22.8815
19.2238 20.1390 21.0543 21. 9696 22.8849
19.2269 20.1423 21.0576 21. 9729 22.8884
19.2301 20.1456 21.0609 21. 9763 22.8918
19.262 20.178 21.094 22.010 22.926
19.294 20.211 21.127 22.044 22.960
19.326 20.243 21.160 22.077 22.994
2100 2200 2300 2400 2500
23.4917 23.6080 23.7192 23.8256 23.9276
22.1053 22.2217 22.3329 22.4393 22.5413
21.M57 21. 6620 21.7732 21. 8797 21. 9817
21.1890 21.3053 21.4165 21.5229 21. 6249
19.8022 19.9187 20.0299 20.1364 20.2385
19.2422 19.3587 19.4701 19.5766 19.6787
18.8851 19.0017 19.1131 19.2197 19.3218
2600 2700 2800 2900 3000
23.7967 24.7120 25.6272 26.5424 27.4576
23.8002 24.7154 25.6307 26.5459 27.4612
23.8036 24.7189 25.6342 26.5495 27.4647
23.8071 24.7224 25.6377 26.5530 27.4683
23.842 24.757 25.673 26.5S9 27.504
23.876 24.792 25.708 26.624 27.540
23.911 24.827 25.743 26.659 27.575
2600 2700 2800 2900 3000
24.0257 24.1200 24.2109 24.2987 24.3834
22.6394 22.7337 22.8246 22.9124 22.9971
22.0798 22.1741 22.2650 22.3528 22.4375
21.7231 21. 8174 21. 9083 2l. 9961 22.0808
20.3366 20.4310 20.5219 20.6098 20.6945
19.7769 19.8713 19.9623 20.0501 20.1349
19.4201 19.5145 19.6055 19.6934 19.7782
>-3
::q ~
~ o
tJ >-1
>z: P>
:s:,.... o
>tJ
!;U
o
>tJ ~
!;U
>-3
H
~
[J2
o
""J
---_ ...
_
... _ - - -
.
-----
-
-
-
-
~
[J2
~
[J2
t
f-L (J)
CO
TABLE
4h-13.
Z T, X
l'atoo
'f'
COMPRI!lSSIBILITY FACTOR FOR HYDROGEN,
4atoo
=
PVjRT
7atoo
10 atm
TABLE
4Oatoo
70e.tm
100 atoo
--- - - - - - - - - -- - - - - - - - - - - -
4h-14.
RELATIVE DENSITY OF HYDROGEN,
T, K
1 atm
4atm
7atm
10atm
40atm
70 atm
pjpo
I-'
-..:t
o
100 atm
--- - - -- - -- - - - - - - - - - - - - - -
40 60 80 100 120
0.9845 0.9955 0.9986 0.9998 1.0003
0.9362 0.9822 0.9946 0.9992 1.0012
0.8853 0.9691 0.9908 0.9987 1.0021
0.8317 0.9564 0.9872 0.9983 1.0030
0.8757 0.9682 1.0029 1.0176
0.8700 0.97.82 1.0222 1.0405
0.9395 1.0174 1.0560 1.0726
40 60 80 100 120
6.9408 4.5761 3.4214 2.7338 2.2771
29.195 18.552 13.740 10.942 9.0999
54.029 32.905 24.138 19.158 15.910
82.160 47.632 34.609 27.379 22.709
208.08 141.15 109.01 89.532
366.53 244.49 187.17 153.23
484.88 335.82 258.83 212.36
140 160 180 200 220
1.0005 1.0006 1.0007 1.0007 1.0007
1.0020 1.0024 1.0028 1.0028 1.0028
1.0036 1.0043 1.0048 1.0048 1.0048
1.0052 1.0062 1.0067 1.0068 1.0067
1.0243 1.0271 1.0283 1.0283 1.0276
1.0488 1.0516 1.0523 1.0513 1.0497
1.0786 1.0798 1.0785 1.0760 1.0730
140 160 180 200 220
1.9514 1.7073 1.5174 1.3657 1.2415
7.7937 6.8167 6.0569 5.4512 4.9557
13.617 11.907 10.578 9.5206 8.6551
19.422 16.978 15.084 13.574 12.341
76.240 66.528 59.067 53.160 48.361
130.30 113.71 101.01 90.995 82.849
181 :01 158.21 140.80 127.01 115.79
240 260 280 300 320
1.0007 1.0006 1.0006 1.0006 1.0006
1.0027 1.0024 1.0024 1.0024 1.0024
1.0047 1.0044 1.0042 1.0042 1.0041
1.0066 1.0064 1.0061 1.0059 1.0057
1.0269 1.0259 1.0247 1.0238 1.0229
1.0480 1.0459 1.0439 1.0420 1.0402
1.0698 1.0667 1.0636 1.0607 1.0579
240 260 280 300 320
1.1381 1.0506 0.97559 0.91055 0.85364
4.5431 4.1949 3.8953 3.6356 3.4084
7.9347 7.3265 6.8045 6.3509 5.9546
11.314 10.446 9.7026 9.0575 8.4931
44.361 40.988 38.105 35.596 33.401
76.068 70.358 65.457 61.204 57.479
106.46 98.553 91.780 85.896 80:740
340 360 380 400 420
1.0005 1.0005 1.0005 1.0005 1.0005
1.0021 1.0020 1.0020 1.0020 1.0019
1.0037 1.0036 1.0035 1.0034 1.0033
1.0054 1.0052 1.0050 1.0048 1.0046
1.0217 1.0209 1.0201 1.0193 1.0185
1.0384 1.0367 1.0353 1.0339 1.0325
1.0553 1.0529 1.0507 1.0486 1.0466
340 360 380 400 420
0.80351 0.75887 0.71893 0.68298 0.65046
3.2088 3.0309 2.8714 2.7278 2.5982
5.6065 5.2956 5.0174 4.7670 4.5404
7.9959 7.5532 7.1571 6.8006 6.4780
31.473 29.748 28.204 26.815 25.558
54.192 51.265 48.632 46.286 44.120
76.178 72.110 68.458 65.165 62.181
440 460 480 500 520
1.0004 1.0004 1.0004 1.0004 1.0004
1.0017 1.0016 1.0016 1.0016 1.0016
1.0030 1.0029 1.0028 1.0028 1.0028
1.0045 1.0043 1.0041 1.0040 1.0039
1.0180 1.0172 1.0165 1.0160 1.0155
1.0314 1.0301 1.0289 1.0280 1.0271
1.0448 1.0431 1.0415 1.0400 1.0385
440 460 480 500 520
0.62095 0.59396 0.56921 0.54644 0.52542
2.4806 2.3729 2.2741 2.1831 2.0991
4.3353 4.1473 3.9749 3.8159 3.6691
6.1842 5.9165 5.6711 5.4448 5.2359
24.408 23.365 22.407 21.522 20.704
42.160 40.377 38.740 37.223 35.823
59.457 56.964 54.675 52.563 50.615
540 560 580 600
1.0004 1.0004 1.0003 1.0003
1.0016 1.0015 1.0013 1.0012
1.0026 1.0026 1.0024 1.0023
1.0037 1.0036 1.0035 1.0034
1.0148 1.0144 1.0140 1.0136
1.0260 1.0252 1.0244 1.0237·
1.0372 1.0360 1.0348 1.0337
540 560 580 600
0.50596 0.48789 0.47112 0.45541
2.0214 1.9494 1.8826 1.8200
3.5339 3.4077 3.2908 3.1815
5.0430 4.8634 4.6961 4.5400
19.951 19.246 18.590 17.977
34.533 33.326 32.202 31.150
48.801 47.113 45.541 44.070
------
~ ~
4-171
THERMODYNAMIC PROPERTIES OF GASES
300
.4
.5
.6
.7
.8
.9
I
I
I
I
I
I
I
I"'M!:::'::'UI'fC.
I II
P, atm
~f-'TIRTo
TABLE
4h-22.
ENTROPY OF NITROGEN,
t ,....
SIR
-1 T, K
--100 200 300 400 500
4 atm 1 atm --- --1.2589 2.5535 2.5358 3.8302 3.8385 5.1244 5.1203 6.4194 6.4178
7 atm
10 atm
--- ---
40 atm 70 atm 100 atm - - - ---- - - -
2.5179 3.8221 5.1164 6.4162
2.4999 3.8140 5.1125 6.4147
2.3140 3.7351 5.0756 6.4005
2.125 3.662 5.0420 6.3891
1.94 3.596 5.013 6.3802
7 atm -----------16.55 19.1705 17.607 100 21.6249 20.2208 19.6431 200 23.0482 21.6549 21.0884 300 24.0586 22.6687 22.1055 400 24.8479 23.4595 22.8977 500 T, K
1 atm
4atm
10 atm
40 atm
- - -- - -
100 atm - - ---70 atm
19.2682 20.7248 21. 7454 22.5390
17.6905 19.2706 20.3246 21.1322
16.932 18.6461 19.7322 20.5532
16.382 18.230 19.3448 20.1781
600 700 800 900 1000
7.7334 9.0735 10.4428 11.8416 13.2683
7.7333 9.0744 10.4444 11.8438 13.2708
7.7332 9.0752 10.4460 11.8459 13.2734
7.7331 9.0762 10.4477 11.8482 13.2760
7.7332 9.0861 10.4647 11.8705 13.3025
7.73549.0977 10.482£ 11. 8937 13.3296
7.7393 9.1103 10.5020 11.9177 13.3573
600 700 800 900 1000
25.5020 26.0662 26.5656 27.0154 27.4260
24.1144 24.6790 25.1786 25.6286 26.0393
23.5534 24.1184 24.6183 25.0685 25.4793
23.1953 23.7607 24.2609 24.7113 25.1223
21.7958 22.3654 22.8682 23.3203 23.7323
21.2236 21. 7970 22.3022 22.7561 23.1693
20.8548 21.4319 21.9396 22.3949 22.8094
1100 1200 1300 1400 1500
14.7203 16.1950 17.6894 19.2014 20.7288
14.7232 16.1982 17.6929 19.2050 20.7325
14.7261 16.2014 17.6963 19.2086 20.7363
14.7290 16.2046 17.6997 19.2122 20.7400
14.7588 16.2369 17.7343 19.2486 20.7779
14.7891 16.2697 17.7691 19.2851 20.8159
14.8197 16.3029 17.8043 19.3221 20.8542
1100 1200 1300 1400 1500
27.8039 28.1543 28.4811 28.7872 29.0751
26.4173 26.7678 27.0947 27.4007 27.6887
25.8574 26.2080 26.5349 26.8410 27.1290
25.5004 25.8511 26.1780 26.4842 26.7721
24.1114 24.4627 24.7901 25.0965 25.3848
23.5491 23.9010 24.2289 24.5357 24.8242
23.1899 23.5424 23.8707 24.1779 24.4666
1600 1700 1800 1900 2000
22.2695 23.8219 25.3848 26.9568 28.5370
22.2734 23.8259 25.3889 26.9610 28.5413
22.2773 23.8299 25.3930 26.9652 28.5455
22.2812 23.8340 25.3971 26.9693 28.5498
22.3203 23.8742 25.4382 27.0113 28.5924
22.3597 23.9146 25.4795 27.0533 28.6352
22.3992 23.9550 25.5209 27.0954 28.6779
1600 1700 1800 1900 2000
29,3467 29.6037 29.8477 30.0799 30.3013
27.9603 28.2173 28.4613 28.6936 28.9150
27.4006 27.6577 27.9017 28.1339 28.3553
27.0438 27.3009 27.5449 27.7772 27.9986
25.6567 25.9140 26.1582 26.3905 26.6120
25.0964 25.3537 25.5981 25.8306 26.0522
24.7390 24.9965 25.2410 25.4736 25.6953
2100 2200 2300 2400 2500
30.1246 31. 7187 33.3187 34.9240 36.5342
30.1290 31. 7230 33.3231 34.9284 36.5387
30.1333 31. 7274 33.3275 34.9329 36.5432
30.1376 31. 7318 33.3319 34.9374 36.5477
30.1808 31.7755 33.3761 34.9819 36.5926
30.2241 31.8193 33.4203 35.0266 36.6377
30.2674 31.8632 33.4647 35.0712 36.6827
2100 2200 2300 2400 2500
30.5129 30.7154 30.9097 31.0963 31.2759
29.1266 29.3291 29.5234 29.7100 29.8896
28.5670 28.7695 28.9638 29.1504 29.3300
28.2102 28.4128 28.6071 28.7937 28.9733
26.8238 27.0264 27.2207 27.4074 27.5870
26.2640 26.4667 26.6611 26.8478 27.0275
25.9072 26.1100 26.3043 26.4911 26.6708
2600 2700 2800 2900 3000
38.1488 39.7676 41.3901 43.0160 44.6452
38.1533 39.7722 41.3947 43.0206 44.6499
38.1579 39.7767 41.3993 43.0252 44.6545
38.1624 39.7813 41.4039 43.0298 44.6591
38.2076 39.8268 41.4496 43.0758 44.7053
38.2530 39.8723 41.4954 43.1218 44.7514
38.2983 39.9179 41.5413 43.1678 44.7976
2600 2700 2800 2900 3000
31.4488 31.6157 31.7769 31. 9327 32.0836
30.0625 30.2294 30.3906 30.5464 30.6973
29.5029 29.6698 29.8310 29.9868 30.1377
29.1462 29.3131 29.4743 29.6301 29.7810
27.7600 27.9269 28.0882 28.2440 28.3949
27.2004 27.3674 27.5287 27.6846 27.8355
26.8438 27.0108 27.1721 27.3280 27.4790
--
Ol
iII t>=J
p... >--3
TABLE
4h-23.
COMPRESSIBILITY FACTOR FOR OXYGEN,
Z T, K
1 atm
4atm
=
PV/RT
7 atm
10 atm
TABLE
4h-24.
RELATIVE DENSITY OF OXYGEN,
p/po
40 atm
70atm
OOatm
.--- - - -- - - - - - - - -- - - ----
T, K
1 atm
4stm
7 stm
10 stm
40 atm
70 stm
100 atm
--- - - -- - ----- - - -- - -- - ----
100 200 300 400 500
0.97724 0.99701 0.99939 1.00001 1.00022
0.98796 0.99759 1.00006 1.00088
0.97880 0.99580 1.00012 1.00154
0.96956 0.99402 1.00019 1.00222
0.8734 0.97731 1.00161 1.00942
0.7764 0.9636 1.0042 1.0173
0.6871 0.9541 1.0079 1.0256
100 200 300 400 500
2.79257 1.36860 0.91023 0.68225 0.54568
5.5245 3.6474 2.72885 2.18129
9.7584 6.39455 4.77519 3.81474
14.073 9.151 6.8212 5.4459
62.4 37.231 27.246 21.628
123 66.082 47.557 37.556
198.5 95.34 67.69 53.217
600 700 800 900 1000
1.00029 1.00031 1.00031 1.00030 1.00029
1.00116 1.00124 1.00124 1.00121 1.00115
1.00204 1.00218 1.00218 1.00211 1.00202
1.00292 1.00312 1.00311 1.00302 1.00288
1.01205 1.01275 1.01265 1.01223 1.01167
1.0216 1.0227 1.0224 1.0216 1.0206
1.0314 1.0328 1.0323 1.0312 1.0296
600 700 800 900 1000
0.45470 0.38974 0.34102 0.30313 .0.27282
1.81723 1.55750 1.36282 1.21143 1.09035
3.17736 2.72307 2.38269 2.11809 1.90646
4.5351 3.8864 3.4006 3.0231 2.7211
17.9767 15.3980 13.4746 11. 9823 10.7901
31.165 26.684 23.355 20.776 18.717
44.098 37.747 33.045 29.404 26.505
1100 1200 1300 1400 1500
1.00027 1.00026 1.00025 1.00023 1.00022
1.00109 1.00104 1.00098 1.00093 1.00088
1.00192 1. 00182 1.00172 1.00163 1.00155
1.00274 1.00260 1.00246 1.00233 1.00221
1.01107 1.01047 1.00991 1.00938 1.00890
1.0195 1.0184 1.0174 1.0165 1.0156
1.0281 1.0265 1.0250 1.0237 1.0224
1100 1200 1300 1400 1500
0.24802 0.22736 0.20987 0.19488 0.18189
0.99129 0.90872 0.83887 0:77899 0.72710
1. 73331 1.58903 1.46694 1.36228 1.27157
2.4741 2.26828 2.09409 1.94476 1.81533
9.8150 9.0024 8.3145 7.7247 7.2131
17.034 15.631 14.443 13.423 12.539
24.131 22.154 20.480 19.041 17.794
1600 1700 1800 1900 2000
1.00021 1.00020 1.00019 1.00018 1.00017
1.00084 1.00080 1.00076 1.00072 1.00069
1.00147 1.00140 1.00133 1.00127 1.00121
1.00210 1.00200 1.00190 1.00181 1.00173
1.00845 1.00803 1.00765 1.00728 1.00696
1.0149 1. 0141 1.0134 1. 0128 1.0122
1.0213 1.0202 1.0193 1.0183 1.0175
1600 1700 1800 1900 2000
0.17053 0.16050 0.15158 0.14361 0.13643
0.68168 0.64161 0.60599 0.57412 0.54543
1.19219 1.12214 1.05987 1.00415 0.95400
1.70206 1. 60210 1.51324 1.43373 1.36215
6.7653 6.3700 6.0184 5.7037 5.4202
11.764 11.080 10.472 9.927 9.436
16.700 15.735 14.874 14.105 13.410
2100 2200 2300 2400 2500
1.00017 1.00016 1.00015 1.00015 1. 00014
1.00066 1.00063 1.00061 1.00058 1.00056
1.00116 1. 00111 1.00107 1.00102 1.00098
1.00166 1.00159 1.00152 1.00146 1.00141
1.00666 1.00638 1.00610 1.00586 1.00564
1.0117 1.0112 1.0107 1.0103 1.0099
1.0167 1.0161 1.0153 1.0147 1.0142
2100 2200 2300 2400 2500
0.12993 0.12403 0.11863 0.11369 0.10915
0.51947 0.49587 0.47432 0.45457 0.43640
0.90862 0.86736 0.82968 0.79515 0.76337
1.29737 1.23849 1.18473 1.13543 1.09007
5.1637 4.9303 4.7173 4.5218 4.3419
8.991 8.587 8.217 7.878 7.566
12.781 12.208 11.686 11.206 10.763
2600 2700 2800 2900 3000
1.00014 1.00013 1.00013 1.00012 1. 00012
1.00054 1.00052 1.00050 1.00049 1.00047
1.00095 1.00091 1.00088 1.00085 1.00082
1.00135 1.00130 1.00126 1. 00122 1.00117
1.00543 1.00523 1.00505 1.00488 1.00471
1.0095 1.0092 1.0089 1.0086 1.0083
1.0136 1. 0131 l.0127 l.0122 l.0118
2600 2700 2800 2900 3000
0.10495 0.10106 0.09745 0.09409 0.09096
0.41962 0.40409 0.38966 0.37623 0.36370
0.73404 0.70688 0.68165 0.65817 0.63625
1.04820 1.00943 0.97342 0.93989 0.90861
4.1758 4.0219 3.8790 3.7458 3.6216
7.278 7.010 6.762 6.531 6.315
10.355 9.976 9.624 9.296 8.990
>-3
p::
IC"J
~
o
t::I
~
~
H
..
-
o
"d :;:d
o
"d IC"J
:;:d
-_.-
>-3
H
IC"J
w
o
"'J Q.
po. w IC"J w
t
i-'
'"'l '"'l
TABLE
4h-25.
SPECIFIC HEAT OF OXYGEN,
4atm
7atm
TABLE
CpjR
4h-26.
ENTHALPY OF OXYGEN,
10 atm
(H - EoO)jRTo
40atm
70 atm
100 "tm
1atm
4atm
7 atm
100 200 300 400 500
1.254 2.5523 3.8424 5.1523 6.5000
2.5308 3.8319 5.1464 6.4968
2.5091 3.8213 5.1406 6.4936
2.4871 3.8108 5.1349 6.4905
2.248 3.705 5.078 6.460
1.972 3.602 5.023 6.431
1.659 3.505 4.971 6.403
4.052 4.120 4.180 4.232 4.277
600 700 800 90a 1000
7.8919 9.3254 10.7951 12.2949 13.8198
7.8903 9.3250 10.7956 12.2960 13.8213
7.8888 9.3245 10.7960 12.2970 13.8228
7.8873 9.3242 10.7965 12.2981 13.8243
7.873 9.321 10.802 12.309 13.840
7.860 9.319 10.807 12.321 13.857
7.848 9.318 10.814 12.333 13.874
4.3085 4.3442 4.3771 4.4076 4.4369
4.316 4.350 4.382 4.412 4.440
1100 1200 1300 1400 1500
15.3653 16.9285 18.5067 20.0985 21.7025
15.3672 16.9307 18.5092 20.1012 21.7054
15.3691 16.9329 18.5116 20.1038 21.7082
15.3710 16.9351 18.5141 20.1065 21.7111
15.391 16.958 18.539 20.134 21.740
15.411 16.981 18.565 20.161 21.769
15.431 17.004 18.591 20.189 21.799
4.4621 4.4905 4.5185 4.5464 4.5739
4.4652 4.4933 4.5209 4.5485 4.5758
4.468 4.496 4.523 4.551 4.578
1600 1700 1800 1900 2000
23.3181 24.9447 26.5820 28.2299 29.8880
23.3211 24.9479 26.5852 28.2333 29.8915
23.3241 24.9510 26.5885 28.2366 29.8949
23.3271 24.9541 26.5917 28.2399 29.8983
23.358 24.986 26.625 28.274 29.933
23.388 25.018 26.658 28.308 29.968
23.419 25.050 26.691 28.342 30.003
4.5999 4.6272 4.6544 4.6812 4.7074
4.6016 4.6287 4.6558 4.6824 4.7085
4.6032 4.6301 4.6570 4.6835 4.7095
4.605 4.631 4.658 4.685 4.710
2100 2200 2300 2400 2500
31.5566 33.2353 34.9239 36.6229 38.3314
31.5601 33.2389 34.9275. 36.6266 38.3352
31.5636 33.2424 34.9312 36.6303 38.3389
31.5671 33.2460 34.9348 36.6340 38.3426
31.6!}2 31.638 33.282 33.318 34.971 . 35.008 36.671 ' 36.708 38.418 38.380
31.674 33.355 35.045 36.745 38.455
4.7331 4.7582 4.7826 4.8064
4.7341 4.7590 4.7834 4.8072
4.7349 4.7598 4.7841 4.8077
4.736 4.761 4.785 4.808
2600 2700 2800 2900 3000
' 40.0500 41.7778 43.5151 45.2614 47.0165
40.0537 41.7816 43.5189 45.2653 47.0204
40.0575 41.7854 43.5227 45.2691 47.0243
40.0613 41.7892 43.5266 45.2730 47.0282
40.099 41.827 43.565 45.312 47.067
10atm
40atm
70atm
100 "tm
T, K
1 atm
200 300 400 500 600
3.519 3.5403 3.6243 3.7415 3.8611
3.5681 3.5584 3.6335 3.7470 3.8648
3.6196 3.5766 3.6427 3.7526 3.8685
3'.6739 3.5951 3.6520 3.7582 3.8722
4.415 3.7862 3.7453 3.8134 3.9087
5.66 3.981 3.836 3.8677 3.9445
7.6 4.165 3.921 3.920 3.980
700 800 900 1000 1100
3.9681 4.0583 4.1332 4.1952 4.2472
3.9707 4.0603 4.1347 4.1964 4.2481
3.9733 4.0622 4.1361 4.1975 4.2491
3.9759 4.0641 4.1376 4.1987 4.2500
4.0016 4.0830 4.1521 4.2101 4.2591
4.0266 4.1017 4.1664 4.2213 4.2681
1200 1300 1400 1500 1600
4.2915 4.3302 4.3653 4.3976 4.4283
4.2922 4.3308 4.3658 4.3981 4.4287
4.2930 4.3315 4.3663 4.3985 4.4291
4.2937 4.3321 4.3669 4.3990 4.4295
4.3012 4.3382 4.3721 4.4034 4.4332
1700 1800 1900 2000 2100
4.4579 4.4869 4.5154 4.5437 4.5716
4.4582 4.4872 4.5156 4.5439 4.5717
4.4586 4.4875 4.5159 4.5441 4.5719
4.4589 4.4878 4.5161 4.5443 4.5721
2200 2300 2400 2500 2600
4.5993 4.6268 4.6540 4.6808 4.7071
4.5995 4.6269 4.6542 4.6810 4 ..7072
4.5997 4.6271 4.6543 4.6811 4.7073
2700 2800 2900 . ;;000
4.7328 4.7579 4.7824 4.8062
4.7329 4.7580 4.7825 4.8063
4.7330 4.7581 4.7826 4.8064
-.--- - - - - - - - - - - - - - - - - - - - - -
T, K
- - - - - -- - -- - -- - - - - - - - - - - -
40.137 ' 40.175 41.904 41.866 43.643 43.604 45.351 45.390 47.107 47.146
t
I-'
"" 00
il:i t<J
~
4-179
THERMODYNAMIC PROPERTIES OF GASES TABLE
T, K
1 atm
4h-27.
4 atm
ENTROPY OF OXYGEN,
7 atm
10 atm
SIR
40 atm
70 atm 1100 atm I
100 200 300 400 500
20.794 23.2553 24.6839 25.7127 26.5337
21.8488 23.2899 24.3224 25.1450
21.2686 22.7224 23.7587 24.5830
20.8908 22.3579 23.3980 24.2239
19.2709 20.8928 21.9719 22.8139
18.431 20.2555 21. 3733 22.2311
17.74 19.825 20.9789 21. 8517
600 700 800 900 1000
27.2266 27.8299 28.3659 28.8484 29.2872
25.8387 26.4425 26.9788 27.4615 27.9005
25.2775 25.8819 26.4185 26.9013 27.3404
24.9193 25.5241 26.0610 26.5440 26.9833
23.5176 24.1272 24.6670 25.1521 25.5926
22.9429 23.5571 24.0999 24.5869 25.0287
22.5712 23.1900 23.7357 24.2246 24.6678
1100 1200 1300 1400 1500
29.6896 30.0610 30.4061 30.7283 31.0307
28.3029 28.6744 29.0196 29.3419 29.6442
27.7430 28.1146 28.4598 28.7821 29.0845
27.3859 27.7576 28.1029 28.4252 28.7276
25.9963 26.3685 26.7144 27.0372 27.3399
25.4334 25.8064 26.1527 26.4760 26.7790
25.0733 25.4471 25.7939 26.1176 26.4209
1600 1700 1800 1900 2000
31.3155 31.5848 31.8404 32.0838 32.3161
29.9290 30.1984 30.4540 30.6974 30.9297
29.3693 29.6387 29.8943 30.1377 30.3701
29.0125 29.2819 29.5375 29.7810 30.0133
27.6250 27.8946 28.1505 28.3941 28.6265
27.0644 27.3342 27.5902 27.8339 28.0664
26.7067 26.9766 27.2328 27.4767 27.7094
2100 2200 2300 2400 2500
32.5385
30.5925 30.8058 31.0108 31. 2083 31. 3990
30.2358 30.4401 30.6541 30.8516 31.0422
28.8490
28.2890
27.9320
29.0625
32.9568 33.1543 33.3449
31.1521 31.3655 31.5705 31.7680 31.9586
28. 5C25
". " "
2600 2700 2800 2900 3000
33.5289 33.7071 33.8796 34.0470 34.2096
32.1426 32.3208 32.4933 32.6607 32.8233
31. 5830 31.7612 31.9337 32.1011 32.2637
31. 2263 31. 4045 31.5770 31. 7444 31.9070
32.7518
29.2675 29.4651 29.6558 29.8399 30.0181 30.1907 30.3581 30.5207
28.7077 28.3508 28. 9053 1 28 . 5485 29,.0960 , 28.7393 29.2802128.9235 29.4585 J 29.1018 29.6310 \29.2744 29.7985 29.4419 29.9612 29.6047
I
4-180
HEAT TABLE
4h-28.
THERMODYNAMIC PROPERTIES OF IONIZED
AIR
T = 4000 K
z
E/RT
H/RT
SIR
-5.00 -4.80 -4.60 -4.40 -4.20
1. 27113 1.25871 1.24863 1.24045 1.23380
7.98674 7.63908 7.35804 7.13130 6.94846
9.25788 8.89779 8.60667 8.37175 8.18225
-4.00 -3.80 -3.60 -3.40 -3.20
1.22834 1.22381 1. 21997 1.21662 1.21356
6.80080 6.6810'1 6.58320 6.50204 6.43313
-3.00 -2.80 -2.60 -2.40 -2.20
1. 21060 1.20755 1. 20419 1.20024 1.19544
-2.00 -1.80 -1.60 -1.40 -1.20
logloP, atm
z*
50.3307 49.4006 48.5423 47.7425 46.9900
-3.72990 -3.53416 -3.33765 -3.14051 -2.94284
1. 27113 1.25871 1.24863 1.24045 1.23379
8.02914 7.90488 7.80317 7.71866 7.64669
46.2755 45.5912 44.9306 44.2884 43.6600
-2.74477 -2.54637 -2.34774 -2.14893 -1.95003
1.22834 1. 22381 1. 21997 1.21662 1.21356
6.37242 6.31608 6.26016 6.20044 6.13223
7.58303 7.52363 7.46434 7.40068 7.32767
43.0411 42.4279 41.8167 41.2033 40.5834
-1. 75108 -1. 55218 -1.35339 -1.15482 -0.95656
1.21060 1. 20755 1. 20418 1.20024 1.19543
1.18943 1.18189 1.17257 1.16133 1.14833
6.05042 5.94985 5.82615 5.67706 5.50363
7.23985 7.13174 6.99871 6.83839 6.65196
39.9524 39.3058 38.6399 37.9533 37.2480
-0.75875 -0.56151 -0.36495 -0.16913 0.02598
1.18941 1.18187 1.17252 1.16127 1.14822
-1.00 -0.80 -0.60 -0.40 -0.20
1.13396 1.11884 1.10369 1. 08918 1. 07585
5.31076 5.10642 4.90000 4.70034 4.51438
6.44471 6.22526 6.00369 5.78952 5.59022
36.5296 35.8065 35.0884 34.3839 33.6994
0.22051 0.41468 0.60876 0.80301 0.99766
1.13380 1.11859 1.10330 1.08856 1.07488
O. 0.20 0.40 0.60 0.80
1.06407 1.05411 1. 04615 1.04038 1.03713
4.34655 4.19894 4.07180 3.96410 3.87406
5.41062 5.25305 5.11795 5.00448 4.91120
33.0390 32.4037 31.7931 31. 2050 30.6367
1.19288 1.38880 1.58551 1. 78311 1. 98175
1.06256 1.05174 1.04242 1.03453 1.02791
1.00 1.20 1.40 1.60 1.80
1.03695 1.04079 1.05028 1. 06811 1.09856
3.79961 3.73861 3.68908 3.64930 3.61790
4.83656 4.77940 4.73936 4.71741 4.71646
30.0848 29.5456 29.0148 28.4877 27.9580
2.18167 2.38328 2.58722 2.79453 3.00674
1.02242 1. 01787 1.01412 1. 01100 1.00837
2.00
1.14848
3.59393
4.74241
27.4175
3.22604
1.00606
log
p/ po
z* is the
number of moles of dissociated gas corresponding to one mole of low-temperature gas.
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-28.
THERMODYNAMIC PROPERTIES OF IONIZED
4--181
AIR (Continued)
T= 6000 K log pi po
z
EIRT
HIRT
SIR
log!oP, atm
z*
-5.00 -4.80 -4.60 -4.40 -4.20
1.98639 1.98008 1. 97116 1.95832 1.93995
19.99067 19.86188 19.68615 19.43841 19.08795
21.97706 21. 84196 21.65732 21.39673 21.02790
68.7753 67.7331 66.6475 65.4948 64.2465
-3.35993 -3.16131 -2.96327 -2.76611 - 2.57021
1.98639 1.98008 1. 97117 1.95832 1.93995
-4.00 -3.80 -3.60 -3.40 -3.20
1. 91430 1.87994 1.83631 1. '18420 1.72580
18.60197 17.95327 17.13119 16.15055 15.05251
20.51627 19.83321 18.96749 17.93475 16.77831
62.8727 61.3500 59.6719 57.8573 55.\)509
-2.37599 -2.18385 -1.99405 -1.80655 -1. 62100
1. 91430 1.87994 1.83631 1.78420 1.72580
-3.00 -2.80 -2.60 -2.40 -2.20
l. 66421 1.60268 1.54398 1.49003 1.44187
13.89543 12.74058 11.63995 10.62989 9.73045
15.55964 14.34326 13.18393 12.11991 11.17232
54.0131 52.1061 50.2811 48.5727 46.9984
-1.43679 -1.25315 -1.06935 -0.88480 -0.69907
1.66421 1.60268 1.54398 1.49002 1.44186
-2.00 -1.80 -1.60 -1.40 -1.20
1.39984 1. 36376 1. 33312 1.30722 1.28534
8.94817 8.27996 7.71677 7.24649 6.85589
10.34801 9.64372 9.04989 8.55371 8.14122
45.5620 44.2577 43.0737 41.9956 41.0082
-0.51192 -0.32326 -0.13313 0.05835 0.25102
1.39983 1.36373 1.33307 1.30715 1.28522
-1.00 -0.80 -0.60 -0.40 -0.20
1.26671 1.25062 1.23641 1. 22347 1.21125
6.53186 6.26209 6.03531 5.84143 5.67145
7.79857 7.51271 7.27172 7.06490 6.88270
40.0\)67 39.2473 38.4480 37.6877 36.9572
0.44468 0.63913 0.83417 1.02960 1.22524
1.26653 1.25035 1.23598 1.22280 1. 21020
O.
1.19932 1.18737 1.17526 1. 16316 1.15159
5.517GO 5.37295 5.23261 5.09308 4.95296
6.71682
36.2482
0.20 0.40 0.60 0.80
6.56032 6.40787 6.25624 6.10456
35.5541 34.8697 34.1918 33.5187
1.42094 1. 61659 1. 81214 2.00765 2.20330
1.19767 1.18478 1. 17121 1.15683 1.14169
1.00 1.20 1.40 1.60 1. 80
1.14152 1. 13447 1.13262 1.13913 1.15861
4.81288 4.67497 4.54223 4.41768 4.30382
5.95440 5.80944 5.67485 5.55681 5.46243
32.8507 32.1889 31. 5344 30.8872 30.2449
2.39949 2.59680 2.79609 2.99858 3.20594
1.12605 1.11030 1.09487 1.08015 1.06639
2.00
1.19794
4.20247
5.40041
29.6019
3.42044
1.05372
4-182 TABLE
BEAT 4h-28.
THERMODYNAMIC PROPERTIES OF IONIZED
AIR (Continued)
T = 8000 K log p/ po
z
E/RT
H/RT
-5.00 -4.80 -4.60 -4.40 -4.20
2.17208 2.13622 2.10717 2.08370 2.06474
20.12586 19.32981 18.68526 18.16490 17.74534
22.29794 21.46602 20.79243 20.24859 19.81007
-4.00 -3.80 -3.60 -3.40 -3.20
2.04939 2.03685 2.02645 2.01753 2.00945
17.40674 17.13225 16.90733 16.71903 16.55509
-3.00 -2.80 -2.60 -2.40 -2.20
2.00151 1.99288 1.98248 1.96897 1.95069
-2.00 -1.80 -1.60 -1.40 -1.20
logloP. atm
z*
74.4276 72.6399 71.0185 69.5334 68.1587
-3.19618 -3.00341 -2.80936 -2.61422 -2.41819
2.17228 2.13640 2.10733 2.08385 2.06487
19.45612 19.16910 18.93378 18.73656 18.56455
66.8730 65.6577 64.4973 63.3778 62.2867
-2.22143 -2.02410 -1.82632 -1.62824 -1.42998
2.04950 2.03696 2.02654 2.01761 2.00953
16.40300 16.24878 16.07573 15.86333 15.58703
18.40452 18.24166 18.05820 17.83229 17.53772
61. 2110 60.1370 59.0485 57.9262 56.7471
-1.23170 -1.03358 -0.83585 -0.63882 -0.44287
2.00158 1.99293 1.98252 1.96900 1.95072
1.92584 1.89274 1.85048 1.79940 1.74129
15.22003 14.73824 14.12817 13.39465 12.56340
17.14587 16.63098 15.97865 15.19404 14.30470
55.4872 54.1259 52.6536 51.0793 49.4326
-0.24844 -0.05597 0.13423 0.32207 0.50782
1.92585 1.89273 1.85044 1.79932 1. 74116
-1.00 -0.80 -0.60 -0.40 -0.20
1.67906 1. 61594 1.55484 1.49788 1.44632
11.67587 10.77874 9.91370 9.11130 8.38943
13.35493 12.39468 11.46854 10.60918 9.83575
47.7575 46.1017 44.5068 43.0017 41. 6021
0.69201 0.87537 1.05863 1.24242 1.42721
1.67884 1.61560 1.55432 1.49708 1.44509
v.
1.40063 1.36078 1.32640 1.29703 1.27233
7.75491 7.20639 6.73723 6.33794 5.99796
9.1[;505
40.3123
0.20 0.40 0.60 0.80
8.56717 8.06362 7.63497 7.27029
39.1282 38.0405 37.0374 36.1060
1. 61327 1.80073 1.98962 2.17989 2.37154
1.35789 1.32195 1. 29017 1. 26172
1.00 1.20 1.40 1.60 1.80
1.25222 1. 23714 1.22829 1.22807 1.24054
5.70678 5.45484 5.23393 5.03758 4.86115
6.95900 6.69197 6.46222 6.26565 6.10169
35.2337 34.4088 33.6205 32.8590 32.1147
2.56462 2.75936 2.95625 3.15617 3.36056
1.23578 1. 21162 1.18866 1.16650 1.14487
2.00
1.27229
4.70179
5.97408
31.3777
3.57153
1.12367
S/R
1.39870
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-28.
THERMODYNAMIC PROPERTIES OF IONIZED
4-183
AIR (Continued)
T = 10,000 K log pi po
z
EIRT
HIRT
SIR
logloP, atm
z*
-5.00 -4.80 -4.60 -4.40 -4.20
3.13590 2.98152 2.83477 2.70036 2.58086
34.42541 31.65851 29.02681 26.61470 24.46888
37.56131 34.64003 31.86158 29.31506 27.04974
94.5501 90.3748 86.4040 82.7180 79.3568
-2.93978 -2.76171 -2.58363 -2.40472 -2.22438
3.13820 2.98385 2.83708 2.70260 2.58300
-4.00 -3.80 -3.60 -3.40 -3.20
2.47709 2.38866 2.31438 2.25270 2.20192
22.60469 21.01522 19.67975 18.57046 17.65711
25.08178 23.40388 21. 99413 20.82315 19.85903
76.3287 73.6195 71. 2017 69.0413 67.1026
-2.04220 -1.85799 -1. 67171 -1.48344 -1.29335
2.47911 2.39054 2.31612 2.25430 2.20338
-3.00 -2.80 -2.60 -2.40 -2.20
2.16037 2.12649 2.09889 2.07632 2.05764
16.90999 16.30150 15.80587 15.40423 15.07428
19.07036 18.42800 17.90577 17.48055 17.13192
65.3514 63.7561 62.2888 60.9250 59.6433
-1.10162 -0.90848 -0.71416 -0.51885 -0.32278
2.16169 2.12769 2.09997 2.07729 2.05850
-2.00 -1.80 -1.60 -1.40 -1.20
2.04181 2.02780 2.01453 2.00076 1.98502
14.79967 14.56421 14.35175 14.14511 13.92488
16.84149 16.59201 16.36629 15.14587 15.90990
58.4248 57.2524 56.1091 54.9779 53.8398
-0.12613 0.07088 0.26803 0.46505 0.66162
2.04258 2.02847 2.01510 2.00123 1.98536
-1.00 -0.80 -0.60 -0.40 -0.20
1.96556 1.94043 1. 90775 1.86624 1.81580
13.66889 13.35298 12.95423 12.45686 11.85896
15.63445 15.29341 14.86198 14.32310 13.67475
52.6740 51. 4585 50.1733 48.8066 47.3606
0.85734 1.05175 1.24437 1.43482 1.62292
1. 96575 1.94041 1. 90744 1.86553 1.81450
O. 0.20 0.40 0.60 0.80
1.75782 1.69501 1.63071 1. 56819 1.51018
11.17605 1U.43853 9.68368 8.94681 8.25507
12.93388 11.31439 10.51500 9.76525
45.8546 44.3219 42.8013 41.3280 39.9277
1.80883 1.99303 2.17623 2.35925 2.54288
1.75567 1.69159 1.62540 1.56007 1. 49781
1.00 1.20 1.40 1.60 1.80
1.45879 1.41573 1.38272 1.36208 1. 35741
7.62528 7.06479 6.57376 6.14771 5.77984
9.08407 8.48053 7.95649 7.50979 7.13726
38.6146 37.3925 36.2576 35.2001 34.2067
2.72785 2.91484 3.10459 3.29806 3.49657
1.44000 1.38714 1.33914 1.29550 1.25553
2.00
1.37455
5.46289
6.83744
33.2617
3.70201
1.21845
1~.13354
4-184 TABLE
HEAT
4h-28.
THERMODYNAMIC PROPERTIES OF IONIZED
AIR (Continued)
T = 12,000 K log p/ po
z
E/RT
H/RT
S/R
loglOP, atm
z*
-5.00 -4.80 -4.60 -4.40 -4.20
3.86391 3.80741 3.73023 3.63012 3.50778
40.69274 39.84992 38.69570 37.19560 35.35895
44.55665 43.65733 42.42592 40.82571 38.86673
107.9424 105.3326 102.4419 99.2462 95.7652
-2.76994 -2.57633 -2.38523 -2.19704 -2.01193
3.86758 3.81182 3.73543 3.63612 3.51451
-4.00 -3.80 -3.60 -3.40 -3.20
3.36735 3.21572 3.06089 2.91034 2.76976
33.24726 30.96381 28.62933 26.35611 24.23093
36.61461 34.17953 31.69022 29.26645 27.00069
92.0699 88.2705 84.4904 80.8427 77.4102
-1.82968 -1.64969 -1.47112 -1.29302 -1.11452
3.37468 3.22348 3.06888 2.91837 2.77766
-3.00 -2.80 -2.60 -2.40 -2.20
2.64278 2.53107 2.43486 2.35334 2.28514
22.30907 20.61675 19.15766 17.92033 16.88443
24.95185 23.14782 21.59252 20.27367 19.16957
74.2427 71.3597 68.7579 66.4186 64.3152
-0.93490 -0.75366 -0.57049 -0.38528 -0.19805
2.65040 2.53833 2.44169 2.35970 2.29103
-2.00 -1.80 -1.60 -1.40 -1.20
2.22862 2.18207 2.14383 2.11234 2.08614
16.02552 15.31821 14.73796 14.26199 13.86943
18.25414 17.50028 16.88179 16.37433 15.95557
62.4174 60.6949 59.1189 57.6631 56.3040
-0.00893 0.18190 0.37422 0.56780 0.76238
2.23402 2.18700 2.14830 2.11636 2.08973
-1.00 -0.80 -0.60 -0.40 -0.20
2.06387 2.04413 2.02548 2.00628 1.98469
13.54099 13.25829 13.00293 12.75541 12.49447
15.60486 15.30243 15.02840 14.76169 14.47916
55.0202 53.7916 52.5992 51.4233 50.2433
0.95772 1.15354 1.34956 1.54543 1.74073
2.06701 2.04681 2.02762 2.00777 1.98533
O.
12.19723 11.84127 11.40910 10.89385 10.36382
14.15587
0.40 0.60 0.80
1.95864 1.92G15 1.88572 1.83703 1.78138
13.29482 12.73098 12.08519
49.0379 47.7871 46.4769 45.1043 43.6808
1.93499 2.12773 2.31851 2.50715 2.69379
1. 95812 1.92397 1. 88113 1.82890 1. 76804
1.00 1.20 1.40 1. 60 1.80
1. 72172 1.66222 1. 60767 1.56321 1.53453
9.66068 8.99461 8.33607 7.70993 7.13311
11.38239 10.65683 9.94374 9.27314 8.66764
42.2310 40.7858 39.3747 38.0189 36.7296
2.87900 3.06372 3.24923 3.43705 3.62901
1.70072 1.62987 1. 55847 1.48888 1.42261
2.00
1.52846
6.61560
8.14406
35.5078
3.82729
1.36034
"0
n V • .41V
13.76742
THERMODYNAMIC PROPERTIES OF GASES
4-185
TABLE 4h-28. THERMODYNAMIC PROPERTIES OF IONIZED AIR (Continued) T = 14,000 K log pi po
z
-5.00 -4.80 -4.60 -4.40 -4.20
3.96453 3.95531 3.94140 3.92053 3.88963
-4.00 -3.80 -3.60 -3.40 -3.20
-
HIRT
SIR
log"P, atm
z*
37.19404 37.07956 36.90620 36.64408 36.25307 .
41.15858 41.03487 40.84760 40.56461 40.14270
110.4755 108.5372 106.5454 104.4727 102.2829
-2.69183 -2.49284 -2.29437 -2.09667 -1. 90011
3.96768 3.95924 3.94630 3.92661 3.89710
3.84491 3.78231 3.69844 3.59192 3.46445
35.68344 34.88151 33.80203 32.42548 30.77278
39.52835 38.66382 37.50047 36.01739 34.23723
99.9317 97.3728 94.5700 91. 5140 88.2358
-1.70513 -1.51226 -1.32200 -1.13469 -0.95038
3.85400 3.. 79320 3.71123 3.60657 3.48078
-3.00 -2.80 -2.60 -2.40 -2.20
3.32103 3.16891 3.01587 2.86883 2.73281
28.90780 26.92442 24.92472 22.99891 21.21359
32.22884 30.09333 27.94059 25.86775 23.94640
84.8080 81.3301 . 77.9061 74.6258 71.5512
-0.76874 -0.58911 -0.41061 -0.23231 -0.05341
3.33872 3.18754 3.03498 2.88800 2.75165
-2.00 -1.80 -1.60 -1.40 -1.20
2.61079 2.50400 2.41233 2.33481 2.26997
19.60888 18.20170 16.99150 15.96627 15.10755
22.21968 20.70570 19.40383 18.30108 17.37752
68.7168 66.1325 63.7909 61.6732 59.7547
0.12675 0.30862 0.49242 0.67823 0.86600
2.62901 2.52138 2.42872 2.35013 2.28418
-1.00 -0.80 -0.60 -0.40 -0.20
2.21612 2.17154 2.13453 2.10343 2.07663
14.39394 13.80342 13.31458 12.90702 12.56120
16.61006 15.97497 15.44911 15.01045 14.63783
58.0086· 56.4081 54.9280 53.5449 52.2367
1.05558 1. 24675 1.43928 1. 63291 1.82734
2.22920 2.18348 2.14528 2.11293 2.08474
O. 0.20 0.40 0.60 0.80
2.05249 2.02925 2.00501 1.97779 1.94576
12.25780 11.97699 11. 69771 11.39771 11.05519
14.31028 14.00624 13.70272 13.37551 13.00095
50.9826 49.7620 48.5537 . 47.3365 46.0904
2.02226 2.21732 2.41210 2.60616 2.79907
2.05892 2.03354 2.00640 1. 97505 1.93701
1. 00 1.20 1.40 1. 60 1.80
1. 90776 1.86404 1.81692 1.77093 1. 73261
10.65244 10.18093 9.64525 9.06324 8.46230
12.56020 12.04497 11.46216 10.83417 10.19491
44.8001 43.4599 42.0767 40.6687 39.2615
2.99050 3.18044 3.36932 3.55818 3.74868
1.89018 1.83349 1.76732 1.69358 1.61516
2.00
1. 70947
7.87630
9.58577
37.8837
3.94284
1.53540
EIRT
4-186
HEAT TABLE
4h-29.
THERMODYNAMIC PROPERTIES OF NITROGJeN
T=4000K log p/po
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
Moles
Z
1.07027 1.05623 1.04494 1.03586 1. 02859 1.02278 1.01814 1.01444 1.01148 1.00913
1.07027 1.05623 1.04493 1.03586 1. 02859 1.02278 1. 01814 1.01443 1.01148 1.00913
E/RT 5.1506 4.7552 4.4368 4.1811 3.9763 3.8124 3.6816 3.5773 3.4941 3.4278
H/RTI~ 6.2209 5.8114 5.4817 5.2170 5.0049 4.8352 4.6998 4.5917 4.5056 4.4370
loglo P
3.4994 3.4844 3.4752 3.4712 3.4716 3.4761 3.4839 3.4945 3 ..5073 3.5215
09 09 09 09 09 09 09 09 09 10
7.6136 6.9786 6.4736 6.0720 5.7527 5.4989 5.2972 5.1369 5.0095 4.9083
6.3877 5.8008 5.3333 4.9612 4.6651 4.4295 4.2423 4.0934 3.9750 3.8810
3.5365 3.5517 3.5065 3.5804 3.5932 3.6048 3.6149 3.6236 3.6311 3.6375
1.37+10 1.72+10 2.17+10 2.72 + 10 3.42+ 10 4.31 + 10 5.42 + 10 6.83 + 10 8.62 + 10 1.09 + 11
4.8279 4.7641 4.7133 4.6730 4.6410 4.6155 4.5953 4.5793 4.5666 4.5566
3.8062 3.7469 3.6997 3.6622 3.6325 3.6089 3.5903 3.5756 3.5641 3.5553
3.6428 3.6474 3.6513 3.6549 3.6584 3.6622 3.6667 3.6727 3.6812 3.6940
2.1721 1.38 + 11 2.3757 1.75+11 2.5814 2.23 + 11
4.5489 4.5430 4.5392
2.7903\2.87 + 11\ 3.00393.73 + 11 3.22474.96 + 11
4.53791 4.5405 4.5505
3.5488 3.7136 3.5445 3.7440 3.5424 3.7914 3.8653 3.54271 3.5463 3.9799 3.5544 4.1560
2.57 3.00 3.51 4.13 4.89 5.82 6.98 8.41 1.02 1.25
+
1.53 1.88 2.32 2.88 3.58 4.46 5.57 6.97 8.73 1.09
+ + + + + + + + + +
1.00726 1.00577 1.00459 1.00365 1.00291 1.00232 1. 00185 1.00149 1.00121 1.00101
1.00726 1. 00577 1.00459 1.00365 1.00290 1.00230 1.90183 1.00145 1.00115 1.00092
3.3751 3.3331 3.2998 3.2732 3.2521 3.2354 3.2220 3.2114 3.2030 3.1963
4.3824 4.3389 4.3044 4.2769 4.2550 4.2377 4.2239 4.2129 4.2042 4.1974
37.8170 37.3115 36.8152 36.3263 35.8432 35.3647 34.8899 34.4180 33.9485 33.4808
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1.00087 1. 00081 1.00082 1.00094 1. 00121 1.00168 1.00249 1.00379 1.00590 1.00926
1.00073 1.00058 1.00046 1.00037 1.00029 1.00023 1.00018 1.00015 1. 00012 1.00009
3.1910 3.1868 3.1835 3.1808 3.1787 3.1771 3.1758 3.1749 3.1742 3.1738
4.1919 4.1876 4.1843 4.1818 4.1800 4.1788 4.1783 4.1787 4.1801 4.1831
33.0145 32.5494 32.0852 31. 6216 31.1585 30.6957 30.2330 29.7701 29.3067 28.8423
.1662 .3662 .5662 .7662 .9664 1.1666 1. 3669 1. 5675 1.7684 1.9698
t
~"
..
a/ao
30.3825 25.1844 20.9369 17.4869 14.6981 12.4520 10.6483 9.2031 8.0473 7.1241
-3.8047 -3.6104 -3.4151 -3.2189 -3.0219 -2.8244 -2.6264 -2.4279 -2.2292 -2.0302
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
~ "~...-
Cv/R
34.3362 28.4237 23.6420 19.7917 16.7015 14.2273 12.2500 10.6719 9.4138 8.4115
44.3262 43.4412 42.6391 41.9044 41. 2243 40.5882 39.9875 39.4151 38.8655 38.3340
1.01460 1.00007 3.1737 4.1883 28.3763 1.02308 1.00006 3.1740 4.1971 27.9076 1.03653 1. 00005 3.1747 4.2113 27.4343 ., 1.611.Ub'IlOll.UOOU41 0.170214.23411213.95391 1.8 1.091661.00003 3.1788 4.2704 26.4621 2.0 1.145261.00002 3.1829 4.3282 25.9522
Cp/R
--- ---
-1. 8310 -1.6317 -1.4322 -1.2326 -1.0329 -.8332 - .6334 - .4335 - .2336 - .0337
1.0 1.2 1.4
N(E)t
N(E) is the number of electrons per cm 3, expressed in the form a
+ 08 + 08 + 08 + 08 +08 + 08 + 08 + 08 + 09 09
+ b, meaning a
X lOb.
4-187
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-29.
THERMODYNAMIC PROPERTIES OF NITROGEN
(Continued)
T=6000K
log p/p,
Z
Moles
B/RT
BIRT
S/R
logtoP
N(E)t
- - - --- - - - - - - - - - " - - - -
Cp/R
C./R
a/a.
--- --- ---
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
1.98949 1.98949 21.9731 23.9626 1.98000 1.98000 21.7840 23.7640 1.96630 1.96630 21. 5179 23.4842 1.94649 1.94649 21.1387 23.0852 1. 91840 1. 91840 20.6050 22.5234 1.87992 1. 87992 19.8771 21. 7570 1. 82974 1. 82974 18.9297 20.7595 1. 76801 1.76800 17.7661 19.5341 1.69676 1.69676 16.4240 18.1207 1.61954 1.61954 14.9701 16.5896
67.4937 66.3905 65.2154 63.9350 62.5110 60.9081 59.1061 57.1136 54.9734 52.7557
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1. 54057 1.46376 1.39214 1.32757 1.27091 1.22225 1.18114 1.14688 1.11861 1.09549
1.54056 13.4836 1.46376 12.0382 1.39213 10.6904 1.32756 9.4755 1.27090 8.4095 1.22223 7.4938 1.18112 6.7204 1.14684 6.0755 1.11855 5.5434 1.09539 5.1078
50.5416 -1.4704 9.73 + 12 80.7463 64.2934 5.1948 48.4046 -1.2926 1.15 + 13 76.9116 61. 2648 5.0624 46.3994 -1.1144 1.35 + 13 70.4385 56.3665 4.9371 44.5585 -.9350 1. 58 + 13 62.5714 50.4523 4.8226 42.8945 - .7540 1.86 + 13 54.3400 44.2225 4.7211 41.4051 - .5709 2.18 + 13 46.4481 38.1688 4.6336 40.0785 - .3858 2.56 + 13 39.2959 32.5899 4.5599 38.8979 - .1986 3.01 13 33.0555 27.6345 4.4996 37.8443 - .0094 3.56 + 13 27.7517 23.3485 4.4516 36.8990 .1815 4.24 + 13 23.3262 19.7134 4.4147
-1.0 -.8 -.6 -'.4 -.2 -.0 .2 .4 .6 .8
1.07670 1.06154 1.04938 1.03970 1.03211 1.02629 1. 02204 1.01930 1.01813 1.01881
1.07655 1.06130 1.04901 1.03912 1. 03120 1.02486 1.01979 1. 01574 1. 01251 1.00993
4.7534 4.4666 4.2354 4.0495 3.9005 3.7812 3.6859 3.6100 3.5494 3.5014
5.8301 5.5281 5.2847 5.0892 4.9326 4.8075 4.7080 4.6293 4.5676 4.5202
36.0447 35.2656 34.5484 33.8816 33.2556 32.6624 32.0956 31.5496 31.0200 30.5030
.3740 5.07 + 13 .5679 6.09 + 13 .7629 6.37 + 13 .9588 8.95 + 13 1.1556 1.09 + 14 1.3532 1.23 + 14 .1. 5514 1.66+14 1.7502 2.05 + 14 1.9497 2.55 + 14 2.1500 3.19 + 14
1.0 1.2 1.4 1.6 1.8 2.0
1.02192 1.02845 1.04009 1.05954 1.09117 1.14194
1.00787 1.00623 1.00492 1.00386 1. 00301 1.00233
3.4633 3.4334 3.4103 3.3930 3.3811 3.3745
4.4853 4.4619 4.4504 4.4526 4.4723 4.5165
29.9952 29.4934 28.9942 28.4938 27.9872 27.4674
2.3513 2.5541 2.7590 2.9670
15.0242 13.5020 12.0825 10.8030 9.6804 8.7161 7.9015 7.2224 6.6620 6.2033
-3.3593 -3.1614 -2.9644 -2.7688 -2.5751 -2.3839 -2.1957 -2.0106 -1.8285 -1.6487
1.27 1.59 1.99 2.48 3.08 3.81 4.67 5.68 6.85 8.20
+ + + + + + +
12 12 12 12 12 12 12 12 + 12 + 12
+
14.2250 16.9096 21.1530 27.3503 35.7322 46.0825 57.4674 68.2367 76.4862 80.7954
11.4527 13.8083 17.5086 22.8446 29.9229 38.4336 47.4846 55.7094 61.7151 64.6166
6.1982 6.1281 6.0481 5.9653 5.8809 5.7917 5.6933 5.5828 5.4604 5'.3294
+
4.00 5.04 6.39 8.18
+ 14 + 14 + 14 + 14 3.179~(06 +15 3.39961.40 + 15
t N(E) is the number of electrons per em', expressed in the form a
19.6816 16.6756 4.3877 16.7080 14.1651 4.3693 14.2982 12.108~ 4.3586 12.3549 10.4340 4.3545 10.7933 9.0784 4.3559 9.5418 7.9850 4.3622 8.5406 7.1059 4.3728 7.7407 6.4007 4.3876 7.1022 5.8360 4-.4067 6.5927 5.3846 4.4314 6.1860 5.8613 5.6018 5.3946 5.2303 5.1030
5.0240 4.7363 4.5071 4.3250 4.1815 4.0700
+ b; meaning a X lOb.
4.4640 4.5088 4.5726 4.6663 4.8064 5.0712
HEAT
4--188 TABLE
4h-29.
THERMODYNAMIC PROPERTIES OF NITROGEN
(Continued)
T=8000K log p/ po
Z
Moles
H/RT
E/RT
loglo P
SIR
N(EJt
--- --- --- --- --- ---
Cp/R
Cv/R
a/ao
--- --- ---
-3. 1936 -3 0009 -2 8070 -2.6120 -2.4161 -2.2194 -2.0222 -1.8245 -1.6267 -1.4287
4.99 + 13 6.35 + 13 8.06 + 13 1.02 + 14 1.29 + 14 1.63+14 2.06 + 14 2.61 + 14 3.28 + 14 4.14 + 14
57.8164 47.9289 39.8826 33.3888 28.1914 24.0755 20.8709 18.4544 16.7528 15.7475
49.5308 41.1283 34.2034 28.5537 23.9896 20.3459 17.4880 15.3165 13.7713 12.8372
7.1542 7.1139 7.0883 7.0759 7.0749 7.0838 7.1001 7.1207 7.1408 7.1540
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
2.18555 2.18576 2.14878 2.14897 2.11897 2.11914 2.09484 2.09499 2.07530 2.07544 2.05938 2.05951 2.04625 2.04636 2.03514 2.03524 2.02528 2.02537 2.01589 2.01596
21.9006 21.0770 20.4097 19.8705 19.4349 19.0820 18.7940 18.5549 18.3499 18.1643
24.0862 23.2258 22.5287 21. 9653 21.5102 21.1414 20.8402 20.5900 20.3751 20.1801
73 .4742 71.6529 70.0032 68.4939 67.0982 65.7936 64.5603 63.3814 62.2415 61.1254
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
2.00601 1. 99447 1.97977 1.96000 1. 93292 1.89629 1.84843 1.78897 1.71942 1.64295
2.00607 1.99453 1.97981 1.96003 1.93295 1.89630 1.84841 1.78893 1. 71934 1.64282
17.9820 17.7843 17.5477 17.2436 16.8391 16.3009 15.6043 14.7437 13.7401 12.6385
19.9880 19.7787 19.5274 19.2036 18.7720 18.1972 17.4527 16.5327 15.4595 14.2815
60.0171 -1.2308 5.21 + 14 15.4825 12.5497 7.1526 58.8981 -1.0333 6.55 + 14 16.0696 12.9991 7.1298 57.7462 - .8365 8.22 + 14 17.6847 14.3226 7.0828 56.5348 - .6409 1.03+15 20.5348 16.6689 7.0142 55.2336 - .4469 1.28 + 15 24.7702 20.1165 6.9286 53.8133 - .2552 1. 59 + 15 30.3278 24.5437 6.8290 52.2540 - .0663 1. 96 + 15 36.7543 29.5100 6.7156 .1195 2.41 + 15 43.1458 34.2646 6.5872 50.5555 .3022 2.93 + 15 48.3501 37.9607 6.4446 48.7437 46.8678 .4825 3.54 + 15 51. 3902 39.9739 6.2911
-1.0 -.8 - .6 -.4 - .2 - .0 .2 .4 .6 .8
1. 56368 1.48571 1.41231 1.34571 1.28704 1.23664 1.19427 1.15944 1.13161 1.11031
1. 56347 1. 48538 1.41182 1.34497 1. 28592 1. 23494 1.19169 1.15549 1.12552 1.10091
11. 4978 10.3759 9.3196 8.3601 7.5129 6.7815 6.1611 5.6422 5.2127 4.8602
13.0614 11.8616 10.7320 9.7058 8.7999 8.0181 7.3554 6.8016 6.3443 5.9705
44.9887 43.1648 41.4415 39.8472 38.3941 37.0820 35.9022 34.8416 33.8849 33.0164
.6610 4.25 +15 .8388 5.08 + 15 1.0168 6.06 + 15 1.1958 7.23 + 15 1.3765 8.62 + 15 1. 5591 1.03+16 1. 7440 1.24 + 16 1. 9311 1.49 +16 2.1206 1. 81 + 16 2.3123 2.21 + 16
32.2214 31.4860 30.7976 30.1442 29. 5142 1 28.8951
2.5064 2.71 2.7032 3.36 2.9030 4.20 3.1067 5.32 3.315816.84 3.53219.00
1.0 1.2 1.4 1.6 1.8 2.0
t N(E)
1.09541 1. 08081 1.08722 1.06447 1.08677 1.05122 1.09618 1. 04047 1.1192211.031741 1.16221 1. 02463
4.5728 4.3397 4.1516 4.0004 3. 8799 1 3.7852
5.6683 5.4270 5.2383 5.0966 4. 9991 1 4.9474
is the number of electrons per em', expressed in the form a
51. 8389 49.8989 46.1972 41. 4889 36.4363 31. 5133 27.0023 23.0350 19.6429 16.7982
+ 16 14.4444 + 16 12.5140 + 16 10.9397 + 16 9.f)5~6 + 161 8. 6204 1 + 16 7.7781
+ b, meaning a
40 .1100 38.5859 35.8563 32.4268 28.7324 25.0899 21. 6986 18.6634 16.0224 13.7710
6.1325 5.9753 5.8257 5.6885 5.5669 5.4626 5.3764 5.3084 5.2586 5.2277
5.2173 5.2308 5.2746 ;;.3591 5.5012 7. 0855 1 5.7266 6.3770
11. 8803 10 .3097 9.0151 7 g!5~!5
X lOb.
4-189
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-29.
Moles
Z
log p/pa
THERMODYNAMIC PROPERTIES OF NITROmJN T = 10,000 K
E/RT
--- --- --- ---
H/RT
S/R
loglO P
N(E)t
--- --- ---
(Continued)
Cp/R
C,/R
------
a/ao
---
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
3.18098 3.02429 2.87425 2.73608 2.61275 2.50536 2.41365 2.33651 2.27238 2.21951
3.18339 36.5970 3.026'14 33.7675 2.87669 31. 0574 2.73845 28.5607 2.61502 26.3316 2.50750 24.3902 2.41565 22.7319 2.33836 21.3367 2.27407 20.1766 2.2210619.2205
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
2.17619 2 .1407~ 2.11183 2.08796 2.06793 2.05053 2.03452 2.01849 2.00081 1.97948
2.17759 2.14206 2.11297 2.08899 2.06885 2.05134 2.03522 2.01909 2.00130 1.97983
18.4376 20.6138 17.7989 19.9397 17.2782 19.3900 16.8522 18.9401 16.4997 18.5676 16.2011 18.2516 15.9374 17.9719 15.6885 17.7070 15.4322 17.4330 15.1426 17.1221
64.4508 -1.0985 4.79 + 15 39.8975 33.2769 8.0938 62.. 8183 - .9057 6.10 + 15 33.6624 28.0792 8.0550 61.3187 -.7116 7.75 + 15 28.6395 23.8389 8.0315 59.9259 -.5165 9.82 + 15 24.6607 20.4418 8.0205 58.6166 - .3207 1.24+16 21.5911 17.7925 8.0185 57.3698 - .1244 1. 58 + 16 19.3381 15.8243 8.0210 56.1655 .0722 1.99 + 16 17.8586 14.5065 8.0217 54.9834 .2688 2.51 + 16 17 .1647 13.8494 8.0131 53.8015 .4650 3.17+16 17.3223 13.9028 7.9870 52,.5952 .6603 3.99 16 18.4357 14.7390 7.9377
1.95237 1. 91648 1. 87011 1.81237 1. 74414 1.66811 1.58820 1.50853 1.43263 1.36297
14.7906 14.3460 13.7838 13.0927 12.2821 11.3829 10.4404 9.5027 8.6105 7.7926
16.7428 16.2625 15.6543 14.9058 14.0275 13.0531 12.0319 11.0163 10.0508 9.1670
51.3376 50.0018 48.5673 47.0276 45.3972 43.7113 42.0177 40.3651 38.7930 37.3273
.8543 1.0463 1. 2357 1.4222 1. 6057 1. 7866 1.9656 2.1438 2.3222 2.5019
1.30088 7.0644 8.3826 1.24680 6.4311 7.7041 7 .1302 1.16131 5.4337 6.6558 1.12842 5.0532 6.2748 1.10089 4.7387 5.9834
35.9795 34.7500
2.6838 3.95 2.8686 4.87 3.05736.06 3.250917.64 3.45079.81 3.65881.29
39.7780 36.7918 33.9316 31.2968 28.9444 26.8956 25.1455 23.6732 22.4490 21.4400
94.4282 90.1701 86.1022 82.3143 78.8543 75.7350 72.9447 70.4563 68.2355 66.2455
-2.9337 -2.7556 -2.5777 -2.3991 -2.2191 -2.0374 -1.8536 -1.6677 -1.4797 -1.2900
3.18 4.37 5.92 7.90 1.04 1. 36 1.77 2.28 2.93 3.75
1.0 1.2 1.~
1.6 1.8 2.0
1.31821 1.27299 1.24027 1.22206 1. 22165 1.24465
t N(E)is
'''"'' , "'"'
14 14 14 14 15 15 15 15 15 15
149.0162 146.4103 137.4614 124.4353 109.5346 94.4607 80.3112 67.6674 56.7445 47.5314
118.0254 115.6397 108.7631 98.9949 87.8303 76.4281 65.5650 55.6889 47.0036 39.5509
9.6774 9.4318 9.1941 8.9726 8.7728 8.5980 8.4492 8.3260 8.2270 8.1504
+
:
-1.0 1.95218 -.8 1. 91650 - .6 1.87042 -.4 1. 81310 -.2 1. 74544 -.0 1. 67024 .2 1. 59152 .4 1.51350 .6 ' 1.44028 .8 1. 37447
+ + + + + + + + + +
".,,"'! 32.6081 31. 6657 30.7843
5.01 + 16 6.26 + 16 7.80 + 16 9.66 + 16 1.19 + 17 1.46 + 17 1. 78 + 17 2.17+17 2.64+17 3.22 + 17
20.5976 23.7932 27.7743 31. 9827 35.6334 37.9783 38.5956 37.5083 35.0854 31.8393
16.4067 18.8518 21.8277 24 .. 8683 27.3928 28.9133 29.2077 28.3484 26.6047 24.3122
7.8634 7.7656 7.6464 7.5072 7.3503 7.1802 7.0037 6.8295 6.6662 6.5218
+ 17 28.2515 21.7767 + 17 24.6832 19.2292 + 17 21.3594 16.8201 + 17118.3922114.6318 + 17 15.8165 12.6971 + 18 13.6213 11.0172
6.4037 6.3194
the number of electrons per em', expressed in the form a
+b,
meaning a X 10'.
6.2779
6.2914 6.3782 6.5650
HEAT
4-190 TABLE
log p/po
4h-29.
Z
THERMODYNAMIC PROPERTIES OF NITROGEN T = 12,000 K
Moles
E/RT
H/RT
SIR
IOgloP
N(Elt
(Continued)
Cp/R
C./R
a/ao
--- --- --- --- --- --- --- ---- --- --- ---5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
3.89384 3.89756 3.84199 3.84648 3.77010 3.77544 3.67524 3.68143 3.55714 3.56413 3.41909 3.42676 3.26763 3.27579 3.11094 3.11939 2.95702 2.96554 2.81223 2.82063
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
2.68073 2.56464 2.46437 2.37925 2.30792 2.24869 2.19980 2.15947 2.12603 2.09787
-1.0 - .8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
42.3391 41.5624 40.4828 39.0550 37.2743 35.1897 32.8994 30.5275 28.1950 25.9985
46.2329 45.4044 44.2529 42.7303 40.8314 38.6087 36.1671 33.6385 31.1520 28.8107
107.6566 105.0980 102.2648 99.1219 95.6750 91. 9834 88.1532 84.3126 80.5832 77.0588
-2.7667 -2.5725 -2.3807 -"2.1918 -2.0059 -1. 8231 -1.6428 -1.4642 -1.2862 -1.1080
5.10 + 14 7.86+14 1.20 + 15 1.80+15 2.65 + 15 3.83 + 15 5.43 + 15 7.56 + 15 1.03 + 16 1.39 +16
35.2358 46.0096 59.4348 74.5153 89.2729 101.2202 108.2871 109.6088 105.6704 97.8534
27.8584 36.8252 47.7151 59.5572 70.7073 79.3388 84.1379 84.7330 81.6338 75.8521
12.2802 12.0582 11. 8445 11. 6258 11.3921 11.1399 10.8726 10.5988 10.3291 10.0732
24.0019 26.6827 22.2375 24.8021 20.7124 23.1767 19.4166 21.7959 18.3302 20.6381 17.4280 19.6767 16.6837 18.8835 16.0714 18.2308 15.5665 17.6925 15.1463 17.2442
73.7980 70.8265 68. 1441 1 65.7336 63.5684 61.6175 59.8493 58.2335 56.7421 55.3496
- .9288 -.7480 -.5653 - .3806 - .1938 - .0051 .1853 .3773 .5705 .7647
1. 85 + 16 2.44 + 16 3.19 + 16 4.13 + 16 5.34 + 16 6.86 + 16 8.80 + 16 1.13 + 17 1.44+17 1.83 + 17
87.8025 76.9582 66.3548 56.6156 48.0408 40.7144 34.5958 29.5848 25.5652 22.4324
68.5000 60.5325 52.6473 45.2877 38.6928 32.9578 28.0871 24.0357 20.7392 18.1344
9.8388 9.6308 9.4515 9.3011 9.1785 9.0818 9.0082 8.9549 8.9182 8.8941
2.07338 2.07676 2.05092 2.05379 2.02865 2.03095 2.00448 2.00608 1.97601 1.97672 1.94072 1.94022 1.89640 1. 89419 1.84185 1. 83722 1.77763 1.76950 1.70635 1. 69318
14.7890 14.4730 14.1759 13.8729 13.5370 13.1398 12.6561 12.0703 11.3836 10.6160
54.0319 52.7664 51. 5298 50.2981 49.0454 47.7461 46.3784 44.9315 43.4110 41. 8410
.9596 1.1549 1.3502 1. 5450 1.7387 1.9309 2.1209 2.3082 2.4928 2.6750
2.33 + 17 2.97 + 17 3.77+17 4.80 + 17 6.08 + 17 7.70 + 17 9.73+17 1.23 + 18 1. 54 + 18 1. 94 + 18
20.1095 18.5591 17.7873 17.8368 18.7592 20.5531 23.0720 25.9489 28.6180 30.4802
16.1739 14.8355 14.1263 14.0758 14.7108 16.0044 17.8091 19.8184 21.6135 22.7989
8.8773 8.8609 8.8367 8.7959 8.7316 8.6409 8.5242 8.3842 8.2255 8.0556
1.0 1. 63231 1.61182 1.2 11. 56070 1.52949 1.4. 11. 4968711. 44987 1.6 4461611. 37563[ 1.414171.30831 1.8 11. 2.0 1. 40779 1. 24849
9.8022 8.9821 8.1916 7.4572 6.7946 6.2102
2.68887 2.57240 2.47168 2.38606 2.31422 2.25448 2.20508 2.16426 2.13035 2.10172
16.8624 16.5240 16.2045 15.8774 15.5130 15.0805 14.5525 13.9122 13.1612 12.3223
11.4345 40.2584 10.5428 38.7033 9.6885 37.2091 8.9034\ 35.7977[ 8.2088 34.4773 7.6180 33.2443
2.8558 2.43 + 18 31.1283 23.1454 7.8856 3.0363 3.06 + 18 30.4801 22.6414 7.7302 3.21813.87 + 18 28.7446 21.4420 7.1\01\9 3.4032[4.96 + 181 26.2816\ 19.7759 7.5362 7.5435 3.59356.48 + 18 23.4606 17. 8661 1 3.79158.70 + 18 20.5783 15.8904 7.6608
t N(E) is the number of electrons per em", expressed in the form a
+ b,
meaning a X lOb.
4-191
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-29.
log pip, __Z_
Moles
THERMODYNAMIC PHOPERTIES OF NITHOGEN T = 14,000 K
EIRT
HIRT
(Continued)
~IIOglOP I_N_C_J!'_'l_t_I_C_p_I_R___C_'I_R_ _al_a_,_
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
3.984423.9875938.440542.4250110.0090 3.97617,3.9801338.338642.3148108.0739 3.96375:3.9686938.184642.1483106.0914 3.945073.9512137.951141.8962104.0366 3.917263.9248437.600741. 5180 101. 8755 3.876673.8859237.085440.9621 99.5650 3.81914 3.83028 36.3503 40.1695 97.0572 3.74084'3.7539935.344439.0852 94.3097 3.63954 3.65471 34.0372 37.6767 91. 3023 3.51598 3.53301 32.4367 35.9526 88.0533
-,3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
3.374393.3929630.596733.9711 3.22182 3.24149 28.6084 31. 8302 3.06640 3.08667 26.5777 29.6441 2.915602.9360124.603027.5186 2.775122.7952422.759325.5344 2.64848 2.66798 21.0937 23.7422 2.53725 2.55588 19.6278 22.1651 2.44152 2.45911 18.3638 20.8053 2.360392.3768517.290719.6511 2.29238 2.30766 16.3900 18.6824
84.6263 81. 1189 77.6405 74.2887 71.1352 68.2214 65.5621 63.1523 60.9741 59.0026
-1.0 -.8 - .6 -.4 - .2 - .0 .2 .4 .6 .8
2.235752.2498215.639717.8754 2.18865 2.2014915.016517.2051 2.14923 2.16082 14.4973 16.6466 2.115662.1259114.059816.1755 2.08604 2.09480 13.6817 15.7677 2.05840 2.06537 13.3400 15.3984 2.03056 2.03525 13.0108 15.0413 2.000122.0017412.667914.6680 1.964661.9619612.284214.2489 1.922151.9132411.835213.7573
57.2100 55.5684 54.0507 52.6315 51. 2860 49.9901 48.7193 47.4481 46.1514 44.8070
1.0 11.871681.8537811.303813.1755 43.4018 1.2 1.814341.7833710.687212.5016 41.9363 1.4 1.753681.70374 9.999211.7529 40.4267 1.611.6956411.6181819.267°110.9626138.90051 1. 8 1. 64812 1. 53063 8.5239 10 .1720 37.3881 2.0 1.620761.44479 7.8019 9.4227 35.9144
+ 14 13.4990 + 14 14.7994 + 15 16.8835 + 15 20.0705 + 15 24.7569 + 15 31.3375 + 15 40.0270 + 16 50.5831 + 16 62.0583 + 16 72.8262 - .7619 3.74 + 16 81.0447 -.58205.29 + 16 85.3575 - .4035 7.33 + 16 85.3746 - .2254 1. 00 + 17 81. 6518 -.04681.35 + 17 75.2978 .13291.80 + 17 67.5224 .31432.37 + 17 59.3377 .49763.10 + 17 51.4482 .68294.04 + 17 44.2666 .8702 5.24 + 17 37.9846 1.05936.78 + 17 32.6513 1.25018.74 + 17 28.2368 1. 4422 1. 13 + 18 24.6792 1. 6353 1. 45 + 18 21. 9149 1. 8292 1. 87 + 18 19.8990 2.02342.40 + 18 18.6156 2.21753.10 + 18 18.0776 2.41104.00 + 18 18.3090 2.60325.16 + 18 19.2999 2.79376.68 + 18 20.9371 2.98218.66 + 18 22.9394 3.16861.13 + 19 24.8634 3.35391.48 + 19 26.2200 3.539211.96 + 19126.65281 3.7269 2.67 + 19 26.0586 3.91963.76 + 19 24.5826
-2.68975.34 -2.49068.43 -2.29201.33 -2.09402.09 -1. 8971 3.26 -1.70165.07 -1.50817.79 -1.31711.18 -1.1291 1. 77 -.9441 2.60
t NCEl is the number of electrons per cma,expressed in the form a
+ b, meaning a
9.1410 14.6494 10.2533 14.4552 12.0340 14.2098 14.742013.9361 18.6854 13 . 6577 24.1420 13.3903 31. 2001 13.1364 39 . 5436 12.8883 48.311412.6342 56.2191 12.3656 61.981412.0803 64.795711.7834 61.563911.4842 61. 7724 11.1936 57.197210.9213 51.634410.6744 45.741710.4573 39.987810.2715 34.664310.1168 29.9255 9.9914 25.8312 22.3849 19.5624 17.3337 15.6769 14.5871 14.0754 14.1534 14.7975 15.9001
9.8926 9.8170 9.7604 9.7177 9.6828 9.6481 9.6049 9.5451 9.4634 9.3593
17.2342 9.2371 18.4806 9.1067 19.3242 8.9836 19.56471 8.8li07 19.1666 8.8586 18.2331 8.9257
X lOb.
4-192
HEAT
TABLE
log
p/po
4h-29.
Z
--- ---
THERMODYNAMIC PROPERTIES OF NITROGEN T ~ 16,000 K
Moles
E/RT
H/RT
SIR
--- --- ---
---
4.00751 34.7983 4.00239 34.6959 3.99778 34.6139 3.99270 34.5354 3.98612 34.4450 3.97675 34.3252 3.96282 34.1541 3.94194 33.9031 3.91094 33.5348 3.86598 33.0044
38.8031 38.6950 38.6075 38.5229 38.4246 38.2938 38.1068 37.8325 37.4303 36.8517
111.2459 109.3006 107.3781 105.4619 103.5369 101.5868 99.5916 97.5253 95.3547 93.0409
Cp/R
C,/R
a/ao
--- --- --16.8199 14.9838 14.0217 13.7384 14.0680 15.0567 16.8539 19.6999 23.8884 29.6715
12.2744 10.5851 9.6837 9.3885 9.6320 10.4430 11.9360 14.2950 17.7333 22.4049
15.1260 15.3666 15.5310 15.5969 15.5578 15 . 4208 15.2059 14.9418 14.6574 14.3724
.6545 .4648 .2780 .0942 .0871 .2665 .4449 .6234 .8025 .9831
4.84+16 7.32 + 16 1.09 + 17 1.59 + 17 2.27 + 17 3.20 + 17 4.42 + 17 6.03 + 17 8.12 + 17 1.08 + 18
37.0841 45.7253 54.6326 62.4355 67.8093 69.9751 68.9216 65.2614 59.8968 53.7136
28.2583 34.8830 41. 471.5 47.0102 50.6395 51.9549 51.0660 48.4401 44.6797 40.3514
14.·0925 13.8123 13 . 5231 13.2193 12.9019 12.5780 12.2580 11.9526 11.6707 11.4183
61.3364 1.1654 1. 3496 59.1652 1. 5358 57.1898 1.7239 55.3866 1. 9136 53.7303 2; 1048 52.1957 2.2972 50.7577 49.3918 2.4903 48.0734 2.6839 46.7773 .2.8774
1.43 + 18 1. 89 + 18 2.48 + 18 3.24 18 4.23 + 18 5.53 + 18 7.23 + 18 9.48 + 18 1.25 + 19 1.65+19
47.4093 41.4486 36.0932 31'.4597 27.5755 24.4242 21.9773 20.2155 19.1374 18.7556
35.9009 31. 6346 27.7384 24.3085 21.3828 18.9677 17.0581 15.6511 14.7523 14.3712
11 .. 1985 11.0119 10.8573 10.7320 10.6326 10 . 5546 10.4928 10.4412 10.3932 10.3420
4.00486 3.99908 3.99363 3.98750 3.97961 3.96862 3.95269 3.92940 3.89553 3.84725
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
3.78057 3.80295 3.69234 3.71857 3.58163 3.61160 3.45067 3.48402 3.30494 3.34100 3.15193 3.18987 2.99944 3.03837 2.85408 2.89317 2.72049 2.75903 2.60128 2.63871
32.2649 31.2783 30.0314 28.5476 26.8877 25.1366 23.3840 21. 7068 20.1596 18.7740
36.0454 34.9707 33.6131 31. 9983 30.1926 28.2885 26.3835 24.5608 22.8801 21. 3753
90.5443 87.8362 84.9136 81.8099 78.5940 75.3562 72.1874 69.1628 66.3326 63.7222
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
2.49733 2.40828 2.33296 2.26977 2.21689 2.17243 2.13446 2.10100 2.07000 2.03934
2.53323 2.44237 2.36503 2.29967 2.24445 2.19740 2.15643 2.11926 2.08338 2.04597
17.5615 16.5193 15.6350 14.8912 14.2677 13.7434 13.2968 12.9060 12.5480 12.1981
20.0588 18.9276 17.9680 17.1610 1(:1.4846 15.9158 15.4313 15.0070 14.6180 14.2375
2.00698 2.00390 11.8307 13.8377 45.4781 1. 9713011. 95408 11.4206 13.3919 44.1519 1. 93189 1. 89399 10.9479 12.8798 42.7802 1.1> L 8Q041; 1 82254 10.4033 12.2937 11.3555 1.8!1.85158!1.7407619.7937111.6453!39.. 8845! 2.0 1.822861.65216 9.144710.9675 38.3899
t
N(Elt
5.39+14 8.53+14 1. 35 + 15 2.13 + 15 3.37+15 5.31 15 8.36 + 15 1.31 16 2.04 16 3.16 + 16
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
1.0 1.2 1.4
IOglOP
(Continued)
-2.6295 -2.4301 ,.-2.2307 -2.0314 -1.8323 -1.6335 -1.4352 -1.2378 -1. 0415 - .8470 -
+ + +
+
3.0704 2.19+19 19.0712 14.5017 10.2831 3.2626 2.95 + 19 20.0236 15.0864 10.2166 3.4539 4.01 + 19 21. 4329 15.9824 10.1495 3.61155.58· l ll) 22.9770 15.963010.0976 3 .. 8354!8.03 -+- 19!24.2625!17.7828!1O.0857 4.02861.23 + 20 25.0006 18.298610 .. 1454
N(E) is the number of electrons per em', expressed in the form a
+ b, meaning a X 10'.
4-193
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-30.
THERMODYNAMIC PROPERTIES OF .ARGON
T=4000K
log
p/PQ
Z
Moles
--- --- ---
E/RT
H/RT
--_.
---
S/R
lOglO
P
N(E)t
Gp/R
--- ---
as as
G,/R
a/ao
---
---
1. 5006 1.5005 1.5004 1.5003 1.5003 1.5002 1.5002 1.5001 1.5001 1. 5001
3.S25S 3.S259 3.S259 3.8260 3.8260 3.8260 3.8261 3.8261 3.8261 3.8261
-5.0 1.00000 -4.S 1. 00000 -4.6 1. 00000 -4.4 1.00000 -4.2 1.00000 -4.0 1.00000 -3.8 1.00000 -3.6 1.00000 -3.4 1.00000 -3.2 ; 1.00000
1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1. 00000 1.00000 1.00000 1.00000
1.5000 1. 5000 1. 5000 1. 5000 1.5000 1. 5000 1. 5000 1.5000 1.5000 1.5000
2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5000
33.9295 33.4690 33.00S5 32.54S0 32.0875 31.6269 31. 1664 30.7059 30.2454 29.7849
-3.S339 -3.6339 -3.4339 -.3.2339 -3.0339 -2.S339 -2.6339 -2.4339 -2.2339 -2. 0339
1. 54 1. 94 2.44 3.07 3.87 4.87 6.13 7.72 9.72 1.22
+ + + + + + + + + +
08 08 08 09
2.5007 2.5005 2.5004 2.5003 2.5003 2.5002 2.5002 2.5001 2.5001 2.5001
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.00000 1.00000 1.00000 1.00000 1. 00001 1. 00001 1.00002 1.00003 1.00005 1.00007
1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1.00000 1. 00000 1.00000
1. 5000 1. 5000 1.5000 1. 5000 1. 5000 1.5000 1. 5000 1. 5000 1. 5000 1. 5000
2.5000 2.5000 2.5000 2 . .5000 2.5000 2.5000 2.5000 2.5000 2.5000 2.5001
29.3244 28.8638 28.4033 27.9428 27.4823 27.0218 26.5612 26.1007 25.6402 25.1796
-1.8339 -1.6339 -1.4339 -1.2339 -1.0339 - .8339 - .6339 - .4339 - .2339 - .0339
1.54 1. 94 2.44 3.07 3.87 4.87 6.13 7.72 9.72 1.22
+ + + + + + + + + +
09 09 09 09 09 09 09 09 09 10
2.5001 1. 5001 2.500] 1. noO] 2.5000 1.5000 2.5000 1. 5000 2.5000 1. 5000 2.5000 1. 5000 2.5000 1. 5000 2.5000 1.5000 2.5000 1. 5000 2.5000 1. 5000
3.8261 3 . 8261 3.8261 3.8261 3.8261 3.8262 3.8262 3.8262 3.8263 3.8264
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1. 00012 1. 00019 1.00030 1.00047 1.00075 1. 00118 1.00187 1. 00297 1. 00470 1. 00745
1 00000 1.00000 1.00000 1. 00000 1.00000 1.00000 1.00000 1.00000 1. 00000 1.00000
1. 5000 1. 5000 1. 5000 1. 5000 1. 5000 1. 5001 1.5001 1.5002 1. 5002 1. 5004
2.5001 2.5002 2.5003 2.5005 2.5008 2.5012 2.5020 2.5031 2.5049 2.5078
24.7191 24.2585 23.7979 23.3372 22.8764 22.4155 21. 9543 21. 4927 21. 0306 20.5675
.1661 .3661 .5662 .7663 .9364 1.1656 1.3669 1.5673 1. 7681 1.9693
1.54 + 10 1. 94 + 10 2.45 + 10 3.08 + 10 3.89 + 10 4.90+10 6.20 + 10 7.85 + 10 9.98 + 10 1.28 + 11
2.5000 2.5000 2.5000 2.5001 2.5001 2.5001 2.5002 2.5003 2.5005 2.5008
3.8266 3.8268 3.8272 3.8278 3.8288 3.8304 3.8330 3.8369 3.8433 3.8532
1.0 1.2 1.4 1.6 1.8 2.0
1. 01181 1.01872 1. 02908 ] . 04703 1.07454 1.11814
1.00000 1.00000 1.00000 1.00000 1. 00000 1.00.000
1.5006 1.5010 1. ;j015 1.5024 1. 5038 1.5060
2.5124 2.5197 2.5312 2.5494 2.5783 2.6242
20.1028 19.6357 19.1G43 18.6878 18.2012 17.6993
2.1712 2.3741 2.0738 2.7860 2.9973 3.2146
1. 65 + 11 2.15+11
2.5013 1.5024 3.8690 2.5022 1.5038 3.8940 l.506C 3.9~33 2.5069 1.5095 3.9950 2.5127 1.5150 4.0915 2.5242 1. 5237 4.2413
t N(E)
"
0'-'
",,00 T
I
08 08
as as
1
~
l.l.
4.00 + 11 5.88 + 11 9.45 + 11
is the number of electrons per em', expressed in the form a
+ b,
1. 5000 1. 5000 1.5001 1.5001 1.5002 1.5002 1. 5004 1.5006 1. 5009 1.5015
, '"""I
meaning a X lOb.
4-194
HEAT TABLE 4h~30. THERMODYNAMIC PROPERTIES OF ARGON
(Continued)
T=6000K log plpo ~
Z
Moles
EIRT
H/RT
SIR
IOglO P
N(E)t
CplR
--- ------ --- --- ---
CvlR
a/ao
---
-'-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
1. 00162 1.00128 1.00102 1.00081 1.00064 1.00051 1.00041 1.00032 1.00026 1.00020
1. 00162 1. 00128 1.00102 1.00081 1.00064 1.00051 1.0004] 1.00032 1.00026 1.00020
1. 5519 1.5412 1.5327 1.5260 1. 5207 1.5164 1.5130 1.5104 1.5082 1. 5065
2.5535 2.5425 2.5338 2.5268 2.5213 2.5169 2.5134 2.5107 2.5085 2.5067
34.5928 34.1210 33.6515 33.1838 32.7176 32.2526 31. 7885 31. 3251 30.8623 30.4000
-3.6572 -3.4573 -3.2574 -3.0575 -2.8576 -2.6576 -2.4577 -2.2577 -2.0577 -1.8578
4.35 + 11 5.47 + 11 6.89 + 11 8.68 + 11 1.09 + 12 1.38 + 12 1. 73 + 12 2.18 + 12 2.74+12 3.46 + 12
3.3885 3.2059 3.0608 2.9455 2.8539 2.7812 2.7234 2.6774 2.6410 2.6120
2.3335 2.1623 2.0262 1. 9181 1.8322 1. 7639 1. 7097 1. 6666 1. 6323 1. 6051
4.3758 4.4211 4.4623 4.4990 4.5309 4.5584 4.5817 4.6011 4.6173 4.6306
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.00016 1.00013 1.00010 1.00009 1.00007 1.00006 1.00006 1.00006 1.00007 1.00009
1.00016 1.00013 1.00010 1.00008 1.00006 1.00005 1.00004 1.00003 1.00003 1.00002
1.5052 1.5041 1.5033 1.5026 1. 5021 1.5016 1. 5013 1.5010 1. 5008 1. 5007
2.5054 2.5043 2.5034 2.5027 2.5021 2.5017 2.5014 2.5011 2.5009 2.5008
29.9381 29.4764 29.0150 28.5538 28.0927 27.6317 27.1708 26.7100 26.2492 25.7885
-1.6578 -l.4.578 -1.2578 -1.0578 -.8578 -.6578 - .4578 - .2578 - .0578 .1422
4.35 + 12 5.48 + 12 6.90 + 12 8.69 + 12 1.09 + 13 1.38 + 13 1. 73 + 13 2.18 + 13 2.75+13 3.46 + 13
2.5890 2.5707 2.5561 2.5446 2.5354 2.5282 2.5224 2.5178 2.5141 2.5112
1.5835 1.5663 1.5527 1. 5419 1.5333 1. 5264 1. 5210 1.5167 1.5133 1.5105
4.6414 4.6502 4.6574 4.6631 4.6678 4.6715 4.6745 4.6769 4.6789 4.6805
-1.0 -.8 - .6 -.4 -.2 -.0 .2 .4 .6 .8
1.00013 1. 00019 1.00030 1.00046 1.00073 1.00115 1.00182 1.00288 1.00456 1.00722
1.00002 1.00001 1.00001 1.00001 1.00001 1.00001 1.00000 1.00000 1.00000 1.00000
1. 5005 1. 5004 1.5004 1. 5003 1. 5003 1. 5003 1. 5003 1.5004 1.5005 1.5008
2.5007 2.5006 2.5007 2.5008 2.5010 2.5014 2.5021 2.5033 2.5051 2.5080
25.3278 24.8671 24.4064 23.9457 23.4849 23.0239 22.5628 22.1013 21. 6392 21.1763
.3422 .5422 .7423 .9423 1.1425 1. 3426 1. 5429 1. 7434 1. 9441 2.1453
4.36 + 13 5.49 + 13 6.92 + 13 8.72 + 13 1.10 + 14 1.39 + 14 1.75+14 2.21 + 14 2.81 + 14 3.57 + 14
2.5089 2.5071 2.5056 2.5045 2.5036 2.5028 2.5022 2.5018 2.5014 2.5012
1. 5084 1.5067 1.5053 1. 5043 1.5035 1. 5029 1.5025 1. 5023 1.5022 1.5025
4.6819 4.6831 4.6843 4.6857 4.6873 4.6895 4.6928 4.6976 4.7052 4.7169
2.3471 4.57 + 14 2.5500 5.91+14 7.75+14 2.9615 1.04 + 15 3.1724 1.45 + 15 3.3892 2.15 + 15
2.5010 2.5010 2.5013 2.5024 2.5054 2.5124
1. 5031 1.5043 1.5062 1.5094 1.5145 1.5228
4.7354 4.7645 4.1Sl02 4.8820 4.9943 5.1685
1.0 1.01145 1.00000 1.2 1.01814 1.00000 1.4 1.6 11. 04557 1. 00000 ''''''1'00''"'1 1.8 1. 07222 1. 00000 2.0 1. 11446 1. 00000
1. 5012 2.5127 20.7120 1. 5019 2.5200 20.2454
'WOO
' ' 'I'"· "'' ' '"'I
1.5047 2.5502 19.2998 1. 5074 2.5796 18.8153 1.5117 2.626218.3169
t NeE) is the nUIl1berof electrons per em', expressed in the form a
+ b. meaning a
X lOb.
4-195
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-30.
THERMODYNAMIC PROPERTIES OF ARGON
(Continued)
T=8000K
log p!p.
Z
Moles
E/RT
H/RT
SIR
loglO P
N(E)t
C./R
- - - - - - - - - - - - --- - - - - - -
a/a.
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
1.08764 1.07028 1.05625 1.04495 1.03588 1.02861 1.02279 1. 01815 1.01445 1.01i49
1.08771 1.07034 1.05630 1.04500 1.03592 1.02865 1.02283 1.01818 1.01447 1.01152
3.6428 3.2185 2.8755 '2.5993 2.3775 2.1998 2.0577 '1.9442 1.8536 1. 7814
4.7304 4.2887 3.9317 3.6443 3.4134 3.2284 3.0805 2.9623 2.8680 2.7929
37.2914 36.3703 35.5378 34.7779 34.0771 33.4241 32.8097 32.2263 31.6677 31.1290
~3.0
-2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.00914 1.00727 1.00578 1.00460 1.00366 1.00291 1.00232 1.00186 1. 00150 1.00123
1.00916 1.00729 1.00580 1.00461 1.00367 1.00292 1.00232 1.00184 1. 00147 1.00117
1. 7239 . 1. 6781 1. 6416 ' 1. 6126 1. 5896 1.5712 1. 5566 1.5450 1.5358 1.5285
2.7330 2.6853 2.6474 2.6172 2.5932 2.5741 2.5590 2.5469 2.5373 2.5297
30.6063 -1.5290 2.46 + 14 30.0962 -1.3298 3.10 + 14 29.5962 -1.1304 3.91 + 14 29.1044 - .9309 4.93 + 14 28.6189 -.7313 6.22 + 14 28.1385 - .5316 7.84+14 27.6622 - .3319 9.88 + 14 27.1892 - .1321 1.24 + 15 26.7187 .0677 1.57 + 15 26.2502 .2676 1.98 + 15
5.4870 4.8761 4.3899 4.0031 3.6953 3.4506 3.2560 3.1013 2.9783 2.8805
4.2370 3.6792 3.2346 2.8804 2.5983 2.3738 2.1951 2.0530 1.9400 1.8501
4.7806 4.8339 4.8898 4.9468 5.0030 5.0571 5.1077 5.1539 5.1953 5.2317
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1:00103 1. 00091 1.00086 1.00090 1.00107 1.00140 1.00199 1.00296 1.00455 1.00710
1.00093 1.00074 1.00059 1.00047 1.00037 1.00030 1.00024 1.00019 1.00015 1.00012
1.5227 1. 5181 1.5144 1.5115 1. 5092 1. 5074 1.5060 1.5050 1. 5043 1. 5039
2.5237 2.5190 2.5153 2.5124 2.5103 2.5088 2.5080 2.5080 2.5088 2.5110
25.7833 25.3177 24.8532 24.3893 23.9261 23.4632 23.0005 22.5379 22.0749 21.6114
.4675 .6675 .8675 1.0675 1.2675 1.4677 1.6679 1.8684 2.0691 2.2702
2.49 3.15 3.97 5.01 6.32 7.99 1.01 1.28 1.62 2.07
15 15 15 15 15 15 16 16 16 16
2.8028 2.7410 2.6918 2.6528 2.6217 2.5970 2.5774 2.5618 2.5494 2.5395
1. 7786 1.7218 1.6766 1.6408 ·1.6123 1.5897 1.5718 1.5577 1. 5467 1. 5382
5.2632 5.2901 '5.3130 ·5.3324 5.3489 5.3635 5.3769 5.3902 5.4049 5.4230
1.0 1.2 1.4 1.6 1.8 2.0
1.01116 1. 01762 1. 02786 1.04411 1.06988 1.11073
1.00010 1.00008 1.00007 1.00006 1.00005 1.00004
1.5038 1.5042 1. 5052 1. 5070 1.5101 1. 5153
2.5150 2.5218 2.5330 2.5511 2.5800 2.6260
21.1467 20.6800 20.2102 19.7352 19.2520 18.7558
2.4719 2.6747 2.8790 3.0858 3.2964 3.5127
2.65 + 16 3.41 + 16 4.45 + 16 5.92 + 16 8.11 + 16 1.16+17
2.5316 2.5254 2.5206 2.5173 2.5162 2.5191
1.5319 1.5276 1.5253 1.5253 . 1. 5279 1.5344
5.4475 5.4827 5.5357 5.6168 5.7420 . 5.9353
t N(E)
-3.4964 -3.3034 -3.1091 -2.9138 -2.7176 -2.5207 -2.3231 -2.1251 -1.9267 -1. 7280
C./R
-----2.36 3.00 3.80 4.81 6.09 7.70 9.72 1.23 1. 55 1.95
is the number of electrons per em', expressed in the form a
+ + + + + + + + + +
+ + + + + + + + + +
13 13 13 13 13 13 13 14 14 14
30.8686 26.6115 25.3133 21. 8364 20.7930 17.9039 17.1368 14.6903 14.1926 12.0800 11.8293 9.9698 9.9369 8.2701 8.4243 '6.9050 7.2169 5.8110 6.2541 4.9360
+ b, meaning a
X 10'.
4.6163 4.5941 4.5817 4.5786 4.5843 4.5984 4.6207 4.6506 4.6878 4.7315
HEAT
4'--196 '1;'ABLEl
4h-30.
THERMQDYN~MIC PROPERTIES OF ARGON
(Continued}
T = 10,000 K
log
piP.
Z
'Moles
,E/RT
H/RT
S/R
lOgl'P
N(E)t
15.9059 49.7398 14.2674 47.4418 12.6499 45.1999 11.1227 43.0787 9.7320 41.1199 8.5019 39.3427 7.4384 37.7495 6.5353 36.3307 5.7792 35.0701 5.1530 33.9485
-3.2206 -3.0419 -2.8640 -2.6859 -2.5069 -2.3264 -2.1439 -1.9594 -1.7728 -1. 5842
-3.2
1.64223 1. 56361 1.48602 1.41277 1.34609 1.28712 1.23616 1.19289 1.15667 1.12668
1.64320 14.2637 1.56461 12.7038 1.48703 11.1639 1.41377 9.,7099 1.34705 8.3859 1.28804 7.2148 1.23701 6.2022 1.19368 5.3424 1.15740 4.6225 1.12736 4.0263
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.10208 1.08202 1.06575 1.05262 1.04206 1.03358 1.02680 1.02137 1.01705 1. 01361
1.10269 1.08258 1.06626 1.05308 1.04247 1.03394 1.02711 1.02165 1.01728 1.01379
3.5369 3.1379 2.8142 2.5527 2.3422 2.1732 2.0378 1.9294 1..8427 1.7736
,-1.0 -.8 -.6 -.4 -.2 -'.0 ,,2 .4.6 .8
1.01089 1.01101 1.00875 1.00879 1.00710 1.00702 1.00586 1.00560 1.00500 1.00448 1.00451 1.00359 1.00444 1.00287 1.00487 1.00231 1.00600 1.00185 1.00814 1.001,50
1. 7184 1. 6744 : 1.6394 1.6114 1.5892 1.5715 1. 5575 1. 5464 1. 5377 1. 5310
2.7293 2.6832 2.6465 2.6173 2.5942 2.5760 2.5619 2.5513 2.5437 2.5391
.5687 26.3338 .7678 25.8248 .9671 25.3256 1.1665 24.8342 24.3489 1.3662 1.5660 23.8686 23.3920 1.7659 22.9183 1. 9661 22.4466 ' 2.1666, 21.9761 2·3675
1.5260 1. 5225 1. 5205 1.5202 1. 5219 1. 5264
2.5378 2.5403 2.5481 2.5634 2.5900 2.6340
21.5061 21. 0353 20.5625 20.0857 19.6017 19.1059
-5.0 -4.8 -4.6 -4.4 -4 ..2 -4.0 ,-3.8 -3.6 -3.4
1.0 1.2 1.4 1.6 1.8 2.0
t N(E)
i.01181 1.01786 1.02762 1.04323 1.06809 1.10757
1.00121 1.00099 1.00082 1.00069 1.00060 1.00054
C./R
C./R
a/a.
--- ------
--- ------ --- --1. 73 + 2.40 + 3.29 + 4.43 + 5.88+ 7.74 + 1.01 + 1.31 + 1.68 + 2.16 +
14 14 14 14 14 14 15 15 15 15
86.0704 87.5084 84.4647 78.0709 69.7159 60.6334 51.7164 43.5056 36.2615 30.0553
69.1039 69.8199 67.2871 62.3681 56.0343 49.1289 42.2718 35.8580 30.0997 25.0792
6.3474 6.1903 6.0341 5.8848 5.7472 5.6246 5.5185 5.4293 5.3567 5.2998
4.6390 32.9461 -1.3938 2.76 + 15 24.8464 20.7949 5.2575 4.2199 32.0443 -1.2018 3.52 + 15 20.5376 17'.1969 5.2287 3.8799 31.2262 -1.0083 4.47 + 15 17.0100 14.2119 5.2125 3,6053 30.4771 - .8137 5.68 + 15 14.1436 11.7583 5.2078 3.3843 29.7844 - .6181 7.20 + 15 11.8268 9.7558 5,2141 3.2068 29.1375 - .4217 9.12 + 15 9.9616 8.1305 5.2306 3.0645 28.5277 - .2245 1.15 + 16 ' 8.4644 6.8169 5.2567 2.9507 27.9477 - .0268 1.46 + 16 7.2651 5.7588 5.2914 .1713 1.85 + 16 6.3058 4.9088 5.3338 2.8598 27.3918 .3699 2.34 + 16 5.5395 4.2272 5.3826 2.7872 26.8551
2.5691 2.7717 2.9758 3.1824 3.3926 3.6084
2.96 + 16 3.74 + 16 4.74 + 16 6.00 + 16 7.60 + 16 9.64 + 16 1.22 + 17 1.56+17 1.98 + 17 2.54 + 17
4.9278 4.4399 4.0508 3.7406 3.4934 3.2965 3.1396 3.0146 2.9151 2.8360
3.6815 3.2452 2.8967 2.6185 2.3965 2.2196 2.0786 1.9665 1.8774 1.8070
5.4364 5.4935 5.5522 5.6106 5.6675 5.7216 5.7726 5.8206 5.8664 5.9120
3.26 4.23 5.54 7.39 1.01 1.45
2.7732 2.7234 2'.6844 2.6545 2.6330 2.6212
1.,7516 1.7087 1.6762 1.6531 1.6389 1.6342
5.9605 6.0168 6.0885 6.1869 6.3291 6.5404
is the number of electrons per em'" expressed in the f,orm a
+ + + + + +
17 17 17 17 18 18
+ b, meaning a
X lOb.
4-197
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-30.
THERMODYNAMIC PROPERTIES OF ARGON
(Continued)
T = 12,000 K
log p/po
Z
Moles
--- --- ---
E/RT
H/RT
SIR
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
1.96966 1.95381 1.93076 1.89835 1.85484 1.79956 1. 73355 1. 65961 1. 58165 1. 50381
1.97102 1.95548 1. 93279 1.90078 1.85768 1. 80280 1.73714 1.66346 1. 58568 1. 50791
17.8020 17.5399 17.1577 16.6191 15.8943 14.9718 13.8687 12.6312 11.3251 10.0195
19.7717 19.4937 19.0884 18.5174 17.7491 16.7714 15.6022 14.2908 12.9067 11.5233
56.3866 55.2208 53.9438 52.5232 50.9338 49.1695 47.2525 45.2335 43.1811 41.1652
-3.0 -2.8 -2.6 -'2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.42960 1. 36147 1.30081 1.24809 1. 20313 1.16535 1.13398 1. 10817 1.08710 1.06998
1.43366 1.36543 1. 30461 1.25167 1.20648 1.16846 1.13684 1.11079 1.08947 1. 07212
8.7734 7.6285 6.6080 5.7202 4.9623 4.3249 3.7949 3.3583 3.0012 2.7107
10.2030 8.9899 7.9088 6.9683 6.1654 5.4902 4.9289 4.4665 4.0883 3.7807
-1.0 - .8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1.05616 1. 04504 1. 03615 1.02910 1.02356 1. 01932 1.01623 1.01424 1. 01340 1.01392
1. 05807 1.04672 1. 03757 1.03022 1. 02432 1. 01960 1. 01581 1.01278 1.01036 1.00844
2.4754 2.2854 2.1324 2.0095 1.9109 1. 8319 1.7688 1.7184 1. 6782 1. 6464
1.0 1.2 1.4 1.6 1.8 2.0
1.01624 1. 02110 1.02975 1.04422 1. 06775 1.10549
1. 00691 1.00570 1.004i7 1.00406 1.00356 1.00327
1. 6215 1.6023 1. 5881 1.5785 1.5735 1. 5741
t N(E)
loglo P
N(E)t
Cp/R
--- --- ------3.0624 -2.8659 -2.6711 -2.4784 -2.2885 -2.1017 -1.9179 -1.7368 -1.5577 -1.3796
Cv/R
a/ao
--- ---2.61 4.07 6.30 9.64 1.45 2.16 3.14 4.48 6.27 8.61
14 14 14 14 15 15 15 15 15 15
13.8208 18.1228 24.0504 31.6594 40.5410 49.6798 57.6164 62.9469 64.8736 63.4370
10.7732 14.4797 19.5007 25.7961 32.9236 39.9900 45.8652 49.5971 50.7572 49.5009
8.1027 7.9430 7.7997 7.6657 7.5311 7.3879 7.2322 7.0651 6.8913 6.7176
39.2439 -1. 2016 37.4566 -1.0228 35.8235 - .8426 34.3492 -.6606 33.0272 - .4765 31. 8447 - .2904 30.7856 - .1022 29.8329 .0878 28.9705 .2794 28.1835 .4726
1.17+16 1. 56 + 16 2.06 + 16 2.69 + 16 3.50 + 16 4.53 + 16 5.83 + 16 7.48 + 16 9.57 + 16 1.22 + 17
59.3379 53.5596 47.0373 40.4836 34.3527 28.8818 24.1545 20.1604 16.8387 14.1068
46.3780 42.0742 37.2186 32.2930 27.6174 23.3735 19.64181 16.4355 13.7273 11.4692
6.5507 6.3961 6.2577 6.1377 6.0366 5.9544 5.8900 5.8425 5.8104 5.7927
3.5315 3.3304 3.1686 3.0386 2.9345 2.8513 2.7850 2.7326 2.6916 2.6604
27.4587 26.7850 26.1529 25.5545 24.9833 24.4340 23.9022 23.3843 22.8774 22.3788
.6669 .8623 1. 0586 1. 2556 1. 4533 1. 6515 1. 8502 2.0493 2.2490 2.4492
1.56 + 17 11.8780 9.6048 1.99 + 17 10.0700 8.0769 2.54+17 8.6094 6.8319 3.23 + 17 7.4329 5.8221 4.12 + 17 6.4874 5.0057 5.27 + 17 5.7286 4.3476 6.73+17 5.1205 3.8183 8.63 + 17 4.6337 3.3936 1.11 + 18 4.2443 3.0535 1.43 + 18 3.9335 2.7820
5.7881 5.7956 5.8140 5.8423 5.8793 5.9237 5.9741 6.0296 6.0892 6.1531
2.6377 2.6234 2.6175 2.6227 2.6413 2.6795
21.8865 21.3983 20.9120 20.4251 19.9344 19.4351
2.6502 2.8522 3.0559 3.2620 3.4716 3.6857
1.86 2.43 3.22 4.34 6.04 8.79
is the number of electrons per em', expressed in the form a
+ + + + + + + + + +
+ 18 + 18 18 + 18 + 18 + 18
+
3.6858 3.4895 3.3352 3.2163 3.1290 3.0740
2.5664 6.2225 2.3965 6.3005 2.2649 6.3931 2.1663 6.5105 2.0979 6.6683 2.0608 6.8895
+ bi meaning a X
10'.
4-198
HEAT TABLE
4h-30.
THERMODYNAMIC PROPERTIES OF ARGON
(Continued)
T = 14,000 K
log p/po
Z
Moles
E/RT
H/RT
SIR
IOglOP
N(E)t
Op/R
a/ao
2.00297 1.99929 1.99546 1.99072 1.98415 1.97455 1.96039 1. 93974 1.91049 1.87073
16.2050 16.1296 16.0595 15.9807 15.8778 15.7326 15.5218 15.2168 14.7866 14.2035
18.2069 57.4144 18.1275 56.4181 18.0532 55.4288 17.9691 54.4330 17.8592 53.4160 17.7037 52.3606 17.4779 51.2452 17.1514 50.0441 16.6909 48.7296 16.0669 47.2786
1. 81108 1. 81946 1. 74784 1. 75721 1.67606 1.68624 1. 59939 1. 61013 1. 52189 1. 53293 1.44720 1.45828 1.37798 1.38888 1. 31585 1.32641 1.26150 1.27157 1.21488 1.22440
13.452.9 12.5426 11.5060 10.3954 9.2696 8.1817 7.1711 6.2619 5.4643 4.7786
15.2640 45.6815 -1.0319 2.20 + 16 37.3149 29.4596 8.1018 14.2904 43.9514 - .8474 3.22 + 16 43.7039 34.1758 7.9307' 13.1821 42.1262 - .6656 4.63 + 16 48.4041 37.4782 7.7485 11.9948 40.2,614 - .4859 6.53 + 16 50.6621 38.9300 7.5591 10.7915 38.4170 - .3075 9.40 + 16 50.3277 38.5294 7.3689 9.6289 36.6457 - .1293 1.23 17 47.8011 36.6121 7.1850 8.5491 34.9849 .0494 1.66 + 17 43.7771 33.6659 7.0135 7.5777 33.4557 .2293 2.20 + 17 38.9803 30.1724 6.8589 6.7258 32.0650 .4110 2.91 + 17 33.9995 26.5204 6.7237 5.9935 30.8094 .5947 3.80+17 29.2345 22.9808 6.6091
-5.0 2.00182 -4.8 1.99786 -4.6 , 1.99368 -4.4 1. 98849 -4.2 1.98137 -4.0 1.97111 -3.8 1.95615 -3.6 1.93458 -3.4 1.90430 -3.2 1.8~344 -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 , -1.6 -1.4 -1.2
O./R
--- - - -
- - - - - - - - - - - -- - --2.9884 --':2.7893 --':2.5902 -2.3914 -2.1929 -1.9952 -1. 7985 -1.6033 -1.4101 -1.2196
2.70 4.26 6.72 1.06 1.67 2.62 4.09 6.114 9.'14 1.48
+ 14 + 14 + 14 + 15 +15 + 15 + 15 + 15 + 15 +16
9.4008 7.0151 8.4235 6.1023 8.1468 5.8214 8.5071 6.1086 9.5486 6.9931 11.4085 8.5810 14.2902 11.0251 18.3997 14.4624 23.8214 18.9035 30.3428 24.0973
9.0622 9.1895 9.2404 9.1991 9.0803 8:9179 8:7442 8.5767 8.4182 8.2626
+
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1.17554 1.14275 1.11571 1.09361 1.07571 1.0in35 1.05003 1.04134 1.03505 1.03113
1.18445 1.1.'n02 1.12332 1.10053 1. 08190 1.06673 1.05443 1.04449 1.03649 1.03007
4.1982 3.7130 3.3111 2.9808 2.7109 2.4914 2.3136 2.1700 2.0546 1.9621
5.3737 29.6790 4.8557 28.6602 4.4268 27.7385 4.0744 26.8997 3.7866 26.1305 3.5528 25.4190 3.3636 24.7552 3.2114 24.1302 3.0896 23.5367 2;9933 22.9686
.7804 .9681 1.1577 1.3490 1. 5418 1.7360 1.9313 2.1277 2.3251 2.5234
4.96 + 6.43 8.32 + 1.08 + 1.39 1.79 + 2.32 + 3.00 3.90+ 5.10.+
1.0 1.2 1.4 1.6 1.8 2.0
1.02977 1. 03154 1. 03749 1.04942 1.07031 1.10481
1.02495 1.02091 1.01778 1. 01546 1.01392 1.01328
1.8886 1.8309 1.7867 1. 7545 1. 7341 1. 7270
2.9184 2.8625 2.8242 2.8039 2.8044 2.8318
2.7229 2.9236 3.1261 3.3311 3.5396 3.7534
6.70 + 18 8.90 + 18 1.20 19 1.65 + HI 2.36+19 3.57 + 19
22.4207 21.8884 21.3680 20.~556
20.3475 19.8402
17 24.9120 21.1295 17 17.9011 18 15.1935 18 12.9506 18 11.1092 18, 9.6072 18 8.3881 18 7.4026 18 6.6092
19.7177 16.8129 14.2916 12.1435 10.3389 8.8390 7.6027 6.5908 5.7674 5.1015
6.5149 6.4402 6.3837 6.3440 6.3194 6.3086 6.3103 6.3233 6.3470 6.3812
5.9735 5.4680 5.0716 4.7699 4.5569 4.4420
4.5671 4.1429 3.8131 3.5671 3.4024 3'.3310
6.4267 6.4858 6.5631 6.6667 6.8091 7.0070
+ 17 + +
t N(E) is the number of electrons per em', expressed in the forlll a,
+
+ b, meaning a X
lOb.
4-199
THERMODYNAMIC PROPERTIES OF GASES TABLE
4h-30.
THERMODYNAMIC PROPERTIES OF ARGON
(Continued)
T = 16,000 K
log p/p,
Z
Moles
E/RT
H/RT
S/R
loglQ P
N(E)t
Cp/R
--- --- ------ --- --- ---
Cv/R
a/a,
--- ---
-5.0 -4.8 -4.6 -4.4 -4.2 -4.0 -3.8 -3.6 -3.4 -3.2
2.10148 2.06759 2.04341 2.02639 2.01427 2.00512 1. 99738 1.98967 1.98066 1. 96888
2.10270 2.06901 2.04508 2.02840 2.01672 2.00814 2.00111 1.99430 1.98640 1.97598
16.7027 15.9723 15.4552 15.0976 14.8515 14.6776 14.5452 14.4293 14.3081 14.1598
18.8042 18.0399 17.4986 17.1240 16.8657 16.6827 16.5426 16.4190 16.2888 16.1287
60.0565 58.3666 56.9032 55.6088 54.4324 53.3331 52.2791 51.2452 50.2097 49.1519
-2.9094 -2.7164 -2.5215 -2.3252 -2.1278 -1. 9297 -1. 7314 -1. 5331 -1. 3351 -1.1377
2.96 + 14 4.55 + 14 7.05 + 14 1.10 + 15 1. 72 + 15 2.71+ 15 4.26 + 15 6.71+15 1.06 + 16 1.65 + 16
51.3510 37.9023 27.6685 20.3499 15.3947 12.2402 10.4361 9.6847 9.8374 10.8736
43.5643 32.1211 23.2395 16.7869 12.3643 9.5191 7.8696 7.1537 7.2328 8.0740
9.1366 9.1189 9.1467 9.2207 9.3367 9.4783 9.6114 9.6899 9.6807 9.5860
-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2
1.95262 1.92992 1.89871 1.85723 1.80466 1.74169 1. 67963 1.59500 1. 51870 1.44519
1.96136 1.94056 1. 91148 1.87227 1. 82198 1. 76111 1.69181 1. 61749 1. 54198 1.46877
13.9605 13.6837 13.3014 12.7897 12.1363 11. 3481 10.4531 9.4951 8.5235 7.5829
15.9132 48.0495 15.6136 46.8783 15.2001 45.6141 14.6469 44.2372 13.9410 42.7403 13.0898 41.1352 12.1237 39.4543 11. 0901 37.7443 10.0422 36.0559 9.0281 34.4330
- .9413 -.7463 - .5534 - .3630 - .1755 .0091 .1910 .3709 .5496 .7280
2.58 + 16 4.01 + 16 6.15+16 9.33 + 16 1.39 + 17 2.05 + 17 2.95 + 17 4.17 + 17 5.80 + 17 7.95+17
12.8644 9.7163 15.9107 12.2114 20.0386 15.5326 25.0616 19.4696 30.4743 23.5737 35.4890 27.2312 39.2635 19.8632 41.2109 31.1302 41.1887 31.0114 39.4686 29.7379
9.4368 9.2662 9.0918 8.9163 8.7355 8.5452 8.3450 8.1386 7.9324 7.7334
-1.0 -.8 -.6 -.4 -.2 -.0 .2 .4 .6 .8
1.37705 1. 31584 1. 26221 1.21617 1.17729 1. 14493 1. 11837 1. 09691 1.07999 1.06722
1.40048 1. 33877 1. 28437 1.23737 1.19738 1.16380 1.13586 1.11283 1.09398 1.07869
6.7069 5.9162 5.2202 4.6196 4.1094 3.6812 3.3255 3.0325 2.7929 2.5985
1.08 1.44 1.92 2.54 3.35 4.40 5.79 7.62 1.01 1.33
+ + + + + + + + + +
18 18 18 18 18 18 18 18 19 19
36.5555 32.9919 29.2300 25.5861 22.2469 19.2997 16.7662 14.6294 12.8530 11.3939
27.6609 25.1353 22.4534 19.8239 17.3771 15.1819 13.2644 11.6230 10.2408 9.0938
7.5479 7.3801 7.2326 7.1065 7.0014 6.9164 6.8500 6.8008 6.7676 6.7497
2.7928 1. 78 2.9909 2.42 3.1911 3.33 3.3939/4.72 3.6001 7.01 3.8107 1.13
+ + + + +
19 10.2097 7.1565 19 9.2635 7.4061 19 8.5272 6.8261 1917.986916.4112 19 7.6550 6.1803 20 7.6148 6.2191
6.7474 6.7626 6.7991 6.8633 6.9645 7.1095
1.0 1.05847 1.06642 1.2 1.05395 1. 05674 1.4 1. 05437 1. 04935 1.6 06109/1. 04415/ 1.8 /1. 1. 07634 1. 04136 2.0 1.10300 1. 04211
8.0839 7.2320 6.4824 5.8358 5.2866 4.8261 4.4439 4.1294 3.8729 3.6657
32.9074 31. 4971 30.2078 29.0369 27.9758 27.0132 26.1366 25.3337 24.5930 23.9044
2.4422 3.5007 23.2588 2.3186 3.3725 22.6490 2.2234 3.2778 22 . 0685 1545 3.2156/21.5128/ 2.1128 2. 1 3. 1892 20.9794 2.1070 3.210020.4722
.9071 1.0873 1.2692 1.4531 1. 6390 1. 8269 2.0167 2.2083 2.4015 2.5964
+
t N(E) is the number of electrons per em', expressed in the form a
+ b,
meaning a X lOb,
TABLE
4h-31.
THERMODYNAMIC PROPERTIES OF HIGHLY IONIZED NITROGEN, OXYGEN, AND
AlRt
Oxygen
Air
Nitrogen
to o
log C, p/po
I E*/RT I
Z*
P,atm
log T -5 -4
-3 -2 -1 0
.....
2.8203 22.4494 1. 4247( -2) 2.3121 14.7619 1. 5204( -1) 2.0344 10.6227 1.8086 1. 9197 9.4752 1.91894(1) 1.5194 6.4984 2.6899(2) ---
---
..
-1
0 +1
-1
0 +1
Z*
p/po
.....
3. 60S( -5) 4.460( -4) 5.087( -3) 6.320( -2) 0.9484 1.71167(1)
3.7715 3.2434 2.9657 2.5823 2.0544 1.5842
30.2600 21. 8559 17.7766 13.7697 8.8117 6.3699
1. 9833( .,...2) 2 .1084( -1) 2.1989 2.3786(1) 2.8398(2) 3.95214(3)
1E*/RT I
P,atm
5.934 5.506 4.531 4.058 3.868 3.182
50.209 1. 386( -3) 43.302 1. 445( -2) 28.177 1. 646( -1) 21.049 1.813 19.134 1. 9042(1) 14.038 2.50(2)
1.846(-5) 2. 266( -1) 2.568(-3) 3.242(-2) 0.4810 8.6281
7.957 i.416 6.412 5.894 5.084 4.079 3.159
68.511 59.297 43.076 35.540 26.894 17.333 12.550
. . . . . . . . . . . 1.11( -6) 2. 9080( -2) 1. 242( -5) 1. 402( -4) 0.3003 1. 643( -3) 3.1009 3.2762(1) 1. 970( -2) 3.5531(2) 0.26574 4.35934(3) . 4.335 -- -_ _ - - -
11. 006 10.054 9.134 8.085 7.076 5.763 4.307
..... ...... . ........... 2.54(-6)
2.5019 18.6759 1. 5319( -2) 2.0914 11.5787 1. 7622( -1) 2.0087 10.1592 1. 8313 1.9877 9.9100 1. 8499(1) 1.8570 8.9608 1. 9925(2)
2.852( -5) 3. 951( -4) 4.859(-3) 5.353( -2) 0.8462
- - - - - -
= 4.6
T
= 39,811 K
::q
. ...... . .......... . .... ..... ..... . ...... . ........... 1. 68( -6)
. . ..... . . . .
4.047( -5) 4.837(-4) 5.327( .,...3) 7 .186( -2) 1.0159 1. 77836(1)
3.4711 3.0672 2.8772 2.3917 1.9843 1. 5623
27.3687 20.3529 17.7458 12.2432 8.1263 5.9211
2.0475( -2) 2.1623( -1) 2.2339 2.5050(1) 2.9381(2) 4.04935(3)
1. 949( ~3) l"J 1. 995( -2) 8 2.118( -1) 2.207 2.402(1) 2.860(2) 3.973(3)
-----------
log; T -5 -4 -3 -2
.
_--
log T -5 -4 -3 -2
.
6. 658( -5) 9 .163( -4) 9: 91i( -3) 0.1012 1.16,58 --
P,atm
= 4.4 T = 25,119 K
. ...... . .......... . .........
.... " ...... 5.493(-5) 7.621(-4) 9. 667( -3) 0.1087 1.9252
IE*/RT I
Z*
p/po
= 4.8
T
= 63,096 K
........... ...... ...... . .......... . ......... . ..... . ...... . 2 .456( -5) 2. 755( -4) 3. 252( -3) 3.879(-2) 0.5297 8.6176
5.0711 4.6294 4.0752 3.5778 2.8880 2.1604
40.7265 33.6748 25.5689 19.8189 13.4425 9.0014
* Air is taken to be O.78847N, + 0.211530,.
2.8770( -2) 0.2946 3.0614 3.2057(1) 3.5337(2) 4.30041(3)
2.589(-5) 3.000( -4) 3. 423( -3) 4. 184( -2) 0.5383 8.8718 -
4.8626 4.3333 3.9217 3.3899 2.8576 2.1272
39.9829 31.2774 25.0767 18.7528 13.4707 _8,8848
...
- - - -
98.885 2 .822( -3) 81.138 2.884( -2) 66.335 0.2958 50.930 3.070 39.187 3.221(1) 26.897 3.538(2) 17.953 4.31288(3)
t The symbols Z* and E* refer to the compressibility factor and energy, respectively. of the gas mixture in the ideal gas approximation, with dissociation and ionization effects included, but without intermolecular and ionic force corrections.
""
4h-31.
TABLE
THERMODYNAMIC PROPERTI])S OF HIGHLY IONIZED NITROGEN, OXYGEN, AND
plpo
I
I E*IRT I
Z*
P,atm
.. .........
.....
2.002( -5) 2.023( -4) 2.166( -3) 2.530( -2) 0.31486 4.5067
5.9941 5.9442 5.6159 4.9529 4.1760 3.2189
.
......
.
39.9015 39.2902 35.2938 27.6217 20.2730 13.8801
..........
.
4.3932( -2) 0.4402 4.4532 4.5876(1) 4.8137(2) 5.3108(3)
I E*/RT I
Z*
I
plpo
log T = 5.0 -5 -4 -3 -2 -1 0 +1
Air
Oxygen
Nitrogen og Ce
AIR (Continued)
plpo
9. 62( -7) 6.6336 54.5680 4.3108( -2) 9.75( -6) 1.007( -4) 6.0370 44.7463 0.4387 1. 093( -3) 5.4160 35.7412 4.4891 4.7695 27.5515 4.6323(1) 1. 2774( -2) 4.0197 19.9701 4.8739(2) 0.1591 3.1133 13.6880 5.3934(3) 2.2736
log T = 5.2
I
Z*
I E*IRT I
12.400 12.259 11.928 11.147 9.828 8.286 6.393
88.347 86.008 80.888 70.777 55.214 40.418 27.679
P,atm
T = 100,000 K
. . . . . . . . . . ..... . 1. 775( -5) 1. 985( -4) 2.264( -3) 2.653( -2) 0.3312 4.7320
P, atm
. ......
.. , ........
..,
4.367(-3) iJ1 t':I 4.376( -2) ~ 0.4398 ~ o 4.461 tj >1 4.596(1) 'Z 4.826(2) iJ> 5.328(3) ~ H
o
T = 158,490 K
":I
-5 -4 -3 -2 -1 0 +1
~
2.000( -5) 2.000( -4) 2.003( -3) 2.025( -2) 0.2194 2.8280
5.9999 5.9994 5.9937 5.9392 5.5589 4.5360
28.5422 28.5379 28.4949 28.0852 25.2956 18.8699
6. 9627( -2) 0.6962 6.9641 6.9784(1) 7.0764(2) 7.4431(3)
1.667(-5) 1. 669( -4) 1. 692( -3) 1. 835( -2) 0.2175 2.8~02
log T -5 -4 -3 -2 -1 0 +1
.. ......... 1. 998( -5) 2.000( -4) 2.000( -3) 2.002( -2) 0.2022 2.1844
=
6.9990 6.9902 6.9085 6.4490 5.5974 4.4719
5.4
T
=
42.1981 42.1008 41.2041 36.2326 27.9500 19.7684
6.769( -2) 0.6770 6.7823 6.8664(1) 7.0637(2) 7.4734(3)
.. ........
..... . . ......
...........
1.1031(-1) 1.1036 1.1034(1) 1.1035(2) 1.1057(3) 1.12054(4)
1. 667( -5) 1. 6(17( -4) 1. 607( -3) 1. 6~'2( -2) 0.1715 1.9859
7.0000 6.9998 6.9981 6.9814 6.8305 6.0354
0.1073 1.0731 1. 0728(1) 1.0734(2) 1. 0772(3) 1.10221(4)
6.0038 6.0003 5.9995 5.9945 5.9465 5.5780
21.4332 21.3407 21.3298 21. 3127 21.1549 19.9145
9.595( -6) 9. 599( -5) 9.6395(-4) 9.9069( -3) 0.1095 1.4194
12.422 12.418 12.374 12.094 11.134 9.045
62.862 62.814 62.367 59.617 51. 714 38.120
6.92( -2) 0.692 6.92 6.95(1) 7.074(2) 7.449(3)
9.5( -7) 9. 59( -6) 9. 594( -5) 9. 596( -4) 9. (l09( -3) 9:140( -2) 1.070
12.481 12.429 12.423 12.421 12.407 12.267 11. 350
48.109 46.705 46.559 46.537 46.467 45.827 41.941
1.090( -2) t':I w. 0.110 1.097 1. 097(1) 1. 097(2) 1. 099(3) t-.:) 1. 1170( 4)
251,190 K
..... . . . . . . . . . . . . . . . . . . .
30.5070 30.5059 30.4954 30.3921 29.4678 24.9055
o
":I
t':I
..,
~ H
t':I
w.
o
";I
§2 [f2
t
o '"""'
TABLE
4h-31.
THERMODYNAMIC PROPERTIES OF HIGHLY IONIZED NITROGEN, OXYGEN, AND
log C. p/po
Z*
I E*/RT I
P,atm
-1
0 +1
1. 553( -5) 7.4409 1. 673( -4) 6.9782 1. 822( -3) 6.4876 (967( -2) 6.0831 0.20046 5 9883 2.0749 5.8194
43.5716 34.2161 25.3735 18.2776 16.9174 16.5657
0.1684 1. 7016 1. 7227(1) 1. 7437(2) 1. 7496(3) 1. 7599( 4)
=
-1
0 +1
-1
0 +1
7.2854 7.0382 7.0037 6.9973 6.9700 6.7442
= 5.8
T
..... . ...... .
.. ......... .. ........ .....
1.429( -5) 1. 430( -4) 1. 438( -3) 1. 499( -2) 0.1657 1.8873
7.9995 7.9953 7.9547 7:6706 7.0362 6.2987
0.2640 2.6410 2.6423(1) 2.6560(2) 2.6932(3) 2.7459(4)
39.3190 39.2610 38.7050 34.8243 26.4910 18.8607
1. 253( -5) 1. 277( -4) 1.371( -3) 1. 485( -2) 0.1621 1. 7010
.
.......... ..... . ...... . .. .........
1.429( -5) 1. 429( -4) 1.429( -3) 1. 4286( -2) 0.1436 1.498
8.0000 8.0000 7.9996 7.9961 7.9618 7.6748
29.2413 29.2410 29.2388 29.2170 29.0039 27.2651
0.4184 4.184 4.1839(1) 4.1820(3) 4.1856(3) 4.2090(4)
=
T
29.2764 23.9473 23.2082 23.1256 23.0593 22.5449
1. 689( -1) 1.6987 1. 7006(1) 1.7001(2) 1.70157(3) 1. 7112( 4)
= 630,960 K . ...... . ...........
8.9802 8.8308 8.2929 7.7337 7.1689 6.8787
6.0
P,atm
p/po
Z*
1~*/RT I
P,atm
T =c 398,110 K
. ..........
log T -5 -4 -3 -2
5.6
1. 591( -5) 1. 656( -4) 1. 666( -3) 1. 667( -2) 0.1675 1.7409
log T -5 -4 -3 -2
I E*/RT I
Z*
p/po
log T -5 -4 -3 -2
Air
Oxygen
Nitrogen
!g
AIR (Continued)
=
50.7353 48.1188 38.7624 29.6449 21.2538 18.6828
0.2599 2.6049 2.6264 2.6530(2) 2.6844(3) 2.7028(4)
14.816 81.096 0.1685 7.80(-6) 8.346( -5) 13.982 64.088 1.701 8.934( -4) 13.194 49.831 1.718(1) 9.476( -3) 12.553 38.606 . 1.734(2) 9.623( -2) 12.392 36.433 1.739(3) 12.300 35.661 1. 7500(4) 0.9970 16.422 83.609 2.62(-2) 6.9(-7) 6.94(-6) 16.414 83.468 0.2631 6. 972( -5) 16.344 82.269 2.633 7.116( -4) 16.052 77.434 2.639(1) 7 .481( -3) 15.368 67.457 2.655(2) 0.08245 14.128 50.766 2.691(3) 0.9225 12.843 37.646 2.7367(4)
1,000,000 K
. .........
. ..... ...... .
1. 250( -5) 1. 250( -4) 1. 250( -3) 1. 254( -2) 0.1288 1. 4231
9.0000 8.9997 8.9971 8.9719 8.7657 8.0268
37.2123 37.2095 37.1809 36.9010 34.6534 27.3929
........... 6.93( -7)
0.41186 4.1186 4.1186(1) 4.1186(2) 4.133(3) 4.1819(4)
6.933( -6) 6.933(-5) 6.934( -4) 6. 942( -3) 0.07011 0.74082
16.423 16.423 16.423 16.421 16.405 16.264 15.498
61.855 61.855 61.853 61.838 61.685 60.398 54.584
4.17(-2) 0.417 4.17 4.17(1) 4.17(2) 4.175(3) 4.2033(4)
~
L:9
>-
.."
TABLE
4h-31.
THERMODYNAMIC PROPERTIJilS OF HIGHLY IONIZED NITROGEN, OXYGEN, AND
AIR (Continued)
Oxygen
Nitrogen
Air
log C, . p/po
Z*
!E*/RT!
P,atm
Z*
p/po
log T = 6.2
!E*/RT!
P,atm
p/po
Z*
! E*/RT!
P,atm
>-'3 ~
t9
~
T = 1,584,900 K
o
I:;:!
-5 -4 -3 -2 -1 0 +1
>
1. 429( -5) 1. 429( -4) 1. 429( -3) 1. 429( -2) 0.1431 1. 4510
8.0000 8.0000 7.9999 7.9988 7.9881 7.8916
22,8785 0.6631 22.8785 6.631 22.8784 6.631(1) 22.8777 6.630(2) 22.8705 6.6326(3) 22.802516. 6440( 4)
1. 250( -5) 1.2tiO( -4) 1. 21iO( -3) 1. 250( -2) 0.1:l52 1.2717
9.0000 9.0000 8.9999 8.9985 8.9851 8.8631
28.4617 28.4616 28.4614 28.4587 28.4318 28.1745
0.65276 6.5276 6.5276(1) 6.5265(2) 6.527(3) 6. 5402( 4)
6.993( -6) 6.933( -5) 6.934( -4) 6.935( -3) 6.945( -2) 0.7045
16.423 16.423 16.423 16.420 16.398 16.194
48.119 48.119 48.119 48.116 48.094 47.878
0.661 6.61 6.61(1) 6.61(2) 6.609(3) 6.6200(4)
Z
....
~ H
o '"d
~
o
'"d
t9
~
log T = 6.4
>-'3 t9
T = 2,511,900 K
H
w -5 -4 -3 -2 -1 0 +1
1. 429( -5) 1. 429( -4) 1. 429( -3) 1. 429( -2) 0.14306 1.4477
8.0000 18.8639 1. 051 8.0000 18.8639 1. 0.51(1) 7.9999 18.8038 1. 0.51(2) 7.9990 18.8637 1. 0.51(3) 7.9899 18.8618 1. 05Il( 4) 7.907411881.'iO\1.0527(5)
1. 250( -5) 1. 21iO( -4) 1. 250( -3) 1. 250( -2) 0.12516 1. 2(j51 ---
9.0000 9.0000 8.9999 8.9989 8.9896 8.9043
22.9401 22.9402 22.9401 22.9399 22.9372 22.9124
1.035 1. 0346(1) 1.0346(2) 1. 0345(3) 1. 0338( 4) 1. 0359(5)
o I:rj 6. 933( -5) 6.933(-4) 6. 934( -3) 6.943( -2) 0.'7024
16.423 16.423 16.421 16.403 16.237
39.452 39.452 39.452 39.448 39.411
1. 047(1) 1.047(2) ] .047(3) 1.0474(4) 1. 0490(5)
4:)
....
w
t9
w
------
t
ow
4---:204
HEAT
at uniform logarithmic intervals to 2.5 million kelvins. The tables taken from Hilsenrath, Green, and Beckett [4] represent the properties of atoms in equilibrium with their ions. The formulation in terms of electron concentration permits a solution of the equations for equilibrium properties in closed form and .allows the computation of properties of a mixture directly from the equilibrium properties of the constituent gases. In these tables the asterisk refers to properties of the gas mixture in the ideal-gas approximation (with dissociation and ionization effects included but without intermolecular and ionic force corrections). References 1. Hilsenrath, J., et a!.: Tables of Thermal Properties of Gases, NBS Cire. 564, 1955. Reprinted in 1960 by Pergamon Press under the title "Tables of Thermodynamic and Transport Properties of Air, Argon, Carbon Dioxide, Carbon Monoxide, Hydrogen, Nitrogen, Oxygen, and Stearn." 2. Hilsenrath, J. and M. Klein: "Tables of Thermodynamic Properties of Air in Chemical Equilibrium including Second Virial Corrections from 1,500 oK to 15,000oK," Arnold Eng. Develop. Cente,. Rept, AEDC-TR-65-58, Mareh, 1965. Available under the designation AD 612301 from the Clearinghouse for Federal Scientific and Technical Information, U.S. Department of Commerce, Springfield, Virginia 22151 (price $3.00). 3. Hilsenrath, J., C. G. Messina, M. Klein, and R. C. Thompson: Thermodynamic and Shock Wave Properties of Argon and Nitrogen in Chemical Equilibrium with Virial and Ionic Corrections, vols. I, II, and III. Air Force Weapons Lab. Rept. AFWL-TR68-60, Kirtland Air Force Base, New Mexico, May, 1969. 4. Hilsenrath, J., M. S. Green, and C. W. Beckett: Internal Energy of Highly Ionized Gases, Proe. IXth Intern. Astronaut. Congr. (Amsterdam), 1958, pp. 120-136, SpringerVerlagOHG Vienna, 1959.
4i. Pressure-Volume-Temperature Relationships of Gases; Virial Coefficients! J. M. H. LEVELT SENGERS, MAX KLEIN, AND JOHN S. GALLAGHER
The National Bureau of Standards
4i-1. Definition. Virial coefficients are the coefficients in the expansion of the compressibility factor PVof a gas in powers of the density l/V, PV = RT
(1 + ~ +~ + .. -)
(4i-l)
or in powers of the pressure P, (4i-2) The density expansion is the more fundamental of the two. It can be proved that such an expansion exists for gases at moderate densities, and its consecutive coefficients can be related to interactions between pairs, triplets, etc., of molecules [1]. The pressure expansion is often more practical, the pressure being more readily meal Supported in part by the Air Force Systems Command, Arnold Engineering Development Center, Tullahoma Tenn., on Delivery Order no. (40-600) 66-938.
VI RIAL COEFFICIENTS
sured than the volume,but it usually converges more slowly, and its coefficients are not as simply related to molecular interaction. In what follows, the emphasis will be on the expansion (4i-1). . 4i-2. Units. The units of the virials depend on the units of volume (4i-1) or pressure (4i-2) chosen. We will express the volume in em B/mol and give the virials in the corresponding units. However, a practical unit of volume frequently used is the amagat unit; the volume in amagat units' is the ratio of the actual volume of a gas over the normal volume, i.e., that which it would occupy at O°C and 1 atm (1.013250 bars). The normal volume for a mole of a real gas differs slightly from the normal volume Vo = 22,413.6 cmB/mol of a perfect gas, owing to deviations from ideality at O°C and 1 atm. The virial expansion used in conjunction with amagat units of volume is PYA
=
AA
+ BA + CA + .. VA
Vi
~.
(4i-3)
In Table 4i-l, the virials Bp, Cp; AA, BA, CA are expressed in terms of By, Cv . TABLE
4i-1.
RELATIONS BETWEEN VOLUME AND PRESSURE VIRIAL COEFFICIENTS
Gas constant
R
I deal-gas normal volume per mole
8.3143 J K-l mol- 1 (= 82.056 em Bat K -1 mol-l)
Vo= 22,413;6 em'mol-1
=
(Both
o~
unified scale)
PreBBure virialB (4i-2)
A magat virialB (4i-3)
V,.
=
Ao =
Bp Cp
= =
AA BA CA
By/RT (Cy - B~)/(RT)1
=
= ==
Vo/Ao 1 - BA (O°C) - CA (0°0) AoTJ273.15 ByAA/V,. CyAAIV~
4i-S. Theoretical Interest. Of great interest is the fundamental relationship of By, Cy, . . . to the molecular interaction. If the molecular field is represented by a function (r)lkT) dr
2 }o
(4i-4)
The virial By(T) is uniquely determined through Eq. (4i-4)if thamolecular interaction .H
Process Initial
Final
kcaI/mol
kJ/mol
fus yap
c liq
liq g, equil.
· . . . . . .. . . . .
TII.. ........
tr fus yap yap
c, II c, I liq liq
c, I liq g g, equil.
. ........... 1.0 1.0 760
TINO, .......
tr fus
c, II c, I
c, I liq
............ ............
416 479.8
0.91 2.264
ThO .........
fus
c
liq
............
852
7.24
30.29
ThO •........
fus
c
liq
............
998
3
12.5
Tm ..........
fus yap
c liq
liq g
............ 1818 2220 760
4.02 45.6
16.82 190.8
TmOla .......
fus yap Yap
c liq liq
liq g g
............. 0.554 760
1103 1173 1763
77.5
324.3
tr fus sub
c, a c, (3 c, (3
liq g
· . . .. . . . . . . . 2.7(E-3) 2.7(E - 3)
1316 1431 1431
88.9
372.0
Tm20 •.....•.
fus
c
liq
............
2665
U ...........
tr tr fus Yap
c, a c, (3 c, 'Y liq
C,
(3 c, 'Y
............
liq g
TIF .........
TmF •........
C,
(3
760
595.4 1099 451 715 715 1099
941 ........... , 1048 ........... , 1405 760 4407
3.315 0.22 3.52 27.3
0.667 1.137 2.036 110.9
13.870 0.92 14.73 114·.2 3.81 9.473
2.791 4.7572 8.5186 464.01.
UBra ........
tr
c
liq
1003
15
UB« ........
fus yap yap
c liq liq
liq g g
5.7 5.7 760
792 792 1039
16 33.9 30.5
UOl •.........
tr fus yap
c, II. c, I Iiq
c, I liq g
............ 32.6 760
820 863 1075
11 20.4
46.0 85.35
UOl,. ........
sub
c
g
1.8
370
17.3
72.38
UF ..........
tL fus yap
c c liq
c liq g
·..... ......
1110 1330 1330
3.4 10.24 57.1
14.2 42.844 238.9
tr fus yap Yap
c, II c, I liq liq
c, I liq g g
............ 13.4 13.4 760
408 621 621 776
11.1 25.1 23.2
46.44 105.0 97.07
UF6 .........
sub sub yap
c c liq
g g g
329.7 337.2 337.2
11.5 11.4 6.9
48.12 47.70 28.9
UI.. .........
fus
c
liq
4.5
779
19.3
80.75
UO, .........
fus
c
liq
·. ..........
3115
18.2
76.15
V ...........
fus yap
c liq
liq g
2.0(E - 3) 760
2175 3682
5.00 108.0
20.92 451. 87
UF ...........
0.013
7.03 7.03
760 1,138 1,138
62.8 66.9 141.8 127.6
4-247
TRANSITION, FUSION AND VAPORIZATION TABLE
4j-1.
TEMPERATURES, PRESSURES, AND I-ImATS
I
State Substance
p
T
mmHg
K
(Continued) b.H
Process
Initial
Final
kcal/mol
kJ/mol
VOl ..........
fUB yap
c liq
liq g
............ 760
252.6 426
2.3 9.5
9.62 39.7
VOOl, .......
fus Yap
c liq
liq g
............ 760
196 400
2.29 8.45
9.581 35.35
V,O, .........
fus
c
liq
.. ..........
947
15.6
65.27
W ...........
fus yap
c liq
liq
0.039 760
3653 5828
8.46 197.0
35.40 824.25
fUB yap
c liq
liq
............ 760 I
5GS 665
4 13.9
17 58.16
fus
c liq liq
liq g
595.5 595.5 604.5
14 13.4 13.2
58.6 56.07 55.23
213 213
458 503.1 554.6 554.6
3.39 1.6 15.0
14.18 6.69 62.76
240 240 413 413 760
264.9 264.9 275.1 275.1 290.2
1.0 8.8 1. 3' 7.70 6.25
4.18 36.8 5.44 32.22 26.15
25.1 25.1 760
377.8 377.8 459.0
WBr' ........ WOB" ......
Yap vap
WOI, ........
WF, .........
WOF" .......
WO, ......... Xe .......... XeF, ........ XeF4. ....... XeF, ........ y ...........
yO], ......... yF, .........
yI, .......... y,O •........
tr tr fus
g
g
g
yap
c, III c, II c, I liq
tr sub fus yap yap
c, II c, II c, I liq liq
c, I
fus yap yap
c liq liq
liq
tr fus
c, f3
fus
C,
a
c, II c, I
liq g
g
liq g g
g
I:, ~ IIq
Iiq
640 640' 760
· ......... , ....
.. .....
"
............ ............
yap
c liq
g
fus sub
e c
g
fus sub
c c
liq
fUB sub
c c
liq
tr fus yap
C,
a
c,
~
liq
g
fus yap
c liq
liq
tr sub fus
c, II c, I c, I
liq
sub fus
c c
liq
............ · , ..........
890 1237
fus
c, cubic
Iiq
............
2556
Iiq
g
g
611 760
1050 1745 161. 36 165.03
1412 1412
1.4 14.8 13.8
5.86 . 61. 92 57.74
0.410 17.03
1.715 73.43
0.548 3.021
2.293 12.640
402.2 402.2
13.0
54.39
811.3 811.3
390.25 390.25
14.40
60.250
159 159
319 319
15.5
64.85
......... . 2.2(E - 3) 760
1752 1799 3611
1.193 2.724 86.8
4.9915 11.397 363.2
g
............ · ...........
973 1100
30.9
129.3
c, I
.,'"
c, ~ liq
g
g
.......
1325 · . . . . . . . . . . . 1325 · . . . . . . . . . . 1420
.
100
53.6
418.4 224.3
4-248
HEAT
(Continued)
TABLE4j-1. TEMPERATURES, PRESSURES, AND HEATS
State Substance
Initial
Final
mmHg
K
I
b.H
kcal/mol
kJ/mol
1033 1097 1467
.......... 1.41
981 1573
59.8
250.2
c
g
· . . . . . . .. . . .
1362
85.5
357.7
e, cubic
liq
· . . . .. . . . . . .
2645
C
liq g
0.15 760
692.65 1184
1.765 27.62
7.3848 115.56
675.2 928.6
3.74
15.65
760
0.021 760
590 989.4
2.45
10.25
tr fus yap
c, a c, f3 liq
c, f3 liq g
YbCb .......
fus yap
C
liq
liq g
YbF •........
sub
Yb,O •.......
fus
Zn ..........
fus yap
liq
fus yap
liq
fus Yap
liq
liq g,.equil.
ZnC[, ........
T
............ 19.8 760
yb ..........
ZnBf2 .......
P
Process
C
C
liq g, equi!.
"
· . . . . . . . . .. .
0.418 l.83 30.8
1.749 7.657 128.9
ZnO .........
fus
C
iiq
'
...........
2248
ZnSO ........
tr
c, a
c, f3
............
1007
4.8
20.1
Zr ...........
tr fus yap sub
c, a c, f3 liq c, a
c, f3 liq g g
l.8(E - 18) l.2(E - 5) 760 l.8(E - 18)
1136 2125 4682 1136
0.94 4.0 139 144.7
3.93 16.9 58l.6 605.42
ZrBr .........
sub
c
g
550
27.2
113.8
ZrC ...... '"
fus
c
liq
· ........... 3765
ZrC[, ........
fus
c
liq
· ...........
995
ZrCl;. .......
sub fus
C
g
C
yap
liq
liq g
760 15,800 15,800
605 710 710
2·1.4 6.9 16:8
102.1 28.9 70.29
tr sub sub fus
c, a
c, f3 c, f3 c, fJ
g liq
......... , .. 2.1(E - 3) 760 819
678 800 1181 1185
53.0 50.4
221.8 210.9
ZrI4 .........
sub
c
g
l.3(E - 3)
425
26.2
109.6
ZrN .........
fus
c
iiq
·
ZrO' .........
tr sub fus
c, II c, I c, I
c, I
· . . .. ....
g
3(E - 4) ......... , ..
ZrF4 .........
c, g
40
fJ
iiq
............
.. .
3225 1473 2400 2979
1.42 165 20.8
5.941 690.4 87.0
TRANSITION, FUSION AND VAPORIZATION TABLE
Substance
4j-2.
4-249
SELECTED REFERENCES*
Reference
Ac
164
Ag AgBr AgCN AgCl AgF AgI AgNO, Ag,S Ag,SO. Ag,Se
164 31, 33, 411 294 31, 33, 205, 209 417 15, 24, 178, 223, 239, 271, 289 5,84,90,169,170,204,308,318 321,383 152 10, 275, 321, 383, 412
Al Al,Br. AI,Cl. AIF. All, AI,O, AlPO.
164 97, 175, 387 112,267 46, 93, 104, 215 387 48, 57, 125, 183, 270, 324, 336 329
Am
164
Ar
129
As AsCla AsF, AsF5 AsF.O AsH, AsI, A~.05
164 212, 266 384 320 249 352, 385 75, 120 374
Au
164
B BBra B(CH,)a BCla BF. B,H 6 B,Hg B20,
164, 196 14, 160 117 4, 133 214 287,407 143, 176,408 30, 262, 313, 333, 368
Ba BaBr, BaCO, BaCh BaF, BaI, Ba(NO.), BaO BaTiO,
164 100, 165, 171 11,220,307 100, 217, 273, 171 19, 150, 292, 293, 301, 317 100, 165 203 166, 260 105, 354, 372, 389
Be BeCr,
164 111, 116, 132, 154, 208, 231
Substance
Reference
BeF, BeO BeSO.
130, 157, 343, 384 8, 103, 131, 182, 363 20
Bi BiBr, BiCla BiF. Bi,O, BioS.
164 76, 305, 391, 410 81, 83, 173, 246, 305, 390, 399 81 76, 119, 222, 370 71, 127
Br, BrF, BrF5
129 276 225,315
C CBr, CCI, CF. CH. CH.Br CH,CI CH,F CH,I CH,OH CH,CI, CH,F, CH,I, CH,O CHBr. CHCI, CHF, CO CO2 COBr, COCI. COF, CS, COS
164 320 320 320 320· 320 320 108 253 110, 230, 359, 398 320 240 320 320 320 219, 312 162 320 320 320 124 284 320 320
Ca CaB,O. Ca,B,O, CaBr2 CaC, CaCO, CaCI, CaF, CaO CaSO. CaSiO, Ca2SiO. CaTiO,
164 200 200 100, 165, 171 320 306 58, 100, 156 37, 86, 301, 340 9,270, 335 135, 144, 394 126 41,70 66, 186
Cd CdBr, CdCl 2 CdF, CdI,
164 33, 391 35, 36, 391 28 33, 391
* Numbers in Reference coluilln refer to items in the list that follows this table.
4-250
HEAT TABLE
4j-2.
SELECTED REFERENCES
Reference
Substance
(Continued)
Substance
Reference
Feo.9.70 Fe20. Fe.O. FeS
388 67 67 68
129 320 137; 232 139
Ga (GaCl,), Gal.
164 133 311,362
Co Cocr. CoF, CoO
164 325 29. 181 320
Gd GdBr. GdCl, GdF, Gd,O.
164 101 101 301, 369 254, 401
Cr CrBn Cr(CO). CrF. Cr,O,
164 357 65, 309 149, 416 335
Cs CsBr CsCI CsF CsI CsNO, CsOH C8'SO.
164 99, 332, 365 99, 339, ?65 99, 332 99, 332, 335 257 319 22, 291
Ge GeBr. GeCl. GeF. GeH. Gel. GeO,
164 320 12 320 320 177 236, 238, 261
Cu (CuBr), (CuCI), CuF, (CuI). Cu,O Cu,S
164 151, 234, 145, 250, 237 163,
Dy
164
Er ErCla ErF.
164 101, 255, 274 369
Eu EuCl. Eu,O.
164 255,298 254, 334; 401
F, F,O
129 337
Fe FeBr, Fe (CO)& FeCr. (FeCla), FeF, FeF. FeI,
164 233 227 328 243 56, 192 416 326
Ce CeO, Ce,O.
164 218,254 254
Cr. CIF CIF. CIO,
351 351 190 351 310
H, HBr HCN HCI HF HI ,HNO. ·H,O H,S H,SO. H,Se H,Te H.PO. 'H2H 'H2HO 'H,O
129 129 62 129 129 129 98 320 320 129 129 320 129 129 129 129
He
129
Hf HfBr. HfCI. HfF. HfI. HfO,
164 331 268,285 111 376 270
Hg HgBr, HgCr. HgF, HgI, HgS
164 168 77, 174, 391 320 120,234 320
Ho HoCla HoF. Ho,Oa
164 101, 255 27 254
TltANSITION, FUSION AND VAPORIZATION TABLE
Substance
4-251
4j-2. SELECTED REFERENCES (Continued)
Reference
Substance
Reference
---I, IF, IF7 In InBr, InC] InCIa Inl, In,O,
129 52 316 47 164 362 106, 362 362 109, 362 334
Ir IrF,
164 50
K KBr KCN KC] KF KI KNO, KOH K 2S04
164 34, 99 320 18, 35, 339, 392 292, 304 35, 99 204, 367 320 320
Kr KrF, KrF.
129 141, 142 138
La LaBra LaCIa
164 101, 353 100, 353
Ie]
I.JaF?
244, 301
Lala La20a
353 254
Li LiBr LiC] LiF Lil LiNOa LiOH Li 2S04
164 99 99, 314 91, 301 99 114, 204 355 290, 397
Lu LuCIa LuFa LU20a
164 255 369,415 254
Mg MgBr2 MgCr, MgF2 MgI, MgaN2 MgO lVIgSO,
164 26 155, 339 155, 317 26 320 335 320
.
----
Mn MnBr2 MnC]' MnF, Mnl, MnO Mn,O.
164 320 235, 325 136, 191 320 360 146
Mo Mo(CO), MoF, MoF 6 MoO,
164 320 51 282 140, 201
N2 NH, N 2H. NH4Br NH.C] NH.F NH,I NH.NO, NO N20
320 320 129 320 129 129 320 129 320 320
Na NaBr NaCN NaC] NaF Nal N,,"iVT,,0, NaNO, NaOH Na,SO, Na2TiO,
164 99, 118 320 85, 99 113, 301, 304 99, 118 320 114, 204, 258 92 69, 300 320
Nb NbCl, NbF, Nb02 Nb20,
164 3, 189, 267 40, 107 199, 347 121, 281
Nd NdBr, NdCl, NdFa Ndl a Nd20,
164 353, 100, 369, 353, 254,
Ne
129
Ni NiBr2 Ni(CO), NiCl, NiF2 NiO
164 229, 327 371 49, 229, 325 55, 102 197
101 272, 353 418 100 286
4-252
HEAT TABLE
4j-2.
SELECTED REFERENCES
Reference
Substance Np NpF,
164 283,405
0, 0,
129 129
Os OsF, OsF, OsOF,
.54, 164, 395 51 50 17
P. PBr, PCI, PCI, PF, PF, PH, P40, P,O'O
129 288 288 288 288 129 129 129 129
Pb PbBr2 Pb(CH')4 PbC!' PbF2 FbI 2 FbO PbS PbSO,
164 32,33 373 13, 18, 35, 251 13 32,96,252 207 358 320
Fd FdC!'
164 21, 280
Po
129
Pr PrBr, FrCls FrFs FrI,
164 101, 100, 369, 100,
Pt PtF,
164 403
Pu FuBra PuCls FuF, PUF4 FuF,
164 296 296 296 296 296
Ra
320
Rb RbBr RbCI RbF
164 99 99, 392 99, 304, 344, 365
353 299, 353 379 353
(Continued)
Substance
Reference
RbI RbNO, RbOH
42,99 6, 115,204 38
Re (ReBr,), (ReC!'), ReF, ReF, ReF, Re,O,
164 45 45 51 50,241 241 128, 366
Rh
164
Rn
129
Ru RuF, RuF, RuO,
164 159 61 264
S SF, SF, SO,
129 43 259 320
Sb SbBr, SbC!' SbCh SbF, SbH, Sbl, Sb,O,
164 78, 356 266 279 158
Sc ScBrs ScCls ScF, ScI,
164 320 64 193, 213 320
Se SeF, SeF, SeO,
288 79, 129 129 245
Si SiBn Si(CH,). SiCI, SiF, SiH, SiF,H SiO,
164 44, 322 382 288 288 320 378 320
Sm Sm20,
164 254,270
25
120, 356 288
TRANSITION, FUSION AND VAPORIZATION TABLE
4]-2,
SELECTED REFERENCES
Reference
Substance Sn SnBr2 SnBr. SnCh SnCI, SnF 2 SnR, Snl2 Snl. SnS
164 320 185 122 265, 277 111,414 320 184 180 63, 206
Sr SrBr2 SrCO, SrCI, SrF 2 Srl2 Sr(NO')2 SrO SrSO, SrTiO, SrWO,
164 100, 165 11 100, 171, 224, 273 19, 293, 301 100, 165 203 320 320 95 361
Ta TaBr, TaC]' Ta2O,
164 23 3, 263, 345 400
Tb TbCI. TbF, Tb20, Tb.O,
164 255 369 254 254
Tc TcF, Tc 2O,
216 341 364
Te TeF. Te02
164 179 247, 302, 303, 413
Th ThCI, ThF. Thl. ThO,
164 58 80,301 123 1, 82
Ti TiEr, TiCI, TiF, Til, TiO Ti02
164, 396 147, 185, 322 226, 256, 277, 402 148 202 320 323
TI TlBr TICI TIF TlI TINO, Tl 20 ThO,
164 16, 205, 419 16, 72, 205, 420 188, 419 16, 73, 419 7, 204 76 348
(Continued)
Substance
Ilefer811ce
Tm TmCI, TmF, Tm20,
164 255 369, 415 254
U UBr, UBn
164 134 134
UCI 4 UCI, UF. UF, UFo UI, U0 2
134, 194, 350 172 194, 198, 221 2,409 195, 393 134 153
V VCI. VOC], V,O,
164 277 277, 278 161, 210
W WBr, WOB" WCI, WF6 WF,O WO,
164, 380 346 211 349, 375, 406 50 51 201
Xe XeF, XeF, XeF,
248 338 338 242,404
Y YC]' YF, YI, YeO,
164 94, 255 193, 301, 386 89 270
Yb YbCI, YbF, Yb,O,
39, 164 297 415 254
Zn ZnBr, ZnCh ZnO ZnSO,
164 74, 187 74, 122, 187 320 167
Zr ZrBn ZrC ZrCl, ZrCl, ZrF,
164 330 320 381 87, 88, 269, 285 53, 59, 111, 342 123 320 60, 228, 270
ZrL:I
ZrN Zr02
4-253
4-254
HEAT
References Ackerman, R. J., R. J. Thorn, and P. W. Gilles: J. Am.Chem. Soc. 78, 1767 (1956). Agron, P. A.: U.S. AEC Rept. TID 5290, 1958. Ainscough, J. B., R. J. W. Holt, and F. W. Trowse: J. Chem. Soc. 1967, 1034. Apple, E. F., and T. Wartik: J. Am. Chem. Soc. 80, 6158 (1958). Arell, A.: Ann. Acad. Sci. Fennicae, Ser. A, VI, 100 (1962). Arell, A., and M. Varteva: Ann. Acad. Sci. Fennicae, Ser. A, VI, 88 (1961). Arell, A., and M. Varteva: Ann. Acad. Sci. Fennicae, Ser. A, VI, 98 (1962). ll. Austerman, S. B.: U.S. AEC Rept. NAA-SR-7654, 1963. 9. Babeliowsky, T. P. J. H.: J. Chem. Phys. 38,2035 (1963). 10. Baer, Y., G. Busch, C. Frolich, and ,E. Steigmeier: Z. Naturforsch. 17a, 886 (1962). 11. Baker, E. H.: J. Chem Soc. 1962, 2525. 12. Balk, P., and D. Dong: J. Phys. Chem. 68, 960 (1964). 13. Banashek, E. 1., N. N. Patsakova, and 1. S. Rassonskaya: Izvest. Sektora Fiz.-Khim. Anal. Akad. Nauk S.S.S.R. 27, 223 (1956). 14. Barber, W. F., C. F. Boynton, and P. E. Gallagher: PB Rept. 148374, 1959. 15. Barrall, E. M., and L. B. Rogers: Anal.Chem. 36, 1405 (1964). 16. Barrow, R. F., E. A. N. S. Jeffries, and M. Swinstead: Trans. Faraday Soc. 61, 1650 (1955). 17. Bartlett, N., and N. K. Jha: J. Chem. Soc. A1968, 536. 18. Barton, J. L., and H. Bloom: J. Phys. Chem. 60, 1413 (1956). 19. Bautista, R. G., and J. L. Margrave: J. Phys. Chem. 69, 1770 (1965). 20. Bear, 1. J., and A. G. Turnbull: Australian J. Chem. 19, 751 (1966). 21. Bell, W. E., V. Merten, and M. Tagami: J. Phys. Chem. 65, 510 (1961). 22. Belyaev, 1. U., and N. N. Chikova: Zhur. Neor(j. Khim. 8, 1442 (1963). 23. Berdonosov, S. S., A. V. Lapitskii, and E. K. Bakov: Zhur. Neor(j. Khim. 10, 322 (1965). 24. Berger, C., M. Richard, and L. Eyrand: Bull. soc. chim. France 5, 1491 (1965). 25. Berka, L., T. Briggs, M. Millard, and W. L. Jolly: J. Inor(j. Nuclear Chem. 14, 190 (1960). 26. Berkowitz, J., and J. R. Marquart: J. Chem. Phys. 37, 1853 (1962). 27. Besenbruch, G., T. V. Charles, K. F. 2mbov, and J. L. Margrave: J. Less-Common Metals 12, 335 (1967). 28. Besenbruch, G., A. S. Kana'an, and J. L. Margrave: J. Phys. Chem. 69, 3174 (1965). 29. Binford, J. S., J. M. Strohmeyer, and T. H. Herbert: J. Phys. Chem. 71, 2404 (1967). 30. Blackburn, P. E., and A. Buchler: J. Phys. Chem. 69,4250 (1965). 31. Blanc, M.: Compt. rend. 2'7, 273 (1958). 32. Blanc, M., and G. Petet: Compt. rend. 248, 1305 (1959). 33. Bloom, H., J. O'M. Bockris, N. E. Richards, and R. G. Taylor: J. Am. Chem. Soc. 80, 2044 (1958). 34. Bloom, H., and J. W. Hastie: Australian J. Chem. 21, 583 (1968). 35. Bloom, H., and S. B. Tricklebank: Australian J. Chem.19, 187 (1966). 36. Bloom, H., and B. J. Welsh: J. Phys. Chem. 62, 1594 (1958). 37. Blue, G. D., J. W. Green, R. G. Bautista, and J. L. Margrave: J. Phys. Chem. 67,877 (1963). 38. Bogart, D.: J. Phys. Chem. 58, 1168 (1954). 39. Bohdansky, J., and H. E. J. Schins: J. Less-Common Metals 12, 248 (1967). 40. Brady, A. P., O. E. Myers, and J. K. Clauss: J. Phys. Chem. 64, 588 (1960). 41. Bredig, M. A.: J. Am. Ceram. Soc. 33, 188 (1950). 42. Bridgers, H. E.: Thesis, Ohio State University, 1953. 43. Brown, F., and P. L. Robinson: J. Chem. Soc. 1966, 3147. 44. Brown, H. C., and W. J. Wallace: J. Am. Chem. Soc. 75, 6279 (1953). 45. Buchler, A., P. E. Blackburn, and J. L. Stauffer: J. Phys. Chem. 70, 685 (1966). 46. Buchler, A., E. P. Marram, and J. L. Stauffer; J. Phys. Chem. 71,4139 (1967). 47. Burbank, R. D., and F. R. Bensey: J. Chem. Phys. 27, 981 (1957). 48. Burns, R. P.: J. Chem. Phys. 44,3307 (1966). 49. Busey, R. H., and W. F. Giauque: J. Am. Chem. Soc. 74,4443 (1952). 50. Cady, G. H., and G. B. Hargreaves: J. Chem. Soc. 1961, 1563. 51. Cady, G. H., and G. B. Hargreaves: J. Chem. Soc. 1961, 1568. 52. Calder, G. V., and W. F. Giauque: J. Phys. Chem. 69, 2443 (1965). 53. Cantor, S., R. F. Newton, W. R. Grimes, and F. F. Blankenship: J. Phys. Chem. 62, 96 (1958). 54. Carrera, N. J., R. F. Walker, and E. R. Plante: J. Research NBS 68A, 325 (1964). 55. Catalano, E., and J. W. Stout: J. Chem. Phys. 23, 1284 (1955). 56. Catalano, E., and J. W. Stout: J. Chem. Phys. 23, 1803 (1955). 1. 2. 3. 4. 5. 6. 7.
TRANSITION, FUSION AND VAPORIZATION
4-2;} 5
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317. 318. 319. 320. 321. 322. 323. 324. 325. 326. 327. 328. 329. 330. 331. 332. 333. 334. 335. 336. 337. 338.
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Osborne, D. W., B. Weinstock, and J. H. Burns: Preliminary communication 1963. Pace, E. L., and M. A. Reno: J. Chem. Phys. 48, 1231 (1968). Palko, A. A., A. D. Ryon, and D. W. Kuhn: J. Phys. Chem. 62,319 (1958). Pankratz, L. B., E. G. King, and K. K. Kelley: U.S. Bur. Mines Rep!. Invest. 6033 1962. Paridon, L. J., G. E. MacWood, and J. H. Hu: J. Phys. Chem. 63, 1998 (1959). Parker, V.: Private communication, 1966. Perrott, C. M., and N. H. Fletcher: J. Chem. Phys. 48, 2143 (1968). Petit, G., and C. Bourlange: Compt. rend. 245, 1788 (1957). Petit, G., and N. N. Chikova: Zhur. Neorg. Khim. 8, 1442 (1963). Petit, G., and A. Cremieu: Compt. rend. 243, 360 (1956). Petit, G., and F. Delbove: Compt. rend. 254, 1388 (1962). Pistorius, C. W; F. T.: J. Inorg. & Nuclear Chem. 19, 367 (1961). Platteeuw, J. C., and S. Meyer: Trans. Faraday Soc. 52, 1066 (1956). Plutonium Handbook, vol. I, chap. 12, C. E. Wick, ed., Gordon and Breach, Science Publishers, Inc., New-York, 1967. Polyachenok, O. G., and G. 1. Novikov: Zhur. Neorg. Khim. 8,2631 (1963). Polyachenok, O. G., and G. 1. Novikov: Zhur. Neorg. Khim. 9, 773 (1964). Polyachenok, O. G., and G. 1. Novikov: YeslinikLeningrad Univ. 13, Ser. Fiz. Khim. 3, 133 (1963). Popov, M. M., and M. Ginzburg: J. Gen. Chem. U.S.S.R. 26, 1107 (1956). Porter, B., and E. A. Brown: J. Am. Ceram. Soc. 45, 49 (1962). Prescher, K. E., and W. Schrlidter:Z. Erzbergbau u. Metallhuttenw. 15,299 (1962). Prescher, K. E., and W. Schrlidter: Z. Erzbergbau u. Metallhuttenw. 16, 352 (1963). Pugh, A. C. P., and R. F. Barrow: Trans. Faraday Soc. 54, 671 (1958). Pustilnik, A. 1., N. D. Denisova, L. G.Nekhamkin, andL. A. Nisel'son: Zhur. Neorg. Khim. 12, 103 (1967). Rao, G. V. S., M. Natorjan, and C. N. R. Rao: J. Am. Ceram. Soc. 51, 179 (1968). Rapoport, E., and C. W. F. T. Pistorius: J. Geophys. Res. 72, 6353 (1967). Reinsborough, V. C., and F. E. W. Wetmore: Australian J. Chem. 20, 1 (1967). Rezukhina, T. N., and V. V. Shvyrev: Yestnile lYIoskov. Univ. 7, Fiz. Mat. i Estestven. Nauk 4, 41 (1952). Richardson, F. D., and J. E. Anthill: Trans. Faraday Soc. 51,22 (1955). Riebling, E. F., and C. E. Erickson: J. Phys. Chem. 67,509 (1963). Rlick, H., and W. Schroder: Z. physik. Chem. [NF] 11, 41 (1957). Rockett, T. S., and W. R. Foster: J. Am. Ceram. Soc. 48, 75 (1965). Rodigino, E. N., K. Z. Gomelskii, and V.F. Luginina: Zhur. Neorg. Khim. 4, 975 (1959) . nogeI'S, 1::1. T., and J. L. Sv1efl::;: J. FhYli, Chem. GO, 1462 (1956). Rogers, M. T., J. L. Spiers, H. B.Thomson, and M. P. Pannish: J. Am. Chem. Soc. 76, 4843 (1954). Rolin, M., and M. Clausier:Rev. Int. Hautes Temp. 4,39 (1967). Rolla, M., and P. Franzosini: Ann. chim. (Rome) 48, 723 (1958). Rollet, A. P., R. Cohn-Adad, and C. Ferlin: Compt. rend. 256, 5580 (1963). Rossini, F. D., D. D. Wagman, W. H. Evans, S. Levine, and 1. Jaffe: Selected Values of Chemical Thermodynamic Properties, NBS Circ. 500, 1952. Roy, R., A. J. Majumdar, and C. W. Hulber: Econ. Geol. 54, 1278 (1959). Sackman, H., D. Demus, and D. Pankow: Z. anorg. allgem. Chem. 318,257 (1962). St. Pierre, P. D. S.: J. Am. Ceram. Soc. 35, 188 (1952). Sata, T.: Rev. Int. Hautes Temp. 3, 337 (1966). Schafer, H., L. Bayer, G. Breil, K. Etzel, and K. Krehl: Z. anoro. a11oem. Chem. 278, 300 (1955). Schafer, H., and W. J. Hones: Z. anorg. allgem. Chem. 288, 62 (1956). Schafer, H., and H. Jacob: Z. anorg. allgem. Chem. 286, 56 (1956). Schafer, H., and K. Krehl: Z. anorg. allgem. Chem. 268, 35 (1952). Schafer, E. C., and R. Roy: Z. physik. Chem. [NF] 11, 30 (1957). Schafer, H. L., and H. Skoludek: Z. Elektrochem. 66,367 (1962). Schafer, H. L., and H. W. Wills: Z. anorg. allgem. Chem. 351,279 (1967). Scheer, M. D., and J. Fine: J. Chem. Phys. 36, 1647 (1962). Schmidt, N. E.: Zhur. Neoro. Khim. 11,441 (1966). Schneider, S. J.: J. Research NBS 65A, 429 (1961). Schneider, S. J.: J. Am. Ceram. Soc. 46, 354 (1963). Schneider, S. J., and C. L. McDaniel: J. Research NBS 'i1A, 317 (1967). Schnizlein, J. G., J. L. Sheard, R. C. Toole, and T. D. O'Brien: J. Phys. Chem. 56, 233 (1952). Schreiner, F., G. N. McDonald, and C. L. Chernick: J. Phys. Chem. 72, 1162 (1968).
4-260
HEAT
Schrier, E. E., and H. M. Clark: J. Phys. Chem. 67, 1259 (1963). Schultz, D. A., and A. W. Searcy: J. Phys. Chem. 67, 103 (1963). Selig, H., and J. G. MaIm: J. Inorg. & Nuclear Chem. 24, 641 (1962). Sense, K. A., M. J. Snyder, and R. B. Filbert, Jr.: J. Phys. Chem. 58,995 (1954). Sense, K. A., and R. W. Stone: J. Phys. Chem. 62,453 (1958). Sense, K. A., and R. W. Stone: J. Phys. Chem. 62, 1411 (1958). Shchukarev, S. A., and A. R. Kurbanov: Vestnik Leningrad Univ. 17, Fiz. Khim. 144 (1962). 346. Shchukarev, S. A., G. I. Novikov, and G. A. Kokovin: Zhur. Neorg. Khim. 4, 2185 (1959) . 347. Shchukarev, S. A., G. A. Semenov, and K. E. Frantseva: Zhur. Neorg. Khim. 11,233 (1966). 348. Shchukarev, S. A., G. A. Semenov, and I. A. Ratkovskii: Zhur. Neorg. Khim. 6,2817 (1961). 349. Shchukarev, S. A., and A. V. Suvorov: Vesinik Leningrad Univ. 16,87 (1961). 350. Shchukarev, S. A., I. V. Vasil'kova, A. I. Efimov, and V. P. Kerdyashev: Zhur. Neorg. Khim. 1,2272 (1956). 351. Shelton, P. A. J.: Trans. Faraday Soc. 57, 2113 (1961). 352. Sherman, R. H., and W. F. Giauque: J. Am. Chem. Soc. 77,2154 (1955). 353. Shimazaki, E., and K. Niwa: Z. anorg. allgem. Chem. 314, 21 (1962). 354. Shirane, G., and A. Takeda: J. Phys. Soc. Japan 7, 1 (1952). 355. Shomate, C. H., and A. J. Cohen: J. Am. Chem. Soc. 77,285 (1955). 356. Sime, R. J.: J. Phys. Chem. 67, 501 (1963). 357. Sime,_R. J., and N. W. Gregory: J. Am. Chem. Soc. 82, 93 (1960). 358. Simpson, D. R.: Econ. Geol. 59, 150 (1964). 359 .. Singh, J., and G. C. Benson: Can. J. Chem. 46, 1249 (1968). 360. Singleton, E. J., L. Carpenter, and R. V. Lundquist: U.S. Bur. Mine8 Rept. Inve8t. 5938,1962. 361. Smirnova, I. N., and I. P. Kislyakov: Izvest. Akad. Nauk S.S.S.R. Neorg. Mater, 1, 1162 (1965). 362. Smith, F. J.,and R. F. Barrow: Trans. Faraday Soc. 1i4, 826 (1958). 363. Smith, D. K., C. F. Cline, and V. D. Frechetti: J. Nuclear Mater. 6,265 (1962). 364. Smith, W. T., Jr., J. W. Cobble, and G. E. Boyd: J. Am. Chem. Soc. 75,5773 (1953). 365. Smith,D. F., C. E. Kaylor, G. E. Walden, A. R. Taylor, and J. B. Gayle: U.S. Bur. Mines Rept. Invest. 5832, 1961. 366. Smith, W. T., L. E. Line, and W. A. Bell: J. Am. Chem. Soc. 74,4964 (1952). 367. Sokolov, V. A., and N. E. Schmidt: Izvest. Sektora. Fiz.-Khim. Anal. Inst. Obshch. i. Neorg. Khim. Akad. Nauk S.S.S.R. 27, 217 (1956). 368. Sommer, A.: Thesis, Ohio State University, 1962. 369. Spedding, F. H., and A. H. Daane: Iowa State Coli. Rept. IS-902, 1957. 370. Speranskaya, E. I., and A. A. Arshakuni: Zhur. Neorg. Khim. 9,414 (1964). 371. Spice, J. E., L. A. K. Staveley, and G. A. Harrow: J. Chem. Soc. 1955,100. 372. Statton, W. 0.: J. Chem. Phys. 19,33 (1951). 373. Staveley, L. A. K., J. B. Warren, H. P. Paget, and D. J. Dowrick: J. Chem. Soc. 1954, 1992. 374. Stevenson, F. D., and C. E. Wicks: U.S. Bur. Mines Rept. Invest. 6212, 1963. 375. Stevenson, F. D., C. E. Wicks, and F. E. Block: U.S. Bur. Mines Rept. Inve8t. 6367, 1964. 376. Stevenson, F. D., C. E. Wicks, and F. E. Block: J. Chem. Eng. Data 10, 33 (1965). 377. Stull, D. R., ed: JANAF Thermochemical Tables, PB Rept. 168370, 1965. 378. Sujishi, S., and S. Witz: J. Am. Chem. Soc. 79,2447 (1957). 379. Stivorov, A. V., E. V. Krzhizhanovskaya, and G. I. Novikov: Zhur. Neorg. Khim. 11, 2685 (1966). 380. Swarc, R., E. R. Plante, and J. J. Diamond: J. Research NBS 69A, 417 (1965). 381. Swaroop, B., and S. N. Flengas: Can. J. Chem. 44, 199 (1966). 382. Tannenbaum, S., S. Kaye, and G. F. Lewenz: J. Am. Chem. Soc. 75,3753 (1953). 383. Tavernier, B. H., J. Vervechev, P. Messieu, and lYI. Baiwir: Z. anorg. allgem. Chem. 356, 77 (1967). 384. Taylor, A. R., and T. E. Gardner: U.S. Bur. Mines Rept. Invest. 6664, 1965. 385. Thiloaud, E., and P. Flogel: Z. anorg. allgem. Chem. 329, 244 (1964). 386. Thomas, R. E., C. F. Weaver, H. A. Friedman, H. Imsley, L. A. Harris, and H. A. Yokel, Jr.: J. Phys. Chem. 65, 1096 (1961). 387. Thonstad, J.: Can. J. Chem. 42, 2739 (1964). 388. Todd, S. S., and K. R. Bonnickson: J. Am. Chem. Soc. 73, 3894 (1951). 389. To"dd, S. S., and R. E. Lorenson: J. Am. Chem. Soc. 74, 2043 (1952). 390. Topol, L. E., S. W. Mayer, and L. D. Ransom: J. Phys. Chem. 64, 862 (1960). 391. Topol, L. E., and L. D. Ransom: J. Phys. Chem. 64, 1339 (1960). 339. 340. 341. 342. 343. 344. 345.
TRANSITION, FUSION AND VAPORIZATION
4-261
392. Treadwell, W. D., and W. Werner: Helv. Chim. Acta 36, 1436 (1953). 393. Trevorrow, L. E., M. J. Steindler, D. V. Steidl, and J. T. Savage: Inorg. Chem. 6, 1060 (1967). 394. Trzebiatowski, W., J. Damm, and T. Romotowski: Roczniki Chem. 30,431 (1956). 395. Tylkina, M. A., V. P. Polyakova, and O. Kh. Khamidov: Zhur. NeoTg. Khim. 8,776 (1963) . 396. Vollmer, 0., M. Braun, and R. Kohlhaus: Z. Naturforsch. 2l2A, 833 (1967). 397. Voskresenskaya, N. K., and E. 1. Banashek: Izvest. Sektora Fiz.-Khim. Anal. Inst. Obshch. Neora. Khim. Akad. Nauk S.S.S.R. 25, 150 (1954). 398. Wadso, 1.: Acta Chem. Scand. 20, 544 (1966). 399. Walden, G. E., and D. F. Smith: U.S. Bur. Mines Rept. Invest. 5859, 1961. 400. Waring, J. L., and R. S. Roth: J. Research NBS 72A, 175 (1968). 401. Warshaw, 1., and R. Roy: J. Phys. Chem. 65,2048 (1961). 402. Weed, H. C.: Thesis, Ohio State University, 1957. 403. Weinstock, B., J. G. MaIm, and E. E. Weaver: J. Am. Chem. Soc. 83,4310 (1961). 404. Weinstock, B., E. E. Weaver, and C. P. Knop: Inorg. Chem. 5,2189 (1966). 405. Weinstock, B., E. E. Weaver, and J. G. MaIm: J. Inorg. & Nuclear Chem. 11, 104 (1959). 406. Welty, J. R.: Thesis, Oregon State University, 1962. 407. Wirth, H. E., and E. D. Palmer: J. Phys. Chem. 60,911 (1956). 408. Wirth, H. E., and E. D. Palmer: J. Phys. Chem. SO, 914 (1956). 409. Wolf, A. S., J. C. Posey, and K. E. Rapp: Inorg. Chem. 4, 751 (1965). 410. Wolten, G. M., and S. W. Mayer: Acta Cryst. 11,739 (1958). 411. Zakharchenko, G. A.: ZhUT. Obshchd Khim. 21, 453 (1951). 412. Zhitaneva, G. M., Y. V. Rumyantsev, and F. M. Bolondz: Trudy Vostochno-Siber. Filiala Akad. Nauk S.S.S.R. 41, 121 (1962). 413. Zlomanov, V. P., A. V. Novoselova, A. S. Pashinkin, Yu. P. Simanov, and K. H. Semenenko: Zhur. Neorg. Khim. 3, 1473 (1958). 414. 2mbov, K. F., J. VV. Hastie, and J. L. Margrave: Trans. Faraday Soc. 64,861 (1968). 415. 2mbov, K. F., and J. L. Margrave: J. Less-Common Metals 12,494 (1967). 416. 2mbov, K. F., and J. L. Margrave: J. InoTg. & Nuclear Chem. 29, 673 (1967). 417. 2mbov, K. F., and J. L. Margrave: J. Phys. Chem. 71,446 (1967). 418. 2mbov, K. F., and J. L. Margrave: J. Chem. Phys. 45, 3167 (1966). 419. Cubic ciotti, D., and H. Eding: J. Chem. Eng. Data 10, 343 (1965). 420. Eding, H. and D. Cubicciotti: J. Chem" Eng. Data 9, 524 (1964).
4k. Vapor Pressure DANIEL R. STULL
The Dow Chemical Company W¥!'"
Tables 4k-l to 4k-4, Vapor Pressures of Inorganic and Organic Compounds, were compiled by the author at The Dow Chemical Company and were published in Ind. Eng. Chem. 39(4), 517 (April, 1947), and 30(12), 1684 (December, 1947). A much more extensive list and references can be found in this journal. The numbers represent temperatures in degrees Celsius at which the vapor pressure is the value appearing at the top of the column. Symbols d decomposes d dextrorotatory dl inactive (50 % d and 50 % I) e explodes 1 levorotatory
M.P. P, p s T,
melting point critical pressure polymerizes solid critical temperature
TABLE
4k-1.
VAPOR PRESSURE OF INO:"GANIC COMPOUNDS-PRESSURES LESS THAN
1
~
ATMOSPHERE
0;,
Temp., °0 Formula
M.P. 1 mm
A B,H12 ....... A Bra. ........ A Ck ......... Al Fa. ......... A I, ........... A ;lOa .......... N ff, .......... N D, .......... N ff,N, ........ N E!,Br ........ N ff,CO,NH2 ... N E!,Cl. ....... N 'i,HS ........ N E!4l ......... N 'i,CN ...... Sb Bra ........ . Sb C!' ......... Sb Clo ......... Sb I, ......... " Sb 20 3 . . . . . . . . . A Bra ......... A Cr, ......... A. F3 .......... A. F, .......... A H, .......... A 20 3 . . . . . . . . . B B,H, ....... B Bn ......... B Cb ......... B I, .......... B Br~ ......... B Cl, .......... B l,CO ........ B ~r8 .......... B JI 3 • . . • • • • • • . B ~~ ...........
t-:J
Name
Aluminum borohydride Aluminum bromide Aluminum chloride Aluminum fluoride Aluminum iodide Aluminum oxide Ammonia Deutero ammonia Ammonium azide Ammonium bromide Ammonium carbamate Ammonium chloride Ammonium hydrogen sulfide Ammonium iodide Ammonium cyanide Antimony tribromide Antimony trichloride Antimony pentachloride Antimony triiodide Antimony trioxide Arsenic tribromide Arsenic trichloride Arsenic trifluoride Arsenic pentafluoride Arsenic hydride (arsine) Arsenic trioxide Beryllium borohydride Beryllium bromide Beryllium chloride Beryllium iodide Bismuth tribromide Bismuth trichloride Borine carbonyl Boron tribromide Boron trichloride Boron trifluoride
,
5mm
20mm
40mm
60mm
-
-
81 3, 100.0, 1238 178.0, 2148 -109.1,
52.2 103.8 116.4, 1298 207.7 2306 - 97.5,
42.9 118.0 123.8, 1324 225.8 2385 - 91.9,
32.5 134.0 131. 8, 1350 244.2 2465 - 85.8,
20.9 150.6 139.9, 1378 265.0 2549 - 79.2,
29.2, 198.3, 26.1, 160.4, 51.1 210.9, 50.5, 93.9 49.2, 22.7 163.5, 574, 41.8 11.4
49.4, 234.5, - 10.4, 193.8, - 36.0 247.0, - 35.7, 126.0 71.4, 48.6 203.8 626, 70.5 11.4
59.2, 252.0, 2.9, 209.8, - 28.7 253.5, - 28.6, 142.7 85.2 61.8 223.5 666 85.2 23.5
+
69.4, 270.6, 5.3, 226.1, - 20.8 282.8, - 20.9, 158.3 100.6 75.8 244.8 729 101.3 36.0
-108.0, -130.8, 242.6, 19.8, 325, 328, 322, 251 242 -127.3 - 20.4 - 75.2 -145.4,
-103.1, -124.7, 259.7, 28.1, 342, 346, 341, 282 264 -121.1 - 10.1 - 65.9 -141.3,
80.1, 290.0, 14.0, 245.0, - 12.3 302.8, - 12.6, 177.4 117.8 91.0 267.8 812 118.7 50.0 2.5 - 92.4, -110.2 299.2, 46.2, 379, 384, 382, 327 311 -106.6 14.0 - 47.8 -131.0,
,
-
-
,
-117.9, -142.6, 212.5, 1.0, 289, 291, 283,
+
,
-139.2, - 41.4 - 91.5 -154.6,
-
10 mm
,
+
,
-
,
,
,
+
,
- 98.0, -117.7, 279.2, 35.8, 361, 365, 361, 305 287 -114.1 1.5 - 57.9 -136.4,
+
,
100mm
200 mm
400 mm
760 mm
-
-
+
+
320.0, 26.7, 271.5, 0.0 331.8, - 0.5, 203.5 148.3 114.1 303.5 957 145.2 70.9 13.2 - 84.3, - 98.0 332.5 58.5, 405, 411 411, 360 343 - 95.3 33.5 - 32.4 -123.0
28.1 227.0 171. 6, 1496 354.0 2874 - 45.4 - 45.4 120.4, 370.9, 48.0, 315 5, 21 8 381.0, 20.5, 250.2 192.2 ........ 368.5 1242 193.5 109.7 41.4 - 54.0 - 75.2 412.2 79.7, 451, 461 461, 425 405 - 74.8 70.0 3.6 -108.3
45.9 - 64. 5 256.3 97. 5 180.2, 192. 4 1537 1040 385.5 2977 2050 - 33.6 - 77. 7 - 33.4 - 74. o 133.8, 39B.0, 58.3, 337.8, 520 33.3 404.9, 36 31. 7, 275.0 96. 6 73. 4 219.0 2. 8 ........ 167 401.0 1425 555 220.0 130.4 - 18 56.3 5. 9 - 52.8 - 79. 8 - 52.1 -115. 3 457.2 312. 8 90.0, 123 474, 490 405 487 487, 488 461 218 441 230 - 64.0 -137. o 91. 7 - 45 12.7 -107 -110.7 -125. 8
13.4 161. 7 145.4, 1398 277.8 2599 - 74.3 - 74.0 86.7, 303.8, 19.B, 256.2, 7.0 316.0, - 7.4, 188.1 128.3 101.0 282.5 873 130.0 58.7 4.2 - 88.5, -104.8 310.3, 51. 7, 390, 395, 394, 340 324 -101. 9 22.1 - 41.2 -127.6,
3.9 176.1 152.0, 1422 29'1. 5 2665 - 58.4 - 67.4 95.25
11.2 199.8 151. 8, 1457 322.0 2765 - 57.0 - 57.0 107.7, 345.3, 37.2, 293.2, 10.5 355.8, 9.6, 225.7 165.9
+ +
d
333.8 1085 157.7 89.2 25.7 - 75.5 - 87.2 370.0 69.0, 427, 435 435, 392 372 - 85.5 50.3 - 18.9 -115.9
+
iI1
toJ i» >-3
B,H5 ... : ....... B,BrH5.... : ... BaH5N, .... :: . .' B,Hlo.: ....... B5H, ....... B5Hll ... :.: ... BIOHl4. . . . . . . .
BrF5. CdC], ......... CdF, .......... Cdr, .......... CdO .......... CBr4- ......... CCk ......... CF4 ........... C,O, .......... CS, ........... C,S,. ......... CSSe .......... CO ........... COCl, ......... COSe ......... COS. CCJ,NO, ...... CCIF, ......... C,N, .......... CBrN ......... CCIN ......... CFN .......... CIN. _ CDN .......... CC12F2 ........ CHChF ....... CHCIF, ...... _ CCIsF ......... CsBr .... CsCI. .... CsF ........... Csl. _... ,. -. ... CIF ..... CIF, ......... C),O .... CIO, .......... CI,06 .......... CIzO, ..........
Dihydrodiborane Diborane hydro bromide Triborine triamine Tetrahydrotetraborane Dihydropentaborane Tetrahydropentaborane Dihydrodecaborane BrOlnine pentafluoride Cadmium chloride Cadmium fluoride Cadmium iodide Cadmium oxide Carbon tetra bromide Carbon tetrachloride Carbon tetrafluoride Carbon sub oxide Carbon disulfide Carbon subsulfide Carbon selenosulfide Carbon monoxide Carbonyl chloride Carbonyl selenide Carbonyl sulfide Chloropicrin Chlorotrifluoromethane Cyanogen
Cyanogen bromide Cyanogen chloride Cy&nogen fluoride Cyanogen iodide Deuterocyanic acid Dichlorodifluoromethane Dichlorofluoromethane Chlorodifluorornethane Trichlorofluoromethane Cesium bromide Cesium chloride Cesium fluoride Cesium iodide Chlorine fluoride Chlorine trifluoride Chlorine monoxide Chlorine dioxide Dichlorine hexoxide Chlorine heptoxide
-159.7 - 93.3 63.0, - 90.9
,
-
50.2 60.0, 69.3,
-
,
1385 416 1000,
,
- 50.0, -184.6, - 94.8 - 73.8 14.0 - 47.3 -222.0, - 92.9 -117.1 -132.4 - 25.5 -149.5 - 95.8, - 35.7, - 76.7, -134.4, 25.2, - 68.9, -118.5 - 91.3 -122.8 - 84.3 748 744 712 738
-149.5 - 75.3 - 45.0 - 73.1 - 40.4 - 29.9 SO.8, - 51.0 618 1504 481 1100.
-144.3 - 66.3 - 35.3 - 64.3 - 30.7 - 19.9 90.2, - 41.9 656 1559 512 1149,
-138.5 - 56.4 - 25.0 - 54.8 - 20.0 9.2 100.0 - 32.0 695 1617 546 1200,
- 19.6 -169.3 - 71.0 - 44.7 54.9 - 16.0 -215.0, - 69.3 - 95.0 -113.3 7.8 -134.1 - 76.8, - 10.0, - 53.8, -118.5, 57.7, - 46.7, - 97.8 - 67.5 -103.7 - 59.0 887 884 844 873 -139.0 - 71.8 - 73.1 - 59.0 42.0 - 13,2
8.2 -164.3 - 62.2 - 34.3 69.3 - 4.4 -212.8, - 60.3 - 86.3 -106.0 20.0 -128.5 - 70.1, 1.0, - 46.1, -112.8, 68.6, - 38.8 5 - 90.1 - 586 - 96.5 - 49.7 938 934 893 923 -134.3 - 62.3 - 64.3 - 51.2 54.3 - 2.1
,
-
98.5
- 30.0, -174.1 - 79.0 - 54.3 41.2 - 26.5 -217.2, - 77.0 -102.3 -119.8 3.3 -139.2 - 83.2, - 18.3, - 61.4, -123.8, 47.2, - 54.0, -104.6 - 75.5 -110.2 '--- 67.6 838 837 798 828 -143.4 - 80.4 - 81.6
+ -
7.5 45.3
-
, ,
,
,
30.5 23.8
,
+
,
-131.6 - 45.4 - 13.2 - 44.3 - 8.0 2.7 117.4 - 21.0 736 1673 584 1257, 96.3 4.3 -158.8 - 52.0 - 22.5 85.6 8.6 -210.0, - 50.3 - 70.4 - 98.3 33.8 -121. 9 - 62.7, 8.6, - 37.5, -106.4, 80.3, - 30.1, - 81.6 - 48.8 - 88.6 - 39.0 993 989 947 976 -128.8 - 51.3 - 54.3 - 42.8 68.0 10.3
+
+ +
+
+
-127.2 - 38.2 - 5.8 - 37.4 - 0.4 10.2 127.8 - 14.0 762 1709 608 1295, 106.3 12.3 -155.4 - 45.5 - 15.3 96.0 17.0 -208.1, - 44.0 - 70.2 - 93.0 42.3 -117.3 - 57.9, 14.7, - 32.1, -102.3, 88.0, -
-
24.78
76.1 42.6 83.4 32.3 1026 1023 980 1009 -125.3 - 44.1 - 48.0 - 37.2 76.3 18.2
-120.9 - 29.0 4.0 - 2S.1 9.6 20.1 142.3 - 4.5 797 1759 640 1341, 119.7 23.0 -150.7 - 36.9 - 5.1 109.9 28.3 -205.78 - 35.6 - 6l.7 - 85.9 53.8 -111.7 - 51. 8, 22.6, - 24.9, - 97.0, 97.6, - 17.5, - 68.6 - 33.9 - 76.4 - 23.0 1072 1069 102,; 1055 -120.8 - 34.7 - 39.4 - 29.4
+ +
-111.2 ' - 15.4 18.5 - 14.0 24.6 34.8 163.8 9.9 847 1834 688 1409, 139.7 38.3 -143.6 - 23.3 10.4 130.8p 45.7 -102.3 - 22.3 - 49.8 - 75.0 71.8 -102.5 - 42.6, 33.8, - 14.1, - 89.2, 111.5, - 5.4, - 57.0 - 20.9 - 65.8 - 9.1 1140 1139 1092 1124 -114.4 - 20.7 - 26.5 - 17.8
+
+
87.7
104.7
29.1
44.6
-
99.6 0.0 34.3 0.8 40.8 51.2
+
-
+
86.5 16.3 50.6 16.1 58.1 67.0
d
........
25.7 908 1924 742 1484, 163.5 57.8 -135.5 - 8.9 28.0
40.0 967 2024 796 1559, 189.5 76.7 -127.7 6.3 46.5
p
65.2 -196.3 - 7.6 - 35.6 - 62.7 91.8 - 92.7 - 33.0 46.0, 2.3 - 80.5, 126.1, 10.0 - 43.9 6.2 - 53.6 6.8 1221 1217 1170 1200 -107.0 4.9 - 12.5 4.0 123.8 62.2
+ +
+
........
85.6 -191.3 8.3 - 21.9 - 49.9 111.9 - 81.2 - 21.0 61.5 13.1 - 72.6, 141.1, 26.2 - 29.8 8.9 - 40.8 23.7 1300 1300 1251 1280 -100.5 11.5 2.2 11.1 142.0 78.8
+
+ +
+ + +
-169 -104. 2 - 58. 2 -119. 9 - 47. 0 -
99. 6 61. 4 568 520 385
90. 1 - 22. 6 -183. 7 -107 -110. 8 O. 4 - 75. 2 -205. 0 -104
+
-138. 8 - 64
'd
0
~
'd
~
I:tJ
-
-
34. 4 58 6. 5
-
12
U2 U2
q
!:d I:tJ
-135 -160 636 646 683 621 -145 - 83 -116 - 59 3.5 -91
t
tv
0;,
IX!
TABLE
4k-1.
VAPOR PRESSURE OF INORGANIC COMPOUNDS-PRESSURES LESS THAN
1
ATMOSPHERE
(Continued)
~
0)
Temp.,oC
Formula
~
M.P.
Name
1 mm
10 mm
20 mm
53.5 58.0 3.2
64.0 68.3 13.8
75.3 79.5 25.7
666 645 610 221. 8, ........ -186.6 67.8, -151.0 43.3 - 24.9 - 22.3 - 54.6 - 69.8 - 12.8
86.3 718 702 656 235.5, 7'00 -182.3 76.5, -145.3 56.8 - 15.0 - 13.0 - 45.2 - 60.1 - 0.9
5 mm
40 mm
60 mm
100 mm
200 mm
400 mm
760 mm
87.6 91.2 38.5 770 11.0 121.5 844 838 786 256 8, 779 -173.0 107.5 -131. 6 88.1 8.0 8.8 - 23.4 - 38.2 26.3 -258.2 -108 3, -123 8, - 30.9, - 45.0 - 85.6, 77.0 - 84.7, -102.3, 6.0 - 59.1, 64.6 32.2 - 45.3, 30.3 686 725
95.2 98.3 46.7 801 18.5 133.2 887 886 836 263.7, 805 -170.0 118.0 -126.7 98.8 16.2 16.2 - 16.2 - 30.7 35.5 -257.6 -103.8, -119.6, - 25.1, - 37.9 - 79.8, 85.8 - 80.2, - 97.9, 12.8 - 53.7, 70.0 40.0 - 39.4, 39.1 711 750
105.3 108.0 58.0 843 29.0 148.5 951 960 907 272.5, 842 -165.8 132.0 -120.3 113.2 27.5 26.5 - 6.3 - 20.3 47.9 -156.6 - 97.7, -114.0 - 17.8, - 28.2 - 72.1, 97.9 - 74.2, - 91.6, 22.0 - 45.7, 77.5 50.0 - 31.9, 50.3 745 784
120.0 121.8 75.2 904 44.4 172.2 1052 1077 1018 285.0, 897 -159.0 152.8 -111.2 135.4 44.4 41.6 8.8 4.7 67.0 -255.0 - 88.1, -105.2 - 5.3 - 13.2 - 60.3, 116.5 - 65.2, - 82.3 35.3 - 32.4 87.9 65.4 - 20.7, 68.0 796 833
136.1 137.2 95.2 974 62.0 198.0 1189 1249 1158 298.0, 961 -151.9 176.3 -100.2 161.6 63.8 58.3d 26.0 13.3 88.6 -253.0 - 78.0 - 95.3 10.2 2.5 - 48.3 137.4d - 53.6 - 71.8 49.6 - 17.2 99.2 81.2 - 8.3, 86.1 856 893
151.0d 151.0 117.1 1050 80.0 225.0 1355 1490 1336 319.0 1026 -144.6 200.0 - 88.9 189.0 84.0 75.0d 44.0 31.5 110.8 -251.0 - 66.5 - 84.8 25.9 19.7 - 35.1 158.0d - 41.1 - 60.4 64.0 2.0 110.0 97.0 4.0, 105.0 914 954
---
HSO,Cl. ...... Cr(CO)' ....... CrO,CIz ....... COCIz ......... Co(OO),NO .... CbF........... Cu2Br ........ . Cu,CIz ........ Cu,1, ......... FeCb ......... FeCI, ......... F,O .. '" ...... GaCh ......... GeR •......... GeB" ......... GeCI .......... GeHOb ....... Ge(CH,).. ....' Ge,H6 ......... Ge,Hs ....... :. HD ........... HBr .......... HCI. .......... HON .......... liF ........ : .. HI. .......... '. H,O, ........ :. H,Se .......... H,S ........ '::. H,S, .......... H,Te ........... NH,OH ....... IF, ........... IF, ........... Fe(CO)' ....... PbBn ......... PbC!,. ........
Chlorosulfonic acid Chromiulll carbonyl Chromyl chloride Cobaltous chloride Cobalt nitrosyl tricarbonyl Columbium pentafLuoride Cuprous bromide Cuprous chloride Cuprous iodide Ferric chloride Ferrous chloride Fluorine monoxide Gallium trichloride Germanium hydride Gerrnanium bromide Germanium chloride Trichlorogermane Tetramethylgermanium Digermane Trigermane Hydrogen deuteride Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen fluoride Hydrogen iodide Hydrogen peroxide Hydrogen selenide Hydrogen sulfide Hydrogen disulfide Hydrogen teluride Hydroxylamine Iodine pentaftuoride Iodine heptafluoride Iron pentacarbonyl Lead bromide Lead chloride
-
32.0 36.0 18.4
, ,
+
,
572 546
,
194.0, ........
-196.1 48.0, -163.0
,
-
45.0 41.3 73.2 88.7 36.9
, , ,
,
,
........
........
-'~59.8
-138.8, -150.8, - 71.0,
-127.4, -140.7, - 55.3, - 74.7 -109.6, 38.8 -103.4, -122.4, - 24.4 - 82.4, 39.0 1.5, - 70.7, - 6.5 578 615
-121.8, -135.6, - 47.7, - 65.8 -102.3, 50.4 - 97.9, -116.3, - 15.2 - 75.4, 47.2 8.5 - 63.0, 4.6 610 648
,
-123.3, 15.3 -115.3, -134.3, - 43.2 - 96.4,
,
- 15.2, - 87.0, ........ 513 547
+
+
,
-
1.3 103.0 777 766 716 246.0, 737 -177.8 91.3 -139.2 71. 8 - 4.1 - 3.0 - 35.0 - 49.9 11.8 -259.1 -115.4, -130.0, - 39.7, - 56.0 - 94.5, 63.3 - 91.8, -109.7, 5.1 - 67.8, 55.8 20.0 - 54.5, 16.7 646 684
+
+
+ +
+
+
+ + +
+
-
80
735 -11 75.5 504 422 605 304 -223.9 77.0 -165 26.1 - 49.5 - 71.1 - 88 -109 -105.6 - 87.0 -114.3 - 13.2 - 83.7 - 50.9 0.9
-64 -
85.5 89.7 49.0 34.0 8.0 5.5 - 21 373 501
~
i:'j ~
>-3
PbF, .......... PbI,. ......... PbO .......... PbS ........... LiBr .......... LiCI. .......... LiF ........... LiI. ........... MgC\, ......... MllC\, ........ HgBn ......... HgC\, ......... HgI, .......... MoF6 ...... MoO, ......... NiCb ......... Ni(CO), ....... NF, ........... NO ........... N,O ........... N,O, .......... N,O ........... NOCI. ........ NOF .......... NO,F ......... OsO, .......... Os04. .........
0, ............ PBr' .......... PCI, .......... PCl. .......... PH, ........... PH,Br ........ PH,CI. ........ PH,I. ......... P,O, .......... POC!,. ... P,O, .......... P,O, .......... PSB" ........ PSCI, ........ KBr ........
Lead fluoride Lead iodide Lead oxide Lead sulfide Lithium bromide Lithium chloride Lithium fluoride Lithium iodide Magnesium chloride Manganous chloride Mercuric bromide Mercuric chloride Mercuric iodide Molybdenum hexafluoride Molybdenum trioxide Nickel chloride Nickel carbonyl Nitrogen trifluoride Nitric oxide Nitrous oxide Nitrogen tetroxide Nitrogen pentoxide Nitrosyl chloride Nitrosyl fluoride Nitroxyl fluoride Osmium tetroxide (white) Osmium tetroxide (yellow) Ozone Phosphorous tribromide Phosphorous trichloride Phosphorous pentachloride Phosphorous hydride (phosphene) Phosphonium bromide Phosphonium chloride Phosphonium iodide Phosphorous trioxide Phosphor'ous oxychloride Phosphorous pentoxide (stable form) Phosphorous pentoxide (metastable form) Phosphorous thiobromide Phosphorous thiochloride Potassium bromide
136.5, 136.2, 157.5, - 65.5, 734, 671,
861 540 1039 928, 840 880 1156 802 877 736 165 3, 166.0, 189.2, - 49.0, 785, 731,
904 571 1085 975, 888 932 1211 841 930 778 179.8, 180.2, 204.5, - 40.8, S14 759,
950 605 1134 1005, 939 987 1270 883 988 825 194.3, 195.8, 220.0, - 32.0, 851 789,
-184.5, -143.4, - 55.6, - 36.8,
-175.5 -180.6, -133.4, - 42.7, - 23.0,
-170.7 -178.2, -128.7, - 36.7, - 16.7,
-165.7 -175.3, -124.0, - 30.4, - 10.0,
-120.3 -132.1 15.6, 22.0, -168.6 34.4 31.5 74.0,
-114.3 -126.2 26.0, 31.3, -163.2 47.S 21.3 83 25
-107.8 -119.8 37.4, 41.0, -157.2 62.4 10.2 92 5,
28.5, 79.6, 9.0, 39.7
21.2, 74.0, 1.1, 53.0 2.0
13 3, 68 0, 7.3, 67.8 13.6
479 943 852. 748 783 1047 723 778
-132.0 -143.7, 5 6, 3.2, -180.4 7.8 51.6 55.5, 43.7, 91.0, 25.2,
+
+
384,
424,
442,
462,
189 50.0 - 18.3 795
220
236 -83:6 16.1 940
253 95.5 29.0 994
72.4
+ 8924.6
1003 644 1189 1048, 994 1045 1333 927 1050 879 211. 5, 212.5, 238.2, - 22.1, 892 821, - 23.0 -160.2 -171.7, -118.3, - 23.9, 2.9, - 60.2 -100.3 -112.8 50.5 51. 7s -150.7 79.0 2.3 102.5,
+
-129.4 5.0, 61.5, 16.1, 84.0 27.3 481, 270 108.0 42.7 1050
1144 750 1330 1160 1147 1203 1503 1049 1223 1028 262.7 256.5, 291.0 4.1, 1014 904, 8.8 -145.2 -162.3, -103.6, 5.0 15.6, 34.0 79.2 93 ..5 89.5 89.5 -132.6 125.2 37.6 131. 3,
1036 668 1222 1074, 1028 1081 1372 955 1088 913 221.0, 222.2, 249.0, - 16.2, 917 840, - 15.9 -156.5 -168.9, -114.9, 19.9, 1.8, 54.3 95.7 -108.4 59.4 59.4 -,146.7 89.8 10.2 10S.3,
lOS0 701 1265 1108, 1076 1129 1425 993 1142 !l60 237.8 237.0, 261.8 8.0, 955 866. 6.0 -152.3 -166.0, -110.3, 14.7, 7.4, 46.3 88.8 -102.3 71.5 71.5 -141. 0 103.6 21.0 117.0,
-125.0 0.3, 57.3, 21.9, 94.2 35.8
-118.8 7.4, - 52.0, 29.3, 108.3 47.4
-109.4 17.6, - 44.0, 39.9, 129.0 65.0
510 s
294 126.3 63.8 1137
+
+
493, 280 116.0
51.8 1087
+ +
1219 807 1402 1221 1226 1290 1591 1110 1316 1108 290.0 275.5, 324.2 17.2 1082 945, 25.8 -137.4 -156.8, 96.2, 8.0 24.4, 20.3 68.2 83.2 109.3 109.3 -122.5 149.7 56.9 147.2,
+
1293 872 1472 1281 1310 1382 1681 1171 1418 1190 319.0 304.0 354.0 36.0 1151 987, 42.5 -129.0 -151. 7 88.5 21.0 32.4 6.4 56.0 72.0 130.0 130.0 -111.1 175.3 74.2 162.0,
855 402 890 1114 547 614 870 446 712 650 237 277 259 17 795 1001 - 25 -183. 7 -161 90. 9 9. 3 30 t)4. 5 -134 -139 42 56 -251 - 40 -111. 8
98.3 28.0, 35.4, 51.6, 150.3 84.3
87.5 -132. 5 38.3d 27.0, 28. 5 62.3, 173.1 22. 105.1 2
532,
556,
591
314 141.8 82.0 1212
339 157.8 102.3 1297
358 175.0d 124.0 1383
~"t:I
o
l=d
~
t<J
1J2 1J2
q l=d t<J
569 38 36. 730
~
Ol
c:.n
TABLE 4k~1. VAPOR PRESSURE OF INORGANIC COMEOUNDS-PRESSURES LESS THAN
1
ATMOSPHERE
(Continued)
t
Temp., °0 Formula
KC!. .... ..... KF ........... KOH .......... KI.. .......... Re'07 ......... RbBr ...... RbCl. .......... RbF .......... RbI. ............ 3e02 ......... _. SeF6 ........ _.. 3eOCb ........ SeCI ........... SiH4 .......... SiO z• "-, •...•.. SiCle ......... SiF4 ........... 3iHaBr ........ 3i.H,Cl. ....... 3iH,F ......... SiH,I. ........ SiBrClzF ...... SiBrFa ........ 3iCIF, ......... SiBl',CIF ...... ~iBT2Fz ........ SiHzBr2_., ...... SiCbF, ........ SiH2F2 ........ SiH212 ......... 3i2HI.i ....... '," (SiHs),O ....... SiC1.1F ......... SizC16,., ........ (SiClaJ,O ...... SbF6 ... '.' ._ ..... ~iaCls, ..._ . , .. , ... SLtH1o,.""., .
M.P.
Name
Potassium chloride Potassium fluoride Potassium hydroxide Potassium iodide Rhenium heptoxide Rubidium bromide Rubidium chloride Rubidium fluoride" Rubidium iodide Selenium' -dioxide Selenium hexafluoride Selenium oxychloride Selenium tetrachloride Silane Silicon dioxide Silicon tetrachloride Silicon tetrafluoride Bromosilane Chlorosilane Fluorosilane IodosiJane Bromodichlorofluorosilane BtomotrifluorosiIane ChlorotrifluorosiIane Dibromochlorofluorosilane Dibromodifluorosilane Dibromosilane Dichlorodifluorosilane Difluorosilane Diiodosilarie Disilane Disiloxane Fluorotrichlorosilane Hexachlorodisilane Hexachlorodisiloxane Hexafluorodisilane Octachlorotrisilane Tetrasilane
1 mm
5 mrn
10 mm
20 mm
40 mm
821 885 719 745 212.5, 781 792 921 748 157.0, -118.6, 34.8 74.0, -179.3
919 988 814 840 237.5, 876 887 982 839 187.7, -105.2, 59.8 !l6.3, -168.6
- 63.4 -144.0,
- 44.1 -134.8, - 85.7 -104.3 -145.5 - 53.0 - 68.4
968 1039 863 887 248.0, 923 937 1016 884 202.5, - 98.9, 71.9 107.4, -163.0 1732 - 34.4 -130.4, - 77.3 - 97.7 -141.2 - 43.7 - 59.0
1020 1096 918 938 261.0, 975 990 1052 935. 217.5, - 92.3, 84.2 118.1, -156.9 1798 - 24.0 -125.9, - 68.3 - 90.1 -1,36.3 - 33.4 - 48.8
-127.0 - 35.6 - 66.8 -29.4 -102.9 -130.4 18.0 - 91.4 - 88.2 - 68.3 38.8 29.4 - 63.1, 89.3 4.3
-120.5 - 24.5 - 57.7 - 18.0 - 94.5 -124.3 34.1 - 82.7 - 79.8 - 59.0 51.5 41.5 - 57.0, 104.2 15.8
,
,
-117.8 -153.0 -
, ,
86.5
,
,
-144.0, - 65.2
-133.0 - 45.5
- 60.9 -124.7 -146.7
- 40.0 -110.5 -136.0 3.8 - 99.:3 - 95.8 - 76.1 27.1 17.:3 - 68.8, 74.'7 - 6.:1
,
,
-114.8 -112.5 - 92.6 4.0 - 5.0 - 81.0, 46.3 - 27.7
+
,
+ +
,
+
,
100mm
200 mm
400 mm
760 mm
1078 1156 976 995 272.0, 1031 1047 1096 991 234.1, - 84.7, 98.0 130.1, -150.3 1867 - 12.1 -120.8; - 57.8 - 81.8 -130.8 - 21.8 - 37.0
1115 1164 1193 1245 1013 1064 1030 1080 280.0, 289.0, 1066 , 1114 1084 1133 1123 1168 1026 1072 244.6, 258.0, - 80.0, - 73.9, 106.5 118.0 137.8, 147.5, -146.3 -140.5 11)69 1911 - 4.8 5.4 -117.5, -113.3, - 51.1 - 42.3 - 76.0 - 68.5 -127.2 -122.4 - 14.3 - 4.4 - 29.0 - 19.5
-112.8 - 12.0 - 47.4 - 5.2 - 85.0 -117.6 52.6 - 72.8 - 70.4 - 48.8 65.3 55.2 - 50.6, 12l.5 28.4
-108.2 4.7 - 4l.0 3.2 - 78.6 -113.3 64.0 - 66.4 - 64.2 - 42.2 73.9 63.8 - 46.7, 132.0 36.6
1239 1323 1142 1152 307.0 1186 1207 1239 11.41 277.0, - 64.8, 134.6 161.0, -131. 6 2053 21.0 -107.2, - 28.6 - 57.0 -115.2 10.7 - 3.2 - 69.8 - 91. 7 23.0 - 18.2 31.6 - 58.0 - 98.3 101.8 - 44.6 - 43.5 - 19.3 102.2 92.5 - 34.2, 166.2 63.6
1322 1411 1233 1238 336.0 1267 1294 1322 1223 297.7, - 55.2, 151.7 176.4, -122.0 2141 38.4 -100.7, -' 13.3 - 44.5 -li:l6.8 27.9 15.4 - 55.9 - 81.0 43.0 - 2.6 50.7 - 45.0 - 87.6 125.5 - 29.0 - 29.3 - 4.0 120.6 113.6 - 26.4, 189.5 81. 7
1407 1502 1327 1324 362.4 1352 1381 1408 1304 317.0, - 45.8, 168.0 191. 5d -111.5 2227 56.8 - 94.8, 2.4 - 30.4 - 98.0 45.4 35.4 - 41. 7 - 70.0 59.5 13.7 70.5 - 3l.8 - 77.8 149.5 - 14.3 - 15.4 12.2 139.0 135.6 - 18.9, 211.4 100.0
,
60 mm
+
,
-
+
,
-101. 7 6.3 31.9 14.1 - 70.3 -107.3 79.4 - 57.5 - 5.5.9 - 33.2 85.4 75.4 - 41. 7, 146.0 47.4
+ -
+
+
+
+
+
cr;, cr;,
790 880 380 723 296 682 715 76.0 642 340 - 34. 7 8. 5 -185 1710 - 68. 8 - 90 - 93. 9 - 57. o ":'112. 3 - 70. 5 -142 - 91}. 3 - 66. 9 - 70. 2 -139. 7 1. o -132. 6 -144. 2 -120. 8 - 1. 2 - 33. 2 - 18. 6
-
-
93. 6
:;q trJ
P> >-:3
3iBr3F ........ 3iHBra ........ SiRC\, ........ SiHF 3 . . . . . . . • • Si 3 H g . . . . . . . (SiH,),N ...... legCI. ........ 8.gI. .......... NaBr ........ NaC!. ........ NaCN ......... NaF .......... NaOH ......... NaI. ... 3nBr4 ......... SnCI4 ......... 3nH1 ......... . 3n14 ...... ..... 3nCh ........ . ~rO ........... ~F6 ........... ~02 ........... 32C12 .......... 302Cb ........ 30a ........... 303 ........... 308 ........... H,SO .......... 30Bn ......... 30Cb ......... raF •.......... reCI .......... reF, .......... TlBr .......... ric I. ......... TlI ........... TiCI ........... WF, .......... UF, ........... VOCIs ..... ZnCt, ......... ZnF, ......... ZrBH ......... ZrCl.. ........ ZrI .......
Tribromofluorosilane Tribrolnosilane Trichlorosilane Trifluorosilane Trisilane Disilazane Silver chloride Silver iodide Sodium bromide Sodium chloride Sodium cyanide Sodium fluoride Sodium hydroxide Sodium iodide Stannic bromide Stannic chloride Stannic hydride Stannic iodide Stannous chloride Strontium oxide Sulfur hexafluoride Sulfur dioxide Sulfur monochloride Sulfuryl chloride Sulfur trioxide (a) Sulfur trioxide (fJ) Sulfur trioxide (-y) Sulfuric acid Thionyl bromide Thionyl chloride Tantalum pentafluoride Tellurium tetrachloride Tellurium hexafluoride Thallium bromide Thallium chloride Thallium iodide Titanium tetrachloride Tungsten hexafluoride Uranium hexafluoride Vanadyl trichloride Zinc chloride Zinc fluoride Zirconium tetrabromide Zirconium tetrachloride Zirconium tetraiodide
46.1 30.5 80.7 -152.0, 68.9 68.7 912 820 806 865 817 1077 739 767
,
22.7 -140.0
,
316 2068, -132 7, 95.5, 7.4 39.0, 34.0, 15.3, 45.8 6.7 52.9
, ,
-111 3,
, ,
440 13.9 71.4, 38.8, 23.2 428 1243 207, 190, 264.
-
25.4 8.0 - 62.0 -142. ~rs - 49.7 - 49.!I 1019 927 903 967 928 1186 843 857 58.:1 - 1.0 -125.:> 156.0 366 2198, -120.(), - 83.1), 15.7 - 35.l - 23.7, - 19.2, - 2.0s 178.0 lS.1 - 32.1
-
+
+
, ,
-
9S 8, 490 487 502 9.4 - 56.5, - 22.0, 0.2 481 1328 237, 217, 297,
+
+
-
-
15.1 3.4 53.4 -138.2, - 40.0 - 40.4 1074 983 952 1017 983 1240 897 903 72.7 10.0 -118.5 175.8 391 2262, -114.7, - 76.8, 27.5 - 24.8 - 16.5, - 12.3, 4.3, 194.2 31.0 - 21.9
3.7 16.0 - 43.8 -132.9, - 29.0 - 30.0 1134 1045 1005 1072 1046 1300 953 952 88.1 22.0 -111.2 196.2 420 2333, -108.4, - 69.7 40.0 - 13.4 9.1, - 4.9, 11.1, 211.5 44.1 - 10.5
233 - 92.4, 522 517 531 21.3 - 49.2, - 13.8. 12.2 508 1359 250, 230,
253 - 860, 559 550 567 34.2 - 41.5, 5 2s 26 6 536 1402 266, 243, 329,
+ -
+
+
,
3118
,
+
9.2 30.0 - 32.9 -127.3 - 16.9 - 18.5 1200 1111 1063 1131 1115 1363 1017 1005 105.5 35.2 -102.3 218.8 450 2410, -101.5, - 60.5 54.1 1.0 1.0, 3.2, 17.9, 229.7 58.S 2.2
+ +
273 78.4, 598 589 607 48.4 - 33.0, 4.4, 40.0 566 1448 281, 259, 344, -
+
17.4 39.2 - 25.8 -123.7 - 9.0 - 11.0 1242 1152 1099 1169 1156 1403 1057 1039 116.2 43.5 - 96.6 234.2 467 .......
-
28.6 51.6 - 16.4 -118.7 1.6 - 1.1 1297 1210 1148 1220 1214 1455 1111 1083 131.0 54.7· - 89.2 254.2 493
+
.
96.8, 54.6 63.2 7.2 4.0, 8.0, 21.4, 241.5 68.3 10.4 110.3 287 - 73 S, 621 612 631 58.0 - 27.5, 10.4, 49.8 584 1480 289, 258,
+ +
3558
45.7 70.2 - 1.8 -111.3 17.8 14.0 1379 1297 1220 1296 1302 1531 1192 1150 152 8 72.0 - 78.0 283.5 533
+
........
. .......
-
-
90.9, 46.9 75.3 17 .8 10.5, 14.3, 28.0, 257.0 80.6 21.4 130.0 ,:04 - 67 9, 653 645 663 710 - 20.3, lS.2, 62.5 010 1527 301, 279, a69s
82.3, 35.4 93.5 33.7 20.5 23.7, 35.8, 279.8 99.0 37.9 159.9 330 - 57.3, 703 694 712 90.5 - 10.0, 30.0, 82.0 648 1602 318, 295, 389,
64.6 90.2 14.5 -102.8 35.5 31.0 1467 1400 1304 1379 1401 1617 1286 1225 177.7 92.1 - 65.2 315.5 577 ..... .. - 72.6, - 23.0 115.4 51.3 32.6 32.6 44.0, 305.0 119.2 56.5 194.0 360 - 48.2, 759 748 763 112.7 1.2 42.7. 103.5 6S9 1690 337, 312, 409,
+
+
83.8 111.8 31.8 - 95.0 53.1 48.7 1564 1506 1392 1465 1497 1704 1378 1304 204.7 113.0 52.3 348.0 623
. ..
..
-
63.5, 10.0 138.0 69.2 44.8 44.8 51.6, 330.0d 139.5 75.4 230.0 392 - 38.6, 819 S07 823 136. 17.3 55.7 127.2 732 1770 357, 331. 431,
°
- 82. 5 - 73. 5 -126. 6 -131. 4 -117. 2 -105. 7 455 552 755 800 564 992 318 651 31. o - 30. 2 -149. 9 144. 5 246. 8 2430 50. 2 73. 2 80 54. 1 16. 8 32. 3 62. 1 10. 5 52. 2 -104. 5 96. S 224 - 37. 8 460 430 440 - 30 - O. 5 69. 2 365 872 450 437 499
~
..."d
o
~
"d ~
trI
U2 U2
q
~
trI
t
t,:) eN
""
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00
TABLE
4k-2.
VAPOR PRESSURE OF INOHGANIC COMPOUNDS--PRESSURES GREATER THAN
1
ATMOSPHERE
Temp.,oC Formula
Name
Pc
I
1 atm
2 atm
5 atm
10 atm 20 atm 30 atm I 40 atm 50 atm 60 atm
T,
- - -- - -- - -- - - - - -- - -- - -- - - - -
NHa......... ; " A .............. BCl a........... BFa ............ Br' ............. COI 4 • • • • • • • • • • . CO 2 • • • • • • • . • • • • CS, ............
00 ............. COCI, ........ " CCIF, .......... O,N, ........... CCLF, ......... OHCI,F ........ OHCIF, ........
Ammonia Argon Boron trichloride Boron trifluoride Bromine Carbontetrachloride Carbon dioxide Carbon disulfide Carbon monoxide Carbonyl chloride Chlorotrifluoromethane Cyanogen Dichlorodifluoromethane Dichlorofluoromethane Chlorodifluoromethane
- 33.6 -185.6 12.7 -100.7 58.2 76.7 - 78.2, 46.5 -191. 3 8.3 - 81.2 - 21.0 - 29.8 8.9 - 40.8
+
-- 18.7 -179.0 33.2 - 89.4 78.8 102.0 - 69.1, 69.1 -183.5 27.3 - 66.7 - 4.4 - 12.2 28.4 - 24.7
+
4.7 -166.7 66.0 - 72.6 110.3 141. 7 - 56.7 104.8 -170.7 57.2 - 42.7 21.4 16.1 59.0 0.3
+ + +
25.7 -154.9 96.7 - 57.7 139.8 178.0 - 39.5 136.3 -161.0 85.0 - 18.5 44.6 42.4 87.0 24.0
50.1 -141. 3 135.4 - 40.0 174.0 222.0 - 18.9 17.5.5 -149.7 119.0 12.0 72.6 74.0 121. 2 52.0
+
66.1 -132.0 161. 5 - 28.4 197.0 251.2 - 5.3 201.5 -141. 9 141.8 34.8 91.6 95.6 144.0 70.3
78.9 89.3 98.3 132.4 111.5 -124.9 ....... ...... . -122.0 48.0 ...... . ....... ...... . 178.8 38.2 - 19.0 ....... ...... . - 12.2 49.2 216.0 230.0 243.5 302.2 121 276.0 ....... ...... . 283.1 45.0 22.4 5.9 14.9 31.1 73.0 222.8 240.0 256.0 273.0 72.9 ....... ...... . ...... . -138.7 34.6 159.8 174.0 ....... 181.7 56.0 52.8 ....... ...... . 53 40.3 106.5 118.2 ....... 126.6 58.2 ....... ...... . ...... . 111. 5 39.6 162.6 177.5 ....... 178.5 .51. 0 85.3 ....... ...... . 96.0 48.7
+
p:j l'rJ
i>fo3
CC :a F .......... Cl HB r ............ HC 1. ........... HC N ........... HI ...... 0
••
••
H, ,........... )
•
.
H" ~e ........... Kr ..... . ...... NO N2 ) ............ N,' ) •........... SiF 4. • • • • • • • • • • • • SiC IF a .......... SiC lzF, ......... SiClaF .......... Sn :a 4 . . . . . . . . . . .
SO : ........... . SO I··········· .
Trichlorofluoromethane Chlorine Hydrogen bromide Hydrogen chloride Hydrogen cyanide Hydrogen iodide Hydrogen sulfide Hydrogen selenide Krypton Nitric oxide Nitrous oxide Nitrogen tetroxide Silicon tetrafluoride Chlorotrifluorosilane Dichlorodifluorosilane Fluorotrichlorosilane Stannic chloride Sulfur dioxide Sulfur trioxide
23.7 - 33.8 - 66 ..5 - 84.8 25.9 - 35.1 - 60.4 - 41.1 -1.52.0 -151. 7 - 88.5 21.0 - 94.8, - 70.0 - 31.8 12.2 113.0 - 10.0 44.8
44,.1 77.3 - 16.9 + 10.3 - 51.5 - 29.1 - 71.4 - 50.5 75.8 41i.8 - 18.9 + 7.3 - 4;"5.9 - 22.3 - 2:5.2 0.0 -14:3.5 -130.0 -145.1 -135.7 - 76.8 - 58.0 37.3 59.8 - 84.4 - 67.9 - 57.3 - 37.2 - 15.1 + 11.6 32.4 64.6 141. 3 184.3 + 6.3 32.1 60.0 82.5
108.2 146.7 172.0 194.0 84.8 101.6 35.6 65.0 - 8.4 + 16.8 48.1 33.9 17.8 - 31. 7 - 8.8 + 5.9 102.7 135.0 153.8 169.9 62.2 32.0 83.2 100.7 - 0.4 + 25.5 41. 9 55.8 + 23.4 .50.8 69.7 84.6 -118.0 -101. 7 - 88.8 - 78.4 -127.3 -116.8 -109.0 -103.2 - 40.7 - 18.8 - 4.3 + 8.0 79.4 100.3 112.3 121.4 - 52.6 - 33.4 - 21.2 ." .... - 18.6 + 4.1 19.4 ....... 36.6 66.2 86.0 . " ' " . 94.2 131. 8 156.0 ....... 223.0 270.0 299.8 ....... 83.8 102.6 118.0 55.5 104.0 138.0 167.8 175.0
·..... . 115.2 60.0 27.9 183.5 116.2 66.7 97.2 - 66.5 - 99.0 18.0 127.0 ...... . ...... . ·...... ...... . ·. . . . . . 130.2 187.8
· . . . . . . 198.0 43. 2 127.1 144.0 76. 1 90.0 84. 4 70.6 51.4 81. 6 36.2 ....... 183.5 .50. o 127.5 1.51. 0 82. o 76.3 100.3 88. 9 91. 108.7 137 ....... - 63 .54 - 94.8 - 92.9 64. 27.4 36 . .5 71. 132.2 158 99 ...... . - 14.2 36. ...... . 34.8 34. . ...... 95.8 34. · . . . . . . 165.3 35. · . . . . . . 318.7 37. 141.7 157.2 77. 198.0 218.3 83.
.,.
>-3
,H4Cl, ........ 1,2-Dichloroethane ,H,O, ........ Acetic acid 2H402.· ... -.... Methyl formate ,H,Br •....... Ethyl bromide ,H,Cl..· ...... Ethyl chloride ,H,F ......... Ethyl fluoride zH 6 .·.·.'.·.- . . . . . Ethane .c ,H,O.·....... Ethanol .C ,H,O .. ·...... Dimethyl ether ,C ,H,S .... ·...... Dimethyl sulfide C ,H,S.,'.· ...... Ethanethiol Ethylamine C ,H7N .. ,'.· .. ,C ,H7N.·.·.·.· .. ·.. ·Dimethylamine C ,N, .. ,' ......... Cyanogen ,0 aH4 .. '.. '.'.'.'.'.'. Propadiene (0 3,H.L ... ·.'.'.·.·.· .. Propyne C ,H,N,Og ..... Nitroglycerine ,C ~H6 ... ','.', ...... Propylene .C ,H,O ......... Acetone .C ,H,O, ......... Propionic acid .C ,H,O" ........ Methyl acetate C ,H,O, ........ Ethyl formate C 3H8 ............... Propane ,H,O ......... I-Propanol ,H,O ......... 2-Propanol ,HsO ........ 'Eth}Cl methyl ether ,HsO, ........ Glycerol· , ,H,N ... : .... Propylamine ,H,N ......... Trimethylamine ~H2 ....... ; .. 1,3-Butadiyne ~H6 ....... :.'. 1,:2.,.Butadiene ,C 4H6 . . . . . . . :. 1,3-Butadiene C ~H6 ... : .. :; .. Cyclobutene ,C ~H6 ... :: .. .' ... 1-Butyne ,H, .......... 2-Butyne c .H,O., ........ Acetic anhydride ,H,O ......... Dimethyl oxalate 4HsO, ........ Butyric acid ,H,02 ........ Isobutyric acid .j.HS02 ........ Ethyl acetate ,H,O, ........ Methyl propionate
.44.5. 17..2, 74.2 74.3 89.8 -117.0 -159.5 - 31.3 -115.1 75.6 76.7 82.3. 87.7 95.8, ~ 120 ..6 -111.0, 127 ~ 131.9 59.4 4.6 57.2 60.5 -128.9 - 15.0 - 26.1 - 91.0 125.5 64.4 - 97.1 -
82.5 8
- 89.0 -102.8 99.1 92.5 73.0, 1.7 20.0 25.5 14.7 43.4 42.0
24.0 6.3. 57.0 56.4 73. 9 -103.8 -148.5 - 12.0 -101.1 58.0 59.1 66.4 72.2 83.2, -108.0 - 97.5 157 -120.7 40.5 2S.0 38.6 42.2 -115.4 5.0 7.0 75.6 153.8 46.3 81.7 68.0. 72.7' 87.6 83.4 76.7 57.9. 24.8 44.0 49.8 39.3 23.5 21.5
+
+
t
i
13.6 17.5 48.6 47.5 65.8 97.7 -142.9 2.3 93.3 49.2 50.2 58.3 64.6 76.8, -101.0 - 90.5 188 ~112.1
31.1 39.7 29.3 33.0 -108.5 14.7 2.4 - 61.8 167.2 37.2 73.8 61.2. 64.2 79.7 75.4 68.7 50.5. 36.0 56.0 61.5 51.2 13.5 1l.8
+
- - - - - - -- - _...
_ ... _-
2.4 29.9 39.2 37..8 56.8 90.0 -136.7 8.0 85.2 39.4 40.7 48.6 56.0 70.1, 93.4 82.9 210 -104.7 20.8 52.0 19.1 22.7 -100.9 25.3 12.7 59.1 182.2 27.,1 65.0 53.8, 54.9 71.0 66.,6 59.9 42.5, 48.3 69.4 74.0 64_0 3.0 1.0
+
+
10.0 43.0 28.7 26.7 47.0 81.8 -129.8 19.0 76.2 28.4 29.8 39.8 46.7 62.7. 85.2 74.3 235 96.5 9.4 65.8 7.9 11.5 92.4 36.4 23.'8 49.4 198 .. 0 16.0 55.2 45.9. 44.3 61.3 56.4 50.0 33.9, 62.1 83.6 88.0 'l7.8 9.1 1l:0
+ +
18.1 51. 7 21.9 19.5 40.6 76.4 -125.4 26.0 70.4 21.4 22.4 33.4 40.7 57.9. 78.8 68.8 251d 91.3 2.0 74.1 0.5 4.3 87.0 43.5 30.5 43.3 20S.0 9.0 48.8 4.1.0. 37.5 55.1 50.0 43.4 27.8 70.8 92.8 96.5 86.3 16.6 18.7
29..4 53:0 12.9 10.0 32.0 69.3 -119.3 34.9 62.7 12.0 13.0 25.1 32 6 51 8, 72.5 61.3 84.1 7.7 85.S 9.4 5.4 79.6 52.8 39.5 34.8 220.1 0.5 40.3 34.0 28.3 46.8 41.2 34.9 18.8 82.2 104.8 108.0 98.0 27.0 29.0
+ + +
+
45.7 80.0 0.8 4.5 18.6 58.0 -110.2 48.4 50.9 2.6 1.5 12.3 20.4 42.6,' 61.3 49.8
+ +
+ +
-,- 73.3 22.7 102.5 24.0 20.0 68.4 66.8 53.0 22.0 240.0 15.0 27.0 20.9 14.2 33.9 27.S 21.6 5.0 100.0 123.3 125.5 115.8 42.0 44.2
+
-
64.0 99.0 16.0 21.0 3.9 45.5 99.7 63.5 37.8 18.7 17.7 2.0 7.1 33.0 48.5 37.2
60.9 39.5 122.0 40.0 37.1 55.6 82.0 67.8 7.8 263.0 31. 5 12.5 6.1 1.8 19.3 12.2 6.9 10.6 119.8 143.3 144.5 134.5 59.3 61.8
+ +
+
82.4 118.1 32.0 38.4 12.3 32.0 88.6 78.4 23.7 36.0 35.0 16.6 7.4 21.0 35.0 23.3
+ -
47.7 56.5 141.1 57.8 54.3 42.1 97.8 82.5 7.5 290.0 48.5 2.9 9.7 18.5 4.5 2.4 8.7 27.2 139.6 163.3 163.5 154.5 77.1 79.8
+ + .+ + +
35.3 16.7' 99.8 -117.8 -139 -183.2 -112 -138.5 - 83.2 -121 - 80.6 - 96 - 34.4 -136 -102.7 11 -185 94.6 22 98.7 79 -187.1 -127 85.8 17.9 83 -117.1 - 34.9
..q ". "d
o ~
"d ~
l'J
l/2 l/2
c:: ~
l'J
-108.9 -130 32.'5 73 4.7 47 82.4 87.5
t
--.:r
i-'
TABL~J
-
4k-3.
VAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES LESS THAN
1
t
(Continued)
ATMOSPHERE
tV "'1 tV
Temp.,oC Formula
Name
M.P. 1 mm
C'HS02 ........ C'HlO ......... C'HlO ......... C,H1OO ........ C'HlOO ........ C,HlOO ....... C'H1OO ........ C'HlOO ........ C'H1OS ........ C4.HuN ........ C4Hl:!Si ........ C'H1OO2 ....... C'HIOO2 ....... C'HlOO2 ....... C'HlOO2 ....... C5HJo02 ....... eliHu ........ . C'HI" ........ C,H" ......... C'HI'O ........ C,H,Br ........ C,H,C!.. ...... C,H,F ........ C,H,I. ........ C,H, .......... C,H,O ........ C,H,N ........ C,H12 ......... C6H14 ......... C,H14 ......... C,H, ......... C'HI O • • • • • • • • • CSHIO......... C,Hls ......... C12Hz 6 . . . . . . . . .
-
Propyl formate Butane 2-Methylpropane Butyl alcohol Me-Butyl alcohol Isobutyl alcohol tert-Butyl alcohol Diethyl ether Diethyl sulfide Diethylamine Tetramethylsilane Ethyl propionate Propyl acetate Methyl butyrate Methyl isobutyrate Isobutyl formate Pentane 2-Methylbutane 2,2-Dimethylpropane Ethyl propyl ether Bromobenzene Chlorobenzene Fluorobenzene Iodobenzene Benzene Phenol Aniline Cyclohexane Hexane 2,3-Dimethylbutane Toluene Heptane Ethylbenzene Octane Dodecane
- 43.0 -101. 5 -109.2 - 1.2 - 12.2 - 9.0 - 20.4, - 74.3 - 39.6
,
- 83.8 - 28.0 - 26.7 - 26.8 - 34.1 - 32.7 - 76.6 - 82.9 -102.0, - 64.3 2.9 - 13.0 - 43.4, 24.1 - 36.7, 40.1, 34.8 - 45.3, - 53.9 - 63.6 - 26.7 - 34.0 - 9.8 - 14.0 47.8
+
5 mm
-
+ + + -
-
-
-
+ +
22.7 85.7 94.1 20.0 7.2 11.0 3.0, 56.9 18.6
,
66.7 7.2 5.4 5.5 13.0 11.4 62.5 65.8 85.4, 45.0 27.8 10.6 22.8 50.6 19.6, 62.5 57.9 25.4, 34.5 44.5 4.4 12.7 13.9 8.3 75.8
10 mm
-
+ -
-
+ + + -
-
+ -
12.6 77.8 86.4 30.2 16.9 21. 7 5.5, 48.1 8.0 33:0 58.0 3.4 5.0 5.0 2.9 0.8 50.1 57.0 76.7, 35.0 40.0 22.2 12.4 64.0 11. 5, 73.8 69.4 15.9, 25.0 34.9 6.4 2.1 25.9 19.2 90.0
20 mm
-
-
1.7 68.9 77.9 41. 5 27.3 32.4 14.3, 38.5 3.5 22.6 48.3 14.3 16.0 16.7 8.4 11.0 40.2 47.3 67.2, 21.0 53.8 35.3 1.2 78.3 2.6, 86.0 82.0 5.0, 14.1 24.1 18.4 9.5 38.6 31. 5 104.6
+ -
+ + -
+
40mm
+ -
-
-
+ + + -
10.8 59.1 68.4 53.4 38.1 44.1 24.5, 27.7 16.1 11.3 37.4 27.2 28.8 29.6 21.0 24.1 29,2 36.5 56.1, 12.0 68.6 49.7 11.5 94.4 7.6 100.1 96.7 6.7 2.3 12.4 31.8 22.3 52.8 45.1 121. 7
60mm
-
-
-
-
-
18.8 52.8 62.4 60.3 45.2 51. 7 31.0 21.8 24.2 4.0 30.3 3,5.1 37.0 37.4 28.9 32.4 22.2 29.6 49.0, 4.0 78.1 58.3 19.6 105.0 15.4 108.4 106.0 14.7 5.4 4.9 40.3 30.6 61. 8 53.8 132.1
+ -
100 mm
-
-
29.5 44.2 54.1 70.1 54.1 61.5 39.8 11.5 35.0 6.0 20.9 45.2 47.8 48.0 39.6 43.4 12.6 20.2 39.1, 6.8 90.8 70.7 30.4 118.3 26.1 121.4 119.9 25.5 15 8 5.4 51.9 41.8 74.1 65.7 146.2
+ -
-
+
+
200 mm
45.3 31.2 41.5 84.3 67.9 75.9 52.7 2.2 51.3 21.0 - 6.5 61.7 64.0 64.3 55.7 60.0 1.9 5.9 - 23.7, 23.3 110.1 89.4 47.2 139.8 42.2 139.0 140.1 42.0 31. 6 21.1 69.5 58.7 92.7 83.6 167.2
-
+
+
400 mm
62.6 16.3 27.1 100.8 83.9 91.4 68.0 17.9 69.7 38.0 10.0 79.8 82.0 83.1 73.6 79.0 - 18.5 10.5 - 7.1 41.6 132.3 110.0 65.7 163.9 60.6 160.0 161.9 60.8 49.6 39.0 89.5 78.0 113.8 104.0 191.0
-
+
+
760 mm
-
81.3 0.5 11.7 117.5 99.5 108.0 82.9 34.6 88.0 55.5 27.0 99.1 101.8 102.3 92.6 9S.2 36.1 27.8 9.5 61. 7 156.2 132.2 84.7 188.6 SO.l 181.9 184.4 80.7 68.7 58.0 110.6 98.4 136.2 125.6 216.2
+
- 92.9 -135 -145 - 79.9 -114.7 -108 25.3 -116.3 - 99.5 - 38.9 -102.1 - 72.6 - 92.5 - 84.7 - 95.3 -129.7 -159.7 - 16.6 -
30.7 45.2 42.1 28.5 5.5 40.6 - 6.2 6.6 - 95.3 -128.2 - 95.0 - 90.6 - 94.9 - 56.8 9.6
+
+
;:q trJ il>
>-3
VAPOR PRESSURE
4-273
Tables 4k-5 to 4k-14, Vapor Pressures of Special Gases, listing values of th~ vapor pressures of He., He" normal and equilibrium H 2,Ne, N 2, and O 2, were taken from Thermometry at Low Temperature, a master's essay at the University of Pittsburgh, 1965, by Edward R. Simco. This booklet is also entitled Research Report 4 and was supported in part by the National Science Foundation. , Table 4k-15, Vapor Pressures of the Chemical Elements, lists values of the vapor pressure, :temperature, and heat associated with the phase transitions for the chemical elements. The numbers represent temperature in degrees Celsius at which the vapor pressure is the value appearing at the top of the column. A circled dot between columns indicates a change of phase. The six columns on the right side list ith~ following iriformation: .
Tm I1B m T, I1B, _
Trans
heat of vaporization at 25°C, or atmospheric boiling temperatUlie if the vahie contains an asterisk (*), cal/mol ' melting temperature heat of melting, cal/mol transition temperature heat of transition, cal/mol designates solid-state transition
Equilibrium vapor pressures are listed for substances with polymorphic' v~por or condensed forms (As, Sb, Bi, P, Po, S, Se, Te). The basic sources should be: consulted for vapor pressures of the various polymorphic forms. The sources for this table are: (1) Ralph Hultgren, RaymondL. Orr, Philip D. Anderson, and Renneth K. Kelley, "Selected Values of Thermodynamic Properties of Metals and Anoys," John Wiley & Sons, Inc., New York, 1963 (updated by privately distributed supplements); (2) Daniel R. Stull and Gerard C. Sinke, "Thermodynamic Properties of the Elements," Advances in Chem: Ser .. No. 18: (3) Richard E.Honig, "Vapor Pressure Data for the Solid and Liquid Elements," RCA Rev. 23 (4), 567-586 .(1962); (4) Richard E. Honig and H. '0. Hook, "Vapor Pressure Data for Some Common Gases," RCA Rev. 21(3), 360-368 (1960). ' Table 4k-16, Vapor Pressure of Ice, has been taken from the NBS Circ. 564, Tables of Thermal 'Properties of Gases, by J. Ril.senrath, C. W. Beckett,W. S. Benedict, L. Fano, H. J. Hoge,' J. F. Masi, R. L. Nuttall, Y. S. Touloukian, and :H. W. Woolley, U.S. Government Printing Office, Washington, D.C., 1955. The: values were smoothed, and adjusted to agree with the ice-point value adopted in Table ~~
,
Table 4k-17, Vapor Pressure of Liquid Water below 100°C, and Table 4k-18; Vapor Pressure of Liquid Water above 100°C, have been taken from the recent ",ork of M. R. Gibson and E. A. Bruges, J. Mech. Eng. Sci., 9(1), 24'-35 (February,: 1967). Table 4k-19, Vapor Pressure of Mercury, is taken from the compilatioljl of J. Johnston, F. Fenwick, and H. G. Leopold, "International Critical Tables," vol. III, McGraw-Hill Book Company, New York, 1928. Table 4k-20, Vapor Pressure of Carbon Dioxide, is from C. H. Meyers and M. S. Van Dusen, J. Research NBS, 10, 409 (1933). Table 4k-21, Vapor Pressure of Ethyl Alcohol, and Table 4k-22, Vapor Pressure of Methyl Alcohol, are reprinted by permission from the "Smithsonian Physical Tables," 9th ed. Smithsonian: Institution, Washington, D.C., 1954. , Table 4k-23, Constants in the Equation for the Rate 6f Evaporation of Metals, is taken by permi~sion from pages 752-754 of "Scientific Foundations of V/Lcuum Technique," by S. Dushman, John Wiley & Sons, Inc., New York, 1949.
!
TABLE 4k-4. VAPOR PRESSURE 'OF ORGANiC COMPOUNDS-PRESSURES GREATE:R THAN 1 ATMOSPHERE
'"'-l ~
Formula OCIFa.... CChF 2 • • • CC1,O .... CClaF .... 001 4 • • • • • OHOIF2.. OH01,F .. OHCla.... OHN ..... CHaBr ... OHaCI. ... OHaF .... CHal .... ; CR •...... CH.O .... CH.S ..... CH.N. '" CO ...... OS2 ...... 02CIFa... 02Cl2F 4 •••
Temp.,oC
Name
Chlorotrifluoromethane Dichlorodifluoromethane Carbonyl chloride Trichlorofluoromethane Carbon tetrachloride Chlorodifluoromethane Dichlorofluoromethane Trichloromethane Hydrocyanic acid Methyl bromide Methyl chloride Methyl fluoride Methyl iodide Methane Methanol Methanethiol Methylamine Carbon monoxide Carbon disulfide l-Chloro-l ,2,2-trifluoroethylene 1,2-Dichloro-l,I,2,2tetrafluoroethane C 2ClaFa... 1,1,2-Trichloro-1,2,2trifluoroethane
1 atm 81.2 29.8 8.3 23.7 76.7 - 40.8 8.9 61.3 25.8 3.6 - 24.0 - 78.2 42.4 -161.5 64.7 6.8 - 6.3 -191.3 46.5 - 27.9 3.5 -
47.6
2.atm - 66.7 - 12.2 27.3 44.1 102.0 - 24.7 28.4 83.9 45.5 23.3 - 6.4 - 64.5 65.5 -152.3 84.0 26.1 10.1 -183.5 69.1 - 11.1 22.8
+
70.0
5 atm 42.7 16.1 57.2 77.3 141.7 0.3 59.0 120.0 75.5 54.8 22.0 - 42.0 101.8 -138.3 112.5 55.9 36.0 -170.7 104.8 15.5 54.0 -
+ +
+
+
105.5
Tc
10 atm 20 atm 30 atm 40 atm - 18.5 34.8 52.8 12.0 42.4 74.0 95.6 . . . . . . . 85.0 119.0 141.8 159.8 108.2 146.7 172.0 194.0 178.0 222.0 251.2 276.0 24.0 52.0 70.:3 85.3 87.0 121.2 144.0 162.6 152.3 191.8 216 ..5 237.5 103.5 134.2 154.0 170.2 84.0 121.7 147.5 170.2 47.3 77.3 97.5 113.8 - 21.0 2.6 15.5 26.5 138.0 176.5 206.0 228.5 -124.8 -108.5 - 96.3 - 86.3 138.0 167.8 186.5 203.5 83.4 117.5 140.0 157.7 59.5 87.8 106.3 i21.8 -161.0 -149.7 -141.9 ....... 136.3 175.5 201.5 222.8 40.0 71.1 91.9 82.3 117.5 140.9 .......
50 atm 60 atm
+
· . . . . . . ....... 174.0 · . . . . . . · . . . . . . ....... ....... ...... . · . . . . . . ....... 177.5 · . . . . . . 254.0 ....... 183.5 · . . . . . . 190.0 ....... 126.0 137.5 43.5 36.0 248.0 ...... .
+
....
.
138.0
177.7
205.0
0
•••
•• "G ••
· . . . .. . · . . . . . . 214.0 172.0 133.7
224.0 185.0 144.6
· . . . . . . ....... 240.0
256.0
...... . ...... . ...... . ••••
•
0
0-
•••
••
0
•
......
.
Pc
----
53 40. 111.5 39. 181.7 56. 198.0 43. 283.1 45. 96 48. 178.5 51. 260 54. 183.5 50. 194 51. II: t 44.9 62. 1-'3 255 54 . - 82.1 45. 8 240.0 78. 7 1fJ6.8 71. 4 156.9 73. 6 -138.7 34. 6 273.0 72. 9 107.0 39 . o 145.7 32. 3 214.1 33 . 7
02H2..... 02H20b " D2H.Ob .. O.H•..... O.H.Br2 .. 02H.0l2 .. 02H.012 .. 02H.02... 02H.02... 02H sBr ... OoH.Ol. .. 02H•F .... OoH •..... OoH.O .... O.H.O .... 02H .S .... 02H.S .... 02H 7N ... OoH 7N ... OoNo..... O.H •..... O.H •..... O.H •..... O.H.O .... O.H.02...
Acetylene cis-l,2-Dichloroethylene trans-l,2,Dichloroethylene Ethylene 1,2-Dibromoethane 1,I-Dichloroethane 1,2-Dichloroethane Acetic acid Methyl formate Ethyl bromide Ethyl chloride Ethyl fluoride Ethane Ethanol Dimethyl ether Ethanethiol Dimethyl sulfide Ethylamine Dimethylamine Oyanogen Propadiene Propyne Propylene Acetone Propionic acid
- 84.0, 59.0 47.8 -103.7 131.5 57.3 83.7 118.1 32.0 38.4 12.3 - 32.0 - 88.6 78.4 - 23.7 35.0 36.0 16.6 7.4 - 21.0 - 35.0 - 23.3 - 47.7 56.5 141.1
- 71.6 - 50.2 - 32.7 - 10.0 + 4.8 82.1 119.3 152.3 194.0 221.5 69.8 104.0 135.7 174.0 199.8 - 90.8 - 71.1 - 52.8 - 29.1 - 14.2 157.7 200.0 237.0 269.0 286.0 80.2 117.3 150.3 192.7 220.0 108.1 147.8 183.5 226.5 254.0 143.5 180.3 214.0 252.0 276.5 51.9 83.5 112.0 147.2 169.7 60.2 95.0 126.8 164.3 188.0 32.5 64.0 92.6 127.3 149.5 - 16.7 + 7.7 30.2 57.5 75.7 - 75.0 - 52.8 - 32.0 - 6.4 + 10.0 126.0 151.8 183.0 203.0 97.5 - 6.4 + 20.8 45.5 75.7 96.0 56.6 90.7 121.9 159.5 184.3 57.8 92.3 124.5 163.8 188.5 35.7 65.3 91.8 124.0 146.0 25.0 53.9 80.0 111.7 132.2 - 4.4 + 21.4 44.6 72.6 91.6 33.2 - 18.4 + 8.0 64.5 85.5 74.0 - 7.1 94.0 4;3.8 19.5 - 31.4 - 4.8 + 19.8 49.5 70.0 78.6 113.0 144.5 181.0 205.0 160.0 186.0 203.5 220.0 228.0
+
-
16.8 26.8 244.5 260.0 220.0 236.5 1.5 + 8.9 295.0 300.0 243.0 261.5 272.0 285.0 297.0 312.5 188.5 213.0 206.5 220.0 167.0 180.5 90.0 ....... 23.6 ....... 218.0 230.0 112.1 125.2 204.7 220.0 209.0 224.5 163.0 176.0 149.8 162.6 106.5 118.2 108.5 118.0 111.5 125.0 85.0 ....... 214.5 ....... 233.0 238.0
34.8
36.0 62. o
...... . .......
243.3 54 . 5 9.6 50. 7 309.8 70. 6 261.5 50 . o 288.4 53 . o 321.6 57 . 2 214.0 59. 1 230.8 61. 5 187.2 52 . o 102.2 49 . 6 32.3 48. 2 243.5 63. 1 126.9 52. o 225.5. 54. 2 229.9 54. 6 183.2 55 . 5 164.5 52 . 4 126.6 58. 2 120.7 51. 8 128 52. 8 91.4 45. 4 235.0 47 . o 239.5 53 . o
...... . 271.0 57 . 9 304.5 ...... .
...... . ...... . • • • • • • 'I
229.5
...... . ...... . .......
242.0 .......
....... ....... ...... . ...... "
••••••
o.
.......
....... ....... ...... .
...... .
~ '"d 0
l:d
~ t;J
!]l !]l
~
t;J
t
l'O
"
c.rr
TABLE
Formula CsH a0 2 ••• CSH 6 0 2 ••• CsHs ..... CsHsO .... CsHsO .... CsHsO .... CsH.N ... C 4H 6 ••••• C4 HaOs ... C4H 60 4 ••• C4H s0 2 ••• C4H s0 2 ••• C4H s0 2 ••• C4H s0 2 ••• C4H s0 2 ••• C4Iho .... C4H 10 •••• C4 H ,O O ... C 4H 100 ... C 4H 100 ... C4H 100 ... C4H 100 ... C4 H 10S ••• C4H nN ... C4H 12Si. ••
4k-4.
VAPOR PRESSURE OF ORGANIC COMPOUNDS-PRESSURES GREATER THAN
1 atm 57.8 54.3 - 42.1 97.8 82.5 7.5 48.5 - 4.5 139.6 163.3 163.5 154.5 77.1 79.8 81.3 - 0.5 - 11.7 117.5 99.5 108.0 82.9 34.6 88.0 55.5 27.0
2 atm 79.5 76.0 - 25.6 117.0 101.3 26.5 69.8 + 15.3 162.0 189.6 188.3 179.8 100.6 103.0 104.3 + 18.8 + 7.5 139.8 118.2 127.3 102.0 56.0 112.0 77.8 48.0
~--.:r
(Continued)
ATMOSPHERE
0:.
Temp.,oC
Name Methyl acetate Ethyl formate Propane I-Propanol 2-Propanol Ethyl methyl ether Propylamine 1,3-Butadiene Acetic anhydride Dimethyl oxalate Butyric acid Isobutyric acid Ethyl acetate Methyl propionate Propyl formate Butane 2-Methylpropane Butyl alcohol sec-Butyl alcohol Isobutyl alcohol tert-Butyl alcohoi Diethyl ether Diethyl sulfide Diethylamine Tetramethyisilane
1
P,
Tc
5 atm lOatm 20 atm 30 atm 40atm 50 atm 60 atm 113.1 144.2 181.0 205.0 225.0 110.5 142.2 180.0 205.0 225.0 ....... ...... . + 1.4 26.9 58.1 78.7 94.8 ...... . ....... 149.0 177.0 210.8 232.3 250.0 ....... ...... . 130.2 155.7 186.0 205.0 220.2 232.0 ....... 56.4 84.0 108.0 141.4 160.0 ....... ...... . 102.8 133.4 170.0 194.3 214.5 .... , .. ...... . 76.0 114.0 139.8 158.0 ....... 47.0 194.0 221.5 253.0 272.8 288.5 ....... ...... . 228.7 ....... ...... . ...... . ...... . ...... . ...... . 225.0 257.0 295.0 319.0 338.0 352.0 ....... 217.0 250.0 289.0 315.0 336.0 ....... ...... . 136.6 169.7 209.5 235.0 ·• ••• 0. . ...... ....... 139.8 172.6 212.5 239.0 142.0 176.4 2i7.5 245.0 ....... ...... . ...... . ...... . 79.5 116.0 140.6 ....... 50.0 39.0 . ...... 66.8 99.5 120.5 ....... 172.5 203.0 237.0 259.0 277.0 ....... 147.5 172.0 204.0 230.0 251.0 ....... ...... . ...... . 156.2 182.0 212.5 232.0 251.0 130.0 154.2 184.2 201.0 222.5 ....... ...... . 90.0 122.0 159.0 183.3 ...... . ....... ...... . ...... . ...... . 153.8 190.2 234.0 263.0 113.0 145.3 184.5 210.0 ....... ...... . ...... . • _0· •• · 82.0 113.0 152.0 178'.0 ....... 0, • • • • • •
•
••••
0
••
0
••••
••
0
••••
•
•••••
0
•
-
233.7 46. 3 235.3 46. 8 96.8 42. o 263.7 49. 9 235 53 164.7 43. 4 223.8 46. 8 161.8 42. 6 296 46 260 9. 5 355 52. 336 40. 250.1 37. 9 257.4 39. 3 264.8 39. 5 152.8 36. o 134.0 37. o 287 48. 4 265 48 265 48 235 49 193.8 35. 5 283.8 39. 223.3 36. 6 185 33
~
~ ~
C,HI0 0 2.. C,HIOO, .. C,HI0 0 2.. C,HI0 0 2.. C,Hl0 0 2 •• CoH l2 .... C,H 12 . • • . C,H 12 . . . • C,H 12 0 ... C,HsBr ... C6H sCl. .. C,HsF .... C,HsI. ... C,H 6 ••••• C,HGO .... C,H 7N ... C,HI2 .... C,H 12 0 2.. C,H 14 • • • • C,H 14 • . • . C 7HS..... C 7H 15 • • • • CSHIO .... CSHIS .... Cl2H 26 ••••
Ethyl propionate Propyl acetate Isobutyl formate Methyl butyrate Methyl isobutyrate Pentane 2-Methylbutane 2,2-Dimethylpropane Ethyl propyl ether Bromobenzene Chlorobenzene Fluorobenzene Iodobenzene Benzene Phenol Aniline Cyclohexane Ethyl isobutyrate Hexane 2,3-Dimethylbutane Toluene Heptane Ethylbenzene Octane Dodecane
99.1 101.8 98.2 102.3 92.6 36.1 27.8 + 9.5 61. 7 156.2 132.2 84.7 188.6 80.1 181.9 184.4 80.7 110.1 68.7 58.0 110.6 98.4 136.2 125.6 216.2
123.8 126.8 121.8 127.5 116.7 58.0 48.8 29.5 85.3 186.2 160.2 109.9 220.0 103.8 208.0 212.8 106.0 135.5 93.0 82.0 136.5 124.8 163.5 152.7 249.2
162.7 165.7 157.8 166.7 155.2 92.4 82.8 61.1 123.1 232.5 205.0 148 ..5 270.0 142.5 248.2 254.8 146.4 174.2 131. 7 120.3 178.0 165.7 207.5 196.2 300.0
197.81 240.0 264.5 ...... . ....... 200.5 242.8 269.0 ....... ...... . 192.4 234.0 261.0 ....... 203.0 244.5 272.0 ....... 190.2 232.0 259.5 124.7 164.3 191. 3 114.5 154.0 180.3 ....... 90.7 127.6 152.5 ...... . 156.2 197.2 223.0 ...... . 274.5 327.0 359.8 387.5 ....... 245.3 292.8 324.4 349.8 ....... 184.4 227.6 257.0 279.3 ....... ...... . 315.7 371.5 406.0 437.2 ....... ••••• 0. 178.8 221.5 249.5 272.3 290.3 ....... 283.8 328.7 358.0 382.1 400.0 418.7 292.7 342.0 375.5 400.0 422.4 ....... 184.0 228.4 257.5 , ....... 210.0 253.0 280.01 ....... 166.6 209.4 ...... ·i······· 155.7 198.7 225.5 ...... . 215.8 262.5 292.8 319.0 ....... 202.8 247.5 ....... ....... 246.3 294.5 326.5 • ••• 0" 235.8 181.4 ....... ...... . 345.8 .............. ...... . ...... . ...... . •••
0
••••
•••
0
••
I
••••
0
••
• • • 0" • • •
272.8 33. 2 276.2 33. 2 278.0 38. 0 281. 2 34. 2 267.5 33. 9 197.2 33 . 0 187.8 32. 8 159.0 33 . o 227.4 32 . 1 397 44. 6 359.2 44. 6 286.5 44. 7 448 44. 7 290.5 50. 1_ 419 60. a 426 52. 4 279.9 39. 8 280.0 30. 0 234.8 29 . 6 227.4 30 . 7 320.6 41. 6 266.8 26. 9 346.4 38 . 1 296.2 24 . 7 385 17 . 5
430 .440
2.6385 2.6577 2.6765 2.6951 2.7133
19 19 19 18 18
6404 6596 6784 6969 7151
20 19 18 18 19
6424 6615 6802 6987 7170
19 19 19 19 18
6443 6634 6821 7006 7188
19 18 19 18 18
6462'19 6652 19 6840 18 7024 18 7206 18
6481 6671 6858 7042 7224
19 19 19 19 18
6500 6690 6877 7061 7242
20 19 18 18 18
6520 6709 6895 7079 7260
19 19 19 18 18
6539 6728 6914 7097 7278
19 18 18 18 17
6558 6746 6932 7115 7295
19 19 19 18 18
'450 460 470 480 490
2.7313 2.7491 2.7665 2.7838 2.8008
18 17 18 17 17
7331 7508 7683 7855 8025
18 18 17 17 16
7349 7526 7700 7872 8041
18 17 17 17 17
7367 7543 7717 7889 8058
18 18 18 17 17
7385 7561 7735 7906 8075
17 17 17 17 17
7402 7578 7752 7923 8092
18 18 17 17 16
7420 7596 7769 7940 8108
18 17 17 17 17
7438 7613 7786 7957 8125
17 18 17 17 17
7455 7631 7803 7974 8142
18 1718 17 17
7473 7648 7821 7991 8159
18 17 17 17 16
500 510 520 530 540
2.817517i 2.8341 16 2.8504 16 2.8665 16 2.8824 16
8192 8357 8520 8681 8840
17 16 16 16 16
8209 8373 8536 8697 8856
16 17 16 16 15
8225 8390 8552 8713 8871
17 16 17 16 16
8242 8406 8569 8729 8887
16 17 16 16 16
8258 8423 8585 8745 8903
17 16 16 16 16
8275 8439 8601 8761 8919
16 16 16 16 15
8291 8405 £617 8777 8934
17 16 16 15 16,
8308 8471 8633 8792 8950
16 17 16 16 16
8324 8488 8649 8808 8966
17 16 16 16 15
4574 4653 4732 4809 4886
4622 4701 4778 4855 4931
8 7 8 8 8
4-286
HEAT
TABLE
p
4k-7. T62H E 3 TEMPERATURES IN K AS A FUNCTION OF VAPOR PRESSURE P. AT O°C AND STANDARD GRAVITY, 980.665 CM/SEC 2 (Continued) P in millimeters of Mercury 1
0
2
3
4
5
6
7
8
9
--- --- --- --- ------ --- --- ---
-550 560 570 580 5QO
2.8981 2.9136 2.9290 2.9441 2.9591
16 16 15 15 15
15 15 15 15 15
9012 16 9167.16 9320 15 9471 15 9621 15
9028 9183 9335 9486 9636
16 15 16 15 14
9044 9198 9351 9501 9650
15 15 15 1.5 15
9059 9213 9366 9516 9665
16 16 15 15 15
9075 9229 9381 9531 9680
15 15 15 15 15
9090 9244 9396 9546 9695
16 15 15 15 15
9106 9259 9411 9561 9710
15 16 15 15 14
9121 9275 9426 9576 9724
600 610 620 630 640
2.9739 2.9885 2.0030 3.0173 3.031,5
15 9754 15 15 9900 15 1f) 0045 14 15 0188 14. 14 0329 14
9769 14 9911i 14 0059 14 0202 14 034314
9783 9929 0073 0216 0357
15 15 15 14 14
9798 9944 0088 0230 0371
14 14 14 14 14
9812 9958 0102 0244 0385
]5 14 14 14 14
9827 15 9972 1.5 011615 0258 15 0399 14
9842 9987 0131 Q273 0413
]4 14 ]4 14 14
9856 0001 0145 0287 0427
15 15 14 14 14
9871 14 0016 14 0159 14 0301 14 OHI14
3.0455 3.0594 3.0731 3.0866 !\jIO 3.1001
14 13 13 14 13
0469 0607 0744 0880 1014
14 14 14 ]3 13
0483 0621 0758 0893 1027
14 14 14 14 14
0497 0635 0772 0907 1041
14 14 13 13 13
0511 0649 0785 0920 1054
13 13 14 14 13
0524 14 066214 0799 13 0934 13 1067 14
0538 0676 0812 0947 1081
11 14 14 14 13
0552 0690 0826 0961 1094
14 13 13 13 13
0565 0703 0839 0974 1107
14 14 14 13 13
0580 0717 0853 0987 1120
14 14 13 14 14
700 710 720 730 740
3.1134 3.1265 3.1396 3.1525 3.1653
13 13 13 13 12
1147 1278 1409 1538 1665
13 14 13 12 13
1160 1292 1422 1550 1678
13 13 13 13 13
1173 13015 1435 1563 1691
14 13 13 13 12
1187 1318 1448 1576 1703
13 13 12 13 13
1200 1331 1460 1589 1716
13 13 13 13 13
121R 1344 1473 1602 1729
13 13 13 12 12
1226 1357 1486 1614 1741
13 13 13 .13 13
1239 1370 1499 1627 1754
13 13 13 13 13
1252 1383 1512 1640 1767
13 13 13 13 12
750 760 770 780 790
3.1779 3.1905 3.2029 3.2152 3.2274
13 12 12 12 12
1792 1917 2041 2164 2286
12 13 13 13 12
180413 1930 12 2054 '12 2177 12 2298 13
1817 1942 2066 2189 2311
13 13 12 12 12
1830 1955 2078 2201 2323
12 12 13 12 12
1842 13 1967 12 2091 .12 2213 13 2335.12
1855 1979 2103 2226 2347
12 13 12 12 12
1867 1992 2115 2238 2359
13 12 13 12 12
1880.12 2004 13 2128 12 2250 12 2371 12
1892 2017 2140 2262 2383
13 12 12 12 12
800 810 820 830 840
3.2395 3.2515 3.2634 3.2751 3.2868
12 12 12 12 12
2407 12 2527 12 2646 11 276312 2880 11
2419 2539 2657 2775 2891
2431 2551 2669 2787 2903
12 12 12 11 12
2443 2563 2681 2798 2915
12 11 12 12 11
2455 2574 2693 2810 2926
2467 12 2586 12 2704 12 2822 ·11 2938,11
2479 2598 2716 2833 2949
12 12 12 12 12
249] 2610 2728 2845 2961
2503 2t>22 2740 2857 2972
12 12 11 11 12'
650 660 670 680
8997 9152 9305 9456 9606
12 12 12 12 12
12 12 11 12 12
12 12 12 12 11
15 15 15 15 15
85013.2984 11 12995 12 3087 11 13018 1213030 11 13041 1213053 11 13064 12 3076 11 3087 12 860 3.3099 11 3110 11 3121 12 3133 11 3144 12 3156 11 3167 11 317.8 12 3190 11 3201 11 870 3.321212 3224 11 3235 11 3246
and for normal hydrogen (75% ortho-H 2 and 25% para-H 2 ), log P (mm)
=
4.658334 -
44.~93
+ 0.021276T
- 0.0000021T2
The equation for equilibrium hydrogen is within El'lCperimental accuracy in agreement with the vapor-pressure data of Hoge and Arnold' over the whole temperature region (14 to 33 K). The equation for normal hydrogen is in agreement with the vapor-pressure data of Woolley, Scott, and Brickwedde. 2 For solid equilibrium hydrogen the vapor-pressure-temperature relation is based on the equation, log P (mm)
I 2
=
4.62438 -
47.~172
+ 0.03635T
R. J. Rage and R. D. Arnold, J. Research NBS, 47, 63 (1951). H. W. Woo!ley,R. B.Scott, and F. G. Brickwedde, J. ReseaTch NBS 41,379 (1948).
VAPOR PRESSURE and for solid normal hydrogen, log P (mm) = 4.56488 -
47.~059
+ 0.039'391'
These equations were obtained by Woolley, ~cott, and: Brickwedde ' from their measurements on the vapor pressure of hydrogen. Tables 4k-8 to 4k-ll give the temperature in kelvins for integral values of vapor pressure in millimeters of mercury at-O°C and standard gravity, 980.665 cm/sec 2, as calculated, from the above equations. TABLE 4k-8. SOLID EQUILIBRIUM HYDROGEN TEMPEJ:tATURES IN K FOR ,INTEGRAL VALUES OF VAPOR PRESSURE, P, IN MILLIMETERS' 'OF MERCURY AT O°C -i\-ND , STANDARD GRAVITY; 980.665 CM/SEC 2 '5 0 2 3 4 1 --P
6
7
8
9
--- ---------
,-
0 10 20 30 40 50
9.463 10:029 10.391 10.662 10.881 11.067 11.228 11.371 11.501 11.619 11.727 11.. 828 11.922 12.010 12.093 12.172 12.247 12.318 12.386 12.452 12.514 12.575 12.633 12.689 12.743 12.795 12.846 12.896 12.944 12.990 13.035 13.080 13.123 13.165 13.206 13.246 13.285 13.323 13.361 13.398 13.434 13.469 13.504 13.,538 ~3 ..571 13.604 13.636 13.668 13.699 13.730 13.760 13.789 13.819 ......
TABLE 4k-9. SOLID NORMAL HYDROGEN TEMPERATURES IN K FOR INTEGRAL VelLUES OF VAPOR PRESSURE P, ,IN MILLIMETERS' OF MERCURY AT O°C AND STANDARD GRAVITY, 980.665 CM/SEC 2 ' P
0,
·1
'
,
2
3
4
- - - - - ---, - - - - - - -,-0
10 20 30 40 50
5
6
7
- - --- ---
8
9
---
...... ' 9.554 10.124 10.488 10.761 18.982 1i'.169 11. '331 11.475 11.605 11. 723 11.832 11.933 12.028 12 ~ 116 12.200 12,279 12.354 12.426 12.494 12.559 12.622 12.683 12.741 12.797 12.852 12.904 12.95,5 13.004 13.052 13.099 13.145' 13.189 13.232 13.274 13.315 1'3.355 13.39i 13.433 13.470 13.507 13.543 13.579 13.613 13.647 13.681 18.713 13.746 13.777 13,808 13:839 13.869 13.899 18.928 13.957 13.985
The vapor-pressure-temperature relation for,neon is based on the equation logP
(m~)
:0
8.746376 _ 126;80 - 0.04368341",
This ~qiIatibn ~~s obtained by Henning and Otto 2 from their experimental measurements on the vapor pressure of neon. Table 4k~12 gives the temperature in K f
1
2
4-288 TABLE
HEAT 4k-IO.
LIQUID EQUILIBRIUM HYDROGEN TEMPERATURES IN
VALUES OF VAPOR PRESSURE
K
FOR INTEGRAL
P,
IN MILLIMETERS OF MERCURY AT STANDARD GRAVITY, 980.665 CM/SEC 2
P
.0
1
2
3
4
5
6
7
8
O°C
AND
9
- - ---- - ---- - - -- - - -- - - - - 5.0 ..... . ...... 13.774 13.8.06 13.839 13.87.0 13.9.01 13.932 13.963 13.993 6.0 14 . .022 14 . .051 14 . .08.0 14.1.09 14.137 14.165 14.192 14.219 14.246 14.273 7.0 14.299 14.325 14.351 14.376 14.4.01 14.426 14.451 14.475 14.499 14.523 8.0 14.547 14.57.0 14.594 14.617 14.64.0 14.662 14.685 14.7.07 14.729 14.751 9.0 14.772 14.794 14.815 14.836 14.857 14.878 14.898 14.919 14.939 14.959 1.0.0 14.979 14.999 15 . .019 15 . .038 15 . .058 15 . .077 15 . .096 15.115 15.134 15.152 11.0 15.171 15.189 15.2.08 15.226 15.244 15.262 15.28.0 15.298 15.315 15.333 12.0 15.35.0 15.367 15.384 15.4.01 15.418 15.435 15.452 15.469 15.485 15.5.02 13.0 15.518 15.534 15.55.0 15.567 15.582 15.598 15.614 15.63.0 15.646 15.661 14.0 15.677 15.692 15.7.07 15.722 15.738 15.753 15.768 15.783 15.797 15.812 15.0 15.827 15.841 15.856 15.87.0 15.885 15.899 15.913 15.928 15.942 15.956 16.0 17.0 18.0 19.0 2.0.0
15.97.0 15.984 15.997 16 . .011 16 . .025 16 . .039 16 . .052 16 . .066 16 . .079 16 . .093 16.1.06 16.119 16.133 16.146 16.159 16.172 16.185 16.198 16.211 16.224 16.237 16.249 16.262 16.275 16.287 16.3.0.0 16.312 16.325 16.337 16.349 16.362 16.374 16.386 16.398 16.41.0 16.422 16.434 16.446 16.458 16.47.0 16.482 16.494 16.5.06 16.517 16.529 16.541 16.552 16.564 16.575 16.587
21.0 22.0 23.0 24.0 25.0
16.598 16.6.09 16.621 16.632 16.643 16.654 16.666 16.677 16.688 16.699 16.71.0 16.721 16.732 16.743 16.753 16.764 16.775 16.786 16.797 16.8.07 16.818 16.829 16.839 16.85.0 16.86.0 16.871 16.881 16.891 16.9.02 16.912 16.923 16.933 16.943 16.954 16.964 16.974 16.984 16.994 17 . .0.04 17 . .014 17 . .024 17 . .034 17 . .044 17 . .054 17 . .064 17 . .074 17 . .084 17 . .093 17.1.03 17.113
26.0 27.0 28.0 29.0 3.0.0
17.123 17.219 17.312 17.4.03 17.491
31.0 32.0 33.0 34.0 35.0
17.577 17.586 17.594 17.6.03 17.611 17.662 17.67.0 17.678 17.687 17.695 17.744 17.752 17.76.0 17.768 17.777 17.825 17.833 17.841 17.849 17.856 17.9.04 17.911 17.919 17.927 17.935
36.0 37.0 38.0 39.0 4.0.0
17.981 17.988 17.996 18 . .0.04 18 . .011 18 . .019 18 . .026 18 . .034 18 . .041 18 . .049 18 . .056 18 . .064 18 . .071 18 . .079 18 . .086 18 . .094 18.1.01 18.108 18.116 18.123 18.131 18.138 18.145 18.153 18.16.0 18.167 18.174 18.182 18.189 18.196 18.2.03 18.21.0 18.218 18.225 18.232 18.239 18.246 18.254 18.261 18.268 18.275 18.282 18.289 18.296 18.3.03 18.31.0 18.317 18.324 18.331 18.338
41.0 42.0 43.0 44.0 4/iD
18.345 18.352 18.359 18.366 18.373 18.379 18.414 18.421 18.427 18.434 18.441 18.448 18.481 18.488 18.495 18.5.02 18.5.08 18.515 18.548 18.555 18.561 18.568 18.574 18.581 18.613 18.62.0 18.626 18.633 18.639 18.646
46.0 47.0 48.0 49.0 5.0.0
18.678 18.684 18.691 18.697 18.7.03 18.71.0 18.716 18.722 18.729 18.735 18.741 18.748 18.754 18.76.0 18.766 18.773 18.779 18.785 18.791 18.798 18.8.04 18.810 18.816 18.822 18.828 18.834 18.841 18.847 18.853 18.859 18.865 18.871 18.877 18.883 18.889 18.896 18.9.02 18.9.08 18.914 18.92.0 18.926 18.932 18.938 18.944 18.95.0 18.956 18.962 18.968 18.974 18.979
17.132 17.142 17.228 17.237 17.321 17.33.0 17 .411 17.42.0 17.5.0.0 17.5.09
17.152 17.161 17.171 17.18.0 17.19.0 17.2.0.0 17.2.09 17.247 17.256 17.265 17.275 17.284 17.293 17.3.02 17.339 17.348 17.357 17.366 17.376 17.385 17.394 17.429 17.438 17.447 17.456 17.465 17.474 17.482 17.517 17.526 17.534 17.543 17.552 17.56.0.17.569 17.62.0 i7.628 17.637 17.7.03 17.711 17.72.0 17.785 17.793 17.8.01 17.864 17.872 17.88.0 17.942 17.95.0 17.958
17.645 17.653 17.728 17.736 17.8.09 17.817 17.888 17.896 17.966 17.973
18.386 18.393 18.4.0.0 18.4.07 18.455 18.461 18.468 18.475 18.522 18.528 18.535 18.541 18.587 18.594 18.6.0.0 18.6.07 18.652 18.659 17.665 18.671
4-289
VAPOR PRESSURE TABLE
4k-IO.
LIQUID EQUILIBRIUM HYDROGEN TEMPERATURES IN
VALUES OF VAPOR PRESSURE
K
FOR INTEGRAL
P,
IN MILLIMETERS OF MERCURY AT STANDARD GRAVITY, 980.665 CM/SEC 2 (Continued)
p
0
1
2
3
4
5
6
7
8
DoC
AND
9
- - - - - - - - - - - - - - - -- - -- - - --510 520 530 540 550
18.985 18.991 18.997 19.003 19.009 19.015 19.021 19.027 19.033 19.038 19.044 19.050 19.056 19.062 19.068 19.073 19.079 19.085 19.091 19.096 19.102 19.108 19.114 19.120 19.125 19.131 19.137 19.142 19.148 19.154 19.160 19.165 19.171 19.177 19.182 19.188 19.193 19.199 19.205 19.210 19.216 19.222 19.227 19.233 19.238 19.244 19.249 19.255 19.261 19.266
560 570 580 590 600
19.272 19.277 19.283 19.288 19.294 19.299 19.305 19.310 19.316 19.321 19.327 19.332 19.338 19.343 19.349 19.354 19.359 19.365 19.370 19.376 19.381 19.386 19.392 19.397 19.403 19.408 19.413 19.419 19.424 19.429 19.435 19.440 19.445 19.451 19.456 19.461 19.467 19.472 19.477 19.482 19.488 19.493 19.498 19.503 19.509 19.514 19.519 19.524 19.530 19.535
610 620 630 640 650
19.540 19.545 19.550 19.556 19.561 19.566 19.571 19.576 19.581 19.587 19.592 19.597 19.602 19.607 19.612 19.617 19.623 19.628 19.633 19.638 19.643 19.648 19.653 19.658 19.663 19.668 19.673 19.678 19.683 19.688 19.693 19.699 19.704 19.709 19.714 19.719 19.724 19.729 19.734 19.738 19.743 19.748 19.753 19.158 19.763 19.768 19.773 19.778 19.783 19.788
660 670 680 690 700
19.793 19.798 19.803 19.808 19.813 19.817 19.822 19.827 19.832 19.837 19.842 19.847 19.852 19.856 19.861 19.866 19.871 19.876 19.881 19.885 19.890 19.895 19.900 19.905 19.909 19.914 19.919 19.924 19.928 19.933 19.938 19.943 19.948 19.952 19.957 19.962 19.967 19.971 19.976 19.981 19.985 19.990 19.995 20.000 20.004 20.009 20.014 20.018 20.023 20.028
710 720 730 740 750
20.032 20.037 20.042 20.046 20.051 20.079 20.083 20.088 20.093 20.097 20.125 20.129 20.134 20.138 20.143 20.170 20.175 20.179 20.184 20.188 20.215 20.220 20.224 20.229 20.233
760 770 780 790 800
20.260 20.264 20.269 20.273 20.278 20.282 20.286 20.291 20.295 20.300 20.304 20.308 20.313 20.317 20.322 20.326 20.330 20.335 20.339 20.343 20.348 20.352 20.356 20.361 20.365 20.370 20.374 20.378 20.383 20.387 20.391 20.396 20.400 20.404 20.409 20.413 20.417 20.421 20.426 20.430 20.434 20.438 20.443 20.447 20.451 20.456 20.460 20.464 20.468 20.473
810 820 830 840 850
20.477 20.481 20.485 20.490 20.494 20.498 20.502 20.506 20.511 20.515 20.519 20.523 20.527 20.532 20.536 20.540 20.544 20.548 20.553 20.557 20.561 20.565 20.569 20.573 20.578 20.582 20.586 20.590 20.594 20.598 20.602 20.607 20.611 20.615 20.619 20.623 20.627 20.631 20.635 20.640 20.644 20.648 20.652 20.656 20.660 20.664 20.668 20.672 20.676 20.680
860 20.684 20.688 20.693 20.696 870 20.725 20.729 20.733 20.737 880 20.765 20.769 20.773 20.777 890 20.805 20.809 20.813 20.817 900 20.844 20.848 20.852 20.856
20.056 20.060 20.102 20.106 20.147 20.152 20.193 20.197 20.238 20.242
20.065 20.069 20.074 20.111 20.116 20.120 20.157 20.161 20.166 20.202 20.206 20.211 20.246 20.251 20.255
20.701 20.705 20.709 20.713 20.717 20.721 20.741 20.745 20.749 20.753 20.757 20.761 20.781 20.785 20.789 20.793 20.797 20.801 20.821 20.825 20.829 20.832 20.836 20.840 20.860 20.864 20.868 20.872 20.876 20.880
910 920 930 940 950
20.884 20.887 20.891 20.895 20.899 20.903 20.907 20.911 20.915 20.918 20.922 20.926 20.930 20.934 20.938 20.942 20.945 20.949 20.953 20.957 20.961 20.965 20.969 20.972 20.976 20.980 20.984 20.988 20.992 20.995 20.999 21.003 21.007 21.011 21.014 21.018 21.022 21.026 21.030 21.033 21.037 21.041 21.045 21.049 21.052 21.056 21.060 21.064 21.067 21.071
960 970 980 990
21. 075 21.079 21.082 21.086 21.090 21.094 21.097 21.101 21.105 21.109 21.112 21.116 21.120 21.124 21.127 21.131 21.135 21.138 21.142 21.146 21.149 21.153 21.157 21.160 21.164 21.168 21.172 21.175 21.179 21.183 21.186 21.190 21.194 21.197 21.201 21.205 21.208 21.212 21.216 21.219
4-290 TABLE
HEAT
4k-U.
LIQUID NORMALliYDROGEN TEMPERATURES IN
VALUES, OF VAPOR PRESSURE
P,
AND STANDARD GRAVITY,
p
0
1
2
3
K
FOR INTEGRAL
IN MILLIMETERS OF MERCURY AT
4
980.665 5
O°C
CM/SEC 2
6
7
- - - -'-- - - - - - - - - -- -- -
8
9
---
13.944 13.976 14.007 14.038 14.068 14.099 50 60 14.128 14.157 14.186 14.215 14.243 14.271 14.299 14.326 14.353 14.379 70 14.406 14.432 14.458 14.483 14.508 14.533 14.558 14.582 14.607 14.631 80 14.654 14.678 14.701 14.724 14.747 14.770 14.792 14.815 14.837 14.859 90 14.880 14.902 14.923 14.944 14.965 14.986 15.007 15.027 15.048 15.068 100 15.088 15.108 15.127 15.147 15.166 15.186 15.205 15.224 15.243 15.261 15.298 15.317 15.335 15.353 15.371 15.389 15.477 15.494 15.511 15.528 15.545 15.562 15.644 15.660 15 .. 676 15.692 15.708 15.724 15.802 15.817 15.833 15.848 .15.863 15.878 15.952 15.966 15.981 15.995 16.010 16.024
15.407 15.578 15.740 15.893 16.038
15.424 15.442 15.595 15.611 15.756 15.771 15.908 15.923 16.052 16.066
110 120 130 140 150
15.280 15.459 15.628 15.787 15.937
160 170 180 190 200
16.081 16.094 16.108 16.122 16.136 16.150 16.163 16.177 16.190 16.204 16.217 16.230 16.244 16.257 16.270 16.283 16.296 16.309 16:322 16.335 16.348 16.361 16.373 16.386 16.399 16.411 16.424 16.436 16.449 16.461 16.473 16.486 16.498 16.510 16.522 16.534 16.546 16.558 16.570 16.582 16.594 16.606 16.617 16.629 16.641 16.652 16.664 16.676 16.687 16.698
210 220 230 240 250
16.710 16.721 16.822 16.833 16.930 16.941 17.035 17..046 17.137 17.147
260 270 280 290 300
17.236 17.245 19'.255 17.265 17.332 17.341 17.351 17.360 17.425 17.434 17.443 17.453 17.516 17.525 17.534 17.543 17.605 17 oJ3 17.622 17.631
17.275 17.284 17.294 17.303 17.313 17.322 17.369 17.379 17,388 17.397 17.407 17.416 17.462 17.471 17.480 17 .489 17 .498 17.507 17.552 17.561 17.570 17.578 17.587 17.596 17.639 17.648 17.657 17.66617.674 17.683
310 320 330 340 350
17.691 17.700 17.776 17 .. 784 17.858 17.866 17.939 17.947 18.018 18.026
17.725 17.809 17.891 17.971 '1.8.049
16.733 16.744 16.755 16.766 16.778 16.844 16.855 16.866 16.877 16.887 16.952 16.962 16.973 16.983 16.994 17.056 17.066 17.076 17.087 17.097 17.157 17.167 17.177 17.187 17.197
17.708 17.717 17.792 17.801 17.875 17.883 17.955 17.963 18.034 18.041
360 18.095 18.103 18.111 18.118 370 18.171 18.179 18.186 18.193 380 18.245 18.253 18.260 18.267 390 ·18.318 18.326 18.333 18.340 400 18.390 18.397 18.404 18.411
16.789 16.800 16.811 16.898 16.. 909 16.. 920 17.004 17.015 17.025 17.107 17.117 17.127 17.206 17.216 17.226
17.734 17.742 17.751 17.759 17.767 17.817 17.825 17;.834 17.842 17.850 17.899 17.907 17.915 17.923 17.931 17.979 17.987 17.994 18.·002 18.oio 18.057 18.064 18.072 18.080 18.088
18.126 18.133 18.141 18.201 18.208 18.216 18.275 18.282 18.289 18.347 18.354 18.361 18.418 18.425 18.432
18.148 18.156. 18.163 18.223 18.231 18.238 18.297 18.304 18.311 18.368 18.376 18.383 18.439 18.446 18.453
410 420 430 440 450
18.460 18.467 18.474 18.481 1.8.488 18.495 18.502 18.508 18.515 18.522 18 .. 529 18.536 18.543 18.549 18.556 18.563 18.570 18.577 18.583 18.590 18.597 18.604 18.610 18.617 18.624 18.630 18.637 18.644 18.650 18.657 18.663 18.670 18.677 18.683 18.690 18.696 18.703 18.709 18.716 18.722 18.729 18.735 18.742 18.748 18.755 18.761 18.768 18.774 18.781 18.787
460 470 480 490 500
18.794 18.800 18.806 18.813 18.819 18.825 18.832 18.838 18.844 18.851 18.857 18.863 18.870 18.876 18.882 18.888 18.895 18.901 18.907 18.913 18.919 18.926 18.932 18.938 18.944 18.950 18.957 18.963 18.969 18.975 18.981 18.987 18.993 18.999 19.005 19.011 19.018 19.024 19.030 19.036 19.042 19.048 19.054 19.060 19.066 19.072 19.078 19.084 19.090 19.095
~291
VAPOR PRESSURE TABLE
4k:-l1.
LIQUID NORMAL HYDROGEN TEMPERATURES IN
VALUES OF VAPOR PRESSURE
P,
AND STANDARD GRAVITY,
P
--
0.
1
2
FOR INTEGRAL
IN MILLIMETERS OF MERCURY AT 980.665 CM/SEC 2 (Continued)
4
3
K
------- - - -- -
5
6
7
O°C
8
9
- -- - - - - - - ---
510. 520. 530. 540 550.
19.10.2 19.10.7 19.113 19.119 19.125 19.131 19.137 19.143 19.149 19.154 19.160. 19.166 19.172 19.178 19.184 19.190. 19.195 19.20.1 19.20.7 19.213 19.219 19.224 19.230. 19.236 19.242 19.247 19.253 19.259 19.264 19.270. 19.276 19.282 19.287 19.293 19.299 19.30.4 19.310. 19.316 19:321 19.327 19.332 19.338 19.344 19.349 19.355 19.360. 19.366 19.371 19.377 19.383
560. 570. 580. 590. 60.0.
1'9.388 19.394 19.399 19.40.5 19.410. 19.416 19.421 19.427 19.432 19.438 19.443 19.449 19.454 19.460. 19.465 19.471 19.476 19.482 19.487 19.492 19.498 19.50.3 19.50.9 19.514 19.519 19.525 19.530. 19.535 19.541 19.546 19.551 19.557 19.562 19.567 19.573 19.578 19.583 19.589 19.594 19.599 19.60.4 19.610. 19.615 19.620. 19.626 19.631 19.636 19.641 19.646 19.652
610. 620. 630. 640. 650.
19.657 19.662 19.667 19.673 19.678 19.683 19.688 19.693 19.698 19.70.4 19.70.9 19.714 19.719 19.724 19.729 19.734 19.740. 19.745 19.750. 19.755 19.760. 19.765 19.770. 19.775 19.780. 19.785 19.790. 19.795 19.80.1 19.80.6 19.811 19.816 19.821 19.826 19.831 19.836 19.841 19.846 19.851 19.856 19.861 19.866 19.871 19.876 19.880. 19.885 19.890. 19.895 19.90.0. 19.90.5
660. 670. 680. 690. 70.0.
19.910. 19.915 19.920. 19.925 19.930. 19.935 19.940. 19.944 19.949 19.954 19.959 19.964 19.969 19.974 19.979 19.983 19.988 19.993 19.998 20..0.0.3 20..0.0.8 20..0.12 20..0.17 20..0.22 20..0.27 20..0.32 20..0.36 20..0.41 20..0.46 20..0.51 20..0.55 20..0.60. 20..0.65 20..0.70. 20..0.75 20..0.79 20..0.84 20..0.89 20..0.93 20..0.98 20..10.3 20..10.8 20..112 20..117 20..122 20..126 20..131 20..136 20..140. 20..145
710. 720. 730. 740. 750.
20..150. 20..155 20..159 20. .164 20. .168 20..173 20..178 20. .182 20..187 20. .192 20. .196 20..20.1 20..20.6 20..210. 20..215 20..219 20..224 20..229 20..233 20..238 20..242 20..247 20..252 20..256 20..261 20..265 20..270. 20..274 20..279 20..283 20..288 20..292 20..297 20..30.1 20..30.6 20..310. 20..315 20..320. 20..324 20..329 20..333 20..337 20..342 20..346 20..351 20..355 20..360. 20..364 20..369 20..373
760. 20..378 20..382 20..387 20..391 20..395 20..40.0. 20..40.4 20..40.9 20..413 20..418 770. 20..422 20..426 20..431 20..435 20..440. 20..444 20..448 20..453 20..457 20..461 780. 20..466 20. .470. 20..474 20. .479 20..483 20..488 20..492 20..496 20..50.1 20..50.5 790. 20..50.9 20..514 20..518 20..522 20..527 20..531 20..535 20..539 20..544 20..548 80.0. 20..552 20..557 20..561 20..565 20..569 20..574 20..578 20..582 20..586 20..591 810. 820. 830. 840. 850.
20..595 20..599 20..60.3 20..60.8 20..612 20..616 20..620. 20..625 20..629 20..633 20..637 20..642 20..646 20..650. 20..654 20..658 20..663 20..667 20..671 20..675 20..679 20..683 20..688 20..692 20..696 20..70.0. 20..70.4 20..70.8 20..712 20..717 20..721 20..725 20..729 20..733 20..737 20..741 20..745 20..750. 20..754 20..758 20..762 20..766 20..770. 20..774 20..778 20..782 20..787 20..791 20..795 20..799
860. 870. 880. 890. 90.0.
20..80.3 20..80.7 20..843 20..847 20..884 20..888 20..923 20..927 20. .. 963 20..967
910 920. 930. 940. 950.
21.0.0.2 21.0.0.6 21. DID 21.014 21.0.18 21.0.22 21.0.26 21.0.29 21.0.33 '21.0.37 21.0.41 21.0.45 21.0.49 21.0.53 21.0.57 21.0.60. 21.0.64 21.0.68 21.0.72 21.0.76 21.0.80. 21.0.84 21.0.87 21.0.91 21.0.95 21.0.99 21.10.3 '21.10.7 21.110. 21.114 21.118 21.122 21:126 21.129 21.133 21.137 21.141 21.145 21.149 21.152 21.156 21.160. 21.164 21.167 21.171 2~.175 21.179 21.182 21.186 21.190.
960. 970. 980. 990.
21.194 21.198 21: 20.1 21.20.5 21.20.9 21.213 21.216 21.220. 21.224 21.227 21. 231 21.235 21.239 21.242 21.246 21.250. 21.254 21.257 21. 261 21.265 21.268 21.272 21.276 21.280. 21.283 21.287 21.291 21.294 21.298 21.30.2 21.30.5 21.30.9 21.313 21.316 21:320. 21.'324 21.327 21.331 21.335 21.338
20..811 20..851 20..891 20..931 20..971
20..815 20..819 20..823 20..827 20..831 20..835 20..839 20..855 20..859 20..863 20..867 20. .. 871 20..875 20..880. 20..895 20..90.0. 20..90.4 20..90.8 20..911 20..915 20..919 20..935 20..939 20..943 20..947 20..951 20..955 20..959 20..975 20..979 20..983 20..986 20..990. 20..994 20..998
,
,.,.
."
4-;--292. TABLE
HEAT
4k-12.
LIQUID NEON TEMPERATURES IN
VAPOR PRESSURE
P,
GRAVITY,
p
0
1
2
- -1 _ 320 330 340 350
K
FOR INTEGRAL VALUES OF·
O°C
IN MILLIMETERS OF MERCURY AT
3
980.665 4
AND STANDARD
CM/SEC'
5
6
7
8
9
- -- -- -- -- -
--
Ii
24.554 24.562 24.570 24.578 24.586 24.602 24.610 24.618 24.626 24.634 24.642 24.650 24.657 24.665 24.681 24.689 24.696 24.704 24.712 24.719 24.727 24.735 24.742 24.758 24.765 24.773 24.780 24.788 24.796 24.803 24.811 24.818 .
24.594 24.673 24.750 24.825
360 370 380 390 400
24.833 24.907 24.979 25.050 25.120
24.840 24.914 24.986 25.057 25.127
24.848 24.855 24.863 24.870 24.877 24.921 24.929 24.936 24.943 24.950 24.993 25.001 25.008 25.015 25.022 25.064 25.071 25.078 25.085 25.092 25.134 25.140 25.147 25.154 25.161
24.885 24.958 25.029 25.099 25.168
410 420 430 440 450
25.188 25.255 25.322 25.387 25.451
25.195 25.262 25.328 25.393 25.457
25.202 25.269 25.335 25.399 25.463
25.208 25.215 25.275 25.282 25.341 25.348 25.406 25.412 25.470 25.476
25.235 25.242 25.249 25.302 25.308 25.315 25.367 25.374 25.380 25.431 25.438 25.444 25.495 25.501 25.507
460 470. 480 490 500
25.514 25.520 25.576 25.582 25.637 25.643 25.697 25.703 25.756 25.762
25.526 25.588 25.649 25.709 25.768
25.532 25.538 25.545 25.594 25.600 25.606 25.655 25.661 25.667 25.715 25.721 25.727 25.774 25.780 25.786
510 520 530 540 550
25.815 25.820 25.872 25.878 25.929 25.935 25.985 25.991 26.041 26.046
25.826 25.832 25.884 25.890 25.941 25.946 25.997 26.002 26.052 26.057
25.838 25.844 25.849 25.855 25.895 25.901 25.907 25.912 25.952 25.957 25.963 25.969 26.008 26.013 26.019 26.024 26.063 26.068 26.074 26.079
25.861 25.918 25.974 26.030 26.085
25.867 25.924 25.980 26.035 26.090
56U 570 580 590 600
26.0\J6 26.101 26.150 26.155 26.203 26.209 26.256 26.261 26.308 26.313
26.107 26.112 26.117 26.123 26.128 26.134 26.161 26.166 26.171 26.177 26.182 26.187 26.214 26.219 26.224 26.230 26.235 26.240 26.267 26.272 26.277 26.282 26.287 26.293 26.319 26.324 26.329 26.334 26.339 26.344
26.13\J 26.193 26.246 26.298 26.350
26.144 26.198 26.251 26.303 26.355
610 620 630 640 650
26.360 26.365 26.370 26.375 26.380 26.385 26.391 26.396 26.401 26.411 26.416 26.421 26.426 26.431 26.436 26.441 26.446 26.451 26.461 26.466 26.471 26.476 26.481 26.486 26.491 26.496 26.501 26.511 26.516 26.521 26.526 26.531 26.536 26.541 26.546 26.551 26.561 26.566 26.570 26.575 26.580 26.585 26.590 26.595 26.600
26.406 26.456 26.506 26.556 26.605
660 670 680 690 700
26.609 26.614 26.619 26.658 26.663 26.667 26.706 26.710 26.715 26.753 26.758 26.763 26.800 26.805 26.809
26.624 26.629 26.672 26.677 26.720 26.725 26.767 26.772 26.814 26.819
26.634 26.682 26.729 26.777 26.823
26.639 26.643 26.687 26.691 26.734 26.739 26.781 26.786 26.828 26.833
26.648 26.696 26.744 26.791 26.837
26.653 26.701 26.748 26.795 26.842
710 720 730 740 750
26.847 26.893 26.938 26.983 27.028
26.860 26.906 26.952 26.997 27.042
26.870 26.915 26.961 27.006 27.050
26.874 26.920 26.965 27.010 27.055
26.883 26.929 26.974 27.019 27.064
26.888 26.934 26.979 27.024 27.068
760 770 780 790 800
27.073 27.077 27.117 27.121 27.160 27.165 27.203 27.208 27 .. 246 27.251
26.851 26.897 26.943 26.988 27.033
26.856 26.902 26.947 26.992 27.037
27.081 27.086 27.125 27.130 27.169 27.173 27.212 27.216 27.255 27 .. 259
26.865 26.911 26.956 27.001 27.046
25.222 25.229 25.289 25.295 25.354 25.361 25.419 25.425 25.482 25.488
25.551 25.557 25.612 25.618 25.673 25.679 25.733 25.738 25.791 25.797
27.090 27.095 27.099 27.134 27.138 27.143 27.178 27.182 27.186 27.221 27.225 27.229 27.263 27.268 27.272
26.879 26.925 26.970 27.015 27.059
24.892 24.899 24.965 24.972 25.036 25.043 25.106 25.113 25.175 25.181
25.563 25.569 25.624 25,631 25.685 25,691 25.744 25.750 25.803 25.809
27.103 27.108 27.112 27.147 27.151 27.156 27.191 27.195 27.199 27.234 27.238 27.242 27.276 27.280 27.285
4--2!}3
VAPOR PRESSURE
TKBLE 4k~12. 'LIQUID NEON TEMPERATURES IN KFOR INTEGRAL VALUES -OF VAPOR PRESSURE :P, 'IN MILLIMETERS OF MERCURY AT O°C AND STANDARD GRAVITY, 980.665 CM/SEC 2 (Continued) p
0
1
2
3
4
5
6
7
'8
9
- - - - - - - - - - - - - --- - - - - - - - - - --810 820 830 840 850
27.289 27.293 27.297 27.302 27.306 27.310 27.314 27.318 27.323 27.327 27.331 27.335 27.339 27.344 27.348 27.352 27.356 27.360 27.365 27.369 27.373 27.377 27.381 27.385 27.390 27.394 27.398 27.402 27.406 27.410 27.414 27.419 27.423 27.427 27.431 27.435 27.439 27.443 27 ;447 27.452 27.456 27.460 27.464 27.468 27.472 27.476 27.480 27.484 27.488 27.492
860 870 880 890 900
27.497 27.501 27.505 27.509 27.513 27.517 27.521 27.525 27.529 27.533 27.537 27.541 27.545 27.549 27.553 27.557 27.561 27.565 27.569 27.573 27.577 27.581 27.585 27.589 27.593 27.597 27.601 27.605 27.609 27.613 27.617 27.621 27.625 27.629 27.633 27.637 27.641 27.645 27.649 27.653 27.657 27.661 27.665 27.669 27.673 27.677 27.681 27.685 27.689 27.692
910 920 930 940 '950
27.696 27.700 27.704 27.708 27.712 27.716 27.720 27.724 27.728 27.732 27.735 27.739 27.743 27.747 27.751 27.755 27.759 27.763 27.767 27.770 27.774 27.778 27.782 27.786 27.790 27.794 27.798 27.801 27.805 27.809 27.813 27.817 27.821 27.824 27.828 27.832 27.836 27.840 27.844 27.847 27.851 27.855 27.859 27.863 27.866 27.870 27.874 27.878 27.882 27.885
'960 27.889 27.893 27.897 27.901 27.904 27.908 27.912 27.916 27.919 27~923 970 27.927 27.931 27.935 27.938 27.942 27.946 27.950 27.953 27.957 27.961 980 27.965 27.968 27.972 27.976 27.980 27.983 27:987 27.99'1 27.994 27.998
Table 4k-13 gives the temperature in kelvins 'for integral values of vapor pressure in millimeters of mercury at O°C and standard gravity, 980.665 cm/sec 2• The following interpolation equation has been derived for oxygen by a least-squares fit of the vapor-pressure data of Hoge l log P (mm) = 8.01602 - 415;909 - 0.0058382T the equation being valid for the region from the triple point (54.363 K) to 90.827 K. Table 4k-14 gives the temperature in kelvins for integral values of vapor pressure P, in millimeters of mercury at O°C and standard gravity, 980.665 cm/sec 2• I
H. J. Hoge, J. Research NBS 44, 326 (1950).
4-294
HEAT
TABLE
4k-13.
LIQUID NITROGEN TEMPERATURES IN
OF VAPOR PRESSURE
P,
IIlTANDARD GRAVITY,
p
0
1
2
K
FOR INTEGRAL VALUES
IN MILLIMETERS OF MERCURY AT
3
- - - -I----- - -
980.665
4 -~~-
0°0
AND
CM/SEC'
5
6
7
8
9
- -- - - - - - - -
90 100 110 120 130 140 150
63.500 64.029 64.520 64.980 65.412 65.820
63.555 64.080 64.568 65.024 65.453 65.859
63.609 64.130 64.615 65.068 65.495 65.899
63.663 64.180 64.661 65.112 65.536 65.938
63.162 63.717 64.230 64.708 65.156 65.578 65.977
63.220 63.277 63.770 63.822 64.279 64.328 64.754 64.799 65.199 65.242 65.618 65.659 66.015 66.054
63.333 63.875 64.376 64.845 65.285 65.700 66.092
63.389 63.926 64.425 64.890 65.327 65.740 66.131
63.445 63.978 64.473 64.935 65.370 65.780 66.169
160 170 180 190 200
66.206 66.244 66.574 66.610 66.925 66.960 67.261 67.294 67.583 67.615
66.281 66.646 66.994 67.327 67.646
66.319 66.681 67.028 67.359 67.677
66.356 66.717 67.061 67.392 67.709
66.393 66.429 66.752 66.787 67.095 67.129 67.424 67.456 67.740 67.771
66.466 66.822 67.162 67.488 67.801
66.502 66.856 67.195 67.520 67.832
66'.538 66.891 67.228 67.552 67.862
210 220 230 240 250
67.893 67.923 67.953 68.191 68.220 68.249 68.479 68.507 68.535 68.757 68.784 68.811 6.9 .025 69.052 69.078
67.984 68.013 68.278 68.307 68.563 68.591 68.838 68.865 69.104 69.131
68.043 68.336 68.619 68.892 69.157
68.073 68.365 68.647 68.919 69.183
68.103 68.393 68.674 68.946 69.209
68.132 68.422 68.702 68.972 69.235
68.162 68.450 68.729 68.999 69.260
69.337 69.588 69.833 70.070 70.301
69.363 69.388 69.613 69.638 69.857 69.881 70.093 70.117 70.324 70.347
69.413 69.439 69.662 69.687 69.904 69.928 70.140 70.163 70.369 70.392
69.464 69.489 69.711 69.736 69:952 69.976 70.186 70.209 70.414 70.437
69.514 69.760 69:999 70.232 70.459
70.593 70.811 71.024 71.232 71.435
70.637 70.659 70.854 70.875 71.066 71.086 71. 273 71.293 71.475 71.495
70.681 70.897 71.107 71.313 71.515
.260 270 280 290 300
69.286 69.312 69.539 69.564 69.784 69.808 70.023 70.047 70.255 70.278
310 320 330 340 350
70.482 70.504 70.526 70.549 70.702 70.724 70.746 70.768 70.918 70.939 70.960 70.981 71.128 71.149 71.170 71.190 71.334 71.354 71.374 71.394
70.571 70.789 71.003 71.211 71.415
360 370 380 390 400
71.535 71.555 71.731 71.751 71.924 71.943 72.113 72.131 72,298 72.316
71. 574 71.594 71.770 71.790 71.962 71.981 72.150 72.169 72.334 72.353
71.614 71.634 71.653 71.673 71.809 71.828 71.847 71.867 72.000 72.019 72.038 72.057 72.187 72.206 72.224 72.243 72.371 72.389 72.407 72.425
410 420 430 440 450
72.479 72.497 72.657 72.675 72.832 72.849 73.004 73.021 73 .172 73.189
72.515 72.692 72.867 73.038 73.206
460 470 480 490 500
73.338 73.354 73.371 73.501 73.517 73.533 73.661 73.677 73.693 73.819 73.835 73.850 73.975 73.990 74.005
73.387 73.549 73.709 73.866 74.021
510 520 530 540 550
74.127 74.278 74.427 74.573 74.717
74.173 74.188 74.323 74.338 74.471 74.485 74.616 74.631 74.760 74.774
74.143 74.293 74.441 74.587 74.731
74.158 74.308 74.456 74.602 74.746
70.615 70.832 71.045 71.252 71.455
71.692 71.886 72.075 72.261 72.443
71.712 71.905 72.094 72.279 72.461 72.640 72.815 72.987 73.156 73.322
72.533 72.551 72.710 72.728 72.884 72.901 73.055 73.071 73.222 73.239
72.569 72.745 72.918 73.088 73.256
72.586 72.762 72.935 73.105 73.272
72.604 72.780 72.952 73.122 73.289
72.622 72.797 72.970 73.139 73.305
73.404 73.566 73.725 73.882 74.036
73.420 73.582 73.741 73.897 74.051
73.436 73.598 73.756 73.913 74.067
73.452 73.614 73.772 73.928 74.082
73.469 73.485 73.630 73.646 73.788 73.804 73.944 73.959 74.097 74.112
74.203 74.218 74.353 74.367 74.500 74.515 74.645 74.660 74.788 74.803
74.233 74.382 74.529 74.674 74.817
74.248 74.263 74.397 74.412 74.544 74.558 74.688 74.703 74.831 74.845
1
4"':"295
VAPOR PRESSURE TABLE
4k-13~
LiQUID NITROGEN TEMPERATURES IN
OF VAPOR PRESSURE
K
FOR
INTE~RAL
VALUES
P,
IN MILLIMETERS OF MERCURY' ATooQ AND S'rANDARD GRAVITY, 980.665 CM/SEC 2 (Continued)
p
0
1
2
3
4
5
6
I
7
8
9
- ----- - - - - - - -- - - -- - - - - ;560 570 580 590 600
74.859 74.873 74.888 74.902 74.916 74.930 74.944 74.958 74.972 74.986 75.000 75.014 75.027 75.041 75.055 75.069 75.083 75.097 75 .. 111 75.124 75.138 75.152 75.165 75.179 75.193 75.207 75.220 75.234 75.247 75.261 75.275 .75.288 75.302 75.315 75.329 75.342 75.356 75.369 75 .. 383 75.396 75.409 75.423 75.436 75.450 75.463 75.476 75.490 75.503 75.516 75.529
610 620 630 640 u50
75.543 75.556 75.569 75.582 75.595 75.609 75.622 75.635 75.648 75.661 75.674 75.687 75.700 75.713 75.726 75.739 75 . 752 75.765 75:778 75,791 75.804 75.817 75.830 7:5.843 75.855 75.868 75.881 75.894 75.907 75.919 75.932 75.945 75.958 75.970 75.983 75.996 76.008 76.021 76.034 76.046 76.059 76.671 76.084 76.097 76.109 76.122 76.134 76.147 76.159 76.172
660 670 680 690 700
76.184 76.197 76 .. 209 76.221 76.234 76.246 76.259 76.271 76.283 76.296 76:308 76.320 76.333 76.345 76:357 76.369 76.382 76.394 76.406 76.418 76.430 76.443 76.455 76.467 76.479 76.491 76.503 76.515 76.527 76.539 76.551 76.564 76.576 76.588 76.600 76.612 76.623 76.635 76.647 76.659 76.671 76.683 76.695 76.707 76.719 .76.731 76.742 76.754 76.766 76.778
710 720 730 740 750 760
76.790 76.801 76.813 76.825 76.837 76.848 76.860 76.872 76.883 76.895 76,907 76.918 76:930 76.942 76.953 76 ..965 76.977 76.988 77.000 77.011 77.023 77.034 77.046 77.057 77.069 77;080 77.092 77.103 77.115 77.126 77.137 77.149 77.160 77.172 77.183 77.194 77.206 77.'217 77.228 77.240 77.251 77.262 77 .. 274 77.285 77.. 296 77.307 77.319 77.330 77 .. 341 77.352 77.363 7i7~375 77.386 77.397 77 .408 77.419 77:430 77.441 77 :453 77.464
,.-,.:-
HEAT
4-296 TABLE
4k-14.
LIQUID OXYGEN TEMPERATURES IN
OF VAPOR PRESSURE
P,
STANDARD GRAVITY,
p
0
1
2
K
FOR INTEGRAL VALUES
IN MILLIMETERS OF MERCURY AT
3
4
980.665 5
ooe
AND
CM/SEC'
6
7
8
9
- - - - - - - - - - - - - - - -- - - - - 53.980 56.278 57.719 58.790 59.650 60.373 0 10 62.499 62.913 63.297 73.654 63.989 64.303 64.601 20 65.652 65.887 66.112 66.329 66.539 66.741 66.936 30 67.659 67.827 67.991 68.150 68.305 68.457 68.605 40 69.164 69.297 69.427 69.554 69.679 69.802 69.922 50 70.383 70.493 70.601 70.708 70.813 70.917 71.019 60 70 80 90 100
71.413 71.508 72.309 72.393 73 .106 73.181 73.821 73.893 74.480 74.543
71.601 72.476 73.255 73.960 74.605
71.694 71.785 71. 875 71.964 72.558 72.639 72.719 72.798 73.329 73.402 73.474 73.545 74.027 74.094 74.159 74.225 74.667 74.728 74.788 74.849
110 75.085 75.143 75.200 75.257 120 75.646 75.700 75.753 75.807 130 76.170 76.221 76.271 76.321 140 76.663 76.710 76.758 76.805 150 77.127 77 .172 77.217 77.262
61. 551 65.151 67.308 68.891 70.156 71.219
62.048 65.407 67.486 69;029 70.270 71.316
72.052 72.139 72.876 72.953 73.616 73.686 74.289 74.354 74.908 74.968
72.225 73.030 73.756 74.417 75.026
60.998 64.883 67.125 68.749 70.040 71.120
75.314 75.370 75.426 75.860 75.912 75.964 76.371 76.420 76.469 76.852 76.898 76.945 17.306 17.350 77.394
75.482 76.016 76.518 76.991 77.438
75.537 76.068 76.566 77.036 77 .481
75.591 76.119 76.615 77.082 77.525
77.821 78.228 78.617 78.989 79.346
77.863 78.268 78.655 79.025 79.381
77.904 78.307 78.693 79.062 79.416
77.945 78.347 78.730 79.098 79.451
77.738 77.780 78.148 78.188 78.540 78.579 78.916 78.953 79.276 79.311
160 170 180 190 200
77.568 77.611 77.653 77.695 77.986 78.027 78.068 78.108 78.386 78.425 78.463 78.502 78.768 78.805 78.842 78.879 79.134 79.169 79.205 79.241
210 220 230 240 250
79.485 79.520 79.554 79.588 79.622 79.656 79.690 7'9.724 7'9.757 79.791 79.824 79.857 79.890 79.923 79.956 79.989 80.021 80.054 80.086 80.118 80.150 80.182 80.214 80.246 80.278 80.309 80.341 80.372 80.403 80.435 80.466 80.497 80.527 80.558 80.589 80.619 80.650 80.680 80.710 80.741 80.771 80.801 80.831 80.860 80.890 80.920 80.949 80.979 81. 008 81. 037
260 270 280 290 300
81. 066 81. 095 81.124 81.153 81.182 81. 211 81. 239 81. 268 81. 296 81. 324 81.353 81. 381 81.409 81.437 81. 465 81. 493 81.521 81.548 81.576 81. 604 81. 631 81. 658 81. 686 81.713 81. 740 81.767 81.794 81. 821 81.848 81. 875 81. 902 81. 928 81. 955 81.981 82.008 82.034 82.060 82.087 82.113 82.139 82.165 82.191 82.217 82.242 82.268 82.294 82.319 82.345 82.370 82.396
310 320 330 340 350
82.421 82.446 82.472 82.497 82.522 82.547 82.572 82.597 82.622 82.646 82.671 82.696 82.720 82.745 82.769 82.794 82.818 82.842 82.867 82.891 82.915 82.939 82.963 82.987 83.011 83.035 83.058 83.082 83.106 83.129 83.153 83.177 83.200 83.223 83.247 83.270 83.293 83.316 83.340 83.363 83.386 83.409 83.432 83.454 83.477 83.500 83.523 83.545 83.568 83.591
360 370 380 390 400
83.613 83.636 83.658 83.680 83.703 83.725 83.747 83.769 83.792 83.814 83.836 83.858 83.880 83.902 83.923 83.945 83.967 83.989 84.010 84.032 84.054 84.075 84.097 84.118 84.139 84.161 84.182 84.203 84.225 84.246 84.267 84.288 84.309 84.330 84.351 84.372 84.393 84.414 84.435 84.455 84.476 84.497 84.518 84.538 84.559 84.579 84.600 84.620 84.641 84.661
4-297
VAPOR PRESSURE TABLE
4k-14., LIQUID
OXYGEN TEMPERATURES, IN
OF VAPOR PRESSURE
P,
K
FOR INTEGRAL VALUES
IN MILLIMETERS OF MERCURY ATO°C AND
STANDARD GRAVITY, 9~O.665 CM/SEC 2
(Continued)
-
P
0.
1
2
3 '"
4
5
6
7
8
9
- - - - - -- - - - - -- -- - - - - - - 410. 420. 430. 440. 450.
84.681 84.70.2 84.722 84.742 84.762 84.783 84.803 84.823 8:4.843 84.863 84.883 84.903 84.922 84.942 84.962 84.982 85.002 85.021 8,'i.041 85.0.6~ 85.0.80 85.10.0. 85.119 85.139 85.158 85.178 85.197 85.216 85.236 85.255 85.274 85.293 85.313 85.332 85.351 85.370. 85.389 85.408 85.427 85.446 85.465 85.484 85.503 85.521 85.540 85.559 85.578 85.596 8,'i.615 85.634;
460 85.652 85.671 85.689 85.708 85.726 85.745 85.763 85.782 85.800 85.818 470. 85.836 85.855 85.873 85.891 85.90.9 85.927 85.946 85.964 85.982 86.000 480. 86.0.18 86.036 86.054 86.071 86.089 86.107 86.125 86.143 86.161 86.178 490. 86.196 86.214 86.231 86.249 86.266 86.284 86.302 86.319 86.337 86.354 500 86.371 86.389 86.406 86.424 86.441 86.458 86.475 86.493 86.510 86.527 510 520 530 540. 550.
86.544 86.561 86.578 86.596 86.613 86.630 86.647 86.664 86.681 86.697 86.714 86.731 86.748 86.765 86.782 86.799 86.815 86.832 86.849 86.865 86.882 86.899 86.915 86.932 86.948 86.965 86.981 86.998 87.014 87.031 87.0.47 87.064 87.080. 87.0.96 87.113 87.129 87.145 87.162 87.178 87.194 87.210 87.226 87.242 87.259 87.275 87.291 87.307 87.323 87.339 87.355
560. 570. 580 590 60.0.
87,.371 87.387 87.403 87.419 87.434 87.450 87.466 87.482 87.498 87.513 87.529 87.545 87.561 87.576 87.592 87.608 87.623 87.639 87.654 87.670 87.686 87.70.1 87.717 87.732 87.747 87.763 87.778 87.794 87.809 87.824 87.840. 87.855 87.870. 87.886 87.901 87.916 87.931 87.947 87.962 87.977 87.992 88.007 88.022 88.037 88.052 88.0.67 88.082 88.0.97 88.112 88.127
610 620 630 640 650.
88.142 88.157 88.172 88.187 88.202 88.217 88.232 88.246 88.261 88.276 88.291 88.306 88.320 88.335 88.350 88.364 88.379 88.394 88.40.8 88.423 88.437 88.452 88.466 88.481 88.496 88.510 88.524 88.539 88. 553 88.568 88.582 88.597 88.611 88.625 88.640 88.654 88.668 88.683 88.697 88.711 88.725 88.740 88.754 88.768 88,782 88.796 88.810 88.824 88.839 88.853
660 670 680 690 700
88.867 88.881 88.895 88.909 88.923 88.937 88.951 88.965 88.979 88.993 89.007 89.0.20 89.034 89.048 89.062 89.076 89.090 89.103 89.117 89.131 89.145 89.158 89.172 89.186 89.200 89.213 89.227 89.241 89.254 89.268 89.281 89.295 89.309 89.322 89.336 89.349 89.363 89.376 89.390 89.403 89.417 89.430 89.443 89.457 89.470 89.484 89.497 89.510 89·524 89.537
710 720 730 740 750
89.550 89.564 89.577 89.590 89.603 89.617 89.630 89.643 89.656 89.669 89.683 89.696 89.709 89.722 89.735 89.748 89.761 89.774 89.787 89.80.0 89.813 89.826 89.839 89.852 89.865 89.878 89.891 89.904 89.917 89.930 89.943 89.956 89.969 89.982 89.994 90.007 90..020 90.033 90..046 90.058 90.071 90.084 90.097 90.109 90.122 90.135 90.147 90.160 90..173 90.185
760 770 780 790 800 810
90.198 90.211 90.223 90.236 90.324 90.336 90.349 90.361 90.448 90.460 90.473 90..485 90.571 90.584 90.596 90.608 90.693 90.70.5 90.718 90.730 90.814 90..826 90.838 90..850
90.248 90.261 90.274 90.286 90.374 90.386 90.398 90.411 90.497 90.510 90.522 90.534 90.620 90.632 90.645 90.657 90.742 90.754 90.766 90.778 90.862 90.874 90.886 90.898
90.299 90.311 90.423 1l0.436 90.547 90.559 90.669 90.681, 90.790 90.802 90.910 90.922
TABLE
Pressure, atm ..........
10-10
I
10-'
I
10'"
I
4k-15. 10-7
I
10-'
I
10-6
I
10-'
Element
Actinium Ac ............ (1025)0 Aluminum A!. .......... 744 Americium Am ........ . , 625 308 Antimony Sb ............ Argon Ar ............... -245 123 Arsenic As, , ............ Astatine At ............ : -10 Barium Ba .............. 360 Beryllium Be ........... 747 366 Bismuth Bi ............. Beron B ............... 1450 Bromine Br ........... _. -139 Cadmium Cd ............ 91 314 Calcium Ca ............. Carbon C ............... 1750 Cerium Ce ............. ~ 1091 Cesium Cs .. ........... " 0 Chlorine C1.. ........... .... 184 902 Chromium Cr ........... Cobalt Co ............. , 995 774 Copper Cu ............. : Dysprosium Dy ......... 667 757 Erbium Er .............. 588 Europium Eu ..... , .... ~ Fluorine F .............. Francium Fa ............ -15 987 Gadolinium Gd ......... i 617 GalliumGa ............ : 851 Germanium Ge .......... 863 GoldAu ................ HafniumHf. ............ 1608 HeliumHe .............. 703 HolmiumHo ............ Hydrogen H ............ -269 533 Indium In .............. Iodine.!.. .............. -86
t
VAPOH PRESSURES OF THE CHEMICAL ELEMENTS
I
10-'
I
10'"
I
10-1
I
1
I
!lH.,,,
I
Tm, °C
I
!lHm \ Tt,OC \ !lHt
I
Trans.
CO 00
Temperature, °0
(1111) 812 689 343 -243 145 +5 409 812 409 1560 -131 115 354 1859 1183 220 -179 974 1072 841 731 827 356 +40 1070 678 9260 938 17260 769 -269 589 -75
(1211) 889 767 381 -240 170 21 466 887 459 1620 -122 143 399 1980 1288 47 -172 1056 1161 918 803 907 404 30 11650 748 1013 10240 1862 844 -268 654 -63
(1325) 979 855 426 -238 198 40 533 974 518 1750 .... 111 175 4530 2115 1410 75 -165 1149 1262 10060 888 1001 459
(1459) 1084 9580 476 -234 231 62 614 1074 586 19000 -100 213 516 2267 1552 109 -157 1257 13790 1109 987 1111 524
57 12700 830 1114 1122 2017
90 1406 926' 1232 1237 21970
932 -268 729 -49
1035 -267 819 -32
(1617) 1209 1085 534 -230 269 87 7120 11930 669 2076 ';:'86 257 591 2439 1721 159 -·147 1384 1517 1237 1150 1242 602
(1806) 1360 1245 6030 -226 313 121 843 1336 768 2291
-71 310 0 683 2636 1923 202 -135 1535 1686 1389 12590 14030 6990
131 1564 lO38 1372 1374 24i7
182 1757 1176 1542 1542 2682
1159 --266 924
1311 0 -265 1053 +9
-14
(2038) (2328) 1546 1782 1444 1710 738 947 -220 -212 366 429 156 201 1015 1250 1520 1752 893 1053 2550 2870 -52 -280 382 473 7990 955 3130 2864 2172 2483 269 359 -120 -1030 17190 1952 1894 2152 1578 1818 1432 1683 1610 1893 821 991 -2230 -215 246 334 1996 2302 1348 1565 1751 2016 1750 2010 3000 3406 0.95 1.23 1503 1769 -264 -2620 1213 1419 35 67
(2702) 2093 2074 1220 -2010 508 2590 1590 2056 1266 3275
+4 595 1171 3446 2886 486 -76 2259 2484 2133 2033 2283 1230 -205 467 2706 1855 2362 2348 3896 2.49 2139 -259 1691 1090
3200 (95,000)* 1050 2520 78,700 660 2614 66,000 995 1587 12,340 631 -186 1,558* -189 612 8,600 817 335 (21,600)* (300) 2125 40,490t 729 2472 77,500 1287 50,100 1564 271 3802 136,500 2027 58 7,170' -7 767 26,720 321 1484 42,600 839 3827 171,290 (3850) 3426 101,000 798 682 18,670 29 -34 4,878' -101 2672 95,000 1857 2928 102,400 1495 2566 1083 80,500 2562 69,400 1409 2863 75,800 1522 1597 41,900 817 1,562* -220 -188 (27) (674) (15,200)* 3266 95,000 1312 2247 30 65,300 2834 937 89,500 2808 1063 87,300 4603 148,000 2227 4.22 20· (3.5) 2695 71,900 1470 -253 216 -259 2070 58,000 156 183 9,970 114
3400 2580 2900 4750 281 6620 (5,700) 2300 (2919) 2700 5290 2520 1480 2040 1305 520 1531 4047 3870 3140 2643 4757 2202 122 (500) 2403 1335 8830 2955 5750 5 2911 28 780 3770
ex-{J
600
1245
(611)
ex-{J
447
220
a;-{J
726
715
,),-0
427
108
a-{J
1384
995
a-{J
1260
935
a-fJ
1740
1610
a-fJ
1428
1121
a-fJ
p:: l'J
» >-3
Iridium Ir ..............
1673
1789
1921
2070
948 Krypton Kr ............. -234
1024 -231
1109 -228
1208 -224
1194 425 303 1141 236
1299 478 344 1239 273
1421 573 397 1351 315
Iron Fe ................
La.nthanum La .......... Lead Ph ................ LithiumLi.. ............ Lutetium Lu .......... Magnesium Mg ..........
Manganese Mn .......... Mercury Hg ...........
Molybdenum Mo ....... Neodymium Nd ......... Neon Ne ............... Nickel Ni ............... Niobium Nb ............ Nitrogen N .............
Osmium Os .............
1102 404 265 1056 204
586 -60 1670 7960 -265 994 1833 -248 2002
Oxygen 0 .............. -243 Palladium Pd ........... 917 Phosphorus P ....... 67 Platinum Pt ............ 1385
Plutonium Pu ...........
Polonium Po ........ . , .. Potassium K .... ........ Praseodymium Pr . ....... Radium R ......... Rhenium Ee ........ Rhodium Rh ........ Rubidium Rb .......
895 132 39 9020 275 2052 1358 16
2242 13210 -220 1564 616 456 1481 365
21410
2685
2980
3343
14550 -214
1617 -208
1820 -199
2075 -189
1733 706 531 16350 424
1937 817 619 1829 496
2187 957 730 2071 5840
2501 1140 871 2383 699
3800 2407 -1740 2908 1389 1068 2800 860
4389
160,000
2454
6300
2862 -153
99,300 2,158
1536 -157
3300 391
3457 1750 1324 3395 1090
103,000 46,620 38,584 102,200 35,000
920 327 180 1663 649
1481 1147 717 4457 2140
640 -460 1862 869 -265 1070 1959 -246 2140
7000 -29 1925 9540 -264 1155 2101 -244 2288
774 -9 2080 1054 -263 1259 2262 -242 2464
858 +14 2259 1173 -262 1373 0 24480 -2390 2662
956 42 24690 1318 -261 1511 2671 -236 28880
1074 0 77 2722 1498 -260 1678 2935 -232 3151
12220 120 3041 1725 -258 1883 3252 -227 3483
1419 176 3436 2025 -255 2139 3640 -220 3874
1683 251 3942 2443 -2520 2469 4124 -211 0 4370
2062 357 4610 3068 -246 2914 4744 -196 4987
67,700 14,692 157,300 78,300 422 102,800 172,400 1,335 187,400
1244 -39 2617 1016 -249 1453 2467 -210 3045
2882 549 6650 1707 80 4176 6302 172 7000
-241 995 86 1484
-239 1085 106 1600
-237 1188 126 17310
-234 1308 153 1882
-2300 14500 182 2058
-226 1625 216 2278
-2200 1844 256 2544
-212 2124 303 2871
-200 2483 362 3286
-183 2964 431 3824
1,630 90,000 42,700 134,970
-219 1552 597 1770
106 (4197) 4500 4700
979 156 620 985 312 2196 1456 350
1076
1189
1323
1485
1681
1927
2240
2656
3230
84,100
640
680
183 88 1082 359 2362 1567 59
2160 120 1196 410 2552 1694 88
258 157 1331 474 2771 18410 123
308 203 1495 547 30320 2017 165
373 260 1698 6340 3344 2223 218
458 333 1958 769 3737 2476 286
572 430 2301 928 4232 2793 376
744 563 2782 1181 4857 3196 503
947 758 3512 1527 5687 3727 694
34,500 21,415 85,000 32,700' 186,100 133,100 19,600
254 63 931 700 3180 19M 39
3000 562 1646 2000 7900 5150 540
911 1392
215 200
a-7
277 861
87 746
a-fj fj-'Y
707 1087 1137
532 507 449
a-fj fj-7 7-0
855
724
a-fj
-238
55
a-fj
-249 -229
22 178
a-fj fj-7
y-o
~"d
o
;,:J
~
t.rJ
U1 U1
122 207 315 457 480
800 140 130 20 440
a-fj fj-7 7- 0 Ii-/J' 0'-'
795
757
a-fj
q
;,:J
t.rJ
- - -- -
Heat of vaporization, kcal/mol. !.lH m Heat of melting, kcal/mo!' tlHt Heat of transition, keal/mo!. Change of ph.se . • At the normal hailing point. 1 !.lH, at 627°C. l1H<J
o
~
:I
>
>-3 1287 234 1363
1200 90 654
a-fJ a-fJ cc-fJ
882
1017
a-fJ
668 775
667 1137
fJ-c'Y
760 1479
418 1193
a-fJ
cc-fJ
crfJ
~301
VAPOR PRESSURE
4k-16. VAPOR PRESSURE OF ICE (Pressure of aqueous vapor over ice from -120 to O°C) TABLE
Temp.,oC
Temp., DC
I
Bars
mm of Hg
0.000 0000001
0.00000009 0.00000011 0.00000015 0.00000019 0.00000025
-70 -69 -68 -67 -66
o.000 002 577 0.000 002 992 o.000 003 469
-65 -64 -63 -62 -61
o.000 005 360
0.000 000 0011
0.00000032 0.00000041 0.00000052 0.00000066 0.00000084
0.000006179 0.000 007 113 0.000008178 O. 000 009 389
0.004021 0.004635 0.005336 0.006135 0.007043
-110 -109 -108 -107 -106
0.0000000014 0.000 000 0018 0.000000 0023 o .000 000 0028 o.000 000 0035
0.00000107 0.00000135 0.00000169 0.00000213 0.00000266
-60 -59 -58 -57 -56
0.000010765 0.000 012 328 0.000 014 098 O. 000016103 0.000 018 369
0.008076 0.009248 0.010576 0.012080 0.013780
-105 -104 -103 -102 -101
o.000 000 0044 o. 000 000 0055 o.000 000 0068 o.000 000 0085 0.000 000 0105
0.00000332 0.00000413 0.00000513 0.00000636 0.00000785
-55 -54 -53 -52 -51
0.00002093 0.00002382 0.00002707 0.000 030 73 0.00003485
0.01570 0.01787 0.02031 0.02305 0.02614
-100 -99 -98 -97 -96
0.000 0.000 0.000 a .000 O. 000
0129 0159 0194 0238 0290
0.00000968 0.000011 90 0.00001459 0.00001785 0.000 02178
-50 -49 -48 -47 -46
0.00003947 0.00004466 0.000 050 47 0.00005697 0.000 064 24
0.02961 0.03350 0.03786 0.04274 0.04819
-95 -94 -93 -92 -91
o .000 000 0354 a .000 000 0430 0.0000000521 0.000 000 0630 0.0000000761
0.00002653 0.00003224 0.00003909 0.00004729 0.00005710
-45 -44 -43 -42 -41
0.000 072 36 0.00008142 0.00009152 0.00010277 0.00011528
0.054 28 0.06108 0.06866 0.07709 0.08648
-90 -89 -88 -87 -86
0.000000 0.000 000 0.000 000 0.000 000 o .000 000
0917 1103 1323 1584 1894
0.00006879 0.00008271 0.00009924 0.000 118 85 0.00014205
-40 -39 -38 -37 -36
0.00012918 0.00014462 0.00016174 0.00018072 0.00020172
0.09691 0.10849 0.12133 0.13557 0.15133
-85 -84 -83 -82 -81
O. 000 000 O. 000 000 O. 000000 O. 000 000 O. 000 000
2259 2689 3196 3792 4490
0.000 1694 0.000 2018 0.000 2398 0.000 2844 0.0003368
-35 -34 -33 -32 -31
O. 0002250 O. 000 2506 0.000 2790 O. 000 3103 O. 0003447
0.1688 0.1880 0.2093 0.2328 0.2586
-80 -79 -78 -77 -76
o.000 000 5307 6262 7376 8673 0182
0.0003981 0.0004697 0.0005533 0.000 6506 0.0007638
-30 -29 -28 -27 -26
0.0003827 0.0004245 0.0004704 0.0005209 0.0005762
0.2871 0.3184 0.3529 0.3907 0.4323
-75 -74 -73 -72 -71
0.000001 1934 0.000 001 3964 0.000 001 6314 0.000 001 9030 0.0000022162
0.0008952 0.0010476 0.0012238 0.0014275 0.001 6625
-25 -24 -23 -22 -21
0.0006370 0.0007035 0.0007764 0.0008561 0.0009433
0.4778 0.5277 0.5824 0.6422 0.7076
-120 -119 -118 -117 -116 -115 -114 -113 -112 -111
o.000 000 0002 o.000 000 0002 o.000 000 0003 o.000 000 0003 o.000 000 0004 o.000 000 0005 O. 000 000 0007 o.000 000 0009
000 000 000 000 000
0.000 000 0.000 000 0.000 000 0.000001
Bars
0.000004017 O. 000 004 643
mm of Hg
0.001933 0.002245 0.002603 0.003013 0.003483
4-302
HEAT TABLE
Temp., °0
Bars
4k-16.
VAPOR PRESSURE OF
mm of Hg
-20 -19 -18 -17 -16
0.0010385 0.0011424 0.0012558 0.0013794 0.0015140
0.7790 0.8570 0.9421 1.0348 1.1358
-15 -14 -13 -12 -11
0.001661 0.001820 0.001993 0.002181 0.002386
1.246 1.365 1.495 1.636 1.790
-10 -9
0.002607 0.002847 0.003107 0.003389 0.003694
1.956 2.136 2.331 2.542 2.771
-8 -7 -6
Temp., °0
ICE (Continued) Bars
I mm of Hg
-5 -4 -3 -2 -1
0.004023 0.004379 0.004763 0.005178 0.005625
3.018 3.285 3.573 3.884 4.220
0
0.006107
4.581
4-303
VAPOR PRESSURE 4k-17. VAPOR PRESSURE OF WATER BELOW 100°0 (Pressure of aqueous vapor over water from -15.0 to 100.0°0) TABLE
Bars
Temp.,-"O.
mm of Hg
Temp., °0
Bars
mm of Hg
-14.8 -14.6 -1404 -14.2
0.001914 0.001946 0.001978 0.002011 ,0.002044
1.436 1.459 1:484 1.508 1.533
-5.0 -4.8 -4.6 -4.4 -4.2
0.004216 0.004280 0.004345 0.004411 0.004478
3.162 3.210 3.259 3.308 3.359
-14.0. -13.8 -13.6 -13.4 -13.2
0.002078 0.002112 0.002147 0.002182 0.002218
1.558 1.584 1.610 1.637 1.663
-4.0 -3.8 -3.6 -3.4 -3.2
0.004545 0.004614 0.004684 0.004754 0.004826
3.409 3.461 3.513 3.566 3.620
-,13.0 -12.8 -12.6 -12.4 -12.2
0.002254 0.002291 0.002328 0.002366 0.002404
1.691 1.718 1.746 1. 775 1.803
-3.0 -2.8 -2.6 -2.4 -2.2
0.004898 0.004972 0.005046 0.005121 0.005198
3.674 3.729 3.785 3.841 3.899
-12.0 -11.8 -11.6 -11.4 -11.2
0.002443 0.002483 0.002523 0.002564 0.002605
1.833 1.862 1.893 1.923 1.954
-2.0 -1.8 -1.6 -1.4 -1.2
0.005275 0.005353 0.005433 0.005513 0.005595
3.957 4.015 4.075 4.135 4.196
-11.0 -c 10.8 -10.6 -10.4 -,-10.2
0.002647 '0.002689 0.002732 .0.002776 . 0.002820
1:985 2.017 2.049 2.082 2.115
-1.0 -0.8 -0.6 -0.4 -0.2
0.005677 0.005761 0.005846 0.005932 0.006019
4.258 4.321 4.385 4.449 4.515
-10.0 -9.8 -9.6 -9.4 -9.2
0.002865 0.002 III 1 0.002957 0.003003 0.003051
2.149 :t.1!>3 2.218 2.253 2.288
0.0 0.4 0:6 0.8
0.006107 10.006190 0.006287 0.006379 :0.006472
4.581 4.648 4.716 4.785 4.854
-9.0 -'-8.8 -8.6 -8.4 -8.2
0.003099 0.003148 0.003197 0.003248 0.003298
2.324 2.361 2.398 2.436 2.474
1.0 1.2 1.4 1.6 1.8
'0.006566 0.006661 0.006758 0.006856 ; 0.006955
4.925 4.996 5.069 5.142 5.217
-8.0 -7.8 -7.6 -7.4 -7.2
' 0.003350 0.003402 0.003455 ' 0.003509 : 0.003564
2.513 2.552 2.592 2.632 2.673
2.0 2.2 2.4 2.6 2.8
0.007055 0.007 157 0.007260 0.007364 • 0.007469
5.292 5.368 5.445 5.523 5.602
-7.0 -6.8 -6.6 '-6.4 -,6.2
0.003619 0.003675 0.003732 0.003790 0.003848
2.715 2.757 2.799 2.842 2.886
3.0 3.2 3.4 3.6 3.8
0.007576 0.007684 0.007794 0.007905 0.008017
5.683 5.7M 5.846 5.929 6.013
-6.0 -5.8 -5.6 -5.4 -5.2
0.003907 0.003967 : 0.004028 0.004090 .0.004152
2.931 2.976 3.021 3.067 3.114
4.0 4.2 4.4 . 4.6 4.8
0.008131 0.008246 0.008363 0.008481 0.008600
6.099 6.185 6.273 6.361 -6.451
~15.0
0.2
I
1-
I
-
4-304 TABLE
Temp.,oC
HEAT
4k-17, -VAPORPRESSURE , ,
Bars
5.0 5.2 , 5:4 5:6 5:8
:0.008721 '0.008844 :0.008968 '
6:0 6.2 6:4 6:6 6:8
iO.009349 ' '0.009479 :0.009611 ' ,0.009745 0.009880 '
7.0 7.2 7:4 7::6 7.8
'0.010 016 :0.010 155 10.010295 ' '0.010437 0.010 580
8.0 8.2 8:4 8:6 8.8 9:0 9.2 9.4 9.6 9:8
~m
OF WATER BELOW
100°0 (Continued)
Temp.,oC
of Hg
Bars
mm of Hg
i
,
6.542 6.633 6.726 6:821 6:9i6
15.0 ,15.2 15:4 15:6 15:8
'0.017049 0.017270 ,0.017493 0.017719 ,0.017947 '
, 13.121
7:012 7.110 7.209 7.309 7.410
i6:0 16.2 16.4 16:6 16:i,j
iO.018178 ' :0.018412 !0.01864;8 '0.018887 ' ;0.019128
13:635 13.810 13:987 :, 14:166, 14:347
7:513 7.617 7.722 7:828 7.936
17:0 17.2 17A 17:6 17.8
0.019373 ' 0.019620 0.019869 ;0.020122 ;0.020377
0.010 725 0.010872 0.011 021 0.011172 0.011324
8.045 8.155 8.267 8:379 8.494
18:0 18.2 18.4 18.6 18.8
iO.020 635 ' : 0.020896 0.021160 0.021427 0.021696
15:478 15.673 15:87i' 16.071 16.274
0.011 478 ' ,0.011 634 0.011 792 0.011952 0.012113
8.609 8.726 8:845 8:965 9.086
19.0 19.2 19.4 19.6 19:8
0.021969 0.022245 0.022523 0.022805 0.023090
16.478 16.685 16:894 17:105 17:319
10.0 10.2 10.4 10:6 10:8
0.012277 ,0.012442 0.012610 0.012779 0.012951
9.209 9.333 9.458 9.585 9:714
20.0 20.2 20.4 20:6 20.8
0.023378 ' : 0.023669 ,0.023963 ' 0.024261 ' '0.024562
17'.535 17.753, 17'.974 18.,197 18.42;1
11.0 11.2 11.4 11'.6 11.8
0.013124 0.013300 ; 0.013 477 0.013657 0.013838
9:844 9.976 10.109 10.243 10.380
21.0 21.2 21.4 21.6 21'.8
0.024866 ' 0.025173 0.025483 0.025797 ' 0.026115
18.651 18.881 19.114 19.350 19.588
12'.0 12.2 12.4 12.6 12'.8
0.014022 0.014208 ,0.014396 ' : 0.014587 0.014779 '
10.518 10.657 10.798 10.941 11'.085
22.0 22.2 22.4 22.6 22.8
0.026435 ' ,0.026759 0.027087 ,0.027418 : 0.027753 '
19.828 20.071 20.317 20.565 20.816
13.0 13.2 13.4 13.6 13.8
'0.014974 0.015171 0.015370 ' 0.015572 ' 0.015776
11.231 11.379 11'.529 11.680 11.833
23.0 23.2 23.4 23.6 23.8
' 0.028091 ' 0.028433 0.028778 ' ; 0.029 127' ,0.029480
21.070 21.326 21.58,5 21.847 22.1],'2
14.0 14.2 14.4 14'.6 14.8
0.015982 0.016191 0.016402 ' 0.016615 0.016831
11.988 12.144 12.302 12.462 12'.624
24.0 24.2 24.4 24.6 24.8
' 0.029836 0.030197 : 0.030561 0.9309,28 0.031300
22.379 22.6:19 22'.922 23.1~8 23':477
iO.009093
I
!
10.009220
, ,
"
,I
!
..
12.788 12.954,
13.290 13:462 I i
, ;
14.531 14.716 14:903 15:093 15.284..
"
-
4-305
VAPOR PRESSURE TABLE
Temp.,oC
4k-17.
VAPOR PRESSURE OF WATER BELOW
Bars
mm of Hg
25.0 25.2 25.4 25.6 25.8
0.031676 0.032055 0.032439 0.032826 0.033217
23.759 24.043 24.331 24.621 24.915
26.0 26.2 26.4 Z6.6 26.8
0.033613 0.034013 0.034416 0.034824 0.035236
27.0 27.2 27.4 27.6 27.8
Temp.,oC
100°0 (Continued) Bars
mm of Hg
35.0 35.2 35.4 35.6 35.8
0.056237 0.056862 0.057493 0.058130 0.058773
42.181 42.650 43.123 43 .. 601 44.083
25.212 25.512 25.814 26.120 26.429
36.0 36.2 36.4 36.6 36.8
0.059422 0.060077 0.060739 0.061407 0.062081
44.570 45.062 45.558 46.059 46.565
0.035653 0.036073 0.036498 0.036928 0.037361
26.742 27.057 27.376 27.698 28.023
37.0 37.2 37.4 37.6 37.8
0.062762 0.063449 0.064143 0.064843 0.065549
47.075 47.591 48.111 48..636 49.166
28.0 28.2 28.4 28.6 28.8
0.037800 0.038242 0.038689 0.039141 0.039597
28.352 28.684 29.019 29.358 29.700
38.0 38.2 38.4 38.6 38.8
0.066263 0.066983 0.067710 0.068443 0.069184
49 .. 701 50.241 50.786 51. 337 51.892
29.0 29.2 29.4 29.6 29.8
0.040058 0.040524 0.040994 0.041469 0.041948
30.046 30.395 30.748 31.104 31.464
39.0 39.2 39.4 39.6 39.8
0.069931 0.070686 0.071447 0.072216 0.072991
52.453 53 .. 019 53.590 54.166 54.748
30.0 30.2 30.4 30.6 30.8
0.042433 0.042922 0.043417 0.043916 0.044421
31.827 32.195 32.565 32.940 33.318
40.0 40.2 40.4 40.6 40.8
0.073 774 0.074564 O. U75 36~ 0.076166 0.076979
55.335 55.928 56.5:l6 57.130 57.739
31. 0 31.2 31.4 31.6 31.8
0.044930 0.045444 0.045964 0.046488 0.047018
33.700 34.086 34.476 34.869 35.267
41. 0 41.2 41.4 41.6 41.8
0.077798 0.078626 0.079460 0.080303 0.081153
58.354 58.974 59.600 60.232 60.870
32.0 32.2 32.4 32.6 32.8
0.047553 0.048094 0.048639 0.049190 0.049747
35.668 36.073 36.483 36.896 37.313
42.0 42.2 42.4 42.6 42.8
0.082011 0.082876 0.083750 0.084631 0.085521
61.513 62.162 62.818 63.479 64.146
33.0 33.2 33.4 33.6 33.8
0.050309 0.050876 0.051449 0.052028 0.052612
37.735 38.160 38.590 39.024 39.462
43.0 43.2 43.4 43.6 43.8
0.086418 0.087324 0.088237 0.089159 0.090090
64.819 65.498 66.184 66.875 67.573
34.0 34.2 34.4 34.6 34.8
0.053201 0.053797 0.054398 0.055005 0.055618
39.904 40.351 40.802 41.257 41. 717
44.0 44.2 44.4 44.6 44.8
0.091028 0.091975 0.092931 0.093894 0.094867
68.277 68.987 69.704 70.427 71.156
I
4-306 TABLE
HEA'I'
4k-17.
VAPOR PRESSURE OF WATER BELOW
Temp.,oC
100°C (Continued)
Bars
mm of Hg
45.0 45.2 45.4 45.6 45.8
0.095848 0.096838 0.097837 0.098844 0.099861
71.892 72.635 73.384 74.139 74.902
55.0 55.2 55.4 55.6 55.8
0.15745 0.15896 0.16049 0.16203 0.16358
118.09 119.23 120.38 121.53 122.70
46.0 46.2 46.4 46.6 46.8
0.100886 0.101921 0.102964 0.104017 0.105079
75.671 76.447 77.230 78.019 78.816
56.0 56.2 56.4 56.6 56.8
0.16515 0.16672 0.16831 0.16992 0.17153
123.87 125.09 126.25 127.45 128.66
47.0 47.2 47.4 47.6 47.8
0.106150 0.107231 0.108321 0.109421 0.110530
79.619 80..430 81..248 82.072 82 .. 904
57.0 57.2 57.4 57.6 57.8
0.17il16 0.17481 0.17646 0.17813 0.17981
129.88 131.12 132.36 133.61 134.87
48.0 48.2 48.4 48.6 48.8
0.111649 0.112777 0.113916 0.115064 0.116222
83.744 84.590 85.444 86.305 87.174
58.0 58.2 58.4 58 .. 6 58.8
0.18151 0.18322 0.18494 0.18668 0.18843
136.14 137.43 138.72 140.02 141. 34
49.0 49.2 49.4 49.6 49.8
0.117390 0.118568 0.119757 0.120955 0.122164
88.050 88.934 89.825 90.724 91. 630
59.0 59.2 59.4 59 .. 6 59.8.
0.19020 0.19198 o .19B 77 0.19558 0.19740
142.60 144.00 145.34 140.70 148.. 06
50.0 50.2 50.4 50.6 50.8
0.12338 0.12461 0.12585 0.12710 0.12837
92.545 93.467 95.336 96.282
60.0 60.2 60.4 60.6 60.8
0.19924 0.20109 O.;W~ 96 0.20484 0.20673
149.44 150.83 152.2il 153.64 155.06
51.0 51.2 51.4 51.6 51.8
0.12964 0.13092 0.13221 0.13352 0.13483
97.236 98.198 99.169 100.147 101.134
61.0 61.2 61.4 61. 6 61.3
0.20864 0.21057 0.21251 0.21447 0.21644
156.50 157.94 159.40 160.86 162.34
.52.0 52.2 52.4 52.6 52.8
0.13616 0.13750 0.13885 0.14021 0.14158
102.129 103.133 104.145 105.166 106.195
62.. 0 62.2 62.4 62.6 62.8
0.21842 0.22043 0.22244 . 0.22448 0.22653
163.83 165.33 166.85 168.37 169.91
53.0 53:2 53.4 53.6 53.8
0.14296 0 . .14436 0.14577 0.14718 0.14861
107.232 108.278 109.333 110.397 111.4'70
63.0 63.2 63.4 63.6 63.8
0.22859 : 0.23067 0.23277 0.23488 0.23701
171.46 173.02 174.59 176.18 177.77
54.0 54.2 54.4 54.6 54.8
0.15006 0.15151 0.15298 0.154 45 0.15594
112.551 113.642 114.741 115.850 116.967
64.0 64.2 64.4 64.6 64.8
0.23916 0.24132 0.243.50 0.245.69 0.24791
179.38 181. 00 182.64 184.29 185.94
Temp.,oC
-
-,.
-
-~-
94.il9~
I
Bars
mm of Hg
4-307
VAPOR PRESSURE TABLE
4k-17.
VAPOR PRESSURE OF WATER BELOW
100°0 (Continued)
Bars
mm of Hg
65.0 65.2 65.4 65.6 65.8
0.25013 0.25238 0.254 64 0.25692 0.25922
187.62 189.30 191. 00 192.71 194.43
75.0 75.2 75.4 75.6 75.8
0.38553 0.38877 0.39203 0.39532 0.39862
289.17 291.60 294.05 296.51 298.99
66.0 66.2 66.4 66.6 66.8
0.26154 0.26387 0.26622 0.26859 0.27097
196.17 197.92 199.68 201.46 203.25
76.0 76.2 76.4 76.6 76.8
0.40195 0.40531 0.40868 0.41208 0.41551
301.49 304.00 306.54 309.09 311.66
67.0 67.2 67.4 67.6 67.8
0.273 38 0.27580 0.27824 0.28070 0.28317
205.05 206.87 208.70 210.54 212.40
77.0 77.2 77.4 77.6 77.S
0.41896 0.42243 0.42592 0.42945 0.43299
314.24 316.85 319.47 322.11 324.77
68.0 68.2 68.4 68.6 68.8
0.28567 0.28818 0.29071 0.29327 0.29584
214.27 216.15 218.05 219.27 221.90
78.0 78.2 78.4 78.6 78.8
0.43656 0.44015 0.44377 0.44742 0.45109
327.45 330.14 332.86 335.59 338.34
69.0 69.2 69.4 69.6 69.8
0.29843 0.30103 0.30366 0.30331 0.30897
223.84 225.79 227.76 229.75 231.75
79.0 79.2 79.4 79.6 79.8
0.45478 0.45850 0.46225 0.46602 0.46982
341.12 343.91 346.71 349.54 352.39
70.0 70.2 70.4 70.6 70.8
0.31166 0.31437 0.31709 0.31984 0.32260
233.76 235.79 237.84 239.90 241.97
80.0 80.2 80.4 80.6 80.8
0.47364 0.47749 0.481 37 0.48527 0.48920
355.26 358.15 361. 05 363.98 366.93
71.0 . 71.2 71.4 71.6 ". 71.8
0.32539 0.32820 0.33102 0.33387 0.33674
244.06 246.17 248.29 250.42 252.57
81.0 81.2 81.4 81.6 81.8
0.49315 0.49713 0.50114 0.50518 0.50924:
369.89 372.88 375.89 378.92 381.96
72.0 72.2 72.4 72.6 72.8
0.33963 0.34254 0.34547 0.34842 0.35139
254.74 256.92 259.12 261.34 263.57
82.0 82.2 82.4 82.6 82.8
0.51333 0.51745 0.52160 0.52577 0.52997
385.03 388.12 391. 23 394.36 397.51
73.0 73.2 73.4 73.6 73.8
0.35439 0.35740 0.36044 0.36350 0.36658
265.81 268.07 270.35 272.65 274.96
83.0 83.2 83.4 83.6 83.8
0.53420 0.53846 0.54275 0.54706 0.55140
400.68 403.88 407.09 410.33 413.59
74.0 74.2 74.4 74.6 74.8
0.36968 0.37281 0.37596 0.37913 0.38232
277.29 279.63 281. 99 284.37 286.76
84.0 84.2 84.4 84.6 84.8
0.55578 0.56018 0.56461 0.56907 0.57356
416.87 420.17 423.49 426.84 430.20
Temp., °0
I
I
Temp., °0
I
Bars
mm of Hg
4-308 TABLE
Temp.,oC
HEAT
4k-17.
VAPOR PRESSURE OF WATER BELOW
Bars
mm of Hg
Temp.,oC
100°C (Continued) Bars
mm of Hg
85.0 85.2 85.4 85.6 85.8
0.57808 0.58262 0.58720 0.59181 0.59645
433.59 437.00 440.44 443.89 447.37,
93.0 93.2 93.4 93.6 93.8
0.78491 0.79078 0.79669 0.80263 0.80861
588.73 593.14 597.57 602.02 606 .. 51
86.0 86.2 86.4 86.6 86.8
0.60112 0.60582 0.61055 0.61531 0.62010
450.88 454.40 457.95 461.52 465.11
94.0 94.2 94.4 94.6 94.8
0.81463 0.82068 0.82678 0.83290 0.83907
611.02 615.56 620.13 624.73 629.36
87.0 87.2 87.4 87.6 87.8
0.62492 0.62978 0.63467 0.63958 0.644 53
468.73 472.37 476.04 479.73 483.44
95.0 95.2 95.4 95.6 95.8
0.84528 0.85152 0.85780 0.86412 0.87048
634.01 638.69 643.40 648.14 652.91
88.0 88.2 88.4 88.6 88.8
0.64951 0.65453 0.65957 0.66465 0.66976
487.18 490.94 494.72 498.53 502.36
96.0 96.2 96.4 96.6 96.8
0.87687 0.88331 0.88979 0.89630 0.90285
657.71 662.54 667.39 672.28 677.20
89.0 89.2 89.4 89.6 89.8
0.67491 0.68008 0.68529 0.69053 0.69581.
506.22 510.10 514.01 517.94 521.90
97.0 97.2 97.4 97.6 97.8
0.90945 0.91608 0.922.76 0.92947 0.93622
682.14 687.12 692.12 697.16 702.23
90.0 90.2 90.4 90.6 90.8
0.70112 0.70646 0.71184 0.71725 0.72270.
525.88 529.89 533.93 537.98 542.07
98.0 98.2 98.4 98.6 98.8
0.94302 0.94986 0.95673 0.96365 0.97061
707,32 712.45 717.61 722.80 728.02
91.0 91.2 91.4 91.6 91.8
0.728.18 0.73369 0.73924 0.744 83 0.75045
546.18 550.32 554.48 558.67 562.88
99.0 99.2 99.4 99.6 99.8
0.97761 0.98466 0.99174 0.99887 1.00604
733.27 738.55 743.87 749.21 754.59
92.0 92.2 92,4 92.6 92.8
0.75610 0.76179 0.767.52 0.77328 0.77908
567.12 571.39 575.69 580.01 584.36
100.0
1.01325
760.00
4-309
VAPOR PRESSURE
TABLE 4kc 18. VAPOR PRESSURE OF WATER ABOVE 100°C (Pressure of aqueous vapor over water from 100° to the critical temperature, 374.15°C)
Temp.,oC
Bars
Temp.,oC
mm of Hg
Bars
mm of Hg
100 101 102 103 104
1. 0133 1.0500 1. 0878 1.1267 1.1667
760.0 787.5 815.9 845.1 875.1
150 151 152 153 154
4.7597 4.8887 5.0205 5.1551 5.2926
3,570.1 3,666.8 3,765.7 3,866.7 3,969.8
105 106 107 108 109
1.2080 1.2504 1.2941 1.3390 1. 3851
906.1 937.9 970.6 1,004.3 1,038.9
1.55 156 157 158 159
5.4331 5.5765 5.7228 5.8723 6.0248
4,075.1 4,182.7 4,292.5 4.404.6 4,519.0
110 111 112 113 114
1.4326 1.4814 1. 5316 1.5831 1. 6361
1,074.5 1,111.1 1,148.8 1,187.4 1,227.2
160 161 162 163 164
6.1805 6.3393 6.5014 6.6668 6.8355
4,635.8 4,754.9 4,876.5 5,000.5 5,127.1
115 116 117 118 119
1.6905 1.7064 1.8038 1.8627 1.9232
1,268.0 1,309.9 1,353.0 1,397.2 1,442.5
165 166 167 168 169
7.0076 7.1831 7.3621 7.5446 7.7306
5,256.1 5,387.8 5,522.0 5,658.9 5,798.4
120 121 122 123 124
1.9853 2.0490 2.1144 2.1815 2.2503
1,489.1 1,536.9 1,585.9 1,636.2 1,687.8
170 171 172 173 174
7.9203 8.1136 8.3107 8.5115 8.7161
5,940.7 6,085.7 6,233.5 6,384.2 6,537.6
125
1,740.7 1,795.0 1,850.6 1,907.7 1,966.1
175 176 177 178 179
8.9247
127 128 129
2.3208 2.3931 2.4673 2.5433 2.6213
9.3535 9.5739 9.7985
6,694.0 6,853.4 7,015.7 7,181.1 7,349.5
130 131 132 133 134
2.7011 2.7829 2.8667 2.9525 3.0405
2,026.0 2,087.4 2,150.2 2,214.6 2,280.5
180 181 182 183 184
10.0271 10.2599 10.4969 10.7383 10.9839
7,520.9 7,695.6 7,873 .4 8,054.4 8,238.6
135 136 137 138 139
3.1305 3.2226 3.3170 3.4136 3.5124
2,348.1 2,417.2 2,487.9 2,560.4 2,634.5
185 186 187 188 189
11.234 11.489 11. 748 12.0n 12.279
8,426 8,617 8,811 9,009 9,210
140 141 142 143 144
3.6135 3.7170 3.8228 3.9310 4.0417
2,710.3 2,787.9 2,867.3 2,948.5 3,031. 5
190 191 192 193 194
12.552 12.830 13.113 13.399 13.693
9,415 9,623 9,835 10.050 10,270
145 146 147 148 149
4.1549 4.2706 4.3889 4.5098 4.6334
3,116.4 3,203.2 3,292. 3,382.7 3,475.4
195 196 197 198 199
13.989 14.291 14.598 14.910 15.228
10,492 10,719 10,949 11,184 11,422
126
°
I
iJ .1371
4-310 TABLE
HEAT
4k-18.
VAPOR PRESSURE OF WATER ABOVE
100°C (Continued)
Temp., °0
Bars
mm of HIl:
Temp., °0
Bars
mm of Hg
200 201 202 203 204
15.550 15.879 16.212 16.551 16.895
11,664 11,910 12,160 12,414 12,672
250 251 252 253 254
39.776 40.452 41.137 41.830 42.533
29,834 30,341 30,855 31,375 31,902
205 206 207 208 209
17.245 17.601 17.962 18.329 18.701
12,935 13,202 13,472 13,748 14,027
255 256 257 258 259
43.244 43.965 44.695 45.434 46.182
32,436 32,976 33,524 34,078 34,640
210 211 212 213 214
19.080 19.464 19.855 20.251 20.654
14,311 14,599 14,892 15,190 15,492
260 261 262 263 264
46.940 47.707 48.484 49.270 50.066
35,208 35,783 36,366 36,955 37,553
215 216 217 218 219
21.062 21.477 21.899 22.326 22.760
15,798 16,109 16,425 16,746 17,072
265 266 267 268 269
50.872 51.687 52.513 53.349 54.195
38,157 38,769 39,388 40,015 40,650
220 221 222 223 224
23.201 23.648 24.102 24.562 25.030
17,402 17,738 18,078 18,423 18,774
270 271 272 273 274
55.051 55.917 56.794 57.681 58.579
41,292 41,941 42,599 43,264 43,938
225 226 227 228 229
25.504 25.985 26.473 26.968 27.470
19,129 19,490 19,856 20,227 20,604
275 276 277 278 279
59.487 60.406 61.336 62.277 63.229
44,619 45,308 46,006 46,712 47,426
230 231 232 233 234
27.979 28.495 29.019 29.550 30.088
20,986 21.373 21,766 22,164 22,568
280 281 282 283 284
64.192 65.166 66.151 67.147 68.155
48,148 48,878 49,617 50,365 51,121
235 236 237 238 239
30.634 31.188 31.749 32.318 32.895
22,978 23,393 23,814 24,241 24,674
285 286 287 288 289
69.175 70.206 71.249 72.304 73.370
51,885 52,659 53,441 54,232 55,032
240 241 242 243 244
33.480 34.073 34.673 35.282 35.899
25,112 25,557 26,007 26,464 26,926
290 291 292 293 294
74.449 75.539 76.642 77.757 78.884
55,841 56,659 57,486 58,322 59,168
245 246 247 248 249
36.524 37.157 37.799 38.450 39.109
27,395 27,870 28,352 28,840 29,334
295 2.96 297 298 299
80.024 81.177 82.342 83.521 84.712
60,023 60,888 61,762 62,646 63,539
4-311
VAPOR PRESSURE TABLE 4k-18.VAPOR PRESSURE OF WATER ABOVE 100°C
(Continued)
Tem'p.,·C
'Bars
mm of Hg
Temp."oO
300 301 302 303 304
85.916 87.133 88.363 89.606 90.863
64,442 65,355 66,278 . 67,210 08,153
340 341 342 343 344
146.08 147.92 149.78 151.66 153.56
109,569 110,949 112,344 113,753 115,177
305 306 . 307 308 ,. ',309
,92.134 93.419 94.717 96.029 97-.356
69,106 70,070 71,044 72,028 73,023
345 346 347 348 349
155.48 157.41 159.37 161. 35 163.35
115,616. 118,070 119,539 121,023", 122,523
310 311 312 ,313 • 314, .
98.696 100.050 101.418 102.801 104.199
74,028 75,044 76,070 77,107 78,156
3050 351 352 353 354
165.37 167.40 169.46 171.54 173.64
124,038 125,563 127,106 128,665 130,242
3105 316 317 318 319,
105;611, 107.039 108 :481 109.939, 111.412
79,215 80,286 81,368 82,461 83,566
355 356 357 358 359
175.77 177.91 180.08 182.28 184.50
131,835 133,446 135,075 136,721 138,385
320 321 322 323 324
112.900 114.403 115.921 117.4;56, 119.006,
84,682 85,809 86,948 88,099 89,262
360 361 362 363 364
186.74 189.00 191.28 193.60 195.,93
140,067 141,761 143,41,5 145,209 146,963
325 326 327 ' 328 329
120.57 122.15 123.75 125.37 127.00
90,437 91,624 92,823 94,035 95,259 ,
365 366 367 3,68 369
198.30 200.69 203.11 205.55 208.03
148,736 150,530 152,344 154,179 156,034
330 331 332 333 334
128.65 130.31 131.99 133.69 135.41
96,495 97,743 99,003 100,277 " 101,564
370 371 372 373 374
210.53 213.06 215.62 218.21 220.84
157,911 159,808 161,728 163,67-1 165,644
335' 336 337" 338 ' 339
137.14 138.89 140,66 142.45 144.26
102,864 104,178 105,505 ' 106,846 108,201
374.15
221.23
165,936
,
;
,
Bars
mm of Hg
1
,
4-312
HEAT
TABLE4kc19. VAPOR .PRESSURE OF MERCURY* (Vapor'pressureof mercury in mm of Hg for temperatures from -38 to 400°0. Note that the values for the first four lines only are to be multiplied by 10- 6 ) I
Temp., °0
-30 -20 -10 - 0 + 0 +10 20 30 40 50 60 70 80 90 . 100 110 120 130 140
0 10- 6 4.78 .18.1 60.6 185
2 10- 6 3.59 14.0 48.1 149
4 10- 6 2.66 10.8 38.0 119
6
8
10- 6 1.97 8.28 29.8 95.4
1O~6
1.45 6.30 23.2 76.2
0.000185 0.000490 0.001201 0.002777 0.006079
0.000228 0.000588 0.001426 0.003261 0.007067
0.000276 0.000706 0.001691 0.003823 0.008200
0.000335 0.000846 0.002000 0.004471 0.009497
0.000406 0.001009 0.002359 0.005219 0.01098
0.01267 0.02524 0.04825 0.08880 0.1582
0.01459 0.02883 0.05469 0.1000 0.1769
0.01677 0.03287 0.06189 0.1124 0.1976
0.01925 0.03740 0.06993 0.1261 0.2202
0.02206 0.04251 0.07889 0.1413 0.2453
0.2729 0.4572 0.7457 1.186 1.845
0.3032 0.5052 0.8198 1.298 2.010
0.3366 0.5576 0.9004 1.419 2.188
0.3731 0.6150 0.9882 1.551 2.379
0.4132 0.6776 1.084 1.692 2.585
150 160 170 180 190
2.807 4.189 6.128 8.796 12.423
3.046 4.528 6.596 9.436 13.287
3.303 4.890 7.095 10.116 14.203
3.578. 5.277 7.626 10.839 15.173
3.873 5.689 8.193 11. 607 16.200
200 210 220 230 240
. 17.287 23.723 32.133 42.989 56.855
18.437 25.233 34.092 45.503 60.044
19.652 26.826 36.153 48.141 63.384
20.936 28.504 38.318 50.909 66.882
22.292 30.271 40.595 53.812 70.543
250 260 270 280 290
74.375 96.296 123.47 156.87 197.57
78.381 101.28 129.62 164.39 206.70
82.568 106.48 136.02 172.21 216.17
86.944 111. 91 142.69 180.34 226.00
91.518 117.57 149.64 188.79 236.21
300 310 320 3.30 340
246.80 305.89 376.33 459.74 557.90
257.78 319.02 391.92 478.13 579.45
269.17 332.62 408.04 497.12 601.69
280.98 346.70 424.71 ' 516.74 624.64
293.21 361. 26 441.94 537.00 648.30
350 360 370 380 390
672.69 806.23 960.66 1138.4 1341.9
697.83 835.38 994.34 1177.0 1386.1
723.73 865.36 1028.9 1216.6 1431.3
400
1574.1
750.43 896.23 1064.4 1257.3 1477.7
* From the compilation of J. Johnston, F. Fenwick, and H. G. Leopold. Tables," Vol. III, p. 206, McGraw-Hill Book Company, New York, 1928.
777.92 928.02 1100.9 1299.1 1525.2
"International Crit'cal
4-313
VAPOR PRESSURE TABLE
4k-20.
VAPOR PRESSURE OF CARBON DIOXtDE* SOLID
Pressure, Microns of Mercury ~
Temp.,oC
-180 -170 -160 -150 -140
-
0
1
2
4
3
5
6
7
8
9
--- --- --- .--- --- --- --- ---
--- ---
0.013 0.008 0.006 0.004 0.003 0.37 0.27 0.14 0.20 0.10 5.9 4.6 2.7 3.6 2.1 60.5 48.8 39.2 25.1 31.4 431 359 298 247 204
0.0005 0.026 0.67 9.8 92
0.0017 0.074 1. 58 19.9 168
0.0011 0.052 1.19 15.8 138
0.0007 0.037 0.90 12.4 113
0.0003 0.018 0.50 7.6 75
Pressure, Mm of Mercury
-130 -120 -110 -100 - 90 - 80 - 70 - 60 - 50
2.31 9.81 34.63 104.81 279.5 672.2 1486.1 3073 .1 . ,-,."_...
1. 97 8.57 30.76 94.40 254.7 618.3 1377.3 2865.1 ........
1
1
1
1.2) 1.0) 1.68 1.43 0.87 1 0.73 0.51 0. 61 1 7.46 6.49 5.63 4.88 4.22 3.64 3.13 2.69 27.27 24.14 21.34 18.83 16.58 14.58 12.80 11.22 84.91 76.27 68.43 61.30 54.84 48.99 43. 71 1 38.94 231.8 210.8 191.4 173.6 157.3 142.4 128.7 116.2 568.2 521.7 478.5 438.6 401.6 367.4 335.7 306.5 1275.6 1180.5 1091.7 1008.9 931.7 859.7 792.7 730.3 2669.7 2486.3 2314.2 2152.8 2001. 5 1859.7 1726.9 1602.5 . ...... ',._'--'-' . -'- - . ...... . " .... ....... 3780.9 3530.2 3294.6 ~
LIQUID
Temp.,oC
-50 -40 -30 -20 -10 - 0 0 10 20 30
0
1
2
5127.8 4922.7 4723.9 7545 7271 7005 10718 10363 10017 B331 1138GI 14781 19312 19872 18764 1 26142 25457 24786 26142 26840 27552 33763 34607 35467 42959 43977 45014 54086 55327
I
3
4
5
4531.1 4344.3 4163.2 6250 6746 6494 9679 9350 9029 13461 j13C!O 12530 18228 17703 117189 24127 23482 22849 28277 29017 29771 38146 36343 37236 46072 47150 48250
7 _61_
8
9
3987.9 3818.2t 3653.9t 3495.0t 5557 5339 6012 5781 7826 8412 8115 8716 11082 11455 111838 16194 115712 115241 20443 21026 21622 22229 30539 31323 32121 32934 39073 40017 40980 41960 49370 50514 51680 52871
I~!!!~
* From C. H. Meyers and M. S. Van Dusen, Nat!. Bur. Standards J. Research 10, 409 (1933: Mercury column density = 13.5951 g/cm'; u = 980.665 em/sec'. t Undercooled liquid. Critical temperature = 31.0°C. Triple point, - 56.602 ± 0.005°C; 3885.2 ± 0.4 mm.
4-314
,HEAT
4k-21.
TABLE
1
I
6
Vapor pressure, mm Hg at
ooe
4
·3
\I
1
0 Temp.,
VAPOR PRESSURE OF ETHYL. ALCOHOL*
1
1
5
1
I
7
s
.1
I
I I
II
°0
0 10 20 30
12.24 '23.78 44.00 78.06
13.18 25.31 46.66 82.50
14.15 27.94 49.47 87.17
40
133.70 220.00 350.30 541.20
140.75 230.80 366.40 564.35
148.10 242.50 383.10 588.35
50 60 70
I
I
TABLE
0
Temp., °C 0
30
40 50
60
16.21 30.50 55.56 97.21
155.80 -163.80 253.80 265.90 400.40 418.35 613.20 638.95
I
* Ramsay and Young,
10 20
15.16 28.67 52.44 92.07
I
18.46 17.31 32.44 34.49 58.86 62.33 102.60 108.24
19.68 36.67 65.97 114.15
20.98 38.97 69.80 120.35
22.34 41.40 73.83 126.86
172:20 278.60 437.00 665.55
190.10 305.65 476.45 721.55
199.65 319.95 497.25 751. 00
209.60 334.85 518,85 781.45
181.00 291.85 456.45 693.10
I
I
I
I
Trans. Roy. Soc. (London) 17'1', part I, 123 (1886).
4k-22. 1
VAPOR PRESSURE OF METHYLALCOHOL*
2 1
1
3
4 1
5 1
1
6
1
8
7 1
I
9
Vapor pressure, mm Hg at O°C
29.97 53.8 94.0
31.6 33.6 35.6 37.8 40.2 42.6 45.2 '47.9 50.8 57.0 60.3 63.8 67.5 71.4 75.5 79.8 84.3 89.0 99.2 104.7 110.4 116.5 122.7 129.3 136.2 143.4 151.0
167.1 175.7 184.7 194.1 203.9 214.1 271.9 285.0 298.5 312.6 327.3 342.5 409 . 4 1427.71446. 6 1466.31486. 6 1507.71529.5 1 624.3 650.0 676.5 703.8 732.0. 761.1 791.1 158.9 259.4
224.7 235.8 247.4 358.3 374.7 391.7 552.01575.31599.4 822.0
* RamBay and Young, Trans. Roy.',Soc. (London),. 178, 313 (1887); Bee also Young, Sci. Proc. Roy. Dublin Soc., 12, 374-443 (1910).
4-315
VAPOR PRESSURE Table 4k-23 concerns the evaporation of metals. a metal is given by the equation log W = A -
B 1 T - 2 log T
The rate of evaporation W of
+c
where W is expressed in g/sec cm 2• The values of A, B, and c given in Table 4k-23 are chosen to yield the value of W in these units. TABLE
4k-23.
CONSTANTS IN THE EQUATION FOR THE RATE OF EvAPORATION OF ~ETALS*
10- 3 X B
10- 3 X B
c+4
Metal
A
10.50(1) 10.71(1) 10.36(1) 10.42(1) [10.53(1) 9.86(1) Cs ...... [10.02(1)
7.480 5.480 4.503 4.132 4.291] 3.774 3.883]
0.1867 0.4468 0.5621 0.7319
Si .......
Th ...... Ge ......
13.20(s) 12.55(1) 11.25(s) 11.98(1) 12.38(s) 13.04(1) 12.52(1) 10.94(1)
19.72 18.55 18.64 20.11 25.87 27.43 28.44 15.15
18.06 16.58 14.85 14.09 18.52 18.22 16.59 7.741
0.6678 Sn ...... Pb ...... V ....... Nb ...... Ta ......
9.97(1) 10.69(1) 13.32 14.37(s) 13.00(s)
13.11 9.60 26.62 40.40 40.21
0.8032 0.9242 0.6195 0.7500 0.8947
Mg ......
12.81(s) 11.72(1) 12.28(s) 11.66(1) 11.65(1) 12.99(s) 11.95(1) 11.82(s)
Ca ...... Sr ....... Ba ...... Zn ...... Cd ......
11.30(s) 11. 13(s) 10.88 11. 94(s) 11.78(s)
9.055 8.324 8.908 6.744 5.798
Sb 2 . . . . . . Bi. ...... Cr ...... Mo ...... W .......
11.42 11.14(1) 12.88(s) 11. 80(s) 12.24(s)
9.913 9.824 17.56 30.31 40.26
0.9592 0.9260 0.6240 0.7570 0.8983
B ....... AI ....... Sc ....... y ....... La ......
14.13(s) 11.99(1) 11.94 12.43 11.88(1)
21.37 15.63 18.57 21.97 18.00
12.88(1) 12.25(s) 12.63(s) 13.41(1) 12.43 13.28(s) 12.55(1)
25.80 14.10 20.00 21.40 21.96 21.84 20.60
0.9544 0.6359 0.6395
Ce ...... Ga ...... In ....... Tl. ...... C .......
13.74(1) 10.79(1) 10.93(1) 11.15(1) 14.06(s)
20.10 13.36 12.15 8.92 38.57
13.50 13.55 11.46 13.59 13.06 12.633
33.80 30.40 19.23 37.00 34.11 27.50
0.7696 0.7722 0.7801 0.9056 0.9089 0.9112
Metal
A
Li. ...... Na ...... K ....... Rb ......
Cu ...... Ag ...... Au ...... Be ......
Ti ....... Zr .......
0.8278
0.7825 0.9135 0.2436 0.4590
0.5675 0.7373 0.8349 0.6737 0.7914 U ....... Mn ...... 0.2831 Fe ....... 0.4814 0.5931 Co ...... 0.7405 Ni ...... 0.8374 0.8392 Ru ...... 0.6877 Rh ...... 0.7959 Pd ...... 0.9212 Os ...... 0.3056 Ir ....... Pt .......
c+4 0.4900 0.4900 0.6061 0.7460 0.9488 0.6965
0.6512 0.6503
* From Saul Dushman, "Scientific Foundations of Vacuum Technique," pp. 752-754, John Wile) & Sons, Inc., New York, 1949.
·41. Heats of Formation and Heats of Combustion BRUNO J. ZWOLINSKI AND RANDOLPH C. WILHOIT
Thermodynamics Research Center, Texas A&M University
Tables 41-],41-2, and 41-3 list values of the enthalpy of formation, !J.Hr, and enthalpy of combustion, 4Hco, of pure elements and compounds in their standard states at one atmosphere pressure and 25°C in units of kilocalories per mole. Data on "key" substances, which play important roles in evaluating the data on other compounds, are collected in Table 41-1. Enthalpies of formation of elements and inorganic compounds are given in Table 41-2. They are arranged in a standard order, based on the order of elements in the periodic table. The organic compounds in Table 41-3 are arranged first by standard order of the elements of which they are composed and then by classes which have certain common molecular structural features or functional groups. 41-1. Sources of Data. All reported values were derived from published experimental measurements, and most of the data were selected from the following compilations: (1) Selected Values of Chemical Thermodynamic Properties: part 1, NBS Tech. Note 270-1, 1965; part 2, NBS Tech. Note 270-2, 1966; (2) Selected Values of Properties of Hydrocarbons and Related Compounds, Am. Petroleum Inst. Research Proj. 44, Thermodynamics Research Center, Texas A&lVI University, College Station. Texas (looseleaf nat.a sheets, extant 1967); (3) Selected Values vf Propertiel:! of Chemical Compounds, Thermodyn. Research Center Data Proj., Texas A&lVI University, College Station, Texas (looseleaf data sheets, extant 1967). These sources were supplemented by information in the files of the Thermodynamics Research Center at Texas A&M University. Data in all three tables are internally consistent, and, wherever necessary, original data have been converted to the units and conventions listed below. 41-2. Symbols and Units calorie the thermochemical calorie defined as equal to 4.184 joules (exactly) mole a unit of mass equal to the formula (molecular) weight in grams, calculated from the 1961 table of unified atomic weights based on carbon-12 standard state for condensed phases, the specified crystal or liquid form at one atmosphere pressure; for gases, the hypothetical ideal gas at one atmosphere pressure g gas l liquid c crystal aq aqueous (water) solution enthalpy, H = U + PV, for a change from an initial to a final state, H 4H = H(final) - H(initial), which is equal to the heat absorbed by the system at constant pressure 4-316
HEATS OF FORMATION AND HEATS OF COMBUSTION
4-317
the heat of formation of one mole of compound or element in its standard state from the elements in their reference states. [For an organic oxygen compound this corresponds to the chemical reaction, aC(graphite) -!bH2(gas) -!cOc(gas) -> CaHbOc(standard state). Reference states for elements are identified by a zero enthalpy of formation in the tables.] AHco, gross the heat of combustion of a compound with excess oxygen gas to produce pure, thermodynamically stable products at 25°C and one atmosphere, with all components in their standard states. [The pronucts of combustion are: CO 2{gas), H 20 (lIquid); HF(gas);Ch(gas), Br2(liquid), 12 (crystal), H 2S0 4 (liquid), and N 2(gas), as appropriate for the stoichiometry of the combustion reaction.] AHco, net the heat of combustion of a compound with excess oxygen to produce the following products: CO. (gas), H.O(gas), HF(gas), Ch(gas), Br2(gas), 12(gas), S02(gas), and N 2 (gas). (These are the principal products formed when a compound is burned in an open flame in the air.) 41-3. Uncertainties. The number of significant figures used in reporting a value of AHr or AHco is related to the estimated uncertainty according to the following scheme. AHr
+
Estimated" uncertainty in AHf" or AHco, kcal mole- 1 0.005--0.05 0.05-0.5 0.5--2 2~1O
+
Value written to 0.001 0.01 0.1 1.
4-318 TABLE
HEAT
41-1. HEATS OF FORMATION AND HEATS OF COMBUSTION OF KEY COMPOUNDS kcal mole- 1 at 25°C
Substance name
Formula and state
Mol. weight
-!J.Hco !J.HjD Gross
H20,g H2O.! Hydrogen fluoride ......... HF,g HF,l in 00 H20 .............. HF,aq Hydrogen chloride ......... HCl,g in 00 H2O .............. HCl,aq Hydrogen bromide ........ HBr,g in 00 H 2O .............. HBr,aq Hydrogen Iodide .......... HI,g Sulfur dioxide ............. S02,g S02.1 Sulfuric acid .............. H,SOd in 00 H 20 .............. H 2S04,aq in 115 H2O ............. H 2S04,aq Orthophosphoric acid ...... H,P04,C H,POd in 00 H2O .............. H,P04,aq Carbon dioxide ........... C02,g Butanedioic acid (succinic C4H,04,g C4H,04,C acid) Benzoic acid .............. C 7H,02,g C7H ,02,C Carbon tetrafluoride (tetrafluoromethane) ........ CF4,g p-Fluorubell~o;c acid ...... C BH,02F,c a,a ,a -Trifluoro-m-toluic acid ................. C BH,02Fa,c Carbon disulfide .......... CS2,g CS2.1 Thianthrene (diphenylene disulfide) ............. C'2H 8S 2 ,C N-Benzoylaminoethanoic acid (hippuric acid) ... C,H,O,N,c Boric oxide ............... B20a,c amorphous ............. B20a,c Boron trifluoride BFa,g Silicon dioxide quartz ................. Si02,C cristo balite ............. Si02,c tridymite ............... Si02,C amorphous ............. Si02,C Silicon tetrafluoride ........ SiF 4,g
Water ................ · ..
· . .. . . .
-57.796 - 68.315 -64.8 71.65 -79.54 -22.062 -39.952 -8.70 -29.05 6.33 -70.944 -76.6 -194.548 -217.32 -212.192 -305.7 -302.8 -307.92 -94.051 -196.8 -224.86 -70.19 -92.04
88.005 140.115
18.015
....... 20.006 ....... · .. . . . . 36.461
.......
12.096
Net
6.836
25.46
16.50
40.49
27.77
384.35 356.29 793.11 771.26
352.79 324.73 761. 55 739.70
-221 -139.56
720.22
6\J!i .1\)
190.123 76.139
761.44
·.... ..
-253.68 21.44 28.05
........ ........
750.92 263.99 257.38
216.326
43.12
1,697.46
1,544.80
179.177 69.620
-145.49 -304.20 -299.84 -271.03
1,008.39
961. 05
80.917
.......
127.912 64.063
.......
98.078
....... .......
97.995
....... .......
44.010 118.090
·......
122.125
·... ... 67.806 60.085
....... ....... .......
104.080
-217.72 -217.37 -217.27 -215.95 -385.98
HEATS OF FORMATION AND HEATS OF COMBUSTION TABLE
41-2.
4-319
HEATS OF. FORMATION OF ELEMENTS AND INORGANIC COMPOUNDS
Substance
Formula
nan~e
Mol. weight Gas
Liquid
Solid
Oxygen and Hydrogen Oxygen ........... " .... Ozone .................. Hydrogen ............... Hydrogen peroxide .......
31.999 47.998 2.016 34.015
. . . .
0.0 34.1 0.0 -44.88
Halogens Fluorine ................ . Chlorine ................ . Chlorine monoxide, ...... . Chlorine dioxide ......... . Dichlorine monoxide ..... . Perchloric acid .......... . Chlorine monofluoride .... . Chlorine trifluoride ....... . Bromine ................ . Bromine monoxide ....... . Bromine dioxide ......... . Bromine trifluoride ...... . Bromine pentafluoride .... . Bromine chloride ........ . Iodine .................. . Todic aCid .............. . Iodine monofluoride ...... . Iodine pentafluoride ...... . Iodine heptafluoride ...... .
F2 C]'
CIO CIO, Cl,O
HCIO.
CIF CIF, Br, BrO BrO, BrF, BrF, BrCI 12 HIO, IF IF5 IF7 ~odillB IllonOChlor. ~u....le . . '. .. . '1 Iel Iodine trichloride ........ . ICla Io_dine mono bromide ..... . IBr
37.997 70.906 51.452 67.452 86.905 100.459 54.451 92.448 159.818 95.908 111.908 136.904 174.901 115.362 253.809 175.911 145.903 221. 896 259.893
0.0 0.0 24.36 24.5 19.2 -9.70 -11.92 -38.0 7.39 30.06
-44.3 0.0 11.6
-102.5 3.50 14.92 -2.10 -196.58 -225.6
152.357
4.2-5
233.263 206.813
9.76
-71.9 -109.6 0.0 -55.0 -206.7 -5.71
I
-8,4 -21.4 -2.5
Sulfur Sulfur ................... rhombic ................ monoclinic ............. Sulfur ................... Sulfur ................... Sulfur trioxide ............ Hydrogen sulfide .......... Sulfur tetrafluoride ........ Sulfur hexafluoride ........ Disulfur dichloride ........ Thionyl'chloride .......... Sulfuryl chloride .......... Thionyl bromide ..........
S
32.064
66.64
.......... . ...... . .......... . ...... .
....... . . ....... ....... . . .......
S, SO, H,S SF, SF, S,C]' SOC]' SO,C]' SOBr,
30.68 31. 7 -94.58 -4.93 -185.2 -289. -4.4 -50.8 -87.0 -17.7
8,
64.128 96.192 80.062 34.080 108.058 146.054 135.034 118.969 134.969 207.881
0.0 0.08 -108.63
-105.41
-14.2 -58.7 -94.2
Nitrogen Nitrogen ................. N, Nitric oxide ..... . . . . . . . . . NO Nitrogen dioxide ......... ; . NO,
28.013 30.006 46.006
0.0 21.57 7.93
I I I
4-320
HEAT TABLE
41-2.
HEATS OF FORMATION OF ELEMENTS AND
INORGANIC COMPOUNDS
Substance name
Formula
I
(Continued)
Mol. weight
!:.HjD, kcal mole- 1 at 25°C Liquid
Gas
I
Solid
Nitrogen (Cont.) Nitrous oxide ............. Nitrogen trioxide ......... Nitrogen tetroxide ........ Nitrogen pentoxide ........ Ammonia ................ Hydrazine ............... Hydrogen azide ........... Nitrous acid .............. Nitric acid ............... Hydroxylamine ........... Ammonium hydroxide ..... Ammonium nitrate ........ Nitrogen trifluoride ....... Nitrosyl fluoride .......... Ammonium fluoride ....... Nitrogen trichloride ....... Nitrosyl chloride .......... Ammonium chloride ....... Hydrazine hydrochloride ... Ammonium perchlorate .... Nitrosyl bromide .......... Ammonium bromide ...... Ammonium iodide ........ Ammonium hydrogen sulfide ............... Sulfamic acid ............. Sulfamide ................ Ammonium hydrogen sulfate ............... Ammonium sulfate ....... '1
N,O N 2O, N 2 O. N,O, NH, N 2H. HN, HNO, HNO, NH20H NH.OH NH.NO, NH, NOF NH.F NCI, NOCl NH.CI N 2H,Cl NH.CIO. NOBr NH.Br NH.!
44.013 76.012 29.011 108.010 17.031 32.045 43.028· 47.014 63.013 33.030 35.046 80.044 71.002 49.005 37.037 120.366 65.459 53.492 68.506 117.489 109.915 94.924 144.943
19.61 20.01 2.19 2.7 -11. 02 22.80 70.3 -19.0 -32.28
I
12.02 -4.66 -10.3 12.10 63.1 -41.61 -27.3 -86.33 -87.37
-29.8 -15.9 -110.89 55 12.36 -75.15 -47.0 -70.58 19.64 -64.73 -48.14
NH.HS H,NSO,H S02(NH')2
51.111 97.093 96.108
-37.5 -161.3 -129.3
NH.HSO. (l'l"H.)2S0.
115.108 132.139
-245.45 -282.23
Phosphorus phosphorus a, white ............... triclinic, red ............ black .................. amorphous, red ......... Phosphorus ............... Phosphorus .............. Phosphorus trioxide ....... Phosphorus pentoxide ..... Phosphine ................ Metaphosphoric acid ...... Pyrophosphoric acid ....... Phosphorus trifluoride ..... Phosphorus pentafiuoride .. Phosphorus oxyfiuoride .... Phosphorus trichloride ..... Phosphorus pentachloride .. Phosphorus oxychloride .... Phosphorus tribromide .... Phosphorus penta bromide .. Phosphorus oxybromide ...
P
.......... . .......... . ...........
P2 P. P.06 P.O' O PH, HPO, H.P 2 O, PF, PF, POF, -PCla PCI, POCI, PBr, PBr, POBr,
30.974
••
D
•••
••
....... ....... ...... .
. ....... . .......
61. 948 123.895 219.892 283.889 33.998 79.980 177.975 87.969 125.966 103.968 137.333 208.239 153:332 270.701 430.494 286.700
34.5 14.08
..0 .....
....... . ....... . 1.3
....... .
........
. ....... . .......
. .......
0.0 -4.2 -9.4 -1.8
........ ........
-392.0 -713.2
........ ........
-226.7 -535.6
-219.6 -381.4 -289.5
........
-76.4
-89.6
........
-33.3
-142.7 -44.1
........ ....... .
........
•••••••
•••
0
0 .••••
-106.0 -64.5 -109.6
HEATS OF FORMATION AND !tElATS OF COMBUSTlON TABLE
41-2.
4-321
HEATS OF FORMATION OF ELEMENTS AND
INORGANIC COMPOUNDS
(Continued) !:J.HjO, kcal mole- 1 at 25°C
Substance name
I w~~tt I--G-a-s--'-L-iq-u-i-d---;--S-o-l-id--
Formula
Phosphorus (Cont.) Phosphorus triiodide. . . . .. Ammonium dihydrogen phosphate .......... , Ammonium hydrogen ... . phosphate ...... " ... , Ammonium phosphate.....
PI,
411.687
-10.9
NH4H,PO,
115.026
-345.94
(NH,),HP04 (NH,)aPO,
132.057 149.087
-347.50 -399.6
Boron Boron ................... amorphous ............ . Diborane ............... . Boric acid ............... . Boron trichloride. : ....... .
B
0.0 0.9
10.811
B,H 6 H,BO, BCla
27.670 61.833 117.170
8.5 -261.55 -96.50
-102.1
Silicon Silicon. . . . . . . . . . . . . . . . . .. amorphous ............ . Silicon .................. . Silicon monoxide ......... . Silane ................... . Disilane ................. . Metasilic acid ........... . Orthosilic acid ........... . Silicon tetrachloride ...... . Silicon tetrabromide ...... . Silicon tetraiodide ........ . Tetramethylsilane ........ . Hexamethyldisiloxane .... .
Si Si, SiO SiH, Si,H 6 H,SiO, H,Si04 SiC14 SiBr4 SiI, Si(CH,), [(CH,)aSij,O
28.086 56.172 44.085 32.118 62.220 78.100 96.116 169.898 347.722 535.704 88.226 162.382
0.0 1.0 142 -23.8 8.2 19.2 -284.1 -354.0 -157.03 -99.3
-164.2 -109.3
-57.15 -185.88
-63 -194.8
-45.3
Beryllium, Sodium, Potassium Beryllium ............... Beryllium oxide .......... Beryllium fluoride ........ Beryllium chloride ....... Sodium ................. Sodium oxide ............ Sodium hydride .......... Sodium hydroxide ........ Sodium fluoride .......... Sodium chloride ......... Sodium carbonate ........ Sodium formate .......... Sodium acetate .......... Potassium ............... Potassium oxide ......... Potassium hydride ....... Potassium hydroxide. Potassium fluoride ....... Potassium chloride .... ...
. . . . . . . . . . . . . . . .
Be BeO BeF, BeClz Na Na,O NaH NaOH NaF NaCl Na,CO, NaCHO, NaC,H,O, K
K,O KH KOH
. KF . KCI
9.012 25.012 47.009 79.918 22.990 61. 979 23.998 39.997 41.988 58.443 105.989 68.008 82.035 39.102 94.203 40.110 56.109 58.100 74.555
78.0 30.2 -186.1 -85.7 25.9 29.88 -70.1 -43.7
21.52 30.0 -78.2 -.51.0
0.0 -145.0 -245.3 -117.2 0.0 -99.4 -13.7 -101.72 -136.6 -98.5 -269.8 -155.03 -169.8 0.0 -86.4 -15.6 -101.52 -134.4 -104.1
4-322
HEAT TABLE
41-3.
HEATS OF FORMATION AND"HEATS OF
COMBUSTION OF COMPOUNDS OF CARBON
Rcal mole- 1 at 25°C
Substance name
Formula and state
Mol. weight
-!!.Hco !!.Hfo
Gross
I
Net
Carbon and Carbon-Oxygen Carbon ..................... graphite ................... diamond .................. Carbon ..................... Carbon monoxide ............ Carbon suboxide .............
C,g C,e C,e C2,g CO,g C30"g C30,,1
12.011
. ...... .0.·.0.
24.021 28.011 68.032
.......
171.29 0.0 0.45 199.03 -26.42 -22.20 -28.03
265.34 94.05 94.50 387.13 67.64 259.95 254.12
265.34 94.05 94.50 387.13 67.64 259.95 254.12
-17.88 -20.23 -24.81 -28.69 -30.14 -35.31 -32.14 -36.88 -34.98 -41.37 -36.90 -42.92 -39.66 -45.00 -39.92 -47.50 -41.62 -48.80 -40.99 -48.26 -44.32 -50.99 -42.46 -49.46 -44.85 -53.61 -46.57 -54.91 -45.92 -54.32 -45.29 -53.75 -49.25 -57.03 -46.78 -55.79 -48.26 -56.15
212.80 372.82 530.60. 526.72 687.64. 682.47 685.64 680.89 845.16 838.78 843.24. 837.22 840.49 835.14 1,002.59 995.01 1,000.89 993.71 1,001.52 994.25 998.19 991.52 1,000.06 993.05. 1,160.02 1,151.27 1,158.31 1,149.97 1,158.96 1,150.55 1,159.59 1,151.13 1,155.63 1,147.85 1,158.10 1;149.09 1,156.62 1,148.73
191. 76 341.26 :488.52 484.64 635.04 629.87 633.04 628.30 782.. 05 775.,66 780:13 774.11 777.38 772.03 928.95 921.38 927.26 920.08 927.89 920.62 924.56 917.89 926.42 919.42 1,075.87 1,067.12 1,074.16 1,065.82 1,074.80 1,066.40 1,075.44 1,066.98 1,071.48 1,063.70 1,073.95 1,064.94 1,072.47 1,064.58
Carbon-Hydrogen, Alkanes Methane .................... Ethane ..................... Propane ..................... n-Butane .................... 2-Methylpropane (isobutane) .. n-Pentane ................... 2-Methylbutane (isopentane) .. 2,2-Dimethylpropane (neopentane) n-Hexane ................... 2-Methylpentane ............. 3-Methylpentane ............. 2,2-Dimethylbutane .......... 2,3-Dimethylbutane .......... n-Heptane .................. 2-Methylhexane .............. 3-Methylhexane .............. 3 -Ethylpentane ..............
2,2-DimethylpentaIle ......... 2 ;3-Dimethylpentane ......... ~,4-Dimethylpentane .........
CH.,g C 2 H"g C 3H a,g C3HaJ C.H,o,g C.H,o,l C.H,o,g C.H,o,l C 5H",g C,H",l C,H",g C,H",l C,H 12,g C,H",l C.Hu,g C,Hu,l C 6H 14 ,g C,Hu,l C,H,.,g C,Hu,l C,Hu,g C.Hu,l C.H 14,g C.H,.,l C7H",g C7Hu,l C,H16,g C,H16,l C7H16,g C7H16,l C7H16,g C7H",l C7H",g C,H16,l C7H16,g C,H",l C,H16,g C7H,~,l
16.043 30.070 44.097 .0
•••••
58.124 ••••
0
••
58.124 ••••••
0
72.151
.......
72.151 .0
••
0
••
72.151
,
....... 86.178 ....... 86.178 ....... 86.178 ....... 86.178 ....... 86.178
,
.0 . . . 0.
100.206
.......
100.206 ••••
0
••
100.206 .0 . . . . .
100.206 ••••
;
••
!
0
••
100.206 0.0
••
100.206 ••••
0
••
100.206
.......
4-323
HEATS OF FORMATION AND HEATS OF COMBUSTION TABLE
41-3.
HEATS OF FORMATION AND HEATS OF
COMBUSTION OF COMPOUNDS OF CARBON
(Continued) Kcal mole-' at 25°0
Formula and state
Substance name
Mol. weight
-t:..Hco t:..Hr Gross
I
Net
Carbon-Hydrogen, Alkanes (Cont.) 3,3-Dimethylpentane ......... 2,2,3-Trimethylbutane ........ n-Octane .................... 2-Methylheptane ............. 3-Methylheptane ............. 4-Methylheptane ............. 3-Ethylhexane ............... 2,2-Dimethylhexane .......... 2,3-Dimethylhexane .......... 2, 4-Dimethylhexane .......... 2,5-Dimethylhexane .......... 3,3-Dimethylhexane .......... 3,4-Dimethylhexane .......... 2-Methyl-3-ethylpentane ...... 3-Methyl-3-ethylpentane ...... 2,2,3-Trimethylpentane ....... 2,2,4-Trimethylpentane ....... 2,3,3-Trimethylpentane ....... 2,3,4-Trimethylpentane ....... 2,2,3,3-Tetramethylbutane .... n-Nonane ................... 2,2-Dimethylheptane ......... 2,2,3-Trimethylhexane ........ 2,2,4-Trimethylhexane ........
C7H 16,g C7H16,1 C7H16,g C 7H16,1 CsH,s,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CSHlS,1 CSHlS,g CSHlS,l CSHlS,g CSHlS,l CSHlS,g CSHlS,l CSHlS,g CSHlS,l CSHlS,g CSHlS,l CSHlS,g CSHlS,l CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CSHlS,l CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 CSHlS,g CsHlS,1 C,H.o,g C,H.o,l C.H.o,g C.H.o,l C.H.o,g C.H.o,l C.H.o,g C.H.o,l
100.206 100.206
....... 114.233
.......
114.233 00
•••••
114.233
....... 114.233
....... 114.233
....... 114.233
......... 114.233
....... 114.233
....... 114.233
....... 114.233 "
.....
114.233
....... 114.233
...... , 114.233
.......
114.233
....... 114.233
.......
114.233
....... 114.233
....... 114.233 .0 • . . . .
128.260
....... 128.260
....... 128.260
....... 128.260
.......
-48.12 -56.05 -48.92 -56.61 -49.79 -59.71 -51.47 -60.96 -50.80 -60.32 -50.66 -60.15 -50.37 -59.85 -53.68 -62.60 -51.10 -60.38 -52.41 -61.44 -53.19 -62.24 -52.58 -61.56 -50.88 -60.20 -50.45 -59.66 -51.36 -60.44 -52.58 -61.41 -53.55 -61.95 -51.70 ...,.60.60 -51.94 -60.96 -53.97 -64.21 -54.56 -65.66 -58.74 -68.85 -57.59 -67.56 -57.85 -67.58
1,156.75 1,148.83 1,155.96 1,148.27 1,317.45 1,307.53 1,315.77 1,306.28 1,316.45 1,306.92 1,316.58 1,307.09 1,316.87 1,307.39 1,313,56 1,304.64 1,316.14 1,306.86 1,314.83 1,305.80 1,314.06 1,305.00 1,314.66 1,305.68 1,316.36 1,307.04 1,316.79 1,307.58 1,315.88 1,306.80 1,314.66 1,305.83 1,313.69 1,305.29 1,315.54 1,306.64 1,315.30 1,306.28 1,313.28 1,303.03 1,475.05 1,463.95 1,470.87 1,460.76 1,472.02 1,462.05 1,471.76 1,462.03
1,072.60 1,064.68 1,071.81 1,064.12 1,222.78 1,212.86 1,221.10 1,211.61 1,221.78 1,212.25 1,221.91 1,212.42 1,222.20 1,212.72 1,218.89 1,209.97 1,221.47 1,212.19 1,220.16 1,211.13 1,219.38 1,210.33 1,219.99 1,211.01 1,221.69 1,212.37 1,222.12 1,212.91 1,221.21 1,212.13 1,219.99 1,211.16 1,219.02 1,210.62 1,220.87 1,211.97 1,220.63 1,211.61 1,218.61 1,208.36 1,369.86 1,358.76 1,365.68 1,355.57 1,366.83 1,356.86 1,366.57 1,356.84
4-324
HEAT TABLE
41-3. HEATS OF FORMATION AND HEATS OF
COMBUSTION OF COMPOUNDS OF CARBON
(Continued) Kcal mole- I at 25°C
Formula and state
Substance name
Mol. weight
-!:J.Hco !:J.Hr
Gross
Net
I Carbon-Hydrogen, Alkanes (Cont.) 2,2,5-Trimethylhexane ........ 2,3,3-Trimethylhexane ........ 2,3,5-Trimethylhexane ........ 2,4,4-Trimethylhexane ........ 3,3,4-Trimethylhexane ........ 2,2-Dimethyl-3-ethylpentane .. 2,4-Dimethyl-3-ethylpentane .. n-Decane ....................
C,H",g C,H,o,l C,H 20 ,g C,H,o,l C,H,o,g C,H,o,l C,H,o,g C,H,o,l C,H,o,g C,H,o,l C,H 20,g C,H·,o,l C,H,o,g C,H,o,l
128.260
. . . . . ..
128.260
.......
128.260 .......
128.260
.......
128.260
.......
128.260 ...
,
...
128.260
.......
Cl0H2~,g
142.287
C,oH 22 ,l
.......
-60.36 -69.97 -57.13 -67.18 -57.91 -67.81 -57.06 -66.87 -56.20 -66.33 -55.21 -65.17 -54.30 -64.42 -59.64 -71.92
1,469.24 1,459.64 1,472.48 1,462.43 1,471.70 1,461. 80 1,472.55 1,462.74 1,473 .41 1,463.28 1,474.40 1,464.44 1,475.31 1,465.19 1,632.34 1,620.06
1,364.06 1,354.45 1,367.29 1,357.24 1,366.51 1,356.61 1,367.36 1,357.55 1,368.22 1,358.09 1,369.21 1,359.25 1,370.12 1,360.00 1,516.63 1,504.35
499.85 655.78 650.22 793.42 786.55 948.86 941.28 1,106.23 1,097.50 1,103.54 1,095.44 1,105.62 1,097.06 1,103.92 1,095.64 1,104.12 1,095.90 1,104.66 1,096.39 1,263.56 1,253.74 1,421.10 1,410.10 1,578.54 1,566.36 1,735.99 1,722.63 1,893.43 1,878.89
468.29 613.70 608.14 740.83 733.96 885.75 878.17 1,032.60 1,023.87 1,029.91 1,021.81 1,031. 99 1,023.43 1,030.29 1,022.01 1,030.49 1,022.27 1,031.03 1,022.76 1,179.41 1,169.59 1,326.43 1,315.43 1,473.35 1,461.17 1,620.28 1,606.92 1,767.20 1,752.66
Carbon-Hydrogen, Cycloalkanes Cyclopropane ................ Cyclobutane ................. Cyclopentane ................ Methylcyclopentane .......... Ethylcyclopentane ........... 1,1-Dimethylcyclopentane .... 1-cis-2-Dimethylcyclopentane.. 1-lrans-2-Dimethylcyclopentane l-cis-3-Dimethylcyclopentane ..
I-trans-3-Dimethylcyclopentane n-Propylcyclopentane ......... n-Butylcyclopentane ......... n- Pentylcyclopentane .........
n-Hexylcyclopentane ......... n-Heptylcyclopentane ........
C,H 6 ,g C 4H s,g C4Hs,1 C 5H' lo ,g CoH,O,l C 6H ,2,g C 6H",l C,H ,4,g C,H ,4,1 C,H 14 ,g C,H 14 ,l C,H ' 4,g C,H, .,! C,H ,4,g C,H ,.,! C 7H14,g C,H ,4,1 C,H 14,g C 7 H 14,l C SH ,6 ,g CSHIO,l C,HIs,g C,H",l C,oH 20,g C,oH2o,1 Cl1H 22 ,g CllH",l C 12 H 24,g C 12 H,.,!
42.081 56.108
.......
70.135
.......
84.163
.......
98.190
.......
98.190 .......
98.190
.......
98.190
....... 98.190 ....... 98.190 .......
112.217 ..... -. 126.244 .......
140.271
..... ..
154.298
.......
168.325 ......
.
12.75 6.32 0.76 -18.41 -25.28 -25.34 -32.92 -30.33 -39.06 -33.02 -41.12 -30.94 -39.50 -32.64 -40.92 -32.44 -40.66 -31.90 -40.17 -35.37 -45.19 -40.19 -51.19 -45.12 -57.30 -50.04 -63.40 -54.96 -69.50
4-325
HEATS OF FORMATION AND HEATS OF COMBUSTION TABLE
41-3.
HEATS OF FORMATION AND HEATS OF
COMBUSTION OF COMPOUNDS OF CARBON
(Continued) Kcal mole- l at 25°C
Formula and state
Substance name
Mol. weight
-t1Hco t1HJO
Gross
I
Net
Carbon-Hydrogen, Cycloalkanes (Cont.) n-Octylcyclopentilne ..........
n-N onylcyclopentane ......... n-DecYlcyclopentane .... , .... Cyc1ohexane ................. Methylcyclohexane ........... Ethylcyclohexane ............ 1,1-Dimethylcyclohexane ..... 1-cis-2-Dimethylcyclohexane .. 1-trans-2-Dimethylcyclohexane 1-cis-3-Dimethylcyclohexane ..
1-trans-3-Dimethylcyclohexane 1-cis-4-Dimethylcyclohexane .. 1-trans-4-Dimethylcyclohexane Cycloheptane ................ Cyclooctane ................. Cyclotetradecane .............
C13H26,g CuH.6,l C14H",g CuH",1 C15H,o,g CuH,o,1 C6H12,g C6Hu,! C,Hu,g C,H",! C 8H",g CsH16,1 C SH l6,g C8Hle.l C SH ,6,g C SH l6,l C,H,6,g CsH",! C SH16,g CSHI.,1 C SH I6,g C 8H 16,1 C sH 16,g CSH,.,1 C sHl. 1,929.47 1,912.77 2,076.69 2,058.81 2,223.30 2,204.24 1,018.82 1,008.43 1,461.11 1,441.61 1,207.83 1,190.46 1,337.00 1,334.29
182.62 173.55 337.02 326.85 494.13 484.75
161.58 152.51 305.46 295.29 452.06 440.68
Carbon-Oxygen-Hydrogen, Alkanols Methanol (methyl alcohol) ....
CH,O,g CH40,1 Ethanol (ethyl alcohol) ....... C2H,O,g C2H,O,1 I-Propanol (n-propyl alcohol) .. C3H80,g C 3H sO,l
32.042
.......
46.070
.......
60.097 ••
•
•••
0
-48.06 -57.13 -56.03 -66.20 -61.28 -72.66
HEAT
4-332 TABLE
41-3.
HEATS 0]' FORMATION AND HEATS OF
COMBUSTION OF COMPOUNDS OF CARBON
(Continued) Kcal mole- 1 at 25°C
Substance name
Formula and state
Mol. weight
-I:!.Hco I:!.HjD
Gross
-
I
Net
Carbon-Oxygen-Hydrogen, Alkanols (Cont.) 2-Propanol (isop:ropyl alcohol) . I-Butanol. .................. 2-Butanol
.
. .... . ..
2-Methyl-l-propanol
... . . . . ..
2"Methyl-2-propanol ......... 1-Pentanol. ................. 2-Pentanol. ................. 3-Pentanol. ................. 2-Methyl-1-butanol .......... 3-Methyl-1-butanol .......... 2-Methyl-2-butanol. .......... 3-Methyl-2-butanol. .......... 1-Hexanol. .......
•••
c C = 4.re(a2 - c2)l[ta~-1 (a 2c- 2 - 1)t]-1 Pr.olate spher.oid .of semiaxes a and b, a > b C = 4.re(a 2 - b2)l[tanh- 1 (1 - b2a- 2)i]-1 Ellips.oid .of semiaxes a, b, and c, a > b > c C = 4.re(a 2
Circular disk .of radius a Elliptic disk .of semiaxes a and b, a > b Tw.o spheres .of radius a in c.ontact Tw.o spheres .of radii a and b in c.ontact C = -4.reab(a
-
c2 )'[F(k,
= alb + (b 2 -
= 2k-~[K(k)
- E(k)]
a 2)1]-1 = (1 - k'2)!
1, the following recurrence formula may be used.to find both P nand Q" (2n
+ 1)P1'+1 -
4na- 1bP1'
+ (2n
- 1)P n _ 1 = 0
A capacitance tfl,ble is given in Australian J. Phys. [7,35.0 (1954)]. Torus formed. by rotation of a circle of diameter d about a tangent line
.,
C = 87rEd
L
[J 1 (k"d)]-1 So.o(knd) "'" 0.970 X lO- IOd
n=l
where So.o(k"d) is a Lommel funqtion and Jo(knd) = O. 1 For additional intersecting sphere-capacitance formulas, see Snow, J. Research Nat!. Bur. Standards 43, 37t-407(1949).
5-14
ELECTRICITY AND MAGNETISM
Aichi's formula for a nearly spherical surface
C = 3.139 X lO-llst where S is surface area. Cube of side a. Close lower limit
Figure of rotation, z = a(cos u C
C
= 0.7283
+
k cos 2u), p
= 4.510 X
= a(sin
u - k sin 2u), 0
b
> e,
a'
> b' > c', and a > a'
Small sphere of radius a midway between planes a distance 2c apart 1 C .." 1.1128?: 10-10 ( Ii
1 In 2 )-' - c
Sphere of radius b on axis of infinite cylinder of radius a C = b[1.11285 - 0.9277r - 0.114r' - 0.1955r 3
where r = bja.
+ 1.8858r(1
The error is less than 1 part in 4,000 for 0
-
r)-0.S463]
a, C, = 2"..[ln (a- 1b)]-1. Confocal elliptic cylinders semiaxes a, b and a', b', b > a, b' > a', a > a' C, = 2"..[tanh- 1 (b- 1a) _. tanh- 1 (b'-l a')]-1
Rectangular prism of n width, a sides, inside coaxial circular cylinder of radius b. b »a, C .."2,,..[ln (a- 1bN)]-I, where N = 2~-lr(1 +2n-1)[r(1 n-1)]-'.
+
If
6-16
ELECTRICITY AND MAGNETISM
The capacitance per unit length of conductor systems 1 to 12 given below is C, = AeK(k) {K[(l - k2)t])-1
where A is20r 4 as indicated, and K(k) is a complete elliptic integral of modulus k. This is given below in terms of the arrangement of straight lines or circular arcs or both that are formed by taking a normal cross section of the two-dimensional conductor system. Any of these configurations, if used as a transmission line and perfectly conducting, has the characteristic high-frequency impedance 'f/.C,-, (see Table 5b-l). 1. Two collinear lines of lengths a and b with a gap e between. Also valid if b = "'.
A
2
=
2. A circle of radius R whose center lies on an interior line of length a, or in a gap of width a between two external collinear semi-infinite lines at a distance e from the near one. Valid for an infinite line normal to a semi-infinite one if R = "'.
A
+ el2R -
k = aR(aR - e 2
= 4
al)-l
3. A radial line of length a at a distance e from a circle of radius R inside (-) with a + c < R, or outside (+) with a a, placed in a field that would be uniform and of strength E except for the spheroid is T
=
27rE v (K - 1)2b 2aE2(3P - 2) sin 2" 3[(K - 1)2P2 (K - 1)(2 - K)P - 2Kj
+
where P = A[(l + A2) cot- 1 A - A], A = a(b 2 - a 2 )-!, and K = If the -above obb_t.e spheroi.rt is eoncillet.ing, the torque is T
=
E' v- 1 •
27rfvb 2aE2(3P - 2) sin 2a 3P(P - 1)
The torque tending to increase the angle a between the field and the major axis of a prolate dielectric spheroid of capacitivity • with semiaxes a and b where b < a placed in a field that would be uniform and of strength E except for the spheroid is 27rEv(K - 1)2b 2aE2(2 - 3Q) sin 2a + (K - 1)(2 - K)Q - 2K]
T = 3[(K - 1)2Q2 where Q = C[(l - C2) coth- 1 C
+ C].
C = a(a 2 - b2)-! and K =
E'v- 1•
If the above prolate spheroid is conducting, the torque becomes!
T
=
27rEv b 2aE2(2 - 3Q) sin 2a 3Q(Q - 1)
The axis of rotational symmetry of a right circular solid conducting cylinder of radius a and length 2b makes an angle e with a field that would be uniform and of strength E except for the cylinder. The torque tending to align the axis with the field is
T
= 7rEa 2bE2
sin 20(al - at)
I For torque on general ellipsoid, see Stratton, "Electromagnetic Theory," p. 215, McGraw-Hill Book Company, New York, 1941.
ELECTRICITY AND MAGNETISM
where
Gt G)
+ 2.1444 (~rB2B + 0.7171 2 + 0.84883 + 0.369
a1 = 1 at =
G)
0.548
6752
tanho.6 (~) 0.712
The torque vanishes at (a/b) = 1.1958. The errors in these formulas are less tlmu i part in 4,000 for 0.25
a c satisfy the scalar Helmholtz equation, (5b-76) with k 2 = W 2P.E. By choosing a appropriately, one may also apply'Eqs. (5b-74) and (5b-75) to the case of an inhomogeneous medium.2 Basic Wave Types
1. Transverse electromagnetic waves (TEM waves)-containing neither an electric nor a magnetic field component in the direction of propagation. 2. Transverse magnetic waves (TM or E waves)-containing an electric field component but not a magnetic field cotnponent in the direction of· propagation. 1 The vector aef> may be identified as the electric Hertz ~ector and, the vector a'lr may be identified as the magnetic Hertz vector. a in this case is a constant vector. 2 c. Yeh, Phys. Rev. 131, 2350 (1963).
6-46
ELECTRICITY AND MAGNETISM
3. Transverse electric waves (TE or H waves)~ontaining a magnetic ·field.component but not an electric field component in the direction of propagation. 4. Hybrid waves (HE waves)-containing all components of electric and magnetic fields. These hybrid waves are obtainable by linear superposition of TE and TM waves. Formal Solutions for the Time-harmonic Vector Wave Equation. INTEGRAL REPRESENTATIONS. Upon direct integration of the wave equation in homogeneous isotropic medium, integral solutions in terms of the sources can be obtained.. Aharmonic time dependence of e'w, is assumed and suppressed in this section. Direct integration of Eqs. (5b-68) to (5b-7I) gives p, ~.
A. = -4 'It"
eiklr-r'l
-I-'-'1 dv'
(5b-77)
V· J(r') r - r
r
[(i)' +
n'
(p';i)2 -
Notes: 1. a = radius of the waveguide ' 2. n I are integers, for both TE and TM Wave, n can be zero but not I. 3. Dominant mode is the TMll wave having the lowest cutoff frequency; TEol mode is the only mode whose aw decreases monotonically as frequencies increase.
n2
] 01
I c.n
c;;:;
5-54
ELECTRICITY AND MAGNETISM
TABLE
5b-2.
FIELD CONFIGURATIONS FOR SEVERAL LOWER-ORDER MODES IN RECTANGULAR AND CIRCULAR GUIDES
TEll
... -.. -. ,e.... . .,. +l+!+ .~".#I e:_
?2 2
?? U
,-------,
. iO 'I'
IG
.Ve ;. -:•• ,
•
1)8'
+1
+~I+
'+
.} ,I,
+1 +!tJ,+ 1+ "!1 .'. +1+. ,+1+ II:..
't. .... po. +I+l + 't... _-"
z'i-;?7jj-/Z
x
(22????
,,~--
eO'
???i"z;": 2
I
- - --. .:.-: = :.:.-----_ .....
. ..
+ + + ++ + + + ++ + + +
2
:3
+ + +
+
·· ··· ··
a·_·" ,
.
I
.
,
'_
;?
?
?
2?
? ? 2 ? ? 2 ? ? ? ?
?
?
:'
3
TE2J 2
[D
... .
3
?2 ? ) ?
+ ,!+ ++ .+ ++
2 ? ? ? ) ?
2?
?
22
·: ·.
2
TM" i~~'
.~+~.
m9JG9Jft • •.~+~ ~+~
I
.~+~ •
.kQ±,JtLzG):,lj 2
5-55
FORMULAS TABLE
5b-2.
FIELD CONFIGURATIONS FOR SEVERAL LOWER-ORDER MODES
IN RECTANGULAR AND CIRCULAR GUIDES
..
TM02
TMOl
(Continued) TMlI '
~,.
--,-
--
,
,
-.... Distributions ;....---Below Alo~ This PIaM
,. .•
--,~+
+ +
fEo!
TEll
Note 1. The solid dots repre3ent vectors coming out of the paper, and the crosses represent vectors going into the paper. Note 2. The solid lines represent electric lines of force. and the dotted lines represent magnetic lines of force. .
with Ez(n)
o on the boundary,
then, for n
> 0,
0,
1, the phase velocities of the propagating surface-wave modes are less than the velocity of light in vacuum. 3. Below the cutoff frequency, a mode simply does not exist. In other words unlike the bounded waveguide' case no evanescent mode exists. 4. The finite number of discrete surface-wave modes does riot represent a complete set of solutions. In addition to.the eigenfunction solutipns there exists solutions with a continuous spectrum. (This property is in direct contrast to the mode property in bounded waveguides.) 5. Only TE, TJJ1, or HE modes may exist on a surface-wave structure. Detailed formulas are given for the circular dielectric waveguide as a representative surface-wave structure. It is understood that all fields vary as ei"{z-iwt. The dielectric rod of radiusa~having· E1 and P.o as its permittivity and permeability" is assumed ,to be embedded in another dielectric medium with E = EO and p. = p.o. F;urthermore E1
>
EO·
FIELD COMPONENTS
1. HEnm modes with n
~ 0: Ez = A nJ n(slr) cos ncf> = B"Kn(sorYcos ncf> Hz = C"Jn(Slr) sin ncf> = DnKn(sor) sin ncf>
r:$a r;:::a r:$a r;:::a
(5b-148) (5b-149) (5b~150)
(5b-151)
2. TMom modes:
E. =A.Jo(slr)
r :$ a
= BoKo(sor) Hz = 0
r;:::a for all r
Ez = 0 Ez = C OJ O(slr)
for all r r:$a r;:::a
3. TEom modes: = DoKo(sor)
All other transverse field components may be found from Eqs. (5b-120) to (5b-123) with E = E1, P. = P.o for r :$ a and E = EO, P. = P.o for r ;::: a. An, Bn, Cn, Dn are amplitude coefficients. I n and Kn are respectively the Bessel and modified Bessel functions. PROPAGATION CONSTANT. The propagation constant 'Y is obtained by solving the following equations: 1. HEnm modes (n ~ 0):
(5b"152) (5b~153)
(5b-154) 2. TMom modes: (EdEO)J~(sla)
slaJO(sla) with Eqs •. (5b-153) and (5b-154)
K~(soa) + soaKo(soa) .
= 0
(5b-155)
TABLE
5b-4.
SEVERAL IMPORTAWI FORMULAS FOR SOME COMMON TRANSMISSION LINES*
Quantity
General lire
Pr pagation constant I' = '" - i{3.
Ideal line
VCR - iwL)(G - iwC)
Ph 'se constant {3 .....................
1m (1')
At enuation constant", ...............
Re (1')
w
-iw VLC w 271'
VLC
= -
v
=-
- iwl~ Ch ,racteristic impedance Z o........... G - iwe: Inp ut impedance Z; . ................. Z (ZL cosh 1'1 -t- Zo sinh 1'1) o Z 0 cosh 1'1 ZL sinh 1'1
Zo
Zo tanh 1'1
-iZo tan {31
1m Jedance of open line ...............
Zo coth 1'1
+iZo cot {31
"'I)
Zo'
(ZL sinh al Z:' cosh Zo sinh al Z1. cosh al (ZL cosh al Zo sinh cd) 1m Jedance of half-wave line ........... Zo Zo cosh al Z}; sinh al Vo tage along line V(z) ..... ........... Vi cosh 'YZ - IiZO sinh 'Yz I i COSh 'YZ - Zo Vi mn . h 'Yz Cu rent along line I(z) . ...............
Re lection coefficient KR . .............
ZL - Zo ZL Zo
Sta llding-wave ratio ..................
1 + IKEI 1 - IKRI
per unit length l = length of line Subscript i denotes input end quantities.
ZL ZL
(3 below)
G'
R' )
+ 8w'C' + 8w'L' GZo
2
~~[l-i(~-J!:...-)J C 2wC 2wL
("'Icoscos
(31 - i sin (31) {31 - ial sin {31 Z (cos {31 - ial sin (31 ) o al cos {31 - i sin {31 Z
o
Zo (Zo + ZLal) ZL + Zoal Zo (ZL + Zoal) Zo + ZLal
I:;j
o
~
cj t"< ~
UJ.
ZL - Zo ZL + Zo
1 + IKRI 1 - IRRI z
= distance along line from input end
A
=
wavelength measured along line
v = phase velocity of line equals velocity of light in dielectric of line for an ideal line
Subscript L denotes load end quantities.
* Ramo and Whinnery,
(See", and RG 1 - 4w'LC J!:...- + 2Zo
Vi cos {3z + iliZo sin (3z .Vi. Ii cos {3z + t Zo sm {3z
+
R. L, G, C = distributed resistance, inductance, conductance, capacitance
VLC
(ZL cos (31 - iZo sin (31) Zo cos {31 - iZL sin {31
1m Jedance of shorted line .............
+ + + +
w
~~
+
Zo
A
(
0
~R
1m Jedance of quarter-wave line ........
Approximate results for low-loss lines
"Fields and Waves in Modern Radio," 2d ed., John Wiley & Sons, Inc., New York, 1953.
en J
~
5-58
ELECTRICITY AND MAGNETISM
Conventional TEM Transmission Lines. For a two-conductor uniform line supporting the TEM waves, the differential equations for the voltage V and current I are aV = -L aI _ RI az at
(5b-140)
'!!
(5b-141)
az
-C aV - GV at
=
where L, C, R, and G are the inductance, capacitance, resistance, and conductance, respectively, all per unit length of the line. If steady-state sinusoidal conditions of the form e-iwt are considered, then the equations become aV -(R - iwL)I (5b-142) az aI -(G - iwC)V (5b-143) az Combining the above equations gives (5b-144) where the propagation constant
x
=
VCR - iwL)(G - iwC)
=
a
+ i(3
(5b-145)
The solution for Eq. (5b-144) is V '= Ae-xz I =
+ Bexz
-.l (Ae-Xz Zo
(5b-146)
_ BeXz)
(5b-147)
where Zo = VCR - iwL)/(G - iwC) and is called the characteristic impedance. A and B are constants to be determined according to the input and termination conditions. TaLles 5L-3 aud 5b-4 summarize constants for some common lines and some important formulas for transmission lines. Another kind of quasi-TEM microwave transmission line is the strip line 1 which basically consists of two (or more) parallel metallic strips of generally different width separated by a dielectric medium. This structure cannot support a TEM wave although the dominant mode closely resembles the TEM wave of a simplified microstrip with dielectric material uniformly filling the entire region. Under this TEM wave approximation, the problem is essentially one of finding the electrostatic potential iI>(x,Y) which satisfies the Laplace's equation V 2
1.5
Right: inductive iris.
5-68
ELECTRICITY AND MAGNETISM
References 1. Marcuvitz, N., (ed.): "Waveguide Handbook," vol. 10 of MIT Rad. Lab. Ser., McGraw· Hill Book Company, New York, 1951. 2. Collin, R. E.: "Foundations for Microwave Engineering," McGraw·Hill Book Company, New York, 1966. 3. Ghose, R. N.: "Microwave Circuit Theory and Analysis," McGraw·Hill Book Company, New York, 1963. 4. Ramo, S., J. R. Whinnery, and T. Van Duzer: "Fields and Waves in Communication Electronics," John Wiley & Sons, Inc., New York, 1965.
6b-l0. Cavity Resonators. Resonant cavities are used at high frequencies in place of lumped-circuit elements, primarily because they eliminate radiation and in general possess very low losses. Only eigenvalue solutions exist in a lossless cavity resonator completely enclosed by perfectly conducting walls. For a cavity filled with a homogeneous, isotropic dielectric, the pth eigenvector Ep satisfies (V2
+ kp )Ep = 2
0
n X Ep = 0
(everywhere within the cavity) (on the enclosing wall)
(5b·206)
where k p = Wp VM. (p = 1, 2, 3,. .) are the eigenvalues. Wp is the resonant frequency for the pth mode. The Qp of a resonator for the pth mode is defined as follows: total time-average energy stored Qp = Wp time-average power dissipated 2.w
(5b-207) (5b-208)
where 2.w is the bandwidth of the resonance curve. Hence Qp is a measure of the amount of power dissipated for the pth mode. For an enclosed cavity with slightly lossy walls, (5b-2U\J)
whereHp is the magnetic field of the pth mode of the cavity without losses, and ii, is the skin depth of the walls. A is the total surface enclosing the cavity region. For a cavity composed of a uniform transmission line (which may support the TE, TM, TEM, or HE mode) with short-circuiting perfectly conducting ends, the Qp of this cavity is related to the attenuation constant <Xp of the transmission line by the relation' (5b-21O)
vghase, v:roup and 'Yp are respectively the phase velocity wp/'Yp, the group velocity awp/a'Yp, and the phase constant of the pth mode. If the end plates possess a very
where
small loss, then the total QT of this cavity is 1
1
QT = Qend plates
+
1 Qtrans. line
where Qend plate, is calculated according to Eq. (5b-209) and according to Eq. (5b-21O). 1
C. Yeh, Proc. IRE 50, 2145 (1962).
QtraD,.line
can be calculated
5-69
FORMULAS
Simple Resonators. The mode functions for a cylindrical waveguide of simple cross section closed at both ends by short-circuiting plates are' (with d = length of the cavity) : For TMmnl modes Ezmnl = Amnipmn
H with (V,2 + frequency
(5b-211) (5b-212)
0
Hzmnl =
E
17rZ
cos d
17r
'mnl =
d
-
Amn . 17rZ rmn(TM) V,ipmn SIn
d
. Amn ( 0) tmnl = 'WE rmn(TM) ezX Vtipmn
rmn(TM)')ipmn
= 0 and
l7rZ
cos d
(5b-214)
= 0 on the cylindrical wall. The resonant
ipmn
1 [ V;
TM Wmnl =
(5b-213)
(TM)' rmn
(I
+ d7r)2J~
For TEmnl modes Ezmnl =
0
H
B
zmnl
=.
(5b-215) mn 'l!mn
.
17rZ
sm d
-iwf.' E'mnl = rmn(TE) Bmn(e,
H tmnl
17r
=
d
(5b-216)
X V
. l7rZ ,'lfmn ) SIn
d
1 'l7rz rmn(TE) Bmn(Vt'lfmn) cos
(5b-218)
d
with (V t 2 + rmn(TE)')'lf mn = 0 and resonant frequency
a'lfmn/an
TE = -1wmnl /"
(5b-217)
= 0 along the cylindrical wall.
The
' 21t o[ r mn,(TE)' '+, (I7r -, dJ 0
,UE
\ 'I
..I
For a rectangular resonator with cross sections a X b we have
with
. m7rX
ipmn =
sma-cos
'lfmn =
cos
rmn(TM) = rmn(TE)
n7ry
T
m7rX sm . Tn7ry a= [C:7r) + (n;) 2
(5b-219) (5b-220)
7
(5b-221)
For a circular cylindrical resonator of radius a, we have (5b-222) (5b-223)
where
rm,,(TM)
and
rmn(TE)
satisfy the following equations: Jm(rmn(TM)a)
= 0 0
J~(rmn(TE)a) =
(5b-224) (5b-225)
1 Solutions are also available for resonators of more complex shapes, such as the ellipsoidhyperbolid resonators [W. W. Hansen and R. D. Richtmeyer, J. Appl. Phys. '10, 189 (1930)J and the reentrant cavities [D, C, Stinson, Trans, IRE MTT-3, 18 (1955)],
6-70
ELECTRICITY AND MAGNETISM
Solutions are also available for spherical cavity of radius a: E;~I = V X (mnrer)
(5b-226)
TI!J i Hmnl = - - V X V X [mnlrerJ
(5b-227)
"'J1.
H;!1
=
V X[¥mnlrerJ
(5b-228)
i
(5b-229)
TM
E m .. 1 = -
"'E
V
X
V
X [¥mnlrerJ
mnl = jm(k~f)r)PlI.z (cos 11)~i: lcf> ¥mnl =jm(k,;!'f)r)Pml (cos 11)~i: lq,
(5b-230) (5b-231)
k~f; and k~f> satisfy
where jm(X) is the spherical Bessel function.
jm(k;"~f)a) = 0, j~(k~'f)a) = 0
(5b-232)
with (TI!J).(TM) _ k,;!1f)·{TM) "'mnl
-
__
r-
VJ1.E
Field configurations for a few lower-order modes are given in Fig. 5b-6. Small Perturbation Formula. The resonant frequency shift of a cavity due to the presence of a small foreign body having a dielectric constant EI and a permeability J1.1 is 8", "'1'
EO
Iv
Eo • Eri dV
+ J1.O
Iv
(5b-233) Ho • Hri dV
where E I, HI denote the resulting field vectors within the volume VI of the foreign body, and Eo, Ho denote the undisturbed field vectors. V is the volume of the cavity. "'1' is the resonant frequency of the unperturbed ,cavity. The resonant frequency shift of a cavity due to a small wall deformation is 8",
J1.o
Iv
(Ho • Hri) dV
+ EO
Iv
(5b-234) (Eo· Eri) dV
where Ll V is the small change in cavity volume. Open, Resonators. For very high frequency waves (such as light waves) any enclosed metallic cavity of reasonable dimensions for machining would have to operate on a very high order mode. The resonances of th,e mode would be so closely grouped that the natural bandwidths of the oscillating modes could not be separated, and the use as a resonant system would be impractical. By removing the sides from a closed cavity, a large number of modes can be eliminated owing to energy loss by radiation from the open sides; oilly the low-loss modes which are essentially TEM modes will remain. Assuming that z is the axis of the open resonator, and x, yare the transverse directions, one may obtain, from Maxwell's equations, the simple beam solutions which are characterized by a direction of propagation (the z axis) and by Ii unique plane phase front perpendicular to this axis: l Emn(z) = Eo Wo W Hm
r x) (- y)
v 2 W H~ V2 w exp
(_
(X2 + y2) ------u;.-
(5b-235)
1 G. D. Boyd and J. P. Gordon, Bell System Tech. J. 40, 489 (1961); A. G. Fox and T. Li, ibid. 453.
5-71
FORMULAS TM 010 ' CYLINDER
i[
j.
~
II
i
I
A =2.61 a Q=
CURRENT
(!-LIe 1/2 2.405 2R.[a/h+l]
ELECTRIC" fiELD - - - MAGNETIC FIELD
A + ++ + ++ + ++ + ++ ++ CROSS SECTION THROUGH A-A
I..
A=
I A
21_
~1+(2Ly 3410
"I
™on,CYLINDER
r@ CROSS SECTION THROUGH A-A TEOll,CYLINDER
~
CROSS SECTION THROUGH A-A
A
0:(: (+: Ais an arbitrary parametlilr with dimensions of length (wo may also be (leaned as ,the minimum spot size of the beam), w(z) = wo[l + (Z/zo)2]t, Zo = ;Wo 2/A, and A is the wavelength of a plane wave in the resonator medium. Possible pqsitions of ·reflectors having radii of
6-72
ELECTRICITY AND MAGNETISM TEIOI1 RECTANGULAR RESONATOR
o z ad
b
A (o2+d2 )1/ 2 Q= 1f (J,tEjI/2 [ 4RR
zb(Q2+ d2)3/2
J
[gd(Q2+d 2 l+z'b(02±d2
71.,=2.290 Q=(J,t!E)1/2/R•
SECTION THROUGH AX IS
SECTION THROUGH EQUATOR
71.=1.391:1
AXIAL SECTION
EQUATORIAL SECTION
FIG. 5b-6 (Continued)
curvature R are given by the relation R(z)
=
dz -w dw
=
-
1
Z (Z2
+ Z02)
(5b-236)
The size of the reflector must be large enough to intercept substantially all the field for the mode of interest (say, m = 0, n = 0), so that energy loss due to diffraction may be acceptable. The modes with large m and n have fields extending farther out from the axis and so will suffer larger diffraction losses. In this way one can discriminate between the transverse modes and ensure that 0nly a few will have low loss. As
5- 73
FORMULAS
an example, let us design an optical resonator by 'Q.sing two reflectors having radii of curvature R, and R 2, and a mirror separation d. From Eq. (5b-236) , we have
R, with
Z, =
Z2 -
=
Zo'
-Z2 - -
z,
d
Solving the above equations for Zo gives
_ [d(Rl - d)( -R, - d)(R , - R, - d)]t (R , -R,-2d)'
Zo -
which is the location of the minimum spot size Wo = (Xzohr)t. The phase variation along the z·axis for the (m,n) mode is (3z = -kz - (m
+ n + 1) tan-
where k = 27r/X, and (3 is the propagation constant. (3d = q7r = kd
q
l
.3!. Zo
(5b-237)
The resonant condition requires
= 1,2, . . .
(5b-238)
where d is the minor separation. The frequency separation between longitudinal modes is !:1f = c/2d; c = velocity of light in the resonator medium . Selected modal patterns are given in Fig. 5b-7. The Q of an optical resonator is given by Q = 27rd
aX
(5b-239)
where a is the fractional power loss per bounce from a reflector and is the sum of diffraction and reflection losses. The diffraction loss is small only if the Fresnel number N = a,a,/Xd, where a, and a, are radii of the mirrors, is much larger than unity. General Considerations. DEGENERATE MODES. Modes with different field distributions but with the same resonant frequency. EXCITA'l'ION OF CAVITY FIELDS. Excitation of cavity fields may be accomplished by the introduction of a conducting probe or antenna in the direction of the electric field lines, or by the introduction of a conducting loop with plane normal to the magnetic field lines, or by the FIG. 5b-7 . Modal patterns in optical introduction of a hole or iris between the cavity resonators. [From H . Kogelnik waveguide. l It is important to note that when and W. W. Riorod, Proc. IRE 50, the walls of the cavity have one or more 220 (1962) .] apertures, the orthonormal sets H p and Ep ) derived from the consideration of a completely enclosed cavity, are no longer adequate for an expansion of the cavity fields.' The electric vector E and the magnetic vector H of an electromagnetic field within a 1 Smythe, W. R., "Static and Dynamic Electricity," 3d ed., McGraw-Hill Book Company, New York, 1968. 2 K. Kurokawa, IRE Trans. ,MTT-6, 178 (1958).
ELECTRICITY AND MAGNETISM o
cavity coupled to an outside source by means of a waveguide must be derived according to the relations E =
H
I
€
L
Ep
fv E . Ep dV
(5b-240)
p=l
Hp
[k~i:E~, fA (n X E) . Hp dA]
p=l
L [i;: fA Gp
(n X E) . G p dA]
(5b-241)
p=l
where A consists of the perfectly conducting surface and the aperature surface, V is· the volume of the cavity, k' = W'Jl.€, and V'E p
+ kp'Ep
=
0 }
in V
(5b-242)
in V
(5b-243)
on A in V
(5b-244)
V· Ep = 0
n X Ep = 0
V'Hp
+ kp'Hp V·
Hp
= 0 } = 0
n X (V X Hp) = 0
V'Gp
+ gp'G
nX (V XG p )
on A
p = 0 } V· G p = 0 = 0 n' G p = 0
on A
HenceGp is derivable from scalar potential as follows: (5b-245)
G = VV p ,References . - -
1.
~. 3.
4. 5.
Bo~gl1is,
F. E., and C. H. Papas: Electromagnetic ·W·aveguides and Resonators, "Handbuch derPhysik," vol. 16, Springer-Verlag OHG, Berlin, 1958. Gdubau, G.: "Electro,magnetic Waveguides and Cavities," Pergamon Press, New York, 1961. Collin, R. E.: "Foundations for Microwave Engineering," McGraw-Hill Book Company, New York, 1966. Ramo, S., J. R. Whinnery, and T. Van Duzer: "Fields and Waves in Communication Electronics," John Wiley & Sons, Inc., New York, 1965. Slater, J. C.: "Microwave Electronics," D. Van Nostrand Company, Inc., Princeton, N.J., 1950.
6b~11. Radiation. Solutions of radiation problems must satisfy not only Maxwell's equations and the appropriate boundary conditions but also Sommerfeld's radiation condition. RadiationFieldfrom Known Current Distributions. Given a distribution of electric and magnetic currents, specified by the density functions J(r) and Jm(r) occupying a finite region of space. Formal expressions for the electric vector E and the magnetic vector H in an unbounded space are given earlier by Eqs. (5b-81) through (5b-84). Consider a reference frame with its origin in the vicinity of the sources; let r be the coordinates of the observation point, and r' be the coordinates of the source point. In the far-zone region (i.e., r »r' and kr » 1), the radiated fields which are purely transverse to the direction of propagation are '
Ee =
iOJI"
eilcr 47fr F e( 0, are the spherical coordinates of the observation point and en ee, e
c, n > 1) at a cone angle of 0 = cos- 1 (c/nu) with respect to the direction of motion. The field components are singular in that direction. c is the speed of light in vacuum. Energy radiated per unit length of path per frequency interval (dU /dl) dw is dU d
dl
w -
q2 411"foC2
(1 _~) w dw n2u2
(5b-314)
and the total radiation rate is dU -
dt' -
~_
411"i(Q,) are the amplitude and phase of the incident field at Q" tis the distance along the diffracted ray from QI to P" s is the distance from P, to P, PI is the principal radius of curvature of the diffracted wavefront on the body, and dq{Q,)/d,q(P , ) is the ratio of the width of a narrow strip of diffracted rays at QI to that at P, on the surface of the body. The diffraction coefficients Dm(P, ) and Dm(Q,) and the decay exponents OI. m are obtained from a canonical problem with the appropriate boundary conditions. Ud corresponds to Ed with u = 0 on the cylindrical body when the incident E field is parallel to the axis of the cylinder while Ud corresponds to H d with,au/an = 0 on the cylindrical body when the incident H field is parallel to the I
For the special case of 01. = '1T" /2 with the boundary condition au/an = 0 on the screen, (5b-360) are not applicable. The revised form is
'~qs. (5b~359)and
D' = -
.;. ~k
[~ aa D(8,0I.) ]
Ia_.. /'
FORMULAS
5-91
axis of the cylinder. Equation (5b-364) is not applicable without modification in the determination of the fields near the diffracting surface or near the shadow boundary. Application of Eq. (5b-364) to the problems of diffraction of waves by circular cylinders, spheres, parabolic cylinders, elliptic cylinders, etc., has been carried out successfully by Keller and his coworkers. ' Babinet's Principle. Consider three cases of a given source (1) radiating in free space, (2) radiating in the presence of an electrically conducting screen, and (3) radiating in the presence of a magnetically conducting screen. The electric and magnetic screens are said to be complementary if the two screens superimposed cover the entire y = 0 plane with no overlapping. Let the fields y > 0 be designated (Ei,Hi), (E',H'), and (Em,Hm) for the cases 1, 2, and 3, respectively. Then Babinet's principle for complementary screens states that (5b-365) The above Babinet's principle allows replacement of the aperture problem with an equivalent "disk" problem. Consider a plane metallic obstacle (disk) at y = 0 immersed in an incident wave (Ei = Eo, Hi = Ho). The scattered fields are (E",H"). If one assumes that a wave [Ei = - V (p./ f) Eo, Hi = V (f/p.) Ho] impinges on a metallic screen at y = 0 with an aperture of the same shape as the disk, the scattered fields on the shadow side of the aperture is E:~reen = V(P./f) H", H:~"'n = V(f/P.) Esc where (ESC,Hsc) are the scattered fields on the y > 0 side of the disk. Diffraction by Simple Objects. DIFFRACTION BY SPHERE. A plane wave in an infinite, homogeneous medium (f,P.), whose electric vector is linearly polarized in the x direction, is incident upon a sphere of radius a and constitutive parameters f1, P.1 from the negative z axis. The incident wave (Ei,H i ), the penetrated wave (Ep,Hp), and the scattered wave (E",Hsc) are respectively Ei
=
exEoeikZ
= Eo[V X V X
+ iwp.V X (Wirer)] X (Virer) + V X V X (Wirer)]
(virer)
Hi = e y !5:.. Eoe;kz= Ed[-iwfV p.w Ep = Eo[v X V X (vpre r) iWP.1V X (wpre r)] Hp = Eo[ -iWflV X (vpre r) V X V X (wpre r)] Esc = Eo[vX V X (v,re r) iwp.V X (w,re r)] H.c = Eo[ -iWfV X (v,re r ) V X V X (w,rer)]
+ + + +
(5b-366a) (5b-366b) (5b367a) (5b-367b) (5b-368a) (5b-369b)
with Vi =
~i
k
COS
q,
'" (i)n2n + 1 . \' 1 n(n + 1) In(kr)Pn (cos 0)
1..
(5b-370a)
n=l
'" (i)n2n - i . . \' Wi = wp. sm q, n(n
+1 . + 1) In(kr)Pn 1(cos 0)
1..
(5b-370b)
n=l
vp =
'"
-i
\'
k; cos q, it
Cn
(i)n2n+1. 1 n( n 1) In(k1r)P n (cos 0)
+
(5b-371)
++1)1 In. (k ,r )Pn l(cos e)
(5b-372)
n=l
'"
_ -i. \' d (i)n2n Wp - WP.1 sm q, 1.. n n(n n=l
v, =
-i
k
'"
cos q,
\' L
(i)n2n+1 an n(n 1) hnCl)(kr)Pn'(cos e)
+
n""l 1
B. R. Levy and J.B. Keller, Communs. Pure Appl. Math. 12, 159 (1959).
(5b-373
5-92
ELECTRICITY AND MAGNETISM -i W8
"'I' sin '"
=
"" \' (i)n2n 1 ~ bn n(n 1) hnCll(kr)P"l(cos 0)
+ +
(5b-374)
n=l
(ErlE)jn(k,a)[kajn(ka)l' an = (E,/E)jn(k,a)[kahnC')(lca)]' b = (f.Lrlf.L)jn(k,a)[kajn(ka)l' n (f.LrI f.L)Jn(k,a) [kahn (I)(ka)]' -
.in(ka) [k,ajn(k,a)]' h,/l)(ka)[k,a,in(k,a)]' jn(ka) [k,a,in(k,a)l' h nCl)(ka) [k,ajn(k,a) l'
(5b-375a) (5b-375b)
(f.LIErif.LE)t {[k . (k )]' [k h CIl(k )]'} [k,a,in(k,a)l' aJn a an a n a
-
Cn -
(5b-375c)
dn = . (kI ) Un(ka) - bnhnCI)(ka)} In ,a _
(5b-375d)
The prime indicates the derivative of the function with respect to its argument, = "'Vf.LIE1I and k = ",V~. jn and hn CI ) are respectively the Bessel and Hankel functions. Pn ' is the associated Legendre function. For a perfectly conducting sphere, an [kajn(ka)l' /[kahnCI)(ka)]', bn jn(ka)/hn(l)(ka), Cn 0, dn = O. Far-zone Scattered Electric Field k,
=
=
=
ikr E far ,e ,one = e r (F ee e + F
(7~/4)
7r
with
'Y
=
7r
(kG}' _ ~ sin 4kG - (57r/2) sin 2kG 7r' (kG) 3
+ .. }
(5b-408)
0.5772.
Transmission through a Circular Aperture of Radius a
t = -""-"'-
=_63-,- (ka)4[1
27ra' ka->O 277r2
t
=
2~~' ka->">
1 -
+ ~(k:g
189 214(d) 240 117.7 99.5 138 157.2
ti H 131
.
.....
...... -89.2 -89 -78.5 -51.6 -34.6
176
0.410
20, 60
-16.3
195
. ...
. ......
-5
213
. ...
. ......
-6
231
.
131
Ul
. ......
'"
~ o ~ ~ H
~
o
~
Q
Ul
2.03 .
...
2.05 . ...
2.07
r t-..? """"'
""
aI
TABLE
5d-4.
I ......
(Continued)
ORGANIC COMPOUNDS (SMALL MOLECULES)
tv
00
Type/Name
Formula
I t,OC I
.'
0 Acids . .•....................... Formic ......................... Acetic ......................... Anhydride .................... Propionic ....................... Butyric ........................ Isobutyric ...................... Succinic ........................ Benzoic ........................ Esters .... ...................... Methyl formate ................. Ethyl formate .................. Propyl formate .................. Methyl acetate .................. Ethyl acetate ...................
Range
10'a (or a)
I
Melting point
Boiling point
8.4 16.6 -73.1 -22 -7.9 -47.0
100.7 118.1 140.0 141.1 163.5 154.4
I
II
R·COOH, -C-O-H H·COOH CH"COOH CH.CO·O·COCH. CH.·CH.·COOH CH.(CH.) "COOH CH.·CHCOOH-CH. HOOC·(CH.).·COOH ·COOH 0
16 20 19 10
20 10 25
58 .• 6.15 20. 7 3.30 2.97 2.71 2.40
.......
....
••
,
,
00
••
•••
· ..........
...........
........... ...........
.
· .......... 10,70
... ........ · .......... ... .... ....
... ........ · ..........
..........
-0.23(a)
· ..........
~85
235(d)
122
249
t"
t'oI
Q
"">-< ~
Q
.....
"">
zt;:!
II
R·COOR', -C-OH·COOCH. H·COOCH.CH. H·COO(CH,).CH. CH.COOCH. CH.COOCH.CH, 0
toi
20 25 19 25 25
8.5 7.1. 7.7. 6.02 6.02
0, 20
5(a) ...........
·.......... 2.2(a) 1.5(a)
·..........
........ , .. 25,40 25
-99.0 -79.4 -92.9 -98.7 -83.6
31.8 54.2 80.9 57.8 77.2
is:
i> 0
Z
t'oI
"" >-
-3 H
W.
:::::
B. Permittivity "Map" for Polchlorotrifluoroethylenet Smoothed .', 80% Crystalline 10- 1 2 X 10- 1 5 X 10- 1 10 0 2 X 10 0 5 X 10 0
2.597 2.582 2.559 2.540 2.522 2.500
2.684 674 661 647 631 605
2.740 735 727 721 713 702
2.772 770 765 762 758 751
2.798 797 796 794 793 791
2.832 831 827 824 821 818
2.862 860 858 856 854 849
2.887 886 883 881 879 877
2.926 923 918 915 913 910
2.958 956 955 955 954 953
2.955 2.946 2.942 2.941 2.940 2.940
10' 2 X 5 X 10' 2 X 5 X
2.486 2.474 2.461 2.454 2.447 2.438
686 565 538 520 503 485
690 675 651 629 604 571
746 737 725 714 700 672
788 785 781 777 772 760
816 815 812 810 808 804
846 842 838 835 832 828
874 871 868 863 861 858
908 905 900 896 892 888
952 950 948 945 942 937
2.939 2.939 2.939 2.938 2.938 2.937
2.433 2.428 2.423 2.418 2.415 2.410
474 464 455 448 441 434
548 529 507 495 485 472
646 618 578 555 534 510
748 733 700 672 641 596
800 796 784 771 751 706
825 822 818 812 807 792
854 852 846 842 839 832
885 882 878 875 871 865
932 927 919 913 908 902
2.937 2.935 2.933 2.930 2.927 2.920
10' 2 X 10' 5 X 10' 10' 3.2 X 10'
2.407 2.404 2.402 2.397 2.393
428 424 420 412 405
464 456 451 441 431
498 488 483 468 454
571 552 541 516 493
671 641 623 581 547
771 744 725 665 602
825 814 808 757 688
860 854 848 823 768
898 892 887 867 825
2.916 2.913 2.909 2.900 2.882
10 7 2.92 X 10 7
2.390
2.397
2.421
2.440 2.402
2.475
2.515
2.552 2.470
2.610
2.700 2.560
2.762
2.849
10 3 2 X 5 X 10' 2 X 5 X
10 ' 10' 10' 10' 10' 10 3 10' 10'
"d
!:d
o
"d
to!
~
)-oj
to!
Ul
o
"'J
tI
H
*
t t
.... .
....... .
........
. .. . . . . .
to! t:-< to!
C':l >-3
!:d )-oj
C':l
Ul
Noteridges (r) and valleys (v) in ,": n (-50°, 5 X 10-1 Hz; 23°, 2 X 10 3 Hz; 150°, 10 7 Hz) T2 (75°, 10-1 Hz; 100°, 2 X 10 2 Hz), T3 (150° 2 X 10- 1 Hz; 175°,5. X 10 3 Hz), V1 (50°, 10- 1 Hz; 75°, 2 X 10' Hz) v, 100°, 10-1 Hz, 125°,2 X 10 1 Hz) v, (175°, 2 Hz; 200°, 10 2 Hz) Adjusted vaiue. Scott, Scheiber, Curtis, Lauritzen, and Hoffman, J. Research NBS 66A 269 (1962). There is a typographical error in the data for specimen 0.80 at l.75°C and 2 X 10' Hz. The listed value of 137 X 10-' for 1= 2.10'Hz, t = 175°C should be 117 X 10-'.
CJ1
I
~
01
TABLE
5d-8.
01
CERAMICS AND GLASSES
I
f-'
Name and Ref. No.
t, °0
10' tan S(j, Hz) 10' 10' 10'
,(f,Hz)
10'
10'
10'
10'
10'
10'
10'
23 25
8.30 14.58
7.70 14.56
7.35 14.54
7.08 14.53
6.90 14.52
6.82 14.50
6.75 14.42
24
4.74
4.70
4.67
4.64
4.62
4.61
-
25
4.80
4.73
4.70
4.60
4.55
4.52
4.52
20
3.M .......................................... 3.M
100
3.M ......................................... 3.M
10'
1010
I:.\:)
10'
10 '
10'
10'
6.71 14.2
780 11.5
400 13.5
220 15.9
140 16.5
100 19.0
-
4.59
78
42
29
22
20
23
-
-
4.52
128
86
65
54
49
45
45
3.82 3.82 3.82
6
6
6
6
6
6
37
17
12
Glass (Corninu no.) Soda lime (0080)-high loss [lJ ...... (7570)-high .' ........... Soda, Pb, borosilicate (7720) Pyrex ............. Sod:e., borosilicate (7740) Pyrex .............
96% silica (7900) Vyeor [lJ ..........
Fused silica 915e [lJ ................. (7940) NBS [2J .......... (7940) NRC [2J .......... (,'940) NPL [2] ........... (7940) NBS [2J ........... Ceramic SteatiteA1SiMag A-196' [IJ .......
25 RT RT RT RT
85 23.5
-10' -
~
10"
170 98
90 33 43
-
85 l:'=J
3.78 ...... ............ ................................... 3.78 (3.83) 3.839 3.830 3.824 3.824 3 82, 3.82, 3.82' 3.82. 3.820 (3 82,) (3.83) 3.839 3.838 3.83, 3.83 3.83 (3.83,) 6.233 6.30, 6.30, 6.279 6.272 6.20
-
6.6
2.6
-
-
-
-
-
0.4 0.4 0.2 0.4 11.2
30 58
59 40
79., 46.5
55 70.5
21
13.7
8.0
4.9 4.5 5.5
3.3 3.5 3.3
-
1.1
-
2 1.8
0.6 1.5
10
~
9.4 10
8.5
0.1 0.4 0.1 0.5 12.7
0.1 0.3 0.1 0.2 14.0
0.3
30.5 66
19 40.5
3.7
3.5
1.6 2.2 3.0
1.7 2.3 5.5
2 4.6 7.0
9.0 3.3 1.6
7.5' 3.2 2.0
9.0 3.0 0.4
-
1
-
-
-
o
13
i-:3
!:d H
1.7 1.2 4 0.8. 77
oH
i-:3 >-
~
Z
t;I
25 81
. 5.90 , 5.90
5.88 5.88
5.84 5.84
5.80 5.80
5.70 5.70
5.65 5.65
85
6.37
6.37
6.37
6.36
6.32
6.28
5.60 5.60
5.24
-
16 24
26 38
Fori~terite>',l
A1SiMag 243 [lJ .......... Titania ceramic* NPOT 96 [lJ ............. N 750 T 96 .......... N 1400 T 110 .. ........ High alumina 85% [lJ .................. 96 % [lJ ................ 99.5% [2J ................ 99.5% [3J ................ BeO (p = 2.88 glee) [3J. Ti02-see Figs. 5d-2 and 3
25 25 25 25 25 23 23 23
1~.5
........................................ ~.5 28.9 83.4 .......... . ............... 83.4 30 :Z" 1 130 . 0 131 130.8 130.7' "130.51 130 . 2 8.22 8.83
-
-
r
8.18. 8.17 8.17 8.16 8.16 8.16 8.83 8.82 8.80 8.80 8.80 8.80 9.43 .................. 9.43 9.43 (9.41) . ............ -,. 9.55(p = 3.83g/em) ..
I II 6.60
I
I
8.08 8.79 9.41 9.55 6'.6
12 5.7 6.7 , 20 14
-
b > c; b is the symmetry axis. :j: The crystallographic axes are labeled such that a < b < c. § Weak ferromagnetism is observed below 81.5 K. 'If Here R = Y, La, and the rare earths. The data refer to the ordering of the Fe sublattices; the moment is temperature dependent because of spin reorientation and rare-earth ordering at.various lower temperatures. *;j. The z axis is ,the threefold symmetry axis, and x is a twofold axis; (j is the polar angle. tt There is a transition to an uncanted state at 260 K. H More than two sublattices are probably required for a descriptive model.
MAGNETIC PROPERTIES OF MATERIALS
5-155
References for Table 5f -10. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.
Sugawara, F., S. lida, Y. Syono, and S. Akimoto: J. Phys. Soc. Japan 25,1553 (1968). Joenk, R. J., and R. M. Bozorth: J. Appl. Phys. 36, 1167 (1965). Burgiel, J. C., V. Jaccarino, and A. L. Schalow: Phys. Rev. 122,429 (1961). Meijer, H. C., and J. van den Handel: Physica 30, 1633 (1964). Shane, J. R., D. H. Lyons, and M. Kestigan: J. Appl. Phys. 38, 1280 (1967). Pickart, S. J., H. A. Alperin, and R. Nathans: J. phys. radium 20,565 (1964). Yudin, V. M., and A. B. Sherman: Phys. Status Solidi 20, 759 (1967). Gurevich, A. G., E. I. Golovenchits, and V. A. Sanina: J. Appl. Phys. 39,1023 (1968). Ogawa, S.: J. Phys. Soc. Japan 15, 2361 (1960). Heeger, A. J., O. Beckman, and A. M. Portis: Phys. Rev. 123, 1652 (1961). White, R. L.: J. Appl. Phys. 40, 1061 (1969); this is a review paper and contains an extensive list of references; for CeFeO, see M. Robbins, G. K. Wertheim, A. Menth, and R. C. Sherwood: J. Phys. Chem. Solids 30, 1823 (1969). Turov, E. A., and V. E. Naish: Phys. Metals Metallog. 9(1), 7 (1960); V. E. Naish and E. A. Turov: ibid, 11(2), 1 and 11(3),1 (1961). Dzialoshinski, I. E.: Soviet Phys.-JETP 6, 1120 (1958). Moriya, T.: Phys. Rev. 117,635 (1960). Joenk, R. J., and R. M. Bozorth: Proc. Intern. Can/. Magnetism, Nottingham, p. 493, The Institute of Physics and the Physical Society, London 1964, p. 493. Rao, R. P., R. C. Sherwood, and N. Bartlett: J. Chem. Phys. 40, 3728 (1968). , Wollan, E. 0., H. R. Child, W. C. Koehler, and M. K. Wilkinson:Phys. Rev. 112, 1132 (1958) . Bozorth, R. M., and V. Kramer: J. phys. radium 20,393 (1959). Hansen, W. N., and M. Griffel: J. Chem. Phys. 30,913 (1959). Shane, J. R.,and M. Kestigan: J. Appl. Phys. 39, 1027 (1968). Dzialoshinski, I. E.: Soviet Phys.-JETP 5, 1259 (1957); J. Phys. Chem. Solids 4, 241 (1958) . Moriya, T.: Phys. Rev. Letters 4, 228 (1960); Phys. Rev. 120,91 (1960). Tasaki, A., and S. lida: J. Phys. Soc. Japan 18, 1148 (1963). Flanders, P. J., and W. J. Schuele: Phil. Mag. 9,485 (1964). Borovik-Romanov, A. S., and M. P. Orlova: Soviet Phys.-JETP 4, 531 (1957). Borovik-Romanov, A. S.: Soviet Phys.-JETP 9, 539 (1959). Borovik-Romanov, A. S., and V. I. Ozhogin: Soviet Phys.-JETP 12, 18 (1961). Kaczer, J.: Soviet Phys.-JETP 16, 1443 (1963). Bizette, H., and B. Tsai: Compt. rend. 241, 546 (1955). Alikhanov, R. A.: J. Phys. Soc. Japan 17, suppl. Bill, 58 (1962). !-Ie.mbourge!') P. D.) 9-nd J. A. lVlarc 1.l'3: Plv!)s 861). 1,58;; 4B8 (1967). Cracknell, A. P.: Phys. Letters 27 A, 426 (1968).
'6-156 III
z
ELECTRICITY AND MAGNETISM
3.0r-I--I--'---I-I--'---'---r--.~F::-e-_"":"v-'"
+ Fe-Cr
~
~
2.5t---t----j,--t---t--::=;;-t--+--+---I
0 Fe - Nl • Fe-co a Nl-Co
2.01---t-----II---t--:Tfy---t''t.--+--+--_l
A N L- Cll. Y Nl-Zn v NL-V
~
::E 0::
6 III ~ 1.51---t-----II--:tA=-----t---+---J&'~;--+_----l
NL - Cr
~
'b Nl-Mn
~ ,.0~--~-~~L--t--~_+--~~¥-+~-~~_l
A Co-Cr 0 Co-Mn
o
::E
u :E
0.5
o
~
0~__~__~~----~--~----~--~----~--_7~---U
Cr
24
Mn 25
Fe
Co
26 27 ELECTRONS PER ATOM
__
~
Cll.
29
FIG. 5f-1. Saturation magnetization of intra-iron-group alloys as dependent on electron concentration. Data by Peschard (1925), Weiss, Forrer and Birch (1929), Forrer (1930), Sadron (1932), Fallot (1936, 1938), Farcas (1937), Marian (1937), and Guillaud (1944). CR. M. Bozorth, Phys. Rev., 79, 887 (1950).]
-2000~~~-~I~O-~'5~~2~O~2~5~~3~O~3~5~~4~O'-4~5-~~~~5~~--~60 ATOMIC PERCENT OF ADDED ELEMENT IN NICKEL
FIG. 5f-2. Change of Curie point with the composition of nickel alloys (atomic percent). Data by V. Marian, Ann. physique [11]7, 459 (1937). (Bozorth, "Ferromagnetism," D. Van Nostrand Company, Inc., Princeton, N.J., p. 721, 1951.)
5-157
MAGNETIC PROPERTIES OF MATERIALS 0.8
I
/
0.7
~ 0.6
j
+ +
Mn
!"
(0)
~:--.
'"z~
~~
"-
o
~ 0.5
.. X
' ' "\ ~'\ ~
,. l~
!;:;
~
...
.0:
L\,\
Q.
en
~ 0.4
l\ ~
...z
~j ... \
(!)
Dy-Tm Oy-Ho ..., Ho-Er Ho-Er ,P Ho-Tm .
(C,I-'I l'J H
U2
0
>:rj
~ ~
>-'I l'J ~
H
~
t-
-
-
. ,... ,: .....
fl flA fl f1 fl fl and flAif •
"."
••
00
••••••••••••
{~ {~
4.7: [100] 7.2: [010] 6.9: [100] 4.6: [010] 2.. 0: 23°, [111] 4.4 6.4: [100] 4.6: [010] 2.S: [001] 9.6: ..i [001] 2.9: varies 5.2: [001] 2.9: varies 3.4: [100] 7.0: [010] 4.3: ..i [001] 2.5, 2.S: ..i [001] 2.5: ..i [010]; 63°, [100] 2.6: varies 1.3: [001 1.9 2.5 varies O.a [001] 2.9 [001]
TbCoO,. '.' . ; ..... ; ; .;; ; ;; ; . . .. 0: 3;31
{~(Tb)
DyCrO, ................... , .. , 0: 146 (2.16) ErCrO' ............. '" ........ , 0: 133 (16.8) HoCrO, ..•................... , 0: 140
G(Cr) compiex(Dy) G(Cr) C(Er) G(Cr)
("'-'12)
0
•••••••••••••••
A
0
G G G(Cr) C(Nd) G G(Cr) F(Pr) G(Crl
,
(4)
(3.05) TmCrO, ......
0
••••••••••••••••
/
0: 124 (>4)
*' The use of f1 and f2
{~(Ho)
T
282 0 112 0 224 ("'-'10) PbCrO' ........................ C: 240 PrCrO, ....................... ' 0: 239 (>4.2) TbCrO' ......... : .............. 0: 158
0.' • • • • _• • ' . ' 0 " , 0 " ' "
>2.6,2.2
f2 (Fig. 5f-13b) G
0 .................
.4· . . . .
fl
Ba2Co WO •........ C: 17 KCoF, ......................... C: 135
KCrF, ........ LaCrO' ........................ LuCrO'.: ...................... N dCrO, .......
1.9, 2.1: [001] 2.2: [001] O.S: [001] 1.7,1.9: [001] 1.7: [001] 1.9: [001]
{ ~(Tb) compiex(Tb) G(Cr) F(Trn)
are explained in Fig. 5f-13; G, A, F, and C in Fig. 5f-14.
Is.5 ..i[001] 2.6 varies O.S [001]
260, 388, 412 148 149, 367 255 246 260, 312 81, 195
~
P>
~
82, 267 143 353 267 70,77 70, 74 62,70
Z
~
>-3 ....
o
"d
l;lj
o
"d ~
l;lj
>-3
.... ~
U1
o 353 70,216,296 70 70, 74
"':I
~
P>
>-3
~
lJj
349 70
.... P> t-
tI
!;tI
o ~ ~H
334 294,338 ,37,358
U1
190 :336 ,127, 157, 187
~
:335 i339 184 330, 331 332 '264 183 :85 88
t<J
ob;j
~ t<J
~
t
o
.Z
't:9 ;~
o
;g o
' 1:1 t:9
!;d .8 H
t:9
U2
o!oj ~
l>
8 t:9
!;d
>'
t"'
U2
305 307 351 146
cr " ~
CI.:I
TABLE
5f-15.
ANTIFERROMAGNETIC M:ATERIALS STUDIED BY NEUTRON DIFFRACTION
(Continued)
cr.... -1
~
Material
Crystal class and Neel temperature, K
Fe,SiO •........................ O(Pbnm): 65
References
350
o (Pbnm) : 23 o (Pbnm) : 34
C(Muu) A complex
[001] [001] [001] [100] [010] 3.2: [001] 2.1: [100] 1.1: [010] 3.9: [001] 3.8: [001] [100] 5.2: [010] [010] [010] [010] [100] 3.6: [010] 3.6: [001] 4.7: [010] [100] ..L[001]
T: T: T: T: T: T: T:
(Fig. (Fig. (Fig (Fig. (Fig. (Fig. (Fig.
1.6: 1.6: 1.9: 2.2: 2.7: 1.0: 0.9:
309 259 50 287 286 387 259
C(FnI) C(F"u)
(23)
{~(FeI)
65
{t
LiFePO •....................... o (Pbnm) : 50 CaMnSiO •..................... o (Pbnm) : 9 LiMnP04. .........•........... O(Pbnm): 35 Mn2SiO •....................... o (Pbnm) : 50 (13)
CFeI )
C(Feu) A G A C(Mnr) C(Mnu) {g(Mnr) {g(Mnr)
LiNiPO •....................... Ni,SiO •........................ PbFCI and related structures UAs, .......................... UBi2 .......................... UOS .......................... UOSe ......................... UOTe ......................... UP, ........................... USb, .......................... Corundum and related structures CoTiO, ........................
Moment (in MB) and direction
Magnetic* structure
283 183 55 90 160 203 206
R: 38
5f-19b) 5f-19a) 5f-19c) 5f-19c) 5f-19a) 5f-19b) 5f-19b)
(Fig. 5f-20c)
[001] [001] [001] [001] [001] [001] [001]
..L[001]
trJ
t"
trJ
141
C':l f.:l
~ C':l H
352 108 303 350
>'3
~
~
Z
t:I
~
141
Q
Z
trJ >'3
351 302
300
~
Nb2CO,0 •...................... [ H 30 Cr203 ......................... R 318 a-Fe 20, . . . . . . . . . . . . . . . . . . . . . . .. R 948
f. [001] chains (Fig. 5f-20a) (Fig. 5f-20b)
a-(Fe,Cr)20' ................... 1R a-(Fe,Rh),O, .................. . a-(Fe, V) 20, ................... . FeTiO, ....................... . R: 68 a-Fe20,-FeTiO, ............... . R MnTiO, ...................... . R: 41 Nb2Mn'0 •..................... H: 125 NiTiO, ....................... . R Cr V 0, type str"ct"res (see also Fig. 5f-21)
spiraltt
°
a.-coso, ...................... '1 ~ 15.5 !'i-CrPO, ....................... 0.22 CrVO' ......................... 0: 50 FeSO, ........................ '1 MnSO' ........................ NiSO, ......................... NiSeO' ........................ C,,80, type str"ctures (see also Fig. 5f-21)
0: 21 0 0: 37 0
{g
~4.0:
[001]
4.6: [001] ~5: [001] 2.3: ..l [001] 2.9: [010] 1.4: [001] 2.5: ..l [001] 2.1: 27 0 , [100]; 64 0 , [010]; 81 0 , [001] 4.1: [010] 4.8 2.1: [010] ..l[001]
spiral A C spiral C A
58 91, 131 122, 135, 147, 284, 297, 320, 342, 363 137 235 235 355 357 354 58 354
.,.
~
~ t'J >-3 ...,
C':l
144, 168 145 168 168 411 168 171
I-d
i:d
o
I-d
t'J i:d >-3
>-
-:l ..... trJ w
o>:rj ~
~
>-:l
trJ !:l:J H ~
t
-']
,
R: 50
l"=:I t"' l"=:I
kj
252 252 153 251 84 123 123 185 130, 185 185 140, 142 213 360, 373, 392 1
3 4 261 214
,.. Z
t:i
,..
~ Q
Z
l"=:I
>-'] H
U1
~
CaG, and related xtructures AlCn .......................... 1 T: 598 MnAu, ........................ T
Cee, .......................... DyC, .......................... HoC, .......................... NdC, .......................... PrC' .......................... TbAu, ......................... TbAg, ......................... TbC, .......................... a-KO, ... ......................
363 T 33 T 59 T 26 T 29 T 15 T 55 (42.5) T: 35 T: 66 (40) T**: 7.1
f. (001) sheets in sequence ( + spiral (Fig.5f-17a) sinusoidal spiral (Fig.5f-17a) (Fig. 5f-17a) sinusoidal f. (100) sheets f. (100) sheets spiral
0.9: 65°, [001]
29
3.0: -1 [001] 1.7: [001] 11.8: [001] 6.9: -1 [100] 3.0: [001] 1.1: [001] [001] 9.0: [001] 9.0: [001] 5.1: -1 [100]
193, 194 30 33 30 30 30 31
~
32 30,32
!Z
f. (001) sheets
~l(O,-);
375
o
C F G
9.8: [001]
- - +)
-1[001]
CsCI and related structures (see also Fig. 5f-14) DyAg ......................... C: 51 FeRh ......................... , C: 678t (338) Fe·-Rh ........................................ . AuMn. . . . . . . . . . . . . . . . . . . . . . . .. C*: 515 (403) Au-Mn ....................... . Au 2MnAl ..................... . c: 147t (65) (ordered) ..................... . Au,(Mn,Al), .................. . MnHg ........................ . C*: 460 Pd,MnAl. . . . . . . . . . . . . . . . . . . . .. (disordered) Pd 2 Mnln ..................... . (disordered) Pd,Mnln ..................... . (ordered) TbAg ........................ . Tb(Ag,In) ............ '" ..... . Tb(Ag,Pd) .................... . TbCu ........................ .
3.3
A A
..i[001] 4.1: [100] and [001]#
F spirat
G
C: 240
G
C
G
4.3
C: 142
f2
C: 100
C
q
C C: 115
{~
C
60, 233, 285, 359 44, 46
(F'ig.
5f-1Sb)
............... ...............
> 8
402
104 107 107 104
[001]
I:;l
~
l"J
!;:d
401
~8.9:
l"J
8...... l"J
49 291, 310, 311 196, 192
~9.0:
. ........................
"d
!;:d U2
4.3: -1[111] ..i [001]
"d !;:d
o
o
401
[001]
l"J 8H
46 49 4.4: -1 [001] 3.7, 3.9: varies 1.7 2.9 4.4
j3-MnZn ....................... j C
26 359
>
~
H
> t-
-3 ~ H
oH
>-3
>
Z
t::I
~
>-
Q
366
c c
T: 353
319 205, 313 313, 368, 369 212, 238, 313 176, 215, 239 212 212, 313 20, 313 20, 21, 313
Jo<j
C
C: 475 (365) 523 (388)
References
o
241 241 240, 241 229,241 103 292 397 207 421 34 17,404 34
Z
t'J >-3 H
Ul
~
MnuCrQ.1Sb ................... 1 T Mnl.'7Cro.o,Sb ............. '" .. 1 T (135) (115) Mnl. ,Cro.lSb,. ,.Ino. Of, • • • • • • • • • • • • 1 T (Mn,Cr),Sb
(Fig. 5f-27b) (Fig. 5f-27a) (Fig. 5f-27b) complex (Fig. 5f-27a) (Fig. 5f-27b) (Fig. 5£-27 a)
[001] 1120 1.4(Mnr), 2.8(Mnu): [001] varies 35 .1.[001] l.S(Mnr), 3.7(Mnu): .1.[001] 1 119 [001] .1.[001] 35
complex spiral ferromagnetic sinusoidal complex spiral spiral spiral distorted spiral distorted spiral sinus»idal (N d,) sinusoidal (N d2) sinus»idal spiral ferromagnetic sinusJidal antiphase complex complex complex spiral
0.6: [001] 9.5.1.[001]
408 409
o
7.6: [001] 9.0
100, 106
l'=l >-3 ......
5.9: .1.[100] .1.[001] .1.[001] 9.5 2.3: [1010] 1.S: 30°, [1010]
298 222, 225, 393
T
Rare-earth metals and alloys (see also Fig. 5f-28)
Ceo .......................... . H: 12.5 Dy ........................... . H: 179 (90t)
Er ........................... . H: 80
RoAL ........................ . TbAL ........................ . TbMn2 ....................... .
(52) (20t) C: 91 H: 130 (""40) (",,20t) H: 19 (7.5) H: 25 H: 226, 229 (216,221 t) H: 56 (40) o 10 o 26t o 72 C 40
TbNb ............ .
C: 46t
Eu ........................... . Ro ........................... . Nd ........................... .
Pr ........................... . Tb ........................... . Tm .......................... .
ErAl. ........................ .
{~
.1.[001] [001] 7.0: [001] 7: .1.[001] S.4: .1.[001] 8.S: .1.[001] 5.0-S.0(Tb), 1.1-2.5(Mn): ..i[001] 7.2(Tb): [111]? .1.[111]?
~
'-cI ~
o
»::f
l'=l ~
281
>-3 l'=l
I-
-3 l'=l ~
H
".
t-
4.5 1.95 2.00 2.29 1.89 1. 45 1. 57
3.3 1.9 4.5 a:l Z
t;l
8......
o
'"d
::d
o
'd t;l
~
...... t;l U2
oI'%j ~
>
8
t;l
~
>
t-'
U2
a.
~ f-'
.....1
6-218
ELECTRICITY AND MAGNETISM TABLE
5f-30.
HALL CONSTANTS OF SINGLE CRYSTALS
B in basal plane Element
Ref.
Gd .........
19H
Dy ........ ;
20
Tb .........
21
Fe .......... Co .......... Ni ..........
22 2, 23 23
B along c axis*
T,K
240 200 150 100 50 148 119 78 39 162 119 79 40 4 to 300 4 to 300 4 to 300
Ra X lOll, m 3 /coul
R, X 10", m 3 /coul
Ra X 1011, m 3 /coul
R, X 1011, m 3 /coul
52.3 8.7 -30.1 -40.0 -34.7
-872 -367 -161 -167 -29 117 210 130 22 163 200 82.2 5.7 -1 to 50 -10 to 10 50
-27.2 -9.4 8.5 25.0 38.9
-4,080 -3,200 -1,900 -890 -170
-
-
29.8 -3.5 -11.7 -15.8 -10 to 1 10 5
I
* Applies only to rare-earth elements.
t See also Volkenshtein [26J.
t
This reference contains data for this alloy for temperature(s) additional to those given here.
References for Tables 5f-26 through 5f-30 1. Soffer, S.: Thesis, Carnegie Institute of Technology, 1964; see also S. Soffer, J. A. Dreesen, and E. M. Pugh: Phys. Rev. 140, A 668 (1965). 2. Dubois, J.: Thesis, Institute de Physique Experimentale de l'U niversite de Lausanne; see also J. Dubois and D. Rivier: To be published. 3. Huguenin. R.: Thesis. Institute de PhYRi'lue Experimf'.ut.ale de l'Universite de L3Usanne, 1964; see also R. Huguenin, and D. Rivier: Helv. Phys. Acta 38, 900 (1965). 4. Ehrlich, A. C., and D. Rivier: J. Phys. Chem. Solids 29, 1293 (1968). 5. Smit, J., and J. Volger: Phys. Rev. 92, 1576 (1953). 6. Jellinghaus, W., and M. P. de Andres: Ann. Physik 5, 187 (1960). 7. Foner, S., and E. M. Pugh: Phys. Rev. 91, 20 (1953). 8. Cohen, P.: Thesis, Carnegie Institute of Technology, 1955; A. 1. Schindler: Thesis, Carnegie Institute of Technology, 1950; see also A. I. Schindler and E. M. Pugh: Phys. Rev. 89, 295 (1953); and E. M. Pugh: Phys. Rev. 97, 647 (1955). 9. Dreesen, J. A., and E. M. Pugh: Phys. Rev. 120, 1218 (1960). 10. Smit, J., and J. Volger: Private communication. 11. Dreesen, J. A.: Phys. Rev. 125, 1215 (1962). 12. Sanford, E. R., A. C. Ehrlich, and E. M. Pugh: Phys. Rev. 123, 1947 (1961). 13. Ehrlich, A. C., J. A. Dreesen, and E. M. Pugh: Phys. Rev. 133, A 407 (1964). 14. Lavine, J. M.: Phys. Rev. 123, 1273 (1961). 15. Beitel, F. P., and E. M. Pugh: Phys. Rev. 112, 1516 (1958). 16. Carter, G. C., and E. M. Pugh: Phys. Rev. 152,498 (1966). 17. Volkenshtein, N. V., and G. V. Fedorov: Soviet Phys.-JETP 11, 48 (1960). 18. Kooi, C.: Phys. Rev. 95, 843 (1954). 19. Lee, R. S.: Private communication; see also R. S. Lee and S. Legvold: Phys. Rev. 162, 431 (1967). 20. Rhyne, J. J.:Phys. Rev. 172,523 (1968). 21. Rhyne, J. J.: J. AppZ. Phys.40, 1001 (1969). 22. Dheer, P. N.: Phys. Rev. 156, 637 (1967). 23. Volkenshtein, N. V., G. V. Fedorov, and V. P. Shivokovskii: Phys. Metali! Metallog. 11, 151 (1961). 24. Okamoto, T., H. Tange, A. Nishomuva, and E. Tatsumoto: J. Phys. Soc. Japan 17, 717 (1952). 25. Volkenshtein, N. V., and G. V. Fedorov: Phys. Metals Metallog. 9,21 (1960). 26. Volkenshtein, N. V., I. K. Grigovova, and G. V. Fedorova: Soviet Physics-JETP 23, 1003 (1966).
MAGNETIC PROPERTIES OF MATERIALS
5-219
lEi
Tb H11 o ANAMALOUS COEF.: Rs NORMAl- COEF. RO
C
-28. I
-39
-44~0~--47·O~--~8~O~--7.12=O~~1~6~O--~~--~240~--~2~8~O--~3L20----3~60 TEMPERATURE T, K
FIG. 5f-37. Temperature dependence of the anomalous and normal Hall coefficients for a single crystal of the heavy rare-earth element terbium. The sign change in R, and the unique maximum occurring near 0.6TN were found also in Dy but were not observed in the S-state ion Gd or in the iron-group elements. The different temperature dependence in Gd is attributed to the absence of orbital angular momentum of the 4f ion. The constant value of R, in the paramagnetic region is a consequence of the dominance of spin-disorder scattering. The broad rise in Ro below 'TN, which remams alter correction for the high field susceptibility, indicates a field dependence of the scattering. This effect is characteristic of Gd also. [After J. J. Rhyne, J. Appl. Phys. 40, 1001 (1969)-recent data included by the editors; see also Phys. Rev. 172, 523 (1968), and R. S. Lee and S. Legvold; Phys. Rev. 162, 431 (1967).J
6f-13. Faraday Effect. Magneto-optical Rotation. l Linearly polarized light incident upon a magnetic material in which the magnetization is parallel to the light path emerges as elliptically polarized light. The major axis of the emergent elliptical light is rotated by the magnetization through an angle IJ relative to the vibration direction of the incident light. a is the Faraday rotation and is proportional to the magnetization M of the material and also to the path length L in the material,
a=
KLM
where the constant of proportionality K is known as Kundt's constant with the units deg/gauss-cm. The sign of the rotation is positive if the major axis of the ellipse is rotated in the same direction as the current flow in a solenoid used to create the magnetization M. Table 5f-31A gives values of saturation rotation
~=KM L
'
(M, is the saturation magnetization) for some ferromagnetic or ferrimagnetic materials below their Curie temperature. I
Prepared by James C, Suits, IBM Research Center, San Jose, Calif,
5-220
ELECTRICITY AND MAGNETISM TABLE
5f-31.
MAGNETO-OPTICAL ROTATION OF VARIOUS MATERIALS
A. Faraday Rotation: Ferromagnetic and Ferrimagnetic
Material
T,K
Saturation rotation, deg/cm
Wavelength, nm
Ref.
--Fe ...................... Co ...................... Ni. ..................... Gd ..................... EuO ....................
RT RT RT 93 5
347,000 363,000 98,000 -325,000 85,000
546 546 546 589 800
1 1 1 2 3
EuSe ................... CrCla ................... CrBra ............... " .. CrI a ....................
4.2 1.5 1.5 1.5
140,000 .3,000 500,000 150,000
750 385 470 950
4 5 5 5
CdCr,Se, ................ CrO' .................... MnBi. .................. RbNio.75COO. "Fa .......... RbFeFa .................
82 RT RT 77 82
-9,200 135,000 570,000 500 3,300
1170 1000 750 550 300
6 7 8 9 10
FeRh ................... MgFe'O' ................ Lio. ,Fe2.50 •.............. NiFe'O' ................. CoFe'O' ............ " ...
348 RT RT RT RT
90,500 -700 -970 27,000 44,000
700 1100 1100 330 360
11 12 12
YFeO •.................. BaFe12019 ............... Ba,Zn 2 Fe120" ........... Y3Fe,012 ................
RT RT RT RT
8000 160 80 4,000
600 6000 8000 530
13 11 11 14
Gd,Fe,012 ............... HoaFe,012 ............... EraFe'012 ......... " ..... Eu.Fe,012 ...... , ........ FeB0 3..................
RT RT RT RT RT
91>,000 60 65 -760 4,800 I
330 1100 3500 3100 480
15 16 17 18 19
7 11
I.
B. Faraday Rotation: Paramagnetic and Diamagnetic
Material
Room-temperature Verdet constant V, min/Oe-cm
Wavelength, nm
Ref.
--EuO .................... EuF, .................... TbAlG .................. Eu glass ................. Tb-Pr borate glass ........ Corning 8363 (lead) glass .. Schott SFS-6 glass ........ AO soda-lime glass ....... Quartz .................. NaC!. .................. CaF, ....... . - . . . . . . . . . .
-10.0 -6.6 -2.256 -2.55 -0.940 0.10 0.490 0.074 0.01664 0.0410 0.00883
1200 435 405 450 405 600
20 20 21 22 23 24
366 334 546 546
25 25 26 27 28
589
MAGNETIC PROPERTIES OF MATERIALS
5-221
For paramagnetic .or diamagnetic materials or for ferromagnetic materials above their Curie temperature, the Faraday rotation is still proportional to M but is usually described in terms' of the applied field H, 6 = VLH,
v
where the constant or proportioniiJity is kiiownas tne Verdet constant with the units min/Oe-cm. Table 5f-31B gives values of Verdet constant at room temperature for a few representative materials. References for l'll.bles 5f-3:1.A_9,l:I,\i .5J-allL .. 1. Breuer, W., and J. Jaumann: Z. Physik 173, 117 (1963). 2. Lambeck, M., L. Michel, and M. Waldschmidt: Z. angew. Phys., 15,369 (1963). 3. Ahn,K. Y., and J.' C. Suits: IEEE Trans. MAG c 3, 453 (1967); Suits, J. C.: Proc. International Con!. on Ferrites, Kyoto, Japan (1970). 4. Suits, J. C., B. E. Argyle, and M. J.Freiser: J. Appl. Phys. 37, 1391 (1966). 5. Dillon, J. F., Jr., H. Kamimura, and J. P. Remeika: J. Phys. Chem. Solids, 27, 1531 (1966). 6. Bongers, P. F., and G: Zanmarchi: Solid State Commun. 6,291 (1968). 7. Stoffel, A. M.: J. Appl. Phys. 40, 1238 (1969). 8. Chen, D., J. F. Ready, and E. Bernal: J. Appl. Phys. 39, 3916 (1968). 9. Suits, J. C., T. R. McGuire, and M. W. Shafer: Appl. Phys. Letters, 12, 406 (1968). 10. Chen, F. S., H. J. Guggenheim, H. J. Levinstein, and S. Singh: Phys. Rev. Letters 19, 948. (19.67). . .... _ .... _ ... 11. Zanmarchi, G., and P. F. Bongers: J. Appl. Phys.40, 1230 (1969). 12. Coren, R. L., and:M. H. Francombe:.lo'U1"!UlI de PhysilLue35,233 (1964), 13. Tabor, W. J., A. W. Anderson, and L. G. Van Vitert: J. Appl. Phys. 41, 3018 (1970). 14. Dillon, J. F., Jr.: J. phys. radium 20, 374 (1959). 15. MacDonald, R. E., O. Voegeli, and C. D. Mee: J. Appl. Phys. 38,4101 (1967). 16. Krinchik, G. S., and M. V. Chetkin: Soviet Phys-JETP, 13, 509 (1961). 17. Krinchik, G. S., and M. V. Chetkin: Soviet Phys.-JETP, 14,485 (1962). 18. Krinchik, G. S.,and G. K. Tyutneva': Soviet Phys.'-JETP, 19, 292 (1964). 19. Kurtzig, A. J., R. Wolfe, R. C. LeCraw, and J. W. Nielsen: Appl.Phys. Letters 14, 350 (1969). 20. Suits, J. C.: Unpublished data. 21. Rubinstein, C. B., L: G. Van Uitert, and W. 1I. Grodkiewicz: J. Appl. Phys. 35, 3069 (1964). 22. Shafer, M. W., and J. C. Suits: J. Am. Ceram. Soc. 49, 261 (1966). 23. Rubinstein, ·C. B., S. B. Berger, L. G. Van Uitert, and W. A. Bonner: J. Appl. Phys. 35, 2338 (1964). 24. Borelli, N. F.: J. Chem. Phys. 41, 3289 (1964). 25. Robinson, C. C.: Appl. Optics, 3, 1163 (1964). 26. Ramaseshan, S.: Proc. Indian Acad. Sci. 24, 426 (1946). 27. Ramaseshan, S.: Proc. Indian Acad. Sci. 28, 360 (1948). 28. Ramaseshan,' S.: Proc: Indian Acad. Sci. 24, 104 (1946).
Faraday Rotation at Microwave Frequencies. 1 The Faraday effect which occurs at microwave frequencies is described .by the relation () = ~ 2c
Ve (v;:t;;- ....;;:=-;) L
where () = rotation, rad '" = angular frequency, rad/sec c = velocity of light L = path length, cm • = dielectric constant and", and K are components of a permeability tensor which describes the behavior of materials under the combined influence of a static and an orthogonal r-f magnetic field. When",» 4n-M-y and",» -yH, the tensor components are given approximately by 47rM-y K ,,"-1
'"
Prepared by C. L. Rogan' and H. Solt,Jr.,Fairchild Camera & Instrument Corp.
5-222
ELECTRICITY AND MAGNETISM
TABLE 5f-32. FARADAY ROTATION IN FERRITE MATERIALS A. Completely Filled Waveguide
Rotation, deg/ em Applied H, oersteds
Mno. sZno.SFe20.* (4'1fM, = 1,500, A = 3.33 em)
0 ....... . 100 ..... . 200 .... .. 400 ..... . 500 ..... . 600 ..... . 1,000 ... . 1,400 ... . 1,500 ... . 2,000 ... . 2,500 ... .
o
MgFe20.t (4'1fM, = 900, A = 3.2 em)
MgAlo .• Fe1.60.t (4'1fM, = 540, A = 3.2 em)
o
o
3
3
MgAlo. ,Fe,. 20.t (4'1fM, = 54, A = 3.2 em)
o 1.1
6
7A
35 9
80
14.3 14.3
1.1 7.4
120 123 123 B. Waveguide Containing Slender Cylinders at Saturation
Composition
Nio .• Zno .• Mno. 2Fe1.80.t ....... Mg1,5MnQ.2Fe1.504 .......... Mgl.OMn D.1Al o. 2Fe1.904t ...... Nio. ,Zno .• Mno. o,Fe,. ,O,t ...... :N'io. 7Zno.2~vlno.lFel. 504i ....... MgD.1Mno. 02AI0,2Fe1.70.+ ...... Ferroxeube 4A ** ............. Ferroxeube 4B** ............. Ferroxeube 4C** ............. Ferroxeube 4D** ............ Ferroxeube 4E** .............
Frequency, GHz
4'1fM"
gauss
Rotation, deg/em
Loss, db/em
4.0§ 4.0§ 4.0§ 1l.2'\f
3,840 1,800 1,600 3,850 2,800 1,600 3,360 4,400 4,365 3,470 2,315
17.5 13.3 10.5 9.4 5.6 3.77 13.8 28.0 20.0 9.8 5.8
0.9 0.6 0.026 0.013
11.2'1
1l.2'\f 24.0tt 24.0tt 24. Ott 24.0tt 24.0tt
......
0.01+
Fig. of merit, deg/db 19.5 21. 7 410 730 2150 370
* C. L.
Hogan, Bell System Tech. J. 31, 1-30 (1952). F. F.: J. phys. radium 12, 305 (1951). :j; Private communication from J. P. Schafer, Bell Telephone Laboratories. '1T 1.35-em-diameter rods supported in polystyrene in 5-cm-diameter waveguide. § 0.355-cm-diameter rods supported in polyfoam in 1.9-cm-diameter waveguide. ** A. A. T. M. van Trier, Thesis, Delft, 1953. tt 1.0-mm-diameter rods.
t Roberts,
where 'Y = ge/2 MHz ~ 1.76 X 10 7 rad/sec-Oe, and M = intensity of magnetization of medium in cgs units. The rotation is then independent of frequencv and field and is!
Table 5f-32 shows the Faraday rotation observed in a completely filled waveguide and in waveguides containing slender cylinders of ferrite along the waveguide axis. 1
For further information, see C. L. Hogan, Bell System Tech. J. 31, 1-30 (1952).
MAGNETIC PROPERTIES OF MATERIALS
5-223
Measurements of completely filled waveguides are reliable only when the materials attenuate the wave appreciably because of the effects of internal reflections arising from the abrupt discontinuities at the ferrite-air interfaces. The data on the completely filled waveguide show the dependence of rotation upon magnetization as evidenced by the fact that the rotation approaches a limit as the applied field saturates the sample. The data on the slender samples give the rotation at a field just sufficient to saturate the sample. The losses observed under these conditions are also shown along with the figure of merit given by the rotation in degrees per decibel of loss. The dependence of Faraday rotation on magnetizing field is given l in Fig. 5f-38 for a slender sample. d"'\
en 20
u.. W
L ......0--'"
o~
~ ~ 10
80..
2,240 2,335 11,640
>80 290 +-+ 480 70 +-+ 300
~3,870
.. 13',060'
.. 90:..i;00· 500 50 +-+ 300 >300 50-300 >8 >300 >155 95-300 77-350
4,700 8,660 13,100 10,860 9,050 5,235 3,520 10,200 9,780 12,400 7,700 7,330 6,860 4,450 6,700 1,610 10,500 10,600 5,320 6,320 1,340
'ii;i;':'670'
... '1',340'
'100" 40 +-+ 300 80 -300
....:>20.. >77 80 ... 290 100 20.4 .
.. 24',500' 28,700
.. 23',400: 27,500
. ioo':'i;oo' 100 +-+ 500 >77 100 +-+ 500 100 .... 500 >77
o 2.7 2.6 5.0 4.2 0.787 0.794 0.717 3.43 1.21. 3.19 3.56 2.08 2.90 ' 2.75 3.18 2.58 3.23 0.49 3.36 2.94 3.72 1.94 2.97 1.82 1.90 2.6 2.94 2.88 1.41 1.84 0.457 0.04 0.50 0.46 13.5 13.6 13.0 13.74 11.0 11.6 8.24 11.18 7.80 3.26 6.81 7.64 3.60 3.37 3.93 2.22 3.88 3.63 3.60 3.52 3.78 4.3 4.2 3.92 3.37 7.8 7.8 7.51 30.0 7.62 7.61 7.45 7.8 7.02 7.8 7.8 8.2,4
0, K
Jleff
-600 -635 -445 -832 -23 -62 -17 -20 -9· -28 18.5 -410 '-50 90
o
8 330 161 -47 -14 -9.2 51 -116 24 -124 70 "'-800 11 19 20
o
-78 -25 -67 -0.7 23 -24 9
-5 11
-8 -2 -6
-1 -294 6
-4
48 12 10 -240 -117 -1,5 -30.5 -1.0 2 -61 . 0 14.7 23
., ''':'''ii'' -3
+
78
2 ..
-18 39
······0· . .... "0"
4.66 4.58 6.3 5.8 2.51 2.52 2.39 5.24 3.11 5.16 5.33 4.08 5.15 4.70 5.18 4.58 5.25 1.85 5.65 5.03 5.64 3.94 4.88 3.82 3.90 4.03 4.6 4.89 4.85 3.43" 3.84 1.97 0.58 2.10 1.92 10.4 10.5 10.22 10.5' 9.37 9.65 8.12. 9.46 7.90 5.11 7.38 7.81 5.37 5.18 5.6 4:22 5.57 5.40 5.20 5.22 5.49 5.9 5.8 5.6 5.46 ",7.9 "'7.9 7.75 7.82 7.80 7:72 "'7.9 "'7.50 +-+7.55 ",7.9 "'7.9 "'8.14
5-227
MAGNET:IC PROPERTIES OF MATERIALS TABLE
5f-34.
MOLECULAR SUSCEPTIBILITIES, CURIE CONSTANTS, AND EFFECTIVE
BOHR MAGNETON NUMBERS OF SOME PARAMAGNETIC MATERIALS*
X 10 6 (2.0°0) (cgs units)
Xmole
Substance
Gd,(S04)'(X') .... Gd2(SO,),·8H20(X!) .. . GdTe [10] .................... . HCr02 [13] ................... . HoNi2( X t) [36] .............. . H020'(X!) .................. , . H02(SO')'(X!)" .. ,."., ...... . Ho 2(S04),-8H20( X l;) ........ , .. KFe[Fe(CN)']'L9H,O [9] ... _ ... . K,Mn04 ............ , .... , . , .. Li,NiF 4 [12]. , . , , .. , ........... . MgCf20,(X~) [35].,." ........ . MgV,04(X!) [35]. , ..... . MnBr' .. ", ..... , ...... . MnCO' ..... , ...... . MnC!' [23] ... " .... , ... . MnCo,O,(xt) [2] .. . MnCf2S4( X t) [2] ... . MnF, [33],. MnF, [14] .... , , .. , . MnI" ....... " .. . MnO., ........ , ... . Mn20'(X!) .... , ....... . MnO' .... , ............ . Mn(OR),. ......... , .. . Mn'P 20'(Xl;) ................ . MnRh [15] ........ , .. . MnS04 .... " .. . 'MnTiO, [5]; , .. . NdCls [16] .. , .. . NdF, ......... , NdNi,(Xt) [36]. Nd,O,(xt) .... Nd2(SO,),( X!) .... '.... Nd,(SO'),'8H20(X t).
NiCh ........ .
NiF2 ............... . Ni 2Ge04(X!) [3.5] .. , .. . Ni(NO')"6H,O [3] .... . NiTiO, [5] .. ". PrC!' [15] .......... . Pr Ni,( X t) [36] ...... . .Pr20,(Xt) ... , . Pr2(SO,),(xt) .. TbNi2( X!) [36]. TbP [8]., .. , ................. . Tb,(SO,),'8H20(Xt) . TIMnF, [17], ... . TmAs [18] ............ . TmNi2( X t) [36] .. , .......... . Tm,O,(X!) [19]"., .. " .... . TmP [18] .. , . , ...... , , , .. . TmSb [18]. , .... '.' .. TD;l,(S04)'(X!), . UCl4 [2.0]." .. , ....... . UBI'4 [2.0]. , , , ... , .. '.. UB" [2.0]" , , ....... . UCJ, [2.0] ..................... . UF, [2.0] ................. . Uh[2D] .......... . KUF, [21] ....... . K2UF, [21] ....... . CaUF, [21] ...... . {fo',UF7[21]: : ::: :: : U,O,(xt).· .. U(SO')2 .... . Yb'O.(Xl;) ......... . Yb,(S04)"8H,O(X!i) . ZnCo,04(X!) [2] ... . ZnCr,S4(Xt) [2] .... .
* Compiled by E.
Range of validity of Curie'Veiss law, ' K
26,6.0.0 27,500 10.0
5.0.0
3,3.0.0 44,8.0.0 45,9.0.0 44,3.0.0 >77
... '1,270 2,800' 1,4.0.0 14,.0.0.0 =11,5.0.0 14,5.0.0 2,82.0 8,20.0 10,73.0
14,800
5,.04.0 7,.08.0 =2,3.0.0 = 13,7.0.0 14,4.0.0 =79.0 (4.2°K) 13,96.0
5',020' 4,700' 5,.07.0 5.39.0 6,25.0 3,450
4,37.0 3,700
4,45.0 =4,9.0.0
77 ;..; 413 >1.0.0 >5.0 7.0 180 2 ..... SDD >3.0.0 >3.0.0 76 3.0.0
35 ,",2.0.0 >12.0 2.0.0 195 17.0
3.0.0 77.0 7.0.0
77
66.0
29.0 57.0 >155
>54.0
10.0 >21
285
7.0.0
65
+4
37.0
37,5.0.0 >15.0 >=2.0
2.0,80.0
8.0 '"" 98.0 >=2.0 >=2.0
>198 2,24.0 525 3,.060 6,7.0.0 =8,6.0.0 625 5,75.0
>10.0 >1.0.0
c 7.S1 8.11 7.8 1.934 13.7 13.7 13.8 13;6 4,.05 .0.383 1.86 1.47 4.26 3.93 4.17 1. 91 2.54 =4.1.0 3 . .01 4.21 4.9.0 3.4.0 1. 8.0 4 .. 6.0 4.58
e,
K
-.0.4 -2 -279,6 12 -14
-S
-7 22 ...,.7 ~35D
-75.0 -2 -4.0 3 -3SD -10 82
8
~4
-68.0 -188 -48.0 2.0 -23 =-26D o K
4.34 4.36 1. 861 1. 76 1.75 1. 53 1. 7.0 1. 82 1.50 1. 37 1. 34 1. 31 1..01 1.24 1. 69 1.6.0 1.62
-22 -219 -57.4 -56 1.0 32 -42 -44 28 71 -97 .0 21 -11 -29.4 4
1.64
-44 35 5 -16 148
12 1O.S 11.S6 4.S7
6.64 7.2 7.2 7.2 6.33 1.35 1. 21 1.35 1.15 1.36 1.36 1.3.0 1.47 1. 31 1.45 1.06 0.24 1.32 2.43 2.92 .0.21 1.67
(Continued)
-71
.... '0" -11.7 -62 -35 25 -29 -147 5 -122 -1.08 ~lD1
-29.0 -185 -17.0 -14.0 -68 -42 -2.0
+10
E. Anderson and A. Stelmach, Clarkson College of Technology.
7.9.0 8 . .06 7.9 3.92 1.0.5 10.5 10.5 10.43 5.7 1. 75 3.18 3.84 3.43 5.84 5.61 5.78 3.91 4.51 5.98 4.91 5,8.0 6.26 5.21 3.18 5.5 6 . .05
5.88 3.87 3.75 3.74 3.5.0 3.69 3.81 3.47 ~.32
3.27 3.24 2.S6 3.15 3.69 3.57 3.6.0 3.62 9.82 9.28 9.74 6.25 =7.6 7.28 7,56 =7.6 "'7.6 7 .11 3.29 3.12 3.29 3 . .03 3.3.0 3.31 3.3.0 3,45 3.25 3.4.0 2.92 .1.39 3.25 4.4.0 4.83 1.3 3.66
6-228
ELECTRICITY AND MAGNETISM
References for Table 5f-34 1. Benoit, R.: Compt. rend. 231, 1216 (1950). 2. Lotgering, F. K.: Philips Research Repts. 11, 190, 337 (1956). 3. Johnson, 'A. F., and H. Grayson-Smith: Can. J. Research 28A, 229 (1950). 4. Elliott, N.: J. Chem. Phys. 22,1924 (1954). 5. Stickler, J. J., S. Kern, A. Wold, and G. S. Heller: Phys. Rev. 164,765 (1967). 6. Hansen, W. N., and M. Griffel: J. Chem. Phys. 30, 913 (1959). 7. Munson, R. A., W. DeSorbo, and J. S. Kouvel: J. Chem. Phys. 47, 1769 (1967). 8. Yaguchi, K.: J. Phys. Soc. Japan 21, 1226 (1966). 9. Davidson, D., and L. A. vVelo: J. Phys. Chem. 32, 1191 (1928). 10. Iandelli, A.: R. C. Accad. Naz. Lincei (Italy) 30,201 (1961). 11. Thoburn, W. C., S. Legvold, and F. H. Spedding: Phys. Rev. 110, 1298 (1968). 12. Yaguchi, K.: J. Phys. Soc. Japan 22,673 (1967). 13. Meisenheimer, R. G., and J. D. Swalen: Phys. Rev. 123, 831 (1961). 14. Klemm, VV., and E. Krose: Z. anor(J. Chem. 253, 226 (1947). 15. Kouvel, J. S., C. C. Hartelius, and L. M. Osika, J. Appl. Phys. 34, 1095 (1963). 16. Sanchez, A. E.: Rev. acado cienc. exact., jis. y nat. Madrid 34, 202 (1940). 17. Kizhaev, S. A., A. G. Tutov, and V. A. Bokov: Fiz. T1lerd. Tela 7, 2868 (1965). 18. Busch, G., A. Menth, O. Vogt, and F. Hulliger: Phys. Letters 19, 622 (1966). 19. Perakis, N., and F. Kern: Phys. Kondens. Materie 4,247 (1965). 20. Dawson, J. K.: J. Chem. Soc. 1951, 429. 21. Elliott, N.: Phys. Rev. 76,431 (1949). 22. Schilt, A. A.: J. Am. Chem. Soc. 85,904 (1963). 23. Watanabe, T.: J. Phys. Soc. Japan 16, 1131 (1961). 24. Bizette, H., C. Terrier and B. Tsai: J. Phys. Radium 20, 421 (1959). 25. Singer, J. R.: Phys. Rev. 104, 929 (1956). 26. Benoit, R.: J. Chim. Phys. 52, 119 (1955). 27. Boravik-Romanov, A. S., V. R. Karasik, and N. M. Kreines: Zh. Eks]). i Teor. Fiz. 31, 18 (1956). 28. Cable, J. W., M. K. Wilkinson, and E. O. Wollan: Phys. Rev. 118, 950 (1960). 29. Wilkinson, M. K., J. W. Cable, E. O. Wollan, and W. C. Koehler: Phys. Rev. 113,497 (1959). 30. Frazer, B. C. and P. J. Brown: Phys. Rev. 125,1283 (1962). 31. Guha, B. C.: Proc. Roy. Soc. (London) A206, 353 (1951). 32. Ishakawa, Y., and S. Akimoto: J. Phys. Soc. Japan 13,1298 (1958). 33. Trapp, C., and J. W. Stout: Phys. Rev. Letters 10, 157 (1963). 34. Escoffier, P., and J. Gauthier: Compt. rend. 252, 271 (1961). 35 ~RlaRs". (L, "n0 .T F. FMt.: Phi"'p~ Re~. Rep!s. 18,393 (1963). 36. Farrell, J., and W. E. Wallace: Inor(J. Chem. 5,105 (1966).
for axial symmetry. Here, D, A, and B are constants and I is the nuclear spin. D is determined by the crystalline electric field, and A and B by the hyperfine coupling. Oi, and O.L al'e the spectroscopic splitting factors for the z direction (parallel to the crystal-field symmetry axis) and in the xy plane, respectively. Terms representing the nuclear electric quadrupole interaction (for I > i) and the direct coupling of the nuclear magnetic moment with the external field have been omitted from Eq. (5f-l). The parameters in the spin Hamiltonian are determined by electron paramagnetic resonance (epr) spectroscopy, and the correctness of the assumed crystal field symmetry can be checked by studying the angular dependence of the resonance pattern. Frequently the line width due to magnetic dipole interaction is comparable with the fine structure and hyperfine structure (hfs) separations. Then the established practice is to dilute the subject salt with an isomorphous diamagnetic salt. In most cases the electric field acting on the ion remains unaltered, but there are instances of drastic modifications occurring. If all the ions in the crystal have the same symmetry axis, the susceptibility will be given by the formulas [1]. -N
XII -
2
011
I-'B
2
8 (S+1)[1
3kT
+
-
D(28-l)(28+3)]
15kT
_ N 2 2 8 (8 1) [1 ' D(28 - 1)(28 X.L (h I-'B 3kT .. T 30kT
+ 3)1J
(5£-2)
5-229
MAGNETIC PROPERTIES OF MATERIALS
el+
C,2+ AND Mn3t
2x2
---~
/r--
,\
\
FREE ION
13 x4
I
,
~
~:"--
I
I
tr---:'==='
7 x4
~\
--f
1x5 1.2 \. /,...-- FIVE 3x2 ,/lx2 \ Z' 5 / FREE 10N\~/ SINGLETS FREE ~~--::::c: CUBIC " 100 CM-I CUBIC ,,~ FIELD ~lX2 FIELD LOWER' LOWER SYM. SYM. ALS. ~
\
2
\ 3 4
x6
SIX DOUBLETS SPLIT BY ""ZOO CM-I .
10N'~-:'----..-=--
2 x6 ,LOWER AL.S. SYM.
CUBIC FIELD
tAL.S
~ I
I
)!L
NiH I
I~r---
.l!..L.//
"
-~-
\
.\~,
3x4 V2t AND C,3tr---
Fe2+
\ FREE ION
/
03CM-1
/
\L:·~-~~Jl~1
\
1.2
I,
,r-----
~r-
,/
\\ FREE ION
3,3 ,~-
3x3
I
1,5
~----
grol~p
TN). A large number of substances undergo first-order transitions as a function of temperature at H = 0 between two different ordered magnetic states below the paramagnetic region, e.g., A-F, A-Fi, A-WF, etc. A related case is the first-order change from paramagnetic (P) to an ordered state. In all these instances a high field can induce a transition from the less magnetic state to the more magnetic one, as manifested by the externally measurable total magnetic moment. The critical fields for these transitions are distinctly temperature-dependent; i.e., H,(T - T t ), where T t is the transition temperature in vanishingly small field. These transitions lend themselves to thermodynamic analysis using the Clausius-Clapeyron equation. One should also note the spiral or helical antiferromagnetic or ferromagnetic-like states (Ah,F h) and their field-induced variants such as fan (Fan) or other intermediate states 1
Prepared by I. S. Jacobs, General Electric Research and Development Laboratories.
5-243
MAGNETIC PROPERTIES OF MATERIALS TABLE
5f-36.
MAGNETIZATION BEHAVIOR IN HIGH FIELDS
Behavior
Substance
CeBi ....... , ............ CeSb .................. CoBr,:2H,O .............. CoClz ................... CbCl,·2H,O . ........ . CoF, ................. . Ii-Co(OH), ........... . ii-CoSO, .............. . Co,y ............... . CoUO, .......... . Cr ......... , ... · . C"BeO .......... . Cr,CuO •. CnFe04 ........ . CrK(SO,)d2H,O. C"Mn:O, ..... CrNaS,. C"O, .......... .
. . . .
CT2ZnSe4 .. .
CUo,sCd O•2Fez04. .. CuCh-2H,O .. Cu(NO,),-2.5H,O. Dy. Dy,A12 ......... . DyAu .... . DyCu2. ...... . DyE" .......... . DySb ....... . Er ............ . ErSb ......... . EuTe ... . Fe ............ . Feo.8 3Alo. 17 ... . FeBr' ......... . FeCO' ......... . FeCI, ........ . FeCl,·2H,O. FeGe ............ . FeK,(CN),. FeNH,(S04) ·12H,O. ,Feo.6Nio.6Bn ........ . FeO .............. . a-FezOa .......... .
A->Fi->P A----lo FiI-+ Fi II -+ P A -+ }I\-+ P SF -> P, dx/dH A->F,->P A-> WF SF -> P, dx/dH A->WF K A--->P
dx/dH Ah ---> Fan (?) XrrF
XRF
PS XHF
A-> SF-> P A---> SF Ali -+ P XHF
A---> SF---> P, dx/dH A--->P K A(?) -> F, H,(T - Tt) A->P .'1.,.-> P Ah-> X---+F A----lo Fi----lo P Fh-+
X----lo F
A---> P, dx/dH SF -> P, dx/dH XHF, Band XHF, Band A-----+P;xvv A--->P Au,.l -+ P, XHF . .1- ., Po, -J. P A---> SF PS PS A--->X--->P dX/dH, T ,G TN .'1.11-> SF A~--->WF
FeRh .......... . Fe'S' ............. . GdAlO, ........ . GdAs ............... ' GdCu, ..••................ Gd,Fe,012 ...... . GdP ................... . Gd,(SO,),-8H,O ........ . RD ................ . HoA!. ............... . HoSb ............... . MnAs .......... . MnAu, ......... . MnCO •............ MnCh .. MnCh·4H,O .... . Mnl.9CrQ.lSb ............. . MnF, ...... . Mn1.31Feo.69As .. . Mn,GaC ........... . MnaGe' ............. .
A -> F, H,(T - Tt) K A -> SF ---> P, dx/dB SF-> P Ah--->X---> P XHF
SF---> P PS .'1.---> F (?) FS A---> Fi---> P P ---> F, H,(T,p) A---> SF
dx/dH, T A --+ A ---> A -> A---> .'1.---> .'1.--+ A --->
> TN
SF -> P, dx/dH SF-> P; PS F" H,(T - Tt) SF F, H,(T - Tt) F, H,(T - Tt) WF, H,(T - Tt)
He;
kOe, or Xv, emu/cc
11,43 7, 22, 38 H II [100] 13.7.29,8 H II b 34 H..L c 31.6, 46.0 H II b 130 H ..L c 35 H..L c 12.5 H II c K = 5:7 X 10 7 erg/ ee 55 tlx/x < 0, = 300 kOe 30, H II b; 48, H II c 1.3 X 10-' 3.9 X 10-' 3.0I'B/Cr'+ 3.6 X 10- 4 20, 138 H..L c 59 H I c 64
7 X 10-', > 110kOe 7, 150 35 H II b K = 4.9 X 10 8 erg/ee 21, Tt = 20 0 22 =20 22, 45 Hila 22, 40 H II [100] 20, 140 H..L c 25 75 3.2 X 10- 5 , 4.3 X 10- 5 3.0 X 10-' 31.5 H II c =150 H II c 10.6, 100 39,40 H i'i '" 67 1.0I'B/Fe3+ 5.0I'B/Fe3+ 35, 60 H ..L e H > 90,150 68 H II c 130, 162 H..L c 270,230; Tt = 3300 K = 10 7 erg/ee 11,34 H II b 165 50, 100 1 X 10-', H > 70 kOe 90 7.0I'B/Gd3+ 106 H II c 7.1 ± 0.2I'B/Ho 17,23 H II [100] 29(p = 0), 110(p = 1 kb) =47 tlx/x = 0.14, 150 kOe g, 32 7.5, 20.6 H II c' =100, Tt = 305 0 93 Ell c 64, Tt = 283 0 150, Tt = 150 0 190, Tt = 160 0
T,K
1.3 1.5 4 .. 2
Ref.
1 2 3 4
.4.,4 . 4.2.
3, 5
4.2
6, 7
4·2 4.2
8
300 4.2 .295
4.2 4 ..2 4.2 1.3 4.2 "-4 4.2 4.2 300 1 1.2 4.2 4.2 4.2 4.2 4.2 1.5 4.2 1.5 2.1 4.2 4.2 2 -4.2 4.2 4.0 4.2 1.3 1.3 4.2 150-400
9 10 11 12 13 14 14 15 14 16,17 . ·18 19 20 21 22 23 23a 24 25 26 27 26 27 4, 28 29-31 32 33 34,6 35, 36
37
38 39 15,39 40 41 42-44 77 45,46 120, 77 47,48 77 49 1.2-300 50, 51 1 52 1.6 53,25 4.2 54 300 28 1.6 15 1.3 55,23 40 56 4.2 57 1.6 58 307,329 59,60 4.2 61 300 62 1.3 0.26; 1 3 63,64 65 265 66, 67 4.2 68 301 69 100 70,65 77
6-244
ELECTRICITY AND MAGNETISM
TABLE
5f-36.
MAGNETIZATION BEHAVIOR IN HIGH FIELDS
Behavior
He, kOe, or Xu, emu/co
A-> SF XHF A-> SF XHF dx/dH, T> TN
SF MnSO' ................. ·· Ah -> SF -> P, dx/dH dx/dH, T > 2'N MnSO,·H 20 ............... A -> SF -> P, dx/dH dx/dH, T > TN MnSn' ................... A -> WF, H,(T - Tt) Ni. ..•....... ·· .... ··.·· . XHF, Band Ni,Al. .... , ............. , . XHF, Band XHF, Band Ni,Ga .............. A->P Ni(OH), ............ XHF, Band Pd ................ PS R aGa6012 ...... XHF, Band [R = Gd,Er, Yb]Sc,In . K Tb .............. Fh(?) -> F, H,(T - Tt) Tb,A1, ........... A->P TbAs ................. Ah-> P Tbeu, ............ Tm ...................... F,-> F TmSb .................... Induced KHF Yb,Fe,012 ................ XHF ZrZn' .................... xHF,.Band
~
. ....
"
......... ,., ....
6.5 X 10-', 40 leOe K= 4.5 X 10 8 erg/ce 30, Tt = 10° =30 22 15, 28 ,11[100] < [110] < [111] 1.4 X 10-3 7.3 X 10- 5
(Continued) T, K
Ref.
4.2 77 4.2 4.2 300 84,4 4.2 4.2 1.6 300 1.6 300 4.2 4.2 4.2 4.2 4.2 4.2,0.1 2.6 1.2 4.2 4 1.6 4.2 4.2 1.6 4.2 4.2
71 72 13
73 61 74 75,76 71 77 61 77 61 78 29-31 79 79 80 81, 82 11 83 23 23a 52 25 84, 85 86 87 88
References for Table 5f-36 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.
23a. 24. 25. 26. 27.
Tsuchida, T., and Y. Nakamura: J. Phys. Soc. Japan 22, 942 (1967). Busch, G., and O. Vogt: Phys. Letters 25A, 449 (1967). Narath, A.: J. Phys. Soc. Japan 19, 2244 (1964). Jacobs, 1. S., and S. D. Silverstein: Phys. Rev. Letters 13, 272 (1964). Kobayashi, H., and T. Haseda: J. Phys. Soc. Japan 19, 765 (1964). Ozhogin, V. 1.: Soviet Phys.-JETP 18, 1156 (1964). Ozhogin, V. 1.: J. Appl. Phys. 39, 1029 (1968). Takada, T.: Y. Bando, M. Kiyama, H. Miyamoto, and T. Sato: J.Phys. Soc. Japan 21, 2726 (1966). Kreines, N. M.: S01lietPhys.-JETP 13, 534 (1961). Hoffer, G., and K. Strnat: IEEE Trans. MAG-2, 487 (1966). Guillot, M., and R. Pauthenet: J. Appl. Phys. 36,1003 (1965). Stevenson, R.: Can. J. Phys. 44, 283 (1966). Ranicar, J. H., and P. R. Elliston: Phys. Letters 25A, 720 (1967). Jacobs, I. S.: J. Phys. Chem. Solids 15, 54 (1960). Henry, W. E.: Phys. Rev. 88, 559 (1952). Blazey, K. W., and H. Rohrer: Helv. Phys. Acta 41, 391 (1968). Bongers, P. F., C. F. Van Bruggen, J. Koopstra, W. Omloo, G. A. Wiegers, and F. Jellinek: J. Phys. Chem. Solids 29, 977 (1968). Foner, S., and S. L. Hou: J. Appl. Phys. 33, 1289 (1962). Plumier, R.: J. phys. radium 27,213 (1966). Rode, V. E., A. V. Vedyaev, and B. N. Krainov: Soviet Phys.-Solid State 5, 1277 (1963) . van der Sluijs, J. C. A., B. A. Zweers, and D. de Klerk: Phys. Letters 24A, 637 (1967). Myers, B. E., L. Berger, and S. A. Friedberg: J. Appl. Phys. 40, 1149 (1969). Rhyne, J. J., S. Foner, E. J. McNiff, Jr., and R. Doclo: J. Appl. Phys. 39,892 (1968). Barbara, B., C. BecIB,J. L. Feron, R. Lemaire, and H. Pauthenet: Compt. rend. 267, B244 (1968). Kaneko, T., J. Phys. Soc. Japan 25, 905 (1968). Sherwood, R. C., H. J. Williams, and J. H. Wernick: J. Appl. Phys. 35, 1049 (1964). Bozorth; R. M.; R. J. Gambino; and A. E. Clark: J. Appl. Phys. 39, 883 (1968). Busch, G., and O. Vogt: J. Appl. Phys. 39, 1334 (1968).
MAGNETIC PROPERTIES OF MATERIALS 28. Busch, G., P. Junod, P. Schwob, O. Vogt, and F. Hulliger: Phys. Letters 9, 7 (1964). 29. Freeman, A. J., N. A. Blum, S. Foner, R. B. Frankel, and E. J. McNiff, Jr.: J. Appl. Phys. 37, 1338 (1966). 30. Stoelinga, J. H. M., and R. Gersdorf: Phys. Letters 19, 640 (1966). 31. Foner, S., A. J. Freeman, N. A. Blum, R. B. Frankel, E. J. McNiff, Jr., and H. O. Praddaude: Phys. Rev. 181,863 (1969). 32. Wakiyama, T., and J. P. Rebouillat: Physical Society of Japan, April 1968 Meeting. 33 . .Jacobs, I. S., and P. E. Lawrence: J. Appl. Phys. 35, 996 (1964). 34. Jacobs, I. S.: J. Appl. Phys. 34, 1106 (1963); USAF Tech. Document. Rept. No. ML-TDR-64-58; and unpublished work. 35. Jacobs, I. S., and P. E. Lawrence: Phys. Rev. 164, 866 (1967); and earlier refs. cited therein. 36. Oarrara, P., J. de Gunzbourg, and Y. Allain: J. Appl. Phys. 40, 1035 (1969). 37. N arath, A.: Phys. Rev. 139, A1221 (1965). 38. Beckman, 0., H. Schwartz, and K. A. Blom: Bull. Am. Phys. Soc. 13,461 (1968). 39. Henry, W. E.: Phys. Rev. 106,465 (1957). 40. Hirone, T., T. Kamigaki, and H. Yoshida: Physical Society of Japan, April 1968 Meeting. 41. Zavadskii, E. A., I. G. Fakidov, and N. Ya . .samarin: Soviet Phys.-JETP 20, 558 (1965) . 42. Foner, S.: Proc. Intern. Can!. Magnetism, Nottingham, p. 438, The Institute of Physics and the Physical Society, London, 1964. 43. Besser, P. J., and A. H. Morrish: Phys. Letters 13, 389 (1964). 44. Kaneko, T., and S. Abe:.J. Phys. Soc. Japan 20,2001 (1965). 45. Voskanyan, R. A., R. Z. Levitin, and V. A. Shchurov: Soviet Phys.-JETP 26,302 (1968). 46. Beyerlein, R. A., and I. S. Jacobs: Bull. Am. Phys. Soc. 14,349 (1969). 47. Zavadskii, E. A., and I. G. Fakidov: Soviet Phys.-Solid State 9, 103 (1967); He linear with IT - Tel. 48. McKinnon, J. B., D. A. Melville, and E. W. Lee: IPPS Solid State Physics Oonference, Manchester, January, 1968; He parabolic with IT - Tel .. 49. Adachi, K., and K. Sato: J. Appl. Phys. 39, 1343 (1968); earlier refs. cited therein. 50. Cashion, J. D., A. H. Cooke, J. F. B. Hawkes, M. J. M. Leask, T. L. Thorp, and M. R. Wells: J. Appl. Phys. 39, 1360 (1968). 51. Blazey, K. W., and H. Rohrer: Phys. Rev. 173, 574 (1968). 52. Busch, G., O. Vogt, and F. Hulliger: Phys. Letters 15, 301 (1965). 53. Jacobs, I. S., and J. S. Kouvel: Unpublished. 54. Rode, V. E., and A. V. Vedyaev: Soviet Phys.-JETP 18, 286 (1964). 55. Flippen, R. B.: J. Appl. Phys. 35, 1047 (1964). 56. BElCle, C., R. Lemaire, and R. Pauthenet: Compt. rend. 266, B994 (1968). 57. Busch, G., P. Schwob, and O. Vogt: Phys. Letters 23,636 (1966). 58. DeBlois, R. W., and D. S. Rodbell: Phys. Rev. 130, 1347 (1963). 59. Jacobs, I. S., J. S. Kouvel, and P. E. Lawrence: J. Ph'jjs. Soc. Japan 17, supp!. BI, 157 (1962). 60. Sato, K., T. Hirone, H. Watanabe, S. Maeda, and K. Adachi: J. Phys. Soc. Japan 17, supp!. BI, 160 (1962). 61. Stevenson, R.: Can. J. Phys. 40, 1385 (1962). 62 .. Giauque, W. F., G. E. Brodale, R. A. Fisher, and E. W. Hornung: J. Chem. Phys. 42, 1 (1965); W. F. Giauque, R. A. Fisher, E. W. Hornung, R. A. Butera,. and G. E. Brodale: ibid., 9. 63. Rives, J. E.: Phys. Rev. 162,491 (1967). 64. Henry, W. E.: Phys. Rev. 94, 1146 (1954). 65. Flippen, R. B., and F. J. Darnell: J. Appl. Phys. 34, 1094.(1963). 66. Jacobs, I. S.: J. Appl. Phys. 32, 61S (1961). 67. deGunzbourg, J., and J. P. Krebs: J. phys. radium 29, 42 (1968). 68. Flippen, R. B.: Phys. Rev. Letters 21, 1079 (1968). 69. Bouchaud, J. P., R. Fruchart, R. Pauthenet, M. Guillot, H. Bartholin, and F. Chaisse: J. Appl. Phys. 37,971 (1966). . 70. Zavadskii, E. A., and I. G. Fakidov: Soviet Phys.-JETP 24, 887 (1967). 71. Breed, D. J.: Physica 37, 35 (1967). 72. Jacobs, I. S., and W. L. Roth: Bull. Am. Phys. Soc. 8, 213 (1963); USAF ASD Tech. Rept. 61-630, February, 1962. 73. Bloch, D., J. L. Feron, R. Georges, and I. S. Jacobs: J. Appl. Phys. 38, 1474 (1967). 74. van der Sluijs, J. C. A.: Thesis, Leiden University, 1967. 75. Jacobs, I. S.: J. Phys. Chem. Solids 11,1 (1959). 76. Moruzzi, V. L.: J. Appl. Phys. 32, 59S (1961).
ELECTRICITY AND MAGNETISM 77. Allain, Y., J. P. Krebs, and J. de Gunzbourg: J. Appl. Phys. 39, 1124 (1968). 78. Kouvel, J. S., and 1. S. Jacobs: J. Appl. Phys. 39,467 (1968). 79. de Boer, F. R., C. J. Schinkel, J. Biesterbos, and S. Proost: J. Appl. Phys. 40, 1049 (1969) . 80. Takada, T., Y. Bando, M. Kiyama, H. Miyamoto, and T. Sato: J. Phys. Soc. Japan 21, 2745 (1966). 81. Foner, S., and E. J. McNiff, Jr.: Phys. Rev. Letters 19, 1438 (1967). 82. Chouteau, G., R. Fourneaux, K. Gobrecht, and R. Tournier: Phys. Rev. Letters 20, 193 (1968). 83. Gardner, W. E., T. F. Smith, B. W. Howlett, C. W. Chu, and A. Sweedler: Phys. Rev. 166,577 (1968). 84. Foner, S., M. Schieber, and E. J. McNiff, Jr.: Phys. Rev. Letters, 25, 321 (1967). 85. Legvold,S., and D. B. Richards: Bull. Am. Phys. Soc. 13,440 (1968). 86. Vogt, 0., and B. R. Cooper: J. Appl. Phys. 39, 1202 (1968). 87. Clark, A. E., and E. Callen: J. Appl. Phys. 39,5972 (1968). 88. Foner, S., E. J. McNiff, Jr., and V. Sadagopan: Phys. Rev. Letters 19, 1233 (1967).
(X). Thenotation (X) is also invoked when the nature of a state is not known, but its field region is well described. Lastly, there is the particularly rich area for high-field studies in mapping out the magnetic phase diagrams of antiferromagnetics. As the field along the moment axis increases, there is often a transition from the antiferromagnetic state (A) to the transverse spin-flopped state (SF). This critical field is a measure of the anisotropy. For a further increase of the field, this state gives way to the nearly saturated P state. Sometimes this SF ---+ P behavior is nonlinear, i.e., (dx/dH)H..
-2.90 -2.89 -2.87
e e e e e
+ !Cl,(g) -+ + +
CltAu'+ -+ tAu
!H+
+ tMn04-:""; iH,O(l)
+ Bk 4+ -+ Bk'+ + Ce 4+ -+ Ce'+ 8 + Am02++ -+ AmO,+ e + Au+--> Au e + Am 4+ --> Am'+ e + H+ + tF2(g) -. HF(aq)
+
Cl-, C12(g) Au'+, Au
1.3595 1.50
I?=J
H+, Mn04-, Mn++
1.51
()
iMn++ Bk 4+, Bk'+ Ce 4+, Ce'+
1.6 1. 61
AmO,++, Am02+ Au+, Au Am4+, Am'+ H+, HF(aq), F2(g)
1.64 1. 68 2.18 3.06
!Ba
e e e e
+
OH-
+
>-']
ki
P>
:z:t;;I P>
o
Ca(OH)2, Ca 8r(OH) 2·8H 20, 8r
-3.03 -2.99
:z:I?=J
Ba(OH) ,·8H,O, Ba
-2.97
112
H 20, H2(g) La(OHla, La Mg(OH)z, Mg
-2.93 -2.90 -2.69
Be20,--, Be Th(OH)4, Th H,AlO,-, Al
-2.62 -2.48 -2.35
8iO,--,8i Mn(OH)" Mn Cr(OH)" Cr
-1.70 -1.55 -1.3
4H,O
>-']
H
4H20
+ H20 -->.!H 2(g) + OH+ tLa(OH), --> tLa + OH+ !Mg(OH) 2 --> tMg + OH+ iBe20,-- + iH,O --> tBe + tOH~ 8 + iTh(OH) 4 --> iTh + OH e + iH,AIO, + tH,O-+ tAl + tOHe + i8iO,-- + iH,O --> i8i + tOHe + tMn(OH), -+ !Mn + OH0+ iCr(OH), -+ tCr + OH-
~
H
() H
~
Basic solution
e + !Ca(OH) 2--> tCa + OHe + !8r(OH)"8H,O--> !8r + HO- + e + !Ba(OH) ,·8H,O -->
~
>-']
~
a + !8n++ -> !8n a + !Pb++ -> !Pb a + H+ -> !H2(g)
8n++, 8n Pb++, Pb H+, H2(g)
a + U02++ -> U02+ a + AgBr-> Ag + Bra + Np'+ -> Np3+
U02++, U02+ Br-, AgBr, Ag Np'+, Np3+
a + !8n'+ -> !8n++ a + Cu++ -> Cu+ a + AgCl -> Ag + Cl-
8n'+,8n++ Cu++, Cu+ Cl-, AgCl, Ag
a + !Cu++ -> !Cu a + H+ + tC 2H.(g) -> !C2H6(g) a + Cu+-> Cu
Cu++, Cu H+, C 2H.(g), C2H6(g) Cu+, Cu
a+!12->1a + !I.- -> ile + 2H+ + !Uo,++ -> !U·+
1-, I, 1-,1.H+, U02++, U'+
e e
+ H20(1)
+ 4H+ + NpO.+ -> Np'+ + 2H,0(1) + Fe'+ -> Fe++ a !Hg2++ -> Hg(l)
H+, Np02+, Np'+ Fe 3+, Fe++ Hg 2++, Hg(l)
a + Ag+-> Ag a + Hg++""'" !Hg2++ a + Puo,++ -> Puo,+ e + Pu'+ -> Pu 3+
Ag+, Ag Hg++, Hg2++ PuO,++, Puo.+ Pu·+, Pu'+
+
-0.136 -0.126 a + +0.0000 a + a + 0.05 0.095 a + 0.147 a + a + 0.15 0.153 a + 0.2223 a + a + 0.337 0.52 a + a + 0.521 a + 0.5355 a + 0.536 a + 0.62 a + 0.75 0.771 a + 0.789 e + a 0.7991 0.920 a + 0.93 a + 0.97 a +
+
a + !Pd++ -> !Pd a + !Br2(1) -> Br-
Pd++, Pd Br-, Br2(1)
0.987 1.0652
a + Np02++ + Np02+ a + 4H+ + PU02+ -> 2H20(1) + Pu'+ a + H+ + 102(g) -> !H20(l)
Np02++, Np02+ H+, PuO,+, Pu'+ H+,O,(g)
1.15 1.15 1.229
a
+ ll'H+ +
H+, Cr,O,--, Cr'+ iCr.07---> tH20(1) + !Cr'+
1.33
!Zn(OH) 2 -> !Zn + OH!Zn02-- + H 20 -> !Zn + 20H!Te -> !Te--
Zn(OH)" Zn Zn02--, Zn Te, Te--
80.-- + H 20 -> !820.-- + 20H- 80.--, 820.-In(OH)., In lln(OH), -> lIn OH!80.-- + !H,O -> !80.-- + OH- 80.--,80.--
+
-1.245 -1.216 -1.14 -1.12 -1.0 -0.93
!8e -> !8e-!P + H 20 -> !PH.(g) + OHtFe(OH),--. !Fe + OH-
8e,8e-P, PH3(g) Fe(OH)" Fe
-0.92 -0.89 -0.877
H 20 -> !H,(g) + OH!Cd(OH) 2-> tCd + OH!Co(OH), -> !Co + OH-
H,O, H,(g) Cd(OH)2, Cd Co(OH)" Co
-0.828 -0.809 -0.73
!Ni(OH), -> !Ni + OHNi(OH)" Ni 80.--, 820.-!80.-- + iH,O -> 1820.-- + iOHFe(OH), -> Fe(OH)2 + OHFe(OH)., Fe(OH),
-0.72 -0.58
02(g) -> 0,!8-> !S-iBi20. + !H20 -> !Bi + OH-
02(g),028,8-,Bi,O., Bi
-0.56 -0.48 -0.44
!CU20 + !H20 -> Cu + OHTIOH-> Tl + OHH02- + H 20 -> OH + 20H-
CU20, Cu TlOH, Tl HO,-,OH
-0.358 -0.345 -0.24
e
+ lCrO.-- + t-H20 -> CrO.--, Cr(OH). .. !Cr(OH). + fOHa + Cu(OH), -> !CU20 + OHCu(OH)" CU20 a + !O,(g) + !H20......, !H02- + !OH- 02(g), H0 2-
+
a !Tl(OH). -> !Tl(OH) + OHTl(OHh, TlOH a + !MnO, + !H,O -> MnO" Mn(OH), !Mn(OH)s + OHa + !NO,!H20 -> !N02OH- NO.-, NO.-
+
+
-0.56
-0.13
trJ
t"
trJ
a
>-3
[:l:j
0
a
III trJ ~ H
a
> t" H
Z
>.;J
0
~
> >-3 H
0
Z
-0.080 -0.076 -0.05 -0.05 0.01
c::n
~
Ql
Ql
~
C;n
Ol
TABLE 5g-3. STANDARD ELECTROMOTIVE FORCES OF HALF CELLS IN WATER AT 25°C
(Continued)
(Eo in absolute volts relative to the standard hydrogen electrode) [>oj
Eo
Eo
Half -cell reaction
Electrode
electrode potential
Electrode
Half -cell reaction
electrode potential
~
C)
>-3 ~
H
C)
Basic solution
H
Basic solution
>-3 ~
e + !8e04-- + !H 20 --> !8eO,-- + OHe + !HgO(r) + !H,O --> !Hg + OHe + Mn(OH), --> Mn(OH), + OH8
+ Co(OH), -->
Co(OH),
+ OH-
e + !PbO, + !H 0 --> !PbO(r) + OHe + !CI03- + !H20 --> !CI0 + OHe + !Ag20 + !H 20 --> Ag + OH2
2-
8e04--, 8eO,--
0.05
HgO(r), Hg Mn(OH)" Mn(OH),
0.098 0.1
Co(OH)" Co(OH), Pb02, PbO(r) ClO,-, CI02-
0.17 0.248 0.33
Ag,O, Ag
0.344
+ t02(g) + !H,O --> OH+ !Ni0 2 + H 20 --> !Ni(OH)2 + OH+ AgO + !H20 --> !Ag20 + OH+ !MnO,-- + H 0 --> !Mn02 + 20He + !CIO, + !H,O --> !ClO- + mIe + !H0 + !H 20 --> iOHe + !CIO- + !H20 --> !Cl- + ORe + !O,(g) + !H20 --> !O,(g) + OHe e e e
2
2-
-
02(g), OHNi0 2, Ni(OH),
0.401 0.49
AgO, Ag,O Mn04--, MnO,
0.57 0.60
ClO 2-, ClO-
0.66
~
:z:tJ s::po. Q
:z:[>oj >-3
H
H0 2-,OHClO-, ClO,(g), O,(g)
0.88 0.89 1.24 ~-
~--
U1
s::
5-257
ELECTROCHEMICAL INFORMATION
TABLE 5g-4. THEORETICAL VOLTAGES FOR BATTERY REACTIONS AT 25° Reaction
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + +
+ +
MnO,(s) Zn(s) 4H+ --> Mn++ Zn++ 2H 2O HgO(s) Zn(s) --> ZnO(s) Hg(l) Pb(s) PbO,(s) 2H,S04 --> 2PbSO,(s) 2H,O Pb(s) Pb02(S) 4H+ --> 2Pb++ 2H,O Mg(s) 2AgCI(s) --> Mg++ 2ClPb(s) Ag,O(s) --> PbO(s) 2Ag(s) 2NiOOH(s) Cd(s) 2H20 --> 2Ni(OH) ,(s) Cd(OH),(s) H,(g) O,(g) OH- --> H0 2H,O Zn(s) Cl,(g) --> Zn++ 2Cl2AgO(s) Zn(s) --> ZnO(s) Ag,O(s) Zn(s) 2AgCl(s) --> Zn++ 2Cl2Ag(s) 2Mn02(s) Zn(s) 3H,O 20H- --> ZnO(s) 2Mn(OH) ,-
+
+
IN
H 20
/::"Go, kcal
EO, yolts
-92.054 -62.100 -94.204 -73.084 -119.246 -42.230 -60.056 -35.193 -97.884 -85.500 -45.396 -52.531
1.996 1. 346 2.042 1.584 2.585 0.916 1.302 0.763 2.122 1.854 0.984 1.139
Similarly the cell
EO
Tl, TIOl(aq), 012(g)
=
1.6958 volts
(5g-6)
involves two opposing half reactions which are PlanA Tl-> Tl+ +8 (e) 01--> t0l. 8 (e)
+
and
Plan B
8
8
+ Tl+-> Tl + t012-> 01-
(f) (d)
(5g-6e, 6}) (5g-5e, 5d)
Since EO of the cell is 1.6958 volts, the tendency of (e) is 1.6958 greater than that of (e) and the tendency of (j) is 1.6958 volts less than that of (el). To simplify the tabulation of relative half-cell emfs it has long been the custom to compare all reactions with (a) in plan A or (b) in plan B. In the same sense that the altitude of sea level is arbitrarily set equal to zero, the half-cell emis of (a) and (b) are ealloo zero and the emfs of all other half cells are listed relatively to (a) or to (b) depending upon the "plan" used by an author. Since the tendency of (e) is 1.6958 volts greater than that of (e), which, in turn, is 1.3595 volts less than that of (a), the appropriate entries for the table are, respectively, ,
Tl-> TI+
Plan A Eo = 0.3363 volt
+8
8
+ Tl+
-,->
Tl
Plan B Eo = - 0.3363 volt
(5g-6e, 6J)
It should be clearly understood that all the standard emfs of Table 5g-3 are equi~ librium values and are valid strictly only when no current is passing or when the current passing is so small that resulting changes in the cell are negligible. The reversal of such a current would not affect the magnitude and, of course, could ~ot alter the algebraic sign of the emf of a cell or half cell. The choice of plan A or plan B is an arbitrary one and has nothing to do with the direction in which current is actually passed through a given cell. Only plan B emfs are listed here. Most electro chemists have preferred this approach, and it has been overwhelmingly recommended by the international commissions concerned with such matters. It has also been adopted in many of the most recent physical chemistry texts. In the past American physical chemists have preferred plan A and it was promoted by the extensive treatise of Professor W. B. Latimer. To use his tables one must note that Latimer's standard half-cell emfs are the negatives of the respective "electrode potentials" and that his equations must be written
C11
TABLl!J5g-5. SELElCTED :JI"hnAN-IONIC-ACTIVITY COEFFICIEN'l;S 'Y± OF ELECTROLYTES IN AQUEOUS SOLUTIONS AT 25°C
tG [H
LOCAL NOON
, , , t
I
8 4 HUANCAYO, PERU (Mag. La!. =9.S'S)
20
12
0
Z----~--~--~--~~
20
16
____----______--
D--~----~~------------
LOCAL NOON
I
20
,
I
,
Nov. 27, 1959
[
0
!
I
•
r
!
!
8 UNIVERSAL TIME
!
I
12
It,
!
!
16 20 Nov. 28,1959
FIG. 5h-6. Magnetograms taken during a magnetic storm (Sec. 5h-11) : examples from highlatitude (top) and low-latitude (middle and bottom) stations.
during an exceptionally large storm. In such a storm the Dst decrease may exceed 400 'Y' The frequency of occurrence and the average intensity of magnetic storms are statistically correlated with solar activity. However, individual magnetic storms can by no means be traced to active regions on the sun, and conversely solar flares do not always produce magnetic storms on the earth. During the International ,Geophysical Year, July, 1957, to December, 1958, representing a period of maximum solar activity, magnetic storms with Dst decreases exceeding 40 'Y occurred at a rate or 55 storms per year, and the average Dst decrease was no 'Y, with a maximum of 'Y
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5-275·
434., observed on September 13, 1957, which was still the largest (as of November 1, 1968) since 1957. In 1964 a year of solar activity minimum, there were only 15 magnetic storms (as defined above), and the average Dst decrease of these storms was 61 " with a maximum of 109 , [22,23]. 5h-12. Magnetic Variations Caused by Compressions and Expansions of the Magnetosphere. Compression or expansion of the magnetosphere responding to an increase or decrease of the solar wind pressure on its boundary surface produces a class of magnetic variations of considerable interest, in spite of their generally small magnitudes. Sudden commencements (SC) of magnetic storms (Sec. 5h-11) and sudden impulses belong to this class. A sudden impulse, often denoted by SI, is a sudden increase or decrease in the magnetic field observed simultaneously over the world [2]. . The theoretical magnetic field change flB at the ground is related to changes in the proton density n and the velocity v of the solar wind approximately by the formula [24]
where flB is in " n in protons/em 3, and v in km/sec. For sudden commencements flB ranges from several to 100 " whereas flB for sudden impulses is normally less than 20,. The effect of an abrupt compression of the magnetosphere boundary is transmitted inward hydromagnetically [25]. Presence of continuous time variations in Dst (Sec. 5h-13) with appreciable amplitudes suggests that occurrences of more gradual, as compared with sudden, compression or expansion of the magnetosphere are not infrequent, but their significance has not as yet been explored. 5h-13. Magnetic Indices [1,26,27]. Planetary 3-hourly Index Kp. The Kp index expresses the intensity of geomagnetic activity mainly at high latitudes (See. 5h-10) for each 3-hr interval of the Greenwich day, in a scale of thirds in the order: 00
0+
1-
10
1+
2-·20
2+··· 8-
80
8+
9-
90
v{hich mn,y be condensed to a scale of integers frolli_O -to 9. Kp is based on-magnetiC" recordsfrom 12 selected observatories lying between 47.7 and 62.5° dipole latitude with the average of 56°. The Kp index is published regularly by the International Association of Geomagnetism and Aeronomy in the No. 12 series of its Bulletin. Indices ap, Ap, Ci, Cp, etc., are also found in the same publication. Three-hourly Equivalent Planetary Amplitudes, ap. The conversion from Kp to ap is made according to the following table:
Kp = 00 ap = 0 Kp = 5ap = 39
0+ 2 50 48
13 5+ 56
10 4
667
1+ 5 60 80
26 6+ 94
20 7 7111
2+ 9 70 132
312 7+ 154
30 15 8179
3+ 18 80 207
422 8+ 236
40 27 9300
4+ 32 90 400
At a standard station the average range of the most disturbed of the three magnetic components is 2 ap (,); for instance, if Kp = 6+, the range is 188,. The scale for ap is linear, while that for Kp is quasi-logarithmic. Daily Equivalent Planetary Amplitude, Ap. The average of the eight values of ap for each day is the daily equivalent planetary amplitude Ap. Hence Ap is also expressed in units of 2 , for a standard station . . Daily Incernational Character Figure Ci, and Daily Planetary Character Figure Cpo The daily international character figure Ci. is the average of the daily character figure C for all collaborating observatories; Ci varies from 0.0 to 2.0. Ci is available for every day since 1884.
6-276
ELECTRICITY AND MAGNETISM
A more recently introduced substitute index Cp is derived from the daily sum of ap according to the following scheme.
ap sum up to: 34 22 Cp = 0.0 0.1
44 0.2
55 0.3
66 0.4
78 0.5
90 0.6
104 0.7
120 0.8
139 0.9
164 1.0
190 1.1
228 1.2
ap sum up to: 273 320 379 453 561 729 1119 1399 1699 1999 2399 3199 3200 Cp = 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 Though values of Ci and Cp are found to be nearly the same, Cp is more reliable and should be used in preference to Ci. Auroral Electrojet Index AE [28]. The AE index is designed to be a measure of global auroral electrojet activity with higher time resolution than Kp. The index is normally given at 2.5-min intervals, but hourly averages are also used. AE represents the instantaneous range of disturbance of the horizontal component H from a set of observatories that are relatively uniformly distributed in longitude between magnetic colatitudes e of 30 and 19°. AE = AH (maximum) + IAH (minimum)l, where AH (maximum) is taken from the observatory showing the maximum positive deviation of H, and IAH (minimum) I is taken from the observatory showing the largest negative value in H. Dst Index [22]. The component of disturbance magnetic field that is axially symmetric with respect to the geomagnetic dipole axis is called Dst. The Dst index, computed at hourly or 2.5-min intervals, is useful for studies of magnetic storm phenomena (Sec. 5h-11). Dst = lin (AH1 + AH2 + AH,,) represents the average deviation of the horizontal component from quiet-day values for a set of n observatories that are relatively uniformly distributed in longitude and located at low ( 40 kev) particles is highly variable usually bounds the outermost magnetic shell of
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5~285
the radiation belts. Within the shells of this transitory region the spherical harmonic and dipole descriptions of the field become less accurate, and large deviations commoruy occur. It has not been clearly established whether nightside field lines in region B (Fig. 5h-10) emanate from the earth at 8 > 83 or 8 < 83; 83 field lines could lie within region B or at the boundary between regions A and B. The uncertainty is greatly influenced by the fact that 83 (as noted in Sec. 5h-10) varies greatly with the level of activity. Close to the nightside equatorial plane beyond region B (Fig. 5h-10), in what can be called the near-tail region, the magnetic field maintains a shelllike structure, but is highly deformed by internal plasma pressures that inflate and stretch the field shells toward the antisolar direction. These shells emanate from the earth at 8. :::; e < 8 3 • For accurate mathematical description of the field in the outer magnetosphere expressions for the distortions created by the solar wind compression and the stresses exerted by plasmas within the magnetosphere and magnetospheric tail need to be added to the spherical harmonic description (Sec. 5h-5). However, as of 1970, expressions which adequately represent these effects analytically throughout the magnetosphere had not been derived. The time variability is one of the principal problems that is illustrated by considering some of the effects observed during storms, below, but present to some degree at all times: (1) a high solar wind pressure compresses the magnetosphere inward (Sec. 5h-12) such that 81 is increased and more magnetic flux is pushed back into the tail; (2) an enhanced plasma belt is created deep in the magnetosphere and exerts stresses that inflate the magnetosphere (Sec. 5h-11); (3) complex changes in the plasma behavior in the near-tail region locally disturb the field [51]; and (4) at the times of magnetic bays (Sec. 5h-10), or substorms, the plasma stress is partially released and the near-tail field sudderuy relaxes, or collapses, toward a more dipolar configuration [45]. 6h-21. Charged Particle Content. Plasmas [20,52,53]. The presence of plasmas in the magnetosphere and their influences on the magnetic field have been mentioned in Sec. 5h-20. High fluxes of plasma are observed in the plasma sheet that lies approximately on the equatorial plane separating the earthward magnetic field in the northern half of the tail from the oppositely directed field in the southern half (Fig.5h-10). The thickness of the sheet iEi 4 to 6R. at the distance from the earth of about 17R •. The electrons in the plasma sheet have a broad, quasi-thermal energy spectrum peaked anywhere between a few hundred and a few thousand electron volts with a non-Maxwellian high-energy tail. In the midnight sector the plasma sheet reaches, under quiet conditions, distances of about lOR. from the earth and comes closer when disturbed. The sheet extends to the flanks and toward the front side, enveloping the magnetosphere, as shown in Figs. 5h-9 and 10. The inner boundary of the plasma sheet is well-defined on the evening to the afternoon side, but appears to be more diffuse on the morning side; however, detailed plasma behaviors on the dayside of the magnetosphere are as yet not known. On the nightside the plasma and the magnetic field show shell-like structures often with distinct discontinuities between neighboring shells. Whenever the ratio f3 of the plasma kinetic energy density (inmv2) to the magnetic field energy density (B2 /8:"') exceeds unity, the magnetic field is disturbed by the diamagnetic effect of the plasma, and the dipolar characteristics of the field are appreciably modified or completely lost. An example of the latter is seen in the outer skirts of the magnetosphere near the dawn and dusk meridians and near the geomagnetic equator where the magnetic field gradient is almost zero from about lOR. to the magnetopause. From ground-based observations of whistlers (Sec. 5h-33) and direct satellite measurements, it has been found that sudden decreases in electron densities occur near the -magnetic equatorial plane at distances from the earth's center that vary with local :time and disturbance from 3.5 to 7R.. The region of higher electron densities, about
I
) 5-286
ELECTRICITY AND MAGNETISM
102 cm- is called the plasmasphere, as shown in Fig. 5h-9. The outer boundary of the plasmasphere is referred to as the plasmapause, and its position moves toward the earth during periods of high magnetic activity [54]. The plasmas inside the plasmasphere are of much lower energy than those in the plasma sheet, and unlike the latter, the plasma within the plasmapause is not known to play any major role in causing magnetic disturbances except that their presence makes the conductivity along the magnetic field lines very large. Energetic Particles [19,55,56]. The magnetosphere is populated with charged particles of a wide range of energies. These particles are distinguished from such transients as galactic and solar cosmic rays by their being "trapped" in the geomagnetic field for varying lengths of time. Hence their motion in the geomagnetic field is of fundamental importance; basic properties of their motion are discussed in Sec. 5h-22. Energies of the plasmas discussed above partially overlap with the low-energy part of particles described here, and the division of the charged-particle content of the magnetosphere into plasmas and energetic particles becomes arbitrary in some cases. Grouping of the particle populations is not definitively settled and is subject to future revisions. However, roughly speaking, the energetic particles in the magnetosphere can be divided into two groups: tmpped and quasi-tmpped particles. The definition of "being trapped" is by no means unambiguous; if a particle drifts around the earth repeatedly, it is considered to be trapped; see Sec. 5h-22 for particle drifts. The region of trapped particles is from L ,....., 1.2 to 6; see Sec. 5h-22 for the definition of L. This population includes the so-called inner and outer radiation zones or belts that were discovered by the early probes. The inner zone contains protons of energies, E > 30 Mev, with fluxes of about 10 4 cm- 2 sec-I, and peak intensities near L ,....., 1.5; these particles are relatively stable with a time constant of the order of 1 year. The outer zone with electrons of E > 1.5 Mev is at L ,....., 3 to 4, and its flux is highly variable, particularly during magnetic storms. The time constant for these electrons is roughly hours to weeks. These early observations of penetrating radiation with heavily shielded Geiger tubes led to the concept of the inner- and outer-zone structure with a "slot" near L "-' 2 where the count rate was a minimum [57]. However, later observations of particles in wider energy ranges have revealed that the structure described above was, to some extent, due to instrumental factors, and that different group of particles have grossly different spatial distributions and time variations, some with double peaks and a minimum near L "-' 2, and others without such a structure. Nevertheless the terms "inner and outer zones" are used to refer to the regions approximately L < 2 and L > 2, respectively, without implying that the two regions are separated by a sharply defined boundary. Protons in the energy range 0.1 Mev < E < 5 Mev occupy the outer zone from L "-' 2 to 6 and are found to be relatively stable with small fluctuations on time scales of days; this population of protons has high fluxes with a peak of the order of 10 8 cm- 2 sec- 1 near L ro.J 3.5 and carries most of the energy content of the trapped particles. Low-energy protons of E from a few kev to about 50 kev occupy a broad region from 3 to lOR., and their fluxes vary greatly during magnetic storms. These low-energy protons are mainly responsible for the inflation of the magnetosphere and the Dst decrease on the earth's surface during magnetic storms, described in Sec. 5h-11. The contribution to the storm effects from electrons in the energy range from a few hundred ev to 50 kev is likely to be appreciable, but .probably only about one-fourth of that from the protons [20]. Electrons with higher energies (e.g., E ;;:: 300 kev) occupy the outer zone, and their fluxes suddenly increase at the time of magnetic storms and decay to an equilibrium level with a time constant of days to weeks [58,59]. The sources of the trapped particles are not as yet well understood. The radioactive decay of albedo neutrons produced by nuclear collisions 'of galactic (and solar) cosmic-ray protons with oxygen and nitrogen nuclei in the ,atmosphere has. been proposed to be .the. main source for the high-energy protons 3
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5-287
in the inner zone. For the outer-zone protons, several processes involving an inward diffusion and acceleration have been proposed; but there are no definitive proofs as to how efficient these mechanisms are. One suggestion is that the diffusion is caused by violation of the third adiabatic invariant (Sec. 5h-22), due to such magnetic perturbations as sudden impulses (Sec. 5h-12), and that conservation of the first and second invariants (Sec. 5h-22) leads to energization of the particles as they diffuse inward. A similar process resulting from fluctuations in the electric field of the magnetospheric convection system (Sec. 5h-23) has also been considered. The series of high-altitude nuclear explosions of 1958 (i.e., the Argus experiment) was designed to test the possibility of trapping energetic particles by the geomagnetic field [60]. Electrons mainly from the {3 decay of the fission fragments were injected into a thin shell near L ~ 2, and were found to be stable in position during their lifet;.me of a few weeks. The Starfish explosion of July 9, 1962 [61] created a more intense and extensive artificial radiation belt; initially, a maximum flux (~10' electrons cm- 2 sec- 1) was near L ~ 1.3 with large fluxes extending to beyond L ~ 4. For L < 1.5 the electron decay was slow, with lifetimes of the order of years, and was in agreement with the theoretical expectation for decay from Ooulomb scattering of the electrons in the atmosphere. Beyond L ~ 1.7 the decay was considerably faster, with lifetimes of months to a week; the rapid decay was thought to be due to resonant interaction of electrons with electromagnetic waves such as whistlers (Sec. 5h-33) or due to processes related to magnetic disturbances. Interactions between particles and electromagnetic waves of various frequencies from VLF to ELF or ULF (Sees. 5h-29 to 5h-33) constitute an important subject concerning the particle behaviors in the magnetosphere [62], but direct observational evidence for these interactions is in most cases still lacking. The quasi-trapped particles occupy regions between the trapping region and the magnetopause on the front to the flanks of the magnetosphere, and the near-earth tail region on the nightside. These particles mainly consist of low-energy protons and electrons with E ;S 50 kev. Their fluxes are highly variable with geomagnetic activity; this population and its extension into the near-tail plasma sheet is probably the rcscr,oir for the particles precipitating illto the atmosphere during high-latitude disturbances. A major supply of particles for the trapping region may also come from the quasi-trapping region. Occasional high fluxes of particles have been observed in different regions; for instance, sudden flux increases of electrons with E ~ 40 kev and with omnidirectional fluxes up to about 10 7 electrons cm- 2 sec- 1 observed in the tail [63] (often referred to as electron "islands") and "spikes" of directional electron fluxes up to 10' electrons cm- 2 sec- 1 sterad- 1 encountered at low altitudes (~1,000 km) [64] are examples of intensified particle activity in the quasi-trapping region. lih-22. Energetic Particle Motion [2,56,65,66]. There are three fundamental characteristics in the motion of a charged particle in a dipole-type magnetic field such as the earth's field: (1) gyration about a line of force, (2) oscillation between mirror points along lines of force, and (3) longitudinal drift around the center of the dipole. Oorresponding to these three periodicities there are three adiabatic invariants that are conserved. For the gyrating motion the first, or magnetic moment, invariant I-' is given by
where P 1.
=
ma B
=
the component of the (relativistic) momentum perpendicular to the magnetic field vector B the particle rest mass
=
IBI
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ELECTRICITY AND MAGNETISM
The motion of a charged particle can be investigated with high accuracies by an approximation in which the center of the gyrating motion, referred to as the guiding center, is followed. For the oscillatory motion of the guiding center between mirror points, the second, or longitudinal, invariant is conserved. This invariant, J, is defined by J = § PI! ds where PI! is the guiding-center momentum parallel to the line of force, and the integral is taken over a complete oscillation. For J to be conserved, the drift velocity perpendicular to the lines of force along which the guiding center oscillates must be small compared with its velocity along the line of force. The guiding center drifts from a line of force to an adjacent line of force such that J is constant, and thus the lines of force, along which the guiding center moves, form a surface on which J is constant. If this surface is closed, namely, if the guidingcenter returns to a line of force which it previously traversed, there is a third periodicity. For this precessional motion of the guiding center, the third, or flux, invariant is conserved. The invariant is the magnetic flux 0.01 volt meter- 1 with values between 0.02 and 0.05 volt metey-l being f.airlycommon [89,90]. Values as high as 0.13 volt meter- 1 have been observed, and as the total time of sampling has been small, it is highly probable that greater. intensities are not uncommon. In contrast, directly on shells of discrete auroral forms E has been observed to drop below 0.00.5 volt meteY-I, which suggests that the E .field is partially short-circuited in local strips. of exceptionally high ionospheri0 conductivity. Observations that visual auroral structures show identical details when observed simultaneously at
+
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ELECTRICITY AND MAGNETISM
conjugate pomts in the northern and southern auroral belts [91] and that the magnetic disturbances are correlated in detail [92] illustrate that the potential distribution maps from hemisphere to hemisphere along magnetic field lines. Corresponding field intensities in the equatorial plane of the magnetosphere, taking into account the magnetic field geometry and its distortion in the near-tail region, are roughly 20 to 100 times less than in the ionosphere along the same magnetic shells. Over the polar cap (Sec. 5h-10) there have not been definitive electric field measurements. If the polar-cap ionospheric currents are Hall currents, it can be estimated that the electric field has properties similar to those observed in the auroral belt. It is also not known whether or not magnetic field lines emanating from the polar cap can be treated as electrical equipotential lines in that plasma densities at large distances along these shells outside the equatorial plasma sheet in the tail have been below measurement thresholds. In middle- and low-latitude regions E and v measurements in .and above the ionosphere have given values in the range 10- 4 to 2 X 10- 3 volt metey-I, which in most cases is close to the magnitude of possible errors in measurement [88-90]. Measurements have not been made during periods of large disturbances, or storms, when one might expect the high-latitude convection system to penetrate more deeply into the magnetosphere. E magnitudes of the order 10- 3 volt meter- I can be expected from the Sq (Sec. 5h-8) dynamo (i.e., winds) in the ionospheric E region [93]. In addition to the convection process, a variety of mechanisms have been proposed for generating electrostatic fields relevant to specific problems in the ionosphere and magnetosphere [74,94,95]. Other than those cases where the indirect evidence is convincing (e.g., the polarization field required for the equatorial electrojet, Sec. 5h-8), their existence and/or importance is unproved. Electrostatic electric fields also play an essential role in a number of theoretical treatments of the magnetopause boundary and the bow shock (Sec. 5h-26). In the case of the bow shock, fields as strong as 5 volts metey-I have been postulated as existing ina thin region at the shock front [96]. However, the limited measurements available indicate that the fields are more of the order -v X B, where v is the plasma bulk velocity as in the hydromagnetic t1pproximt1tion (Sec. 5h·23) [89J. Similarly, in the interplanetary medium, E, as indicated in the spacecraft frame of reference, is compatible with -v X B for the solar wind velocity v (Note. This field does not exist in the frame of reference of the solar wind which is moving with velocity v.) For typical ranges of solar wind-interplanetary magnetic field parameters, the range of E (in spacecraft coordinates) is roughly 10- 3 to 10- 2 volt metey-I [89]. Relative to accelerating charged particles that enter the earth's (magnetospheric) frame of reference from inertial space, an additional electric field exists which is caused by charge separation induced by the rotation of the ionosphere with the earth [72,73]. The potential of this corotational field in the ionosphere is V = 90 sin' e in kilovolts, where e is the colatitude. As the corotational field is zero in the earth's reference frame, it does not create currents.
WAVE PHENOMENA 6h-29. Magnetohydrodynamic Waves [66,69,97]. Alfven Waves. In a perfectly conducting fluid permeated by a uniform magnetic field B o, Alfven waves propagate in the direction of Bo with the Alfven velocity V A given by Eo
VA =
V41rp
where Eo = IEol (in emu, i.e., in gauss) and p = density (in cgs units, i.e., g cm-S). The magnetic perturbation b and the fluid velocity v are both transverse to Bo; and b'/81r= tpv2; i.e., an equipartition of energy holds.
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5~295
M agnetoacoustic Waves. In a perfectly conducting, compressible fluid permeated by a uniform magnetic field B o, magnetohydrodynamic waves propagate with a phase velocity V that satisfies
where V A = Alfven velocity (= Eo/V 47rp) Co = sound velocity (= V'YP/p; 'Y = ratio of specific heats, P = pressure, and p = density) () = angle between Bo and direction of propagation When () = 0, the roots of the above equation are ± Co and ± V A, corresponding to a pure acoustic wave and a pure Alfven wave propagation along Bo. When () = 1r /2, there is only one mode propagating with phase velocity, V = ± (Co' + V A')t; in this wave the fluid velocity v is perpendicular to B o, and the magnetic perturbation b is parallel to Bo· The latter velocity is called the magnetoacoustic velocity. Between () = 0 and 1r /2 the two modes are coupled. 5h-30. Plasma Waves [98,99]. Geneml. For a two-component (electron-ion) cold plasma in a uniform magnetic field Eo the dispersion equation is given by
An 4
-
En'
+C
=
0
where n = refractive index (= Iklc/Wi k = angular wave number, light) A = S sin' () + P cos' () E = RL sin' () + PS (1 + cos' (J) C =PRL S = t(R +L) D = t(R - L)
+
C
= velocity of
R = 1 - aw'/[(w fli)(w - fl,)] L = 1 - aw'/[(w - fli)(w fl,)]
P
=
a = =
II.' IIi' fl, fli
=
+
1 - '"
(II.' + IV) /w' 47l"n,e' /m, 471"niZ'e' /mi
= e Eo/m,c = electron cyclotron frequency
Z e EO/mic = ion cyclotron frequency angular frequency of the wave Eo = IBol e(or Ze) = magnitude of electron (or ion) charge in esu units m,,; = electron or ion mass in grams n.,i = electron or ion number density, cm- 3 (J = angle between the propagation direction (i.e., that of k) and Bo The dispersion equation is quadratic in n', and hence there are in general two modes. In particular, for (J = 0: n' = R (with right-handed circular polarization), and n' = L (with left-handed circular polarization); and for () = 71"/2: n' = RL/S (the extraordinary mode), and n' = P (the ordinary mode). Polarization, left- or righthanded, is defined, for positive w, with respect to the direction of the ambient magnetic field Bo. Resonances occur when n' = ± 00, and cutoffs, when n' = o. Resonances: (1) (J = 0: the electron cyclotron resonance at w = fl, (R -+ ± 00); and the ion cyclotron resonance at w = fli (L-+ ± 00). (2) () = 1r/2: the lower hybrid resonance at WLH, where WLH approximately satisfies . =
w =
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ELECTRICITY AND MAGNETISM
and the upper hybrid resonance at
WUH,
where
WUH
approximately satisfies
Numerous modes of plasma waves have been investigated extensively, but only those that are frequently encountered in the geophysical environment are mentioned below. All these modes are defined in a homogeneous plasma. The plasma in the magnetosphere cannot necessarily be regarded as being homogeneous, and drift waves may play an important role in inducing instabilities, but these and other instabilities are not discussed here since they are not as yet adequately understood under geophysical conditions. M agnetohydrodynamic Waves (w «rli) n' = 1 n' cos' (} = 1
+ l' + l'
for the fast mode (compressional wave) for the slow mode (Alfv8n wave)
(5h-l) (5h-2)
where p =
plasma density
the characteristic velocity c/ vi 1 + l' is called the Alfv8n velocity. When l' » 1, this reduces to B o/~, which is V A given in Sec. 5h-29. The slow mode disappears at W = £1;, The fast mode exists at frequencies above £Ii and continues· on to the whistler mode. The phase velocity of the fast mode is isotropic. Ion Cyclotron Waves (w :> oil. The slow wave inEq. (5h-2) has a characteristic dispersion relation just below the ion cyclotron frequency. In the neighborhood of W = £Ii, n' for the two modes are approximately for the fast modA
(5h-3)
for the slow mode
(5h-4)
The ion cyclotron resonance appears in the slow mode; for this mode the dispersion relation can be rewritten as
W'
~ £Ii' ( 1
II,' )-1 + -'+ krr'c' II·' kll'c +' k,Lc' 2
where kll and k,L denote.the components of k parallel and perpendicular to B o, respectively. Waves in this mode are called ion cyclotron waves. The "Whistler" Mode (£Ii < W < £I,). The branch that is an extension of the fast mode in Eq. (5h-l) is called the whistle?' mode. The term "whistler mode" originates from the circumstance .that whistlers (Sec. 5h-33) propagate.in this mode; however, the use of this term is not limited to the propagation of natural whistlers. The refractive index for this mode is approximately given by
n'
= 1 W
-:-
aw £I, cos
(J
provided that £I, sin 4
()
«4w'(1 - a) 2
COS' (}
(quasi-longitudinal propagation)
and that
0,' sin'
e«
12w 2 (1 - a) I
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5-297
where", = II,2/w 2 in the present approximation. For IJ = 0 the wave has a righthanded, circular polarization, and exhibits a resonance at w = [le, i.e., the electron cyclotron frequency j the wave becomes evanescent above [l,. Ion Acoustic and Electrostatic Ion Cyclotron Waves. In a plasma with finite electron and ion temperatures T, and T i , respectively, ion acoustic waves propagate in the direction parallel to Eo with a dispersion relation
if (3, (== 8rrn,KT,/Bo2) is small and if Ti « T" where K is the Boltzmann constant. If Ti is comparable to T" the ion thermal velocity becomes comparable to the wave phase velocity, and the wave will be strongly Landau-damped. For IJ r" 0, and for frequencies above [li but close to it, the electrostatic ion cyclotron wave can propagate, under certain conditions, with a dispersion relation
where k.L is the component of k perpendicular to Bo. Electrostatic Plasma Waves. In the absence of a magnetic field, a plasma resonates electrostatically with the frequency II, (= V 4rrn,e 2/m" ignoring the ion motion). This frequency is called the Langmuir or plasma frequency. The reflection of radio waves from the ionosphere is due to this resonance (Sec. 5h-19). 5h-31. Geomagnetic Pulsations [100-102]. Rapid geomagnetic fluctuations with periods approximately from 0.2 sec to 10 min (or roughly 5 to 0.001 Hz in frequency) are generally referred to as pulsations or micropulsations. Fluctuations (or signals) in the frequency range 3,000 to 3 Hz are often grouped under ELF (extra low frequency) waves and those with frequencies 300 km in the late morning hours along L shells (Sec. 5h-22), corresponding to invariant latitudes of 55 to 65° [106,89]. The percentage of time of occurrence as a function of signal intensity decreases markedly for E between 60 and 180 }LV metec" (rms) at an altitude of 700 km [89]. Similarly, for samples distributed between 240 and 2,700 km altitude, occurrences decrease markedly for B between 2 and 6 milligammas (rms) [106]. Although occurrence is most frequent near 60° invariant latitude in the late morning, the total region of frequent occurrence (e.g., > 10 percent of the time) extends throughout the dayside hours 6h to 18h local time and invariant latitudes 50 to 70°. Although the ELF hiss signal is relatively steady in the sense that rapid changes in intensity are absent, it is frequently accompanied by a second signal, called ELF chorus. The chorus signals consist of a long series of wave packets, each having a duration of the order of one second, and the characteristic that the frequency rises with time within each packet. The time-space distribution of ELF hiss and chorus observed from satellites, and the fact that their occurrence at the earth's surface is less common and more erratic, suggest that these signals are repeatedly reflected from hemisphere to hemisphere from ionospheric levels. There is evidence that this reflection occurs roughly at the altitude where the signal frequency equals the proton gyrofrequency (but is presumably affected by the presence of heavier ions), and that the effective gyrofrequency also acts as a low-frequency cutoff [107]. Some signal apparently reaches the earth's surface through mode-coupling mechanisms. ELF signals of a more transient nature than the ELF hiss, noted above, are encountered in the auroral-belt and polar-cap regions. These are frequently associated with irregularities (Sec. 5h-17) in electron density and electric fields when observed by satellites [89]. Although mo"t ~T,F p.miRRions propagating in the whistler mode are believed to be generated in the magnetosphere, it has been suggested that a strong sigral near 700 Hz in the auroral zone might be caused by proton cyclotron radiation in the ionosphere [108]. Part of the energy of the ELF (and VLF) emission from a lightning impulse propagates upward into the ionosphere and sometimes triggers a proton whistler [109]. In a frequency-time display, such as in a sonogram, a proton whistler has a dispersion characteristic of slowly rising frequeney that asymtotically approaches the proton cyclotron frequency at the point of observation by a satellite. The frequency at which this proton whistler originates in the frequency-time display is an extension of the trace that corresponds to the "electron whistler," to be discussed in Sec. 5h-33. Proton whistlers are thought to be ion cyclotron waves (Sec. 5h-30). 6h-33. Whistlers and VLF Emissions [100,104]. Whistlers are electromagnetic signals in audio frequencies originating from lightning strokes. They are called whistlers because of their whistling sound when converted into audio signals. Whistlers typically have a descending tone from above 10 to 1 kHz; however, the upper limit can be as high as 30 kHz or even higher, and the lowest may extend to the ELF or even ULF range. The duration of a whistler is about one second, but some whistlers last only for a fraction of a second and others for two or three seconds. Whistlers propagate in the whistler mode (Sec. 5h-30), which is roughly a guided mode along the magnetic field lines. Only a slight electron density gradient is required to make tubes of magnetic force act like ducts for whistler propagation. Ducted whistlers often propagate back and forth between the two hemispheres repeatedly. The
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ELECTRICITY AND MAGNETISM
group velocity, with which wave energy propagates, has a maximum at a frequency of say, /I, and decreases for frequencies above and below f,. Therefore, in a frequencytime display (e.g., in a sonogram) a signal trace for a whistler that traveled a long distance shows the earliest arrival at /I and a gradual delay in arrival time as f departs from fl above and below. A whistler exhibiting such a dispersion characteristic is called a nose whistler, and the frequency fl of the minimum delay, the nose frequency. In a homogeneous medium fl is i fH, where f H is the electron cyclotron frequency (= fl,/27r). The group delay time, say t, for a whistler that has traversed a one-hop path from one hemisphere to the other can be approximately expressed by t = Df-t
for f well below the nose frequency; the constant D, called the dispersion constant or simply the dispersion, is given approximately by
D
= (2C)-1
r
jpath
(fp/fHt) ds
sect
where c is the velocity of light, and fp the electron plasma frequency (= rr,/27r). Apart from a constant, the integrand reduces to (n,/B)! where n, is the electron density, and B the magnetic field intensity. Thus various models for the electron density in the magnetosphere can be tested by comparing the observed D with the calculated values. Studies of electron densities in the magnetosphere by means of whistlers have shown that there is a "knee" in the electron density profile at several earth radii and that the electron density drops substantially beyond this distance (Sec. 5h-21). Whistlers have been detected by satellites at various altitudes in the magnetosphere, and their behaviors are now being investigated in detail. In addition to whistlers, there are other types of emissions in the VLF range; these are called VLF emissions. Several types of these emissions are observed in close association with whistlers, suggesting that they are triggered by the latter. VLF emissions may last steadily for minutes, or even hours, or may occur in bursts; converted to sound waves, they may produce a hissing sound or show a musical tone. (A division of hiss into ELF and ',TLF groups is entirely artificial.) 'v'LF emissions are most frequently observed at middle and high latitudes, and indicate similarity in occurrence and form at magnetically conjugate areas in the northern and southern hemispheres. Such mechanisms as electron cyclotron radiation and Cerenkov radiation have been suggested for the origin of VLF emissions. The possibility of these VLF waves having significant interaction with energetic particles in the radiation belt has been extensively investigated [56,62]. References 1. Chapman, S., and J. Bartels: "Geomagnetism," Clarendon Press, Oxford, 1940, 1951, 1962 (corrected). 2. Matsushita, S., and VV. H. Campbell, eds.: "Physics of Geomagnetic Phenomena," Academic Press, Inc., New York, 1967. 3. Vestine, E. H., L. LaPorte, 1. Lange, and W. E. Scott: The Geomagnetic Field, Its Description and Analysis, Carnegie Inst. Wash. Publ. 580, 1947. 4. Adopted at the International Association of Geomagnetism and Aeronomy Symposium on Description of the Earth's Magnetic Field, Washington, D.C., Oct. 22-25, 1968. 5. Vestine, E. H.: Chap. II-2, p. 181, in ref. 2. 6. Cain, J. C.: Personal communication December, 1968. 7. Vestine, E. H., L. Laporte, C. Cooper, I. Lange, W. C. Hendrix: Description of the Earth's Main Magnetic Field and Its Secular Change, Carnegie Inst. Wash. Publ. 578, 1947. 8. Symposium on Magnetism of the Earth's Interior: J. Geomag. Geoel., 17 (3-4) (1965). 9. Cain, J. C., and S. J. Hendricks: The Geomagnetic Secular Variation 1900-1965, NASA Tech. Note TN-D-4527, 1968.
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5-301
10. Cain, J. C., S. J. Hendricks, R. A. Langel, and W. V. Hudson: J. Geomag. Geoel. 19,335 (1967). 11. Beloussov, V. V., P. J. Hart, B. C. Heezen, H. Kuno, V. A. Magnitsky, T. Nagata, A. R. Ritsema, and G. P. Woollard, eds.: The Earth's Crust and Upper Mantle, Am. Geophys. Union Geophys. Monograph 13, 'Washington, D.C., 1969; in particular, chap. 5. 12. Serson, P. H., and W. L. W. Hannaford: J. Geophys. Research 62, 1 (1957). 13. McCormac, B. M., ed.: Aurora and Airglow, Proc. NATO Study Inst., 1966, Reinhold Book Corporation, New York, 1967. 14. McCormac, B. M., ed.: Aurora and Airglow, Proc. NATO Study Inst., 1968, Reinhold Book Corp., New York, 1969. 15. Harang, L.: Terrest. Magnetism and Atmospheric Elea., 51, 353 (1946). 16. Fukushima, N.: J. Fac. Sci. Univ., Tokyo, 8,293 (1953). 17. Heppner, J. P.: Ref. 13, p. 75. 18. Akasofll, S.-I.: Space Sci. Rev. 4, 498 (1965). 19. McCormac, B. M., ed.: Earth's Particles and Fields, Proc. NATA Advanced Study Inst., 1967, Reinhold Book Corporation, New York, 1968. 20. Frank, L. A., Ref. 19, p. 67. 21. Hoffman, R. A., and L. J. Cahill, Jr.: J. Geophys. Research 73,6711 (1968). 22. Sugiura, IVI:.: Ann. IGY 35,9, Pergamon Press, New York, 1964. 23. Sugiura, M., and S. J. Hendricks: NASA Tech. Note, NASA TN D-5748, 1970. 24. Mean, G. D.: J. Geophys. Research 69, 1181 (1964). 25. Sugiura, M.: J. Geophys. Research 70, 4151 (1965). 26. Bartels, J.: Ann. IGY 4,227, Pergamon Press, New York, 1957. 27. Lincoln, J. V.: Chap. 1-3, p. 67, in ref. 2. 28. Davis, T. N., and M. Sugiura: J. Geophys. Research 71, 785 (1966). 29. Rikitake, T.: "Electromagnetism and the Earth's Interior," Elsevier Publishing Company, Amsterdam, 1966. 30. Price, A. T.: Chap. II-3, p. 235, in ref. 2. 31. Madden, T. R., and C. M. Swift, Jr.: In ref. 11. 32. Ratcliffe, J. A., ed.: "Physics of the Upper Atmosphere," Academic Press, Inc., New York, 1960. 33. Rishbeth, H.: Rev. Geophys. 6, 33 (1968). 34. Donahue, T. M.: Science, 159,489 (1968). 35. Cohen, R.: Chap. III-4, p. 561, in ref. 2. 36. Herman, J. R.: Rev. Geophys. 4,255 (1966). 37. Symposium on Upper Atmospheric 'Winds, 'Waves, and Ionospheric Drifts, IAGA Assembly, 1967; J. Atmospheric and Terre"t. Phys. 30(5), (1968). 38. Smith, E. K., and S. Iviatsushita, eds.: "Ionospheric Sporadic E," Pergauloll Prebtl, Oxford, 1962. 39. Smith, E. K., Jr.: Chap. III-5, p. 615, in ref. 2. 40. Baker, VY. G., and D. F. Martyn: Phil. Trans. Roy. Soc. London, Ser. A, 246, 281 (1953). 41. Chapman, S.: Nuovo Cimento 4 (suppl.), 1385 (1956). 42. Ratcliffe, J. A.: "The Magneto-ionic Theory and its Applications to the Ionosphere," Cambridge University Press, London, 1959. 43. Hess, VV. N., and G. D. Mead, eds.: "Introduction to Space Science," 2d eeL, Gordon and Breach, Science Publishers, Inc., New York, 1968. 44. King, J. W., and VY. S. Newman, eds.: "Solar-Terrestrial Physics," Academic Press, Inc., New Yorl" 1967. 45. Heppner, J. P., M. Sugiura, T. L. Skillman, B. G. Leclley, and M. Campbell: J. Geophys. ReseaTGh 72, 5417 (1967). 46. Ness, N. F.: Ref. 44, p. 57. 47. Heppner, J. P.: In ref. 14. 48. Ness, N. F., K. VY. Behannon, S. C. Cantarano, and C. S. Scearce: J. Geophys. Research 72,927 (1967). 49. Ness, N. F., C. S. Scearce, and S. C. Cantarano: J. Geophys. Research 72,3769 (1967). 50. Wolfe, J. H., R. W. Silva, D. D. McKibbin, and R. H. Mason: J. Geophys. Research 72,4577 (1967). 51. Sugiura, lVI., T. L. Skillman, B. G. Ledley, and J. P. Heppner: Presented "t International Symposium on the Physics of the Magnetosphere, Washington, D.C., September, 1968. Sugiura, M.: In "The World Magnetic Survey 1957-1969," IAGA Bulletin No. 28. 52. Bame, S. J.: Ref. 19, p. 373. 53. Vasyliunas, V. M.: J. Geophys. Research 73, 2839 (1968). 54. Carpenter. D. L.: J. Geophys. Research 71, 693 (1966).
5-302
ELECTRICITY AND MAGNETISM
55. McCormac, B. M., ed.: Radiation Trapped in the Earth's Magnetic Field, Proc. Advanced Study Inst., Bergen, 1965, D. Reidel Publishing Co., Dordrecht, Holland, 1966. 56. Hess, W. N.: "The Radiation Belt and Magnetosphere," Blaisdell Publishing Company, a division of Ginn and Company, Waltham, Mass., 1968. 57. Van Allen, J. A., and L. A. Frank: Nature 183, 430 (1959). 58. Brown, W. L., L. J. Cahill, L. R. Davis, C. E. Mcilwain, and C. S. Roberts: J. Geophys. Research 73, 153 (1968). 59. Williams, D. J., J. F. Arens, and L. J. Lanzerotti: J. GeophY8. Research 73, 5673 (1968). 60. Symposium on Scientific Effects of Artificially Introduced Radiations at High Altitudes, J. Geophys. Re8earch 64(8),865 (1959). 61. Collected Papers on the Artificial Radiation Belt from the July 9, 1962, Nuclear Detonation, W. N. Hess,ed., J. Geophys Research 68(3), 605 (1963). 62. Kennel, C. F., and H. E. Petschek: J. Geophys. Research 71, 1 (1966). 63. Anderson, K. A.: J. Geophys. Research 70, 4741 (1965); P. Serlemitsos: ibid. 71, 61 (1966); A. Konradi: ibid. 2317; E. W. Hones, Jr., S. Singer, and C. S. R. Rao: ibid. 73, 7339 (1968). 64. McDiarmid, I. B., and J. R. Burrows: J. Geophys. Research 70, 3031 (1965). 65. Northrop, T. G.: "The Adiabatic Motion of Charged Particles," Interscience Publishers. a division of John Wiley & Sons, Inc., New York, 1963. 66. Alfven:, H., and C.-G. Fiilthammar: "Cosmical Electrodynamics," Clarendon Press, Oxford, 1963. 67. McIlwain, C. E.: Ref. 55, p. 45. 68. Hines, C. 0.: Space Sci. Rev. 3, 342 (1964). 69. Cowling, T. G.: "Magnetohydrodynamics," Interscience Publishers, Inc., New York, 1957. 70. Dungey, J. W;: "Cosmic Electrodynamics," Cambridge University Press, London, 1958. 71. Gold, T.: J. Geophys. Research 64, 1219 (1959). 72. Axford, W. I., and C. O. Hines: Can. J. Phys. 39, 1433 (1961). 73. Taylor, H. E., and E. H. Hones: J. Geophys. Research 70, 3605 (1965). 74. Obayshi, T., and A. Nishida: Space Sci. Rev. 8, 3 (1968). 75. Parker, E. N.: "Interplanetary Dynamical Processes," Interscience Publishers, a division of John Wiley & Sons, Inc., New York, 1963. 76. Axford, W. I.: Space Sci. Rev., 8, 331 (1968). 77. Snyder, C. W., M. Neugebauer, and U. R. Rao: J. Geophys. Research 68, 6361 (1963). 78. Hundhausen, A. J., J. R. Asbridge. S. J. Bame, H. E. Gilbert, and I. B. Strong: J. Geophys. Research 72, 87 (1967). 79. Frank, L. A.: (abstract) Tran8. Am. GeophY8. Union 49, 262 (1968). 80. Wilcox, J. M.: Space Sci. Rev. 8, 258 (1968). 81. Ness, N. F., C. S. Scearce, J. B. Seek, and J. M. Wilcox: "Space Research," vol. VI, p. 581, R. L. Smith-Rose, ed., Spartan Books, Washington, D.C., 1966. 82. McCracken, K. G., and N. F. Ness: J. Geophys. Research 71, 3315 (1966). 83. Colburn, D. S., and C. P. Sonett: Space Sci. Rev. 5, 439 (1966). 84. Spreiter, J. R., A. L. Summers, and A. Y. Alksne: Planet. Space Sci. 14, 223 (1966). 85. Coroniti, S. C., ed.: Problems of Atmospheric and Space Electricity, Proc. 3d Intern. Con!. Atmospheric and Space Elec., 1963, Elsevier Publishing Company, Amsterdam, 1965. 86. Smith, L. G., ed.: Recent Advances in Atmospheric Electricity, Proc. 2d Con!. Atmospheric Elec., Pergamon Press, New York, 1958. 87. Fahleson, U.: Space Sci. Rev. 7, 238 (1967). 88. Haerendel, G., R. Liist, and E. Rieger: Planet. Space Sci. 15, 1 (1967). 89. Aggson, T. L., J. P. Heppner, N. C. :lVIaynard, and D. S. Evans: Personal Communications; presentations at International Symposium on the Physics of the Magnetosphere, September, 1968. 90. Wescott, E. M., J. Stolarik, and J. P. Heppner: Trans. Am. Geophys. Union 49, 155 (1968). 91. Davis. T. N.: In ref. 14. 92. Wescott, E. M., and K. B. Mather: J. Geophys. Research 70, 29 (1965). 93. Maeda, H.: J. Geomag. Geoelec. 7, 121 (1955). 94. Kern, J. W.: In ref. 2. 95. Chamberlain, J. W.: "Physics of the Aurora and Airglow," Academic Press, Inc., New York, 1961. 96. Tidman, D. A.: J. Geophys. Research 72,1799 (1967). 97. Ferraro, V. C. A., and C. Plumpton: "An Introduction to Magneto-fluid Mechanics," Oxford University Press, London, 1961.
MAGNETIC FIELDS IN THE EARTH'S ENVIRONMENT
5-303
98. Stix, T. H.: "The Theory of Plasma 'Waves," McGraw-Hill Book Company. New York, 1962. 99. Akhiezer, A. I., I. A. Akhie7.er, R. V. Polovin, A. G. Sitenko, and K. N. Stepanov: "Collective Oscillations in a Plasma," tr. H. S. H. Massey, tr. ed. R. J. Tayler, The MIT Press, Cambridge, Mass., 1967. 100. Bleil, D. F., ed.: "Natural Electromagnetic Phenomena below 30 kc/s," Plenum Press, Plenum Publishing Corporation, New York, 1964. 101. Campbell, W. H.: Ref. 2, p. 822. 102. Troitskaya, V. A.: Ref. 44, p. 213. 103. Madden, T., and W. Thompson: Re1J. Geophys. 3, 211 (1965). 104. Helliwell, R. A.: "'Whistlers and Related Ionospheric Phenomena," Stanford University Press, Stanford, Calif., 1965. 105. Gurnett, D. A.: Ref. 19, p. 349. 106. Taylor, W. W. L., and D. A. Gurnett: J. Geophys. Research 73, 5615 (1968). 107. Gurnett, D. A., and T. B. Burns: Univ. Iowa Preprint 68-28, Department of Physics and Astronomy, 1968. 108. Egeland, A., G. Gustafsson, S. Olsen, J. Aarons, and W. Barron: J. Geophys. Research 70, 1079 (1965). 109. Gurnett, D. A., S. D. Shawhan, N. M. Brice, and R. L. Smith: J. Geophys. Research 70, 1665 (1965).
Si. Lunar, Planetary, Solar, Stellar, and Galactic Magnetic Fields M. SUGlURA,l J. P. HEPPNER,l AND E. BOLDT 2
NASA -Goddard Space Plight Center H. W. BABCOCK S AND ROBERT HOWARD 4
Hale Observatories Carnegie Institution of Washington California Institute of Technology
LUNAR AND PLANETARY MAGNETIC FIELDS oi-1. Moon. 5,s According to the measurements made aboard the satellite Explorer 35, there appeared to be no magnetic field attributable to the moon at the distance of 800 km from the lunar surface. On the basis of the Explorer 35 observations the magnetic moment of the moon, even if the moon is magnetized, must be less than 4 X 10 20 cgs units, which is less than 10- 5 times the earth's magnetic moment. The conductivity of the moon seems to be sufficiently low to allow the interplanetary Lunar and planetary fields. Galactic fields. Stellar fields. 4 Solar fields. 5 N. F. Ness, K. ,V. Behannon, C. S. Scearce, and S. C. Cantarano, J. Geophys. Research 72, 5769 (1967). 5 C. P. Sonett, D. S. Colburn, and R. G. Currie, J. Geophys. Research 72, 5503 (1967). I
2
3
5-304
ELECTRICITY AND MAGNETISM
magnetic field to be convected through it without noticeable change; the upper limit to the effective average conductivity has been estimated to be 10- 5 mho metec i . 6i-2. Venus.! Mariner V detected a bow shock around Venus; the bow shock appeared to be similar to, but much smaller in dimension than, that of the earth (Sec. 5h-20). The creation of the bow shock has been attributed to the presence of a dense ionosphere which prevents rapid penetration of the solar wind magnetic field and plasma into the atmosphere. The standoff distance of the bow shock at the time of the Mariner V traversal appeared to be about 4,000 km (or about 0.7 Venus radii) from the surface of the plane. No planetary magnetic field was detected at this distance. The upper limit to the magnetic dipole moment of Venus was estimated to be about 10- 3 times that of the earth. The observation that trapped charged particles (electrons with E, > 45 kev and protons with Ep > 320 kev) were absent in the vicinity of Venus is in agreement with the above estimate.
SOLAR FIELD 6i-3. General Magnetic Field of the Sun. Magnetic fields on the solar surface are measured by means of the Zeeman effect in solar spectrum lines. Since 1952 measurements of magnetic fields outside sunspots have been made with the solar magnetograph. 2 Tables 5i-1 and 5i-2 summarize data on magnetic fields in polar regions. TABLE 5i-1. THE POLAR MAGNETIC FIELDS OF THE SUN: 1912-1954 Investigator
Field intensity at North Pole a
Hale, Langerb .......... -4 gauss Nicholson, Ellerman, +3 ± 1.7 and Hickox' -2.0 ± 2.8 von Kluber d . . . . . . . . . . lly all :of which showl fields in the range of several hundred to a few thousand gauss. All stellar fields adequately tested are found to be variable; many of the variations are periodk Among the spe~trum variables, the magnetic variations, roughly sinusoidal, are synchronous with periodic variations in the intensity of lines of vario1l;s groups of elements such as the rare earths, chromium, and strontium; These variations are generiJ,lly attributed to axial rotation of a star carrying an asymmetric distribution of magnetic areas. The periods of variation are characteristically a few days, but range up to 226 days for HD188041 and 2,350 days for HD187474. Preston S has tabulated the periodic magnetic variables as identified in 1967. Of these, 15 show reversals of magnetic polarity; only 3-HD188041, 78 Virginis, and HD215441-show always the same polarity. The strongest magnetic field yet measured in nature is that of the AOp star HD215441; for this the field at maximum has been measured at 35,700 gauss. Table 5i-3 summarizes data for 89 magnetic stars as of 1958,1 except that recently determined periods have been added for several stars from the work of Preston, Renson, Steinitz, and Wehlau. Table 5i-4 provides data for 38 additional magnetic stars discovered between 1958 and 1966. Much of the observational and interpretive work on the subject is reviewed by various authors in the Proceedings of the American Astronomical Society-National H. W. Babcock, Astrophys. J. 128, 228 (1958). H. W. Babcock, Astrophys. J .. Supp. 3 (30), ,(1958). S G. W. Preston, Astrophys. J. 150, 547 (1967).
1
2
5-310
ELECTRICITY AND MAGNETISM
TABLE 5i-4. MAGNETIC STAR DATA (FOR STARS DISCOVERED 1958-1966) Sp
Star or HD
R.A.*
Dec.*
2837 5797 9393 12288 16778 17775 18078 24712 50729 51106 E Pup} 55719 59435 89069
Oh29 m 59' 058 6 1 30 53 2 o 14 240 51 250 48 253 34 353 23 652 19 653 52
9.1 8.8 8.5 8.0 7.7 8.8 8.0 5.9 9.1 7.7 5.4
AO AOp AOp AOp B9p(?) AOp A2p A5, FO A5p A3p
710 56
+43°29' +6014 +4341 +6923 +5940 +6143 +56 1 -12 13 - 451 - 130 -4026
727 42 10 17 42
-910 +7859
7.9 8.1
94660 115606 133652 141988 143939 162950 170973 171782 177984 179259 183806 186343 190145 190068 189932 355163 192687 +29°4202 200311
10 53 13 16 15 4 1547 16 2 1750 1830 1834 19 4 19 8 19 30 19 41 19 58 20 o 20 1 20 10 20 13 2049 2059
-42 2 +13 13 -3046 +6228 -3920 +2712 + 338 + 515 + 737 +4430 -45 18 +2212 +6722 +15 15 -3354 +1352 +1343 +2939 +4354
6.3 8.3 6.0 8.3 7.0 7.8 6.3 7.9 9.1 8.9 5.9 8.2 7.4 8.0 6.9 8.7 8.6 8.8 7.9
201174 204411
21 4 56 2125 26
+45 6 +4840
8.5 5.3
212385 215441 220147 221568
2222 16 2242 42 2319 3 2330 55
-3920 +5522 +6211 +5741
6.9 8.6 7.6 8.0
A5p (AOp) A3p AO A2 AOp A2p B9p A3 AOp AOp A2p A5p AOp A2p A2p AOp FOp AOp A2 AOp (AOp) B9p AOp (A3p) FO? A2p AOp B9p AOp
m.
w
No. of obs.
He extremes
-- ---
12 4 7i 53 3 57 7 31 45 36 27 17 48 52 3 44 47 3 47
2
A2
"'0.1 "'0.3 =0.5 "'0.5
1/1 3/3 4/4 4/5 3/6 1/1 3/3 3/4 1/1 1/3 1/1
0.4 "'0.3
± 90 ± 60 ± 88
+700 +575 -540
± 88 ± 114
2/2 6/6
-430 -440
7/12 2/4 1/4 4/5 2/3 1/1
-1960 ± 87 -810 ± 139 -2080 ± 320 -810 ± 122 +690 ± 236 -565 ± 87 ~1140 ± 71 -1380 ± 130 -785 ± 110 -540 ± 77 -720 ± 271 -430 ± 60 -580 ± 77 +990 ± 192
8/8
"'0.5
o ± 148 -1960 ± 272 -1345 ± 95 +21 ± 153
11/16 1/1 2/3 1/3 1/1 1/2 4/4 1/4 1/1 1/2 4/4 7/13 27/32 5/6 1/2 28/37 4/5 6/8
-'-1520
± 90
-1900
±
159
± 143 -515 ± 41 -1260 ± 319 +4100 ± 370 -1825
-835 -225
± ±
151 172
+700 ± 127 +1420 ± 120 +2790 ± 170 -195 ± 109 +1620 ± 141 +1290 ± 111 +1075 ± 115 +1000 ± 125 +890 ± 190 +1215 ± 150
± 103 ± 112
+848 +445
-1020 ± 108 -60 ± 143 +1235 ± 129 +730 ± 260 +755 ± 52 +1190 ± 181 +40
±
118
+1780 ± 183 +525 ± 86 +790 ± 228 +1120 ± 264 +1500 ± 134 +760 ± 139 +1765 +665
± 177
±
70
+35, 700 +735 ± 138 +470 ± 69
* PositIon for 1960.
Aeronautics and Space Administration Symposium held at Greenbelt, Maryland, in 1965. 1 The book is replete with references.
GALACTIC MAGNETIC FIELD 5i-6. Summary. Some of the gross features of the galactic magnetic field have been inferred from information related to cosmic rays (cf. Ginzburg and Syrovatskii, 1964). A comparison of the observed cosmic-ray electron spectrum with the nonthermal radio spectrum arising from galactic synchrotron radiation indicates (Okuda and Tanaka, 1968) that the magnetic field is 10 to 20 microgauss near the galactic center, 5 to 10 microgauss near the solar system, and ~2.5 mic,rogauss for the halo. Dynamical considerations (Parker, 1968) of the cosmic-ray pressure, due mainly to energetic protons, suggest that the average field of the disk is about 5 microgauss. 1 "The Magnetic and Related Stars," Robert C. Cameron, ed., Mono Book Corporatioll, Baltimore, 1967.
GALACTIC MAGNETIC FIELDS
5-311
Polarization measurements (cf. van de Hulst, 1967) of galactic nonthermal radio emission indicate that the coherence scale of the magnetic field of the disk is about 10 2 light years. The Faraday rotation measure for the polarization of distant discrete radio sources varies quite smoothly with galactic coordinates (Morris and Berge, 1964; Gardner and Davies, 1966) and corresponds to a field whose lines of force run parallel to the galactic plane in the direction III "" 70° for bII > 0, while below the plane (b II < 0) the direction of the field is opposite. These directions are in general agreement with the studies of the polarization of starlight by magnetically aligned interstellar grains (Smith, 1956; Behr 1959) and with the direction of the local Orion spiral arm (Sharpless, 1965). A search (Verschuur, 1968) for the Zeeman splitting of the 21-cm-absorption line by the atomic hydrogen of this local arm yields a limit to this HI-associated field as 0.6 ± 0.9 microgauss. A relatively strong magnetic field of 20 microgauss in the Perseus spiral arm, in the direction of Cassiopeia A, was clearly detected by the Zeeman effect in the course of the same observations. This measurement of a strong HI-associated magnetic field suggests that the search for detectable Zeeman effects in other absorption or emission spectra throughout the galactic disk should yield much new information. References Behr, A.: Nachr. Akad. Wi8s. Gottingen Math.-physik. Kl. IIa 185 (1959). Gardner, F. F., and R. D. Davies: Australian J. Phys. 19, 129, 441 (1966). Ginzburg, V. L., and S. I. Syrovatskii: "Origin of Cosmic Rays," Pergamon Press, New York, 1964. Morris, D., and G. L. Berge: Astrophys. J. 139, 1388 (1964). Okuda, H., and Y. Tanaka: Can. J. Phys. 46, S642 (1968). Parker, E. N.: "Stars and Stellar Systems," vol. 7., "Nebulae and Interstellar Matter," B. Middlehurst and L. Aller, eds., University of Chicago Press, Chicago, 1968. Sharpless, S.: "Stars and Stellar Systems," vol. 5, "Galactic Structure," A. Blaauw and M. Schmidt, eds., University of Chicago Press, Chicago, 1965. Smith, E. van P.: Astrophys. J. 124, 43 (1956). van de Hulst, H. C.: "Annual Review of Astronomy and Astrophysics," vol. 5, L. Goldberg, ed., Annual Reviews, Inc., Palo Alto, 1967. Verschuur, G. L.: Phys. Rev. Letters 21, 775 (1968).
Section 6 OPTICS BRUCE H. BILLINGS, Editor
Joint Commission on Rural Reconstruction, Taipei, Taiwan.
CONTENTS 6a. 6b. 6c. 6d: 6e. 6f. 6g. 6h. 6i. 6j. 6k. 61. 6m. 6n. 60. 6p. 6q. 6r. 6s.
Fundamental Definitions, Standards, and Photometric Units. . . . . . . . . . .. Refractive Index of Special Crystals and Certain Glasses ............... Transmission and Absorption of Special Crystals and Certain Glasses. . .. Geometrical Optics and Index of Refraction of Various Optical Glasses.. Index of Refraction for Visible Light of Various Solids, Liquids, and Gases Optical Characteristics of Various Uniaxial and Biaxial Crystals ......... Optical Properties of Metals ........................................ Reflection ........................................................ Glass, Polarizing, and Interference Filters ............................ Colorimetry ...................................................... Radiometry...................................................... Wavelengths for Spectrographic Calibration .......................... Magneto-, Electro-, and Photo elastic Optical Constants. . . . . . . . . . . . . . .. Nonlinear Optical Coefficients ....................................... Specific Rotation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Radiation Detection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Radio Astronomy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Far Infrared. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. Optical Masers ..................••....••....••.....•....•.........
6-1
6-2 6-12 6-58 6-95 6-104 6-111 6-118 6-161 6-170 6-182 6-198 6-222 6-230 6-242 6-248 6-252 6-271 6-277 6-313
6a. Fundamental Definitions, Standards, and Photometric Units
6a-1. Fundamental Definitions Absorptance. The ratio of the radiant flux lost by absorption to the incident radiant flux. If Io represents the incident flux, Ir the reflected flux, It the transmitted flux, the absorptance is given by the expression
Absorption, Bouger's Law. If Io is the incident flux, I the flux passing through a thickness x of a material whose absorption coefficient is 0
WAVELENGTH, p.m
FIG. 6b-5. Refractive index vs. wavelength for Irtrans 1 to 6. U-71, 1968.)
(From Kodak Pamphlet
The temperature coefficient of refractive index dn/dT of Irtran 4; from 198 to 295 K, has essentially a constant value of 4.8 X 10- 6 per K from 3 to 13 }Lm [adapted from A. R. Hilton and C. E. Jones, Appl. Opt. 6, 1513 (1967)].
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
6-33
Lanthanum Fluoride TABLE 6b-23. REFRACTIVE INDEX OF LANTHANUM FLUORIDE A, p,m
n. (observed)
n. (computed)
no (observed)
no (computed)
0.25365 0.31315 0.36633 0.40465 0.43583 0.54607
1.64866 1.61803 1.61803 1.61184 1.60950 1.60223
1.64866 1. 61694 1. 61694 1.61216 1. 60916 1.60223
1.65587
1.65587 1.63639 1.62520 1. 61733 1.61546 1.60597
1.61797 1. 61664 1.60597
Adapted from M. P. Wirick, Appl. Opt. 6, 1966 (1966).
Dispersion equations:
n. = 1.58330
77.850 1346.5
+A_
.
no = 1.57376
153.137 686.2
+A_
A mean value between n. and no of about 1.58 between 0.8 and 2.0 p,m is reported by J. B. Mooney, Infrared Phys. 6, 153 (1966).
Lead Fluoride TABLE 6b-24. REFRACTIVE INDEX OF LEAD FLUORIDE A, p,m
n
A, p,m
n
0.3088 0.3188 0.3338 0.3462 0.3645 0.3810 0.4045 0.4266 0.4565 0.4876 0.5277
1.915 1.887 1.882 1.854 1.849 1.826 1.824 1.804 1.801 1.787 1.785
0.5711 0.6259 0.6930 0.7775 0.8861 1.031 1.237 1.545 12 15 18
1.771 1.764 1. 758 1.753 1.748 1.744 1.743 1.742 1.62 1.52 1.40
The index values from 0.3088 to 1.545 pm are for a 0.8869-p,m film of lead fluoride on fused quartz, and were adapted from J. M. Bennett, E. J. Ashley, and H. E. Bennett, Appl. Opt. 4, 961 (1965). The last three values are adapted from B. Welber, Appl. Opt. 6, 925 (1967).
6-34
OPTICS
Lithium Fluoride TABLE
A, /Lm
0.1935 0.1990 0.2026 0.2063 0.2100 0.2144 0.2194 0.2265 0.231 0.254 0.280 0.302
6b-25.
REFRACTIVE INDEX OF LITHIUM FLUORIDE
n
A, /Lm
n
A, /Lm
n
1.4450 1.4413 1.4390 1. 4367 1.4346 1.4319 1.4300 1.4268 1.4244 1.41792 1.41188 1.40818
0.366 0.391 0.4861 0.50 0.80 1.00 1.50 2.00 2.50 3.00 3.50 4.00
1. 40121 1.39937 1.39480 1.39430 1.38896 1. 38711 1.38320 1. 37875 1.37327 1.36660 1.35868 1.34942
4.50 5.00 5.50 6.00 6.91 7.53 8.05 8.60 9.18 9.79
1. 33875
1.32661 1.31287 1.29745 1.260 1.239 1.215 1.190 1.155 1.109
Data at a temperature of 20°0 for wavelengths 0.193 to 0.231 /Lm are taken nom Z. Gyulai, Z. Physik 46, 84 (1927); at 20°0 for 0.254 to 0.486 /Lm are taken from H. Harting, Sitzber. Deut. Akad. Wiss. Berlin IV, 1-25 (1948); at 23.6°0 for 0.50 to 6.0 /Lm from L. W. Tilton and E. K. Plyler, J. Res. NBS 47, 25 (1951); at 18°0 for 6.91 to 9.79 /Lm from H. W. Hohls, Ann. Physik 29, 433 (1937). The data for the four spectral regions reported here fit together to within a few parts in the fourth decimal place. For computational purposes, a dispersion equation for the wavelength range 0.5 to 6.0 /Lm is given by M. Herzberger andO. D. Salzberg, J. Opt. Soc. Am. 52, 420 (1962) : n = A BL CLZ D)..' E)..t
+
1
where L = - - - A' - 0.028 A = 1.38761 B = 0.001796 C = -0.000041 D = -0.0023045 E = -0.00000557
+
+
+
6-35
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
Magnesium Fluoride TABLE 6b-26. REFRACTIVE INDEX OF MAGNESIUM FLUORIDE AT 21°0 A
A
(10-< }Lm)
no
n.
(10-" }Lm)
no
n.
1,780 ± 2 1,849.68 2,536.5 2,893.59 4,046.56 4,340.465 4,358.35 4,471.48 4,678.16 4,799.92 4,921.93
1.43975 1.43424 1.40208 1.39485 1.38359 1.38215 1.38207 1. 38160 1.38082 1.38039 1.37001
1.45365 1.44797 1.41483 1.4073 1.39566 1.39415 1.39407 1.39357 1. 39275 1.39231 1. 39192
5,015.68 5,085.82 5,460.74 5,875.62 5,893.7 6,234.37 6,438.47 6,562.79 6,678.15 6,907.16 7,065.25
1.37972 1.37953 1.37859 1.37774 1.37770 1. 37713 1.37681 1.37662 1. 37647 1.37618 1. 37599
1. 39163 1.39142 1.39043 1.38954 1.38950 1.38889 1.38858 1.38838 1.38822 1.38790 1.38771
The index values from 0.1780 to 0.289359 }Lm are from D. L. Steinmetz, W. G. Phillips, M. Wirick, and F. F. Forbes, Appl. Opt. 6, 1001 (1967). The values from 0.404656 to 0.706525 are those of A. Duncanson and R. W. H. Stevenson, Proc. Phys. Soc. (London) 72, 1001 (1958). The birefringence of magnesium fluoride in the vacuum ultraviolet is discussed by V. Chandrasekharan and H. Damany, Appl. Opt. 7, 939 (1968), and 8, 671 (1969), and many values are listed. For computational purposes Duncanson and Stevenson also give two dispersion equations: 35.821 no = 1.36957 A _ 1492.5
n. =
+ 37.415 1.38100 + A _ 1494.7
TABLlil 6b-27. TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX A,
}Lm
0.4047 0.7065
dno/dT (1O- 6 / o C)
dn./dT (1O- 6;oC)
+0.23 +0.19
+0.17 +0.10
From A. Duncanson and R. W. H. Stevenson, loco cit.
6-36
OPTICS
Magnesium Oxide TABLE 6b-28. REFRACTIVE INDEX OF MAGNESIUM OXIDE AT 23.3°C A,
/Lm
0.36117 0.365015 1.01398 1.12866 1.36728 1.52952 1.6932 1.7092 1.81307
n
).., /Lm
n
1.77318 1.77186 1.72259 1.72059 1.71715 1. 71496 1.71281 1.71258 1.71108
1.97009 2.24929 2.32542 3.3033 3.5078 4.258 5.138 5.35
1.70885 1. 70470 1.70350 1.68526 1.68055 1.66039 1.63138 1.62404
Dispersion equation:
n 2 = 2.956362 - 0.01062387)..2 - 0.0000204968)..4 - A2
~0~.~91~2~~22
From R. E. Stephens and 1. H. Malitson, J. Res. NBS 49,249 (1952). The earlier measurements of J. Strong and R. T. Brice, J. Opt. Soc. Am. 25, 207 (1935), are discussed therein. A systematic difference in values of n appears to exist, the data of Strong and Brice being about 37 X 10- 5 higher. TABLE 6b-29. TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX dn/dT (10- 6 ;00)
A,
p.m
7.679 7.065 6.678 6.563 5.893 5.461 4.861 4.358 4.047
20°0
25°0
30°0
35°0
40°0
13.6 14.1 14.4 14.5 15.3 15.9 16.9 18.0 18.9
13.7 14.2 14.5 14.6 15.4 16.0 17.0 18.1 19.0
13.8 14.3 14.6 14.7 15.5 16.1 17.1 18.2 19.1
13.9 14.4 14.7 14.8 15.6 16.2 17.2 18.3 19.2
14.0 14.5 14.8 14.9 15.7 16.3 17.3 18.4 19.3-
From R. E. Stephens and I. H. Malltson, IDe. cit.
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
6-37
Muscovite Mica 6b-30.
TABLE
t
AF,
5.24
=
AS,
pm
REFRACTIVE INDICES OF MUSCOVITE 1\1ICA
thick
pm
t = 20.82 pm thick
ns
nF
pm
AF,
AS,
pm
pm
--- --0.6665 0.6188 0.5573 0.5082 0.4538 0.4320
0.6675 0.6210 0.5590 0.5090 0.4555 0.4330 _...
t
-------pm
13.91
=
1.592 1. 600 1.600 1.603 1.608 1.611
1.590 1.594 1.595 1.600 1.602 1.608 .
--
--
0.6960 0.6316 0.5539 0.4935 0.4600 0.4310
--- - - -
thick
t
0.6985 0.6336 0.5555 0.4950 0.4615 0.4326
np
ns
---
---
1.598 1.593 1.596 1.600 1.062 1.604
1.594 1.598 1.601 1.605 1.607 1.610
---- - - - = 48.68 pm
thick I
AF,
pm
0.6910 0.5995 0.5293 0.4740 0.4300
AS,
nF
ns
---
---
1.590 1.595 1.598 1.602 1.607
1.594 1.599 1.603 1.606 1.611
pm
0.6930 0.6010 .0.5308 0.4754 0.4308
AF,
pm
0.6914 0.6110 0.5470 0.4958 0.4667 0.4408
AS,
nF
ns
---
---
1.591 1.594 1.596 1.599 1. 601 1.603
1.596 1.598 1.601 1.603 1.606 1.609
pm
0.6935 0.6125 0.5487 0.4971 0.4680 0.4425
Ada,)ted from M. A. Jeppeson and A. M. Taylor, J. Opt. Soc. Am. 56,451 (1966).
The values for the fast and slow rays are for four different thicknesses t. J?otassiun::. Bron::.ide TABLE
A,
6b-31. n
pm
REFRACTIVE INDEX OF POTASSIUM BROMIDE AT
A,
pm
n
A,
n
pm
A,
22°0
pm
n
-----
0.404656 0.435835 0.486133 0.508582 0.546074 0.587562 0.643847 0.706520
1.589752 1. 581479 1.571791 1. 568475 1.563928 1.559965 1.555858 1.552447
1.01398 1.12866 1.36728 1.7012 2.44 2.73 3.419 4.258
1.54408 1.54258 1. 54061 1.53901 1. 53733 1.53693 1.53612 1.53523
6.238 6.692 8.662 9.724 11.035 11.862 14.29 14.98
1.53288 1.53225 1.52903 1.52695 1.52404 1.52200 1.51505 1.51280
17.40 18.16 19.01 19.91 21.18 21.83 23.86 25.14
1.50390 1. 50076 1.49703 1.49288 1.48655 1.48311 1. 47140 1.46324
From R. E. Stephens, E. K. Plyler, W. S. Rodney, and R. J. Spindler, J. Opt. Soc. Am. 43, 111-112 (1953). Di~persion
n2
=
equation:
2.361323 - 0.000311497A 2 - 0.000000058613A 4
+
0.007676 A2
0.0156569 _ 0.0324
+ A2
The average value of the temperature coefficient of refractive index is given as 4.0 X 10- 5 per °0.
6-38
OPTICS
Potassium Chloride TABLE 6b-32. REFRACTIVE INDEX OF POTASSIUM CHLORIDE A,
I~m
0.185409 0.186220 0.197760 0.198990 0.200090 0.204470 0.208216 0.211078 0.21445 0.21946 0.22400 0.23129 0.242810 0.250833 0.257317 0.263200 0.267610 0.274871 0.281640 0.291368 0.308227 0.312280 0.340358 0.358702 0.394415
n 1. 82710 1.81853 1.73120 1.72438 1.71870 1. 69817 1.68308 1. 67281 1. 66188 1.64745 1. 63612 1.62043 1.60047 1.58979 1.58125 1.57483 1.57044 1.56386 1.55836 1.55140 1.54136 1.53926 1.52726 1. 52115 1. 51219
A,
p.m
0.410185 0.434066 0.441587 0.467832 0.486149 0.508606 0.53383 0.54610 0.56070 0.58931 0.58932 0.62784 0.64388 0.656304 0.67082 0.76824 0.78576 0.88398 0.98220 1.1786 1.7680 2.3573 2.9466 3.5359 4.7146
n 1.50907 1.50503 1.50390 1.50044 1.49841 1.49620 1. 49410 1.49319 1.49218 1.49044 1.490443 1.48847 1.48777 1.48727 1.48669 1.48377 1.483282 1.481422 1.480084 1.478311 1.475890 1.474751 1.473834 1.473049 1. 471122
A,
p.m
5.3039 5.8932 8.2505 8.8398 10.0184 11. 786 12.965 14.144 15.912 17.680 18.2 18.8 19.7 20.4 21.1 22.2 23.1 24.1 24.9 25.7 26.7 27.2 28.2 28.8
n 1.470013 1.468804 1.462726 1.460858 1.45672 1. 44919 1.44346 1.43722 1. 42617 1.41403 1.409 1.401 1.398 1.389 1.379 1. 374 1.363 1.352 1.336 1.317 1.300 1.275 1.254 1.226
Dispersion equations (for the ultraviolet and visible, respectively):
a' = 2.174967 = 0.008344206 A,' = 0.0119082 M, = 0.00698382 A,' = 0.0255550 M,
k = 0.000513495 h = 0.06167587 b' = 3.866619 Ma = 5,569.715 A3' = 3,292.47
Refractive-index data for the wavelength ranges indicated are from the following sources: (1) 0.185409 to 0.76824 p'm at 18°C, F. F. Martens, Ann. Physik 6, 619 (1901); (2) 18.2 to 28.8 p'm, H. W. Hohls, Ann. Physik 29,433 (1937); (3) 0.58932 to 17.680 p'm at 15°C, F. Paschen, Ann. Physik 26, 120 (1908). Note that the data of Paschen and of Martens overlap in a small region, and both sets are presented. There is less spread between Hohls's data and Paschen's data than there is among Paschen's data in the region where they join. The fit in this region is good (~0.0005). Paschen also presents two dispersion curves which fit the data of Martens to about five parts in the fifth decimal.
6-39
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
Temperature coefficient of refractive index: n
=
1.490443 - (T - 15)0.000034
_260r-------~------r_----_r--_r----r_----_r----~
-240
;-> -220 "-
'f'
o
r:
~-200 '0
-180
-160 40.0
0.4
FIG. 6b-6.Average temperature coefficient of refractive index dn/dT of potassium chloride near room temperature. [From F. Paschen, Ann. Physik 26, 120 (1908).]
Potassium Iodide TABLE
6b-33.
REFRACTIVE INDEX OF POTASSIUM IODIDE
A, I'm
n
A, I'm
n
A, I'm
0.248 0.254 0.265 0.270 0.280 0.289 0.297 0.302 0.313 0.334 0.366 0.391 0.405 0.436 0.486 0.546 0.588 0.589
2.0548 2.0105 1. 9424 1.9221 1.8837 1. 85746 1.83967 1. 82769 1.80707 1. 77664 1. 74416 1.72671 1. 71843 1.70350 1.68664 1.67310 1.66654 1.66643
0.656 0.707 0.728 0.768 0.811 0.842 0.912 1.014 1.083 1.18 1.77 2.36 3.54 4.13 5.89 7.66 8.84
1.65809 1.6537 1.6520 1.6494 1. 6471 1.6456 1.6427 1.6396 1. 6381 1.6366 1. 6313 1.6295 1.6275 1.6268 1.6252 1.6235 1.6218
10.02 11.79 12.97 14.14 15.91 18.10 19 20 21 22 23 24 25 26 27 28 29
I
n
1.6201 1. 6172
1.6150 1.6127 1.6085 1.6030 1.5997 1.5964 1.5930 1.5895 1.5858 1.5819 l. 5775 1.5729 l. 5681 1.5629 1.5571
6-40
OPTICS
The values for the wavelengths 0.248 through 1.083 /Lm are from H. Harting, Sitzber. Deut. Akad. Wiss. Berlin IV, 1 (1948); for 1.18 through 29 /Lm the values are from K. Korth, Z. Physik 84, 677 (1933). The temperature coefficient of refractive index for 0.546 /Lm in the temperature region 38 to 90°C is -5.0 X 10- 5 per DC. Ruby TABLE 6b-34. REFRACTIVE INDEX OF RUBY AT 22°C A, /Lm
no
0.4358 0.5461 0.5876 0.6678 0.7065
1. 78115 1.77071 1.76822 1. 76445 1. 76302
1. 77276 1. 76258
1.76010 1.75641 1. 75501
From M. J. Dodge, 1. H. Malitson, and A. 1. Mahan, Appl. Opt. 8, 1703 (1969).
Several. refractive-index values at high temperatures are given by T.'W. Houston, L. F. JGhnson, P. Kisliuk, and D. J. Walsh, J. Opt. Soc. Am. 53, 1286 (1963). Sapphire TABLE 6b-35. REFRACTIVE INDEX OF SAPPHIRE FOR THE ORDINARY R.il:Y:AT 24°C .
A, /Lm
no
A, /Lm
no
A, /Lm
no
A, /Lm
no
0.26520 0.28035 0.28936 0.29673
1.83360 1.82427 1. 81949 1.81595
0.435834 0.546071 0.576960 0.579066 0.64385 0.706519 0.85212 0.89440 1.01398 1.12866 1.36728 1.39506
1.78120 1.77078 1.76884 1.76871
1.52952 1.6932 1.70913 1. 81307
1.74660 1.74368 1. 74340 1.74144
8.3026 3.3303 3.422 3.5070 3 7067 4.2553 4.954 5.1456 5.349 5.419 5.577
1.70231 1.70140 1. 69818 1.69504 1 1\8746 1.66371 1.62665 1.61514 1.60202 1.59735 1.58638
0.30215
1.81351
0.3130 0.33415 0.34662 0.361051 0.365015 0.39064 0.404656
1.80906 1. 80184 1.79815 1.79450 1.79358 1.78826 1. 78582
1.765-17 1. 76303
1.75885 1.75796 1.75547 1.75339 1.74936 1. 74888
1.0701
1.73833
2.1526 2.24929 2.32542 2.4374 3.2439 3.2668
1.73444 1.73231 1.73057 1.72783 1.70437 1.70356
Adapted from I. H. M,tlitson, J. Opt. Soc. Am. 52, 1377 (1962).
The refractive index n, for the extraordinary ray !at 1.014 /Lm was also measured by Malitsonand determined to be 1.74794. The birefringence of sapphire in the vacuum ultraviolet is discussed by V. Chandrasekharan and H. Damany, Appl. Opt. 7,939 (1968), and 8, 671 (1969); andmany values are listed. Temperature coefficients of index dn/dT were determined from differences between indices measured at 19°C and those at 24°C. The results indicate that the coefficient is positive and decreases from about 20 X 10- 6 per °Cat the short wavelengths to about 10 X 10- 6 per °C near 4/Lm. An average value of 13 X 10- 6 per °C for the visible region was determined from additional measurements made at 17, 24, and 31°C. (From I. H. Malitson, loco cit.) For computational purposes, Malitsongives a dispersion equation for the wavelength region 0.270 to 5.60 )tm: n2 _ 1
=
~
A' - AI'
+~+ A' - A,2
A,A'
A2 -- A3'
6-41
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
TABLE 6b-36. CONSTANTS OF THE DISPERSION EQUATION AT 24°C Al = 0.06144821 A2 = 0.1106997 Aa = 17.92656
A, = 1. 023798 A, = 1. 058264 A3 = 5.280792
AI' = 0.003'17588 A" = 0.0122544 Aa' = 321.3616
Selenium TABLE 6b-37. REFRACTIVE INDEX OF SELENIUM AT 23°C (±2°C) A,
no
",m
n. 3 .608 ± 3.573 ± 3.46 ± 3.41 ±
2.790 ± 0.008 2.737 ± 0.008 2.65 ± 0.01 2.64 ± 0.01
1.06 1.15 3.39 10.6
O. 008 0.008 0.01 0.01
These values are for single-crystal selenium [from L. Gampel and F. M. Johnson, J. Opt. Soc. Am. 59, 72 (1969)]. For the region 9 to 23 ",m, the index values are 2.78 ± 0.02 for the ordinary and 3.58 ± 0.02 for the extraordinary ray with no appreciable variation [from R. S. Caldwell and H. Y. Fan, Phys. Rev. 114,664 (1959)]. For amorphous selenium in the region 2.5 to 15 ",m, index values of 2.46 to 2.3g are referenced by Caldwell and Fan. Silicon TABLE 6b-38. REFRACTIVE INDEX OF SILICON AT 26°C
i\,
",m
I
n
I
A,
",m
I
n
II
A. .um
I
n
I
A,
",m
I
n
--1.3570 1.3673 1. 3951 1.5295 1.6606 1.7092 1.8131 1.9701
3.4975 3.4962 3.4929 3.4795 3.4696 3.4664 3.4608 3.4537
2.1526 2.3254 2.4373 2.7144 3.00 3.3033 3.4188 3.50
3.4476 3.4430 3.4408 3.4358 3.4320 3.4297 3.4286 3.4284
4.00 4.258 4.50 5.00 5.50 6.00 6.50 7.00
3.4255 3.4242 3.4236 3.4223 3.4213 3.4202 3.4195 3.4189
7.50 8.00 8.50 10.00 10.50 11.04
3.4186 3.4184 3.4182 3.4179 3.4178 3.4176
From C. D. Salzberg and J. J. Villa, J. Opt. Soc. Am. 47,244 (1957).
The purity of the silicon sample is not specified. These data are about five parts in the third decimal place lower than those reported by H. B. Briggs, Phys. Rev. 77, 287 (1950). The refractive index of adequately pure (30 ohm-em) cast polycrystal silicon should have refractive-index values very near those of single crystals. The relative temperature coefficient of refractive index is (lin) dnldT = (3.9 ± 0.4) X 10- 5 per °C in a temperature range from 77 to 400 K [from M. Cardona, W. Paul, and H. Brooks, J. Phys. Chem. Solids 8, 204 (1959)1. For computational purposes, a dispersion equation for the wavelength region 1.3 to 11.0 ",m is given by M. Herzberger and C. D. Salzberg, J. Opt. Soc. Am. 52, 420 (1962); n = 3.41696
+ 0.138497L + 0.013924£2
where L = I/(A' - 0.028).
-0.0000209A'
+ 0.000000148A4
6-42
OPTICS
Silver Chloride TABLE 6b-39. REFRACTIVE INDEX OF SILVER CHLORIDE AT 23.9°C
X,}J.ffi
n
X, }J.ffi
n
X, }J.ffi
n
).., }J.ffi
n
1.99866 1.99745 1. 99618 1.99483 1.99339 1.99185 1. 99021 1. 99847 1. 98661 1.98464 1.9tl255 1.98034 1. 97801 1.97556 1.97297 1.97026 1. 96742 1.96444
13.5 14.0 14.5 15.0 15.5 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5
1. 96133
--
0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2
2.09648 2.06385 2.04590 2.03485 2.02752 2.02239 2.01865 2.01582 2.01363 2.01189 2.01047 2.00931 2.00833 2.00750 2.00678 2.00615 2.00559 2.00510
2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0
2.00465 2.00424 2.00386 2.00351 2.00318 2.00287 2.00258 2.00230 2.00203 2.00177 2.00151 2.00126 2.00102 2.00078 2.00054 2.00030 2.00007 1.99983
4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0
1.95807 1.95467 1. 95113 1. 94743 1.94358 1.93958 1.93542 1.93109 1.92660 1.92194 1. 91710 1.91208 1.90688 1. 90149
From L. W. Tilton, E. K. Plyler, and R. E. Stephens, J. Opt. Soc. Am. 40, 540 (1950).
Dispersion equation:
n 2 = 4.00804 - 0.00085111)..2 - 0.00000019762)..4
+)..2
0~~~g!;84
The temperature coefficient of refractive index is given as approximately 6.1 X 10- 5 per vO at 0.61 lUll,
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
~43
Sodiu.m Chloride TABLE 6b-40. REFRACTIVE INDEX OF SODIUM CHLORIDE A, p.m
n
A, p.m
n
A, p.m
n
A, p.m
n
4.0 4.1230 4 .. 7120 5.0 5.0092 5.3009 5.8932 6.0 6.4825 6.80 7.0 7.0718 7,22 7.59 7.6611 7,9558 8.0 8.04 8.8398 9.0 9.00 9;50 .10.0 ·10.0184 11.0 11.7864 12.0
1.52190 1.52156 1. 51979 1.51899 1. 51883 1. 51790 1.51593 1. 51548 1. 51347 1. 51200 1. 51136 1.51093 1. 51020 1.50850 1.50822 1.50665 1.50655, . 1.5064 1.50192 1. 50105 1. 50100 1.49980 1.49482 1.49462 1.48783 1.48171 1.48004
12.50 12.9650 13.0 14.0 14.1436 14.7330 15.0 15.3223 15.9116 16.0 17.0 17.93 18.0 19.0 20.0 20.57 21.0 21.3 22.3 22.8 23.6 24.2 25 .. 0 25.8 26.6 27.3
1.47568 1.47160 1. 47141 1. 46189 1.46044 1.45427 1.45145 1.44743 1.44090 1.44001 1.42753 1.4149 1.41393 1. 39914 1.38307 1.3735 1.36563 1.352 1.3403 1. 318 1.299 1.278 1 .. 254 1.229 1.203 1.175
I
0.19 0.20 0.22 0.24 0.26 0.28 0.30 0.35 0.40 0.50 0.589 0.6400 0.6874 0.70 0.7604 0.7858 0.80 0.8835 0.90 0.9033 0.9724 1.0 1.0084 1.0540 :1:0810 1:1058 1.1420
1.85343 1.79073 1.71591 1. 67197 1.64294 1.62239 1. 60714 1.58232 1. 56769 1.55175 1.54427 1.54141 1.53930 1. 53881 1.53682 1.53607 1. 53575 1.53395 1.53366 1.53361 1.53253 1.53216 1.53206 1.53153 1.53123 1.53098 1.53063
1.1786 1. 2016 1.2604 1.3126 1.4 1.4874 1.5552 1.6 1.6368 1.6848 1.7670 1.8 2.0 2.0736 2.1824 2.2464 2.3 2.3560 2.6 2.6505 2.9466 3.0 3.2736 3.5 3.5359 3.6288· 3.8192
1.53031 1.53014 1.52971 i.52937 1.52888 1.52845 .1. 52815 1.52798 1. 52781 1.52764 1.52736 1.52728 1.52670 1.52649 1. 52621 1. f2606 1.52594 1.52579 1.52525 1.52512 1.52466 1.52434 1.52371 .1.52317 1. 52312 1.52286 1.52238
Refractive-index data for rock salt are from the following sources for the indicated wavelengths: the data for wavelengths given with two-figure accuracy (0.19, 0.50, . . . ) or three-figure accuracy (10.0, 11.0, . . . ) are reported for 20°C by F. Kohlrausch, "Praktische Physik," vol. II, p. 528, B. G. Teubner, Leipzig, 1943; the data reported to four figures (1.299) in index at 18°C (even though they are three figures in wavelength) are from R. W. Rohls, Ann. Physik 29, 433 (1937); other data at 20°C are from W. W. Coblentz, J. Opt. Soc. Am. 4, 443 (1914.). Still more data have been published by Langley, Martens, Paschen, Rubens, Trowbridge, Nichols, and others, but all have apparently measured natural crystals of undetermined purity; the data all agree to the fifth decimal place.
6-44
OPTICS
TABLE 6b-41. TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX ATAHOUT-60"C --).,P.ffi
0.202 0.206 0.210 0.214 0.219 0.224 0.226 0.229 0.231 0.257 0.274 0.288 0.298 0.313 0.325 0.340 0.361 0.441 0.467 0.480 0.508
dn/dT (1O-5;oC)
3.134 2.229 1.570 0.861 0.235 -0.187 -0.382 -0.598 -0.757 -1.979 -2.396 -2.602 -2.727 -2.862 -2.987 -3.068 -3.194 -3.425 -3.454 -3.468 -3.517
A,
dn/dT
P.ffi
0.589 0.643 0.656 1.1
1.6 2.7 3.96 4.96 6.4 8.85 10.02 11.79 12.97 14.14 14.73 15.32 15.91 17.93 20.57 22.3
(10-5 ;oC)
-"
-3.622 -3.636 -3.652 -3.642 -3.557 -3.427 -3.286 -3.172 -3.149 -2.405 -2.2 -1.6 -1.4 -1.2 -1.0 -0.8 -0.7 -0.5 0 Q
From F. J. Micheli, Ann. Physik 4, 7 (1902) for the region 0.202 through 0.643 p'm; from E. Liebreich, Verhandl. Deut. Physik. Ges. 13, 709(1911) for the region 0.656 through 15.91 p.mj and from H. Rubens and E. F. Nichols, Weid. Ann. 60,454 (1897)for the region 17.93 to 22.3 pm.
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
6-45
Sodium Fluoride TABLE
6b-42.
n
A, /-LID
REFRACTIVE INDEX OF SODIUM FLUORIDE
A, /-LID
n
A, /-LID
n
0.186 0.193 0.199 0.203 0.206 0.210 0.214 0.219 0.227 0.231 0.237 0.240 0.248 0.254 0.265 0.270 0.280 0.289 0.297 0.302 0.313 0.334 0.366 0.391 0.405 0.436
I
1.3930 1.3854 1.3805 1.3772 1. 3745 1.3718 1. 3691 1.3665 1.3630 1.3606 1.3586 1.35793 1.35500 1.35325 1.34999 1.34881 1.34645 1.34462 1.34328 1.34232 1.34062 1.33795 1.33482 1.33290 1.33194 1.33025
0.486 0.546 0.588 0.589 0.656 0.707 0.720 0.768 0.811 0.842 0.912 1. 014 1.083 1.27 1.48 1. 67 1.83 2.0 2.2 2.4 2.6 2.8 3.1 3.3 3.5 3.7
1.32818 1.32640 1.32552 1.32549 1.32436 1.32372 1.32349 1.32307 1.32272 l.32247 l. 32198 1.32150 1. 32125 1.320 1. 319 1.318 1.318 1.317 1. 317 1.316 1.315 1.314 1. 313 1.312 1.311 1.309
3.9 4.1 4.5 4.7 4.9 5.1 5.3 5.5 5.7 5.9 6.1 6.3 6.5 6.7 6.9 7.1 7.3 7.5 7.7 7.9 8.1 8.3 8.5 8.7 8.9 9.1
A, /-LID
n
---
~~-
1.309 1.308 1.305 1.303 1.302 1.301 1.299 1.297 1.295 1.294 l.292 1.290 1.288 1.286 1.284 1.281 1.279 1.277 1.274 1.272 1.269 1.266 1.263 1.261 1.258 1.252
9.4 9.8 10.3 10.8 11.3 11.7 12.5 13.2 13.8 14.3 15.1 15.9 16.7 17.3 18.1 18.6 19.3 19.7 20.0 20.5 21.0 21.5 22.0 22.5 23.0 23.5 24.0
1.251 1.241 1.233 1.222 1.209 1.193 1.180 l.163 1.142 1.118 1.093 1.065 1.034 1.000 0.963 0.924 0.881 0.838 0.82 0.75 0.70 0.65 0.55 0.45 0.33 0.25 0.24
I From Alexander Smakula, U.S. Dept. Comm. Office Tech. Servo Doc. 111,052, pp. 88-89, October, 1952, \vho references these values.
The data fit together well (within a few parts in the fifth decimal place). TABLE
6b-43.
TEMPERATURE COEFFICIENT OF REFRACTIVE INDEX
A, /-LID
dn/dT (10- 5 per DC)
T, DC
0.546 3.5 8.5
-1.6 -1.6 -0.7
18-80 18-80 18-80
From H. W. Hohls, Ann. Physik 29, 433 (1937).
6-46
, OPTICS
Sodium Nitrate TABLE
, A,
6b-44. no
n.
1.6126 1.6121 1.5998 1.5968 1.5899
1.340 1.340 1.338 1.337 1.336
)Lm
0.434 0.436 0.486 0.501 0.546
REFRACTIVE INDEX OF SODIUM NITRATE
A,
)Lm
0.578 0.589 0.656 0.668
no
n.
1.5860 1.5840 1.5791 1.5783
1.336 1.336 1.334 1.334
From International Oritical Table., vol. VII, p. '26, McGraw-Hill Book Company, New York, 1930.
Spinel 6b-45.
TABLE
REFRACTIVE INDEX OF SPINEL
A, )Lm 0.4861 0.5893 0.6563
n 1.736 1.727 1.724
From Linde Air Products Company Teohnical Data Sheets.
Strontium Titanate TABLE
6b-46. A,
REFRACTIVE INDEX OF STRONTIUM TITANATE;
)Lm
0.404657 0.435834 0.486132 0.546074 0.576960 0.579066 0.587562 0.589262 0.643847 0.656279 0.667815 0.706519 0.767858 0.85212 0.89440 1.01398 1.12866 1.3622 1.39506 1.517
n
2.6481 2.5680 2.4897 2.4346 2.4149 2.4137 2.4090 2.4081 2.3837 2.3790 2.3750 2.3634 2.3488 2.3337 2.3276 2.3147 2.3055 2.2921 2.2906 2.2859
A,
)Lm
1.52952 1.7012 1.81307 1.871 1. 918 2.1526 2.3126 2.4374 2.5628 2.6707 2.7248 3.2434 3.3026 3.4226 3.5070 3.5564 3.7067 4.2553 5.138 5.3034
n
2.2848 2.2783 2.2744 2.2710 2.2704 2.2624 2.2564 2.2525 2.2466 2.2438 2.2404 2.2211 2.2181 2.2124 2.2088 2.2063 2.1990 2.1680 2.1119 2.1004
From I. H. Malitson, National Bureau of Standards, private communication, 1960.
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
6-47
Tellurium TABLE 6b-47. REFRACTIVE INDEX OF TELLURIUM X, )Lill
A, )Lill
n,
no
- - --- --4.0 5.0 6.0 7.0 8.0
4.929 4.864 4.838 4.821 4.809
6.372 6.316 6.286 6.270 6.257
n,
no
-----
9.0 10.0 12.0 14.0
---
4.802 4.796 4.789 4.785
6.253 6.246 6.237 6.230
The data are for single-crystal tellurium [from R. S. Caldwell and H. Y. Fan, Phys. Rev. 114, 664 (1959)]. The data of P. A. Hartig and J. J. Loferski, J. Opt. Soc. Am. 44, 17 (1954), may be compared: The latter are probably in error, owing to an averaging effect of the two indices. (Hartig's data are lower for the high index and higher for the low index.) The 8-)Lm value reported here (the datum of Caldwell) is probably about 0.002 too low. Thallium Bromide TABLE 6b-48. REFRACTIVE INDEX OF THALLIUM BROMIDE A, )Lill
n
A, )Lill
n
0.438 0.546 0.578 0.589 0.650
2.652 2.452 2.424 2.418 2.384
0.750 9.98 13.95 19.76 24.39
2.350 2.338 2.321 2.321 2.321
I
I
The indices in the visible region are from Tom F. W. Barth, Am. Mineralogist 14,358 (1929). The indices in the infrared region were measured at 45°C by D. E. McCarthy, Appl. Opt. 4, 878 (1965). Thallium Chloride TABLE 6b-49. REFRACTIVE INDEX OF THALLIUM CHLORIDE A, )Lill
n
A, )Lill
n
0.436 0.546 0.578 0.589 0.650
2.400 2.270 2.253 2.247 2.223
0.750 10.0 12.47 18.35
2.198 2.193 2.191 2.182
The indices in the visible region are from Tom F. W. Barth, Am. Mineralogist 14,358 (1929). The indices in the infrared region were measured at 45°0 by D. E . . McCarthy, Appl. Opt. 4, 878 (1965).
6-48
OPTICS
Thallium Bromide-Chloride (KRS-6) TABLE
6b-50.
REFRACTIVE INDEX OF THALLIUM BROMIDE-CHLORIDE
A, I'm
n
A, I'm
n
X, I'm
n
Na-D 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9
2.3367 2.3294 2.2982 2.2660 2.2510 2.2404 2.2321 2.2255 2.2212 2.2176 2.2148 2.2124 2.2103 2.2086 2.2071
2.0 2.2 2.4 2.6 2.8 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0
2.2059 2.2039 2.2024 2.2011 2.2001 2.1990 2.1972 2.1956 2.1942 2.1928 2.1900 2.1870 2.1839 2.1805 2.1767
11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 21.0 22.0 23.0 24.0
2.1723 2.1674 2.1620 2.1563 2.1504 2.1442 2.1377 2.1309 2.1236 2.1154 2.1067 2.0976 2.0869 2.0752
From G. Hettner and G. LeiBegang, Optik 3, 305 (1948).
The composition of the KRS-6 used was 44 percent thallium bromide and 56 per. cent thallium chloride.
6--49
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
Thallium B.romide-Iodide (KRS-5) TABLE
A,
n
pJJl
-- -2.68059 2.64959 2.62390 2.60221 2.58261 2.56748 2.55337 2.54092 2'.52986 2.51998 2.51110 2.50309 2:49583 2.48922 2.48318 2.47766 2.47258 2.46790 2.46358 2.45958 2.45587 0.~60 2.45242 0.980 2.44920 1.00 2.44620 1.02 2.44339 1.04 2.44076 1.06 2.43830 LOg 2.43598 1.1C 2.43380 1.12 2...43175 1.l4 2.42981 1.16 2.42798 1.18 2.42625 1.20 2.42462 1.22 2.42307 1.24 2.42159 1.26 2.42020 t:2ii 2.41887 1.30 2.41760 1.32 2.41640 1.34 2.41525 1.3'6 2.414i6 1.38 2.41312 1.40 2.41212 1.42 2.41117 1.44 2.41025
0.540 0.560 0.580 0.600 0.620 0.640 0.660 0.680 0.100 0.7.20 0.140 0.160 0.7g0 0.800 0.820 0.840 0.860 0.880 O.llOO 0.920 0.940
6b-51. A, J.'ID
REFRACTIVE INDEX' OF THALLIUM BROMIDE-IoDIDE AT
n
-- - 1.46 1.48 1.50 1. 52 1.54 1. 56 1.58 L60 1. 62 1.64 1. 66 1.68 1. 70 1. 72 1.74 1. 76 1. 78 1.80 1.82 1.84 1.86 1. 88 1. !f0 1. 92 1. 94 1. 96 1. 98 2.00 2.20 2.40 2.60 2.8.0 3.00 3.20 3.40 3.60 3.80 4.00 4.20 4.40 4.60 4.Se 5.00 5.20 5.40 5.60
~+n--
-A, J.'ID
-
n
n
- - -- - - -- - -
2.40938 5.80 2.37832 15.0 2.35812 2.40854 6.00 2'.37797 15.2 2.'35751 2.40774 6.20 2.37763 15.4 2.35690 2.40697 6.40 2.37729 15.6 2.35629 2.40623 6.60 2.37695 15.8 2.35566 2.40552 .6.80 2.37661 16.0 2.35502 2.40484 7.00 2.37627 16.2 2.35438 2.40419 7.20 2.37592 16.4 2.35373 2.~0355 7.40 2.37558 16.6 2.35307 2.40295 7.60 2.37523 16.S 2.35240 2.40236 7.80 2.37488 17.0 2.35173 2.40180 8.00 2.37452 17.2 2.35104 2.40125 8.2C 2.37416 17,4 2.35035 2,40073 8.40 2.37380 17.6 2.34965 2.40022 8.60 2.37343 17.8 2.34894 2.39974 8.80 2.37305 18.0 2.34822 2.39926 9.00 2.37267 18.2 2.34750 2.39881 9.20 2.37229 18.4 2.34676 2.39837 9.40 2.37190 18.6 2.34602 2.39794 9.60 2.37150 18.8 2.34527 2.39753 9.80 2.37110 19.0 2.34451 2.39713 10.0 2.37069 19.2 2.34374 2.39674 10.2 2.37027 19.4 2. 342~6 2.39637 10.4 2.36985 19.6 2.34217 2.39600 lIT. 6 2.36942 19.8' 2.34138 2.39565 10.8 2.36898 20.0 2.34058 2.39531 11.0 2.36854 20.1 2.34017 2.39498 11.2 2.36809 20.2 2.33916 2:.39214 1(4 2.36763 20.3 2.33935 2.38997 11. 6 2.36717 20.4 2.33894 2.38826 11.8 2.36669 20.5 2.33853 2.38688 12.0 2.36622 20.6 2.33811 2.38574 12.2 2.36573 20.7 2.33770 2.38478 12:4 2.36523 20.8 2.33727 2.38396 12.6 2.36473 20.9 2.33(185 2.3832.5 J2..8 2.36422 21.0 2..33643 2.38261 13.0 2.36371 21.1 2.33600 2.38204 13.2 2.36318 :ii.2 2.33557 ~. 38153 13.4 2.36265 21.3 2.33514 ;\1.38105 13.6 2.36211 21.4 2.33471 2.38061 13.8 2.36157 21.5 2.33427 2.38019 14.0 2.36101 21. 6 2.33383 2.37979 14.2 2.36045 21. 7 2.3333g 2.37940 14.4 2.35988 21.8 2.33295 2.37903 14.6 2.35930 21. 9 2.33251 2.37867 14.8 2.35871 22.0 2.33206
Dispersion equation:
A, J.'ID
:.22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23.0 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.8 23.9 24.0 24.1 24.2 24.3 24.4 24~5
24.6 24.7 24.8 24.9 25.0 25.1 25.2 25.3 25.4 25.5 25.6 25. 'i' 25.8 25.9 26.0 26.1 26.2 26.3 26.4 26.5 26.6
2.33161 2.33116 2.33070 2.33025 2.32979 2.32933 2.32887 2.32840 2.32793 2.32746 2.32699 2.32652 1. 32604 2.32556 2.32508 2.32460 2.32411 2.32362 2.32313 2.32264 2.32215 2.32165 2.32115 2.32065 2:32014 2.31964 2.31913 2.31861 2.31810 2.31758 2.31707 2.31555 2.31602 2.31550 2.31497 2.31444 2 ..31391 2.31337 2.31283 2.31229 2.31175 2.31121 2.31066 2.31011 2.30956 2.30900
A,
I'm
n
A, "ID
-- ~6. 7 2.30844
26.8 2.30789 26.9 2.30732 ~7.0 2.30676 27,-1 2'.30619 ZZ.2 2.30562 27.3 2.30505 27.4 2.30448 27.5 2.30390 27:!l 2.30332 27.7 2.30274 27.8 2.30216 27.9 2.30157 28.0 2.30098 28.1 2.30039 28.2 2.29979 28.3 2.29920 28.4 2.29860 28.5 2.29800 28:6 2.29739 28.7 2.29679 28,8 2.29618 28.9 2.29556 29.0 2.29495 29.1 2:2'9433 29.2 2.29371 29.3 2:29309 29.4 2:29247 29.5 2.29184 29.6 2.29121 29.7 2.29058 29.8 2.28994 29.9 2.28931 30.0 2.28867 30.1 2.28802 30 .. 2 2.287.38 30:3 2.28673 30.4 2.28608 30.5 2.28543 30.6 2.28477 30.7 2.28411 30.8 2.28345 30.9 2.28279 31.0 2.28212 31.1 2.28145 31.2 2.28078
25°C
n
A, J.'ID
n
-- - --
31.3 2.28011 31.4 2.27943 31.5 2.27875 31.6 2.27807 31. 7 2.27738 31.8 2.27669 31.9 2.27600 32.0 2.27531 32.1 2.27461 32.2 2.27391 32,3 2.27321 32.4 2.27251 32.5 2;27180 32.6 2.27109 32.7 2.27038 32.8 2.26966 32.9 2.26895 33.0 2.26823 33.1 2.26750 33.2 2.26678 33.3 2.26605 33.4 2.26532 33.5 2.26458 33.6 2.26384 33.7 2.26310 33.8 2.26236 33.9 2.26161 34.0 2.26087 34.1 2.26011 34.2 2.25936 34.3 2.25860 34.4 2.25784 34.5 2.25708 S4.6 ??.5631 34.7 2.25554 34.8 2.25477 34.9 2.25400 35.0 2.25322 35.1 2.25244 35.2 2.25166 35.3 2.25087 35.4 2.25008 31i.5 2.24929 35.6 2.24849 35.7 2. 24769. 35:8 2.24689
35.9 2.24609 36.0 2.24528 36.1 2.24447 36.2 2.24366 36.3 2.24284 36.4 2.24202 36.5 2.24120 36.6 2.. 24038 '36.7 2.23955 36.8 2. 23S72 36.9 2.23788 37.0 2.2370.5 37.1 2.23621 37.2 2.23536 37.. 3 2.23452 37.4 2.23367 37.5 2.23281 37.6 2.23196 37.7 2.23110 37.8 2.23024 37.9 2.22937 38.0 2.22850 38.1 2.22763 3.8.2 2.22676 38.3 2.22588 38.4 2.22500 38.5 2.22412 38.6 2.22323 38.7 2.2223.4 38.8 2.22145 38.9 2.22055 39.0 2.21965 39.1 2.21875 ~9.2 2.21784 39.3 2.21693 39.4 2.21602 39.5 2.21510 39.6 2.21418 39.7 2.21326 39.8 2.21233 39.9 2.21140 40.0 2.21047
6-50
'OPTICS
TABLE 6b-52. CONSTANTS OF THE DISPERSION: EQUATION -
,. 1 2 -3 4 5
25°0 '
.x.
}..;2 .'
-
:AT
0.0225 . 0.1>625 0.1225 '0.2025 27,089.737
1.8293958 1.6675593' 1.1210424 0,04513366' 12.380234
"From ·w. S.,Rodney and I. H. Malltson, J. Opt. Soc. Am: 46,956. (1956).
,.:'
Dataa:r;e also given i~ the reference for te~:rieratures of 19, and 31°C., A ~~mpai:is~'n 'of ,these data,' taken: with the 45.7 to 54,3 mole percent miXed crystal, is'made with the older data taken with 42 to 58 crystal material JlyL. W.,Tilton, E. ,K. Plyler, and R. E. Stephens, J. Res. NBS 43, 81(1949). The 45.7 to .54.3 composition, which has the 10westfreezing temperaturef :tlj.e binarysyste~,' should gIve)he,.be~t op,tical homogeneity. ' . , . ' . , '.l'ABLE 6b-,53. TEMPERATURE COEFlfICIE~T ~F R~~RACTIYE iNDE~ ..
dn/dT
A"lim-
(1O--G/KJ.
0,.577 , 1.1 I .2 4 6 8 10 12
14 ' i6 '
-254 -240 ' -238 -237 -237 -236 :"'235 ,-232
dn/dT "
A, ,Jim
20
25 30, 35 40
(10-& IK).,.-.
~228
-225 ,-217 • ..,...207 -195 -175 :...152
. :
From A. I; Funai, Lockheed Mi8:1ite8ct Spa'ce Co. Rept; LMSC/6"78~68-34, p.46;· (1968) :who referImees Rodney and Mallts!'n. . , ' '" .' . ' "', ',)
, The composition of KRS-5 in Table, vb-52 was 45.7parcellt thalliu:mbrom"ide and 54.3 percent,. thallium iodide. ' , Titanium, DioXide
A,
/Lm
0.4358 0.4916 0.4960 0.5461 0.5770 0.5791 0.6907 0.7082 1.0140 1.5296
no~_
2.853 2.725 2.718 2.652 2.623 2.621 2.555 2.548 2.484 2.454
n. 3.216 3.051 3.042 2.958 2.921 2.919 2.836 2.826 2.747 2.710
, ,J\.,
/Lm
2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 5.5000
no 2.399 2.387 2.380 2.367 2.350 2.322 2.290 2.200
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
~51
Dispersion equation-.,.,.-ordinary ray: • . .2.441 X 10 7 no= 5.913 +1.' _ 0:803 X 107 Dispersion equation-(Jxtraordinary ray:, •
_
-.
3.322 X 10 7
n.=Z.I 97 + X'·;';'; 0.843 X 10 7 For wavelengths between 0.4358 and 1.5296 /Lm, the calculated refractive-index data from J. R. DeVore, J. Opt. Soc. Am. 41,418(1951), are given. Thedispersion equ~tions are also due to DeVore i note that wavelength must be specified in angstroms in theseequations. The other data are the observed values ofW.F. Parsons,private communication. It should be hotedthat the data of Parsons and of DeVore do not fit together smoothly, probably indicating that there are differences from sample to sample. Data for dn/dT are listed by Alexander Smakula, U.S. Dept. Comm. Office Tech. Servo Doc. 111,052, October, 1952; the original data of Z. Schroeder, Z. Krist. 67,509 (1928), are quoted herein. The refractive index of the anastase form of titanium dioxide is discussed by T. N. Krylova and G. O. Bagdyk'yants,Opt. Spectr. U:S.S.R.·9, 339 (1960), and several other references are listed. Zinc Sulfide TABLE 6b-55. REFRACTIVE INDICES OF HEXAGONAL ZINC SULFIDE
A,/Lm 0.3600 0.3750 0.4000 0.4100
0.4200 0.4250 0.4300 0.4400 0.4500 0.4600 0.4700 0.4750 0.4800 0.4900
no
A, /Lm
n.
no
2.705 2.637 2.560
0.5000 0.5250 0.5500 0.6750 0.6000 0.6250 0.6500. 0.6750 0.7000 0.8000 0.9000 1.0000 1.2000 1.4000
2.425 2.407 2.392 2.378 2.368 2 . 358 2.350 2.343 2.337 2.328 2.315 2.303 2.294 2.288
2.421 2.402 2.386 2.375 2.363 2.354 2.346 2.339 2.332 2.324 2.310 2.301 2.290 2.285
n,
2.709 _ 2.640 2.564 2.544 2.525 2.514 2.505 I 2.488 2.477 2.463 2.453 2.449 2.443 2.433
2.6i:S9
2.522 2.511 2~502 2.486 2.473 2.459 2.448 2.:'1045 2:438 2.428
From T. M. Bieniewski and S. J. Czyzak, J. Opt. Soc. Am. 53,496 (1963). TABLE-6b"56:REFRACTIVE INDEX OF CmHC-ZINCSULFI'DE-
A,J.L.m 0.4400 0.4600 0.4800 0.5000. 0.5250 0 ..5,50.0 0.5750
---- -
I
n
2.488 2.458 2.435 2.414 2.395 2.384 -. 2.375
. .A,FIrl .. ___ ..n
0.6000 0.6500 0.7000 0.9000 1. 0500 _._1.2000 1.4000
2.359 2.346 2.334 ·2.306 2.293 2.282 ·2.280
I
s-J52
()PTICS
These values are for synthetic cubic zinc sulfide [from S.·J. Czyzak,W. M. Baker, R. C. Crane, and J. B. Howe, J: .opt. Soc. Am. 47, 240 (1957)]. Refractive-index values in the wavelength region 0.365 to 1.53 Mmfor natural cubic zinc sulfide are give by J. R. DeVore, J. Opt. Soc. Am. 41, 416 (1951). For computational purposes, Czyzak, Baker, Crane, and Howe and give a dispersion equation: 2-5·3. 1.275.XI07 n _ .. 1 1 ),,2_ 0.732 X 107
+
The hexagonal form of zinc sulfide is called wurtzite, and the cubic form is c~ned sphalerite. Natural~crystal zinc sulfide occurs in the cubic form only and is.called sphalerite or zincblende. Note ,that the birefringence of hexagonal zinc sulfide is very small but fairly constant. Cubic zinc sulfide evidences electro-optic properties. Group Ill-Group V Compounds Gallium· Antimonide TABLE6b-57. REFRACTIVE INDEX OF GALLIUM ANTIMONIDE
F.l.'om D. F. Ed-;,yards
)", Mm
nD
nR
1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5
3.820 3.802 3.789 3.780 3.764 3.758 3.755 3.749
3.61 3.59 3.57 3:55 3.54 3.53 3.52 3.49
4nd G,-S. Haynes, J. Opt. ,soc. A.m·, 69~:414 (1959).
These values are for p-typesingleccrystal gallium, antimonide which has a purity corresponding to 7.5 X 1016 carriers/em 3 measured at room temperature. The refractive index nD was calculated from the relation for the angle .ofminimum deviation, with an estimated error of 0.3 percent. The refractive index nR was deduced from reflectivity measurements, with an error of less than 2 percent. The discrepancy between the values of nDand nR is not explained. Gallium Arsenide TABLE 6b-58. REFRACTIVE INDEX OF GALLIUM ARSENIDE n
A, Mm
0.78 8.0 10.0 11.0 13.0 13.7
± ± ± ± ± ±
0.01 0.05 0.05 0.05 0.05 0.05
3.34 3.34 3.135 3.045 2.97 2.895
± ± ± ± ± ±
n
'A, Mm
0.04 0.04 0 ..04 0.04 0.04 0 ..04
14.5 15.0 17.0 19.0 21. 9
± ± ± ± ±
0.05 0.05 0.05 0.05 0.1
2.82 2.73 2.59 2.41 2.12
± ± ± ± ±
0.04 0.04 0.04 0.04 0.04
6-53
REFRACTIVE INDEX OF CRYSTALS AND GLASSES
The experimental data seem to be somewhat more scattered than the reported experimental errors indicate. The data are from L. O. Barcus, Phys. Rev. 111, 167 (1958), and L. O. Barcus, Lowell Institute of Technology, private communication. The index is approximately 3.34 from about 2 to 7 !-1m. Indium Antimonide TABLE 6b-59. REFRACTIVE INDEX OF INDIUM ANTIMONIDE A,!-Im
n
A, !-1m
n
7.87 8.00 9.01 10.06 11.01 12.06 12.98 13.90
4.00 3.99 3.96 3.95 3.93 3.92 3.91 3.90
15.13 15.79 16.96 17.85 18.85 19.98 21.15 22.20
3.88 3.87 3.86 3.85 3.84 3.82 3.81 3.80
From R.' G. Breckenridge, PhI/B. Rev. 96,571 (1954).
These values are for a sample of indium antimonide which has a purity corresponding to 2.0 X 10 16 carriers/em a; measured at room temperature. These data are in agreement with values reported by T. S. Moss, Proc. Phys. Soc. (London), ser. B, 70, 776 (1954). The temperature dependence of index of refraction for three different temperatures is given by R. F. Potter, Appl. Opt. 6, 35 (1966). Nonoxide Chalcogenic Glasses Arsenic-modified Selenium Glass TABLE 6b-60. REFRACTIVE INDEX OF ARSENIC-MODIFIED SELEN IUM GLASS AT 27°0 A,!-Im
n,
n,
n,
prism B
A,!-Im
n,
prism A
prism A
prism B
1. 0140 1.1286 1.3622 1.5295 1.7012 2.1526 3.00 3.4188 4.00 4.50 5.00 5.50 6.00 6.50
2.5774 2.5554 2.5285 2.5173 2.5089 2.4950 2.4861 2.4841 2.4825
2.5783 2.5565 2.5294 2.5183 2.5100 2.4973 2.4882 2.4858 2.4835 2.4822 2.4811 2.4804 2.4798 2.4792
7.00 7.50 8.10 8.50 9.10 9.50 10.00 10.50 11.00 11.50 12.00 13.00 13.50 14.00
2.4778
.. , . , .
2.4803
..... .
2.4789
..... .
......
2.4772
......
2.4765 .,
....
2.4756
......
2.4752 ., ••
.... ,
"0
.... - .
...... ......
From C. D. Salzberg and J. J. Villa, J. Opl. Soc. Am. 47,244 (1957).
2.4787 2.4784 2.4778 2.4775 2.4771 2.4768 2.4767 2.4759 2.4758 2.4753 2.4749 2.4760[sicj
2.4748 2.4743
6-54
OPTICS
Arsenic Trisul:fide Glass TABLE 6b-61. REFRACTIVE INDEX OF ARSENIC TRISULFIDE GLASS AT 25°C
A,l'm
n
A, I'm
n
A, I'm
n
0.560 0.580 0.600 0.620 0.640 0.660 0.680 0.700 0.720 0.740 0.760 0.780 0.800 0.820 0.840 0.860 0.880 0.900 0.920 0.940 :0.960 0.980 1.000 1.200 1.400 1.600
2.68689 2.65934 2.63646 2.61708 2.60043 2.58594 2.57323 2.56198 2.55195 2.54297 2.53488 2.52756 2.52090 2.51483 2.50928 2.50418 2.49949 2.49515 2.49114 2.48742 2.48396 2.48074 2.47773 2.45612 2.44357 2.43556
1.800 2.000 2.200 2.400 2.600 2.800 3.000 3.200 3.400 3.600 3.800 4.000 4.200 4.400 4.600 4.800 5.000 5.200 5.400 5.600 5.800 6.000 6.200 6.400 6.600 6.800
2.43009 2.42615 2.42318 2.42086 2.41898 2.41742 2.41608 2.41491 2.41386 2.41290 2.41200 2.41116 2.41035 2.40956 2.40878 2.40802 2.40725 2.40649 2.40571 2.40493 2.40414 2.40333 2.40250 2.40166 2.40079 2.39991
7.000 7.200 7.400 7.600 7.800 8.000 8.200 8.400 8.600 8.800 9.000 9.200 9.400 9.600 9.800 10.000 10.200. 10.400 10.600 10.800 11.000 11.200 11.400 11.600 11.800 12.000
2.39899 2.39806 2.39709 2.39610 2.39508 2.39403 2.39294 2.39183 2.39068 2.38949 2.38827 2.38700 2.38570 2.38436 2.38298 2.38155 2.38007 2.37855 2.37698 2.37536 2.37369 2.37196 2.37018 2.36833 2.36643 2.36446
i=5
Dispersion equation:
nl - 1 =
" 1..
AIKiA' _ A,B
i=1 TABLE 6b-62. CONSTANTS FOR THE DISPERSION EQUATION FOR 25°C
i
A,'
K,
1 2 3 4 5
0.0225 0.0625 0.1225 0.2025 750
1.8983678 1.9222979 0.8765134 0.1188704 0.9569903
From I. H. Malitson, W. S. Rodney, and T. A. King, J. Opt. Soc. Am: 48, 633 (1958).
REFRACTIVE INDEX OF
C~YSTALS
AND GLASSES
6-55
120
100
80
\ \
I
I
40
\ I
\ \
\
I
20
\
\
\NBS
o
,~
o FIG. 6b-7. The temperature coefficient of refractive index dn/dT for two types of arsenic trisulfide glass. [From I. H. Malitson, W. S. Rodney, and T. A. King, J. Opt. Soc. Am. 48, 633 (1958).]
It should be noted that arsenic and sulfur form an entire glass system, with varying properties. Therefore, one should expect different values of transmission, refractive index, and so forth, for samples from different batches.
6-56
OPTICS
Special Glasses Corning Vycor TABLE
6b-63.
REFRACTIVE INDEX VS. TEMPERATURE FOR
CORNING
X,!-,ID
0.26520 0.28936 0.29673 0.30215 0.3130 0.33415 0.36502 0.40466 0.43584 0.54607 0.5780 1. 01398 1.12866 1.254* 1.36728 1.470* 1.52952 1.660* 1.701 1. 981 * 2.262* 2.553*
No. 7913
(VYCOR), OPTICAL GRADE
n,28°C
n,526°C
dn/dT (1O- 6 ;oC)
n, 826°C
dn/dT (1O- 6 / o C)
1.49988 1.49074 1.48851 1.48694 1. 48416 1.47949 1. 47415 1.46925 1.46628 1.45960 1. 45831 1.44968 1.44831 1.44677 1.44554 1.44422 1.44356 1.44206 1.44137 1.43750 1.43298 1.42825
1.50799 1.49831 1.49587 1.49423 1.49121 1.48622 1.48065 1. 47547 1. 47234 1.46544 1.46407 1.45526 1.45373 1.45222 1.45095 1.44965 1.44896 1.44750 1.44677 1.44291 1.43839 1.43373
+16.3 +15.2 +14.8 +14.6 +14.2 +13.5 +13.1 +12.5 +12.2 +11.7 +11.6 +11.2 +10.9 +10.9 +10.9 +10.9 +10.8 +11.0 +10.8 +10.9 +10.9 +11.0
1. 51438 1. 50418 1.50164 1.49990 1.49679 1.49158 1.48570 1.48027 1. 47708 1.46992 1.46849 1.45924 1.45779 1.45627 1.45504 1.45370 1.45306 1.45157 1.45088 1. 44702 1.44258 1.43824
+18.2 +16.8 +16.5 +16.2 +15.8 +15.2 +14.5 +13.8 +13.5 +12.9 +12.8 +12.0 +11.9 +11.9 +11.9 +11.9 +11.9 +11.9 +11.9 +11.9 +12.0 +12.5
lie Wavelength determination by narrow-bandwidth interference filters. From J. H. Wray and J. T. Neu, J. Opt. Soc. Am. 69, 774 (1969).
REFRACTIVE INDEX OF CRYSTALS AND GLASSES TABLE
6b-64.
Wavelength Region, J.Lm
Material
Refractive index
Barium titanate .................... , Visible and infrared Cadmium fluoride ................... , 2 5.5 Cadmium iodide. . . . . . . . . . . . . . . . . . . .. Cadmium selenide. . . . . . . . . . . . . . . . . .. Cuprous chloride ..................... Lead bromide ...................... , Lead chloride ................... ' ..... Lead selenide ........................ Lead sulfide ..
00
..
00
...
00
....
00
00.
00'
Lead telluride ....................... Rubidium bromide. . . . . . . . . . . . . . . . . .. Rubidium chloride. . . . . . . . . . . . . . . . . .. Rubidium iodide .... T-12 ............................... Gallium phosphide................... 00..
..
..
..
..
..
...
Indium arsenide .... Indium phosphide .................... Arsenic triselenide glass .............. , 00
..
6-57
MISCELLANEOUS REFRACTIVE-INDEX DATA
0 0 ,. . . . . . . .
00'
Telluride glass (Ge-As-Te) ........... , Texas Instruments Glass No. 1173. . . ..
2.40 1.63 1. 53 11 1.45 O. 6 2.7 1-8 2 .45 >8 2.42 0.4-20.5 1.93 "White light" 2.53 "Yellow light" 2.2 1-3.5 3.5-4.6 5 4.6 3.0 4.10 ± 0.06 6.0 4.19 ± 0.06 dn/dT = 6 X 10-' per DC in the temperature range 20-300"C 1-3.5 4.1-5.3 3.9-20 5.10 1-8 1. 53 1-8 1.48 1-8 1.62 "Near infrared" 1.41 8 2.8 4-15 3-3.5 2-15 3-3.5 4 2.796 2-16 2.812-2.768 5 3.5 3.3 2.63 5 2.62 dn/dT = 79 X 10 'per"C III the region 3-13 J.Lm 0.589 at 25 DC 1.540
I
Cer-Vit material C-101 ................
I
Reference
1 1 1 2 3 3 4 5 6 7 8 7 9 9 7 10 11 11 11 12 13 13 13 14 14 15 15 16 16 17 17 18
References for Table 6b~64 1. Adapted from B. Welber: Appl.Opt. 6, 925 (1967). 2. Adapted from P. O. Nilsson: Appl. Opt. 7, 435 (1968). 3. Vitrikhovsky,N. r., L. F. Gudymenko, A. F. Maznichenko, V: N.Malinko, E.V. Pidlinsu, and S. F. Terekhova: Ukr. Fiz. Zh. 12,796 (1967). 4. Heilmeier, G. H.: Appl. Opt. 3, 1281 (1964). 5. Moss, T. S., and A. G. Peacock: Infrared Phys. 1, 104 (1961). 6. "Handbook of Chemistry and Physics," Chemical Rubber Publishing Co., Cleveland, Ohio, 1960. 7. Avery, D. G.: Proc. Phys. Soc. (London), ser. B, 66, 134 (1953). 8. Smakula, A.: Opt. Acta 9, 205 (1962). 9. Avery, D. G.: Proc. Phys. Soc. (London), ser. B, 67,2 (1954). 10. Smakula, A., J. Kalnajs, and M. J. Redman: Appl. Opt. 3, 323 (1964). 11. Mott, N. F., and R. W. Gurney: "Electronic Processes in Ionic Crystals," p. '12, Oxford University Press, New York, 1950. (From the values given for the dielectric constants.) 12. Ballard, S. S.: Japan. J. Appl. Phys. 4, supp!, 1, 23 (1965). 13. Willardson, R. K., and A. C. Beer: "Semiconductors and Semimetals," vol. 3, Academic Press, Inc., New York, 1967. 14. Oswald, F., and R. Schade: Z. Naturforsch. 9a., 611 (1954). 15. Savage, J. A., and S. Nielson: Infrared Ph'lls. Ii, 195 (1965). 16. Ballard, S. S., and J. S. Browder: Appl. Opt. Ii, 1873 (1966). 17. Hilton, A. R., andC.E.Jones: Appl. Opt. 6, 1513 (1967). 18. Monnier, R. C.: Appl. Opt. 6, 1437 (1967).
6c. Transmission and Absorption· of Special Crystals and Certain Glasses . STANLEY S. BALLAItD JAMES STEVE BROWDER - - JOHN F. EBERSOLE
University of Florida
The transmittances of the following materials are discussed in this section: Ammonium dihydrogen phosphate (ADP) and Potassium dihydrogen phosphate (KDP) Barium fluoride Barium titanate Cadmium selenide Cadmium sulfide Calcite Calcium fluoride Cesium bromide Cesil1m iodide Crystal quartz Cuprous chloride --Diam(md _._--. Fused silica Germanium Irtrans 1 to 6 Lanthanum fluoride Lead bromide Lead chloride . Lead fluoride Lead selenide Lead sulfide Lead telluride Lithium fluoride Magnesium fluoride Magnesium oxide Mica Potassium bromide Potassium chloride Potassium iodide Rubidium bromide Rubidium chloride Rubidium iodide
Ruby Sapphire Selenium Silicon Silver chloride Sodiumohloriae, - Sodium fluoride . Spinel· Strontium titanate Sulfur T-12 Tellurium Thallium hrmuide Thallium chloride Thallium bromide-chloride (KRS~6) Thallium bromide-iodide (}\:RS-5) Titanium dioxide Group III-Group V compounds:' Gallium antimonide Gallium arsenide Gallium phosphide Indium antimonide Indium arsenide Indium phosphide Nonoxide chalcogenic glasses: Arsenic-modified selenium glass Arsenic triselenide glass Arsenic trisulfide glass A tellurid-e glass ~ Texas Instruments Glass No. 1173 Special glasses: Cer-Vit Corning glasses
6-58
TRANSMISSION AND ABSORPTION OF CRYSTALS AND GLASSES
6---,59
The. materials listed above can be used inthe infraEed, visible, and/or ultraviolet regions of the spectrum for-prisms,lenses,- windows, :and other components..of optical systems. "Standard" glasses,of which there are many kinds, are not discussed here, but certain unusual glasses are included, When transmission data are given, external or internal transmittance is specified. The external transmittance is the fraction of the incident intensiWthatistransmitted; it is determined by both the absorbing and the reflecting propertieE of the material. Internal transmittance is descriptive of the result of absorption processes only (if scattering can be neglected). .. Transmittance data, usually in the form of curves, over the ultraviolet, ,iisible, and/or infrared regions of the spectrum are included when available for each material. The transmission curves are often given with just the long- and short-wavelength extremes shown. Unless the accompanying text indicates otherwiseiinterpolation between the short- and long-wavelength curves can be made by a straight line with reasonable accuracy. Since the transmission of a material. depends upon its temperature, instances in which the temperature dependence for a material is known to be appreciable are pointed out. Notes are included to give information of possible interest and practicarvalue on most of the materials. Unless stated otherwise, wavelengths are given in micrometers· (I-'m) , and temperatures are in kelvins (K), employing the new Systeme International units. Many sets of data were recorded using degrees Celsius (OC), and no attempt has been made to convert these to kelvins. An overall concept of the spectral regions of transparency of the materials is given in Fig. 6c-1. This figure indicates the wavelength range over which a sample 2 mm thick has an external transmittance of 10 percent or more. When light is incident on a sample, part of it is reflected, part is absorbed, and part is transmitted through the sample. The absorption of a material is expressed by the Lambert-Beer-Bouguer law, which can be written as
where I is the intensity of light at a distance x in the material, II is the intensity just inside the front surface,and a is the absorption coefficient.
6-60
OPTICS
05
01
.
10 1.7
.1
KDP
50
10
50
..
100p.m
1.
0.4 BOROSILICATE GLASS
3.51
~ GALLIUM ANTIMONIDE
RY TAL
Ie 12
UARTZ
US
4.5 4.
I 'CA
•
10.6. GA.L UM PHOS L 0.2
L 5.5
CALCITE
< .6
SPINEL
6.0
RUTILE
0.43 0.14
6.2 6.5
SAPPHIRE 0.39
6.8
STRONTIUM TITANATE
_~ INDIUM ARSENIDE 13.
7.0 LEAD SULFIDE (FILM)"
" ;.: "f",,", ",
5.~~ LElD SELENIDE (FILM)'
0.5
BARIUM TITANATE
MAGNESI M FLUORIDE
0.11
3.5 0.~5
MA
B.O TELLURIUM
8.5
SlUM XIDE IRTRAN-l
1.0
8.5 9.0
LITHIUM FLUORIDE
0.12
CALCIUM FLUORIDE
0.13
0.6
12
ARSENIC TRISULFIDE GLASS 1.0 1.0
14
IRTRAN-2
14.5
GALLIUM ARSENIDE
1.2 0.25
13
INDIUM PHOSPHIDE
1.0
15 15~
SILICON
BARIUM FLUORIDE
15
SODIUM FLUORIDE
40
THALLIUM BROMIDE
0.25
POTASSIUM IODIDE
0.3
45 55
CESIUM BROMIDE
0.25
CESIUM IODIDE
0.25
DIAMOND
0.5
1.0
23
30
KRS-6 0.42
20
28
POTASSIUM CHLORIDE
0.21
18.>
26~
SODIUM CHLORIDE 0.4
0.1
16
ARSENIC MODIFIED SELENIUM GLASS 1.8
0.21
16
CADMIUM TELLURIDE
1.0
16> INDIUM ANTIMONIDE" 16
LEAD FLUORIDE 0.9
"'~.
75
5.0
80 80..>
10
50
100filil
FIG. 6c-1. Transmission regions. The limiting wavelengths, for both long and short cutuff, have been chosen as those wavelengths at which a sample 2 mm thick has 10 percent transmittance. Materials marked with an asterisk (*) have a maximum external tran!!mittance less than 10 percent.
TRANSMISSION AND ABSORPTION OF CRYSTALS AND GLASSES
6-61
For comparison purposes the short- and long-wavelength absorption edges of several materials are included in Figs. 6c-2 to 6c-4. (The literature search extended back to January, 1959. It was restricted primarily to "optical" journals, i.e., Journal of the Optical Society of A merica, Applied Optics, Optics & Spectroscopy, Optica Acta, and Infrared Physics. It is realized that optical data on semiconductor materials are to be found also through the literature of solidstate physics.)
1:
.... CsI
u
...:
f5 2.0
KI
u u:: ..... w
TICI AgCI
TIBr
AgBr TI(Br,1l
esSr
8 z
~ 1.0 "-
KBr
Nacl~
""
o
'" «
LiF'-.]
aJ
o
\ \\
Na~-t:---KCI
0.2
0.3
0.4 WAVELENGTH, p-m
\
\
0.5
0.6
FIG. 5c-2. The short-wavelength 8.bsorption edges of several alkali, silver, and thallium halides. [From A. Smakula, Opt. Acta 9, 205 (1962).]
UF
NoF I
KBr
..
E'
U
MgO-AI 203
~
z
~
u
10
u:: .....
,,:
w 0
u
z
0
0
(f)
aJ
«
KI
I I I I I
J
I
i= c..
""
5;,0\ I
5
J I I
,J
FIG. 50-3. The long-wavelength absorption edges of several ionic crystals. Sma kula , Opt. Acta 9, 205 (1952).]
[From.£.
6-62
OPTICS
100
.,e
...
...... z
·AISb
75
AISb
w
U
u: tb 50 0 u
GaAs .
:z 0
ii: g
25
Ge
(J)
III
SrO·OO. BaO·C02 CaO·C02 6(Ca, Mn)0·2Al203·B203·8Si02·H20 8Al.03·B203·6Si02·H20 A120 3-8i0 2 4CaO·3 (AI, Fe) 203·6Si02·H 2O 3CuO·CuCI2·3H 2 O 2FeO·Si02 2(Pb, Cu)O·S03·H2O 2CuO·C02·H2O 2PbO·S0 3 4PbO·S0 3·2C02·H2O PbO·C0 2 PbCI2·PbO·H2O PbO·PbCI2 Zr02 Fe203·H2O 2Fe203·3H 20 in part Fe 203·H2O Sb20 3 2Fe 2 U3·H 20 in part AsS Hg200I (TI, Ag)2S·PbS·2As 2S3 Sb 2S3
1.520 1.529 1.531 1.678 1.678 1.712 1.729 1. 831 1.824 1.818 1.655 1.930 1.870 1.804 2.077 2.040 2.130 1.930 2.170 2.210 2.180 2.450 2.460 2.350 3.078 3.194
1.667 1.667 1.676 1.677 1.682 1.686 1.685 1.688 1.686 1.689 1.720 1.728 1.763 1.780 1.861 1.880 1.864 1.874 1.866 1.909 1.875 1.909 1.990 2.020 2.000 2.010 2.076 2.078 2.116 2.158 2.150 2.150 2.190 2.200 2.210 2.510 2.290 2.310 2.350 2.350 (Li) 2.350 2.350 2.550 2.550 (Li) 2.590 2.610 (Li) 2.640 2.660 (Li) 3.176 3.188 4.303 4.460
Smithsonian Physical Tables," 1954, Table 548. The values are arranged in the order of increasing f3 index of refraction and are for the sodium D line except where noted. Selected by Edgar T. Wherry from private compilation of Esper S. Larsen, of the U.S. Geological Survey.
6g. Optical Properties of Metals GEORG HASS
U.S. Army Electronics Command, Night Vision Laboratory LAWRENCE HADLEY
Colorado State University
The optical properties of metals are usually characterized by two parameters, the index of refraction n and the extinction coefficient k. The refractive index is defined as the ratio of the phase velocity of light in vacuum to the phase velocity of light ill the material. The extinction coefficient is related to the exponential decay of the wave as it passes through the medium. Both of these parameters are contained in the equation for the propagation of a wave in an absorbing medium:
where Eo is the amplitude of the wave measured at the point x = 0 in the medium, E is the instantaneous value of the electric vector measured at a distance x from the first point and at some time t, p is the frequency of the source, and Ao is the wavelength in vacuum. The two parameters nand k (called the optical "constants," even though they vary strongly with frequency) can be combined to give a complex index of refraction N = n - ik. It should be noted that in much of the older literature the complex index of refraction is written as N = n(l - iK). Consequently, the k used here will equal thc no: which is fVUllo. tabulated in many places elsewhere. This K is called the absorption index. In much of the current literature the real and imaginary parts of the complex dielectric. constant are given instead of the index of refraction and the extinction coefficient. They are related through the following equations
•=
e1 -
if2
=
N2
=
n2
-
k2
-
2ink
A second point on which some confusion has arisen in the literature is that of the absorption coefficient a, which appears in the familiar equation I = loe- ax • The absorption coefficient a is related to the extinction coefficient by a = 47rk/Ao. The use of the above absorption equation implies, however, that the intensities I and 10 are to be measured within the absorbing medium and that the total thickness of the medium is sufficiently great that there are no interference effects arising from multiple reflection. When light is reflected from a metal surface, it experiences a phase shift which is g function of the gngle of incidence and the state of polarization of the incident light. If rp and T, represent respectively the amplitude ratios of the reflected electric vector to the incident electric vector for light polarized parallel and perpendicular to the plane of incidence, then
OPTICAL PROPERTIES OF METALS
6-119
It may be shown that the phase angle L'l and the azimuth angle if; are related to the refractive index and the extinction coefficient for a particular angle of incidence (PI by the following equations
r, = -ir,pie-i.{3p- = ---"' r"
• 2 n' - k' -_ n, , am ,
nk
=
Jr"ie,{3,
eit;
tan if;
{1 + tan' ,(cos' 2if; - sin' 2if; sin' L'l} (1 + sin 2if; cos L'l)'
n,' sin' , tan' , sin 2if; cos 2f sin L'l (1 sin 2f cos L'l)'
+
where n, is the refractive index of the incident medium. Since these angles are relatively easily measured quantities, these equations form the basis of several of the methods used to determine the optical constants of metals. Reference 1 also lists a number of other methods for these determinations. Since reflection methods are used in determining the constants, they aTe strongly dependent on the characteristics of the metallic surface. These characteristics vary considerably with the chemical and mechanical treatment. Accordingly, there has always been a certain degree of controversy on the subiect of the optical constants of metals. Since the oldest measurements were made, there has been considerable development in the preparation of metallic surfaces by evaporation in a vacuum. The properties of such surfaces are frequently quite different from those of surfaces of bulk metals prepared by polishing. By no means all the metallic constants have been determined on such freshly prepared surfaces. It is also well known that the presence of an extremely thin surface film on a metal will significantly alter the values of the phase and azimuth angles, making ellipsometric measurements subject to some difficulties. The appropriate corrections to be IDllde in the presence of such surface films are given in ref. 2. The relationships existing among nand le and the reflectance, transmittance, and phase shift are given here for several cases of interest. Since the properties of an absorbing dielectric material can also be expressed by a complex index N = n - ik, the following equations have general application. CASE I. Reflection at the boundary between two homogeneous, isotropic massive media, the one a dielectric of refractive index no, which is assumed to be the medium of incidence, and the other an opaque absorbing medium whose complex refractive index will be denoted by N, = n, - ik , :
Incident light --'>
a. Intensity r-eflectance (normal incidence):
R b. Phase change on
r'ej~ection
p
=
(no - n,)' (no n,)'
+
+ k,' + le,'
(6g-l)
(normal incidence): = tan- 1
no' - n,' - k ,'
(6g-2)
6-120
OPTICS
CASE II. Reflection, transmission, and a.bsorption of light by a thin absorbing film Nl of true thickness hI surrounded by homogeneous, isotropic, massive media, the incident medium being a dielectric of refractive index no and the emergent medium being an absorbing medium whose complex refractive index is given by N 2 = n2 - ik 2 :
Nl
no Incident light ~
a. Intens1'ty reflectance (normal incidence):
R = aleu b1e u
+ a2e- + as cos + a. sin + b,e + bs cos + b. sin U
U
p
JJ
p
JJ
(6g-3)
where: al a, as a.
= = = =
nl)' + k1'][(nl + n,)2 + (k 1 + k,)'] + nl)' + k1'][(nl - n,)' + (k 1 - k,)'] - (nl' + k 1')][ (nl' + k 1') - (n,' + k,')] + 4nokl (nlk, - n,k1) } - (nl' + k1')](n1k, - n,k1) - nOk1[(nl' + k 1') - (n,' + k,')])
[(no [(no 2 {[no' 4{[no'
47rk 1h 1
AO = vacuum wavelength
u = -AO
4~lhl ,,=-AO b1 = [(no + nl)' + k1'][(nl + n,)2 + (k 1 + k,)'] b, = [(no - nl)' + k1'][(nl - n.)' + (k 1 - k.)'] bs = 2{[no' - (11. + k1')][(nl' + k 1') - (n.' + k,')] - 4nok 1(n 1k. - n,k1)} b. = 4{[no' - (nl' + k 1')] (n1k. - n,k1) + nOk1[(nl' + k 1') - (n,' + k,')]} 12
b. Phase change on reflection (normal incidence): (6g-4) where
+
+
+
= 2nokl[(nl n.)' (k 1 k.)'] c. = -2nokl[(nl - n.)' (k 1 - k.)'] Cs = 8nOnl[ntk. - n,k J] c. = -4nOnJ[(n,' k , ') - (n,' k.')] dl = [no' - (nl' kl')][(nl n.)' (k 1 k.)'] d. = [no' - (nJ' k,')][(n, - n.)' (k , - k.)'] d s = 2[no' (n,' k,')][(n,' k,') - (n.' k.')] d. = 4[no' (nJ' k,')](n,k, - n.k,) Cl
+ +
The symbols a and
p
+ + + + +
+
+ + + + +
+
+
have the same definitions as in Eq. (6g-3).
c. Intensity transmittance (normal incidence): This denotes the percentage of inci-
dent intensity which is transmitted into the final medium.
T = b,eu
16non,(n,' + k,') + b.e + bs cos + b. sin" U
where b" b., ba, b 4, u, and" are defined as in Eq. (6g-3). T = (1 - R)'I!
(6g-5)
p
Alternatively, one can write (6g-6)
OPTICAL PROPERTIES OF ME'.t.\ LS
where
+ g,e + g, cos v + g. sin v , ~4~- = n,[(n1 + n,) + (k, + k,)'] no g,e U
g,
=
6-121
U
b, - a,
d. Intensity absorptance (normal incidence): A = (1 - R - T) = (1 - R) (1 - 'If)
(6g-7)
This is the percentage of incident intensity which is absorbed by the film. In the simpler case where the emergent medium is a nonabsorbing material of refractive index n" the formulas for R, T, and 'If can be obtained from Eqs. (6g-3) and (6g-6) by setting k, = O. CASE III. The effect of a nonabsorbing surface film of refractive index n, and thickness h, on the reflectance of an opaque metal of complex index N, = n, - ik" where no is the index (real) of the incident medium: no
-
Incident light
LU ....J
"'-
LU
40
0::
30 20 10 0
15
10
20
30
40
50
60 70 80 90100
WAVELENGTH, ILm 6h-1. Reflection of MgO and of some alkali halide crystals relative to an aluminum mirror. [M gO data from Burstein, Oberly, and Plyler, Proc. Indian Acad. Sci. 28, 388 (1948). Other data from Hohls, 1937.]
FIG.
100 90
M'~
80 70 ~
60
z0
;::: L> W ....J
u... w
50
-/'i'
J
~'.,
/
I
,...-
... , ~ ~ ,,",', /.
,/
, //
,,
\
N
40
0::
- - HARDY AND SILVERMAN. ANGLE OF INCIDENCE 30· - - - - COBLENTZ, ANGLE OF INCIDENCE 25°
30
20 10
o
8.0
8.2
8.4
8.8 9.0 WAVELENGTH, jlm
8.6
FIG. 6h-2. The reflection of crystalline quartz. 176 (1931).]
9.2
9.4
9.6
[From Hardy and Silverman, Phys. Rev. 37,
6-168
OPTICS
100 90 - - HARDY. AND SILVERMAN, ANGLE OF INCIDENCE 30· - - - - COBLENTZ, ANGLE OF INCIDENCE 25· 80
70
.
~ 60
Z
0
t "-'
50
~
~
"-' II:
/ ~ V
MlA ''11' r
M
" ,
..
40
/\1\
30
~V
v
~
---20
----'
.... ~""-',\
,
I
,.-
I
"\
\
\ ~\ \
........ -
10
0
B.2
8.0
B.6 B.B 8.4 WAVELENGTH, 11m
FIG. 6h-3. The reflection of fused quartz. (1931) .J 100
80 70 "e Q
Z o
II
,,1\" ,, I \I
\,
i= 50 ~ -'
~40
20
,J.
\
60
30
I
\
---- EXTRAORDINARY RAY - - ORDINARY RAY
~
2
3
R
4
5
I I I
, I
I I
I I
1\ - v+J
'~-
---- '----6
..........
I I
-............
/L
I
r-"J
7 10 8 9 WAVELENGTH, Itm
FIG. 6h-4. The reflection of calcite (CaCO,).
9.4
[From Hardy and Silverman, Phys. Rev. 37, 176
n
90
9.2
9.0
11
12
13
14
15
16
[From Nyswander, Phys. Rev. 28, 291 (1909).}
6-169
REFLECTION 100
100
KBr
12°
~
52°
>'" f--
:>
u>=50 w
--' "w
a:
o
0
30
,
40
50 60 70 80 90 100 30 40 50 60 70 80 90 100 WAVELENGTH, 11m WAVELENGTH, Itm REFLECTIVITY OF PLANE POLARIZED L1GHl" BY KBr CRYSTAL AT INCIDENT ANGLES OF 12' AND 52"
100 KC!
100 52°
Ir-\
,,
:>
.........f3 50
l
"w
60
70 80 90 100
\
" I 1\
:\
I
a:
30
\\
,
f--
O'---L--=~--'-"-"--L.'_,-'-1'--"
., ... ,: \ I
.,.::
: lip
\
: 0 30
;Il"
40
\
"--__
50
60
e_
70 80 90 100
WAVELENGTH,l1m WAVELENGTH, 11m REFLECTIVITY OF PLANE POLARIZED LIGHT BY KCl CRYSTAL AT INCIDENT ANGLES OF ]2° AND 52°
100
100 NaCl
12°
o~
>'" !:::
>
.........t; 50 ........
.~
0::
S·COMP
"''''''~ ...
P-COMP o30
50
60
70 80 90 100
i ! O~-'-~~~~~-=~=-~ 30 40 50 60 70 80 90 100
WAVELENGTH, ~m WAVELENGTH, 11m REFLECTIVITY OF PLANE POLARIZED LIGHT BY Nael CRYSTAL AT INCIDENT ANGLES OF 12· AND 52" FIG. 6h-5. The reflectivity of variou3 crystals for different states of polarization. A.. Mitsuishi, J. Opt. Soc. A.m. 50,433 (1960).]
[Fro",
6i. Glass, Polarizing, and Interference Filters P. BAUMEISTER
University of Rochester J. EVANS
Air Force Cambridge Research Laboratories Sacramento Peak Observatory
This chapter briefly surveys methods of spectral filtering, by which we mean the technique of isolating a portion of the electromagnetic spectrum with filters which function in either reflection or transmission. Several survey articles [1,2] discuss these filters in detail. The important classes of filters which are discussed here are absorption filters, polarizers, mesh filters, interference devices, and polarization interference filters. 6i-1. Absorption Filters. There are many types of these filters, such as: (1) Glassdoped with impurities such as metal ions [3]. The commonly available filters [4,5] are useful in the spectral region from 0.25 to 2.5 }Lm. (2) Crystals, such as alkali halides or semiconductors. Spectral transmittance data are tabulated by several authors [6,7] and also by manufactures [8]. (3) Gelatin sheets impregnated with organic dyes [9] are inexpensive filters for the region 0.3 to 1.5 }Lm. (4) Gas cells and liquid solutions are often excellent filtering devices [1,10,11]. Infrared filters consisting of alkali halide powders dispersed in a matrix of polyethene [12,13] exhibit passbands in the spectral region from 20 to 200 }Lm. (6) Thin films of metals such as aluminum and indium [14] are used as bandpass filters in the spectral region below 0.1 }Lm, and the alkali metals [15] are effective at longer wavelengths. Absorption filters have several advantages: (1) They are relatively inexpensive, compared to the usual interference type of filter. (2) The spectral transmittance changes eomparatively little as the incidence angle of the flux changes. 6i-2. Sheet Polarizers. Sheet polarizers have several advantages over the nicol prism and other early types of linear polarizers. They accept a wide cone of light (half angle of 30 to 45 deg, for example). They are thin, light, and rugged and are easily cut to any desired shape. Pieces many feet in length can be made. The cost is almost negligible compared with that of a nicol prism. If a sheet polarizer is mounted perpendicular to a beam of 100 percent linearly polarized radiation, and if the polarizer is slowly turned in its own plane, the transmittance k varies between a maximum value kl and a minimum value k2 according to the following law: (6i-1) When such a polarizer is placed in a beam of unpolarized radiation, the transmittance is t(k 1 + k2). When two identical polarizers are mounted in the bean with their axes crossed, the transmittance is k 1 k 2 • The principal transmittance values k, and k2 vary with wavelength, the variation being different for different types of polarizers. Table 6i-l presents data for several
6-170
6-171
GLASS, POLARIZING, AND INTERFERENCE FILTERS TABLE
Wavelength, p.m
6i-1.
SPECTRAL PRINCIPAL TRANSMITTANCE OF SHEET POLARIZERS*
HN-22 sheet
HN-32 sheet
k,
k,
k2
k2
HN-38 sheet
KN-36 sheet k,
k2
kl
HR sheet k,
k2
0.375 0.40 0.45 0.50 0.55 0.60 0.65 0.7
I
k2
I
--'--
--
I
.21 .45 .55
.000,005 .000,01 .000,003 .000,002
.33 .47 .68 .75
.001 .003 .000,5 .000,05
.54 .67 .81 .86
.02 .04 .02 .005
.42 .51 .65 .71
.002 .001 .000,3 .000,05
.48 .43 .47 .59
.000,002 .000,002 .000,002 .000,003
.70 .67 .70 .77
.000,02 .000,02 .000,02 .000,03
.82 .79 .82 .86
.000,7 .000,3 .000,3 .000,7
.74 .79 .83 .88
.000,04 .00 .00 .000,03 .01 .00 .00 .000,08 I .05 ,10 I .00 .02
.11
.00 .00 .00 .00
I
I
.00 .00 .00 .00
I
.55 .65 .70
1.0 1.5 2.0 2.5
.10
I
.05 .00 .00 .02
* Data supplied by R. C. Jones, Polaroid Corporation, Cambridge, Mass.
For each type of polarizer, the transmittance values near the ends of the useful range depend on the type of supporting sheet or lamination used. Also Borne variation from lot to lot must be expected.
well-known types, produced by Polaroid Corporation, Cambridge, Mass. H sheet, perhaps the most widely used sheet polarizer, is effective throughout the visual range; it is produced in three modifications having total luminous transmittance (for C.LE. Illuminant C light) of 22 percent (Type HN-22), 32 percent (Type HN-32), and 38 percent (HN-38). Type HN-22 provides the best extinction, Type HN-38 provides the highest transmittance, and Type HN-32 represents a compromise that is preferred in many applications. K sheet, also useful throughout the visual range, is particularly intended for applications involving very high temperature. Its transmittance is 35 to 40 percent. HR sheet is effective in the infrared range from 0.7 to 2.2 .urn. Table 6i-2 presents data for a Polaroid Corporation ultraviolet light-polarizing filter HNP'B. The characteristics for wavelengths longer than 0.400 .urn are the same as for HN-32 in Table 6i-1. In Fig. 6i-l are curves showing a range of k values which can be achieved with this class of ultraviolet polarizer. Absorbing polarizers are also made by Polacoat, Inc., Blue Ash, Ohio. TABLE
6i-2.
SPECTRAL PRINCIPAL TRANSMITTANCE OF
ULTRAVIOLET SHEET POLARIZER
HNP'B (3.5)
A
kr
k2
A
k,
k2
(275)* 280 290 300 310 320 330
(0.250) 0.328 0.340 0.372 0.448 0.546 0.611
(0.0126) 0.0110 0.0040 0.0017 0.0009 0.0006 0.0003
340 350 360 370 380 390 400
0.602 0.568 0.550 0.568 0.604 0.644 0.688
0.0002 0.0001 0.0003 0.0007 0.0009 0.0008 0.0005
* This is the effective cutoff wavelength of the supporting plastic layer. The HNP'B foil itself transmits to about 250 nrn. In this region the foil has much lower dichroism.
6-172
OPTICS
6i-S. Mesh Filters and Interference Devices. Metal mesh filters consist of an array of thin metal strips, rectangles, disks, apertures, etc., which are either unsupported or deposited on a thin plastic sheet. They have an effect similar to an iris in a microwave guide, with the exception that the mesh array functions in free space. They have been used principally in the spectral region from 100 J"m to one millimeter
w --' od:
lur G M'e a2l = a22
b2
+
a22b 2 a23 = 'b 2 _ 1
m2
~
where a22 is the normalization constant. Finally, in terms of the slope rna and y-axis intercept ba of the line through the Rand G primaries the coefficients in the formula for Bare ba - 1 ba + rna a31 = a33 --b-aa2 = aaa -b-aa where aaa is the normalization constant.
a"
=
aaa(l - Ba- I )
In terms of the two axis intercepts, a32
=
aaa(l - ba-I)
The reverse transformations are X = A , [(b 2 - ba)R + (b a - b,)G + (b , - b2)B] Y = A2[(rnab2 - rn 2 ba)R + (m,b a - rnab,)G + (m l b2
Z
=
A, [ (m, - m2)R
+ (rn,
- rna)G
+ (m2
-
rn2b,)B]
- m,)W - ; , -
IJ
where A" A 2 , Aa are constants that depend on the normalizations of R, G, B. They can be determined by calculating R, G, B and the corresponding values of the expressions in the brackets for some one color, e.g., the illuminant, and dividing those results into the original values of X, Y, Z. Note that the last two terms in the brackets in Z are simply the quantities that appear in brackets in the formulas for X and Y.
6k. Radiometry J. KASPAR
The A.erospace Corporation
6k-1. Blackbody Radiation. These tables contain vaTlOUS radiation functions derived from the Planck function c,
W(A, T)
where W(A,T) is defined as the power radiated per unit wavelength interval at wavelength A by unit area of a blackbody at temperature T K. C2 was taken to be 1.438 cm K. The constant c, does not enter into the functions here tabulated. The maximum value of W (A, T) is given by
W max(T)
=
1.290 X 1O-15T5
w/ (cm2 . ,urn)
while the Stefan-Boltzmann function is given by \T,l/CTil 2
Sk-2. Optical Pyrometry (Narrow-band Radiation). When an optical pyrometer which has been calibrated to read the true temperature of a blackbody source is sighted on a nonblack source, it reads values of "brightness temperature" Tb,(A,T) lower than the true temperature T K. Brightness temperature is related to true temperature through the following formula, which is derived from Planck's formula:
where
C2
=
1.4350 cm . K (international temperature scale of 1948)
.(lI,T) = emittance of the source at wavelength A and temperature T
Commercial radiation pyrometers, although broad-band, do not utilize the complete spectrum of radiant energy. Hence there is no simple formula for precise calculation of the effect on temperature readings of varying emittance of the source. Table 6k-IO was calculated using the relation T(K) = Tappar:nt(K) ft·
where Et is the total emittance. in radiation pyrometry.
It may be \Ised to estimate approximate corrections 6-198
6-199
RADIOMETRY TABLE
XT,
em·deg
0.050 0.051 0.052 0.053 0.054 0.055 0.056 0.057 0.058 0.059 0.060 0.061 0.062 0.063 0.064 0.065 0.066 0.067 0.068 0.069 0.070 0.071 0.072 0.073 0.074 0.075 0.076 0.077 0.078 0.079 0.080 0.081 0.082 0.083 0.084 0.085 0.086 0.087 0.088 0.089 0.090 0.091 0.092 0.093 0.094 0.095 0.096 0.097 0.098 0.099 0.100 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.140 0.145 0.150
6k-1.
W(X, T) Wmax(T)
2.999 4.775 7.452 1.142 1.718 2.545 3.709 5.326 7.544 1.054 1.455 1.985 2.676 3.570 4.713 6.613 7.984 1.025 1. 305 1.649 2.066 2.571 3.176 3.897 4.751 5.757 6.934 8.304 9.891 1.172 1.382 1.621 1.893 2.201 2.548 2.938 3.373 3.859 4.397 4.993 5.651 6.373 7.165 8.030 8.973 9.998 1.111 1.231 1.360 1.500 1.649 2.563 3.785 5.350 7.281 9.588 1.227 1.530 1.866 2.232 2.622
X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X
10- 7 10- 7 10- 7 10- 6 10- 6 10- 0 10- 6 10- 6 10- 6 10- 5 10- 6 10- 6 10- 6 10-' 10- 6 10- 6 10- 6 10-' 10-' 10-' 10-' 10-' 10-' 10-' 10-' 10- 4 10-' 10- 4 10- 4 10- 3 10- 3 10- 8 10- 3 10-' 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10- 3 10-' 10- 2 10- 2 10- 2 10- 2 10- 2 10- 2 10- 2 10-' 10-' 10- 1 10- 1 10- 1 10- 1 10- 1
BLACKBODY RADIATION FUNCTIONS*
faA fo~
W dX
IoAw
W(X, T) Wmax(T)
fo~·
W dX
1.316 X 10- 9 2.184 X 10- 9 3.552 X 10- 9 5.665 X 10- 9 8.871 X 10- 9 1.366 X 10- 8 2.068 X 10- 8 3.084 X 10- 8 4.532 X 10- 8 6.568 X 10- 8 9.395 X 10- 8 1.327 X 10- 7 1.853 )< 10- 7 2.558 X 10- 7 3.493 X 10- 7 4.721 X 10- 7 6.319 X 10- 7 8.380 X 10- 7 1.101 X 10- 6 1.435 X 10- 6 1.856 X 10- 6 2.380 X 10- 6 3.030 X 10- 6 3.831 X 10- 6 4.810.X 10- 6 5.999 X 10- 6 7.436 X 10- 6 9.162 X 10- 6 1.122 X 10- 6 1.367 X 10- 6 1. 657 X 10- 6 1.997 X 10- 6 2.395 X 10- 6 2.859 X 10- 6 3.398 X 10- 5 4.020 X 10- 6 4.735 X 10- 6 5.555 X 10- 6 6.491 X 10- 6 7.556 X 10- 5 8.763 X 10-' 1.013 X 10-' 1.166 X 10-' 1.339 X 10-' 1.532 X 10-' 1.747 X 10-' 1. 986 X 10- 4 2.252' X 10- 4 2.546 X 10-' 2.870 X 10-' 3.228 X 10-' 5.591 X 10-' 9.162XlO-' 1.431 X 10- 3 2.145 X 10- 3 3.099 X 10- 3 4.336 X 10- 3 5.897 X 10- 3 7.822 X 10- 3 1.015 X 10-' 1.290 X 10- 2
* Table by Reynolds et aI., ref. 4.
XT,
em·deg
~
0.155 0.160 0.165 0.170 0.175 0.180 0.185 0.190 0.195 0.200 0.22 0.24 0.26 0.28 0.30 0.32 0.34 0.36 0.38 0.40 0.42 0.44 0.46 0.48 0.50 0.52 0.54 0.56 0.58 0.60 0.62 0.64 0.66 0.68 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0
3.032 3.457 3.892 4.332 4.772 5.208 5.636 6.053 6.455 6.840 8.169 9.126 9.712 9.972 9.971 9.771 9.432 8.999 8.512 7.997 7.475 6.961 6.464 5.990 5.543 5.125 4.735 4.375 4.042 3.735 3.453 3.193 2.956 2 . 73'/ 2.537 2.354 2.185 2.030 1.888 1.758 1.638 1.528 1.426 1.332 1.246 1.166 1. 093 1.024 9.613 9.029 6.679 5.035 3.862 3.007 2.375 1.899 1.536 1.255 1.035 8.612
X X X X X X X X X X X
)
- 0.6 ~ 0.5 ~ 0.4
I
:
t
A-EMISSIVITY OFGLOBAR B-REFLECTIVITY OF SINGLE CRYSTAL OF SiC
~ 0.3 0.2 _-----__ ~_----,______
0.1
: :
I
\
,,
"
100 90 80 70 ~ 60 ::50 ~ 40
t
;
30 ~
; "\/
20 ~ 10
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
WAVELENGTH, JLm FIG. 6k-2. Emissivity of globar.
Sk-4. Stellar Radiation. Brightness of stars as seen by any photoreceiver may be expressed as a stellar magnitude, related to the effective irradiance I in watts/cm' received from the star: Stellar magnitude m
I -2.510g 10 To
The effectiveirradiance I from the star as seen by a photoreceiver is I =
where JA
!o '"
J(A)fI(A) dA
spectral distribution of radiation received from the star, in watts/cm' per wavelength increment dA. J(A) for stars approximates blackbody distribution lur Lhe a~bumed surface temperatures. fI(A) = photoreceiver's spectral-response function normalized at the response peak. For visual magnitude =
10 = 6§5 X
10-(·4.18/ •. 5) =
3.1 X 10- la W/cm'
(Of. definition of lumen, page 6-5; definition of stellar magnitude, "Smithsonian Tables," 8th ed., Table 798.) Star brightness as seen by photoreceivers other than the eye is also expressed as a stellar magnitude (e.g., bolometric magnitude, photographic magnitude). The magnitude scales are generally adjusted by setting 10 so that a class AO star (surface temperature 11,000 K) appears of the same magnitude to each photoreceiver. For stars at other temperatures the effective-irradiance integral can be evaluated to obtain an index, which when added to visual magnitude gives the star's magnitude as seen by other receivers. Early stellar photometry used the non-color-sensitized (blue-sensitive) photographic plate; the difference between photographic and visual magnitude was called color index. Difference between bolometric and visual magnitude was called heat index. Indices for the principal spectral classes of stars and for several photoreceivers are given in Table 6k-15.
6-214 TABLE
OPTICS
6k-15.
COLOR INDICES OF VARIOUS STELLAR SPECTRAL CLASSES
Index Spectral class
Appro:.; eff. surf ace temp., K
BO ........... AO ........... FO ........... gGO .......... gKO .......... gMO ..........
20,000 11,000 7,500 5,000 4,200 3,400
.. Photographic, visual
Bolometric, visual
S4 photosurface, visual
PbS, visual
-0.30 0 +0.33 +0.70 +1.12 +1.70
-1.4 0 +0.6 +0.4 +0.1 -O.S
-0.15 0 +0.30 +0.7 +1.0 +1.1
+0.2 0 -0.4 -1.d -1.5 -2.6
Effective temperature: Kuiper, Astrophys; J. 88, 464 (1938). 84 index: computed from manufacturers' data on 1P21 photomultiplier. Bolometl'ic index: Kuiper, Astrophys. J. 88,452 (1938). Photographic. index·: "Smithsonian Tables," 8th ed. PbS index: computed from rn'anuf!1cturers' data.
Sk-5. Luminance of a Blackbody and Tungsten. l The luminance of a blackbody and of tungsten ribbon can beJepresented as a function of temperature by the followng formulas: log L
7.2010 _ 1.l376T X 10 4
log L
68045 _ 1.1236 X 10
.
T
4
+ 0.0061;, X 10 + 0.00.538 X 10 T'
where L is the luminance and T is the temperature. 1
J. C. De Vos, Physica 20. 715 (1954).
8
8
for a blackbody for a tungsten ribbon
6-215
RADIOMETRY TABLE 6~-16. BRIGHTNESS OF STARS AS SEEN
Star
Spectral type
Visual magnitude
Sirius ............... Canopus ............ a Centauri. .......... Vega ................ Capella ............. Arcturus ............ RigeL .............. Procyon ............. Achernar ............ Betelgeuse (var.) ..... fJ Centauri. ....... , .. Altair ............... a Crucis ............. Aldebaran ........... Pollux .............. Spica ............... Antares ............. Fomalhaut .......... Deneb .............. Regulus ............. fJ Crucis ..... , ....... Castor .............. l' Crucis ............. e Canis Majoris ...... e Ursa Majoris ....... l' Orionis ............ A Scorpii ............ e Carniae ............ E Orionis ............ fJ Tauri. ............ fJ Carniae ............ a Triang. Aust ....... a Persei. ............ 1] Ursa Majoris ....... l' Geminorum ........ a Ursa Majoris ....... e Sagitarii ........... il Canis Maj oris ...... fJ Canis Majoris ......
AO FO GO AO GO KO B8p F5 B5 MO B1 A5 B1 K5 KO B2 MO A3 A2p B8 B1 AO M3 B1 AOp B2 B2 KO BO B8 AO K2 F5 B3 AO KO AO F8p Bl
-1.58 -0.86 0.06 0.14 0.21 0.24 0.34 0.48 0.60 0.7 ± 0.5 0.86 0.89 1.05 1.06 1.21 1.21 1.22 1.29 1.33 1.34 1.50 1.58 1.61 1.63 1.68 1.70. 1.71 1. 74 1.75 1.78 1.80 1.88 1.90 1. 91 1.93 1.95 1.95 1.98 1.99
BY
VARIOUS PHOTORECEIVERS
S4 photosurface magnitude -1.6 -0.6 0.8 0.1 0.9 1.3 0.3 1.0 0.5 1.8 0.7 1.0 0.9 2.1 2.2 1.1 2.3 1.4 1.4 1.3 1.4 1.6 2.7 1.5 1.7 1.6 1.6 2.7 1.6 1.7 1.8 2.9 2.4 1.8 1.9 3.0 2.0 2.6 1.9
± 0.5
Lead sulfide magnitude -1.6 -1.3 -0.9 0.1 -0.8 -1.3 0.3 -0.2 0.7 -1.9 1.1 0.7 1.3 -0.8 -0.3 1.4 -1.4 1.2 1.2 1.4 1.7 1.6 -1.4 1.8 1.7 1.9 1.9 0.2 2.0 1.8 1.8 0.2 1.2 2.1 1.9 0.5 2.0 1.1 2.2
± 0.5
6-216
OPTICS TABLE
I
6k-17.
SOLAR SPECTRAL IRRADIANCE*
Dl\
A
PI>.
Dl\
0.420 0.425 0.430 0.435 0.440
0.1758 0.1705 0.1651 0.1675 0.1823
11.19 11.83 12.45 13.06 13.71
0.00760 0.0152 0.0207 0.0288 0.0420
0.445 0.450 0.455 0.460 0.465
0.1936 0.2020 0.2070 0.2080 0.2060
14.41 15.14 15.90 16.66 17.43
0.00575 0.00649 0.00667 0.00593 0.00630
0.0609 0.0835 0.1079 0.1312 0.1534
0.470 0.475 0.480 0.485 0.490
0.2045 0.2055 0.2085 0.1986 0.1959
18.19 18.95 19.72 20.47 21.20
0.245 0.250 0.255 0.260 0.265
0.00723 0.00704 0.0104 0.0130 0.0185
0.1788 0.2053 0.2375 0.2808 0.3391
0.495 0.500 0.505 0.510 0.515
0.1966 0.1946 0.1922 0.1882 0.1833
0.270 0.275 0.280 0.285 0.290
0.0232 0.0204 0.0222 0.0315 0.0482
0.""163 0.4960 0.5758 0.6752 0.8225
0.520 0.525 0.530 0.535 0.540
0.1833 0.1852 0.1842 0.1818 0.1783
25.43 26.12 26.80 27.48 28.14
0.295 0.300 0.305 0.310 0.315
0.0584 0.0514 0.0602 0.0686 0.0757
1.020 1.223 1.430 1.668 1.935
0.545 0.550 0.555 0.560 0.565
0.1754 0.1725 0.1720 0.1695 0.1700
28.80 29.44 30.08 30.71 31.34
0.320 0.325 0.330 0.325 0.340
0.0819 0.0958 0.1037 0.1057 0.1050
2.227 2.555 2.925 3.312 3.702
0.570 0.575 0.580 0.585 0.590
0.1705 0.1710 0.1705 0.1700 0.1685
31.97 32.60 33.23 33.86 34.49
0.345 0.350 0.355 0.360 0.365
0.1047 0.1074 0.1067 0.1055 0.1122
4.090 4.483 4.879 5.271 5.674
0.595 0.600 0.605 0.610 0.620
0.1665 0.1646 0.1626 0.1611 0.1576
35.11 35.72 36.33 36.93 38.11
0.370 0.375 0.380 0.385 0.390
0.1173 0.1152 0.1117 0.1097 0.1099
6.099 6.529 6.949 7.359 7.765
0.630 0.640 0.650 0.660 0.670
0.1542 0.1517 0.1487 0.1468 0.1443
39.26 40.39 41.50 42.00 43.67
0.395 0.400 0.405 0.410 0.415
0.1191 0.1433 0.1651 0.1759 0.1783
8.189 8.675 9.245 9.876 10.53
0.680 0.690 0.700 0.710 0.720
0.1418 0.1398 0.1369 0.1344 0.1314
44.73 45.78 46.80 47.80 48.79
A
PI>.
0.140 0.150 0.160 0.170 0.180
0.0000048 0.0000176 0.000059 0.00015 0.00035
0.00050 0.00059 0.00087 0.00164 0.00349
0.190 0.200 0.205 0.210 0.215
0.00076 0.00130 0.00167 0.00269 0.00445
0.220 0.225 0.230 0.235 0.240
--
I
1
21.92 22.65 23.36 24.07 24.76
,
,
, !
6-217
RADIOMETRY TABLE
6k-17.
SOLAR SPECTRAL IRRADIANCE*
(Continued)
P)o.
D)o.
A
0.730 0.740 0.750 0.800 0.850
0.1290 0.1260 0.1235 0.1107 0.0988
49.75 50.69 51.62 55.95 59.83
3.6 3.7
0.00135 0.00123
98.720 98.816
0.900 0.950 1.000 1.1 1.2
0.0889 0.0835 0.0746 0.0592 0.0484
63.30 66.49 69.42 74.37 78.35
3.8 3.9 4.0 4.1 4.2
0.00111 0.00103 0.00095 0.00087 0.00078
98.902 98.982 99.055 99.122 99.182
1.3 1.4 1.5 1.6 1.7
0.0396 0.0336 0.0287 0.0244 0.0202
81.61 84.32 86.62 88.59 90.24
4.3 4.4 4.5 4.6 4.7
0.00071 0.00065 0.00059 0.00053 0.00048
99.238 99.289 99.335 99.376 99.414
1.8 1.9 2.0 2.1 2.2
0.0159 0.0126 0.0103 0.0090 0.0079
91. 58 92.63 93.48 94.19 94.82
4.8 4.9 5.0 6.0 7.0
0.00045 0.00041 0.000383 0.000175 0.000099
99.448 99.480 99.509 99.716 99.817
2.3 2.4 2.5 2.6 2.7
0.0068 0.0064 0.0054 0.0048 0.0043
95.36 95.85 96.287 96.664 97.001
8.0 9.0 10.0 11.0 12.0
0.000060 0.000038 0.000025 0.0000170 0.0000120
99.876 99.912 99.935 99.951 99.962
2.8 2.9 3.0 3.1 3.2
0.0039 0.0035 0.0031 0.0026 0.00226
97.305 97.579 97.823 98.034 98.214
13.0 14.0 15.0 16.0 17.0
0.0000087 0.0000055 0.0000049 0.0000038 0.0000031
99.969 99.975 99.9785 99.9817 99.9843
18.0 19.0 20.0
0.0000024 0.0000020 0.0000016
3.3 3.4 3.5
0.00192 0.00166 0.00146
98.368 98.501 98.616
99.9863 99.9879 99.9893 100.0
A
A",
PA
D"
* NASA Rept. X-322-68-304, August, 1968. Based on measurements on board NASA-711 Golilea at 38,000 ft. A Wavelength,.urn Px Solar spectral irradiance averaged over small bandwidth centered at )0., W l(cm'.I'm). DX Percentage of the solar constant associated with wavelengths shorter than X Solar constant 0.013510 W Icm'.
6-218
OPT!CS TABLE
6k-18.
ENERGY DISTRIBUTION IN THE SPECTRA OF THE SELECTED S'l'ARS IN CGS UNITS*
E(A), erg/(em 2'sec) per unit 6,A
No.
At Ori
(j Tau
(j Ari
I Per
(j Ori
3
4
5
6
7
E
€
Ori
IOri
'" Leo
8
9
10
-- --I
2
-- --2 3 4 5
3,300 3,400 3,500 3,600 3,700
0.0245 0.0244 0.0243 0.0244 0,0251
0.060 2 0.0577 0.0552 0.0528 0.0502
0.71, 0.695 0.670 0.648 0.671
0.31, 0.284 0.263 0.246 0.226
0.15, 0.154 0.148 0.141 0.131
0.313 0.301 0.281 0.261 0.242
0.31, 0.288 0.278 0.259 0.238
0.180 0.172 0.164 0.157 0.148
6 7 8 9 10
3,800 3,929 3,970 4,036 4,102
0.035, 0.0539 0.0586 0.0600 0.0581
0.0510 0.0487 0.0475 0.0461 0.0442
0.74, 0.710 0.696 0.673 0.649
0.23, 0.233 0.230 0.220 0.208
0.17, 0.199 0.198 0.195 0.186
0.22, 0.199 0.197 0.190 0.179
0.21, 0.195 0.192 0.184 0.174
0.21, 0.259 0.258 0.251 0.238
11
12 13 14 15
4,221 4,340 4,500 4,600 4,700
0.0550 0'.0527 0.0495 0.0475 0.0455
0.0410 0.0388 0.0364 0.0350 0.0335
0.603 0.559 0.510 0.478 0.448
0.189 0.172 0.153 0.143 0.134
0.170 0.156 0.141 0.132 0.123
0.163 0.148 0.133 0.124 0.117
0.158 0.143 0.129 0.121 0.113
0.219 0.199 0.179 0.168 0.158
16 17 18 19 20
4,861 5,000 5,150 5,300 5,500
0.0418 0.0384 0.0355 0.0333 0.0307
0.0315 0.0300 0.0287 0.0274 0.0255
0.413 0.386 0.356 0.327 0.290
0.120 0.110 0.0990 0.089, 0.079,
0.111 0.102 0.0937 0.0857 0.075,
0.106 0.096, 0.087, 0.079 , 0.069,
0.103 0.0950 0.086, 0.079, 0.0700
0.142 0.130 0.118 0.107 0.094,
21 22 23 24 25
5,700
0.0283
0.0263 0.0246 0.0225 0.0209
0.O:!33 0.0219 0.0208 0.0195 0.0186
O.:lol
5,850 6,000 6,200 6,400
0.243 0.230 0.218 0.206
0.070, 0.064, 0.058, 0.0530 0.0510
0.066, 0.0608 0.056, 0.051, 0.0487
0.062, 0.0580 0.054 2 0.049, 0.047 8
0.060 2 0.055 0 0.0500 0.0460 0.042,
0.083, 0.077, 0.0730 0.067, 0.063,
26 27 28 29 30
6,500 6,563 6,600 6,700 6,800
0.0202 0.0198 0.0195 0.0189 0.0180
0.0181 0.0176 0.0173 0.0165 0.0156
0.198 0.192 0.188 0.176 0.165
0.048, 0.0460 0.0450 0.042, 0.039 0
0.0470 0.045, 0.0448 0.0420 0.0392
0.0470 0.045, 0.044, 0.0412 0.0388
0.040 5 0.039, 0.0380 0.035, 0.033 2
0.061, 0.059, 0.0588 0.0560 0.0522
31 32 33
7,000 7,100 7,200
0.0160
0.0139
...... ......
. .....
0.144 0.134 0.125
0.034 0.032 0.030
0.033, 0.031, 0.028,
0.0337 0.032, 0.0300
0.0287 0.026, 0.024,
0.0448 0.041, 0.036,
I
. .....
6-219
RADIOMETRY TABLE
6k-18.
ENERGY DISTRmUTION IN THE SPECTRA OF THE
SELECTED STARS IN CGS UNITS*
(Continued)
ECA), erg/Cem"see) per unit
No.
~A
At
'YUMa
'lUMa
a Oph
a Lyr
~
Cyg
a Aql
a Cyg
a Peg
--
--
I
2
11
12
13
14
15
16
17
18
2 3 4 5
3,300 3,400 3,500 3,600 3,700
0.029. 0.0296 0.0298 0.0300 0.0302
0.16, 0.156. 0.147· 0.139 0.129
0.033 0.0344 0.0349 0.0354 0.0383
0.33, 0.320 0.314 0.308 0.306
0.024. 0.0249 0.0248 0.0247 0.0246
0.12. 0.124 0.126 0.128 0.135
0.10. 0.106 0.109 0.112 0.158
0.033. 0.0336 0.0340 0.0339 0.0342
6 7 8 9 10
3,800 3,929 3,970 4,036 4,102
0.0518 0.0784 0.0804 0.0806 0.0770
0.14. 0.161 0.163 0.157 0.150
0.059. 0.0750
0.045, 0.0620 0.0612 0.0596 0.0571
0.197 0.232
0.0896 0.0866
0.50. 0.778 0.798 0.795 0.765
0.294 0.288
0.21, 0.214 0.212 0.208 0.201
0.055, 0.0874 0.0906 0.0873 0.0831
11 12 13 14 15
4,221 0.0710 4,340 0.0667 4,500 ·0.0615 4,600 0.0584 4,700 0.0552
0.137 0.127 0.114 0.107 0.099.
0.0830 0.0796 0.0758 0.0739 0.0712
0.709 0.655 0.598 0.564 0.531
0.0525 0.0484 0.0438 0.0413 0.0389
0.276 0.268 0.258 0.250 0.243
0.187 0.176 0.165 0.159 0.153
0.0770 0.0707 0.0642 0.0607 0.0570
16 17 18 19 20
4,861 5,000 5,150 5,300 5,500
0.0504 0.0471 0.0438 0.0406 0.0368
0.089. 0.082. 0.074, 0.068. 0;060.
0.0650 0.0609 0.0571 0.0535 0.0491
0.484 0.449 0.413 0.382 0.345
0.0356 0.0332 0.0306 0.0285 0.0256
0.226 0.212 0.198 0.186 0.174
0.143 0.135 0.127 0.119 0.110
0.0520 0.0482 0.0443 0.0411 0.0371
21 22 23 24 25
5,700 5,850 6,000 6,200 6,400
0.0329 0.0304 0.0286 0.0266 0.0246
0.052, 0.048. 0.044. 0.040, 0.0377
0.0453 0.0425 0.0401 0.0379 0.0354
0.313 0.290 0.272 0.248 0.230
0.0230 0.0212 0.0196 0.0180 0.0170
0.162 0.154 0.146 0.137 0.128
0:102' . 0.0333 0.095, . 0.0388 0.090. 0.0286 0:083, 0.0261 0.077, 0.0245
26 27 28 29 30
6,500 6,563 6,600 6,700 6,800
0.0234 0.0225 0.0221 0.0208 0.0199
0.036, 0.035. 0.034. 0.032. 0.0295
0.0336 0.0324 0.0318 0.0300 0.0282
0.220' 0.209 0.204 0.190 0.178
0.0166 0.0161 0.0156 0.0144 0.0133
0.122 0.119 0.117 0.112 0.107
0.074, 0.072, 0.071. 0.0675 0.0645
0.0234 0.0227 0.0221 0.0205 0.0190
31 32 33
7;000 7,100 7,200
..... . ..... .
......
0.026
0.0245 0.023 0.021
0.154 0.145 0.136
0.0115 0.0105
0.095 0.090 0.086
.0.056, 0.0525 0.0475
0.0162 0.0146 0.0131
-I
* Kharitonov,
...... ..... .
..... .
A. V., Soviet Astron.-AJ '1, 258 (1963).
t Wavelength in angstroms.
......
.....
6-220 TABLE
OPTICS
6k-19.
SOLAR ULTRAVIOLET FLUX INCIDENT ON EARTH'S ATMOSPHERE*
A, A.
log I, to Wj(cm'·A)
log U/E),t photons/ (cm 2' sec' A.)
A, A.
log I, t W/(cm 2.A.)
log U/E),t photons/ (cm 2 ·sec·A.)
10 20 50 100 200 400 600 800
-11 -10.2 -9.6 -9.5 -9.4 -9.8 -9.8 -9.8
4.7 5.8 6.8 7.2 7.6 7.5 7.7 7.8
900 1,000 1,100 1,200 1,400 1,600 1,800 2,000
-9.4 -9.3 -9.8 -9.7 -9.3 -8.3 -7.6 -7.1
8.2 8.4 7.9 8.1 8.5 9.6 10.4 10.9
* Compiled by G. R.
Cook, The Aerospace Corp. IV. Allen, "Astrophysical Quantities," 2d ed., p. 173, Athlone Press, University of London, London, 1963. Mean solar intensity with spectrum lines smoothed less the dominant resonance lines:
t c.
f.-.........
t Photon energy E TABLE
HI 1216 6 X 10-7 W 10m 2 HeI 584 A ......... 0.1 X 10- 7 IV 10m' Herr 303 A. ..... , .0.3 X 10- 7 W Icm' = he/A.
6k-20.
LABORATORY VACUUM ULTRAVIOLET SOURCES*"
Gas
Name
Pressure, torrs
Wavelength, A.
Excitation method
I I
Flux, photonst (cm 2 ·sec·A)
Continua
Hopfield ................. 1 Argon .................. . Krypton ................ . Xenon .................. . Hydrogen ............... . Lyman/90 % He 10 % air Synchrotron ............. . X-ray fluorescence ....... .
+
He Ar Kr Xe Hz
50 200 50-200 50-200 50-200 1-2 0.02-0.05 .. . . . . . . . .........
600···1,000 1,060-1,500 1,250-1,800 1,500-1,800 1,600-5,000 300 ~ 5,000 100-5,000 10-100
ICondensed ;park I 101D_l011b Condensed spark Condensed spark Condensed spark A-c or d-c glow Condensed spark 180 MeV Soft X-ray tube
101O-10 11b 10' _101Ob 10' -10· ob 10'-10 8e d
10'-10" I
Line Emission Hydrogen ................ Resonance line/He 10 %
+ Resonance line / Ar + 10 % . Resonance line / Ar + 10 % . Resonance line / Ar + 10 % . Spark spectra He + 10 % .. Hollow cathode ...........
* Compiled by G. R.
H2 Ar
1-2 ~1
H2
~1
02
~1
N2 Air He
0.05 0.1
~1
Cook, The Aerospaoe Corp.
850-1,600 1,165,1,236 1,470, 1,295 1,216 1,302-1,306 1,743-1,745 200-1,500 231-1,640
A-c or d-c glow Microwave Microwave Microwave lVIicrowave Condensed a-c D-c glow
~10"·
10·'" 10·,h 10·2h 10· 2h i
10'-10 7 ;
RADIOMETRY
6-221
Notes for Table 6k-20 a An account of this subject may be found in J. A. R. Samson, "Vacuum Ultraviolet Spectroscopy," chap. 5, John Wiley & Sons, Inc., New York, 1967. b Fluxes are approximate, and represent values that one may expect to obtain at the maximum of the continuum with a 1- or 2-m normal-incidence monochromator with a 600- or 1,200-line/mm grating. Absolute flux measurements have been reported by Metzger and Cook, J. Opt. Soc. Am. 55,516 (1965), and by R. E. Huffman, J. C. Larabee, and Y. Tanaka, Appl. Opt. 4, 1581 (1965). The Ar, Kr, and Xe continua may also be excited with less intensity by microwaves. See P. G. Wilkenson and E. T. Byran, Appl. Opt. 4, 581 (1965). Greater intensity may be obtained in high-energy single-flash technique. See J. A. Golden and A. L. Myerson, J. Opt. Soc. Am. 48, 548 (1958). C At about 1,850 A. See D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 699 (1951). d This source requires current densities of 30,000 A/cm 2 or more in the light-source capillary tubes. Flash tubes have been designed which produce a well-developed photographic spectrum after two or three flashes. See W. R. S. Garton, J. Sci. Instr. 36, 11 (1959), and M. Nakamura, Sci. Light (Tokyo) 16, 179 (1967). For wavelengths shorter than about 1,000 A the continuum contains numerous emission lines. 'These values are for the NBS 180-MeV, R = 83 cm, electron synchrotron at a distance of about 2 m along the tangent to the orbit before entering the spectrograph with A = 304 A. See K. Codling and P. Madden, J. Appl. Phys. 36, 380 (1956). For 6-GeV electrons in a 31.7-m orbit see R. Haensel and C. Runz, Z. Angew. Phys. 23, 276 (1967). The wavelength of the maximum of the continuum decreases according to A = 2.35R/ E', where A is in A, R is in meters, and E in GeV. For 1 GeV and R = 31.7 m, the maximum of the continuum is at about 75 A. f Fluorescence in the 10- to 100-A region is detected with proportional counters containing P-lO or methane gas. For analysis of the light elements Mg to Be typical counting rates vary from 30 to 7,200 per sec, with peak to background ratios between 4 and 55. See B. L. Henke in "Advances in X-ray Analysis," vol. 8, p. 269, Plenum Press, Plenum Publishing Corporation, New York, 1965. a This is the flux observed at A = 1215.6 with a 1-m monochromator with the light source operated 400 mAo See D. M. Packer and C. Lock, J. Opt. Soc. Am. 41, 699 (1951). A wavelength table of the H2 and many line spectra with relative intensities has been prepared by K. E. Schubert and R. D. Hudson, ATN-64 (9233)-2, October, 1963, The Aerospace Corp., P. O. Box 95085, Los Angeles, Calif. 90045. h About 50-W microwave power at 2450 MH coupled to the gas in a 13-mm OD capillary. See H. Okabe, J. Opt. Soc. Am. 54, 478 (1964). A table of wavelengths of emission lines from neutral and ionized atoms in the 6 to 2,000 A range has been prepared by R. L. Kelly, UeRL 5612, University of California, Lawrence Radiation Laooratory, Liverillore, Calif. For each line there are one or more references to the original literature. i Current densities less than for the Lyman discharge allow pulse rates in the 50 to 400 per sec region. These rates are convenient for photoelectric detection. Details of this source have been published by P. Lee and G. E. Weissler, J. Opt. Soc. Am. 42, 80 (1952). ; These are photon fluxes at the entrance slit of a I-m grazing incident monochromator necessary to produce an output current of 10- 9 amp from a Bendix magnetic-type multiplier. See E. Hinnov and F. Hofmann, J. Opt. Soc. Am. 53, 1259 (1963).
61. Wavelengths for Spectrographic Calibration!
-
Q
TABLE
61-1.
Wavelength, A
WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*
Intensity
Spectrum
Estimated relative error
Wavelength, A
Intensity
Spectrum
1,774.941a 1,769.658 a 1,753.113 a 1,749.771 a
20
Si r Si r Si r Si r Nr NIl Nr Nn Si r Hg II Nr Si I On On Hgn Si r Si r Hg n Si I Si r Si 1 Hg II 01 Or Or Or Or Or Or 01 Or Or Hg II
(±mA)
1,942.273 1,930.902 1,900.284 1,880.969 1,870.547 1,869.548 1,867.590 1,864.742 1,862.806 1,861.750 a
1,859.406 1,857.956 1,853.260 1,850.665 1,849.497 1,849.380 1,848.237 1,846.014 1,844.304 1,842.066 1,839.995 1,833.264 1,831. 973 1,830.458 1,820.336 1,816.921 1,808.003 1,807.303 1,803.888 1,796.897 1, 787. 805 a 1,782.817 1,775.677 1
20 10 5 5 20 8 1
5 2 1 3 8 3 5 50Rb
5 5 8 10 1 4 1 5 4 20 8 5 30 2 15 10
15 1
Hg II Or Hg II Si I HgII HgII Nn Nn Nn Si r Ni r Ni r Si r Si r Hgr Ni r Si I NIl NIl NIl Si r 0 NIl NIl Hgu Si II Si II NIl Hg n Hg II Si I Na III Hgr
2 2 2 2 4 2 3 2 5 2 2 4 4 5 4 4
4 4 4
5 4 5 4 4 4 2 4 5 2 4 2 4 4
1
1,657.374c
2 1 30 10 60 15 8 15 2 4 20 18 4 4 8 8 3 15 5 2 20 15 1 10
1,657.243
1
1,657.001c 1,656.923 c
30 15 4 15 5 2
1,745.246 1,743.322 1,742.724 1,740.327 1,736.582 1,732.142 1,730.874 1,727.332a
1,721.081 1,720.158 1,707.397 1,704.558 a 1,702.805 a
1,702.733 1,700.522 1,693.756 1,676.913 1,672.405 1,658.117c 1,657.899 c
1,657.541
1,656.454 1,656.259 1,654.055 1,653.644
Estimated relative error (±mA)
--4 4 3 5 3 4 3 3 4 4 3 3 3 4 4 4 4 4 4 4 4 3 1
4 5 1
5 1 1 4 1
3 3
This section presents calibration standards in the ultraviolet and infrared wavelength For corresponding data on visible wavelengths, see Sec. 7.
~egions.
6-222
WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION TABLE
61-1.
WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*
Wavelength, A
Intensity
Spectrum
1,649.932 1,640.474 1,640.342 1,630.180 1,629.931 1,629.830 1,629.366 1,613.251 1,605.321 1,602.598 1,592.245 1,589.607 1,574.035 1,561.433 1,561. 339 1,560.687 d 1,560.301 1,504.474 1,494.673 1,492.824 1,492.624 1,485.600 1,481. 7GO 1,470.082 1,469.844 1,467.405 1,466.723 1,463.838 1,463.346 1,459.034 1,439.094 1,411.948 1,393.322 1,364.165 1,361. 267 1,357.140 1,355.598 1.354.292 1,350.074 1,335.692 1,335.184 1,334.520 1,331. 737
10 80 d
Hg II Hen Hen Si I Si r Nn Si r Hen Hen Or Si 1 Si r NIl Or Or Or
lOOd 2 4 4 4 4 1 15 4 2 1 20 5 15 2 5 60 30 80 8 30
5 15 20 5 40 40 20 10 30 1 8 8 5 2 8 4 80 8 60 20
01 Hg III Nr Nr Nr Si n r. _
0 Or Or Si II Nr Hg III
01 II
01 Or Or Hg II
On Hg
On Hg
4 4 2 3 4 4 4 4 3 3 3 3 3 2 4 12 5 4 4 4 5 2 3
v~
Or Or Or NI
Hg
Estimated relative error (±mA)
II
3 4 3 4 3 2 4 2 3 2 4 4 2 3 3 2 5 3 5 4
Wavelength, A
Intensity
Spectrum
1,329.590 1,329.108 1,328.836 d 1,327.927 1,326.572 1,321. 712 1,319.684 1,319.003 1,316.287 1,311.365 1,310.952 1,310.548 1,309.278 1,307.928 1,306.036 1,304.872 1,302.173 1,288.430 1,280.852' 1,280.604' 1,280.403' 1,280.340' 1,280.140' 1,279.897' 1,279.230 1,277.727 1,277.551 1,277.282 1,276.754 1,265.001 1,261.559' 1,261.4301 1,261.1281 1,261.000 1 1,260.930 1 1,260.7381 1,259.523 1,253.816 1,251.164 1,250.586 1,248.426 1,246.738 1,243.309
40 40 15 10 15 20 30 20 1 20 25 25 3 10 25 30 30 5 10 8 5 15
Or Or Or Nr Nr Hg n Nr Nr Nr Or Nr Nr Si n Hgn Or Or Or Or Or Or Or Or
S
10 8 20 50 40 3 1 15 8 8 8 8 8 10 5 8 4 5 1
15
6-223
(Continued)
Estimated relative error (±mA
1 2 10 2 4 3 4 2 1 3 1
3 5 3 3 5 1 3 1 3 4 1
r-
1
Or Or Or Or Or NIl Si II
1 3 1 4 1
01 Or
01 01 Or Or Or
1 1 1
4 1 1 2 1
3
Or
1
Si II Hg 1 Si II Si II Nr
4 4 4 3 4
6-224 TABLE
OPTICS
61-1.
WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET*
Wavelength, Intensity A
1,243.179 1,229.172 1,228.790 1,228.410 1,225.372 1,225.028 1,215.662 1,215.167 1,215.086 1, 200. 708 g 1,200.226 g 1,199.718 g 1,199.551 g
1,194.496 1,194.060 1,193.674 1,193.388 d
1,193.243 1,193.013 1,189.628 1,189.244 1,188.972 1,177.694 1,176.626 1,176.508 1,170.276 1,169.692 1,168.537 1,168.334 1,167.450 1,164.322 1,163.884 1,158.138 1,158.030 1,152.149 1,134.988 1,134.426 1,134.176 1,101. 293 1,100.362 1,099.259 1,099.153 1,098.264
Spectrum
Nr Nr Nr Nr Nr Nr 100Rb H 5 Hell 5 Hell 30 Nr 40 Nr 2 Nr 50 N r, 0 r 5 Si r Or 3 3 Or 3 Or 15 Or Or 15 5 Nr 3 Nr 5 Nr 15 NI Nr 3 15 Nr Nr 1 1 Nr 20 Nr 8 Nr 25 Nr 8 Nr 12 Nr Or 1 8 Or 2 Or 25 Nr 25 Nr 20 Nr 40 Nr 30 Nr 40 Hg n 25 Nr 40 NI 20 1 10 5 10 15
Esti- I mated relative Wavele~gth, Intensity A error (±mA) 1 1 4 4 1 4 5 5 4 2 1 4 5 1 3 3 8 2 4 4 3 1 3 5 1 3 1 4 4 4 3 4 5 4 5 4 4 4 5 4 3 5 5
1,098.103 1,097.990 1,097.245 1,096.749 1,096.322 1,095.940 1,085.707 1,085.546 1,085.442 1,084.970 1,084.910 1,084.579 1,083.990 1,070.821 1,069.984 1,068.476 1,067.607 1,041. 688 1,040.941 1,039.233 1,037.627 1,037.020 1,028.162 1,027.433 1,025.728 1,025.298 990.805 h 990.210h 990. 132h 988. 776h 988. 661 h •d
977.967 964.626 963.991 953.658 953.415 952.522 952.414 952.304 950.114 949.742 910.279 909.692
40 25 50 35 35 35 50 3 3 2 2 30 20
°
30 35 35 1 15 20
°°8 20 60 2i
2 8 1 15 2 1 1 5 15 15 4 8 8 0 25
°°
(Continued)
Spectrum
Nr Nr Nr Nr Nr Nr NIl NIl NIl Hell Hen Nn NIl Nr Nr Nr Nr Or Or Or 0
On Or Or H Hen Or Or Or Or Or Or Nr Nr Nr Nr Nr Or Nr Or H NI Nr
Estimated relative error (±mA) 5 4 4 4 2 3 3 5 3 4 5 3 4 5 1 4 4 4 4 4 3 1 3 3 3 5 4 4 4 4 4 4 4 4 4 3 4 4 4 4 4 5 5
WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION TABLE
61-1.
6-225
WAVELENGTH STANDARDS FOR THE VACUUM ULTRAVIOLET* (Continued)
Wavelength, A
Intensity
Spectrum
906.722 906.426 906.202 905.829
--1 15 10 5
NI NI NI NI
Estimated relative error (±mA)
2 4
3 4
Wavelength, A
Intensity
893.079 888.363 888.019 875.092
0 0 0 5
Spectrum
Hgn
NI NI NI
Estimated relative error (±mA)
2 2 4 5
* J. Opt. Soc. Am. 46, 10 (1955). • Identification: A. Fowler, Proc. Roy. Soc. (London), Ber. A, lllS, 422 (1929); J. C. Boyce and H. A. Robinson. J. Opt. Soc. Am. 26, 133 (1936). b Self-reversed resonance line. , Resolved 2p2 'P - 38'PO multiplet. d Blended line. • Completely resolved 2p2 'P - 4 • •po multiplet. I Completely resolved 2p2.p - 3d .po multiplet. D Resolved 2p' 'So - 38 'P multiplet. • 2p' 'P - 3.' 'DO multiplet. ; Diffuse line.
6-226
OPTICS TABLE
61-2.
PROPOSED INTERNATIONAL WAVELENGTH STANDARDS IN THE VACUUM ULTRAVIOLET
Wavelength,
A,
ISpectrum
this research
1,930.902 1,745.246 1,742.724 1,740.327 1,658.117 1,657.899 1,657.374 1,657.001 1,656.259 1,560.301 1,494.673 1,492.624 1,481. 760 1,335.692 1,329.590 1,329.108 1,277.282 1,261.559 1,200.708 1,200.226 1,199.551 1,177.694 1,176.508 1,167.450 1,134.988 1,134.426 1,134.176 1,085.546 1,084.579 1,083.990 990.805 990.210
Cr Nr Nr NIl Cr Cr Cr Cr Cr Cr Nr Nr O,r CIl Cr Cr Cr Cr Nr Nr NT Nr Nr Nr Nr Nr Nr NIl NIl Nn Cr Cr
Wavelength,
Wavelength,
Wavelength,
A,
A,
A,
More and Rieke"
Boyce and Riekei'
Weber and Watson'
....
0.900 0.246 0.734 . .... 0.126 .... . 0.380 0.005 .... . 0.316 0.669 0.630 .... . .... . .... . 0.101 0.2H 0.560 0.706 0.220 0.547 .... . ..... ..... 0.980 0.419 0.171 0.546 0.579 0.991 0.797 0.213
0.889 0.255 0.733 0.320 0.127 ..... 0.381 ..... ..... .... . 0.668 0.634 ..... .....
.
. .... . ....
.. . . .
.... . 0.909 .... . .... .
0.266 0.308 0.672 .... . 0.771 0.700 0.587 0.102 ..... ..... 0.719 0.217
o .~.5Z 0.701 0.506 0.442 0.977 .... . ..... .....
0.584 ..... 0.790 0.198
.....
.... . . .... . .... 0.693 0.215 0.557
0.677 0.498 0.454 0.980 0.416 0.169 0.546 0.582 0.990 ..... .....
a K. R. More and C. A. Rieke. Phys. Rev. 50, 1054 (1936). b J. C. Boyce and C. A. Rieke, Phys. Rev. 47, 653 (1935). 'R. L. Weber and W. W. Watson, J. Opt. Soc. Am. 26,307 (1936). d A. Fowler, Proc. Roy. Soc. (London), ser. A, 123,422 (1929). 'A. G. Shenstone, Phys. Rev. 72, 411 (1947). f E. Ekefors, Z. Physik 63,437 (1930). 'B. Edlen, Z. PhjJsik 98,561 (1936); Nature 159, 129 (1947). h F. Paschen and G. Kruger, Ann. Phys. 7, 1 (1930).
1 Wavelength,
A,
Wavelength,
A,
other observers
mean value
...... ...... ......
1,930.897 1,745.249 1,742.730 1,740.321 1,658.123 1,657.900 1,657.378 1,657.001 1,656.260 1,560.308 1,494.670 1,492.630 1,481. 760 1,335.692 1,329.587 1,329.104 1,277.279 1,261.561 1,200.708 1,200.219 1,199.552 1,177.691 1,176.504 1,167.449 1,134.981 1,134.420 1,134.172 1,085.546 1,084.580 1,083.990 990.797 990.207 ..-
0.315 d
...... 0.891' ...... 6.998' 0.255' "'0' •
...... ...... 0.750 1
0.684" 0.583h
...... 0.280 h 0.565 h
...... ...... ...... ...... . ..... . .....
...... ...... . ..... . ..... ...... . ..... . ..... . .....
6-227
WAVELENGTHS FOR SPECTROGRAPHIC CALIBRATION
TABLE 61-3. INFRARED STANDARD WAVELENGTHS '.'
I
\V'2~Ve-
I
length, .urn
State
0.54607 0.57696 0.57907 1.01398 1.12866 1.140 1. 35703 1.36728 1.39506 1.52452 1.6606 1.671 1.69202 1. 69419 1.70727 1. 71090 1.81307 1.97009 2.008 2.150 2.1526 2.22 2.24929 2.3126 2.32542 2.37 2.4030 2.4374 2.439
Emission Emission Emission Emission Emission Liquid Emission Emission Emission Emission Liquid Liquid Emission Emission Emission Emission Emission Emission Gas Liquid Liquid Liquid Emission Liquid Emission Solid Liquid Liquid Gas
2.464 2.4944 2.5434 2.688 2.7144 2.765 2.79 2.996 3.2204 3.230
Liquid Liquid Liquid Gas Vapor Gas Solid Gas Solid Gas
3.2432 3.2666 3.3033 3.3101
Solid Solid Solid Solid
I
Description
AH-41amp AH-41amp AH-41amp AH-41amp AH-4lamp
Mercury Mercury Mercury Mercury Mercury ................ Benzene AH-4lamp Mercury AH-41amp Mercury AH-41amp Mercury AH-4lamp Mercury 0.5-mm cell 1,2,4-Trichloro benzene . . . . . . . . . . . . . . . . Benzene AH-4lamp Mercury AH-4lamp Mercury AH-41amp Mercury AH-4lamp Mercury AH-4lamp Mercury AH-41amp Mercury ................ Carbon dioxide ................ Benzene D.5-mm cell 1,2,4-Trichloro benzene ................ Carbon disulfide AH-41amp Mercury 0.5-mm cell 1,2,4-Trichlorobenzene AH-4lamp Mercury 25-.um film Polystyrene 0.5-mm cell 1,2,4-Trichloro benzene 1,2,4-Trichlorobenzene 0.5-mm cell ................ Carbon oxysulfide central min ................ Benzene 0.5-mm cell 1,2,4-Trichlorobenzene 0.5-mm cell 1,2,4-Trichlorobenzene ........ . . . . . . . . Carbon dioxide Methanol 5.0-cm cell . . . . . . . . . . . . . . . . Carbon dioxide ................ Lithium fluoride 200-mm 5. O-cm cell Ammonia-zero branch 25-.um film Polystyrene Carbon oxysulfide central min 25-.um film Polystyrene 25-.um film Polystyrene 25-.um film Polystyrene 25-,um film Polystyrene ~
••••••••••••
9
....
Ref .
Substance
9 9 9 9 9 6 9 9 9 9 9 6 9 9 9 9 9 9
9 9 9 9 9 Wright 9 9 8 5 9 9 Barker and Wu 9 Barker and Wu 9 2 9 8
j9
I:
-.
6-228
OPTICS TABLE
Wavelength, p.
61-3.
INFRARED STANDARD WAVELENGTHS
I Description
State
(Continued)
-
I
Substance
Ref.
-3.320 3.3293 3.4188 3.426
Gas Gas Solid Gas
3.465
Gas
3.5078 4.258 4.613
Solid Gas Vapor
4.866 4.875
Vapor Gas
5.138 5_284
Solid Gas
5.292 5.549 5.847
Gas Solid Gas
6.154 6.238 6.692 6.753 6.925 7.268 7.681 8.241 8.362 8.490 8.623 8.762 9.057 9.216 9.295 9.378 9.548
Gas Solid Solid Liquid Gas Liquid Gas Gas Gas Gas Gas Gas Gas Gas Gas Gas Gas
9.608 9.672 9.673 9_724 9.807 9.85
Vapor Vapor Gas Solid Vapor Gas
~
................
Methane-zero branch Methane 5.0-cm cell 25-p.m film Polystyrene Carbon oxysulfide central min Hydrogen chloride central min Polystyrene 25-p.m film Carbon dioxide Atmospheric ................ Carbon disulfide I central min Methanol 5.0-em cell Carbon oxysulfide ................. central min 50-p.m film Polystyrene ................ Carbon oxysulfide central min Ethylene central min ................ Polystyrene 50-I'm film ................ Carbon oxysulfide central min 200 mm 5 _O-cm cell Ammonia-zero branch Polystyrene 50-I'm film 50-I'm film I Polystyrene ................ Benzene · , . . . . . . . . . . . . . . Ethylene-zero branch 0_ 05-mm cell Methylcyclohexane ................ Methane-zero branch 200-mm 5 _O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia 200-mm 5 _O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia 200-mm 5 _O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia 200-mm 5. O-cm cell Ammonia ................ Carbon oxysulfide central min ................ Methyl chloride 5-cm cell Methanol ................ Ammonia 50-I'm film Polystyrene ................ Methyl chloride · . . . . . . . . . . . . . . . Ammonia •••••••••••••
•
••
~
••
~
••
0
0ihble, E€nsitivity of a detector is often expr'lssed as noise equivalent power. Noise Equivalent Power (N EP). The incident radiation that it takes to produce a detector output signal equal to detector noise in a specified bandwidth (generally 1 Hz). Generally the incident radiation is chopped and expressed in watts as the rms value of the fundamental component of the chopped radiation. Specific detectivity D* is the reciprocal of the noise equivalent power of the detector referred to unit area and I-Hz bandwidth.
:r: ciEe
D* =
VA
Ilf
watt- 1 cm sec- t
NEP
(6p-3)
where A = detector area, cm Ilf = effective noise bandwidth, Hz Time Constant. Dynamic response of many detectors to a step function can be approximated by a single exponential of the form (1 - .-tlT), in which t is time and T is the time constant. The frequency response is then approximately 2
1
(6p-4)
where f is the electrical frequency of the signal. The signal and noise as a function of frequency for a typical lead sulfide detector I1nd a typical lead selenide detector are shown in Figs. 6p-2 and 6p-3. ~+-~~~------"------------------~100~
z o
+ =CURRENT ON
c...
= CURRENT OFF • =SIGNAL
o
(J)
LoJ
a:: -.J
10 ~ (!)
en
LoJ
I : II :,,:
FIG.
6p·2. PbS detector at 25°C.
~
I
ti:f
105
a::
I ! 111l!
103 FREQUENCY, Hz
>
Signa] vs. chopping frequency, and noise
frequency.
VS.
I00 ~ III
~
o
> o
..........
....
a:::
u
~ 1.0
w
r-
(J')
-"'-
o
z
I
NOISE x " CURRENT ON o " CURRENT OFF GO " SIGNAL
iii
-
.......
,...
Z
o
a. (J')
"'-
'Ii\.
w
\
a::
'\
I
o
..J !ili
I I
II
Iii
15Ul 40 I
/
1&1
j
II!
'-\
~
II
\
\
40
~ 20
\
!q
"
I
\
~ ~O
i\ \
~
3000 5000 7000 9000 11000 13000 WAVELENGTH, ANGSTROMS I I
80
E Ul
\ ..
3000
..
140
I!! 120
I!! I 20
II
RANGE OF MAX. VAWE
-I
>-
\
l:j40
...J UJ II:
I
Z :::;)
Z
m
II
SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-5 RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
140
~IOO
5000 7000 9000 11000 13000 WAVELENGTH, ANGSTROMS ,I
SPECTRAL SENSITIVITY CHARACfERISTIC OF PHOTOTUBE HAVING S-4 RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
:::;)
R!,~NGE ~tE AX VAL
):'
1\
20
,
-
-;-
~IOO
H1
,..100
;i
~
a:
~
,..::>
RANGE OF MAX. VALUE
~IOO
I J \ \ I \ I
I-
m
\
53 80 a:
~
80
>" !::
~
>
~20 .J
Lil20
\
W
a::
a:
\
~
3000 5000 7000
9000
11000 13000
WAVELENGTH, ANGSTROMS II
II
I
3000 5000 7000 9000 11000 13000 WAVELENGTH, ANGSTROMS
.
II
7IiI
140 FOR VALUE OF RADIANT SENSITIVITY AT 100-UNIT POINT. SEE DATA SHEET FOR SPECIFIC TUBE TYPE
120
II
U)
~120
I FOR VALUE OF RADIANf SENSITIVI rv i-(J.LAMP/!-'WATnAT 100-UNIT POINTSEE DATA SHEET FOR SPECIFIC TYPE
,..
>-
-1
0:
;;;100 U)
I
=>
I-
E rij BO
I r
SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTO TUBE HAVING S-II RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING S-IO RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
140
"
J
I
iiI- lOO
\ \
iii
\
RANGE OF MAX. VALUE
I
0:
'> E SO tf)
\
.J W
w
U)
I-
w
ti 60
\
z
U)
\
a::
40
w 40
>
\
ti
\
20
Lil20
a:
\.
o
3000 5000
-rOOO
\
o 9000
11000 13000
3000
WAVELENGTH, ANGSTROMS ~II
II
-?-
FIG. 6p-4 (Continued)
5000 7000 9000 11000
WAVELENGTH, " ; , : II
ANGSTROMS
6-261
RADIATION DETECTION SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING' S-12 RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
SPECTRAL SENSITIVITY CHARAcTERISTIC OF PHOTOTUBE HAVING , S-19 RESPONSE FOR. EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
140
~120 :::>
140
FOR VALUE OF RADIANT SENSITtVITiL HI'AMP/I'WATT) AT 100- UNIT POINT SEE DATA SHEET FOR SPECIFIC TYPE
FOR VALUE OF RADIANT SENSITIVITY AT IOO-UNIT POINT. SEE DATA SHEETFOR SPECIFIC TUBE TYPE
120
~ [2100
> I-
> f= ~ 80 w en
f= 60
w
10
a:
: 80
:;
>
in
li-'
z
w (f)
I
I
60
It- ~i~~~AruE
'\
\
\
\
w a: 40
w 40
>
~
\
J
i>l!l20 a:
o
-j
~100
I-
20
/ V
\ \
\....
o
3000
4000 5000 6000 7000 WAVELENGTH, ANGSTROMS II I I I I I
\
3000 5000 7000 9000 11000 WAVELENGTH, ANGSTROMS
ill IS
Ul
:1 w II)
SPECTRAL SENSITIVITY CHARACTERISTIC OF PHOTOTUBE HAVING Se 21 RESPONSE FOR EQUAL VALUES OF RADIANT FLUX AT ALL WAVELENGTHS
SPECTRAL SENSITIVITY CHARACTERIST.IC OF PHOTOTUBE HAVING S-20 RESPONSE ' FOR EQUAL VALUES OF RADIANT FLUX " . T ALL WAVE L ENGTHS A 140
120
~IOO
120
~
80
en w
IV
\' I
> f= ~ 80 w en w > 60
,
\ \
~ 60
-' w
w a:
[\
20
\
I
/
II
1\
I! , I I , I
40
20
I'-
1000 3000 5000 7000 9000 WAVELENGTH, ANGSTROMS
-E----
;-;>-!1f\C
o
c:
~30~--I--4-~~-~--+--~~~-+-----+---~
.z w
c:
~20rr-~~~~
20
40
60
80
VOLTAGE ACROSS DIODE, MV
700
600
.../'
500
/
«
::I...
~400 w
-----
~
I
a: a:: =>
301 LUMENS 1FT-=-
2000 LUMENS / FT 2
'r
~300
o
o 200
100
1300 LUMENS / FT 2
IIMEN;~FT2
/"
585 I '1'15 LUMENS/FT2 145 LUMENS IFT2
lr"':
ARK CURRENT
o
-10
-20
-30
-40
-50
VOLTAGE ACROSS DIODE, VOLTS FIG. 6p-5. Germanium photodiode curves showing biased and unbiased photovoltaic characteristics.
RADIATION DETECTION
where
e,/2,j,
=
WI
=
6-263
quantities defined under shot noise unchopped background radiation reaching the photocathode, effective watts C = cathode sensitivity, amp per effective watt 6p-3. Germanium Photo diodes and Silicon Cells. The characteristics of germanium photo diodes are shown in Fig. 6p-5. Silicon photovoltaic cells (ref. 2) are used largely for the conversion of solar energy into electrical energy. Typical data are shown in Fig. 6p-6. 6p-4. Cadmium Sulfide, Cadium Selenide, and Selenium Detectors. CdS and CdSe cells (ref. 3), listed in Table 6p-6, are available in photoconductive surfaces, areas 1 to 100 mm', potted in transparent resin or sealed in glass envelope. Some CdSe cells have very low dark conductance: --
t:: :z ~
U1
1,000 FOOTCANDLES I
1
E
O. 5 0. 2
a:
O. 1
3 0.05
I
0.0 2 ~4l----N~~12%
10% ~~~~*-+l---=O"'1
8%
1'\
100 FOOTCANDLES
f-
~
r\
10 FOOTCANDLES
0.0 1
0.00 5 0.002 1 0.00 1
2
5
'"
'"
10 20 50 100 200 500 1000 VOLTAGE, MV
FIG. 5p-5. Characteristics of silicon solar cells.
OPTICS
6--266
CL-405 CL-404 CI:403 CL-402 Cl=407
100~--~----~~T-~~--~~~'-----~----'
90
80
..... >-
(!)
w 70 z !l::
W
..J
0
w w 50 If) z 0
a. w a:: 40
If)
lI.I
:::
~ 30 ..J lI.I
a::
CL-405
10
CL-404~~~-----r----~~~r-~~~~H
CL-403
4000
5000
6000
WAVELENGTH,
7000
8000
9000
ANGSTROMS
FIG. 6p-7. Spectral response of CdS and CdSe photoconductive cells. IMAGE ORTHICON TYPE
7198
DATA
t
Sensitive area ............ " Approximately 1.1 X 1.4 in. Spectral response ....... '" S-10 Resolution .............. " Limited at high light level to approximately 600 lines; diminishes to approximately 75 lines at 2 X 10- 5 ft-c tSeeref.6,
The light-transfer characteristics of this tube are shown in Fig. 6p-12; the effect of photocathode illumination on the signal-to-noise ratio is given in Fig. 6p-13. Other types (ref. 10) (5820, 6849, 7389A, 7513, 7611, and 4401) have similar sensitive area,
6-267
RADIATION DETECTION
~
2~-+-+~~~~-~-+~~~~~--+~-+~~WL
__L-LL~~
I 1-,4~17---l~r-I-+++l-l-bil""6;;;;:"/-J..4-+++-I+I-t.....---"~...fo
If)
_UJ
1-0:
~-.J
wet
0:0: IU W Cl.
If)
400
450
500
550
600
650
700
WAVELENGTH, nm FIG. 6p-9. Spectral response of selenium photocell.
TABLE 6p-7. IMAGE CONVERTERS
Type Spectral Screen no. response volts
6914 6929 7404
S-1 S-1 S-21
Cathode diameter, in.
----
------
16,000 12,000 12,000
1.00 0.75 0.75
Resolution (Note 3) Conversion index
15 (Note 1) 10 (Note 1) 6,000 (Note2)
At center
At 0.3 in. from center
28 33 33
13 9 9
Notes: 1. Ratio of output lumens to incident lumens at photocathode (2870 K). 2. Number of output lumens produced by one incident watt at 2.537 A. 3. Resolution in line pairs per millimeter at photocathode. 4. Equivalent screen background input in incident microlumensfcm8 • 5. Equivalent screen background input in incident watts/em'.
Screen background
0.16 (Note 4) 0.21 (Note 4) 10-10 (Note 5)
6-268
OPTICS TABLE
(Sensitive area,
!
6p-8. VIDICON TYPE 7262 DATA by i in.; limiting resolution, 600 to 750 lines) Max
Avg sensitivity operation
I sensitivity opemtion
2
w w a..
a:: :2
0.1
:E
I-" ::> a.. l=>
o
G 0.01 u;
0.2-0.3 0.08-0.1
0.3-0.4
0.3-0.4 0.1-0.2
.A"
~,I a7- ~
S~>'7,\'Z
1;>-~Y
#
8 6 4
r:.,~a
x.-'i:-";L,
2f-- r-:~*-
-' c{
0.4-0.5
100
15-25 0.004
3rCf
2
C3 5
60-100 0.2
ILLUMINATION: UNIFORM OVER PHOTOCONDUCTIVE LAYER" SCANNED AREA OF PHOTOCONDUCTIVE LAYER = 1/2" x 3/8 PPRO\ I FACEPLATE TEMPERATURE =
8 6 4
U)
15 30-50 0.02 0.3-0.4 0.3-0.4 0.1-0.2
2
Highlight illumination, ft-c .............. Target voltage ......................... Dark current, p.a ....................... Highlight target current, p.a ............. Signal current, peak p.a ................. Signal current, avg p.a ..................
Min lag operation
-0~«' G;.-'
/
~
8 6 4
V
as:
/'
V
"'"
/'
aaC!,,/' a·
.-
/' :,...-
L
/'
,/
/~ ./
""
""
2 I
0.001
2 0.01
I
2 4 6 8 4 68 4 6 8 2 2 2 0.1 1 10 100 2870 K TUNGSTEN ILLUMINATION ON TUBE FACE, FOOT -CANDLES 4
6 8
4 6 8
1000
FIG. 6p-10. Typical light-transfer characteristics of Vidicon Type 7262. 0.Q35
~>- 0.030
"'''' 0.025 ~5 u:z;
~~ 0,020
[jz
5~0.015 ~
;§~0.01O "'0 ~ 0.005
o
"" r\
f:to
+
0.8731 1.746 2.619 3.492 4.365 5.238 6.111 6.983 7.856 8.72, 9.60.
11 12 13 14 15 16 17 18 19 20
10.6. 11.52 12.41 13.29 14.1, 15.06 15.9, 16.83 17.7. 18.60
10.47 11.34 12.21 13.0. 13.9. 14.88 15.7. 16.57 17.43 18.30
From K. D. Moller et al., J. Opt. Soc. Am. 66, 1233 (1965).
TABLE
6r-7.
CALCULATED WAVE NUMBERS OF THE PURE
ROTATIONAL SPECTRUM OF HYDROGEN CHLORIDE*
...111
-+ J'
0 ..... 1-> 2 ..... 3 -> 4 ..... 5 -> 6 -> 7 .....
*
1 2 3 4 5 6 7 8
HCI"
HCI·7
20.878. 41.7437 65.583. 83.3861 104.1377 124.826 145.43, 165.963
20.846, 41.681. 62.489. 83.260, 103.9818 124.63, 145.221 165.71.
J" ..... JI
8 ..... 9 -> 10 ..... 11 ..... 12 -> 13 -> 14 .....
9 10 11 12 13 14 15
HCI"
HCl>7
186.387 206.69, 226.88. 246.93. 266.82, 286.56. 306.127
186.10, 206.38, 226.54, 246.56. 266.42, 286.13. 305.66.
D. H. Martin, "Spectroscopic Techniques," North-Holland Publishing Company, Amsterdam, 1967.
6-288
OPTICS TABLE
Wave number, cm- 1
Br-8.
PURE ROTATIONAL WATER-VAPOR ABSORPTION LINES*
Intensity,t grams/em'
Wave number, cm- 1
Assignment
Intensity, t grams/em'
Assignm,ent ~
0.742 6.115' 10.846 12.683 14.645
0.01 2.63 3.06 28.0 2.37
6 3 5 4 6
1 1 1 1 4
6 3 5 4 3
5 2 4 3 5
2 2 2 2 5
3 0 2 1 0
73.262 74.109 74.881 75.523 77.322
7,170 7,350 113 10,10Q 28Q
3 5 8 4 9
3 1 3 2 4
0 4 6 3 5
3, 2 5. 0 7 4 4j 1 9, 3
1 5 3 4 6
14.944 15.834 18.577 20.705 25.085
29.2 3.67 1,790 19.1 1,180
4 5 1 5 2
2 3 1 1
3 3 0 2 1
3 4 1 4 2
3 4 0 4 0
0 0 1 1 2
78.200 78.918 79.774 80.999 81. 622
2,690 2,670 10,100 404 254
7 3 4 9 8
2 3 0 3 4
5 1 4 6 4
T 3: 3' 9 8
1 2 f 2 3,
6 2 3 7 5
30.561 32.367 32.953 36.604 37.137
48.4 54.3 858 5,590 1,710
4 5 2 3 1
2 2 0 1 1
2 4 2 2 1
3 4 1 3 0
3 3 1 0 0
1 1 1 3 0
82.155 85.636 87.760 88.076 88.882
9,700 351 2,900 39,600 1,840
4 7 5 4 7
3 3 3 1 4
2 4 3 4 3
4, 6: 5' 3 7
2 4 2 0 3
3 3 4 3 4
38.245 38.464 38.640 38.790 38.965
3.65 862 82.0 6,090 3.66
7 3 6 3 8
2 1 3 2
5 2 4 1 4
8 2 5 3 7
1 2 4 1
8 1 1 2
89.583 92.528 96.070 96.208 96.231
3,060 34,200 6,000 2,110 1,230
5 2 6 6 6
2 2 3 1 4
4 4 5 2
5 1 6 6 6
1 1 2 0 3
5 0 5 6 3
39.113 39.715 40.283 40.988 42.640
6.66 1. 27 1,900 1,640 23.9
7 8 4 2 7
4 5 2 2 4
4 3 2 0 3
793 10,900 12,100 555 42,600
6 2 5 8 5
2 2 1 2 0
4 0 4 6 5
5 1 4 8 4
3 1 2 1
3
43.240 43.639 44.099 44.859 47.055
23.1 1. 65 192 1. 22 4,860
8 8 6 7 5
2 4 2 4 2
7 5 5 4 3
5,780 1,960 15,700 6,020 7,150
5 4 5 4 6
4 4 1 4 2
3
(j
1
6 7 4 2 6
5 6 1 1 5
1 2 3 2
98.808 99.025 99.095 100.026 100.509
'7
8 5
3 1 3 1 1
4 8 2 7 4
101. 529 104.293 104.573 105.592 105.659
9
5
1
1
1
1
1
3 7 4
1
5 3
2
0 5 1 5
4 4 4 6
3 0 3 1
1 4 2 6
I
48.058 53.444 55.405 55.701 57.265
31 2,360 6,190 14,700 13,800
7 4 2 2 3
2 1 2 1 0
6 3 1 2 3
6 4 2 1 2
3 0 1 0 1
3 4 2 1 2
106.147 107.091 107.747 111. 051 111. 124
2,090 1,250 4,500 880 13,500
5 7 6 7 3
4 3 4 4 2
2 5 3 4 2
5 7 6 7 2
3 2 3 3 1
3 6 4 5 1
58.777 59.871 59.950 62.301 63.996
1,040 1,270 1,670 5,330 989
6 6 7 5 5
3 2 3 3 2
3 4 4 2 3
6 6 7 5 4
2 1 2 2 3
4 ll6.596 5 . 117.066 5 ll7.969 3 120.072 2 120.523
1,340 288 4,560 15,000 2,070
8 9 7 6 8
4 5 1 0 3
5 4 6 6 6
8 9 7 5 8
3 4 0 1 2
6 5 7 5 7
64.022 67.249 68.062 69.196 72.187
3,090 281 2,500 1,700 9,130
3 8 4 4 3
2 3 3
2 5 1 3 3
3 8 4 3 2
1
2 2 2 0
3 6 2 2 2
46,700 155 895 1,610 256
6 8 9 7 8
1 3 2 2 5
6 5 51 9 7 8
0 4 1 1 4
5 4 8 7 4
1
1
121. 905 122.415 122.847 123.128 124.137
:
~I
6-289
FAR INFRARED TABLE
6r-8.
(Continued)
PURE ROTATIONAL WATER-VAPOR ABSORPTION LINES*
Wave number, cm- 1
Intensity, t grams/em'
124.659 126.697 126.995 128.599 130.856
200 5,740 41,500 1,650 909
9 6 4 7 6
4 1 2 5 5
6 5 3 2 1
9 5 3 7 6
3 2 1 4 4
131. 742 131. 877 131. 904 131.966 132.459
2,990 2,770 578 1,000 871
5 6 7 5 8
5 5 5 5 5
0 2 3 1 4
5 6 7 5 8
132.658 133.433 134.097 135.213 135.855
33,000 3,450 124 241 338
3 7 9 0 9
2 2 5 4 3
1 5 5 7 7
137.385 138.823 138.993 139.785 140.711
139 935 38,800 13,100 12,500
0 8 7 7 5
5 1 0 1 2
141.435 144.958 148.655 149.054 150.515
2,880 139 535 26,400 80,000
8 0 3 3 3
151. 303 152.507 153.455 154.088 155.736
17,000 444 30,300 208 159
7 0 6 9 8
156.372 156.447 156.451 156.480 156.556
867 350 483 1,050 290
157.588 157.923 158.904 160.169 160.207 161.789 165.829 166.217 166.704 170.359
vVave number, cm- 1
Intensity, t grams/em'
7 4 2 3 2
173.282 173.500 176.010 176.151 177.540
4,300 8,370 18,200 6,080 22,600
8 4 9 9 4
1 2 0 1 3
7 2 9 9 1
7 3 8 8 3
2 1 1 0 2
6 3 8 8 2
4 4 4 4 4
1 3 4 2 5
178.474 178.663 179.073 179.106 181.389
235 271 709 200 14,500
0 7 0 8 8
1 7 2 7 2
9 0 9 2 7
0 7 0 8 7
0 6 1 6 1
0 1 0 3 6
2 6 9 0 9
1 3 4 3 2
2 4 6 8 8
183.465 188.189 193.480 194.328 194.387
1,120 15,700 7,990 3,410 10,200
5 5 9 0
2 3 8 0 0
5 4
~
3 3 1 0 1
9 9
0 2 2 1 0
5 2 7 9 9
6 7 7 7 4
0 8 6 6 4
4 0 1 0 1
7 8 6 6 3
195.804 197.256 197.498 197.719 202.470
2,650 108 2,810 297 29,700
9 0 9 1 6
2 3 2 1 3
7 7 8 0 4
8 9 8 1 5
3 4 1 0 2
6 6 7 1 3
2 2 3 3 3
7 8 0 1 0
8 0 3 2 2
1 1 0 2 2
8 9 3 0 1
202.690 202.915 208.451 210.884 212.566
89,800 30,000 47,400 476 5,100
4 4 5 5 1
4 4 3 4 0
1 0 2 1 1
3 3 4 5 0
3 3 2 1 1
0 1 3 4 0
1
3 2 6 6
2 8 5 3 2
6 0 5 9 8
2 2 1 5 5
5 9 4 4 3
212.591 212.633 213.924 214.556 214.855
1,700 1,410 5,690 4,330 218
1 0 7 0 6
1 1 3 2 3
1 9 5 9 3
0 9 6 9 6
0 2 2 1 0
0 8 4 8 6
7 6 8 6 7
6 6 6 6 6
1 0 3 1 2
7 6 8 6 7
5 5 5 5 5
2 1 4 2 3
214.878 215.126 216.876 221. 673 221. 735
217 362 112 15,800 518
6 3 2 5 0
4 3 2 2 2
2 1 1 3 8
6 2 2 4 9
1 0 1 1 3
5 2 2 4 7
9,510 28,700 1,500 505 443
8 8 9 9 9
0 1 1 2 3
8 8 8 8 6
7 7 9 9 8
1 0 0 1 4
7 7 9 9 5
223.712 226.273 227.030 227.825 230.732
9,060 21,200 523 64,300 756
8 5 7 5 2
3 4 4 4 0
6 2 3 1 2
7 4 7 4 1
2 3 1 3 1
5 1 6 2 1
385 169 1,170 7,410 66,200
4 1 8 7 4
3 2 2 2 3
1 9 6 6 2
4 1 7 6 3
0 1 3 1 2
4 0 5 5 1
230.743 231. 213 231. 874 232.118 233.327
2,270 1,960 188 659 1,490
2 1 1 1 9
1
2 0 8 0 7
1 0 0 0 8
0 2 4
1 9 7 9 6
Assignment
Assignment
1
3 2 3
1
2
6-290 TABLE
OPTICS
fir-8.
(Continued)
PURE ROTATIONAL WATER-VAPOR ABSORPTION LINES*
Wave number,
Intensity, t grams/em'
Wave number, cm- 1
Intensity, t grams/em'
244.216 244.535 245.344 245.753 247.915
2,040 737 8,920 3,690 38,500
0 1 6 4 6
3 2 3 3 4
8 9 3 2 3
9 0 5 3 5
2 3 2 0 3
7 8 4 3 2
311. 744 314.741 315.088 323.633 323.935
146 382 3,060 5,330 9,280
2 4 8 6 8
4 4 4 3 5
9 1 4 4 4
1 3 7 5 7
3 1 3 0 4
8 2 5 5 3
248.826 248.831 249.477 249.900 253.814
904 301 268 808 13,200
3 3 2 2 6
0 1 1 2
3 3 1 1 2
2 2 1 1 5
1 0 2 1 3
2 2 0 0 3
327.571 327.610 328.173 334.617 335.160
5,060 15,200 3,160 435 4,700
7 7 8 5 7
6 6 5 4 2
2 1 3 2 5
6 6 7 4 6
5 5 4 1 1
1 2 4 3 6
253.946 253.975 256.117 257.109 266.199
20,500 61,600 272 281 6,600
5 5 7 1 7
5 5 3 3 4
1 0 4 9 4
4 4 7 0 6
4 4 0 2 3
0 7 8 3
340.556 343.212 349.792 349.792 351.786
1,710 1,220 3,160 9,500 7,120
8 9 7 7 8
3 5 7 7 6
5 5 1 0 3
7 8 6 6 7
2 4 6 6 5
6 4 0 1 2
266.843 266.845 267.552 271.851 276.150
108 325 295 316 2,960
4 4 3 2 6
0 1 1 3 2
4 4 2 0 4
3 3 2 1
1 0 2 2 1
3 3 1 9 5
352.006 354.125 354.595 357.270 358.492
2,380 3,390 3,850 2,370 1,250
8 9 9 6 0
6 4 5 4 5
2 5 4 3 6
7 8 8 5 9
5 3 4 1 4
3 6 5 4 5
277.430 278.263 278.523 280.358 281. 168
123 37,700 12,600 8,840 101
7 6 6 8 9
5 5 5 4 4
2 2 1 5 5
7 5 5 7 9
2 4 4 3 1
5 1 2 4 8
369.343 370.002 374.521 374.527 375.342
124 1,250 4,420 1,470 976
1 7 8 8 9
5 3 7 7 6
7 5 2 1 4
0 6 7 7 8
4 0 6 6 5
6 6 1 2 3
281. 915 282.263 284.381 284.778 289.451
1,870 20,800 103 105 12,500
5 7 3 5 7
3 4 2 0 3
3 3 1 5 4
4 2 4 6
0 3 3 1 2
4 4 0 4 5
376.224 376.377 383.826 384.845 385.502
2,940 100 447 904 400
9 2 0 7 5
6 5 5 4 4
3 8 5 4 1
S 1 9 6 4
5 4 4 1 1
4 7 6 5 4
290.737 298.430 301. 871 303.001 303.005
1,180 1,310 6,710 28,500 9,5lO
9 0 7 6 6
4 4 5 6 6
6 7 3 1 0
8 9 6 5 5
3 3 4 5 5
5 6 2 0 1
394.272 394.272 396.435 397.325 397.681
2,360 786 791 1,950 1,050
8 8 8 9 0
8 8 2 3 6
1 0 6 6 5
7 7 7 8 9
7 7 1 2 5
0 1 7 7 4
303.116 304.895 309.474
20,300 151 116
7 1 6
5 4 4
2 8 3
6 0 6
4 3 1
3 7 6
398.959 398.994
606 1,820
9 9
7 7
3 2
8 8
6 6
2 3
Assignment
cm- 1
"
1
* Only the following lines are included in the table: 50 1
< v < 400 < v < 50
cm- 1 cm- 1
p
cm~l
100 1>1
Private Communication from Clough, S. A. and W. S. Benedict.
t Intensity values are good at best to three significant figures.
Assignment
6-291
FAR INFRARED
Sr-5. Far-infrared Polarizers. Polarizers for the far infrared have been made of stacks of dielectric plates at the Brewster angle, wire grids, and pyrolitic graphite. In addition, a Michelson interferometer acts as a polarizer when the radiant flux is incident on the beam splitter at the Brewster angle (cf. section on beam splitters). Pile-of-plates polarizers have been discussed by Bird and Schurcliff [1], and a polarizer using polyethylene sheets has been reported by Mitsuishi et al [2]. The light is incident on the plates at the Brewster angle, and the polarizance of the device is
p
(6r-1)
where n is the refractive index andm the number of plates. (Polarizance is defined as the percent polarization of the output beam when the input is completely unpolarized.) Forfar-infrared polarizers two different plate thicknesses must be used to avoid interference effects which seriously reduce the polarizance at certain wavelengths. This polarizer is more easily built in the laboratory than the grating polarizer, but occupies more instrument space. Figure 6r-11 illustrates the polarizance of pile-of-platespolarizers using various combinations of polyethylene (n = 1.5) sheets. Equation (6r-1) gives P = 88 percent with 10 sheets and 97.5 percent with 15 sheets. 100
~---_c.._A_._J!._f:,.-"'-·~·~~::';:'·-~"~_~
(4)
(3)
~~-,IJ..,'"
I
______
... _ ---~-"---A"''' -- .6.......
,
.... It.
I
f
I
. /
\
I
\(2),/ .... A'
I
.'
'----0-
9 SHEF:TS d=20 ,um
-A---A-
9 SHEETS d=30 fLm
- - - - - 9 SHEETS (20 fLm)
+9 SHEETS (30 p,m)
-.-'-12 SHEETS (20 fLm) +12 SHEETS (30 p,m)
r!
70 80 90 100 WAVELENGTH, fLm
I
120
150
200
FIG. 6r-11. Degree of polarization with different numbers and thicknesses of polyethylene sheets.
The wire grid operates on the principle (discovered by Hertz) that radiation polarized parallel to the grids is reflected, while that polarized perpendicular is transmitted, for wavelengths larger than the grid constant. These polarizers have been made by evaporating metal at a large angle of incidence onto transmission gratings of the appropriate spacing so that one side of each groove is coated while the other remains transparent. The results obtained by Hass and O'Hara [3] are summarized in Tables 6r-9 and 6r-10, and the transmittance of their polarizers is shown in Fig. 6r-12.
6-292
OPTICS TABLE
Designation
DP1 DP2 NRL 13M
6r-9.
DESCRIPTIONS OF POLARIZERS
Substrate and thickness
Source of grating
Diffraction products Polymethyl methacrylate, 0.051 mm Diffraction products Polymethyl methacrylate, 0.051 mm Naval Research Lab. Polyethylene, 0.152 mm Buckbee Mears Mylar sheet, 0.038 mm
Conductor
Periodicity
Aluminum (lightly coated) Aluminum (heavily coated) Aluminum (medium coat) Gold strips 0.01 mm wide
2,160 grooves/mm* = 0.463 Jlm/groove 2,160 grooves/mm* = 0.463 Jlm/groove 600 grooves/mm* = 1.69 Jlm/groove 39.3 lines/mm = 25.4 Jlmjline
* The blaze angle is about 20°. TABLE
Wave number, cm- 1
2.5 49.5 83 160 300 600 1,025 2,000 3,500 5,710 10,000
6r-IO.
TRANSMITTANCE AND DEGREE OF POLARIZATION
Degree of polarization P, % DPI
DP2
99.0 97.8 98.8 98.9 98.1 98.2 96.3 88.0 71.0
.... ... . . ...
....
....
99.0
. ... ... . 99.4 99.5 98.4 95.0 84.1
Transmittance Tl
NRL
BM
DPI
DP2
... .
>99.5 98.4 98.4 89.0
0.985 0.86 0.86 0.86 0.65 0.94 0.86 0.90 0.90
.... .... ....
96.4 97.9 98.0 96.6 96.0 89.0 63.0 33.0
. ..... ... ... ...... ' . 0 •••
...... . .....
... . ....
. .....
.
...
. ....
0.80
.... .... 0.53 0.65 0.54 0.39 0.27
NRL
BM
....
>0.995 0.81 0.86 0.67
0.87 0.88 0.83 0.84 0.81 0.57 0.43 0.35
1LI
~ ~
I-
~ 0.50 :i0.25
c::
I-
0.7 0.50 0.25
\ 100
BM 300
500
1500 2500 3500
WAVE NUMBER, em-! FIG. 6r-12. Transmittance of gratings. The DP polymethyl methacrylate grating and the NRL polyethylene grating were unaluminized and measured in unpolarized radiation. The BM metal-strip grating was measured in the high-transmission direction in polarized radiation.
6-293
FAR INFRARED TABLE
6r-11.
TRANSMITTANCE OF PYROGRAPHITE POLARIZER PGPI FOR
. RADIATION WITH ELECTRIC FIELD IN THE C DIRECTION
Wave number, cm- 1 17.1 22.7 33.3 42.0 51.0 58.8 66.2 71.0 77.0 81.5
TABLE
6r-12.
± 2% 0.519 0.504 0.512 0.487 0.495 0.519 0.520 0.505 0.507 0.494
T,
PERCENTAGE POLARIZATION OF PYROGRAPHITE POLARIZER PGPI
Wave number, cm- 1
T2 X 10'*
16.7 21. 7 28.6 500 666.7 1,000 2,000
1.7 4.5 2.4 7.5 10.7 11.4 7.7
Percentage polarization
99.65 99.11 99.53 98.03 97.45 96.20 93.58
± 0.35 ± 0.21 ± 0 .. 06
* T2 is the transmittance for the unwanted direction of polarization. A thin foil of pyrolitic graphite, which has a layered crystal structure, acts as a polarizer [4] in both the far and the near infrared. The transmittance for the desired polarization is rather low (about 50 percent), but the polarizance is above 99 percent. The results obtained by Rupprecht et al. [4] are summarized in Tables 6r-ll and 6r-12. References for Sec. 6r-1i 1. Bird, G. R., and W. A. Schurclff: J. Opt. Soc. Am. 49, 235 (1959). 2. Mitsuishi, A., Y. Yamada, S. Fujita, and H. Yoshinaga: J. Opt. Soc. Am. 50,433 (1960). 3. Hass, M., and M. O'Hara: Appl. Opt. 4, 1027 (1965). 4. Rupprecht, G., D. M. Ginsberg, and J. D. Leslie: J. Opt. Soc. Am. 52, 665 (1962).
Gr-G. Optical Constants of Far-infrared Materials. Precise values of refractive index and reasonably good values of absorption coefficient have been determined for far-infrared materials by two techniques. Both are basically interferometric: one is the use of a Michelson Fourier spectrometer with the sample in one arm [1,2], referred to as an "asymmetric Michelson"; the other is the analysis of the channelspectrum fringes (fringes of equal chromatic order) resulting from interference between the multiple beams produced by internal reflections in a plane-parallel sample of material [3]. In the asymmetric Michelson method, the sample is placed in one arm, and an interferogram is taken; the amplitude of the resulting spectrum gives the absorption coefficient while the phase gives the refractive index. The analysis of the channel spectra is based on the fact that the fringe position depends on the index only, whereas the amplitude depends on both index and absorption coefficient. The channel-spectrum fringes are revealed by spectra, which may be taken with either a conventional or a Fourier spectrometer. In spite of the fact that the absorption coefficient can in theory be derived by the above methods, in most of the data given below it is derived from anBJysis of a low-
6-294
OPTICS
resolution transmission spectrum, using the refractive index found in the interferometric method. This is so because discrepancies between absorption coefficients calculated from the asymmetric Michelson or channel spectrum and those calculated from the transmission measurements are always resolved in favor of the latter. The tables and graphs below list the optical constants for the following materials: Mylar (polyethylene terephthalate) Irtran VI (hot-pressed CdTe) Teflon (polytetrafluoroethylene) CdTe (crystalline) GaAs (crystalline)
Crystal quartz Sapphire Germanium Silicon Fused quartz
The quantites given are index and absorption coefficient imaginary part of the complex refractive index, by Ol
=
Ol
which is related to k, the
4... k
, 10 ) (11'0) 11 -> (04 00) (11'0) 10 -> (0400)9 HCN (04 00)9 -> 8
2
11
CH,CN 334.4 334.8
29.90 29.87
18
CH, and 16NH, 110.240 113.311 138.768 165.150
90.711 88.253 72.063 60.551
1
CD, 181. 789 189. 948 (CW) 194.706(CW) 204.387
55.009 52.646 51. 359 48.927
2 X 10- 4 3 X 10-.
+ ND, (22 00)23 -> (22 00)22 } (22 00)22 -> (09"0)21 (2200)21-> (09"0)20 DCN (09"0)20 -> (09"0) 19
1,8, and 14
FAR INFRARED TABLE
A, pom
6r-23. U,
LASER LINES OBSERVED INH 20 AND
cm- 1
Peak power, W
D 20
Assignment
Refs.
H 20
53.906 55.077(CW) 57.660 67.177
185.51 181. 56 173.43 148.86
0.0008 0.06 0.02 0.01
73.402 78. 455 (CW) 79.106(CW) 89.775 115. 32(CW) 118. 65(CW) 120.08 220. 23 (CW)
136.24 127.46 126.41 111.39 86.64 84.28 83.28 45.407
0.002 0.007 0.006 0.006 0.0007 0.001 •
o.
••
,
0.' 0
••
(020) 550 -> (100)9,. -> {(100)6,, -> (020)441 ->
(020) 541 (020)8" (020)550} (020)432
3 4,5,6
(100)808 -> (020)8 •• (020) 8" -> (020) 8aG (020)835 -'+ (001)642 -> (001)642 -> (100)523 ->
(020)82. (020)661 (001)633 (020)560
8
D 20 56.845 71.965 72.429 72.747 73.337 74.545 76.305 84.111 84. 291(CW) 107. 71 (CW)
175.92 138.96 138.07 137.46 136.36 134.15 131. 05 118.89 118.64 92.84
TABLE
6r-24.
3
7
LASER LINES OBSERVED IN NEON
Continuous power, W
A, pom
u, cm- 1
50. 70 (CW) 52. 39(CW) 55. 68 (CW) 72. 15 (CW) 86.9(CW) 88. 46 (CW) 89. 93(CW) 93. 02 (CW) 106. 02 (CW) 124.4(CW)
197.2 190.9 179.6 138.6 115.1 113.0 111.20 107.50 94.322 80.39
"'10-' ",10-'
79.30 75.30
"'10-' "'10-'
Assignment
Ref.
--
126. 1 (CW) 132.. 8(CW)
>1O-~
7p[3/2], - 6d[3/2],0 7p'[l/2h - 6d'[3/2],o 7p[3/2h - 6d[7/2].0 8p'[l/2]0 - 7d'[3/2h o 8p'[3/2],- 7d'[5/2].0 8p[3/2h - 7d[5/2],0 8p[5/2]3 - 7 d[7 /2]3 0
lOp[l/2]0 - 9d[3/2h o 9p[3/2h - 8d[5/2],0 9p[3/2], - 8d[5/2]3 0
9
6-312
OPTICS TABLE
6r-25.
A,
Gas
ICN He CHaCN and (CHa),SO.
TABLE
LASER LINES OBSERVED IN MISCELLANEOUS GASES
6r-26.
/Lm
773.5 95.788 119.0
U,
cm- 1
12.928 109.94 84.0
Peak power, W
3
Assignment
3 p 'P , O
-
Ref.
3d l D,
12 10 18
LASER LINES WHOSE FREQUENCIES HAVE BEEN DETERMINED BY DIRECT COMPARISON WITH A KLYSTRON
(The wavelengths are calculated using C = 2.997925 X 10 8 m/sec.) Gas
Frequency, GHz
I
lI.,/Lm
U,
cm- 1
Ref.
--
DCN
1,466.787 1,539.257 1,539.745 1,577.789 1,578.279
204.3872 194.7644 194.7027 190.0080 189.9490
48.92674 51. 34409 51. 36035 52.62937 52.64571
15
D.O
1,578.279
189.9490
52.64571
16
C.N,
1,539.756
194.7013
51. 36072
16
310.8874 336.5583
32.16599 29.71253
17
HGN
964.3123 890.7595
References fer Sec. Sr-8 1. Mathias, L. E. S., A. Crocker, and M. S. Wills: IEEE J. Quantum Electron. QE-4, 205 (1968). Lide, D. R., Jr., and A. G. Maki: Appl. Phys. Letters 11, 62 (1967). Mathias, L. E. S., and A. Crocker: Phys. Letters 13, 35 (1964). Hartman, B., and B. Kleman: Appl. Phys. Letters 12, 168 (1968). Benedict, W. S.: Appl. Phys. Letters 12, 170 (1968). Pollack, M. A., and W. J. Tomlinson: Appl. Phys. Letters 12, 173 (1968). Muller, W. M. and G. T. Flesher: Appl. Phys. Letters 8, 217 (1966). Muller, W. M., and G. T. Flesher: Appl. Phys. Letters 10, 93 (1967). Patel, C. K. N., W. L. Faust, R. A. McFarlane, and C. G. B. Garrett: Proc. IEEE 52, 713 (1964). 10. Mathias, L. E. S., A. Crocker, and M. S. Wills: IEEE, J. Quantum Electron. QE-3, 170 (1967). 11. Steffen, H., J. Steffen, J. F. Moser, and F. K. Kneubuhl: Phys. Letters 20, 20 (1966). 12. Steffen, H., J. Steffen, J. F. Moser and F. K. Kneubuhl: Phys. Letters 21, 425 (1966). 13. Gebbie, H. A., N. W. B. Stone, W. Slough, J. E. Chamberlain, and W. A. Sheraton: Nature 211, 62 (1966). 14. Maki, Arthur G.: Appl. Phys. Letters 12, 122 (1968). 15. Hocker, L. 0., and A. Javan: Appl. Phys. Letters 12, 124 (1968). 16. Hocker, L. 0., D. Ramachandra Rao, and A. Javan: Phys. Letters 24A, 690 (1967). 17. Hocker, L. 0., A. Javan, D. Ramachandra Rao, L. Frenkel, and T. Sullivan: Appl. Phys. Letters 10, 147 (1967). 18. PrettI, W., and L. Genzel: Phys. Letters 23, 443 (1966). 19. Gebbie, H. A., N. W. B. Stone, and F. D. Findlay, Nature 202, 685 (1964). 20. Kotthaus, J, p,: Appl. Opt. 7,2422 (1968). 2. 3. 4. 5. 6. 7. 8. 9.
6s. Optical Masers ROBERT J. COLLINS
University of Minnesota
68-1. Introduction. In the short time since the first explicit proposals [1] that stimulated emission be used as an amplifying mechanism, devices employing this principle have become common in the microwave and optical regions of the spectrum. Less than three years passed between the proposal and the observation by Zweiger and Townes [2] of gain ammonia gas at 23.879 kmc. After these initial experiments, it was clear that stimulated emission could be used to build either amplifiers or oscillators. The original work led to the construction of an amplifier using ammonia gas, in which the inverted system was prepared by the electromagnetic separation of the excited ammonia molecules. The device was called a maser, which is an acronym for Microwave Amplification by Stimulated Emission of Radiation. In 1960, when Maiman [3J first reported stimulated emission in the optical region of the spectrum, an additional acronym came into use-"laser" for Light Amplification by Stimulated Emission of Radiation. The extension from the microwave region to the optical portion of the spectrum of the use of stimulated emission as an amplifying mechanism followed an explicit proposal to use a 3-level energy system for a maser. In this suggestion, pumping or inversion was to be accomplished by an external energy source and stimulated emission was to occur between two of the three levels. This Bloembergen proposal was first successfully carried out by Scovil, Feher, and Seidel [5]. In the construction of oscillators the active material must be contained in a cavity with means to control the mode of oscillation. At frequencies 4
. ... '" .
2P2
'"
.. . 4d 4f ... .. .
19 3 83 17 2,300
4 --+ 3
2Pl 5f
2 1 3 1 6 1
.
.. .... '" . . ... . ... '" .
500 1,500 2,500
105,000
6,950
lOt 1 20 70 10 5,000
* Change in the I, scale. From here on National Bureau of Standard. values. t Wavelengths and intensities from here on from Humphreys and Kostkowski, J. Research Nat!. Bur. Standards 49, 73 (1952). The classification is indicated by capital letters for singlets, lower-case letters for triplets. A few of the He I! lines are also listed. They have elaborate fine structures. Neon 1. The neon spectrum is moderately rich in lines and may serve, like the other rare-gas spectra, as an easily obtained comparison spectrum. Any neon-sign manufacturer can produce a satisfactory tube. The wavelengths of the strong lines have been measured with great accuracy and have been adopted as international secondary standards,1 often replacing the primary standard for interferometric measurements. Table 7e-2 lists the principal neon lines. The wavelengths are interferometric wavelengths when followed by a capital letter. B, BurriS, Adams, Longwell, J. Opt. Soc. Am. 40, 339 (1950) iI, Humphreys, J. Research Natl. Bur. Standards 20, 17(1938) I
Trans. Intern. Astron. Union 6,86 (1935); 9, 204 (1957); 10,229 (1958).
7-33
IMPORTANT ATOMIC SPECTRA
TABLE 7e-2.THESPECTRUMOF,NEON I Classification Wavelengtli 2,647,42 2,675;2.4. ' 2,675[64 ' 2 ;.872. 663 2,913: 168
3s 12 3s11
2,982 2,992 2,992 3,012 3,012
8p, 7p;, 7p;,
3811 38: 0 3812
2,932; 721, , 2,947f2.97 2,974: 7Ho. , 2,980:642 2,980: 922. 663 420 , 438 129 955
5P:,
IS 6
.41/' , ,
1~,
6poo 5p12 5p12 5P:, 5p;,
1~4
3S12
5p23 5poo 5po, 5p" 5p11
lS6 1~4
3s,. 3s11
3,126i1986B 3,148~6107 B
7p,.7·
6P:o
Is 6 IS 4 1s4 Is,
3s:,
3811
61/4
5R' 4P4 4p. 4p, 4p6
1s6 Is, Is,
'4p,
1~4
4p,o 4p,
1~4
4117 4p,
5p2'
1;S4
3s:, 3s:, 3s61 3s:,
5p;0 5]1;. 5poo 5pu
1~. .' 4p, liS. 1"'4p4
,.
!
..... .....
. .... . ....
2.73. 3.16
7 ..... 8 , .. " " , 9 .. '," 5,5 .. '." ..... 6
·.... ..... · .... -. . ....
3,30 3.21 3.6? 2.7 2.80
9
.....
3.52
. ....
3.32
.-,
.. _.
.' .
'-'-'-~
2.93 2.98
I
.....
6' 9 8 8 7
0.'
•
••
0,0'
0
•
•••
.... ••
•
i
"
"
0,'"'
'-"',
..... .....
.....
.... " .....
.....
6 6 10 15 6
. .... ..... .. , .
. .... . ....
10 6 6 8 6·
.... .
.
....
3.12 2.7 2.80 3.61 2.44
I
3) 11)3[4107 B
3,167~5762 B
3 ,369~8076. B , 3,36919069 B ' 3,375:6489 B ', .
'3&.,
3s~:
5p22
Is.
4PB
5po,
lb.
411,0
3s.,. 3s 12 3s12
4p;. 4P:, 4p;,
1iS6
3P4 3p. 3p5
I
1s6 1s, 5
: 3,417 9.o3LB' 3,418 0066 H 3,423,9120 B 3,447,7022 B 3,450.7641.B
3s 11 3s 11 3s11 3s12 3s12
4P;. 4P;, 4p;, 4p12 4p11
3s11 3s;0 3s12
4poo 4p~,
3P4 3p, 3p, 3p,
ls4
1~4 1s4 1s6 1s6
3~7
,
3,454; 1942 B . 3,460,5235 3,464.3385 3,466.5781 3,472.5706
log I,
--- ---
6. 6
4p, ,4p7.
,
8 8 8 5 8
n
411'
1s6
If' Is.
,
6P6 5p,
3811 i
log 12
Paschen
. ,3811 .3812 38: 0 38:.
3811
3,017 348 3,057 388 3,076 971
log I,
10 System.
B B B B
3,498: 0632. B 3,501.2154B 3,510.7207 B 3,515.1900 B 3,520.4714 B
3s~0 3s 12 '3s 11 3s 11 3s12 3s 11 3s~, 1
4P22 4p;, 4p23 4P12 4p11 4p01 4P22
4p~0
Is, Is 5 Is, Is 6
3p, 3p, 3pB 3p6 3p,
1s4 1s4
3p, 3P7
186
3p,o
h4
1s4 l~,
I
3PB ;3p,
..-
I
7 8 6 8 20
..... ..... .. ,'.. · .. . . .... . .... . ....
4.62 4,14 3.57 4.91 4.18
.... ..... . .... . .... .....
4.72 4.37 4.27 4.64 4,90
..... ..... . .... .... . ..... ..... . .... ...... "' ....
4.45 4.53 3.85 4.55 5.32
';'"
.
. ..... , .. . . ','"
0
••••
~
,.'
.... . .....
.....
:1
2.21 3,QO 4,36 2,98
"
7 7 7 8 10
2.4?
ATOMIC. AND MOLECULAR PHYSICS
7-34
TABLE.
7e-2.
I (Continued)
THE SPECTRUM OF NEON
..
Classification System. -
_ ..
--_..
B3,59315263 B 3,593,639 B 3 ,600 ~ 1694B 3/609: 1787B : i
3s11 3S~1 38~1 3S~1 38~0
4pOI 4P~2 4P~1 4P~1 4pOl
1s4 "3pI0 1:s 2 3p4 1s2 3P2 182 .' 3P6 3P10 lila
3~1
1~2
38~1 · 38~1
4poo 4p12 4p11 4P22 4pOl
.3pOl 3pOl 'gPOl .3Pfr1 ' .3paa
7 7 7 7 6
7df)0 6d;2 8812 78~1 9d' 4
7d 6 2p10 681If" 2p10 686 2P10 ·582 2P10 2Pe T 9~~
4 5 5 5 5,
10812 9d3a 6d12 6d01 6doo
2p& 2Pa 2p10 ,: 2p10 2p10'
9£14 6da 6d 6 6da
3 4 8. 8 ·,7
8du 4,433;7239 B ·3P2a 9812 4,460i175 M 3p2' 4;466;8120B 3p22 ' 8d 33 4,,:475!656M' · 3P11 7d~2 7811 4,483! 199B : 3pOl
2p& 2ps 2Pa 2P7 2P10
8~ 786 8d, 781" 584
5 6 5 6 .. 7
3p~1 , 7812
i
4,381 ;220 . .M 4;-395,556 M 4,422 5205.B: 4,424~8096 B ' 4o,'425.! 400 M
i
4.488;0926 4,500!182 4,517!736 4,525:764 4,'5361312
'
B M M M
4,.537:7545B 4;538:2927 B 4,MO;3801B: 4;552.598 M 4';565!888 M 4;575:0620 4;:582 : 035· 41..582;4521 4;'609:910 .. 4,'614.391
B M B ' M M
. 38~1
3~1
· ·3pa. ,3p22 · 3pOl · ·3P01 · 3pOl
I
I
1s2 182 1~2
!.s2
88~
3Pll 3p;2 3Pll 3pOl
8d;2 8d~a 8d22 5d~1
2P10 2p6 2P4 2P7 2P10
586 ,88;' 881'" 8d;' 58;
8, 4 6 5' 7
3pOl 3P2'd 3p2' 3pa 3p12 '
5d~2 7d23 7d'4 9s 11 8d23
2p10 2ps 2h 2p7 2Pa
581"" 7d~ 7d~ 784 8d~
10
3P22 3P22 3pas 3p;1 3p22
7i1 s, 6d~s 8812 7d;2 8811
2Pa 2ps 2pg, 2p6 2ps
7d, 68'"1 68s 78"1 684
i
log Ia ---
3 10 9 7 6
3Pa 3pa 3P7 3pa 3p10
3;633;6643B: 3j682;2421B: 3 i685i7351B ' 37
j
(]
.J
.
W
.
0>
8 lil FIG. 7e-1. Photoelectric traces of the neon spectrum, microwave discharge at 1.25 mm. Wavelength range is 3,000 to 10,000 A.
Neon Microwave 1.25 mm Pressure End-on View
4.0 3.5
------'----~-----------------
3.0
. .. 2~~====~==~==========:=====~====~::: ;: f! f! ... !:! '" '""-
?-.
H
-
P Q
5881
~?
H
o
:;;1
~
5589 5585
A
~
5872 5868 5852
:;;1
o
Il
~
~
5562 5559
I-
5828
f-
5820 5816 5811 5804
f-= 6421 6409
I
=b}
-
-1=1
-
~
~
-
;l
°i'c"
-R
1-1= .
--:
-
2-
.,.
- - 1:
57~
-.::Ii -.::Ii
\ I:-
~ ~ ~~
ltIOIt>OltlOIt>
co co
l
~~i~
~.
. _t9,ogb'5;;;;;b
!8 '"
'"fi:i
~:s
FIG. 7e-2. Photoelectric traces of the argon spectrum, microwave discharge at 6.5 mm pressure. Wavelength range is .3,500 eto 10,000 A.
50000 20000 10000 5000
I
!
2000 1000
!!
.g :.. '" t 0
.500 200 100 50 20 0.
.... 0
-i
.N'
ll! 20000 10 000
5 000 2 000 1 000 500
I
c:.:;;
I
II
200 100 50 20 0
FIG. 7e-2 (Cont?:nued)
\I\.
,
~
IX! I.e
-I-
5495
J..
4746
I-
4989
05473 ".5457 05451 05439
i-
"""
: - t-=~
5421 5410
:-
4956
4702
f-,i:j
1-
f-.
.5888 ·5882
5373 5860
'"
"' .... .... '"
0>
5.0
4.5 4.0
3.5 3.0 2.5
1.11 \1, .....,.jW'
~~
II I
"""" FIG. 7e-3 (Continued)
III
...
...C;;
,.....; ~
I
l;4739 KrU 4724
I I
r
III
5993 5977
ifPr
5476 490 -5458
-
. 5447
4969 4955
'">
I......,
4694 '"
~ ~ ~
~ ~
§ ~:>
E-
'"
FIG. 7e-3 (Continued)
III
~ III ~,
II I
I
1"
7-63
IMPORTANT ATOMIC SPECTRA
Krypton Microwave 1.6 mm Pressure End-on View
5.5
--
5.0 4.5 4.0 3.5
\A
1
AJ
A
~
6.0
5.5
5.0 4.5 i
I
4.0 3.5
I
!
...
I
FIG. 7e-3 (Continued) Krypton Microwave 1.6 mm Pressure End-on View
5.S~
5.0
:::
4.5 4.0
====:;oj )g
t
'"fil
...
~~
~'" ~'"
6.5 6.0 5.5 5.0 4.5 4.0
!
'"~ 0
'"....ex>
"'''' ........ ...... o~
....... "'''' ... '" "'~
!II '"ex> ~
FIG. 7e-3 (Continued)
Xenon 1. Wavelengths in Table 7e-5 are from Humphreys and Meggersl and Humphreys and Kostkowski 2 (above 11,000 A). Notation is the same as for Ne I and A I. Intensities are as follows: Io, conventional estimates quoted from the literature; II, microwave discharge, pressure of 0.002 mm; 1 2, same, p = 0.07 mm; la, same, p = 16 mm; 1 4, d-c glow discharge, p = 4.1 mm.a For significance of the intensity scale, see Table 7e-2. 1
2 3
C. V. Humphreys and W. F. Meggers, J. Research Nail. Bur. Standards 10, 139 (1933). Humphreys and Kostkowski, J. Research Nail. Bur. Standards 49, 73 (1952). The I, to I, intensities were measured by M. Thekaekara, S.J.
7-64
ATOMIC AND MOLECULAR PHYSICS TABLE
Wavelength
7e-5.
THE SPECTRUM OF XENON
Classification
log 1,
10
I
log I.
log I4
log 13
-
9P12 9p.3 6f,. 5f'3 5f'2
40 40 10 40 60
3.06
3.70
2.89
2.32
6S12 6s12 6S12 6s12 6s 11
8Pl.
120 200 40 30 100
3.86 3.94 3.02 2.91 4.06
4.55 4.66 3.70 3.60 4.32
3.62 3.74 2.71 2.65 3.40
3.21 3.34 2.34 2.26 2.76
4,109.7093 4,116.1151 4,135.1337 4,193.5296 4,203.6945
6s11 6s 11 6s 11 6s 12
8Pl.
60 80 20 150 50
3.33 3.56 2.66 3.62 2.91
4.00 4.17 3.31 4.51 4.01
3.05 3.23
2.66 2.71
3.54
3.25
68 12
8P11 8P22 4f23 4f12
4,205.404 4,372.287 4,383.9092 4,385.7693 4,500.9772
6S12 6s 11 6s11 6s11 6S12
4f11 4fz2 4f12 4f11 6p~,
10 20 100 70 500
....
3.02
3.08 '" . 4.06
4.13 2.80 5.13
3.12 2.82 4.23
2.83 2.55 2.98
4,524.6805 4,582.7474 4.611.8896 4,624.2757 4,671.226
6S12 6s11
6p~2 6p~0
400 300 100 1,000 2,000
3.97 4.16 2.86
4.76 4.98
4.85 4.66 3.86 5.61 5.81
3.96 3.68 2.84 4.72 4.99
3.64 3.42 2.61 4.44 4.70
100 300 600 150 500
3.29 4.21 4.25 3.48 4.52
4.46 5.17 5.27 4.32 5.31
3.43 4.13 4.39 3.29 4.35
3.25 3.92 4.10 3.12 4.12
400 300 500 500 200
4.27 4.50 4.04 4.30 3.54
5.19 5.06 5.15 5.22 4.52
4.21 4.07 4.16 4.21 3.42
3.97 3.84 3.95 3.99 3.25
10
2.86
3.30
3.12
I5} 30
2.97
3.24
3.20
100} 20
3.31
3.86
3.35
3,685.90 3,693.49 3,745.38 3,796.30 3,948.163
6s12 6s 12 6s 11
3,950.925 3,967.541 3,974.417 3,985.202 4,078.8207
6s , • 6s11
8p.3 8p.2
8pOl 8poo
6s H
7Pll
6s 12 6s 12
7P12 7p23
4,690.9711 4,697.020 4,734.1524 4,792.6192 4,807.019
6s 12 6s 11 6s 12 6s 11
6p~, 7P22 6p;2
7poo
4,829.709 4,843.294 4,916.508 4,923.1522 5,028.2796
6s 11 6s 11 6s 11 6s11
7p11 7P12 6p~, 7P22
68 11
7pOl
5,162.711 5,362.244 5,364.626 5,392.795 5,394.738
6Sl2
6s~o
6pOl 6pOl 6s~o
6pOl
7pOl
7f11 10d ol lOd '2 6f" 7S~,
,
i I
I
2.46 ..-
IMPORTANT ATOMIC SPECTRA
7-65
TAl'fLE7e-5. THE SPECTRUM OF XENON I (Continued) Classification
Wavelength ~
10
log I,
log 12
log 13
log I.
-
-
5,439,923 5,460.037 5,488.555 5,552.385 5,566.615
6S~, 6pOl 6p22 6pOl 6pOl
7f12 l1s 12 11d" 9d '2 9dOl
5,581.784 5,618.878 5,688.:373 5,695.:750 5,696.'479
6pOl 6p22 6S~, (iS~, 6S~,
10d" 6fa2 6f,2
3.65 3.23 2.85 3.. 32' 3.41
3.49 3.. 12 3.22 3!.78 3.86
3.21 2.81 3.56 3.48 3.52
3'.13 3.21 2.97
8.53 3;.60 3,.41
3.52 3.61 2.84
2.21
3.61
4.06
3.50
2.62
3.56
4.00
3.83
2.57
2,.39 3.16 3.96
2.93 3.58 4.65
2.67 3.31 . 2.16 4.08 . 3.23
8dol !!ld 2,
150 15 100 100 20
2.61 4.03 3'.92 3.15
3:.21 5.41 4.44 3.42
2.81 3.77 3.85 3·16
6p2'
3.23
i
5,715.716 5,716.,252 5,807.,311 5,814.505 5,823.890
6pOl 6P2' 6P22 6p22
5,824.800 5,856.509 5,875.018 5,894.988 5,904.,462
6p22 6pOl
?S~o
(lPOl 6POl 6p2'
9doo '
~fl1
,
10s12 10d,. 9d 2, 9d 22 5fl1 9d 33 8d 22 8d 12
30 15 20h
80 100 50 80 40 100} 80 70} 80 15 60 300
5,922.;550 5,931.1241 5,g34.)72 5,974.'152 5,989.;18
9d 33
20
3.02
3.52
(jiPOl
Sdoo
6pn 6P12 ?P12
9d,. lOd 2, 10d 12
80} 100 40 20
3.83
4.32
3.50 2;.90
3,.42 3.19
5,998.115 6,007.909 6,111.;759 6,111. 951 6,152.069
6p22 6p22 6pl1 6p2' 6p22
lOs 11
30
10s 12 9d 22 10s 12 8d 2,
15
3.11 2.87
3.51 3.20
30} 40 20
3.63
..
3.46
6,163 .. 660 6,163.935 6,178.302 6,179.665 6,182.420
6p22 6S~, 6S~, 6S~, 6P22
8d 22 5fa2 5f'2 I?fl1 Sd"
90} 80 150} 120 300
3.95 3.99
20 100} 60 20 40
6,189.10 6,198.260 6,200.890 6,206.297 6,224.169
I
6pOl
9s11"
6pOl
9Sl2
tip12
Gd 2,
6p22 6p12
Sdo! 9d 12
4.05
I
2.03 2.42 2.10
2.98 3.02
2.95
il.51
3.17 3.12 2.79
i3. 72
2.56
....
3.85
3.07
,
3.95
3.28
4.19
.. . .. . ,
4.19
3.42
2.89
3.43
3.16
3.72
3.64
3.72
3.18 ....
.... 3.67
3.27 3.39
.,
3.01
ATOMIC AND MOLECULAR PHYSICS
7-66
TABLE
Wavelength
7e-5.
THE SPECTRUM OF XENON
Classification 8dn
10
log I,
log 12
log 13
log 14
50 40 100 50 500
3.39 3.18 3.34 3.43 4.34
4.03 3.87 3.82 4.06 4.93
3.45 2.96 3.84 3.47 4.42
3.66
20 300 150 120
.... 4.15 3.92 3.90
3.44 4.92 4.57 4.59
4.05 3.70 3.72
3.56 3.20 3.22
3.89 4.16 3.25 3.56
3.09 3.05
3.78
4.44 4.37 3.88 4.32 3.95
3.54 4.08 3.76
4.02 4.61 4.32
3.78 4.05 3.73
3.20
4.19
3.69
6,261.212 6,265 . 301 6,286.011 6,292.649 6,318.062
6P23 68~0 5d3• 6Pn 6P23
6,430.155 6,469.705 6,472.841 6 ,487 .. 765 6.497.43
6p12
10812
6pOl 6pOl 6pOl
7d 12 7d" 7d22 7f33
6,498.718 6,504)8 6,521.508 6,533.159 6,543.360
6p" 68~, 6p" 6p22 6P22
8d22
100
8poo
200h
8d '2
9811 9812
40 100 40
6,554.196 6,595.561 6,632.464 6,666.965 6,668.920
5d12 6P12 6p12 6p23
7f23 8dn 8d ' 2
100 50
i?d3.
8POI 8f45 8d 33 8d3•
I (Continued)
30hZ
50hZ
3.90 3.82 3.30
9812 7doo
60} 150
4.26
5.03
68~;
8pOl
4.12
6f" 7d01 6f12 6f"
25 20 200
3.49
5doo 6pOl
4.48
5.22
4.34
3.8!>
3.86
4.32
3.85
2.96
6pOl
I
6,678.972 6.,681 .'036 6,728.008 6,777.57 6,778.,60
5do1 5do1
50} 40
,
6,827.,315 6,846.613 6,866.,838 6,872.107· 6,882.'155
6p22 6p22 5d 34 · 6P22
4f11 7d12 7d22 6f.5 7d3 3 .
200 60 50 100 300
3.91 3.95 3.87 4.19 4.77
4.12 4.72 4.56 4.84 5.41
4.27 4.03
3.83 3.45
4.52 4.68
3.58 4.14
6,925.53 6,976)82 7,119.598 7,257.94 7,262.54
5d12 6pn 6P23 5d33 6p"
6f23 7d23 7d 3• 6f44 7d 12
100 100 500 60 20
3.97 4.07 4.91 4.07 4.02
4.51 4.93 5.62 4.73 4.70
3.88 3.99 4.92 4.07 3.83
3.25 3.52 4.43 3.39 3.26
7,266.49 7,283.961 7,285.301 7,316.272 7,321.452
6p" 68~, 6p" 68~, 68~,
7d" 4f22 7d22 4f12 4f"
25
....
4.60
40} 60 70 80
4.61
5.33
4.50
4.00
5.07 5.00
4.35
3.83
68;0
4.09
....
I
7-67
IMPORTANT ATOMIC SPECTRA TABLE
Wavelength
7e-5.
THE SPECTRUM OF XENON
Classification
I (Continued)
10
log II
log 12
log 13
log 14
4.57 3.80 4.26 4.49 4.05
5.02 5.63 5.16 5.30 4.80
3.97 3.79 4.27 4.46 3.89
3.56 3.26 3.. 85 3.96 3.46
....
7,336.480 7,355.58 7,386.002 7,393.793 7,400.41
6p22 5doo 6pOI 6P12 6p12
- 5d~3 5f11 7d23 7d12
50 40 100 150 30
7,451.00
5d 01
t7 ,472.01
5d01 5d01 6p23 5d 34
5f22 5f12 5f11 5d~3 5f"
25 40 25 20 40
3.69 4.37
4.46 4.94
4.19
3.05 3.65
4.18 3.76
4.65 4.72
3.64 3.88
3.27 3.35
5f46 6p;1 5f" 5f12 7d 01
200 500} 100 30 40
4.59
5.42
4.86
4.28
4.98
5.92
5.36
4.88
4.26 3.87
4.83 4.59
4.00 3.67
3.47 3.17
50 100 100 300 40
3.90 4.31
4.55 5.19 4.73 5.66 4.42
3.84 4.33 4.90 3.50
3.17 3.89 3.45 4.45 3.05
4.82 3.95 4.55 4.53 3.92
5.45 4.85
6f"
500 100 200 150 100
5.38 4.71
4.97 3.79 4.67 4.55 3.93
4.53 3.46 4.10 4.12 3.25
68;0 6812 68;1 6811
8p22 6p;1 6P12 6p;1 6poo
100 700 10,000 500 7,000
4.52 4.85 5.66 4.75 5.99
4.97 6.01 7.16 5.93 6.73
4.01 5.20 6.87 5.20 6.71
3.55 4.85 6.37 4.72 6.21
68;1 6812 68;0
6p;2 6P11 7poo
2,000 2,000 30 30 200
5.50 4.96 3.69 3.79 4.38
6.36 6.60 4.72 4.74 5.26
5.82 6.01 3.69 3.83 4.42
5.29 5.63 3.28 3.39 3.98
4.07 4.65
5.00 5.56 5.13 5.19 ....
4.10 4.77 4.31 4.46 3.84
3.65 4.32 3.87 3.86
7,474.01 7,492.23 1,559.79 7,584.680 7,642.025 7,643.91 7,664.56 7,740.31
5d34
68;0 5d12 5d12 6P12
88[2
7,783,.66 7 ,802 .. 651 7,881.320 7,887.395 7,937.41
5d22 6p22 6p22
6f"
68;1
6p;0 7d11
7,967.341 8,029.67 8,057.258 8,061.340 8,101.98
68;0
8,171.02 8,206.341 8,231.6348 8,266.519 8,280.1163 8,346.823 8,409.190 8,522.55 8,530.10 8,576.01 8,624.24 8,648.54 8,692.20 8,696.86 8,709.64
6poo
5d" 5d" 6p23 5d., 5d01
8811 8812
7P11 5f" 5fH
8812
6P12
8811
68;1
7poo
6p12
8812
68;1 68;1
7P11 7P12 5f" 5f22
5d22 5d ..
-
80 250 100} 200 40
5.20 3.75
4.47 3.93
5.33
ATOMIC AND MOLECULAR PHYSICS TABLE
-w;wel.en~th
7e-5.
THE SPECTRUM OF XENON
Classification
10
I (Oontinued)
log II
log h
log 13
log 14
300 100 5,000 300 200
4.99 4.13 5.75 5.10 4.76
6.03 5.35 .... 6.17 5.94
5.22 4.8 7.02 5.44 ' 5.12
4.80 4.01 6.51 4.99 4.71
200 1,000 100 200 30
4.93 5.92 4.34 4.73 4.58
6.02 6.76 5.61 5.82 5.25
5.25 6.72 4.61 5.00 4.38
4.74 6.23 4.. 23 4.55 3 .. 87
4.69 5.73 4.53
4.14 5.28 3.98
6.94
·6.39
8,739.39 8,758.20 S,819.412 8,862.32 8,908.73
6pOl
8,93q.83 _8,952.254 8,981.05 ...8,987.57 9,025.98
6S~1 6s 11 6P2' 6p22
6d 2, 6d22
6pu
6dll
5doo
4fll 6p22 5f" .4f22 6Pll .
50 400 50 20 500
4.49 5.60 4.39 4.16 5.97
5.36 6.00 5.32 5.30 6.93
6p22 5d ol 5dol 5d,. 6S~1
,6d" 4ft2 4fll 4f"
100 30 25 30 40
'" . 4.60 4.21 .... 4.74
6.22 5.67 5.40 5.46 5.59
4.88 4.73 4.73 4.75
4.36 4.06 4.20 4.33
.9,374,.76 9,412.01 9,445:.34 . 9,497.07 9,513.379
5d,. 6P2' 5d12 5d 12 6p23
4/45
100 60 80 40 200
4.86 4.66 4.81 4.40 5.48
5.66 5.10 5.86 5.50 6.30
,5.61 5.05 5.31 4.71 5.91
5.08 4.56 477 4.19 5.41
'9,585'.14 9,685.32 .9,700.99 9,718.16 9,799'.699
6P22
6pll
6dol 6d2, 6dj. 6d 22
6s 12
6pOl
20 150 20 100 2,000
3.95 5.04 4.14 5.04 5.79
.... 6.04 6.00 6.95 6.78
4.27 5.40 4.31 5.31 7.00
3.77 4.88 3.82 4.80 6.49
9,923.192 10,023'.72 10,107;.34 10,838.34 11,742.26
6s 11 ,5dl2 5dl2 6s 11 5d 2,
6p22 4f" 4f..
3,000 50 80 1,000 90
6.19 4.49
....
7.03 4.85
6.51 4.39
12,623.32 13,656.48 14,142.09 14,732.38 15,418.01
6pOl
7S12
6p22 6p22 6P2'
7s 11 7s 12 7s12 7s 11
~
9,032.18 9,045,.446 9',096.13 9.,15~.12
9.,1621.65.4 9,167,.52 - 9 /.lO3:. 20 .9,211.38 9,301. 95 9,306.64
6p22 6s 12
6pOl 6po!
6S12 5d2, 5dol '6s 11 '
I
6Pl2 6p2'
6Pll
6d12 6d2, 6p2'
6dol 6doo 6p;1 6Pl2
7pOl
6d" 4f2' 4f12 6d,.
6pOI 4fa.
300 150 80 200 110
0."
•
IMPORTANT ATOMIC SPECTRA
7-69
Xenon Microwave 16mm
O.002mm
FIG. 7e-4. Photoelectric traces of the xenon spectrum, microwave discharges at 16 mm (upper traces) and 0.002 mm (lower traces). Wavelength range is 3,500 to 10,000 A. The 16-mm trace shows the Xe I spectrum with the lines broadened. The strongest lines in the 0.002-mm trace are those for Xe II.
Xenon Microwave 16mm
O.002mm
4.0 3.5 3.0 2.5 2.0
. I
I
1J
XelI FIG. 7e-4 (Continued:)
,I
JL
Jj
·.JJL •
,. 4245 4238
ill
.....
c: ~ E o 3: E
i>
M
0
M
-
4251
1£)0 ~ ('oj('oj
0>
X
"
t-
ei
~
7-71
IMPORTANT ATOMIC SPECTRA
5.0
Xenon
4.5
Microwave 16mm
4.0 3.5
3.0
I
2.5
I 4.5
)(eI
...
~ N
§
~ Rl...
'"~
."
lA._
..'"
~
$$ 0 ....
4.0 0.002mm
3.5
3.0 2.5 2.0
I
II
~r
I
,It
I
..
-1
25 Manganese
KLu KLuI /3,,3 KMU,III 14 Silicon /35 KMIV,V /33,4Lr M u,ru 7.12791 9 1. 73938 7J LuMr 7.12542 1.73998 /31 LIIMrv 9 6.753 1 1. 8359 I LmMr 135.5 4 0.0915 aI,2 LrIIMrv,v Mn,urMrv, v a2
"'I
2.10578 2.101820 1. 91021 1.8971 17.19 21.85 19.11 22.29 19.45 273
2 9 2 1 2 2 2 1 1 6
m H
26 Iron
5.88765 1,939980 5.89875 1.936042 6.49045 1. 75661 6.5352 1. 7442 0.721 15.65 0.5675 19.75 0.6488 17.26 0.5563 20.15 0.6374 17.59 0.045 243
9 9 2 1 2 4 1 1 2 5
o
6.3908 4 6.4038 4 7.0579 8 7.1081 0.792 0.628 0.7185 0.6152 0.7050 0.051
m
15 Phosphorus a
"'(3"
,(LII r(Lru ~M
(3, '1 KLIIr fJ. KMrr (31 KMm fJ2 KNu,IIr {3s KMrv,v fJ. KNrv,v (3, LIMU (3, LrMm 'Y2,' LINu,ur 'T) LrrMr (31 LrrMrv 'Y5 LnNrv I LmMr £>2 LrrrMrv. <XI LnrMv {3, LrrrNr
0.92969 0.925553 0.82921 0.82868 0.81645 0.8219 0.8154 6.8207 6.7876 6.0458 8.0415 7.0759 6.7553 8.3636 7.3251 7.3183 6.9842
1 9 3 2 3 1 2 3 3 3 4 3 3 4 3 2 3
13.3358 13.3953 14.9517 14.9613 15.1854 15.085 15.205 1. 81771 1.82659 2.0507 l. 54177 l. 75217 1.83532 1.48238 1.69256 1.69413 1.77517
I
7.304 7.264
5 5
7.576+ 7.279
1.6366 3 5 , 1.703
7.817t 7.510 7.250
3 4 5
I
1. 697 1.707
1.5860 1. 6510 1. 710
38 StTont·;1tm
0.87943 0.87526 0.78345 0.78292 0.77081 0.7764 0.76989 6.4026 6.3672 5.6445 7.5171 6.6239 6.2961 7.8362 6.8697 6.8628 6.5191
1 1 3 2 3 1 5 3 3 3 3 3 3 3 3 2 3
14.0979 14.1650 15.8249 15.8357 16.0846 15.969 16.104 1. 93643 1. 94719 2.1965 1.64933 1.87172 l. 96916 1. 58215 1. 80474 1.80656 1. 90181
MuMrv MrrNr MrIIMv MmNr MmMrv,v I Mrv,vNrr,Irr lVhv,vOrr,IIr KLrr al KLrrI (3. KMrr (31 KMm (32rr (32 KNrr,rrr (3. KNrv,v (3,rr KMrv (3,r KMv (34 KNrv,v (34 LIMrr (3, LrMm 'Y2,aLrNrr,ru 'T) LrrMr (31 LrrMrv 'Y' LrrNr 'YI LrrNrv I LrrrMr a2 LrrIMrv al LruMv (36 LmNr (32,1' LurNrv, V "iJ1 rr Mrv MrrNr MrrNIV M lII lIly MrrrNr 'Y MrnNIY,V I Mrv, vNrr,III Mrv,vOrr,III "--3
0.62708 0.62692 0.62001 5.0488 5.0133 4.3800 5.8475 5.17708 4.8369 4.7258 6.1508
19.771 19.776 19.996 2.4557 2.4730 2.8306 2.1202 2.3948 2.5632 2.6235 2.0156 8 2.2898 5 2.2931 6
5,0488 4.9232 68.9 35.3
5 5 9 3 3 2 3 8 2 2 3 8 8 5 2 2 3
74.9 37.5
1 2
0.1656 0.331
64.38 54.8
7 2
0.1926 0.2262
5A1437 5A0655
2A557
2.5183 0.1798 0.351
~
U2
~
8 ~
>-3
o
~ H
Q
trJ
Z trJ
~
Q >--
l:d
~ ~
....
U2
Cl [f1
Mrr Mrn (32r [(Nn (3, Nn,rII f35 r [(Mrv (33
f31
(30 1 f3, (35 f34 f33
~Mv
Nrv,v Mrv,v 11fn Jl.{nr ),2, SINn,nI YJL Mr f31 :rMrv rNr 'Y5 1'1 'rNIv IL Mr a, nMrv 1 rTil.{ v f36 ITNr f32,
LrnNrv,v
0.546200 0.545605 0.53513 0.53503 0.54118 0.54101 0.53401 4.2888 4.2522 3.6855 4.9217 4.37414 4.0451 3.9437 5.2169 4.60545 4.59743 4.2417 4.1310
4 4 5 2 9 9 9 2 2 2 2 4 2 2 3 9 9 2 2
f3lo 'r1l1rv f39
Mv
Mr II,nr Mr I1rv Mr VI Mr vrv Mr I1v Mr NI I'M [[[Nrv,v 1M V,vNII,rn Mr vOn,nr
59.3 28.1
1 2
65.5 29.8 25.01 47.67 40.9
1 1
9 9 2
22.0089 22.7236 23.168 23.1728 22.909 22.917 23.217
0.521123 0.520520
4 4
23.7911 23.8187
(33 KMn (3, KMrII (32 KNn,ur
0.510228
4
24.2991
KOn,IIl (35 U KM rv (35 r KMv
0.5093 0.51670 2 ..8908 4.0711 2.9157 4.0340 3.3640 3.4892 2.5191 4.6605 2.83441 4.14622 3.8222 3.0650 3.7246 3.1438 2.3765 4.9525 2.69205 4.37588 2.69674 4.36767 4.0162 2.9229 3.90887 3.0013 3.7988 3.7920 20.1 0.2090 56.5 26.2 0.442 22.1 0.1892 62.9 0.417 27.9 23.3t 0.496 0.2601 43.6 37.4 0.303
2 9 2 2 2 2 5 2 2 3 7 5 2 4 2 2 2 1 2 1 1 1 1 1 2
I
!
I
24.346 23.995 3.0454 3.0730 3.5533 2.6603 2.99022 3.2437 3.3287 2.5034 2.83329 2.83861 3.0870 3.17179 3.2637 3.2696 0.616 0.2194 0.474 0.560 0.1970 0.445 0.531 0.2844 0.332
,6., KNrv, v (3, L r lvI n (33 LIMnr 'Y2,3 LrNn,lIr 'Y' LrOrr,IlI
YJ LrrMr (3, LuMrv 'Y5 LnNr 1'1 LrrNrv I LmMr
"" LrnMrv "" LurJvIv (36 LInNr
P2,15 LrnNrv, v (37 LurOr (310 Lr]}Irv (39 LrMv
Jl.{nMrv ArnNr MrrNry kInrMv JvIrrrNr "yMnrNrv,v 1I1rvOn,nr I Mrv,vNn,rn MvOrrr
51 Antimony
-
"" 1
Lrn
(33
MIl
f31 (32 (35
lIf III
'NIT,III 'Mrv,v
0.563798 0.5594075 0.497685 0.497069 0.487032 0.49306
4 6 4 4 4 2
27.2377 27.2759 27.8608 27.940 27.491 27.499 27.928 3.5353 3.5731 4.1605 4.2367· 3.11254 3.48721 3.8159 3.92081 2.90440 ?27929 3.28694 3.60823 3.71381 3.730 3.7868 3.7942
0.435877 0.435236 0.425915 0.42467 0.43184 0.43175 0.42495 3.34335 3.30585 2.8327 2.7775 3.78876 3.38487 3.08475 3.00115 4.07165 3.60891 3.59994 3.26901 3.17505 3.1564 3.12170 3.11513 47.3 20.0 16.93 54.2 2l.5 17.94 25.3 3l. 24 25.7
5 5 8 3 3 3 3 9 3 2 2
9 3 9 3 9
4 3 9 3 3 9 9 1
1 5 1 1 5 1 9 1
28.4440 28.4860 29.1093 29.195 28.710 28.716 .29.175 3.7083 3.7500 4.3768 4.4638 3.2723 4 3.6628 o 4.Q192 4.1311 2 3.0449 9 3.4354 2 3.4439 8 3.7926 3.9048 6 3.9279 3.9716 3.9800 0.2621 0.619 0.733 0.2287 0.575 O. G91 0.491 0.397 0.483
48 Cadmium
47 Silver Lrr
0.455181 4 0.454545 ·4 1 0.44500 0.44374 3 2 0.45098 2 0.45086 0.44393 4 3.50697 9 3.46984 9 2.9800 2 2 ..9264 2 3 ..98327 9 4 3.55531 3.24907 9 4 3.16213 4.26873 9 6 3.78073 4 3.77192 3.43606 9 3 3.33838 4 3.324 3.27404 9 9 3.26763
2l. 9903 22.16292 24.91l5 24.9424 25.4564 25.145
0.539422 0.535010 0.475730 0.475105 0.465328
3 3 5 6 7
22.9841 23.1736 26.0612 26.0955 26.6438
"" KLrr "" KLuI (33 KMn f31 EMIlI f3 2 KNn,ur
0.474827 0.470354 0.417737 0.417085 0.407973
3 3 4 3 5
26.1l08 26.3591 29.6792 29.7256 30.3895
52 Tellurium
0.455784 0.451295 0.400659 0.399995 0.391102
3 3 4 5 6
27.2017 27.4723 30.9443 30.9957 31.7004
:xl
~ kj
~
~
rg t-' rg
Z ~
iI1
rn
po.
Z t;I po. >-l
o
~
H
Q
rg
Z
rg
;:d
Q
kj
~
~
t o""""'
00
TABLE
Wavelength,
Designation
p.e.t
7£-1.
keY
A*
0.40666 0.41388 0.41378 0.40702 3.19014 3.15258 2.6953 2.6398 3.60765 3.22567 2.93187 2.85159 3.88826 3.44840 3.43941 3. ll513 3.02335 3.0052 2.97917 2.97261 45.2 18.8 15.98 52.2 20.2 16.92
~5IIKMrv ~5r
10vIv KNry,v LrMrr ~3 LIMrrr 1'2,3 LrNn,rII 1" LIOn,rII 7J Lrr 11Ir 8, Lnk[Iv 1'5 LnNr 1'1 LnNry I LrrrMr a" Lrn1VIrv '''' Lruj\!Iv ~6 LrrINr ~2,'5 LrnNrv,v ~7 LmOr ~10 Lr1VIrv ~9 LrMv MuMry MuNr Mrr N rv .MmMv 1VIrIINr I' 1JiIrrr NIY, v MryOII,rII r 1VIrv, vNrr,rII Jl1yOm ~, ~,
1
28 . 88
Wavelength,
A*
Designation
keY
p.e.1"
UNITS AND IN KEV
A*
51 Antimony (Cant.)
KOrr,m
X-RAY WAVI%ENGTHS IN
1 1 1 1 9 9 2 2 9 4 9 3 9 6 4 9 3 3 9 9 1 1 5 1 1 4 8
30.4875 29.9560 29.9632 30.4604 3.8864 3.9327 4.5999 4.6967 3.43661 3.84357 4.2287 4.34779 3.18860 3.59532 3.60472 3.9800 4.10078 4.1255 4.1616 4.1708 0.2743 0.658 0.776 0.2375 0.612 0.733 0.429
52 Tellurium (Cant.)
0.38974
1
3l. 8114
1" LrOrr,rrr 7J Ln1vIr ~,
3.04661 3.00893 2.5674 2.5ll3 3.43832 3.07677 2.79007 2.71241 3.71696 3.29846 3.28920 2.97088 2.88217 2.8634 2.84679 2.83897
9 9 2 2 9 6 9 6 9 9 6 9 8 3 9 9
17.6
1
50.3 19.1 15.93 2l. 34 26.72 2l. 78
1 1 4 5 9 5
I
4.0695 4.1204 4.8290 4.9369 3.60586 4.02958 4.4437 4.5709 3.33555 3.7588 3.76933 4.1732 4.30l7 4.3298 4.3551 4.3671
LnMrv 1'5 LIINr 1'1 LnNry I LmMr a" LllrMrv a" LrrrMv ~6 LmNr ~"lG LrrrNry,v ~7 LmOr ~'0 LrJl![rv ~9 Ljll![v I' J11mNrv, V 1VIrvOrr J11r yOrII r MvNm 1VIvOnr NIyOrr NryOrII NvOIIr
1
(Continued)
Wavelength,
p.e·t
keY
f-L
orf.;:... Wavelength,
keY
p.e.1"
A*
A*
55 Cesium (Cont.)
56 Barium (Cont.)
2.1741 2.9932 2.6837 2.4174 2.3480 3.2670 2.9020 2.8924 2.5932 2.5ll8 2.4849 2.4920 2.4783
2 2 2 2 2
2 2 2 2 2 2 2 2
1 1 1
188.6 183.8 190.3
5.7026 4.1421 4.6198 5.1287 5.2804 3.7950 4.2722 4.2865 4.78ll 4.9359 4.9893 4.9752 5.0026
2.0756 2.8627 2.56821 2.3085 2.2415 3.1355 2.78553 2.77595 2.4826 2.40435 2.3806 2.3869 2.3764 12.75 15.91 15.72 20.64 16.20 0.06574 163.3 0.06746 159.0 0.06515 164.6
5.9733 4.3309 4.82753 5.3707 5.53ll 3.9541 4.45090 4.46626 4.9939 5.1565 5.2079 5.1941 5.2171 0.973 0.779 0.789 0.601 0.765 0.07590 0.07796 0.07530
3 3 5 3 2 2 5 5 2 6 2 2 2 3 5 9 4 5 2 2 2
0.703 I
0.2465 0.648 0.778 0.581 0.464 0.569
57 Lanthanum
a"
KLrr KLIIr {33 KMII ~, KMIIl al
0.375313 0.370737 0.328686 0.327983
2 2 4 3
33.0341 33.4418 37.7202 37.8010
58 Cerium
0.361683 0.357092 0.316520 0.315816
2 2 4 2
34.2789 34.7197 39.1701 39.2573
>>-3
o
~, H
o
>-
!Z
o ~
o
I:"' t'J.
o
c::j
~
!:>:I
~Io<j l/l H
o
l/l
53 Iodine ,,,KLu "'1 KLIn I'l. KMn I'll KMIlr I'l, KNn.nr 1'l4 LIMn I'l. LrMm Y2 •• LINn.nI Y4 LIOn.III '1 LnMI I'll LrrMIv y.LI,NI Y1 LnNrv ~ LmMI "', LnIMlv "'1 LrnMv 11, LniNr 1'l'.16 LlnNrv.v 117 LmOI I'110 LrMIY 11. LIMv
0.437829 0.433318 0.384564 0.383905 0.37523t 2.91207 2.87429 2.4475 2.3913 3.27979 2.93744 2.65710 2.58244 3.55754 3.15791 3.14860 2.83672 2.75053 2.7288 2.72104 2.71352
7 5 4 4 2 9 9 2 2 9 6 9 8 9 6 6 9 8 3 9 9
54 Xenon
28.3172 28.6120 32.2394 32.2947 33.042 4.2575 4.3134 5.0657 5.1848 3.7801 4.22072 4.6660 4.8009 3.48502 3.92604 3.93765 4.3706 4.5075 4.5435 4.5564 4.5690
0.404835 0.400290 0.355050 0.354364 0.34611
2.6666 2 .. 6285 2:2371 2.2328
4 4 4 7 2
2 2 2 2
3.0166:\:
2 2 2 2 3
29.458 29.779 33.562 33.624 34.415
2
4.1099
56 Barium
55 Cesium "', KLII "'1 KLrn I1.KMu 111 KMrn fl. KNIl.nI KOn.nI {3.n KMIV {35IKM v {34 KNIV.V {34 LIMn {3. LIMm 'Y' LINn 'Y' LrMnr
0.42087:1: 0.41634:1: 0.36941:1: 0.36872:1: 0.36026:\:
30.6251 30.9728 34.9194 34.9869 35.822
4.6494 4.7167 5.5420 5.5527
0.389668 0.385111 0.341507 0.340811 0.33277 0.33127 0.33835 0.33814 0.33229 2.5553 2.5164 2.1387 2.1342
5 4 4 3 1 2 2 2 2 2 2 2 2
31. 8171 32.1936 36.3040 36.3782 37.257 37.426 36.643 36.666 37.311 4.8519 4.9269 5.7969 5.8092
{3, KNn.m KOn.nI (3.n KMIV {3.r KMv {34 KNrv.v {34 LrMn (3. LrMm ~-, LrNn 'Y' LINrn 'Y 4 LrOn .nr '7 LnMr {31 Ln 21fIv 'Yo LnNr 'Y1 LnNIv 'Y8 LnOI I LmMI '>2 LrnMrv ll'l LInMv {3, LmNI. {3'.16 LIUNrv.v {37 LmOr {310 LrMrv {3,LrM v 'Y MnINIV.V {3 MIVNvI r MvNm a MvNvr.vn MvOIl.rn Nrv. vOn.III
0.320117 0.31864 0.32563 0.32546 0.31931 2.4493 2.4105 2.0460 2.0410 1.9830 2.740 2.45891 2.2056 2.1418 3.006 2.67533 2.66570 2.3790 2.3030 2.275 2.290 2.282 12.08 14.51 19.44 14.88 152.6
7 2 2 2 2 3 3 4 4 4 3 5 4 3
38.7299 38.909 38.074 38.094 38.828 5.0620 5.1434 6.060 6.074 6.252 4.525 5.0421 5.621 5.7885
3 5 5 4 3 3 3 3 4 5 5 5
4.124 . 4.63423 4.65097 5.2114 5.3835 5.450 5.415 5.434 1.027 0.854 0.638 0.833
6
0.0812
59 Praseodymium
0.30816 0.30668 0.31357 0.31342 0.30737 2.3497 2.3109 1. 9602 1. 9553 1. 8991 2.6203 2.3561 2.1103 2.0487 2.0237 2.8917 2.5706 2.5615 2.2818 2.2087 2.1701 2.1958 2.1885 11.53 13.75 18.35 14.04 14.39 144.4
1 2 2 2 2 4 3 3 3 4 4 3 3 4 4 4 3 2 3 2 2 5 3 1 4 4 2 5 6
40.233 40.427 39.539 39.558 40.337 5.2765 5.3651 6.3250 6.3409 6.528 4.7315 5.2622 5.8751 6.052 6.126 4.2875 4.8230 4.8402 5.4334 5.6134 5.7132 5.646 5.6650 1. 0749 0.902 0.676 0.883 0.862 0.0859
60 Neodymium
P1:I ~
i>
>--
8
o
~ H
Q
>-
Z
t::J
~
o ~ o
c:::t
E ~ ~
H
o
Ul
fl5 KMrv.v ,8, LIMn fl' LrMm 'Y2 LrNn
2.0421
I
4
'Y' LrNnr 'Y' LIOn.nr '7 LnMr
fll LnMrv 'Y5 LrrNr on LnNrv 'Y6 LuOrv I LmMr a2 LIIIllfrv al LIIrMv fl. LmNr fl2.15 LnINrv. v fl7 LmOr
2.0797
4
1. 7989
9
2.2926 2.2822
4 3
1.9559
6
fl' LmOrv.v fllo LrMrv fl' LIMv ~I
MruNrv.v fl MrvNvr !; MvNIll
MvNvr.vn Nrv.vNvr.vII Nrv. vOII.IIr
a
0.27111 2.00095 6.071 1. 96241 1.66044 1. 65601 1.60728 2.21824 5.961 1.99806 1.77934 6.892 1.72724 1.6966 2.4823 5.4078 2.21062 5.4325 2.1998 1. 94643 6.339 1. 88221 1.85626 1. 84700 1.86990 1. 86166 9.600 11.27 14,91 11.47 98 117.4
63 Europium
3 6 3 6 3 3 3 3 3 3 9 4 3 2 3 3 3 9 3 3 9 1 4 3 1 4
45.731 6.1963 6.3180 7.4668 7.4867 7.7137 5.5892 6.2051 6.9678 7.1780 7,3076 4.9945 5.6084 5.6361 6.3697 6.5870 6.6791 6.7126 6.6304 6.6597 1. 291 1.0998 0.831 1. 081 0.126 0.1056
64 Gadolinium
fll KMm fl2 KNn.m KOn.ur
fl5 KMrv .v fl' LrMn fl' LrMm 'Y2 LrNn 'Y' LrNrn 'Y' LIOn .rn '" LrrMr
fll LnMrv 'Y5 LrrNr 'Yl LnNrv 'Y8 LnOr 'Y6 LrrOrv I LnrMr lX2
LlnMrv
a'I
LnMv
fl6 LrnNr LnrNrv.v fl7 LIlIOr fl5 LlnOrv. v fl2.15
fllo LrMrv fl. LrMv LrOrv.v
'Y NIrrrNrv.v fl MrvNvr !; MvNIll
MvNvr.vII Nrv.vNvr.vn Nrv. vOII.IIr lX
a2
KLII
Cll KLrn fl' KMn {3l KMm
132
KNIl,III
KOn.rIl
135 KMrv.v
13. LrMn 13, LrMm
0.303118 0.298446 0.264332 0.263577 0.256923 0.255645 1.9255 1.8867
2 2 5 5 8 7 2 2
40.9019 41.5422 46.9036 47.0379 48.256 48.497 6.4389 6,5713
0.293038 0.288353 0.25534 0,25460 0.24816 0,24687 0.25275 1.8540 1. 8150
2 2 2 2 3 3 3 2 2
42.3089 42,9962 48.555 48.697 49.959 50.221 49.052 6.6871 6.8311
0.24608 0,2397+ 0.23858
2 2 3
50.382 51. 72 51. 965
1.7864 1. 7472 1.4764 1.4718 1.4276 1.9730 1.7768 1. 5787 1. 5303 1. 5097 1.5035 2.2352 1. 9875 1. 9765 1. 7422 1. 6830 1.6585 1. 6510 1.6673
2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 2 2 2 3
6.9403 7.0959 8.398 8.423 8.685 6.2839 6.978 7.8535 8.102 8.212 8.246 5.5467 6.2380 6.2728 7.1163 7.3667 7.4753 7.5094 7.436
1.4228 8.486 9,792 12.98 10.00 86 102.2
3 9 6 2 2 1 4
8.714 1. 461 1.2661 0.955 1. 240 0.144 0.1213
67 Holmium
0.23788 0.2317+ 0.23056 0.23618 1. 72103 1.6822 1.42278 1. 41640 1. 374.59 1. 89743 1.71062 1. 51824 1.47266
2 2 3 3 7 2 7 7 7 7 7 7 7
52.119 53.51 53.774 52.494 7.2039 7.3702 8.7140 8.7532 9.0195 6.5342 7.2477 8.1661 8.4188
1.44579 2.15877 1. 91991 1. 90881 1. 68213 1. 62369 1. 60447 1. 58837 1. 60743 1. 59973
7 7 3 3 7 7 7 7 9 9
8.5753 5.7431 6.4577 6.4952 7.3705 7.6357 7.7272 7.8055 7.7130 7.7501
9 6 2 2 1 8
1.522 1,3250 0.998 1.293 0.149 0.128
~ I
~
'" >-1
~
~
l'=J
t"'
l'=J
Z
~
i:Q
[JJ.
'" 'o" is: Z
t:I
>-:3
H
()
8.144 9.357 12.43 9.59 83 97.2
68 Erbium
l'=J
Z
l'=J
~
o><j t"'
~
l'=J
lX2 lX'
{3, fll
KLII KLIIr KMn KMm
0.265486 0.260756 0,23083 0.23012
2 2 2 2
46.6997 47.5467 53.711 53.877
0.257110 0.252365 0.22341 0.22266
2 2 2 2
48.2211 49.1277 55.494 55.681
t"'
[JJ.
~
I-'
o
~
TABLE
Designation
Wavelength,
A*
p.e·t
7£-1.
keY
0.2241:1: 0.22305 0.22855 1. 6595 1. 6203 1. 3698 1. 3643 1. 3225 1.8264 1. 6475 1. 4618 1.4174 1. 3983 1. 3923 2.0860 1. 8561 1.8450 1. 6237 1. 5671 1. 5378 1. 5486 1.3208
Wave c length,
A*
67 Holmium (Cont.)
(32 KNrr,rn KOII.IIr (36 KMrv.v (34 LrMrr (3, LrMrrr 'y2 LrNrr 1" LrNru 'Y4.Lr Ou.HI 7J LnMr (31 LrrMrv 'Y6 LIlNr 'YI LrrNrv 'V8 LnOr 'Y6 LuOrv I LrrrMr a2 LIIrMrv al LruMv (36 LrnNr (32.1' LrnNrv.v (3, LrrrOI (3. +-rnOlv. v (310 LrMrv Lr01v.v (3,Lr M v MIIrNIV 'Y MrIINrv.v 1'Mrrr.Nv (3 MrvNvr I MvNrn a MvNvr.vrr NrvNvr NvNvr.vrr
X-RAY WAVELENGTHS IN -
2 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3
55.32 55.584 54.246 7.4708 7.6519 9.051 9.087 9.374 6.7883 7.5253 8.481 8.747 8.867 8.905 5.9434 6.6795 6.7198 7.6359 7.911 8.062 8.006 9.387
7.865
9
1.576
8.965 11.86 9.20
4 1 2
1. 3830 1.0450 1.348
p.e·t
keY
A* UNITS
AND IN KEV
Designation
~
3 3 1 1 2 1 2 I
1 3 2
57.21 57.450 5.6.040 7.7453 7.9392 9.38.5 9.4309 9.722 7.0579 7.8109 8.814 9.089
1.3397 2.015 1. 7955 1. 78425 1. 5675 1. 51399 1. 4941 1.4848 1.4941
3 1 2
3 3 3
9.2S5 6.152 6.9050 6.9487 7.909 8.1890 8.298 8.350 8.298
1.4855 7.60
5 1
8.346 1.632
8 3 1 1 9 7
1.643 1.4430 1. 0901 1.406 0.171 0.163
7.546 8.592 11.37 8.82 72.7 76.3
Wavelength,
A*
68 ErbiurYI (Cont.)
0.2167:1: 0.21581 0.22124 1.6007 1. 5616 1.3210 1. 3146 1. 2752 i. 7566 1. 5873 1. 4067 1.3641
(Continueil)
--".
9
2 9
.-
keY
p.e·t
a MvNvr.VII NrvNvr NvNvr.vII
8.48
1
1.462
I I 71 Lutetium
a2KLrr al KLm
(3, KMu (31 KMru (32 KNu.rrr KOu.tlI (3. KMrv.v (34 LrMu (33 LrMrrr 'Y2 LrNn 'Y3 LrNnr 'Yl.LrOrr 'Y4 LIOu.rrr TJ LuMr (31 LuMrv 'Y' LrrNr 'YI LuNrv 'Y8 LuOr 'Y6 LuOrv I LrrrMr a2 LrrrMrv al LIIIMrv (36 LrrrNr (316 LrnNrv (32 LrrrNv (3, LrnOr
Wavelength,
0.234081 0.229298 0.20309:1: 0.20231:1: 0.1969:1: 0.19S89 0.20084 1.44056 1. 40140 1. 1853 1. 17953
2 2 4 3 2 2 2 5 5 2 4
52.9650
1.1435 1.5779 1.42359 1.2596 1.22228 1.2047 1.1987 1.8360 1.63029 1. 61951 1.4189 1.3715 1.37012 1.34949
1 1 3 1 4 1 1 1 5 3 1 1 3 5
10.8425 7.8575 S.7090 9.8428 10.1434 10.2915 10.3431 6.7528 7.6049 7.6555 8.7376 9.0395 9.0489 9.1873
540.0698
61.05 61. 283 62.97 63.293 61. 732 8.6064 8.8469 10.460 10.5110
keY
p.e·t
A*
69 Thulium (Cont.)
~ f-L o
-
00
70 Ytterbium (Cont.)
8.149 65.1 69.3
I~ I
1. 5214 0.190 0.179
72 Hafnium
0.227024 0.222227 0.19686:j: 0.19607:1: 0.1908:1:
3 3 4 3 2
54.6114 55.7902 62.98 63.234 64.98
~
o ~ Q P>
§ ~
o
t"' t;rj
Q
1.39220 1.35300 1. i4442 1.13841 1.10376 1.10303 1.52325 1. 37410 1. 21537 1. 17900 1. 16138 1.15519 1.78145 1.58046 1.56958 1. 37410 1. 32783 1. 32639 1.30564
5 5 5 5 5 5 5 5 5 5 5 5 5
[,
5 5 5 5 5
8.9054 9.1634 10.8335 10.8907 11.2326 11.2401 8.1393 9.0227 10.2011 10.5158 10.6754 10.7325 6.9596 7.8446 7.8990 9.0227 9.3371 9.3473 9.4958
c::j
E ~>-<j U1 H
Q
U1
6.9 Thulium "" KLlI <Xl KLuI 0, [(lvIu B, KMlII B2 KNII,IiI
KOII,!Ti B, K1WIV ,V (3, LIMn B, LdvIru 1'2 LINU 1" LINnI 1" LrOlI,lII 17 Llljl,{I B, Lnjl,Irv 1'5 LnNI 1'1 LnNIY YH LnOI yo LlIOIV !LluMr "" LruMrv '-"I LurlYIv
B, LurNr B,,15 LUI Vrv,v B, LurOI 13,. LrlIOrV,y 13 ,0 LIM l v I3,L I M v LIOr LIOrv,v LnMn LuOu,ur t LIlIMlI LlIrOlI,IU MmNr
0.249095 0.244338 0.21636 0.21556 0.20981: 0.20891 0.21404 1.5448 1.5063 1. 2742 1.2678 1.2294 1.6963 1.5304 1.3558 1. 3153
2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
49.7726 50.7416 57.304 57.517 59.09 59.346 57.923 8.026 8.231 9.730 9.779 10.084 7.3088 8.101 9.144 9.426
1.2905 1.9550 1. 7381 1.7268:1: 1. 5162 1. 4640
2 2 2 2 2 2
9.607 6.3419 7.1331 7.1799 8.177 8.468
1.4349 1. 4410 1. 4336
2 3 3
8.641 8.604 8.648
1.2263
3
10.110
8.249
7
1.503
l' AllIINv
(3 MrvNvr I lYI VNIll
70 Ytter/)ium
0.241424 0.236655 0.2096:1: 0.20884 0.20331: 0.20226 0.20739 1. 49138 1.45233 1.22879 1.22232 1.1853 1. 63560 1. 47565 1. 3063 1.26769 1.24923 1. 24271 1. 89415 1. 68285 1. 67189 1. 4661 1.41550 1.3948 1.38696 1. 3915 1.3838 1.1886 1.1827 1.58844 1.2453 1. 83091 1.3898 8.470 7.024 7.909 10.48
2 2 1 8 2 2 2 3 5 7 5 1 5 5 1 5 5 3 5 5 4 1 5 1 7 1 1 1 1 9 1 9 1 9 8 2 1
51. 3540 .52.3889 59.14 59.37 60.98 61. 298 59.782 8.3132 8.5367 10.0897 10.1431 10.4603 7.5802 8.4018 9.4910 9.8701 9.9246 9.9766 6.5455 7.3673 7.4156 8.4563 8.7588 8.8889 8.9390 8.9100 8.9597 10.4312 10. il833 7.80.52 9.9561 6.7715 8.9209 1.464 1. 765 1. 5675 1.183
.B5 LrlIOrv,v LIMI
1. 34183
(3,0 LrlYIrv
1.3430 1.3358 1. 16227 1.16107
2 1 9 9
9.232 9.2816 10.6672 10.6782
1.53333
9
8.0858
(39 LrMy LINIV I'll LINv
LIOI LIOIV L n l1In (317 LnMln
7
9.2397
LrrNv
LnNvr LlIOU,lII t LrIlMn "' Lurjl,{lIr LlIINu LlIINru u LIlINvr,vI LIUOH,IU lWnI NI 1' M ru N v 12 (3 MrvNvr 1)
1. 2014 1.7760
1. 34524
1 1
9
10.3198 0.9810
a MyNvr,vr
5 9 9 9 9 9 9 9 9 9 9 9
1.72305 1.66346 1.35887 1.35053 1. 30165
9 9 9 9 9
7.887 6.544 9.686 7.303 9.686 7.539
9 4 7 1 7 1
9.55M 8.668f
9.550:: 9.609C 11.0451 11.055-3
o
~
H Q
~
!Z
o
~
o
t"'
trJ
Q
q
~
!J:j
h;:j
::q
....q 7J2 H
Q
7J2
LrOrv.v LuMu {317 LrrMrII LrrMv
LrrNn LrrNm
LrrNv v LrrNvr LrrOH LrrOm t LrrrMu
LruMur LruNu LrrrNrn
8
uLruNvr.vu
LIuOn.rn MrNm
1.06192 1.43048 1.3864 1.3.1897 1.1600 1.1553 1.13687 1.1158. 1.11789 1.11693 1.67265 1.61264 1.3167 1.3086 1.25778 1. 2601 5.40
9 9
t 9 2 1 9 1 9 9 9 9 1 1 4 3 2
11. 6752 8.6671 8.94.28 9.3998 10.688 10.7316 10.9055 11.1113 11.0907 11.1001 7.4123. 7.6881 9.4158 9.4742 9.8572 9.839 2.295
¥rOn.m MuNI MnNrv
MmNr MurNIV "Y MmNv
MmOr MurOrv.v
5' MIVNu MIVNHI {3 MrvNvr
MrvOrr 5' MvNru a MvNvr.vrI a. MvNvI a, MvNvrr MvOm NrrNrv NrvNvr
NvNvr.vrr
5.570 7.612 6.353 6.312 5.83 5.67 9.330 8.90 7.023 7.09 9.316 7.252 .7.30 58.2 61.1
4 9 5 4
2
3 5 2 1 2 4 1 2 1
2
2.226 1.629 1.951 1.964 2.126 2.19 1. 3288 1.393 1.7655 1. 748 1.3308 1. 7096 1.700 0.2130 0.2028
NvNvr NvNvII ..
1.0250
2
12.095
1.3387 1.2728 1. 1218 1.1149
2 2 3 2
9.261 9.741 11.052 11.120
1.0771
1
11.510
1.0792 1.624,4 1.5642 1.2765 1.2672 1.21868 1. 2211 5.172 4.44 6.28 5.357 7.360 6.134 6.092 5.628
2 3 3 2 2 5 2 9 2 2 4 8 4 3 8
11.488 7.632 7.926 9.712 9.784 10 .1733 10.153 2.397 2.79 1.973 2.314 1. 684 2.021 2.035 2.203
8.993 8.573 6.757 6.806 8.962
5 8 1 9 4
1.3787 1.446 1.8349 1. 822 1. 3835
6.992 6.983 7.005 54.0 55.8
2 1 9 2 1
59.5 58.4
3 1
{3,o LrMrv {3,Lr M v LINr LiNrv "Yll LrNv LIOr LrOrv.v LnMrr {317 LrrMrr LuMv LrrNu
LuNur v LnNvr LuOur t LmMrr LIIIMru LmNI 8
LrIINru u LInNvr.vu
1.17218 1.16487 1.0420 1. 0119 1. 0108 0.9965 0.9900 1. 3366 1.2927. 1.2305 1.0839 1.0767 1.0404 1.0397 1.5789 1. 5178
5 4 1 1 1
1 1
10.5770 10.6433 11.899 12.252 12.266 12.442 12.524 9.2761 9.5910 10.0753 11.438 11. 515 11.917 11.925 7.8525 8.1682
1. 2283 1. 1815
1 1
10.0933 10.4931
1. 1 1 1 1 1 1 1 1
MrNm MuNr MuNIV
MrrrNr lYlrIINrv "Y MmNv
5' MrvNn MrvNru {3 MrvNvr \"' MvNrn a MvNvr.vn
NrvNvr 1.7731 NvNvr.vn 1. 7754 1.770 0.2295 0.2221 a. KLrr a, KLnr {3, KMu 0.208 0 .. 2122 {3, KMm
5.931 5.885 8.664 8.239 6.504 8.629 6.729
5 2 5 8 1 4 1
2.090 2.1067 1.4310 1. 505 1. 9061 1. 4368 1.8425
77 Iridium
1.13353 1.12637
5 6
10.9376 11.0071
0.9772 0.9765 0.96318 0.95603 1.2934 1.2480 1.18977
3 3 7 5 2 2 7
12.687 12.696 12.8721 12.9683 9.586 9.934 10.4205
1.03973 1.0050 1.0047 1.5347 1.4735 1. 20086
5 2 2 2 2 7
11.9243 12.337 12.340 8.079 8.414 10.3244
1.14537 4.79 5.81 4.955 6.89 5.724 5.682 8.359
7 2 2 4 2 5 4 5
10.8245 2.59 2.133 2.502 1.798 2.166 2.182 1.4831
1 4 1 1 2.
1. 9783 1. 4919 1. 9102 0.2388 0.2266
6.267 8.310 6.490 51. 9 54.7
78 Platinum
~
~ "'" ~ ~toj t"
t9
Z
o>-:I
ill
Ul
P.
§ P.
o""
l5:
1-1
Q
t9
Z
t9 ~.
Q
"'t""
~
t"
0.195904 0.191047 0.169367 0.168542
2 2 2
.2
63.2867 64.8956 73.2027 73.5608
0.190381 0.185511 0.164501 0.163675
4 4 3
3
65.122 66.832 75.368 75.748
Ul
l' ..... ..... .......
TABLE
Designation
Wavelength,
A*
p.e.t
7f-1.
keY
0.16415 0.163956 0.163019 0.16759 0.167373 0.16352 1.17958 1.14085 0.96545 0.95931 0.92831 0.92744 1.28448 1. 15781 1. 02175 0.99085 0.97409 0.96708 1.54094 1.36250 1. 35128 1.17796 1.13707 1.13532 1.11489 1.10585 1.2102 1.09702 1. 08975 0.9766 0.9459
Wavelength,
A*
77 Iridium (Cont.) {J2 ll KNn {J,r KNm KOn,IIT {J.u KMrv {J.r KMv {J4 KNIV,V {J4 LrMIT {J, LrMm 'Y2 LrNn 'Y' LrNnr 'Y' 4 LrOn 'Y4 LrOrrr 1] LnMr {J, LnMrv 'Y' LuNr 'Yl LuNrv 'Y8 LuOr 'Y6 LuOrv I LmMr "" LruMrv al LUIltlv {J5 LmNr {J15 LmNrv {J2 LIlINv {J7 LIlIOr {J5 LmOrv,v LrMr {J,0 LrMrv {J. LIMv LrNr LrNlv
X-RAY WAVELENGTHS IN
1 7 5 2 9 2 3 3 3 5 3 3 3 3 5 3 3 4 3 5 3 3 3 3 3 3 2 4 5 2 2
75.529 75.619 76.053 73.980 74.075 75.821 10.5106 10.8674 12.8418 12.9240 13.3555 13.3681 9.6522 10.7083 12.1342 12.5126 12.7279 12.8201 8.0458 9.0995 9.1751 10.5251 10.9036 10.9203 11.1205 11.2114 10.245 11.3016 11. 3770 12.695 13.108
p.e·t
keY
A* UNITS
Designation
0.15939 0.15920 0.15826 0.16271 0.16255 0.15881 1.14223 1.10394 0.93427 0.92791 0.89747 0.89659 1.2429 1.11990 0.9877 0.95797 0.9411 0.9342 1.4995 1.32432 1. 31304 1.14355
1 1 1 2 3 2 5 5 5 5 4 4 2 2 2 3 1 2 2 2 3 5
77.785 77.878 78.341 76.199 76.27 78.069 10.8543 11.2308 13.2704 13.3613 13.8145 13.8281 9.975 11. 0707 12.552 12.9420 13.173 13.271 8.268 9.3618 9.4423 10.8418
1.10200 1. 08168 1.0724 1.16962 1. 06183 1.05446 0.9455
3 3 2
11.2505 11.4619 11.561 10.6001 11.6762 11. 7577 13.113
7 5 2
(Contint!eli)
Wavelength,
p.e.t
keY
79 Gold (Cont.) {J, KMm {J2U KNn {J,r KNm KOu,rrr KLr {J.u KMrv {J.r KMv {J5 KMrv,v {J4 KNrv,v {J4 LrMn {J, LrMm 'Y2 LrNn 'Y' LrNur 'Y' 4 LrOn 'Y4 LrOru 1] LrrMr {J, Lultfrv 'Y' LuNr 'Yl LuNrv 'Y8 LuOr 'Y6 LuOrv I LmMr a2LruMrv a, LurMv {J5 J"mNr {JI. LmNIv {J2 LUINv {J7 LmOr {J. LmOIv,v LrMr {J,0 LIMrv
0.158982 0.15483 0.154618 0.153694 0.18672 0.158062 0.157880
3 2 9 7 4 7 5
77.984 80.08 80.185 80.667 66.40 78.438 78.529
0.154224 1.10651 1.06785 0.90434 0.89783 0.86816 0.86703 1.20273 1.08353 0.95559 0.92650 0.90989 0.90297 1.45964 1.28772 1.27640 1.11092 1.07188 1.07022 1.04974 1.04044 1.13525 1.02789
5 3 9 3 5 4 4 3
80.391 11.2047 11.6103 13.7095 13.8090 14.2809 14.2996 10.3083 11.4423 12.9743 13.3817 13.6260 13.7304 8.4939 9.6280 9.7133 11.1602 11.5667 11.5847 11.8106 11.9163 10.9210 12.0617
3
3 3 5 3 9 3 3 3 5 3 8 3 5 7
l' Wave"length,
A*
A*
78 Platinum (Cont.)
9
AND IN KEV
f-' f-'
t-:>
p.e·t
keY
80 Mercury (Cont.)
0.154487 0.15040 0.15020 0.14931
3 2 2 2
80.253 82.43 82.54 83.04
~ >-:3
o
Is: H Q
~
0·15353 0.14978 1. 07222 1.03358 0.87544 0.86915 0.84013 0.83894 1. 1640 1.04868 0.92453 0.89646 0.87995 0.87319 1.4216 1.25264 1.24120 1. 07975 1.04151 1.03975 1. 01937 1.00987 1. 0999 0.9962
2 2 7 7 7 7 7 7 1 5 7 5 7 7 1 7 5 7 7 7 7 7 2 2
80.75 82.78 11. 5630 11.9953 14.162 14.265 14.757 14.778 10.6512 11.8226 13.410 13.8301 14.090 14.199 8.7210 9.8976 9.9888 11.4824 11. 9040 11.9241 12.1625 12.2769 11. 272 12.446
§ Is:
o
t"
t9
Q
q
~
~
~
~H
Q
rJl
'I'll LrNv
LrOrv.v LIOr LrOrv LrOv LnMu (317 LrrMnI LuMv LIlNu LnNrrr
v LrrNvr LrrOnr t LuIlVln 8 Lrn1l1nr LnrNn LUI NUL u LruNvI.vU LIlIOn.ur 111INIU 111u Nrv 111 rrr N r MnINIv 'I' MrrrNv MrnOr .MIIrOIV.V l2 MrvNu MIvNnr (3 MrvNVI lI ll1v N rrr "" MvNvI "'I ll1 VN VII 111vOnI NIVNvI NvNvr.vII
0.9446 0.9243
2 3
1.2502 1.2069 l. 1489 l. 0120 1.0054 0.97161 0.96979 1.4930 1. 4318 ~.1654;5
1.1560 l.11145 l. 10923 4.631:1: 4.780 6.669 5.540 5.500 4.869 8.065 7.645 6.038 8.021 6.275 6.262 50.2 52.8
3 2 2 2 3 6 5 3 2 5 3
4 6 9 4 9 5 4
13.126 13.413
9.917 10.273 10.791 12.251 12.332 12.7603 12.7843 8.304 8.659 10.6380 10.725 1l. 1549 11.1772 2.677 2.594 1.859 2.238 2.254
9 5 8 1 4 3 1
2.546 l. 5373 1.622 2.0535 l. 5458 l. 9758 1.9799
1 1
0.2470 0.2348
79 Gold "" KLrr
"" KLuI (33 KMn
0.185075 0.180195 0.159810
2 2 2
66.9895 68.8037 77.580
0.9143
:2
i3.560
(39 LrJvlv LrNI
0.8995 0.8943 0.8934 l. 213 1.1667 l. 1129 0.9792 0.97173 0.93931
2 1 1 1 1 2 2 4 5
13.784 13.864 13.878 10.225 10.6265 11.140 12.661 12.7588 13.1992
LrNrv 'I'll LINv
LrOr LrOrv .v LrrMrr (317 LuMrII LrrMv LnNIII
v LnNvr LuOu 1.4530 2 8.533 LuOur 1.3895 2 8.923 t LIuMrr l. 1310 2 10.962 8 LIUMUI 1.1226 2 1l. 044 LruNu l. 07896 5 11.4908 LUINnI l. 0761 3 11.521 u LurNvr.vII 4.460 9 2.780 u'LrnNvI 4.601 4 2.695 u LIUNVU 6.455 9 l. 921 LurOu.Iu 5.357 5 2.314 LlIIOn 5.319 4 2.331 LnrOur 4.876 9 2.543 LIlrPn.Iu 8 4.694 2.641 MrNuI 7.790 5 1.592 MuNrv 7.371 8 1.682 MurNI 1 5.828 2.1273 MIUNIV 7.738 4 1.6022 'YMIUNv 6.058 3 2.047 MurOI 6.047 1 2.0505 MnIOlv.v 5.987 9 2.071 l2 MrvNn 48.1 2 0.258 MIVNUI 50.9 1 0.2436 (3 MrvNvI II MvNrrl 80 Mercury "" MvNvI "'I MvNvu 68.895 0.179958 3 MvOrrr 70.819 0.175068 3 NIVNvI 0.155321 3 79.822 NVNVI.VII
1.02063 0.9131 0.88563 0.88433 0.87074 0.86400 l. 1708 1.12798 l. 0756 0.9402 0.90837 0.90746 0.90638 l. 41366 l. 35131 l. 09968 1.09026 l. 04752 1.0450 l. 03876 4.300 4.432 6.259 5.186 5.145 4.703 4.522 7.523 7.101 5.624 7.466 5.854 5.840 5.767 46.8 49.4
7 1 7 7 5 5 1 5 2 2 5 7 7 7 7 7 7 5 2 7 9 4 9 5 4 9 6 5 8 1 4 3 1 9 2 1
12.1474 13.578 13.999 14.020 14.2385 14.3497 10.5892 10.9915 1l. 526 13.186 13.6487 13.662 13.679 8.7702 9.1749 1l. 2743 11.3717 11.8357
0.9871 0.8827
2 2
0.85657 0.8452 0.8350 1.1387 l. 0916
7 2 2 5 5
0.90894 0.87885 0.8784 0.8758 l. 3746 l.3112 1.0649 1.0585
7 7 1 1 2 2 2 1
l. 01769 l. 01674
7 7
l. 01558 l. 01404
7 7
1l. 865 11.9355 2.883 2.797 l. 981 2.391 2.410 2.636 2.742 l. 648 l. 746 2.2046 1.6605 2.118 2.1229 2.150 0.265 0.2510
~
~
P>
>
~ tl>' ~ t9
t-'
t9
!Z Q
>-3 ~
"(Jl
p...
Z
tI·
p... >-3
o
;S:' H'
o 6.09
2
4.984:1:
2
t9:
!Z t9 ~
~ 6.87 5.4318:1:
2 9
5.6476:1:
9
t-'
~t9
t-'
45.2:/: 47.9:/:
3 3
m
f
I-'
c,.., '"'"'
TABLE
Designation
Wavelength,
p.e.t
7f-1.
keY
A*
Wavelength,
p.e.t
A*
UNITS AND IN KEV
Designation
keY
A* 81 Thallium
"" KLu a, KLur (3. KMu (3, KMm (3,IIKNu (3,r KNIlr KOrr .ru KP (35 KMrv.v (3.II KMrv (3.r KMv (3. KNrv.v (3. LrMn (3. LrMnr 'Y2 LrNn 'Y' LINnr 'Y" LIOn 'Y' LrOHr 7J LuMr (3, LnMrv 'Y' LlINr 'Y1 LnNrv 'Ys LnOr 'Y6 LnOrv LuPr I LIllMr a, LrIlMIv a, LrnMv (36 LmNr (316 LmNrv (3, LmNv (37 LIllOr
X-RAY WAVELENGTHS IN
0.175036 0.170136 0.150980 0.150142 0.14614 0.14595 0.14509
2 2 6 5 1 1 1
70.8319 72.8715 82.118 82.576 84.836 84.946 85.451
0.14917
1
83.114
0.14553 1.03918 1.00062 0.84773 0.84130 0.81308 0.81184 1.12769 1. 01513 0.89500 0.86752 0.8513 0.8442
2 3 3 5 4 5 5 3 4 4 3 2 2
85.19 11.9306 12.3904 14.6251 14.7368 15.2482 15.2716 10.9943 12.2133 13.8526 14.2915 14.564 14.685
1.38477 1. 21875 1.20739 1.04963 1.01201 1. 01031 0.99017
3 3 4 5 3 3 5
8.9532 10.1728 10.2685 11. 8118 12.2510 12.2715 12.5212
(Continued)
Wavelength,
A* 82 Lead
2 2 4 6 2 1 8 1
72.8042 74.9694 84.450 84.936 87.23 87.364 87.922 88.06
0.14512 0.14495 0.14155 1. 0075 0.96911 0.8210 0.8147 0.78706 0.7858 1. 09241 0.98291 0.86655 0.83973 0.82365 0.81683 0.81583 1. 34990 1.18648 1.17501 1. 0210 0.98389 0.98221 0.9620
2 3 3 1 7 2 1 7 1 7 3
85.43 85.53 87.59 12.306 12.7933 15.101 15.218 15.752 15.777 11.3493 12.6137 14.3075 14.7644 15.0527 15.1783 15.1969 9.1845 10.4495 10.5515 12.143 12.6011 12.6226 12.888
3 5 5 5 7 5 2 1 7 7 1
MvNvr a, JvlvNvII MvOru NrvNvr NvNvr,vII NvrOIv NvrOv NVIIOV
'>2
2 1
5.472 5.460 46.5 115.3 113.0 117.7
KLn a, KLnr (3. KMII (3, KMm (3,n KNn (3,r KNm KOn.ln (35 KMrv.v (3. KNrv,v (3. LrMn (3. LrMm 'Y2 LrNrr 'Y' LINrII 'Y" LrOll 'Y' LrOrl! 'Y13 LrPIl.llr 7J LnMr (3, LnMrv 'Y' LnNr 'Y1 LnNrv 'Y8 LIlOr
5.299 5.286 5.168 42.3 0.267 45.0 0.1075 102.4 0.10968 100.2 0.10530 104.3
2 2 1 1
0.165717 0.160789 0.142779 0.141948 0.13817 0.13797 0.13709 0.14111 0.13759 0.97690 0.93855 0.79565 0.78917 0.76198 0.76087 0.75690 1. 05856 0.951978 0.83923 0.81311 0.7973
2 2 7 3 1 1 1 1 2 4 3 3 5 3 3 3 3 9 5 2 1
H:>.
82 Lead (Cont.)
2.2656 2.2706
83 Bismuth -
8 ;> >-3
o
is: >-< Cl
t;l
Z
t;l !;O Q
..q
~ t;l
~
f ...... tv
CI.:>
TABLE
Wavelength,
.A*
7f-2.
WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER
p.e.t Element
Designation
keY
Wavelength,
.A*
Designation
p.e·t Element
~ f-'
(Continued)
keY
~
----0.31864 0.31931 0.320117 0.320160 0.324803 0.32546 0.32563 0.327983 0.328686 0.33104 0.33127 0.331846 0.33229 0.33277 0.336472 0.33814 0.33835 0.340811 0.341507 0.344140 0.34451 0.34611 0.348749 0.354364 0.355050 0.357092 0.3584 0.36026 0.361683 0.36872 0.36941 0.370737 0.37381
2 2 7 4 4 2 2 3 4 1 2 2 2 1 2 2 2 3 4 2 1 2 2 7 4 2 5 3 2 2 2 2 1
57 57 57 61 61 57 57 57 57 56 56 60 56 56 60 56 56 56 56 59 55 55 59 55 55 58 54 54 58 54 54 57 53
La La La Pm Pm La La La La Ba Ba Nd Ba Ba Nd Ba Ba Ba Ba Pr Cs Cs Pr Cs Cs Ce Xe Xe Ce Xe Xe La I
Kf3.I Kf3, Kexl Kex2 Kf35 1 Kf30 II Kf31 Kf3, K Kexl Kf3.II Kf3, Kex, Kf351 Kf35 II Kf31 Kf3, Kexl K Kf3, Kex, Kf31 Kf3, Kexl K Kf3, Kex, Kf31 Kf3, Kexl K
KOII,III KNIV,V KNn,III KLm KLn KMv KMlv KMm KMII
Abs. edge KOU,III KLm KNIV KNII,III KLII KMv KMIV KMIII KMrr
KLIII Abs. edge KNrr ,III KLII KMnI KMu KLm
Abs. edge KNu,III KLrr KMm KMII KLm
A,bs, edge
38.909 38.828 38.7299 38.7247 38.1712 38.094 38.074 37.8010 37.7202 37.452 37.426 37.3610 37.311 37.257 36.8474 36.666 36.643 36.3782 36.3040 36.0263 35.987 35.822 35.5502 34.9869 34.9194 34.7197 34.59 34.415 34.2789 33.624 33.562 33.4418 33. 166/?
0.451295 0.454545 0.455181 0.455784 0.46407 0.465328 0.470354 0.474827 0.475105 0.475730 0.48589 0.4859 0.487032 0.490599 0.49306 0.495053 0.497069 0.497685 0.5092 0.5093 0.510228 0.512113 0.516544 0.51670 0.520520 0.521123 0.53395 0.53401 0.535010 0.53503 0.53513 0.5365 0.539422
3 4 4 3 1 7 3 3 6 5 1 9 4 3 2 3 4 4 1 2 4 3 3 9 4 4 1 9 3 2 5 1 3
52 Te 49 In 49 In 52 Te 48 Cd 48 Cd 518b 518b 48 Cd 48 Cd 47 Ag 47 Ag 47 Ag 508n 47 Ag 508n 47 Ag 47 Ag 46 Pd 46 Pd 46 Pd 49 In 49 In 46 Pd 46 Pd 46 Pd 45 Rh 45 Rh 48 Cd 45 Rh 45 Rh 94 Pu 48 Cd
Kexl Kf31 Kf3, Kex, K Kf32 Kexl K/Y.2 Kf31 Kf3, K Kf3. Kf3, Kexl Kf35 Kex, Kf31 Kf3, K Kf3. Kf3, Kexl Kex, Kf35 Kf31 Kf3, K Kf3.1 Kexl Kf3, Kf3,II LI
KIm KMm KMn KLII
K9i1
KLn
Abs. edge KNn ,III KLUI KLII KMln KMu
Abs. edge KNIV,V KNIl,III KLIII KMIV,v KLII KMru KMII
Abs. edge KNIV.V
KNII.III KLIII KLII KMIV,V KMm KMu
Abs. edge KNIV,V KLIII KNII,III KNII
Abs. edge
27.4723 27.2759 27.2377 27.2017 26.7159 26.6438 26.3591 26.1108 26.0955 26.0612 25.5165 25.512 25.4564 25.2713 25.145 25.0440 24.9424 24.9115 24.348 24.346 24.2991 24.2097 24.0020 23.995 23.8187 23.7911 23.2198 23.217 23.1736 23.1728 23.168 23.109 22.9841
>-
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0.37523 0.375313 0.383905 0.384564 0.385111 0.389668 0.38974 0.38974 0.391102 0.399995 0.400290 0.400659 0.404835 0.40666 0.40668 0.40702 0.407973 0.41378 0.41388 0.41634 0.417085 0.417737 0.42087 0.42467 0.42467 0.42495 0.425915 0.43175 0.43184 0.433318 0.435236 0.435877 0.437829 0.44371 0.44374' 0.44393 0,44500 0.45086 0.45098
2 2 4 4 4 5 1 1 6 5 4 4 4 1 1 1 5 1 1 2 3 4 2 3 1 3 8 3 3 5 5 5 7 1 3 4 1 2 2
53 I 57 La 53 I 53 I 56 Ba 56 Ba 52 Te 52 Te 52 Te 52 Te 55 Cs 52 Te 55 Cs 51 Sb 51 Sb 51 Sb 51 Sb 51 Sb 51 Sb 54 Xe 51 Sb 51 Sb 54Xe 50 Sn 50 Sn 50 Sn 50 Sn 50 Sn 50 Sn 53 I 50 Sn 50 Sn 53 I 49 In -49 Tn 49 In 49 In 49 In 49 In
K(32 Ka2 K(3, K(3, Kal Ka2 K K(32 K(3, Kal K(3, Ka2 K K(3.r K(32 K(3,r K(3,n Kal K(3, K(3, Ka2 K K(3.r K(3. K(3,I K(3,n Kal K(3, K(3, Kix2 K K(3.1 K(3. K(361 K(35II
KNlI,nr KLn KMrn KMn KLrn KLn KOn,rn Abs. edge KNll,ur KMnr KLm KMn KLn KOn,ln Abs. edge KNrv,v KNn,rn KMv KMrv KLrn KMnI KMn KLu KOu,nI Abs. edge KNIV,v KNn,nr KMv KM rv KLrn KMrn KMn KLu Abs. edge KOii,III KNrv,v KNn,rn KMv KMrv
33.042 33.0341 32.2947 32.2394 32.1936 31.8171 31.8114 31.8114 31. 7004 30.9957 30.9728 30.9443 30.6251 30.4875 30.4860 30.4604 30.3895 29.9632 29.9560 29.779 29.7256 29.6792 29.458 29.195 29.1947 29.175 29.1093 28.716 28.710 28.6120 28.4860 28.4440 28.3172 27.9420 27.940 27.928 27.8608 27.499 27.491
0.54101 0.54118 0.5416 0.54311 0.5432 0.545605 0.546200 0.5544 0.5572 0.5585 0.5594075 0.55973 0.56051 0.56089 0.56166 0.561886 0.563798 0.564001 0.5658 0.56785 0.5680 0.5695 0.5706 0.57068 0.572482 0.5725 0.573067 0.57499 0.576700 0.57699 0.578882 0.5810 0.585448 0.5873 0.58906 0.589821 0.58986 0.59024 0.59096
9 9 1 2 1 4 4 2 1 5 6 2 1 9 3 9 4 9 1 9 2 1 1 2 4 1 4 9 9 5 9 5 3 5 1 3 5 5 5
45 Rh 45 Rh 94 Pu 95 Am 94 Pu 45 Rh 45 Rh 95 Am 94 Pu 93 Np 47 Ag 94 Pu 44 Ru 44 Ru 44 Ru 95 Am 47 Ag 94 Pu 94 Pu 44 Ru 44 Ru 92 U 92 U 94 Pu 44 Ru 92 U 44 Ru 92 U 92 U 93 Np 94 Pu 93 Np 46 Pd 93 Np 43 Te 46 Pd 92 U 43 Tc 92 U
K(35 r K(3,n L,,/, L"/6 L"/l K(3, K(3, L"/2 Lu L,,/, Kal L"/6 K K(3. K(32 L"/l Ka2 L,,/. L"/B K(3,I K(3,u LI L"/I' L,,/. K(3, K(3, L,,/, L,,/.' L"/6 L"/l L"/3 Koo L,,/, K Ka. L"/ll K(32
KMv KMrv LrOm LnOrv LrOn KMm KMn LrNn Abs. edge LrOn,nr KLrrr LrrOrv Abs. edge KNrv,v KNn,III LnNrv KLn LrNm LnOr KMv KM IV Abs. edge LIPu,nI LrNn KMur LIOIV,V KMu LIOru LIOn LnOrv LUNIV LINuI KLm LrNn Abs. edge KLn LrNv KNu,ur LrNlv
22.9 22.9' 22.8 22.8 22.8 22.7 22.6 22.3 22.2 22.2 22.1 22.1 22.1 22.1 22.0 22.0 21. 9 21. 9 21. 9 21. 8 21. 8 21. 7 21. 7 21.1 21. 6 21. 6 21. 6 21. 5 21.4 21. 4 21.4 21. 3 21. l' 21.1 21.0· 21. 0: 21. 0 21. O( 20. 9~
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0.62636 0.62692 0.62708 0.6276 0.6299 0.62991 0.6312 0.6316 0.632288 0.63258 D.632872 0.63358 0.63557 0.63559 0.6356 0.6369 0.63898 0.64064 0.6416 0.64221 0.643083 0.6445 0.64513 0.6468 0.647408 0.64755 0.6482 0.64891 0.64965 0.65131 0.6521 0.65298 0.65313 0.65318 0.65416 0.6550 0.657655 0.6620 0.6654
9 5 5 1 1 9 1 1 9 4 2 9 2
4 1 1
5 9 1 4
4 1 5 1
5 5 1 2 5 5 1 1 3 5 4 1 9 1 1
90 42 42 90 90 90 90 90 42 90 42 91 92 90 90 90 90 90 94 90 44 88 88 88 44 90 94 95 88 88 90 41 90 41 41 91 95 90 88
Th Mo Mo Th Th Th Th Th Mo Th Mo Pa U Th Th Th Th Th Pu Th Ru Ra Ra Ra Ru Th Pu Am Ra Ra Th Nb Th Nb Nb Pa Am Th Ra
L,11 K{3,r K{3,II LII
K{3, L" K{3, L" L,5 L" L,8 Lv L(39 L" K0I. 1 Lr L,13 KOI.' L(31O L(3, L" L,.' K L" K(3, K(3, L,,/, L(3, L,l1
LrNv KMv KM rv LrNrv Abs. edge LIIPrv LUPU,Uf LuPr KMm LnOrv KMu LnNrv LuNr LrNnr LnOur LuQu LnOr LnNvr LrMv LrNu KLur Abs. edge LrPu,rII LrOrv,v KLu LrNr LtMrv LrMur LrOur LIOU LnNv Abs. edge LnNrv KNrv,v -kNn,m LnNr LnMrv LuNru LrNv
19.794 19.776 19.771 19.755 19.683 19.682 19.642 19.6-29 19.6083 19.599 19.5903 19.568 19.5072 19.507 19.506 19.466 19.403 19.353 19.323 19.305 19.2792 19.236 19.218 19.167 19.1504 19.146 19.126 19.1059 19.084 19.036 19.014 18.9869 18.9825 18.981 18.953 - - " 18.930 18.8520 18.729 18.633
0.7003 0.701390 0.70173 0.7018 0.70228 0.7031 0.70341 0.7043 0.70620 0.70814 0.7088 0.709300 0.71029 0.713590 0.71652 0.71774 0.71851 0.719984 0.7205 0.7223 0.72240 0.7234 0.72426 0.72521 0.726305 0.72671 0.72766 0~72776
1 9 3 1 4 1
2 1 2 2 2 1 2 6 9 5 2 8 1 1
5 1 5 5 9 2 5 5 4 1 1 5 1 2
0.72864 0.7301 0.7309 0.73230 0.7333 _0.73418 " - 10.7345 0.73602 ,6, 0.736230 9 0.738603 9 0.73928 9
94 Pu 95 Am 40 Zr 91 Pa 40 Zr 94 Pu 95 Am 88 Ra 94 Pu 93 Np 91 Fa 42 Mo 92 U 42 Mo 87 Fr 88 Ra 94 Pu 92 U 94 Pu 92 U 92 U 90 Th 92 U 92 U 92 U 93 Np 39 Y 39 Y 39 Y 90 Th 92 U 91 Pa 92 U 95 Am -39Y 92 U 93Np 92 U 86 Rn
L{3, L{3, K{3, L{39 K{3, Lu L{315 L{3. L{3, L{3,o KOI.i L{3, KOI.' L,I L" L{3, L{31 L(315 Lrn L(39 . L(3, . L(3. K K{3. K(3, L{3ro L(3, L(3, K(35 L{37 L{3, Lu L,I
LurOr LmNv KMm LrMv -KM u LtnNvr ,VII LmNrv LuNru LrMu LnrOrv,v LrMrv KLru LrMru KLu LnNIV LnNr LurNv LnMrv LtIrNrv Abs. edge LnrPrv,v LIMV LIuPu,rn LnrPr LnrOrv,v LrMn Abs. edge KNrv,v KNu,UI LrMrv LUIOu LrMur LurOn LurNr KMrv, v LurO! LnrNv LurNvr,vII LuNrv
17. 705 17.6765 17.6678 17.667 17.654 17.635 17.6258 17. 604 17. 5560 17.5081 17.492 17.47934 17.4550 17.3743 17.303 17.274 17.2553 17.2200 17.208 17.165 17.162 17.139 17.118 17.096 17.0701 17.0607 17.038 17.036 17.0154 16.981 16.962 16.930 16.907 16.8870 16.879 16.845 16,8400 16.7859 16.770
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TABLE
Wavelegth,
A*
7f-2.
WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER
p.e.t Element
Designation
keV
Wavelength,
A*
Designation
p.e·t Element
~ f-'
(Continued) keV
tv 00
"---
0.74072 0.74126 0.74232 0.74503 0.7452 0.74620 0.747985 0.75044 0.75148 0.7546 0.754681 0.75479 0.756642 0.75690 0.7571 0.7579 0.75791 0.7591 0.7607 0.76087 0.76087 0.76198 0.7625 0.76289 0.76338 0.7641 0.7645 0.76468 0.765210 0.76857 0.769 0.7690 0.7691
2 3 5 5 2 1 9 1 2 2 9 3 9 3 1 1 5 1 1 9 3 3 2 9 5 5 2 5 9 5 1 1 1
39 39 91 92 91 41 92 41 94 91 92 90 92 83 83 90 83 94 90 90 83 83 90 85 90 83 84 90 90 88 93 90 92
Y Y Pa U Pa Nb U Nb Pu Pa U Th U Bi Bi Th Bi Pu Th Th Bi Bi Th At Th Bi Po Th Th Ra Np Th U
K{1, K{13 L{1, L{117 L{15 Ka1 L{1, Ka. L{16 L{17 L{1. L{13 L{115 L1'13 Lr
KMnr KMrr LnMrv
LnMrn LrnOrv,v KLm Lr 11in KLu LnrNr
LruOr LlIrNv
LrMnr LnrNrv LIPn . m Abs. edge LuMv
LrOrv.v L"f/ LUI L1" L1'.'
LnMr
Abs. edge LIIIPrv.V LrOrn LrOu
LurPn.IIr L1'1
LnNrv
LurPr LrNvr.vn L1'6 L{15 L{1, L{19 L{16
LIIOrv
LIuOrv.v LuMIV LIMV LIUNI
LIn anI LIUNIII
16.7378 16.7258 16.702 16.641 16.636 16.6151 16.5753 16.5210 16.4983 16.431 16.4283 16.4258 16.3857 16.3802 16.376 16.359 16.358 16.333 16.299 16.295 16.2947 16.2709 16.260 16.251 16.241 16.23 16.218 16.213 16.2022 16.131 16.13 16.123 16.120
0.7973 0.8022 0.80233 0.80273 0.8028 0.80364 0.8038 0.8050 0.80509 0.80627 0.8079 0.8081 0.8082 0.80861 0.81163 0.81184 0.81308 0.81311 0.81375 0.8147 0.81538 0.8154 0.81554 0.8158 0.81583 0.8162 0.81645 0.81683 0.8186 0.8190 0.8200 0.8210 0.8219
1 1 9 5 1 7 1 1 2 5 1 1 1 5 9 5 5 2 5 1 5 2 5 1 5 1 3 5 1 2 1 2 1
83 83 82 88 88 82 88 88 92 88 91 81 90 81 90 81 81 83 88 82 82 37 37 81 82 88 37 82 88 90 82 82 37
Bi Bi Pb Ra Ra Pb Ra Ra U Ra Pa Tl Th Tl Th Tl Tl Bi Ra Pb Pb Rb Rb Tl Pb Ra Rb Pb Ra Th Pb Pb Rb
L1'8 L1'1l L{13
LrlI
LnOr LrNr LrNv
LrMnr Abs. edge LrNrv
LnrPn,ru L"f/ L{16 L{16 Lr
LIlrPr LnMr
LrnOrv,v LnrNr
Abs. edge LrnNrn LIOrv.v LrMr
L1" L1'l L1'1 L{1, L1" Lu K{1, K L{17 K{1. L1" Lu
L1" K{15
LrOrrI LrOn L,rNrv LrrMrv
LrNur Abs. edge KNrv.v
Abs. edge LrOr LuPr LrLIOr KNu.UI LnOIv LInNVI. vu LIUNII LnOIII LINu KMrv.v
15.551 15.456 15.453 15.4449 15.444 15.427 15.425 15.402 15.3997 15.3771 15.347 15.343 15.341 15.3327 15.276 15.2716 15.2482 15.2477 15.2358 15.218 15.2053 15.205 15.2023 15.198 15.1969 15.190 15.1854 15.1783 15.146 15.138 15.120 15.101 15.085
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0.76973 0.7699 0.76989 0.77081 0.7713 0.772 0.7737 0.77437 0.77546 0.7764 '0.77661 0.77728 0.77822 0.77954 0.78017 0.7809 0.78196 0.78257 0.78292 0.78345 0.7858 0.78593 0.78706 0.78748 0.78838 0.7884 0.7887 0.78903 0.78917 0.7897 0.79015 0.79043 0.79257 0.79257 0.79354 0.79384 0.79539 0.79565 0.79721
5 1 5 3 1 1
1 4
5 1
5 5 9 5 9 2 5 7 2 3 1 1 7 9 2 1 1 9 5 1
1 3 4 4 3 5 5 3
9
38 Sr 91 Pa 38 Sr 38 Sr 90 Th 84 Po 91 Pa 90 Th 88 Ra 38 Sr 90 Th 83 Bi 89 Ac 83 Bi 92 U 93 Np 82 Pb 82 Pb 38 Sr 38 Sr 82 Pb 40 Zr 82 Pb 84 Po 92 U 82 Pb 83 Bi 89 Ac 83 Bi 82 Pb 40 Zr 83 Bi 90 Th 90 Th 90 Th 83 Bi 90 Th 83 Bi 83 Bi
K L{3, K{34 K{32 L-y, L{32 L{37 L{310 K{35 Lu L-Yll L{33 LI) Lr K{31 K{33 L-Y4 Ken L-yl L-Yl L{36 Ln L{31 L-Y3 Ka, L-Y6 L{34 L{317 L{32 L{315 L"/2 Lv
Aos. edge LrMn KNrv.v KNn.rn LrnOn LrNn LmNv LurOr LrMrv KMrv.v LnrNvr.vn LrNv LrMnr LrNrv LruNn LuMr
Abs. edge LrGrv.v KMrn KMn LrGur
ELm LrGn LnNrv LurNr LrNvr.vlr
Abs. edge LnMrv LrNnr LrGr KLn LnGrv LrMn LnMnr LnrMv LnGur LnrNlV LINn LrrNVI
16.107 16.104 16.104 16.0846 16.074 16.07 16.024 16.0105 15.988 15.969 15.964 15.951 15.931 15.904 15.892 15.876 15.855 15.843 15.8357 15.8249 15.777 15.7751 15.752 15.744 15.7260 15.725 15.719 15.713 15.7102 15.699 15.6909 15.6853 15.6429 15.6429 15.6237 15.6178 15.5875 15.5824 15.552
0.82327 0.82365 0.8248 0.82789 0.82790 0.82859 0.82868 0.82879 0.82884 0.82921 0.8295 0.83001 0.83305 0.8338 0.8344 0.8350 0.8353 0.83537 0.83722 0.8382 0.83894 0.83923 0.83940 0.83973 0.84013 0.84071 0.84130 0.8434 0.8438 0.8442 0.8452 0.84773 0.848187 0.8490 0.85048 0.8512 0.8513 0.85192 0.85436
7 5 1 9 8 7 2 5 1 3 1 7 1 1 9 2 1 5 5 2 7 5 9 3 7 5 4 1 1 2 2 5 9 1 5 1 2 7 9
82 82 83 87 90 82 37 81 39 37 91 81 39 90 83 80 80 88 88 82 80 83 87 82 80 88 81 81 88 81 80 81 95 81 81 88 81 82 86
Pb Pb Bi Fr Th Pb Rb TI Y Rb Pa TI Y Th Bi Hg Hg Ra Ra Pb Hg Bi Fr Pb Hg Ra TI TI Ra TI Hg TI Am TI TI Ra TI Pb Rn
Lv L-Y8 L{33 L{36 K{31 L-Yll Ken K{33 LI) Ka,
Lr L{3, L{316 L-Y4 L-Y5 L{31 L-Yl L-y{ L{34 L-Y3 Ln L{317 L-Y6 L-Y2 Lal Lv L-Y8 L{3,
LnNvr LnOr LnNrn LrMnr LmNr LrNr KMur LrNv XLrn KMn LuMr LrNrv KLn LnMn LnNn LrGrv.v
Abs. edge LrnNv LnrNrv LnNv LrGur LnNI LnMrv LnNrv LrGn LrMn LrNrn
Abs. edge LnMrrr LnGrv LIGr LrNn LlnMv LnGn LnNvr LrnNur LnGr LnNrn LrMrrr
15.060 15.0527 15.031 14.976 14.975 14.963 14.9613 14.9593 14.9584 14.9517 14.946 14.937 14.8829 14.869 14.86 14.847 14.842 14.8414 14.8086 14.791 14.778 14.7732 14.770 14.7644 14.757 14.7472 14.7368 14.699 14.692 14.685 14.670 14.6251 14.6172 14.604 14.5777 14.566 14.564 14.553 14.512
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TABLE
7f-2.
WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER
~ I-'
(Continued)
CJ,:)
Wavelength,
A* 0.85446 0.8549 0.85657 0.858 0.8585 0.860266 0.8618 0.86376 0.86400 0.8653 0.86552 0.86605 0.8661 0.86655 0.86703 0.86752 0.86816 0.86830 0.86915 0.87074 0.8708 0.87088 0.8722 0.87319 0.87526 0.87544 0.8758 0.8784 0.8785 0.87885 0.8790 0.87943 0.87995
p.e·t Element
4 1 7 2 3 9 1 5 5 2 1 9 1 5 4 3 4 2 7 5 2 5 1 7 1 7 1 1 1 7 1 1 7
90 Th 81 TI 80 Hg 87 Fr 82 Pb 95 Am 88 Ra 79 Au 79 Au 36 Kr 36 Kr 86 Rn 36 Kr 82 Pb 79 Au 81 TI 79 Au 94 Pu 80 Hg 79 Au 36 Kr 88 Ra 80 Hg 80 Hg 38 Sr 80 Hg 80 Hg 80 Hg 36 Kr 80 Hg 36 Kr 38 Sr 80 Hg
Designation
L'1/
LrrMr LINr LrNv
L'Yll LfJ2
LnrNv
La2
LrrNrr LmMrv
Lr KfJ< K LfJl KfJ2 L'Y' L'Y< L'Yl L'Y-3
o
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0.87996 0.88028 0.88135 0.8827 0.88433 0.88563 0.8882 0.889128 0.8931 0.8934 0.89349 0.8943 0.89500 0.89646 0.89659 0.89747 0.89783 0.89791 0.8995 0.8996 0.901045 0.90259 0.90297 0.90434 0.90495 0.90638 0.90742 0.90746 0.90837 0.90894 0.9091 0.90989 0.910639 0.9131 0.9143 0.9204 0.92046 0.9220 0.922558
5 2 9 2 7 7 2 9 1 1 9 1 4 5 4 4 5 3 2 2 9 5 3 3 4 7 5 7 5 7 3 5 9 1 2 1
2 2 9
81 Tl 94 Pu 85 At 80 Hg 79 Au 79 Au 81 Tl 93 Np 78 Pt 78 Pt 85 At 78 Pt 81 Tl 80 Hg 78 Pt 78 Pt 79 Au 83 Bi 78 Pt 84 Po 93 Np 79 Au 79 Au 79 Au 83 Bi 79 Au 88 Ra 79 Au 79 Au 80 Hg 84 Po 79 Au 92 U 79 Au 78 Pt 35 Br 35 Br 84 Po 92 U
La2 L~a
LOYll LOll Lr L~,
Loy, L-Yl Loy. L-yl L-Ya L~9 L~5
L0l2 Ln L-y. LOY2 L~,O
L." Lv L~3
L-ys LOll
L-Yll K K~2 L~,
La2
LnNru LnrMrv LrMur LrNr LrNv LrNrv LuMu LIUMV Abs. edge LrOv LnMrv LrOrv LnNr LnNlv LrOru LrOn LrNm LrMv LrOr LrnOrv,v LmMrv Abs. edge LuOrv LrNu LrMrv LnOur LuMr LuOn LuNvr LuNur LrMnr LuOr LmMv LrNr LrNv Abs. edge KNn,rn LnMrv LruMrv
14.0893 14.0842 14.067 14.045 14.020 13.999 13.959 1
8:
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1.10394 l. 10477 1.1053 1.1058 1.10585 l. 10651 1.10664 1.10882 l.10923 l. 11092 l.11145 l. 1129 l. 1137 1. 11386 l. 11388 l. 11489 l. 1149 l.11508 l.11521 1.1158 1. 11658 1. 11686 1. 11693 l. 11789 l. 1195 l. 11990 1.1205 l. 12146 l. 1218 1.12250 l. 1226 1.12548 1.12637 l. 12769 1.12798 1.12894 l.12936 l. 1310 1:13235
I
5 2 1 1 3 3 9 2 6 3 4 2 1 4 3 3 2 4 9 1 5 2 9 9 1 2 1 9 3 9 2 5 6 3 5 2 9 2 3
78 Pt 34 Be 73 Ta 77 Ir 77 Ir 79 Au 72 Hf 34 Be 77Ir 79 Au 77Ir 78 Pt 73 Ta 84 Po 73 Ta 77Ir 74 W 90 Th 73Ta 73 Ta 32 Ge 32 Ge 73 Ta 73 Ta 32 Ge 78 Pt 73 Ta 72 Hf 74 W 72 Hf 78 Pt 84 Po 76 Os 81 Tl 79 Au 32 Ge 32 Ge 78 Pt 74 W
L{3, Kai L,,(, LIn L{35 L{3. Ka, L{36 Lu Lu Lai L"(6 L{37 Ll Lv
K K{32 K{35 ,L{3, iL"(8 ,L"(li
La, :L{39 ;LTJ L{317 K{3, :K{33
,
L"(5
LIMln KLIII LINn Abs·. edge LUIOIY.Y LIMn LIOI KLu LuIOjI.ln LIUNI LUIN '1'1. VII LuMy Abs. edge LIUMy LuOrv LlnOI LuNuI LIUMI LINI LnNYI Abs. edge KNn.ln LuOnI LnOn KMIy.y LUMIY LIlOI LrNy LnNn LINry LruNIII LrnMrv LjMy LuMr LuMnr KMIII KMn LnrNn LnNI
,
1l.2308 1l. 2224 1l.217 1l.212 1l. 2114 1l.2047 1l.2034 1l.1814 11.1772 1l. 1602 n.1549 1l. 140 1l. 132 1l.1308 1l.1306 11.1205 1l.120 1l.1186 11.1173 1l.1113 Ll. 1036 Ll.1008 Ll. 1001 1l.0907 1l. 0745 1l. 0707 Ll. 0646 1l. 0553 Ll. 052 L1. 0451 Ll. 044 1l. 0158 n.OO71 lO.9943 LO.9915 10.9821 LO .9780 lO.962 lO.9490
l. 16545 l. 1667 1.16719 1.16962 l. 16979 l. 1708 l. 17167 l. 17218 l. 1729 l.17501 l. 17588 l. 17721 l. 1773 l. 17788 l. 17796 l. 17900 l. 17953 l. 17955 l. 17958 l. 17987 l. 1815 l. 1818 1.1827 l. 1853 1.1853 l. 18610 l. 18648 1.1886 1.18977 l. 1958 l. 19600 1.19727 1.1981 1.1985 1.1987 l. 20086 l. 2014 1.20273 1:2047
5 1
i
5 9 8 1 5 5 1
2 1 5 1 9 3 5 4 7 3 1 1 1 1 1 2 5 [;
1
:
7 1 2 7 2 1 1 7 1 3 1
77Ir 78 Pt 88 Ra 7"8 Pt 76 Os 79 Au 76 Os 75 Re 73 Ta 82 Pb 33 As 75 Re 75 Re 72 Hf 77 Ir 72 Hf 71 Lu 76 Os 77Ir 33 As 75 Re 70 Yb 70 Yb 70 Yb 71 Lu 75 Re 82 Pb 70 Yb 76 Os 31 Ga 31 Ga 76 Os 31 Ga 71 Lu 71 Lu 76 Os 71 Lu 79 Au 71 Lu
L{3'7 Ll L{32 L{3'5 L{3'0 L"(5 Lai Kc", L{35 LUI L{36 L"(I L"(3 L{33 L{34 Ka, Lu LI L"(4 L,,(, L{37 La, K K{32 L{3, K{35 Lrr L"(6 L1J L"(8
LliINn LiIMliI LUIMi LIMI LinNy LnMII' LmNiy LIMIy LnNI LliIMy KLIII LlbOIV.Y Abs. edge LuNv LrirNI LnNlv LINIU LiMm LIMU KLu LnINYI.. vu Abs. edge LIOiv.v LIOU.III LINn" LiiIOi LinMry LrOr LnMy Abs: edge KNn,nr LnMry KMry,v Abs. edge LnOrv LUINn LuOu.IIr LuMr LUOI
10.6380 10.6265 10.6222 10.6001 10.5985 10.5892 10.5816 10.5770 10.5102 10.551'5 10.543'72 10.5318 10.5306 10.5258 10.5251 10.5158 10.5110 10.5108 10.5106 10.50799 10.4931 10.4904 10.4833 10.4603 10.460 10.4529 10.4495 10.4312 10.4205 10.3682 10.3663 10.3553 10.348 10.3448 10.3431 10.3244 10.3198 10.3083 10.2915
P;1
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~ t>oJ
t-< t>oJ
Z
Q
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t>oJ
Z t>oJ ;u
Q Kj
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to!
Cl
q
t'
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~
::rl
~ Ul >-I
Cl
Ul
1.2429 1.24385 1.24460 1. 2453 1. 24631 1.2466 1.2480 1. 24923 1,2502 1. 25100 1.25264 1. 2537 1.254054 1.2,553 1.2555 1.25778 1.258011 1. 25917 1. 2596 1. 2601 1.26269 1.26385 1.2672 1.26769 1.2678 1. 2706 1. 2728 1. 2742 1. 2748 1. 2752 1.27640 1. 2765 1. 27807 1. 281809 1.2829 1.2834 1. 28372 1.28448 1.28454
2 7 3 1 3 2 2 5 3 5 7 2 9 1 1 4 9 5 1 3 5 5 2 5 2 1 2 2 1 2 3 2 5 9 5 1 2 3 2
78 Pt 82 Pb 74W 70 Yb 74W 73 Ta 76 Os 70 Yb 77 Ir 75 Re 80 Hg 73 Ta 32 Ge 73 Ta 73 Ta 73 Ta 32 Ge 75 Re 71 Lu 73 Ta 74W 73 Ta 74W 70 Yb 69 Tm 68 Er 74W 69 Tm 83 Bi 68 Er 79 Au 74W 81 Tl 74W 84 Po 30 Zn 30 Zn 77 Ir 73 Ta
LTJ L8 L{3. L{3H L{3. L{317 L-ys L{3. LOl. L{310 KOlI Lru L{35 Lu K0l2 L{34 L'Y5 L{3. L{3r L'YI L'Y3 Lr L'Y' Lt L'Y4 LOll L8 L{31 Ll K K(3. LTJ L{3.
LuMr LrrrMur LurNv LuOu,ru LurNrv LrMv LuMur LuOr LuMu LrrrNr L'ruMrv LrMrv KLrrr Abs. edge
LrrrOrv,v LruNvr,vn KLu LrMu LnNr LIlrOu,nr LrMrrr LrrrOr LrIINur LrrNrv LrNrrr Abs. edge
LuMv LrNn LrnMu LIOn,uI LIUMV LIIrNu LruMnr LuMrv LruMr Abs. edge
KNrr,ru LUMI LruNv
9.975 9.9675 9.9615 9.9561 9.9478 9.946 9.934 9.9246 9.917 9.9105 9.8976 9.889 9.88642 9.8766 9.8750 9.8572 9.85532 9.8463 9.8428 9.839 9.8188 9.8098 9.784 9.7801 9.779 9.7574 9.741 9.730 9.7252 9.722 9.7133 9.712 9.7007 9.67235 9.664 9.6607 9.'6580 9.6522 9.6518
1.32698 1.32783 1. 32785 1.33094 1.3358 1. 3365 1. 3366 1. 3386 1. 3387 1.3397 1.340083 1.3405 1.34154 1. 34183 1.3430 1. 34399 1.34524 1. 34581 1.34949 1.34990 1.35053 1.35128 1. 35131 1.35300 1.3558 1.35887 1.36250 1. 3641 1. 3643 1.3692 1. 3698 1. 37012 1.3715 1.37342 1. 37410 1. 37410 1. 37459 1. 3746 1. 38059
3 5 7 8 1 3 1 1 2 3 9 1 5 7 2 1 9 3 5 7 9 3 7 5 2 9 5 2 2 1 2 3 1 5 5 5 '7 2 5
73 Ta 72 Hf 76 Os 73 Ta 71 Lu 74W 75 Re 68 Er 74W 68 Er 31 Ga 71 Lu 81 Tl 71 Lu 71 Lu 31 Ga 71 Lu 73 Ta 71 Lu 82 Pb 72 Hf 77 Ir 79 Au 72Hf 69 Tm 72 Hf 77 Ir 68 Er 67 Ho 66 Dy 67 Ho 71 Lu 71Lu 75 Re 72 Hf 72 Hf 66 Dy 80 Hg 29 eu
L{31 L{316 LTJ L{36 ' L{3.
LuMrv LruNrv LnMr LrrrNr LrMv LIMI LuMu
Lrr L{317 L'Y6 KOlI Lrrr Lt L{35 L{310 KOl.
Abs. edge
L{34 L{3r Ll LOll L8 L{3. L'Y5 La. L'YI L'Y' Lr L'Y' L{3. L{j16 LTJ L{31 L(36 L'Y4 Lt K
LuMur LuOrv KLrrr Abs. edge
LrrrMrr LrrrOrv,v LrMrv KLn LrnOn ,rrr LrMn LrrrOr LrrrMr LrnNrrr LrnMv LruMur LrMrrr LuNr LnINn LrrrMrv LnNrv LrNnr Abs. edge
LrNn LrrrNv LnrNrv LnMr LrrMrv LInNI LIOn,III LrrrMrr Abs. edge
9.3431 9.3371 9.3370 9.3153 9.2816 9.277 9.2761 9.2622 9.261 9.255 9.25174 9.2490 9.2417 9.2397 9.232 9.22482 9.2163 9.2124 9.1873 9.1845 9.1802 9.1751 9.1749 9.1634 9.144 9.1239 9.0995 9.089 9.087 9.0548 9.051 9.0489 9.0395 9.0272 9.0227 9.0227 9.0195 9.019 8.9803
P;'4
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TABLE
1.....
7f-2. WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER (Continued)
CI.:)
Wavelegth,
A*
p.e.t
Element
1.38109 1. 3838 1. 38477 1.3862 1.3864 1. 38696 1.3895 1.3898 1.3905 1.39121 1.3915 1.39220 1.392218 1. 3923 1. 3926 1.3948 1. 3983 1.40140 1.40234 1.4067 1.41366 1.41550 1.41640 1.4174 1.4189 1.42110 1. 4216 1.4223 1.42278 1.4228 1.42359 1.4276 1.43025
3 1 3 1 1 7 2 1 1 5 1 5 9 2 1 1 2 5 5 3 7 5 7 2 1 3 1 1 7 3 3 2 9
29 eu 70 Yb 81 TI 70 Yb 73 Ta 70 Yb 78 Pt 70 Yb 67 Ho 76 Os 70 Yb 72 Hf 29 eu 67 Ho 29 eu 70 Yb 67 Ho 71 Lu 76 Os 68 Er 79 Au 70 Yb 66 Dy 67 Ho 71 Lu 74W 80 Hg 65 Tb 66 Dy 65 Tb 71 Lu 65 Tb 72 Hf
Designation
KfJ. LfJ. Ll Lrn LfJ17 LfJ5 L8
Ln Lell.1 LfJlD LfJ. KfJl" L-Y6 KfJ. LfJ7 L-y& LfJ. La. L-y, Lt LfJ".,. L-Y3 L-Yl LfJ. L'1/ Ll Lr L-y.· LfJl L-y.
KMIV,V LrMv LrnMr Abs. edge LnMrn LIIrOrv,v LurMlIr LnrOn,rn Abs. edge LmMv LrMrv LrMn KMn,rn LnOrv KMn LmOr LnOr LrMnr LmMrv LnNr LmMn LrnNrv,v LrNnr LnNrv LmNr LnMr LnlMr Abs. edge LrNIl LrOrv,v LnMrv LrOn,Ilr LrMr
keY
8.9770 8.9597 8.9532 8.9441 8.9428 8.9390 8.923 8.9209 8.9164 8.9117 8.9100 8.9054 8.90529 8.905 8.9029 8.8889 8.867 8.8469 8.8410 8.814 8.7702 8.7588 8.7532 8.747 8.7376 8.7243 8.7210 8.7167 8.7140 8.714 8.7090 8.685 8.6685
Wavelength,
A* 1.4941 1.4941 1.4995 1. 500135 1.5023 1.5035 1.5063 1.5097 1. 51399 1.5162 1.5178 1.51824 1.52197 1.52325 1.5297 1.5303 1.5304 1.53293 1. 5331 1. 53333 1. 5347 1. 5368 1. 5378 1.5381 1. 540562 1.54094 1.5439 1.544390 1.5448 1.5486 1. 5616 1. 5632 1. 5642
Designation
p.e.t Element
3 3 2 8 1 2 2 2 9 2 1 7 2 5 2 2 2 2 2 9 2 1 2 1 2 3 1 9 2 3 1 1 3
68 Er 68 Er 78 Pt 28 Ni 65 Tb 65 Tb 69 Tm 65 Tb 68 Er 69 Tm 75 Re 66 Dy 73 Ta 72 Hf 64Gd 65 Tb 69 Tm 73 Ta 64Gd 71 Lu 76 Os 67 Ho 67 Ho 63 Eu 29 eu 77Ir 63 Eu 29 eu 69 Tm 67 Ho 68 Er 64 Gd 74W
LfJ7 LfJIO Ll KfJ',3 Ln L-y. LfJ, L-Y8 LfJ.,15 LfJ. L8 L-Y6 Lal L." L-Y3 L-Yl LfJl La. L-y. Lt Lur LfJ. Lr Kal Ll L-y. Ka2 LfJ. LfJIO LfJ. Ln L8
LmOr LrMrv LmMr KMn,rn Abs. edge LnOrv LrMnr LnOr LmNrv,v LmNr LrnMnr LnNr LmMv LnMr LrNnr LnNrv LnMrv LrnMrv LrNn LnMn LmMn Abs. edge LrnOrv,v Abs. edge KLm LmMr LrOn,Ilr KLn LrMn LrMrv LIMnr Abs. edge LnrMnr
keY
8.298 8.298 8.268 8.26466 8.2527 8.246 8.231 8.212 8.1890 8.177 8.1682 8.1661 8.1461 8.1393 8.105 8.102 8.101 8.0879 8.087 8.0858 8.079 8.0676 8.062 8.0607 8.04778 8.0458 8.0304 8.02783 8.026 8.006 7.9392 7.9310 7.926
00
;.8
o
~
.....
Q
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o ~ Q q
~
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1.43048 1.4318 1.43290 1.4334 1.4336 1.4349 1. 435,155 1.43643 1.439000 1.44056 1.4410 1.44396 1.4445 1.44579 1.45233 1.4530 1.45964 1".4618 1.4640 1.4661 1.47106 1.4718 1. 47266 1. 4735 1.47565 1. 4764 1.47639 1.4784 1.48064 1.4807 1.4835 1.4839 1.4848 1.4855 1.48743 1.48807 1.48862 1.49138 1.4930
9 2 4 1 3 2 7 9 8 5 3 5 1 7 5 2 9 2 2 1 5 2 7 2 5 2 2 1 9 3 1 2 3 5 2 1 4 3 3
73 Ta 77Ir 75 Re 69 Tm 69 Tm 69 Tm 30 Zn 72 Hf 30 Zn 71 Lu 69 Tm 75 Re 66 Dy 66 Dy 70 Yb 78 Pt 79 Au 67 Ho 69 Tm 70 Yb 73 Ta 65 Tb 66 Dy 76 Os 70 Yb 65 Tb 74W 64 Gd 72 Hf 64 Gd 68 Er 64Gd 68 Er 68 Er 74W 28 Ni 28 Ni 70 Yb 77Ir
La Len Lnr L(j. L(j, Kal L(j17 Ka. L(j4 L(jlO La. Lu L'Y6 L(j3 Lt Ll L'Y5 L(j.,l' L(j6 L'1/ L'Y3 L'Yl Ls L(jl L'Y' Lal LI
LnMn LrnMnr LmMv
Abs. edge LrMv LmOrv,v KLm LuMnr KLn LrMn LrMrv LurMlv
Abs. edge LnOrv LrMUI LnrMn LmMr LIINI LrIINrv, v LmNr LnMr LrNm
LuNrv LIIIMur LnMrv LINu LmMv
Abs. edge LnMu LrOrv,v
LUI L'Y4 L(j5 L(j. La, K K(j5 L(j. Lt
Abs. edge
LIOn ,III LmOrv,v LIMv LIuMrv
Abs. edge KMrv,v LIMU LIUMU
8.6671 8.659 8.6525 8.6496 8.648 8.641 8.63886 8.6312 8.61578 8.6064 8.604 8.5862 8.5830 8.5753 8.5367 8.533 8.4939 8.481 8.468 8.4563 8.4280 8.423 8.4188 8.414 8.4018 8.398 8.3976 8.3864 8.3735 8.373 8.3575 8.355 8.350 8.346 8.3352 8.33165 8.3286 8.3132 8.304
1. 5644 1.5671 1. 5675 1. 56958 1.5707 1.5779 1.5787 1.5789 1.58046 1.58498 1. 5873 1. 58837 1.58844 1. 5903 1.5916 1.5924 1.5961 1.59973 1.6002 1. 6007 1. 60447 1.60728 1. 60743 1. 60815 1. 60891 1. 61264 1.61951 1. 6203 1. 62079 1. 6237 1. 62369 1. 6244 1. 6271 1. 6282 1. 63029 1.63056 1. 6346 1.63560 1. 6412
2 2 2 5 2 1 2 1 5 7 1 7 9 2 1 2 2 9 1 1 7 3 9 1 3 9 3 2 2 2 7 3 1 2 5 5 2 5 2
64Gd 67 Ho 68 Er 72 Hf 64 Gd 71 Lu 65 Tb 75 Re 72 Hf 76 Os 68 Er 66 Dy 70 Yb 63 Eu 66 Dy 64 Gd 63 Eu 66 Dy 62Sm 68 Er 66 Dy 62 Sm 66Dy 27 Co 27 Co 73 Ta 71 Lu 67 Ho 27 Co 67 Ho 66 Dy 74W 63 Eu 63 Eu 71 Lu 75 Re 63 Eu 70 Yb 64Gd
L'Y6 L(j., 15 L(j6 Lal L'Y8 L'1/ L'Y5 Lt La. Ll L(jl L(j. L'Y3 LUI L'Yl L'Y' L(j. Lr L(j. L(j7 L'Y4 L(jlO K K(j5 Ls Lal L(j3 K(jl,3 L(j6 L(j"l5 Lt Lu L'Y6 La. Ll L'Y8 L'1/ L'Y5
LnOrv LmNrv,v LmNr LmMv
LnOr LuMr LnNr
LrnMn LrnMrv LmMr LuMrv
LUIOIV,V LnMn LrNur
Abs. edge LnNrv LrNu LrMv
Abs. edge LIMII LmOr
LrOII,IIr LrMrv
Abs. edge KMrv,v LnrJ.!ur LmMv
LrJ.!nI KMn,III LrnNr LnrNrv,v LIUMu
Abs. edge
LUOIV LIUMIV LmMI LUOI LUMI LuNI
7.925 7.911 7.909 7.8990 7.894 7.8575 7.8535 7.8525 7.8446 7.8222 7.8109 7.8055 7.8052 7.7961 7.7897 7.7858 7.7677 7.7501 7.7478 7.7453 7.7272 7.714 7.7130 7.70954 7.7059 7.6881 7.6555 7.8519 7.64943 7.6359 7.6357 7.6324 7.6199 7.6147 7.6049 7.6036 7.5849 7.5802 7.5543
~
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8 ~
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o
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C":l
l:'J
Z
l:'J ~
o k1
~
l:'J
t
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l/l
..... Cl
l/l
3.011 3.0166 3.02335 3.0309 3.0342 3.038 3.04661 3.068 3.0703 3.0746 3.07677 3.08475 3.0849 3.0897 3.094 3.11513 3.11513 3.115 3.12170 3.131· 3.1355 3.1377 3.1473 3.14860 3.15258 3.1557 3.1564 3.15791 3.16213 3.17505 3.19014 3.217 3.22567 3.245 3.24907 3.2564 3.2670 3.26763 3.26901
2 2 3 1 1 2 9 5 1 3 6 9 1 2 5 9 9 7 9 3 2 2 1 6 9
i
3 6 4 3 9 5 4 9 9 1 2 9 9
90 Th 54Xe 51 Sb 21 Se 21 Se 91 Pa 52 Te 90 Th 20 Ca 20 Ca 52 Te 50 Sn 48 Cd 20 Ca 83 Bi 50 Sn 51 Sb 92 U 50 Sn 90 Th 56 Ba 48 Cd 49 In 53 I 51 Sb 50 Sn 50 Sn 53 I 49 In 50 Sn 51 Sb 82 Pb 51 Sb 91 Pa 49 In 47 Ag 55 Cs 49 In 50 Sn
Lal
L{32,l6 K.al Ka2 L{34
Mnr K K{36
L{3l L-Y5 Lr
K{3l" Mr L{3g
L{3G L{3l0 Ll L-Y2
Ln Lal L{3,
LIn L{37 La2
L-)'l L{32,15 L{34
MI L{3l
KLn
MrnOlv,v LrMn Abs. edge Abs. edge KMrv,v LnMlv LnNr
Abs. edge KMn,nr Abs. edge LrMv LruNr MurOI LIMIV MmOrv,v LrI1Mr LINn
Abs. edge LmMv LrMnI Abs. edge LnrOr LnrMrv LnNrv LnrNrv,v LrMn Abs. edge LnMlv MurOr
L-Y6
LnNr
Lr
Abs. edge LmMr LrMv LnINr
Ll L{3g L{3.
4.117 4.1099 4.10078 4.0906 4.0861 4.081 4.0695 4.041 4.0381 4.0325 4.02958 4.0192 4.0190 4.b127 4.007 3.9800 3.9800 3.980 3.9716 3.959 3.9541 3.9513 3.9393 3.93765 3.9327 3.9288 3.9279 3.92604 3.92081 3.90486 3.8364 3.854 3.84357 3.82 3.8159 3.8072 3.7950 3.7942 3.7926
MnNIV LmMv LlnNlv,'v KLnI
.
_.
- -----------_.
3.46984 3.478 3.479 3.4892 3.492 3.497 3.5047 3.50697 3.51408 3.5164 3.521 3.52260 3.537 3.55531 3.557 3.55754 3.576 3.577 3.59994 3.60497 3.60765 3.60891 3.61158 3.614 3.61467 3.61638 3.616 3.629 3.634 3.64495 3.679 3.68203 3.6855 3.691 3.6999 3.70335 3.716 3.71696 3.718
9 5 1 2 5 5 1 9 4 1 2 4 9 4 5 9 1 1 3 9 9 4 9 2 9 9 5 5 5 9 2 9 2 2 1 3 1 9 3
49 In 80 Hg 92 U 46 Pd 82 Pb 92 U 48 Cd 49 In 48 Cd 47 Ag 92 U 47 Ag 90 Th 49 In 90 Th 53 I 92 U 91 Pa 50 Sn 47 Ag 51 Sb 50 Sn 47 Ag 91 Pa 48 Cd 47 Ag 79 Au 45 Rh 81 Tl 48 Cd 90 Th 48 Cd 45 Rh 91 Pa 47 Ag 47 Ag 92 U 52 Te 90 Th
L{Ja
MI M-y L-Y2"
Mn Mv Lm L{34
L{32,l6 Ln L-Yl
LIMIT! Abs. edge MmNv
LINn,In Abs. edge Abs. edge Abs. edge LIMn LurNlv,v Abs. edge MnrNlv LnNlv MnNI
L{3l M rv Ll M-y Lal L{3. L1J La2
L{3l0 L{3G L-Y6
Mr Lr Mn L{3, M-y L{34 L-Y2,3
LnMrv Abs. edge LmMI MlvOn MmNv
LnIMv LrMv LnMr LmMlv L1Mrv MurNrv LmNr LnNl
Abs. edge Abs. edge Abs. edge LrMnr MnrNv
LrMn
LrNu,n~
LIn L{32,l6
MrvOn Abs. edge LmNrv,v
M{3 Ll
MrvNvr
LmMr MmNlv
3.57311 3.565 3.563 3.5533 3.550 3.545 3.5376 3.53528 3.52812 3.5258 3.521 3.51959 3.505 3.48721 3.485 3.48502 3.4666 3.4657 3.44398 3.43917 3.43661 3.43542 3.43287 3.430 3.42994 3.42832 3.428 3.417 3.412 3.40145 3.370 3.36719 3.3640 3.359 3.35096 3.34781 3.3367 3.33555 3.335
~
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t-'l
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TABLE
Wavelength,
A*
7f-2.
WAVELENGTHS OF X-RAY EMISSION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER
p.e·t Element
Designation
keY
Wavelength,
A*
p.e·t
Element
1
(Continj.led)
I-'
keY
Designation
fI>. 00
--
4.84575 4.85381 4.861 4.865 4.869 4.876 4.879 4.8873 4.909 4.911 4.913 4.9217 4.9232 4.946 4.952 4.9525 4.9536 4.955 4.955 4.984 5.004 5.0133 5.0185 5.020 5.0233 5.031 5.0316 5.0361 5.043 5.0488 5.0488 5.050 5.076
5 7 1 5 9 9 5 8 1 5 1 2 2 2 5 3 3 4 5 2 9 3 1 5 3 1 2 3 5 3 5 2 1
44 Ru 44 Ru 77Ir 81 Tl 77Ir 78 Pt 40 Zr 43 Tc 83 Bi 90 Th 42 lVIo 45 Rh 42 lVIo 92 U 81 Tl 46 Pd 40 Zr 76 Os 82 Pb 80 Hg 82 Pb 42 lVIo 16 S 73 Ta 16 S 41 Nb 16 S 41 Nb 76 Os 42 lVIo 42 lVIo 92 U 82 Pb
Lal La,
LIIIMv LIrrMrv
MIlr
Abs. edge MnrNIv MrnOrv.v 111m Or Abs. edge
Lr L(h M{1
LIlMIV MrvNvI
Lnr
MrvNnr Abs. edge
L'f/ L{1,,15
LnMr LrrrNrv,v
MIl .Mrv
MvNrn Abs. edge
Ll L,2"
LIlrMI
Mv M, L{1, K
Mrr
LINrr,rn MrrNrv Abs. edge MnINv
MrvOn LIMIn Abs. edge Abs. edge KM
K{1z Ln K{1l L"
KM LrrNIv
MIn
Abs. edge
L{14 L{16
LIMn LIIINr
Ml'
MrvNn MIvNvr
M(3
Abs. edge
2.55855 2.55431 2.5505 2.548 2.546 2.543 2.541 2.5368 2.5255 2.524 2.5234 2.5191 2.5183 2.507 2.504 2.5034 2.5029 2.502 2.502 2.4875 2.477 2.4730 2.47048 2.470 2.4681 2.4641 2.46404 2.4618 2.458 2.4557 2.4557 2.4548 2.4427
5.40655 5.41437 5.4318 5.435 5.460 5.472 5.4923 5.4977 5.500 5.5035 5.537 5.540 5.570 5.579 5.584 5.5863 5.59 5.592 5.624 5.628 5.6330 5.6445 5.6476 5.650 5.6681 5.67 5.682 5.704 5.7101 5.724 5.7243 5.7319 5.756
8 8 9 1 1 2 3 3 4 3 8 5 4 1 5 3 1 5 1 8 3 3 9 5 3 3 4 8 3 5 2 3 1
42 42 80 74 81 81 41 40 77 44 83 77 73 40 79 40 78 38 79 74 40 38 80 73 40 73 76 82 40 76 41 41 39
lVIo lVIo Hg W Tl Tl Nb Zr Ir Ru Bi Ir Ta Zr Au Zr Pt Sr Au W Zr Sr Hg Ta Zr Ta Os Pb Zr Os Nb Nb Y
g'
2.29316 2.28985 2.2825 2.2811 2.2706 2.2656 2.2574 2.2551 2.254 2.2528 2.239 2.238 2.226 2.2225 2.220 2.2194 2.217 2.217 2.2046 2.203 2.2010 2.196.5 2.1953 2.194 2.1873 2.19 2.182 2.174 2.1712 2.166 2.16589 2.1630 2.1540
>->-3
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o
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t"
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o
cj
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o
rn
5.092 5.1148 5.118 5.130 5.145 5.1517 5.153 5.157 5.168 5.172 5.17708 5.186 5.193 5.196 5.2050 5.217 5.2169 5.230 5.234 5.2379 5.245 5.249 5.2830 5.286 5.299 5.3102 5.319 5.340 5.3455 5.357 5.357 5.36 5.3613 5.37216 5.374 5.37496 5.378 5.3843 5.40
2 3 1 2 4 3 5 5 9 9 8 5 2 9 2 5 3 1 5 3 5 1 3 1 2 3 4 5 3 4 5 1 3 7 5 8 1 3 2
91 Pa 43 To 83 Bi 83 Bi 79 Au 41 Nb 81 Tl 80 Hg 82 Pb 74 W 42 Mo 79 Au 91 Pa 81 Tl 44 Ru 39 Y 45 Rh 41 Nb 75 Re 41 Nb 90 Th 81 Tl 39 Y 82 Pb 82 Pb 41 Nb 78 Pt 90 Th 41 Nb 74W 78 Pt 80 Hg 41 Nb 16 S 79 Au 16 S 40 Zr 40 Zr 73 Ta
MSI Lal kIal Ma, M'( L'(5 My
Mry
kIyNm LmMy MyNyu
MyNYr MmNy LuNr Abs. edge Abs. edge
MyOrII MINIIr L{j,
Ms,
LIIkIrv MII1Nrv MrvNII
MrvOu L'1 Lr Ll
LIIr MIIr L{j,,15
MSI M{j L,(,,3 Mal Ma, L{j3 M,(
LIIMr Abs. edge LmMr Abs. edge Abs. edge LurNIv,y MvNIIr
MrvNvr LINn,rII MvNYII MyNvr
LrMrn MmNv
Ms,
MryNII
L{j,
L r101II MUNIV MIIrNIV Abs. edge LInNr KLm Abs. edge KLII Abs. edge
Mv L{j6 Kal MIV Ka, Ln L'(l
LIINry kIrNm
2.4350 2.4240 2.4226 2.4170 2.410 2.4066 2.406 2.404 2.399 2.397 2.39481 2.391 2.3876 2.386 2.38197 2.377 2.3765 2.3706 2.369 2.3670 2.364 2.3621 2.3468 2.3455 2.3397 2.3348 2.331 2.322 2.3194 2.314 2.314 2.313 2.3125 2.30784 2.307 2.30664 2.3053 2.3027 2.295
5.767 5.784 5.796 5.81 5.81 5.828 5.83 5.83 5.8360 5.840 5.8475 5.854 5.8754 5.884 5.885 5.931 5.962 5.9832 5.987 6.008 6.0186 6.038 6.0458 6.047 6.05 6.058 6.0705 6.073 6.0778 6.09 6.092 6.0942 6.134 6.1508 6.157 6.160 6.162 6.173 6.2109
9 1 2 2 1 1 2 1
3 1 3 3 3 8 2 5 1 3 9 5 3 1 3 1 1 3 2 5 3 2 3 3 4 3 1 1 8 1 3
79 Au 15 P 15 P 76 Os 78 Pt 78 Pt 73 Ta 77 Ir 40 Zr 79 Au 42 Mo 79 Au 39 Y 81 Tl 75 Re 75 Re 39 Y 39 Y 78 Pt 37 Rb 39 Y 77 Ir 37 Rb 78 Pt 77 Ir 78 Pt 40 Zr 76 Os 40 Zr 80 Hg 74W 39 Y 74W 42 Mo 15 P 15 P 83 Bi 38 Sr 41 Nb
K K{j My M{j
Mry L{jl kIal L'1 Ma, L'(5 M'(
LIIr L{j3 LI L{j, M{j L,(,,3 Mal My Ma, Lal
Mry La, kf'( L{j6 Ll Ka, Kc-3
::c: r:J2
:>-
Z
t::I
:>-
>-3
o
l::: H a t::l
Z
t::l !:d
o
~
t"'
~
t::l t"'
r:J2
t
I-' ~
""
'TABLE 7f"2.·-W:A:VELENGTHS -OF X"RAy-E-MISSTO"l-LINES· AND ABSORPTION EDGEs: IN-NUMERICAL
...;J
ORDER-(Cominued)
I
f-' Q1
Wavelength,
A* 6.2120 6.209 6.262 6.267 6.275 6.28 6.2961 6.30 6.312 6.33 6.353 6_3672 6.384 6.387 6.4026 6.4488 6.455 6.4558 6.47 6.490 6.504 6.5176 6.5191 6_521 6.544 6.560 6.585 6.59 6.6069 6.6239 6.644 6.669 6.729
p.e·t
Element
3 9 1 1
39 Y 79 Au 77Ir 76 Os 77Ir 74 W 38 Sr 76 Os 73 Ta 75 Re 73 Ta 38 Sr 82 Pb 38 Sr 38 Sr 39 Y 78 l't 39 Y 36 Kr 76 Os 75 Re 41 Nb 38 Sr 83 Bi 72 Hi 75 Re 83 Bi 74W 40 Zr 38 Sr 37 Rb 77 Ir 75 Re
3
2 3 1 4 1 5 3 7 1 3 2 9 3 1 1 1 3 3 4 4 5 5
1 3
3 1 9 1
Designation
L(31 Mal M(3 Ma2 L1'5 Mv MI' Mry L(33 Lm
L(3, Lal La2 Lr Ma M(3 Ll L(3, M.\l MI' Mv M.\2 Mrv L'J L(31 Ln Ma
LnMrv MmNr M"NvIl MrvNvr MvNvI MnNI LnNr Abs. edge MnrNv Abs. edge MllINrv L rlJ1m MrvNrn Abse .edge LIMn LIUMV MmNr LrnMrv Abs.edge MvNvr.VII MlvNvr LmM'i LnINr lJ1vNrII MnrNv Abs. edge MIVNu Abs. edge LrrMr LnMrv Abs. edge MnrNr MvNvr.vn
. keV-
Wavelength,
A*
p.e·t
1.99584 1. 981 1.9799 1.9783 1. 9758 1.973 1.96916 1.967 1.964 1. 958 . 1. 951 1. 94719 1.942 1. 9411 1.93643 1.92256 1. 921 1. 92047 1.915 1. 9102 1. 9061 1.90225 1. 90181 1. 901 1.895 1.890 1.883 1.880 1. 87654 1. 87172 1.8661 Ui59 1.8425
7.30 7.303 7.304 7.3183 7.3251 7.3563 7.360 7.371 7.392 7.466 7.503 7.510 7.5171 7.523 7 . 539 7.546 7.576 7.60 7.601 7.612 7.645 7.738 7.753 7.767 7.790 7.817 7.8362 7.840 7.865 7.887 7.909 7.94813 7.960
2 1 5 2 3 3 8 8 1 4 1 4 3 5 1 8 3 1 2 9 8 4 5 9 5 3 3 2 9 9 2 5 2
Element
73 72 36 37 37 39 74 78 36 79 34 36 38 79 72 68 36 68 71 73 77 78 35 35 78 36 38 71 67 72 70 13 13
Ta Hi Kr Rb Rb Y W Pt Kr Au Se Kr Sr Au Hi Er Kr Er Lu Ta Ir Pt Br Br Pt Kr Sr Lu Ho
I
Designation
M(3 L(34 Lal La2 Ll Lur M.\I Li L(3, L'J Ml2 Ma MI' L(31
M(3 MIl Lu L(33,4 M.\2 Lal,2 Ll Ma MI'
Hf
Yb Al Al
M(3 K KfJ
MvOm MrvNvr LrMn LIull1 v LIuMrv LInMr lJ1llI NI MIvNur Abs. edge MvNm Abs. edge LrnNr LnMr MrvNu MvNvr,vu MllINv Lull1rv MurNrv MrVNVI MIIrNr MrvNIU MvNrn Abs.-edge LrMII,IIr MrvNn LurMrv,v LIuMr MvNvr,vn MnrNrv,v MlnNr MrvNvr Abs. edge KM
keY
1.700 1. 6976 1.697 1.69413 1.69256 1.68536 1.684 1.682 1. 6772 1.6605 1.6525 1. 6510 1.64933 1. 648 1. 6446 1.643 1.6366 1.632 1. 6312 1.629 1.622 1. 6022 1.599 1. 596 1.592 1.5860 1. 58215 1. 5813 1. 576 1. 572 1. 5675 1. 55988 1.55745
o
~
s::: H
Q
P>
§ s:::
o
t-
8 P> 1-3
o
is: H ()
trI
Z
trI
::0 Q
t-1
t"
trI
& ;s:: o t"'
to!
Cl
q
~
~
;g ;3 ,..... Cl Ul
10.254 10.294 10.31 10.359 10.40 10.4361 10.46 10.48 10.505 10.711 10.734 10.750 10.828 10.96 10.998 11. 013 11. 023 11. 072 11.07 11. 100 11.200 11.27 11.288 11.292 11. 37 11.47 11. 53 11. 552 11. 56 11.569 11.575 11. 609 11. 862 11. 86 11.9101 11.965 11.983 12.08 12.122 to~-
6 1 1 9 7 8 3 1 9 5 1 7 5 3 9 5 2 1 7 1
7 1 5 1 1
3 1 5 5 1 2 2 1 1 9 2 3 4
3
64 Gd 34 Se 30 Zn 31 Ga 92 U 32 Ge 64 Gd 70 Yb 60 Nd 63 Eu 33 As 63 Eu 31 Ga 63 Eu 59 Pr 63 Eu 31 Ga 33 As 90 Th 31 Ga 30 Zn 62 Sm 62 Sm 31 Ga 68 Er 62 Sm 58 Ce 62 Sm 90 Th 11 Na 11 Na 32 Ge 30 Zn 67 Ho 11 Na 32 Ge 30 Zn 57 La 29 Cu
M(3 L1
MrvNvr LruMr
Lr
Abs. edge
L(3,,4
LrMn,rn NnPr
La1,2 Ma
Mr MI'
LruMrv,v MvNVI,VU MvNnr MurNrv,v
M rv
Abs. edge
Ll1 M(3
LuMr MrvNvr
Ln
Abs. edge
Ma MI' Mv L(3, L1
MvNvI,vn MrnNrv,v LnMrv LmMr
Lnr
NnPr Abs. edge
L(33,4 M(3
LrMn,nr MrvNvr
Abs. edge
Mrv
Abs. edge
La1"
LrnMrv,v
Mr
MvNnI
Ma
.Llf"
MvNvI,vn MurNrv,v
Mv
Abs. edge
NnOrv Abs. edge KM
K K(3 Ll1
LuMr
Lu Mr
Abs. edge MvNrII
Ka1,2 Ll L(3, MI' L(3,,4
KLn,rII LrnMr LuMrv MurNrv,v LrMn,ru
1. 2091 1.2044 1.197 1.197 1.192 1.18800 1.185 1.183 1.180 1. 1575 1. 1550 1. 1533 1. 1450 1.131 1.1273 1.1258 1.1248 1. 1198 1. 120 1. 1169 1.1070 1. 0998 1.0983 1.09792 1. 0901 l.081 l. 0749 1.0732 1.072 l. 07167 l. 0711 1.0680 1. 04523 1.0450 1.04098 l. 0362 l. 0347 l.027 1. 0228
14.39 14.452 14.51 14.525 14.561 14.610 14.88 14.90 14.91 15.286 15.56 15.618 15.65 15.666 15.72 15.89 15.91 15.915 15.93 15.972 15.98 16.20 16.27 16.46 16.693 16.7 16.92 16.93 17.19 17.202 17.26 17.38 17.525 17.59 17.6 17.87 17.94 17.9 18.292
5 5 5 5 3 3 5 2 4 9 1 5 4 8 9 1 5 5 4 6 5 5 3 4 9 1 4 5 4 5 1 4 5 2 1 3 5 1 8
58 Ce 10 Ne 57 La 28 Ni 28 Ni 10 Ne 57 La 29 Cu 62 Sm 29 Cu 56 Ba 27 Co 26 Fe 27 Co 56 Ba 56 Ba 56 Ba 27 Co 52 Te 27 Co 51 Sb 56 Ba 28 Ni 60 Nd 28 Ni 24 Cr 51 Sb 50 Sn 25 Mn 26 Fe 26 Fe 59 Pr 26 Fe 26 Fe 52 Te 27 Co 50 Sn 24 Cr 27 Co
MvOn,nr K(3 M(3
Lrn LCQ,2
KM
MrvNvr Abs. edge
LrIIMrv,v
Ka1,2 Ma Ll1 Mr L1
MvNvI,VII LnMr MVNUI LnrMr
M rv Ln
Abs. edge Abs. edge
L(33,4 L(3,
LrMn,In LnMrv MrvOm
Mv
Abs. edge
KLu,III
MrvOn LIU
Abs. edge
MI' La!"
MrnNrv,v LrnMrv,v MnNrv MvOnr
Ll1
LnMr
Mr L1
MvNrn LrnMr
Lr
Abs. edge
MI' L(33,4
MnrNrv,v MnNrv LrMIT,nr
Ln
Abs. edge
L(3!
LuMrv
Mr Lur
MvNrIT Abs. edge
La!,2
LrnMrv,v MnNr
Ll1 MI'
LuMr MnrNrv,v
Lu
Abs. edge
L1
LrnMr
0.862 0.8579 0.854 0.8536 0.8515 0.8486 0.833 0.832 0.831 0.8111 0.7967 0.7938 0.792 0.7914 0.789 0.7801 0.779 0.7790 0.778 0.7762 0.776 0.765 0.762 0.753 0.7427 0.741 0.733 0.733 0.721 0.7208 0.7185 0.714 0.7074 0.7050 0.703 0.694 0.691 0.691 0.6778
?1I
~
>
~
~ t:oI
t-< t:oI
Z
~
ill w. iJ>
~
iJ> 8
o
~ H
o t:oI
Z
t:oI
!:d
Q
>1 t-
:l
Q
q
~
;:0
"C ~
"4
l/1
1-1
Q
l/1
23.62 23.88 24.25 24.28 24.30 24.4 24.5 24.78 25.01 25.3 25.50 25.7 26.0 26.2 26.72 26.9 27.05 27.29 27.34 27.42 27.77 27.9 28.1 28.13 28.88 29.8 30.4 30.8 30.82 30.89 30.99 31. 02 31.14 31. 24 31. 35 31.36 31. 60 31. 8 32.3
3 4 3 5 3 2 1 1 9 1 9 1 1 2 9 1 2 1 3 2 1 1 2 5 8 1 1 1 5 3 1 2 5 9 3 2 4 1 2
80 23 Va 23 Va 508n 24 Cr 47 Ag 48 Cd 24 Cr 45 Rh 508n 44 Ru 508n 47 Ag 46 Pd 52 Te 44 Ru 22 Ti 22 Ti 23 Va 22 Ti 23 Va 46 Pd 45 Rh 48 Cd 518b 45 Rh 48 Cd 48 Cd 47 Ag 22 Ti 7N 218e 47 Ag 50811 218e 22 Ti 7N 92 U 44 Ru
Ka L(3, La,.2 Mrv.v LTJ
KL LuMrv LrnMrv.v
Ll
LruMr
My
MurNrv.v
Abs. edge LnMr MvNr MnrNr
MrvOu.ru MuNrv MvOrII MruNr MnNr
Mr My L(3,
Mrv.vNn.IIr MmNrv.v LnMrv
Ln.rn
Abs. edge
LTJ La,.2 Ll
LnMr
LrIIJ.lrv.v LIIrMr
MIIrNr .NluNr
M rv.v Mr
M rv
Abs. edge Mrv.vNII.rn MnrNr MrvOn.nr MvOrn Abs. edge
LTJ K L(3,
LnMr
Mv Mr
Abs. edge Mrv.vNu.ru LruMrv.v LruMr
Lal.2 Ll Ka
Abs. edge LnMrv
KL NrvNvr MnNr
0.5249 0.5192 0.5113 0.511 0.5102 0.509 0.507 0.5003 0.496 0.491 0.486 0.483 0.478 0.474 0.464 0.462 0.4584 0.4544 0.4535 0.4522 0.4465 0.445 0.442 0.4408 (J.429 0.417 0.408 (J.403 0.4022 0.4013 0.4000 0.3996 0.3981 0.397 0.3954 0.3953 0.3924 0.390 0.384
45.2 46.48 46.5 46.8 47.24 47.3 47.67 47.74 47.9 48.1 48.2 48.5 49.4 49.5 50.0 50.2 50.3 50.9 51.3 51. 9 52.0 52.2 52.34 52.8 53.6 M.O 54.0 54.2 54.7 54.8 55.8 55.9 56.3 56.5 57.0 58.2 58.4 58.7 59.3
1 9 2 2 2 1 9 1 3 2 1 2 1 1 1 1 1 1 1 1 2 1 7 1 1 2 1 1 2 2 1 1 1 1 2 1
1 2 1
518b 39 Y 81 Tl 79 Au 19 K 508n 45 Rh 19 K 80 Hg 78 Pt 90 Th 39 Y 79 Au 90 Th 90 Th 771r 52 Te 78 Pt 388r 76 Os 48 Cd 518b 44 Ru 77 Ir 388r 74 W 47 Ag 508n 76 Os 42 Mo 74W 18 A 18 A 46 Pd 37 Rb 73 Ta 74W 48 Cd 45 Rh
Ll
Mr Ll
Mn.Nhv MnNr NvNvr.vn NrvNvr LnMr
MrrMrv Mrv.vNu.ur LruMr NvNvr.vr NrvNvr NvrOv
MnrNr NvNvr.vn
NvrOrv NvnOv NrvNvr MmMv
NvNvr.vu MnNr NrvNvr
Mr
lWn M rv MmMv .Nhv. "Nu.nr NvNvr.vII .NlmNr NnNrv
MnMrv MnrMv NvNvr.vn 1Wrv. vOn.nr NrvNvr LTJ Ll
LnMr LmMr
MnMrv MnNr
NrvNvr NvNvn MnrMv MnMrv
0.2743 0.267 0.267 0.265 0.2625 0.2621 0.2601 0.25971 0.259 0.258 0.2572 0.256 0.2510 0.2505 0.2479 0.2470 0.2465 0.2436 0.2416 0.2388 0.2384 0.2375 0.2369 0.2348 0.2313 0.2295 0.2295 0.2287 0.2266 0.2262 0.2221 0.2217 0.2201 0.2194 0.2174 0.2130 0.2122 0.2111 0,2090
~
~ ~
:f1 ~ t<J
t"'
t<J
Z
Q t-3 ~
Ul ~
§ ~
t-3
o
~ H
(":l
t<J
Z
t<J ~
~
~t<J t"'
Ul
jI f-1
0-. 0-.
TABLE
7f-2.
WAVELENGTHS OF X-RAY EMISS'ION LINES AND ABSORPTION EDGES: IN NUMERICAL ORDER
-.t .1
(Continued)
~
I
Wavelength,
A* 59.5 59.5 60.5 61.1 61.9 62.2 62.9 63.0 64.38 65.1 65.5 65.7 67.33 67.6 67.90 68.2 68.3 68.9 69.3 70.0 72.1 12.19 72.7 74.9 76.3 76.7 76.9 78.4 79.8 80.9 81.5 82.1 83.
p.e.t
Element
3 2 1 2 2 1 1 5 7 7 1 2 9 3 9 3 1 2 5 4 3 9 9 1 7 2 2 2 3 3 2 2
74W 37 Rb 47 Ag 73 Ta 41 Nb 44 Ru 46 Pd 71 Lu 42 Mo 70 Yb 45 Rh 71 Lu 17 Cl 5B 17 Cl 90 Th 44 Ru 42 Mo 70 Yb 40 Zr 41 Nb 41 Nb 68 Er 42 Mo 68 Er 40 Zr 35 Br 41 Nb 35 Br 40 Zr 39 Y 40 Zr 66 Dy
t
Designation
Mr
Ln
Ka Ll
Mr
Mr
NvNvr MIUNI MmMv NvNvr.vrI MIV.VOU.UI MUMIV MUIMv NrvNvI MIV.vNu.IU NIVNvr MmMv NVNVI.VII LuMI KL LIUMI OruPlv.v MurMv MuMrv NvNvr.vu Mrv.vOII.III MuMrv Mrv.vNu.IIr NIVNvr MmMv NvNvr.VII MUMIV MuNr MmMv MuiNr MmMv MnMrv Mrv.'vNII.UI Nlv.VNvr.vrI
Wavelength,
keY
0.208 0.2083 0.2048 0.2028 0.2002 0.1992 0.1970 0.197 0.1926 0.190 0.1892 0.1886 0.i841 0.1833 0.1826 0.1817 0.1814 0.1798 0.179 0.177 0.1718 0.1717 0.171 0.1656 0.163 0.1617 0.1613 0.1582 0.1554 0.1533 0.1522 0.1511 0.149
A*
I
117.4 117.7 123. 126.8 127.8 128.7 128.9 135.5 136.5 137.0 142.5 143.9 144.4 144.4 152.6 157. 159.0 159.5 163.3 164.6 164.7 166.0 170.4 171.4 173. 181. 183.8 184.6 188.4 188.6 189.5 190.3 190.
p.e·t Element
4 1 1 2 2 2 7 4 4 5 1 5 6 3 6 3 2 5 2 2 3 5 1 5 3 5 1 3 1 1 3 1 2
628m 81 Tl 148i 37 Rb 37 Rb 37 Rb 60 Nd i48i 59 Pr 30 Zn 13 AI 30 Zn 58 Ce 37 Rb 57 La 30 Zn 56 Ba 29 Cu 56 Ba 56 Ba 35 Br 29 Cu 13 AI 13 AI 29 Cu 90 Th 55 Cs 35 Br 28 Ni 55 Cs 35 Br 55 Cs 28 Ni
Designation
LU.IU Mr. Mrl
Mu LI Mrn
MIl
MUI Lu.ur
MnI
NIV.VOU.UI NvuOv Abs. edge MIvNm MIVNn MvNuI NIV.VOU.III Lu.mM NIV;vOu.ur Abs. edge Abs.' edge Abs. edge NIV.VOU.UI MIMm Nlv.VOU.IU MII.lnMlv.v NrvOm Abs. edge NrvOn NVOIII MiMm Abs. edge Abs. edge Lu.ruM Mu.lnMrv.v OIV. VQII .III NrvOm MrMu Abs. edge NIVOU MIVNIU NvOm MU.IUMIV.V
Ot
keY
0.1056 0.10530 0.1006 0.0978 0.0970 0.0964 0.0962 0.0915 0.0908 0.0905 0.08701 0.0862 0.0859 0.0859 0.0812 0.079 0.07796 0.0777 0.07590 0.07530 0.0753 0.0747 0.07278 0.0724 0.072 0.068 0.06746 0.0672 0.06581 0.06574 0.0654 0.06515 0.0651
q;,
~ ....~ a o
~
Z c;
~
o ~
a
q
f;
!;O
~
a
Ul
83.4 85.7 86. 86.5 91.4 91. 5 91. 6 93.2 93.4 94. 96.7 97.2 98. 100.2 102.2 102.4 103.8 104.3 107. 108.0 108.7 109.4 110.6 111. 112.0 113.0 113. 113.8 114. 115.3
3 2 1 2 2 2 1 1 2 1 2 8 1 2 4 1 4 1 1 2 1 3 5 1 6 1 1 3 1 2
16 38 65 39 38 37 83 83 39 15 37 66 62 82 65 82 15 82 60 38 38 35 29 4 63 81 59 35 4 81
S Sr Tb Y Sr Rb Bi Bi Y P Rb Dy Sm Pb Tb Pb P Pb Nd Sr Sr Br Cu Be Eu TI Pr Br Be TI
LI.71
LII.IIIMI 111II .MIy Nry,yNYI.YII lvIIIr M IY, Y lVIrIIMIy , Y
MIIMry
MI LII,III
MI2 MIl
NYIOIY NYIIOy Mry, yNII,rn
Abs, edge lVI uIlVI IY, Y N I y,yOII,I1I NIy,yNYI,YII NYIOy NIy,yOU,III NyrOIY LII ,III 1vI NYIIOy NIy,yNyr.yu ll1I yNII ,1lI
MyN m Mu ll1 ry
111r [(
Abs. edge Abs. edge N I y, yOII, II I NYrOy Nry,yNYI.YIl
Kex
lVIrIIMIy , v KL NyrOry
0.1487 0.1447 0.144 0.1434 0.1357 0.1355 0.1354 0.1330 0.1328 0.132 0.1282 0.128 0.126 0.1237 0.1213 0.1211 0.1194 0.1189 0.116 0.1148 0.1140 0.1133 0.1121 0.111 0.1107 0.10968 0.1095 0.1089 0.1085 0.1075
191.1 192.6 197.3 202. 203. 214. 224. 226.5 227.8 228. 230. 230. 243. 249.3 250.7 251. 5 273. 290. 309. 317. 337. 376. 399. 405. 407.1 417. 444. 525. 692.
2 2 1 5 1 6 1 1 1 1 2 1 5 1 1 5 6 1 9 1 9 1 5 5 5 5 5 9 9
35 35 12 27 16 27 53 3 34 3 34 26 26 12 12 12 25 13 24 12 23 11 35 11 11 17 53 20 19
Br Br lVlg Co S Co I Li Se Li Se Fe Fe Mg Mg Mg Mn Al Cr Mg V Na Br Na Na CI I Ca K
M I, MIl LI MIl ,III
MIyNn MyNIII
Abs. edge Abs. edge LILU.III lVIrr,IIIlVIIy,y
NIY,Y [(
My [(ex 111 U ,III
Abs. edge Abs. edge Abs. edge KL MyNm
Abs, edge MII,IIIMly, Y
Lu Lm
Abs. edge Abs. edge LII ,III lVI MU,IIIMIy• Y LILn,III lVIII,IIIMIy,y LILII,IIr lVIu,InMIY, Y LILII,IU
Nr Ln,Iu
Abs. edge Abs. edge Ln,IIIM
Mr 01
Abs. edge Abs. edge MII,IUNI .MII,IUNI
0.06488 0.06437 0.06284 0.061 0.061 0.058 0.0552 0.05475 0.05443 0.0543 0.0538 0.0538 0.051 0.04973 0.04945 0.04929 0.045 0.0428 0.040 0.0392 0.0368 0.03299 0.0311 0.0306 0.03045 0.0297 0.0279 0.0236 0.0179
~ ~
...;<j
-3
~ U1
...
8 ...>-3 o
~ ~
o
l:rJ
Z
l:rJ
~
Q
~
t"
~
t;I t"
U1
~
I-'-
e,;.... -l
..;(
d:
......
q-, 00 (
!:
TABLE
7f-3.
RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EV*
....
I
Level
K ... ,,,
.1
Lr. ....... LII,III, ,
1H
13.59811-
I 1
..............
2 He
I
24.58~
(54.75) . ..............
.................
······1········
5B
4 Be
7N
6e
>."
80
o
, 54.75 ±·0.0,2
·:.····t········
..............
3 Li
111.0 ± 1.0
188.0 ± 0.4 [188.0]'
(111.0) ...............
... , .. , ...... ,...
:
. .............. 4.7 ± 0.9
283.8 :!: 0.4 [283.8]' (283.8) . .............. 6.4 ± 1..9
401.6 ± 0.4 .. [401.6]'"
...............
,
9.2± 0.6
~,
532~0 ± 0.4 [532.0]'
n
23:7.± 0,4
Z,
[23.7]d
7.1 ± 0.8
H'
~.
1::1.
~
0Level
9F
10 Ne
11 Na
12 Mg
13 Al
14.Si
15 P
§;i
16 S
Q
---, K ....... I Lr.... ...•. 1 Ln,III . .. 1
685.4 ± 0.41 [685.4]' .
(866.9) (45.)
(31.) .
8.6 ± 0.8
866.9 ± 0.3
1
18.3 ± 0.4
I 1
1072.1 ± 0.4 [1072.1]' (1072.) 63.3 ± 0.4 [63.3Jd 31.1 ± 0.4 (31.)
1305.0 ± 0'.4 [1305:0]' (1303.) 89.4 ± 0.4 [89.4]d
(63.) 51.4 ± 0.5 (50.)
1559.6 ± 0.4 , [1559.6]' (1559.8) 117.7 ± 0.4 [117.7]d
(87.) 73.1 ± 0.5 (72.8)
1838.9 ± 0.4 [1838.9]'
2145.5 ± 0.4 [2145.5].d
[148.7]d
189;3 ± 0.4' [189.3]d
99.2 ± 0.5 (100.6)
132.2·± 0.5 (132.)
148.7 ± 0.4
* Where applicable, photoelectron direct measurements are listed in sQ,llare brackets [ ] immediately under the recommended values. X-ray absorption energies" are shown in parentheses.( ). Interpolated values are enclosed in angular brackets ( ).
±0.4
: 2472 .. 0 1[2472.0]' ~2470.)
i 229.2 ± 0.4 : [229.2]d
164.8 ± 0.7
~
1>'
~
't1 i;I:1.. >: H Ll. U>
The measurobd values·of the '
1· :
TABLE
Level
17
7f-3.
cr
RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EV*
18 Ar
19 K
20 Ca
21 Sc
3202.9 ± 0.3
4038.1 ± 0.4 [4038.1]' (4038.1) 437.8±0.4 [437.8Jd 350.0 ± 0.4 346.4 ± 0.4 43.7 ± 0.4 25.4 ± 0.4
4492.8 ± 0.4 [4492.8J'
. ..............
22 Ti
(Continued)
23 V
:>4I
24 Cr
~
po. f<j;
IC ...... Lr. ......
2822.4 ± 0.3 [2822.4]' (2020.) 270.2 ± 0.4
..... . .. .. ....
...............
3607.4 ± 0.4 [3607.4]' (3607.8) 377.1 ± 0.4 [377.1Jd 296.3 ± 0.4 293.6 ± 0.4 33.9 ± 0.4 17.8 ± 0.4 . ..............
25 Mn
26 Fe
27 Co
28 Ni
7112.0 ± 0.9
721.1±0.9
7708.9 ± 0.3 [7708.9]' (7709.5) 925.6 ± 0.4 [925.6jd 793.6 ± 0.3
8332.8 ± 0.4 [8332.8J' (8331.6) 1008.1 ± 0.4 [1008.1]d 871.9 ± 0.4
(720.8) 708.1 ± 0.9
(793.8) 778.6 ± 0.3
(870.6) 854.7 ± 0.4
[270.2]d
Ln ...... LIII_ . . . .
MI. ..... MIl,III. .. Mrv,v ...
201.6 ± 0.3 200.0 ± 0.3 17.5 ± 0.4 6.8±0.4
(3202.9) 320. (320. )d
247.3 245.2 25.3 12.4
± ± ± ±
0.3 0.3 0.4 0.3
500.4 ± [500.4Jd 406.7 ± 402.2 ± 53.8 ± 32.3 ± 6.6 ±
0.4
4966.4 ± 0.4 [4966.4Jd (4964.5) 563.7 ± 0.4
5465.1 ± [5465.1]' (5464.) 628.2 ± [628.2Jd 520.5 ± 512.9 ± 66.5 ± 37.8 ± 2.2 ±
[563.7]d
0.4 0.4 0.4 0.5 0.5
461.5 455.5 60.3 34.6 3.7
± ± ± ±
0.4 0.4 0.4 0.4
0.3 0.4 0.3 0.3 0.4 0.3 0.3
5989.2 ± [5989.2]' (5989.) 694.6 ± [694.6Jd 583.7 ± 574.5 ± 74.1 ± 42.5 ± 2.3 ±
0.3 0.4 0.3 0.3 0.4 0.3 0.4
---
Level
LIl ......
6539.0 ± 0.4 [6539.0J' (6538.) 769.0 ± 0.4 [769.0Jd 651.4 ± 0.4
LIn . ....
640.3 ± 0.4
LI. ......
MI.
83.9 ± 0.5
~~~r}" .
48.6 ± 0.4
Mrv,v.
~
M
r
(9,
Z
0: >-3
iI1
(J2
po. 29 Cu
31 Ga
30 Zn
32 Gs
Z
11103.1 ± 0.7 [11103.8]" (11103.6) 1414.3 ± 0.7
0~
---
IC ......
~
3.3 ± 0.5
[7111. 3J'.1
(7111.2) 846.1 ± 0.4 [846.1]d
(707.4) 92.9 ± 0.9
(779.0) 100.7 ± 0.4
(853.6) 111.8 ± 0.6
54.0 ± 0.9 (54.) 3.6 ± 0.9
59.5 ± 0.3 (61.) 2.9 ± 0.3
68.1 ± 0.4 (66.) 3.6 ± 0.4
8978.9 ± [8978.9]'," (8980.3) 1096.1 ± [1096. Old 951.0 ± [950. OJ" (953.) 931.1 ± [931.4J" (933.) 119.8 ±
0.4 0.4
9658.6 ± 0.6 [9658.61u (9660.7) 1193.6 ± 0.9
10367.1 ± 0.5 [10367.1Ju (10368.2) 1297.7 ± 1.1
[1413.6Ju
0.4
1042.8 ± 0.6
1142.3 ± 0.5
1247.8 ± 0.7
0.4
(1045.) 1019.7 ± 0.6
1115.4 ± 0.5
(1249.) 1216.7 ± 0.7
0.6
(1022.) 135.9 ± 1.1
73.6 ± 0.4 (75.) 1.6 ± 0.4
86.6 ± 0.6 (86.) 8.1±0.6 ----
{
(1117.) 158.1 ± 0.5 106.8 ± 0.7 102.9 ± 0.5
(1217 .0) 180.0 ± 0.8 127.9 ± 0.9 120.8 ± 0.7
17.4 ± 0.5
28.7 ± 0.7
ti' p.. >-3
H
Q
t:J;
Z (9, ~
0: f<j
r'
(9
~ r
(J2
~
~
CO
~ TABLE
7f-3.
RECOMMENDED YALUI~S OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EY*
I
(Contimted)
I-'~
Level
33 As
34 Se
L, .......
11866.7 ± 0.7 [11866.7]' (11865.) 1526.5 ± 0.8
(12654.5) 1653.9 ± 3.5
Ln ......
(1529.) 1358.6 ± 0.7
(1652.5) 1476.2 ± 0.7
Lm . ....
(1358.7) 1323.1 ± 0.7
(1474.7) 1435.8±0.7
(1323.5) 203.5 ± 0.7 146.4 ± 1.2 140.5 ± O.!!
(1434.0) 231.5 ± 0.7 168:2 ± 1.3 161.9 ± 1.0
35 Br
36 Kr
o
40 Zr
39 Y
38 Sr
37 Rb
--K .......
Mr. .....
Mri ..... Mm ..... Mrv} Mv ... N, ...... Nn } Nm ...
41.2 ± 0.7 .............. 2.5 ± 1.0
12657.8 ± 0.7
13473.7 ± 0.4
14325.6 ± 0.8
15199.7 ± 0.3
16104.6 ± 0.3
17038.4 ± 0.3
17997.6 ± 0.4
(13470.) 1782.0 ± 0.4 [1782.0]1
(14324.4) 1921.0 ± 0.6 [1921.2]'
(15202.) 2065.1 ± 0.3 [2065.4ji
(16107.) 2216.3 ± 0.3 [2216.2]'
(17038.) 2372.5 ± 0.3 [2372.7]'
(17999.) 2531.6 ± 0.3 [2531.6]'
1596.0 ± 0.4 [1596.2ji
1727.2 ± 0.5 [1727.2]' (1730.) 1674.9 ± 0.5 [1674.8]· (1677.) ................ 222.7 ± 1.1 213.8±1.1
[12657.8]D
56.7 ± 0.8 . .............. 5.6 ± 1.3
i>
1-3
1549.9 ± 0.4 [1549.7]; 256.5 189.3 181.5 { 70.1 69.0 27.3 5.2 4.6
{
± ± ± ± ± ± ± ±
0.4 0.4 0.4 0.4 } 0.4 0.5 0.4 } 0.4
88.9 ± 0.8 24.0 ± 0.8 10.6 ± 1.9
1863.9 ± 0.3 [1863.4]; 1804.4 ± 0.3 [1804.6]; 322.1 ± 0.3 247.4±0.3 238.5 ± 0.3 p11.8 ± 0.3 110.3 ± 0.3 29.3 ± 0.3 { 14.8 ± 0.4 } 14.0 ± 0.3
2006.8 ± [2006.6]' (2008.5) 1939.6 ± [1939.9]' (1941.) 357.5 ± 279.8 ± 269.1 ± 135.0 ± 133.1 ± 37.7 ±
0.3 0.3 0.3 0.3 0.3 0.3 0.3 0.3
19.9 ± 0.3
2155.5 ± [2155.0]' (2154.0) 2080.0 ± [2080.2]' (2079.4) 393.6 ± 312.4 ± 300.3 ± 159.6' ± 157.4 ± 45.4 ±
0.3 0.3 0.3 0.4 0.4 0.3 0.3 0.3
25.6 ± 0.4
2306.7 ± [2306.5]' (2305.3) 2222.3 ± [2222.5]' (2222.5) 430.3 ± 344.2 ± 330.5 ± 182.4 ± 180.0 ± 51.3 ±
0.3
o
~
H
0.3 0.3 0.4 0.4 0.3 0.3 0.3
28.7 ± 0.4
o i>
~ ~
o
t
Z tI
P>
0.3
1-3.
o
:S:. H
[5247.3Ji
0.4 0.5 0.5 0.3 0.3 0.5 0.7 0.6 0.5 0.5 0.6 0.5 0.5
o
to!
Z
to!
l:d 0kj
t'
~ trj, t'
[fl
~
i-L
0":>
......
TABLE
7f-3.
RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN E V*
jI
(Cont1:nlled)
I-'-
O'l
Level
57 La
58 Ce
59 Pr
60 Nd
61 Pm
628m
63 Eu
45184.0 ± 0.7 (45198.) 7427.9 ± 0.8 [7427.9]"
1511.0 ± 0.8 1337.4 ± 0.7 1242.2 ± 0.6 9.51.1 ± 0.6 931.0 ± 0.6 304.5 ± 0.9 236.3 ± 1.5 217.6 ± 1.1 113.2±0.7 2.0 ± 0.6 37.4 ± 1.0 22.3 ± 0.7
43568.9 ± 0.4 (43574. ) 7126.0 ± 0.4 [7125.8]"" (7129.) 6721.5 ± 0.4 [6721. 8]" (6723.) 6207.9 ± 0.4 [6208.0]" (6209.) 1575.3 ± 0.7 1402.8 ± 0.6 1297.-4 ± 0.5 999.9 ± 0.6 977.7 ± 0.6 315.2 ± 0.8 243.3 ± 1.6} 224.6 ± 1.3 117.5 ± 0.7 1.5 ± 0.9 37.5 ± 0.9 21.1±0.8
120.4 ± 2.0 . ... , - ......... . .. . . ...... .. .. . ..............
46834.2 ± 0.5 (46849.) 7736.8 ± 0.5 [7736.2]n (7748.) 7311.8±0.4 [7312.0]" (7313.) 6716.2 ± 0.5 [6716.8]n (6717 .) 1722.8 ± 0.8 1540.7 ± 1.2 1419.8± 1.1 1106.0 ± 0.8 1080.2 ± 0.6 345.7 ± 0.9 {265.6 ± 1.9 247.4±1.5 129.0 ± 1.2 5.5 ± 1.1 37.4 ± 1.5 21.3 ± 1.5
48519.0 ± 0.4 (48519.) 8052.0 ± 0.4 [8051. 7]n (8061.) 7617.1 ± 0.4 [7617 .6]n (7620.) 6976.9 ± 0.4 [6976.7]n (6981. ) 1800.0 ± 0.5 1613.9 ± 0.7 1480.6 ± 0.6 1160.6 ± 0.6 1130.9 ± 0.6 360.2 ± 0.7 283.9 ± 1.0 256.6 ± 0.8 133.2 ± 0.6 0.0 ± 3.2 31.8±0.7 22.0 ± 0.6
67 Ho
68 Er
69 Tm
70 Yb
71 Lu
----
-
38924.6 ± 0.4 (38934.) 6266.3 ± 0.5 [6266.3]"
40443.0 ± 0.4 (40453. ) 6548.8 ± 0.5 [6548.5]"
41990.6 ± 0.5 (42002.) 6834.8 ± 0.5 [6834.9]n
II . . . . . .
5890.6 ± 0.4 [5890.7]"
6164.2 ± 0.4 [6164.3]"
6440.4 ± 0.5 [6440.2]"
L HI . . . . .
5482.7 ± 0.4 [5482.6]"
5723.4 ± 0.4 [5723.6]n
5964.3 ± 0.4 [5964.3]"
[, ......
1361.3 ± 0.3 1204.4 ± 0.6 1123.4 ± 0.5 848.5 ± 0.4 831.7 ± 0.4 270.4 ± 0.8 205.8 ± 1.2 191.4 ± 0.9 98.9 ± 0.8 . , ............ 32.3 ± 7.2 14.4 ± 1.2
........
r .......
(II . . . . .
(III ..... (,V . . . . . [v . . . . .
rr ..... rII ...... rnr .....
rrv,v ... rY1,VII .. I .......
II ,III . . .
~
64 Gd
1434.6 1272.8 1185.4 901.3 883.3 289.6 223.3 207.2 110.0 0.1 37.8 19.8
± ± ± ± ± ± ± ± ± ± ± ±
0.6 0.6 0.5 0.6 0.5 0.7 1.1 0.9 0.6 1.2 1.3 1.2
7012.8 ± 0.6 [7012.8]" 6459.3 ± 0.6 [6459.4]"
.... - , .. , ...... 1471.4 ± 6.2 1356.9 ± 1.4 1051.5 ± 0.9 1026.9 ± 1.0 ............... 242.
± 16.
50239.1 ± (50233.) 8375.6 ± [8375.4]n (8386.) 7930.3 ± [7930.5]" (7931.) 7242.8 ± [7242.8]n (7243. ) 1880.8 ± 1688.3 ± 1544.0 ± 1217.2 ± 1185.2 ± 375.8 ± 288.5 ± 270.9 ± 140.5 ± 0.1 ± 36.1 ± 20.3 ±
0.5 0.5 0.4
> >-3 o
0.4
(')
0.5 0.7 0.8 0.6 0.6 0.7 1.2 0.9 0.8 3.5 0.8 1.2
8
--_. Level
~ .....
>
~
o
t"' t?:j
(')
q
~
~
~ ~
65 Tb
66 Dy
72 Hf
U1
.....
(')
U1
........ I ••...•.
II . . . . . .
51995.7 ± 0.5 (52002.) 8708.0 ± 0.5 [8707.6]" (8717.) 8251.6 ± 0.4 [8251.81' (8253.)
53788.5 ± 0.5 (53793.) 9045.8 ± 0.5 [9046.5]" 8580.6 ± 0.4 [8580.4]" (8583.)
55617.7 ± 0.5 (55619. ) 9394.2 ± 0.4 [9394.3]" (9399.) 8917.8 ± 0.4 [891S .2]" (8916.)
--_._-_._---
--
-----
57485.5 ± 0.5 (57487.) 9751.3 ± 0.4 [9751. 5]" (9757.) 9264.3 ± 0.4 [9264.3]" (9262.) -
-
59389.6 ± 0.5 10115.7 ± 0.4 [10115.6]" (10121. ) 9616.9 ± 0.4 [9617.1]" (9617.1)
61332.3 ± 0.5 (61300.) 10486.4 ± 0.4 [10487.3]" (10490.) 9978.2 ± 0.4 [9977 .9]" (9976.)
63313.8 ± 0.5 (63310 .) 10870.4 ± 0.4 [10870.1]" (10874.) 10348.6 ± 0.4 [10349.0]" (10345.)
65350.8 ± 0.6 (65310. ) 11270.7 ± 0.4 [11271.6]" (11274.) 10739.4 ± 0.4 [10738.9]" (10736.)
[,m . . • . .
Mr....... Mn .....
MIll ..... MIY ..... My ..... Nr. ... .. NIl ......
Nm ..... NIY} Ny'" !VYI.yn. Or .......
gn }.... III
7514.0 ± 0.4 [7514.2)' (7515.) 1967.5 ± 0.6 1767.7 ± 0.9 1611.3 ± 0.8 1275.0 ± 0.6 1241.2±0.7 397.9 ± 0.8 310.2 ± 1.2 385.0 ± 1.0
7790.1 ± [7789.6)" (7789.7) 2046.8 ± 1841.8 ± 1675.6 ± i332.5 ± 1294.9 ± 416.3 ± 331.8 ± 292.9 ±
0.4 0.4 0.5 0.9 0.4 0.4 0.5 0.6 0.6
8071.1 ± [8070.6)" (8068.) 2128.3 ± 1922. 8± 1741.2 ± 1391.5 ± 1351.4 ± 435.7 ± 343.5 ± 306.6 ±
0.4 0.6 1.0 0.9 0.7 0.8 0.8 1.4 0.9
147.0 ± 0.8
154.2 ± 0.5
161.0 ± 1.0
2.6 ± 1.5 39.0 ± 0.8
4.2 ± 1.6 62.9 ± 0.5
3.7±3.0 51.2 ± 1.3
25.4 ± 0.8
26.3 ± 0.6
20.3 ± 1.5
8357.9 ± [8357.6)" (8357.5) 2206.5 ± 2005.8 ± 1811.8 ± 1453.3 ± 1409.3 ± 449.1 ± 366.2 ± 320.0 ± {176.7 ± 167.6 ± 4.3 ± 59.8 ±
0.4 0.6 0.6 0.6 0.5 0.5 1.0 1.5 0.7 1.2 } 1.5 1.4 1. 7
29.4 ± 1.6
9244.1 ± 0.4 [9243.8)"
5.3 ± 1.9 53.2 ± 3.0
8943.6 ± 0.4 [8942.6)" (8944.1) 2398.1 ± 0.4 2173.0 ± 0.4 1949.8 ± 0.5 1576.3 ± 0.4 1527.8 ± 0.4 487.2 ± 0.6 396.7 ± 0.7 343.5 ± 0.5 {19S.1±0.5 184.9 ± 1.3 6.3 ± 1.0 54.1 ± 0.5
32.3 ± 1.6
23.4 ± 0.6
28.0 ± 0.6
8648.0 ± [8647.8]" (8649.6) 2306.8 ± 2089.8 ± 1884.5 ± 1514.6 ± 1467.7 ± 471.7 ± 385.9 ± 336.6 ±
0.4 0.7 1.1 1.1 0.7 0.9 0.9 1.6 1.6
179.6 ± 1.2
2491.2 2263.5 2023.6 1639.4 1588.5 506.2 410.1 359.3 204.8 195.0 6.9 56.8
± ± ± ± ± ± ± ± ± ± ± ±
0.5 0.4 0.5 0.4 0.4 0.6 1.8 0.5 0.5 0.4 0.5 0.5
9560.7 ± 0.4[9560.4)' (9558. ) 2600.9 ± 0.4 2365.4 ± 0.4 2107.6 ± 0.4 1716.4 ± 0.4 1661. 7 ± 0.4 538.1±0.4 437.0 ± 0.5 380.4 ± 0.5 223.8 ± 0.4 213.7 ± 0.5 17.1 ± 0.5 64.9 ± 0.4 { 38.1 ± 0.6 30.6 ± 0.6
>1I !:d
>>--3
o
~
H
(13423. ) 12824.1 ± 0.3 [12824.0)'.' (12820. ) 11215.2 ± 0.3 [11215.1]',' (11212. ) 3173.7 ± 1.7
[,n ......
>-
78394.8 ± 0.7 (78381.) 13879.9 ± 0.4
(')
t;J
Z
t;J
!:d >---3
o
:::::: .....
o
Level
89 Ac
90 Th
95 Am
96 Gm
t::l
Z K ....... £1. ......
106755.3 ± 5.3 19840. ± 18.
Ln ......
19083 . 2 ± 2.8
Lm .....
15871.0 ± 2.0 (15871.0)
lIfr. .....
MIl .....
(5002. ) 4656. ± 18.
109650.9 ± 0.9 20472.1 ± 0.5
112601. 4 ± 2.4 21104.6 ± 1.8
115606.1 ± 1.6 21757.4 ± 0.3
(20464.) 19693.2 ± (19683. ) 16300.3 ± [16299.6]' (16299.) 5182.3 ± [5182.3l' 4830.4 ± [4830.6]'
0.3
(21128. ) 20313.7 ± 1.5 (20319.) 16733.1 ± 1.4
0.3
(16733. ) 5366.9 ± 1.6
(21771.) 20947.6 ± 0.3 (20945.) 17166.3 ± 0.3 [17168.5]' (17165.) 5548.0 ± 0.4
0.4
5000.9 ± 2.3
5182.2 ± 0.4 [5180.9]'
0.4
_.. __ ._-
-
._-----
118678. ± 33. 22426.8 ± 0.9
121818. ± 44. 23097.2 ± 1. 6
t::l
125027. ± 55. 23772.9 ± 2.0 (23772.9)
128220 2±460
22944.0 ± 1.0
23779
176lO.0 ± 0.4
(23lO9. ) 22266.2 ± 0.7 (22253.) 18056.8 ± 0.6
18504.1 ± 0.9
18930
(17606.2) 5723.2 ± 3.6
(18053.1) 5932.9 ± 1.4
(18504.1) 6120.5 ± 7.5
6288
5366.2 ± 0.7 [5366.4]'
5541.2 ± 1.7
5710.2 ± 2.1
5895
21600.5 ± 0.4
- -
._-
:;:0 Q
Kj
t"'
~
t::l t"'
[fl
jI f-'
OJ
Cn
-;!
I'
TABLE
7£-3.
RECOMMENDED VALUES OF THE ATOMIC ENERGY LEVELS, AND PROBABLE ERRORS IN EV*
f-""
(Continued)
~
OJ
90 Th
Level
89 Ac
.MIll .....
3909. ± 18.
111rv .....
3370.2 ± 2.1
Mv .....
Nr ......
3219.0 ± 2.1 (1269. )
NIl .... __
1080. ± 19.
NIll ....
890. ± 19.
Nrv .....
Nv .....
674.9 ± 3.7 ..............
J.VVI . . . . .
..............
JVVII . . . .
· . . . . . '. . . . . . . .
Or. .. __ .. OIl ......
.............. ..............
Om . ....
..............
Orv .....
·... . .. .......
Ov ......
·.... ..... . .. .
Pr .... __ . PII .... .. Pur . ....
.............. ••
G
••
•
•••••
•••
..............
4046.1 ± [4046.1]' (4041.) 3490.8 ± [3490.7J' (3485.) 3332.0 ± [3332.1J' (3325.) 1329.5 ± [1329.8Jq 1168.2 ± [1168.3J' 967.3 ± [967.6Jq 714.1 ± [714AJ' 676.4 ± [676.4J' 344.4 ± [344.2Jq 335.2 ± [335.0jq 290.2 ± 229.4 ± 181. 8 ± [181. 8j' 94.3 ± [94.4J' 87.9 ± [88.1]' 59.5 ± 49.0 ± 43.0 ±
N'P
95 Am
94Pu
96 em
91 Pa
92 U
0.4
4173.8 ± 1.8
4434,7 ± 0.5 [4434.6]'
4556.6
1.5
4667.0 ± 2.1
4797
0.3
3611.2 ± 1.4
3850.3 ± 0.4 [3849.8J'
3972.6 ± 0.6 [3972.7J'
4092.1 ± 1.0
4227
0.3
(3608.) 3441.8 ± 1.4
0.1
708.2 ± 1.8
0.3
371.2 ± 1.6
4303.4 ± 0.3 [4303.6]' (4299.) 3727.6 ± 0.3 [3728.1J' (3720.) 3551.7 ± 0.3 [3551. 7J' (3545.) 1440.8±0.4 [1441.3J' 1272.6 ± 0.3 [1272.5J' 1044.9 ± 0.3 [1044.9l' 780.4 ± 0.3 [779.7J' 737.7 ± 0.3 [737.6J' 391.3 ± 0.6
0.4
359.5 ± 1.6
380.9 ± 0.9
0.8 1.1 }
309.6 ± 4.3
323.7 ± 1.1 f59.3 ± 0.5
0.1
222.9 ± 3.9
0.4
(3436.) 1387.1 ± 1.9
0.4
1224.3 ± 1.6
I
0.4
1006.7 ± 1.7
,
0.4
743.4 ± 2.1
0.4 } 0.3 1.1 2.5 2.5
i
195.1 ± 1.3 C05.0 ± 0.5
94.1 ± 2.8
I:::::::::::::::
96.3 ± 1.1 70.7 ± 1.2 42.3 ± 9.0 32.3 ± 9.0
93
3665.8 ± 0.4 [3664.2J' 1500.7 ± [1500.7J' 1327.7 ± [1327.7]' 1086.8 ± [1086.8J' 815.9 ± [817.1J' 770.3 ± [773.2]' 415.0 ± [415.0J' 404.4 ± [404.4J'
±
3778.1 ± 0.6 [3778.0]'
~
"'3 3886.9 ± 1.0
3971
o ~
>-
-1 ~,
t'"
~,
Z
'"' 1-3. ~,
m i>-
Z
tj
>1-3.
o
~
H,
0. ~,
Z
trl
~
'"'
kj
t",
I?)
-1
7g. Constants of Diatomic Molecules K. P. HUBER
National Research Council of Canada
Explanation of Columns in Table 7g-1 (1) Identification of molecule. (2) Mass numbers of the constituent atoms to which the data refer. If, in the original paper, the mass numbers are not clearly specified, or, if the data refer to the normal isotopic mixture, the mass numbers for the most abundant isotope are given in parentheses. (3) Reduced mass J.t in unified atomic mass units (12C = 12.0000000). Precise atomic masses were taken from the 1961 nuclidic mass table [L. A. Konig, J. H. E. Mattauch, and A. H. Wapstra, Nucl. Phys. 31, 18 (1962)]. (4) Designation of the ground state of the molecule. For multiplet II, A, . . . states the spin-orbit coupling constant A has been added. (5) (6) (8) (9) Rotational constant Be. Rotation-vibration interaction constant a. (from Bv = Be - ae(v + i) + ... ). Vibrational frequency We' Anharmonic constant WeXe (from G(v) = we(v
+ i) -
w,xe(v
+ i)2 + ... ).
All constants in cm- I . They are derived from the analyses of molecular spectra in the microwave, infrared, visible, and vacuum uv region. For 12; states, the constants in these columns correspond to the coefficients YO!, - Y l1 , Y!O, and - Y 20, respectively, in the Dunham series expansion for the term values TvJ =
.l
Y1m(v
+ i)IJm(J + l)m
1m
(7) Equilibrium internuclear distance re in
A,
calculated without correction from
(10) Dissociation energy Doo in electron-volts (eV). Data obtained by a large variety of both spectroscopic and thermochemical methods have been included. Uncertain quantities are enclosed in parentheses ( ). Quantities in square brackets [ ] in columns (5) and (8) refer to Bo and AG(i) respectively. ,. after We and W,x, indicates that these numbers are for the natural isotopic mixture rather than for the isotope specified in column (2). The physical constants and conversion factors given in Appendix VII of the following book have been used throughout: G. Herzberg, "Electronic Spectra and Electronic 7-168
CONSTANTS OF DIATOMIC MOLECULES
7-169
Structure of Poly atomic Molecules," D. Van Nostrand Company, Inc., Princeton, N.J., 1966. Thedata included in the table are taken from a new compilation of vibrational and rotational constants for the electronic states of all known diatomic molecules.· This compilation is presently being prepared by G. Herzberg and K. P. Huber and will provide further details and the literature references. A critical table of dissociation energies has recently been published by A. G. Gaydon in his book "Dissociation Energies and Spectra of Diatomic Molecules," 3d edition, Chapman & Hall, Ltd., London, 1968.
-::J TABLID
7g-1.
I
CONSTANTS OF DIATOMIC MOLIDCULIDS
f-' ~
m,
m,
f.L
Ground state
B,
a,
T,
W,
WeXe
Doo
(1)
(2)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Ago ............ AgAI. .......... AgAu .......... AgBr ........... AgCI. .......... AgCu .......... AgF ............ AgGa .......... AgH ...........
107 107 (107) 107 107 (107) 107 (107) 107 107 107 107 107
109 27 197 79 35 (63) 19 (69) 1 2 127 115 16
53.94779 21.544070 (69.29476) 45.40207, 26.349782 (39.611998) 16.131608 (41. 90678,) 0.99841288 1.9768579, 58.02466 55.38014 13.913242,
· ........... '1;+ · .. .. . . .. ... '1;+ '1;+ ............ '1;+ ·. . .. . . . . ... '1;+ '1;+ 11;+ ·. . ....... ..
., . . . . . . . . . .
· . . . . . ... ...
AgI. ........... AgIn ........... AgO ............
2ll(r)
A AgSe ........... AgSn ........... AgTe ........... Ab. ............ AIAu ........... AlBr ........... AICI. .......... AIF ........... AlH ............ AIH+ ........... AIL ............ AIO ............ AlP ............ AIS ............ AISe ........... AITe ........... Arz ............ An+ .......... " As" ............ AS2+ . . . . . . . . . . .
AsCI. .......... AsF ............
(107) (107) (107) 27 27 27 27 27 27 27 27 27 27 27 27 27 27 40 40 75 75 75 75
(80) (120) (130) 27 197 79 35 19 1 2 1 127 16 31 32 (80) (130) 40 40 75 75 (35) 19
(45.73067,) (56.51557) (58.64437) 13.490767, 23.730767, 20.1070870 15.230144, 11.1484731 0.97153601 1. 8741981, ....... ' ...... 22.2507357 10.0419499 14.4200738 14.6327874 (20. 171277.) (22.341268) 19.9811919 .............. 37.460790 ......... . (23.841218) 15.1553527
=
(+135) ('II)
............
('II) a~g-
11;+(0+)
'1;+ 11;+ 11;+ 11;+ 11;+ '1;+ 11;+ '1;+ ............ '1;+ ('1;) ('1;) (11;,+)
·. . . . . . . . . . . l~u+
('1;~+)
('1;-) ('1;-)
0.12796
... 0.06483378 O. 122983860
... . . . . . .
. ........... 0.2657 · .... . . . . .. . 6.449 3.2572 0.044876 . ........... 0.3028 ............ . ........... ..... ....... 0.2054 0.12991, 0.1591 0.2439267 0.552468 6.39066 3.3186 6.763 ............ 0.6413, · ........... 0.2799 ............ · . .. ...... . . ............ . ......... " 0.1016·5 ........... . ............ ............
0.00076
·. . . . . . . . . . . 0.0002359, 0.00059540,
· . ... . ... .. . 0.0019 . ........... 0.201 0.0722 0.0001473 .., .....
,
...
0.0025
·. . . . . . . . . . . . ...........
............
0.0012 0.00066, 0.000853 0.001602, 0.004950 0.1858, 0.0697 0.398 . ........... 0.00580 · ........... 0.0018 . ........... . ...........
·... ..... . .. · . . . . . . . . .. . 0.00034 ............ · ........... . ...........
2.4728 . ...... " ,2.3931 2.2808 . .......... 1.983 . .......... 1.618, 1.6180 2.5444
· . . . .. . . . . . 2.000
. ........ ,.., ........ . ......... 2.466, 2.3384 2.296 2.1302 1.6544 1. 6478 1.6463 1. 6018 . .......... 1. 6178 . ........ " 2.0288
192.4 256.60 (200) 250.49 343.49 229.5 513.45 184.7 1759.9 1250.7 206.52 155.8 490.4*
195.3 350.01 333.00 378.0 481.30 801. 9, 1682.56, 1211. 95
0.6871 1.17 1 2.59 0.65 34.06 17.17 0.445 0.42 3.0*
. .......... 0.30 2.022 1.16, 1.28 1. 95 4.70 29.090 15.138
~ ~
0
~ H
(")
2.4, 2.4. 2.6, (2.4) 1.3,
~
Z
t1
~ 0
t-'
tel
(")
1.86 3.3, 4.4, 5.0, 6.8, 2.91 2.94
q
t-'
p,~
"d
IIi
>-4
Ul H
316.1 979.23
.. .. .. . ... .
· ........ .. . ..........
(~680)
........... . ........ ,. ...... , ' ,2.1040 '" ....... -
. . .. . . . . .. .
1.63 (1. 7,) 2.06 3.0 3.2, 1. 7, 3.6,
(233)
617.12 467.6 . .......... 30.7 ........... 429.4 314.8 443
·...... .. . .
0.643 1.13
0
1.0 6.97 ...... - , ." 3.33 2.08 ........... 2.64 . . . . . . . . . ,-
1.12 1.25 2 (2.7)
3.77 4.9, 2.20 3.70 3.4, 3.37 0.0096, ~1.04,
3.94 2.7
(")
Ul
ABH ........... ABN ............ ABO ............ ABO+ ...........
Au, ............ AuBa .......... AuBe ........... AuBi ........... AuCa ........... AuC!. .......... AuCr ........... AuCu .......... AuGa .......... AuGe .......... AuH .......... AuMg ......... AuPb ......... AuPd ......... AuSe ......... AuSi ...........
75 75 75 75
1 2 14 16
0.99444817 1.96137493 11.797993, 13.180933,
75 197 197 197 197 197 197 197 197 197 197
16 197 (138) 9 209 40 35 (52) (63) 69 (74)
.............. 98.483276 (81.11371) 8.6178757 101.397856 33.2221413 29.6966074 (41.101862,) (47. 692224) 51. 058482 (53.74919)
197 197 197 197 197 197 197
1 2 24 (208) (106) (80) 28
1.00269470 1.9937152, 21. 3813867 (101.160960) (68.87247) (56.850280) 24.4973488
':!;':!;':!;+ 'II,
A = +1027 ':!;+ l1;q+
(':!;+) ':!;+
....... . .... (':!;+) (1:!;+) ............ ............ (0+) ('lIt)
A = +(1550) ':!;+ 1:!;+ ':!;+ ('II!)
.....
,
.....
('II) ('lIt)
[7.199,] [3.669,] 0.5457 0.48519
~
0.5199 0.028013
· . . .. . . . . . . . 0.46074
·....... ... .
AuSr ........... AuTe .......... . AuU ........... BL ......... , .. BaBr ........... BaC!. .......... BaF ........... BaH ........... BaO ............ BaS ............ BBr ............ BC ............. BCl. ........... BeBr ........... BeC!. ..........
197 197 197 197 11 (138) 138 (138) (138) (138) 138 (138) 11 (11)
11 9 9
(120) (88) (130) 238 11 79 35 19 1 2 16 (32) 79 12 35 (79) 35
(74.53153) (60.77977) (78.27889) 107.78430, 5.5046525, (50. 1940b) 27.895369 (16.698012,) (1.00051336) (1.98510967) 14.3325535 (25.954702) 9.6615017 (5.74166236) 8.3731666 (8.0885079) 7.1654925
0.0031 0.0000723 . ........... 0.00400
·. .... .. ... .
............ ............ . ........... . ........... ............ ............
. ........... ............ . ........... ·. ... . .. .. . .
7.2401 3.641.5 0.13214 ............
0.2136 0.07614 0.00073 . ...........
·.,
·,.,
,
'
, ,
'
..,
,
............ ............
A = +(107(,)
AuSn ...........
...........
[1.5344] [1.5304] 1. 618, 1.6236
............ 0.0038 0.003320
............ . ...........
,
,
... .. .
. ...........
·.
'
.... ... . .
1. 568. 2.4719
.
· . . .. . .... 2.0605 ........... . .......... . .......... . .......... ·.. . . . ....
.
1068.0 966.5,
-3
p..-
Z
>-3
'(f2
0
':rJ t;I
......
p..-
>-3 0 :::::: ...... 0
:::::: 0
t-< toJ
0 2.23 . .......... 2.592 3.5,* 4.2* 7.929 23.200 13.228 3.3,
. ..........
8.2, 5.96 1.117 4.3, 4.8, 5.9, 2.4289 2.4510 3.57
3.5,
0
t-< toJ
'(f2
-::J
I
f-'
'"'"
TABLE
7g-1.
CONSTANTS OF DIATOMIC MOLECULES
j'I
(Continued)
;....;
m1
m2
I'
Ground state
B,
a,
r,
w.
WeX"
Doo
(1)
(2)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
LiRb ........... LuO ............ Mg, ............ MgBr .......... MgCl. ......... MgF ........... ~1gH ...........
(7) (175)
(85) 16 24 79 35 19 1 2 1 2 127 16 (32) 55
(6.4805375) (14.655002.) 11.9925223 18.394535, 14.226871. 10.6012335 (0.96718516) (1. 85807370) ..............
12;+ ............
M,gH+ ..........
MgI ............ MgO ........... MgB ........... Mn2 ............ MnBr .......... MnCI .......... MnF ........... MnH ........... Mnl ............ MnO ........... MnB ........... MoO ........... N, .. _ .......... N-.J+ . . . . . . . . . . . . N z++ .......... .
Na2 ............ NaBr ........... NaC!. .......... NaCs, .......... NaF ........... NaH ........... NaI. ........... NaK ........... NaRb ..........
24 24 24 24 (24) (24) (24) (24) (24) 24 (24) 55 55 55 55 55 55 55 55 55 (98) 14 14 14 23 23 23 23 23 23 23 23 23 23
(79) (35) 19 1 2 127 16 (32) 16 14 14 14 23 79 35 133 19 1 2 127 (39) (85)
ll,;g+
(22;+) 22;+ 22;+ 22;+ 22;+ 12;+ 12;+ (22;+) 12;+
... . .. . . ..... . (20. 1724350) 9.5957763 (13.7042728) 27.469026,
(92;0+)
............ ............ ........... ........... ............ . ........... 0.00378 3.891 0.09287 ............ ............ ·.. .. .. .. . . 0.0015, 0.24502 2.1991 0.51922 0.00470 1. 7500 1.730, 5.818 0.1668 3.0307 0.0654 1. 7302 6.411 0.206 1.6488 1.652, 3.321 0.064 ............ ............ ·... . .. . ... 0.5743 0.0050 1. 7490 (oonstants for lowest observed state) ............ ............ · .........
(72;+) (72;+) (72;+) 72;+ 72;+ ('2;+) ............ ............ ............
(32.390087) (21.3678887) 14.1166536 0.98966997 1. 94287385 38.340221 12.3881675 (20.2103432) (13.748766) 7.00153719 .............. Data for lowest 11.4948863 17.8034377 13.8706876 19.599477 10.4021901 0.96549966 1.8518630, 19.463752, (14.458700,) (18.091511)
12;a+ 21;a+ 12;0+ 12;a+
12;+ 12;+ 12;+ 12;+ 12;+ 12;+ 12;+ 12;+ 12;+
.
. ... . ... ... . ............ ............ 5.6841 2.8956 ............ . ........... . ........... . ........... 1.9987 1.932 [1. 8801] 0.15471 0.15125329 0.2180630,; ............ 0.4369005, 4.9012 2.5575 0.11780550 ............ ............
............ . ........... ............ 0.1570 0.0514
·...........
. ........... ·.. .. . .. .. . ·. . ... . . ... . 0.01781 0.020 ·. ... ... .... 0.00079 0.0009409, 0.0016248
.
. ...........
0.004.5571 0.1353 0.0520 0.00064777
· . . . . . .. . . . . . ...........
· . . . . . . .. . . ........... ·.. ... . .... 1.7311 1.7310 . .......... . .......... . .......... . .......... 1. 0976 1.116 [1.1316] 3.0788 2.5020 2.3608 2.6 1.9259 1. 8874 1. 8866 2.7114 . .......... . ..........
(185) 841.6 51.12 373.8 [462.12] [711.69] 1497.0 1077.76 1695.3 1226.6 [312] 785.0, 525.2 . .......... 288 383 618.5 1548.0 1102.5 (240) 839.5
. .. ... ..... . .......... 2358.07 2207.19 (1960) 159.23 302* 366* (98) 536 1172.2 [826.10] 258 123.29 106.64
.
3.30 1.64, 1.34 (2.05) (4.94) 32.4 16.09 30.2 16.30 .......... 5.1, 2.93
·.... ...... (0.9) (0.7) 2.6 28.8 13.9 (1.5) 4.7 . ..........
· . . .. . . . . . . 14.188 16.14 0.726 1. 50 2.05*
*
·. . . . . ..... 3.4 19.72 1.0, 0.400 0.455
7.2. 0.0495 :::;3.35 3.26 4.75 :::;z .49
"" 00
>
>-3
0 ~ ...... Q
(2.1) (2.4) 3.5, Z 0
~ 0
t' trI
Q
q t'
~
!:O "d
il1 ><j
[fJ.
......
Q
[fJ.
NbO ...........
93
16
13.6456486
NBr ........... , NCl. ........... NdF ......... NdO ........... NF ............ NH ............
14 .14 (142) (142) 14 14 14 14
79 35 19 16 19
11.8928388 9.9990236 (16.7552338) (14.3746906) 8.0613378, 0.94016028 1.76083610 ..............
NH+ ...........
1 2 1
C'L'.) iAi'" 15 '2;'2;............ ............ '2;'2;32;-
'IT,
0.4321 0.444 [0.6468,] · ........... ......... ... 1.2056. 16.667, 8.9074 [15.35]
0.0021
1. 690,
989.0,
0.0040
1. 78, [1. 6144] . ..........
691. 75 827.0 . .......... . .......... 1141. 37 [3125.5,] (2418) [2922]
·...... ... .. · ........... · , .......... 0.01492 0.6457 0.2530 . ...........
1. 3170 1. 0372 1. 0367 [1. 081]
A = +78 14 (58) (58) (58) (58) 58 58
2 (58) (79) (35) 19 1 2
.............. (28.967671) (33.409121) (21.8066850) (14.3068434) 0.99059317 1.9464350,
NiL ...........
(58)
NiO ............ NO ............
(58) 14
127 16 16
(39.776343) (12.5343926) 7.46643320
NO+ ........... NS ....
14 l4
Hi
. .... ..... . ...
32
NS+ ............ NSe ............
14 14 16 1'6
32 (80) 16 16
....... ....... (11.9152661) 7.99745747 . .............
16 16 16
16 19 1
.... . , ........ 8.6838822, 0.94808710
2
l. 78884794 . . ............. .............. ..... .... ..... 15.4868817 ..............
Niz ............ NiBr ........... NiCl. .......... NiF ............
NiH ............
0, ............. O 2+ . . . . . . . . . . . 02~
.
........ -....
OF ........ " ... ·OH ...........
P, ............. P,+ ............
16 16 16 16 31 31
Ph ............. PbBr ...........
(208) (208)
OH+ ........... OH~ ...........
9.7380290,
2II r
............ · ........... ·.. . . . . .. . . . ............ 'L'.
[8.244] · ........... ............
· . . . . . ..... . ............ 7.815 4.037
26§
Ao = -490 . ... . .. ... . .............
·
'IT,
· . . . ... . . . .
.
. ........... . ........... ·....... .. . · ........... · . . . . . . . . ... 0.231 0.090
.
· . . . . . . . .. . .
1. 70485
........... 0.0176,
2.002 0.7754,
0.0202 0.0061
. . . . . . . . . ...
·
(208) 79
(103.988322) (57.20968,)
· . . .. . . .... . .......... · . ... . . .. .. 1. 476 ; 1.465
· .......... ........... l.1508
[2143.04]
.. ..... . . .. (315) (410) (740) 2000 1430
. . .. ...... .
4.720 5.1
· .... . . . . . . · .. ... . . ... 8.99 (79) (45)
· .. ...... . .
7.81 2.90 (4.1) 5.87 7.4, (4.4) 3.5, 3.6. 4.1
· .... ..... . .......... . .......... ·
40 20
·.. . .... .. . ·.. . .. .. . . .
2.3, 3.6, 3.8, 2.6
i:E+
'IT,
A = +223 12;+
'IT,
3:E u-
21I u ,T A = +195 2II u.i 2lli 2lli 2IIi
32;'2;(12;+) l:E u+ 2:Eu+
. .. ; ... ;. IItS"~
1. 0620 1. 4941
(1.09) ............ 1.44567 1.6920
............ . ........... 0.01579 0.01984
(1.26) . .......... 1. 2075 1.1161
............ · ......... . 18.867
. ........... . ........... 0.708
(1. 30) . .......... 0.97078
9.991 16.781 8.900 ............ 0.30348 >0.3038
0.258 0.724 0.274, · ........... 0.00143 0.0021
.
:z:
W
>-3
;:...
:z:>-3
W
0
1904.12
14.088
2.9, 3.7, 6.507
2377.1 1219.6
16.35 7.6
10.858 (6.0)
5.4 12.0730 16.18
(5.1) 5.115, 6.67.
. ..........
(")
0
A = +123
Ao = -140 1 2 1 31 31
.
[l.0776] ..........
3.8,
'?'l t:I >-
-3
0
a:>-< (")
>944 1580.361, 1903.85
1108 9 [1028.5] in Ar matrix: 3739.94 86.350
4.10
a::
0
t-< trJ
(")
q
4.39,
t-
~
6.983 6.57 .
(5) ......... 2.96
>1
,
3.3 4.87
.. . .... . ... . .........
0.71 0.096 0.46 0.92 1.9
p::
Ul
...........
1051.18 [2293.50] ...... .... 256.2 57.28 169 228* 376*
is: H
(3.05)
[1666] 1337.24 1233.33 1405 (820) 739.1
>-3
0
. ..........
-\-224
· ...........
=
2.2868 2.4022
[8.412] [4.363] 8.5051
1~+
.........
A PS+ ............ PtB ............ PtC ..... , ...... PtH ........... PtO ........ RaCl. ...... ' . ' . Rb,. ...... , . RbBr.,., .. RbC!. ....... RbF .... , .... ,.
=
0.0019148 0.0004365 0.00012993
\l>
160.5 721. 8 429.40 277.6* 211.96 . ..........
-\-296
'IT,
........... ... 9.64336165 10.5479381 A
PO+ ............ PrO ............ PS .............
=
'IT,
q
i
A'= -\-(8200) PbI ............ PbO ........... PbS ............ PbSe ........... PbTe ........... Pd, ............ PdC, .......... PdH .......... , PdO ............ PF, ........... , PF+., .........
00
7.8, (5.6) (6.6) 4,9, 6.30 (3.6) 3.8, 0.490 4.00 4.40 5.10
H
Cl Ul
SbO ............
(85) 85 103 103 (102) (102) 32 (121) (121) (121) (121) (121) (121) (121) (121) (121)
1 127 12 16 12 16 32 (123) 209 (79) 35 19 1 2 14 16
SbSe ........... SbTe ........... Se' ............. SeF ............ SeO ............ SeS ............ Se2 ............. SeF ............
(121) (121) 45 45 45 45 80 (80)
(80) (130) 45 19 16 (32) 80 19
SeH ............
(80)
RbH ........... RbI ............ RhC ........... RhO ........... RuC ........... RuO S, .............. Sb, ............. SbBi ........... SbBr ........... ShC!. .......... SbF ............ SbH ............ Sb~\f ............
(0.99600356) 50.872750 10.746788, 13.843208 (10.735774.) (13.824938) 15.9860369 (60.94787) (76.59208) (47.75009,) (27.123853) (16.418463) (0.99949368) (1.98109960) (12.549581,) (14.126107,)
1~+ 1~'+ ,~
........ , ... ............ ....... ..... 3~u-
l~fl+ 1~+
....... .....
·..... .. ... . · .. . . . . . . . . . ,~3~-
,~+
'II,
A = +2272 (48.11370,) (62.62182) 22.4779595 13.3546989 11. 7974776 (18.684147,) 39.958256 (15.349416,)
3.020 0.03283293 0.6027 . ............
· .. .. .. . .. .. · .. .. ...... . 0.2954, ............ · ........... ·.. . ... . . .. . ...... -, ... · . . . . .... .. . [5.87] [2.94] ............ · .......... .
.
('II ) ('II!)
· ........... · ...........
· ...........
· ...........
1~+
0.3950 [0.51340] ............ 0.08992 [0.363]
,~+
('~+)
0 0+ 2IIi
A = -560 (0.99527385)
[7.98]
2IIi
0.072 0.00010946 0.00396 ............
· . . . . . . . . . .. · .. . . . . .. ... 0.001570 . ........... ............ ·.. ... . ... .. ............ ............ ..... ..... . ............ . ........... ............
·
·........... . ........... . ........... 0.00266 · ........... · .. . . . ..... . 0.000288 · ........... ...........
,
2.367 3.1769 1.613,
·. . . . . . . . .. ·.......... . .......... 1. 8892 . ....... , ..
·. . . . . . . . . . . .......... . ..........
·... .., ... .
80
16
13.3274820
.~-
SeS ........... . SH .............
(80) 32
(32) 1
(22.836079,) 0.97702732
..... ....... 2IIi
SH+ ............ Sb ............. SiBr ............
32 32 28 (28)
2 1 28 (79)
Ao 1. 8947416, ....... . . . . . . .
13.9884630 (20.654728)
0.4704 0.00326 (constants for F, levels) ............
[9.46lt]
,~-
8:E 11 -
'II,
[4.900,] [9.1340] 0.2390 .............
A = +418 SiBr+ ........... SiC ............ SiC!. ...........
(28) (28) 28
(7il)
12 35
....... ....... (8.3979222,) 15.542282,
SiF ............
28
19
11.3148106
,~+
·.... . . . ....
.
...........
·. . . . .. .. . ..
'II,
0.25619
'II,
0.5813,
. ..........
·.. . ....... . .......... 1. 787, [1.6683] . .......... 2.1660 [1.73,] [1.457]
326.1 (284) . .......... 735.6 971. 55 .... . . . . . . .
385.3028 (2400) 915.43
·. .. . ...... (1940)
0.0013 · ...........
[1.3474] [1. 3744] 2.245 . ..........
·.. . . ...... . . ........... 0.00163
. .......... . .......... 2.0576
(0.300) (O.ll,)
· . .. . . . . ... .
0.00490
(1.9) 3.4, 6.01 4.3 6.5, 5.3 4.38 3.06 (3.0) (3.2) (4.6) (4.2)
1.6008
C":l
0
Z
Ul
942.0 817
1.6398
A = +207 A = +162
880.8 725.64, 269.85 220.0 (242.1) (369.0) (614.2)
. .......... [1.3504]
· . . .. .......
= -377 2IIi
· ... . ...... · . .. .......
14.21 0.34 4.94 ........... . .......... 13.1 2.844 0.59 0.50 (0.56) (0.92) (2.77)
[1.69,] [1. 70,]
·. ...... .. . ·..........
Ao = -1600 SeO ............
936.9, 139 1049.87
(2702)
510.98 425.4 535.8
· . . . . . . . . .. 535.89
857 _20
5.6 5.0
1.04 (0.2) . .......... 3.8 3.95 . .......... 0.96363
(4.8) (4.1) (3.1) 2.78 1.65 6.0, 6.9, 4.9, 3.410
,..>-3 Z
>-3
Ul
0
"':.I
,..,...t:I >-3
0 ~
3.2
>-< C":l
4.52
4.3,
~ 0
........... (60)
(3.90) 3.53
...........
t"
t"J
C":l
cj
(31)
3.57,
2.02 1.5
3.10 (3.7)
1.6 ........... 2.29
(5.5) 4.6. (4.5)
4.74
5.5,
t" l':I
Ul
-'l
I
f-'
00
....,.
~ ....... TABLE
7g-1.
CONSTANTS OF DiATOMIC MOLECULES
.:
m, (1)
SiR ............
m,
~ ~ (28)
1
SiN ............ SiO ............ SiO+ .......... , SiS ............. SiSe ............ SiTe ........... SmO ........... 8n2 ............. SnBr ...........
(28) 28
2 127
28 28
.. . 28 28 28 (152) (120) (120)
14 16 "
.
32 80 (130) 16 (118) (79)
Ground state
B,
a,
T,
w,
WtlXtI
D oo.
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(0.97278225)
'11,
(1.8788414,) 22.923324, 9.3321338 10.1767074
'11, 2n.~
A = +(757) '};+ 1};+
. .............
14.920688, 20.722468, (23.019425) (14.471297,) (59.44677) (47.59307,)
1};+ 1};+ 1};+ ....... ..... ........... . '11,
A = +2467
SnC!. ..........
(120)
35
(27.073116)
SnF ............
118
19
16.361890
SnR ............
(120)
1
(120) Snl ....•....... (120) 120 SuO ............ SnS ............ 120 SnSe ........... 120 SnTe ........... (120) SO ............. 32 SrBI' ........... (88) (88) SrCI. .......... SrF ........... _ (88) (88) SrR ............ (88) (88) SrI. ............ SrO ............ 88 (88) 81'S ............
2 127 16 32 80 (130) 16 79 35 19 1 2 127 16 (32)
~
.
I"
7.4979
1. 5203
0.2149
A = +143 Sil.. ...........
00
(Continued)
(0.99942466) (1.9808284,) (61.65195) 14.112333, 25.241415 47.954285 (62.35204) 10.6613029, (41.58494,) (25.017065) (15.622111) (0.99640162) (1.9689885,) (51.93244) 13.5325857 (23.444936)
3.8849
· .. . . . . . . . . .
1};+ 1};+ 1};+
0.3557190 0.136861, 0.0649977, · ........ ". 0.720817 · ........... ..... , ...... 0.25045 3.6751 1. 8609
'};-
36
3.06
1471 360.5
19 1.0,
3.09
>>-3 o
~
(6.2) 8.26 6.37 5.45 4.60 6.10 1. 9, (3.0)
H
Q
i»
Z
ti
~
o
t"
t>:l
Q
· . . . . . . . . .. .
'};+ '};+ '};+ '};+ '};+ ('};+) 1};+ (1};)
·
2045
0.7310 0.00567 1.5720 1151.680 6.5600 0.0050385 1.5097 1241.4, 5.92 0 . 7267514 Spectrum previously attributed to SiO+ now known to be due to SiN. 0.0014736 1.9293 749.6, 2.58 0.3035290 2.0583 0.0007767 0.1920116 580.0* 1. 78* ... ......... ........... 481.2 ........... . 1. 30 ........... . .......... . ........... . .......... ..... " ...... · . . . . . . . . . . . . ........... ...... , .... . .......... . .......... 247.7 ......... .. , . . . . . . . . . . . . ........... 0.62
'11, A = +2361 '11, A = +2317 '11, A = +2178 '11, 211
I};
0.0801 ............
1. 5197' ........ "
............
· . . . .... ...
0.2733
0.0011
1. 942
5.383
0.137
1.770,
2.7195 ............
· . ..... . .. .. 0.33798
·...........
0.049 ............ 0.002142, 0.000506, 0.0001704, ..... ' , ..... 0.00573, ............ ..... ' , ..... 0.00148 0.0814 0.0292 ... ......... 0.00219 ............
1. 7690 . .......... 1. 8325 2.2090 2.3256 ........... 1. 4811 , .. , . , ' .... ...........
2.0757 2.1456 2.1449 · .......... 1.9198 ...........
354.0
1.1
586.,*
2.76*
1715 1218 199.0 822.1 487.26 331. 2* 259.5 1148.19 216.5 302.3 500.1 1206.2 ..... ...... 173.9 653.2* ...........
30 15 0.55 3.73 1.358 0.736* 0.50 6.116 0.51 0.95 2.21 17.0 ......... 0.42 3.92* . .......... "
:0;4.25 4.7, 2.60
q
~
t:d
"d
::q
>-1.
(2.2) 5.49 4.7, 4.09 3.65 5.358 (3.9) 4.25 5.5. ' >-3 o
~
H
(")
>-
8 a:::
o ~ (") q
t"'
>-
!;d
~
~ 1Tl H
(")
1Tl
7h-3. Rotational Constants and Geometrical Parameters TABLE
C12 02 ............ C 130 2............ 00 2+ ............ CS2 ............. FCUN" ......... FC13N14 ....... .'. FC12N" ......... RC12N .......... RC 13 N .......... DC12N .......... DC"N .......... RC12P ........... RC"P ........... DC12P ........... DC"P ........... P27C12N ......... I127C"N ......... N 2'-'0 ........... N14N"O ......... N"N 140 .........
N ,"0 ........... O"C 12S 32 ........ O"C·"S32 ........ o 16C 12S " '.' ...... O"C12S34 ........ O"C12S" ........ O"C12S" ........ 016C"S" ........ O"C14S32 ........ o 17C 12S 32 ........ 018C12S" ........ 018C12S34 ........ 018C13S32 ........ 016C12Se 74 • • • • . .. 016C12Se" ....... o 16C 12Se 77 •••••••• o "c 12Se" ........ o "C 12Se 79 ........ 0"C12Se 80 . . . . . . . o "C 12Se" ........ o 16C13Se" ..... .. 0"C13Se 80 ....... Te 122 C12S32 ....... Te 12 'C12S32 ....... Te 12-lC12S" ....... Te '25 C12S" ....... Te 126C 12S 32 ....... Te 128 C12S" ....... Te130C12S32 .......
TRIATOMIC LINEAR MOLECULES
Point group
Blo]. cm- 1
Molecule Br79C12N" ....... Br 79 C13N" ....... Br"C 12N" ....... B r 81C12N" ....... B r 81C13N14 ....... B r 81C12N15 ....... Cl"C12N ......... Cl"C13N ......... Cl"C12N ......... Cl"C12N ......... Cl"C13N .........
7h-5.
0.1374348 0.1358729 0.1315857 0.1366539 0.1350802 0.1308165 0.1991648 0.1981294 0.19707 0.195043, 0.1939576 {0.39020 B, = 0.3916, 0.39025 0.3804 0.1092 0.3520502 0.3518367 0.3397823 { 1. 47822 B, = 1.4849 1.43999 {1.20775 B, = 1.2118 1. 18707 0.6663292 0.6384179 0.5665385 0.5479633 0.1075931 0.105974 O { B,.4190ll3 = 0.42118, 0.4189825 '0.4048567 B, = 0.406935 0.404859, 0.202857 0.2022025 0.2003016 0.1978974 0.19564 0.193456 0.197194 0.201581 0.196258 0.190292 0.185458 0.189829 0.1366207 0.1357085 0.1352681 0.1348404 0.1344213 0.1340143 0.1332276 0.1335960 0.1327598 0.05284063 0.05273401 0.05262940 0.05252608 0.05242467 0.05222620 0.05203367
l} }
}
l} l }
t
Geometrical parameters
Cct:!L'
{ ro(CBr) = 1. 7901 To(CN) = 1.. 1.591
COO"
{ ro(CCl) = 1. 631 1 ro(CN) = 1. 1591
Dooh
roCCO) = 1.1621 1; r;(CO) = 1. 1601A
Dooh Dooh Dooh
ro(CO) = 1.16181 roCCO) = 1.1771 ro(CS) = 1. 554 1 ro(CF) = 1.2621 ro(CN) = 1.1591
Cr:t;)v
..
CC¢l'
{ ro(CR) = 1. 064 ~; r,(CR) = 1.06571 ,0(CN) = 1. 156 A; r,(CN) = 1.15301
COOl'
ro(CR) = 1.06671 ro(CP) =1.1i421
Coo
{ ro(CI) =.1.995 ~ ro(CN) = 1.159 A
(I
C06~'
{ ro(NN) = 1.126 1; r,(NN) = 1.1261 .rcCNO) = 1. 191 A; ~,(N()) = 1 186 A
{ ro(CO) =1.16371
C
OXlV
ro(CS) =1.55841
CCCt,
{ ro(CO) = 1.15881 'o(CSe) = 1. 70901
CtX)u
{ ro(TeC) = 1. 9041 ro(CS) = 1. 557 1
1 '/-191
7-192
ATOMIC AND MOLECULAR
0.3 r-
f=0,485
,
,, \
0.2 -
3s 2S-4p 2po
-
x •
Prokof'ev (centrol field opproximation) \, Stewart" and Rotenberg (ThomasFermi potential) \ .\ .. Weiss (SCF calculation) , 6 Douglas and Garstang (SCF calculation) '., 0 Coulomb approximation \ e Hinnovand Kohn (Emission experiment)
,,
1 f-value
~,
, " '~
,,
0.1 -
-
,
0,
" '6
Fe:IlZl: CaX Si:rli'".. _A ~------~~I------~I~I--~I--~~I--_~I~'~~.~-~--~
o
0.02
0.04
0.06
0.08
0.1
1/2-FIG. 7i-3. Oscillator strengths vs. liZ for the 38 'S-4p 'po transition of the sodium isoelectronic sequence. (From Ref. [10], where the quoted authors and methods are discussed in detail.)
10r-----------~----------------------__,
LiI
7
2s-np SERIES 5
x Weiss (variational calculation) o Fillipov (hook,relotive;normalized to Weiss) • Anderson and Ziliti.{.emi-empirical calculation)
3
2
1.0 0.7
FIG. 7i-4. Oscillator strengths multiplied by n*' vs. effective principal quantum number n* for the resonance series 2s-np of Li 1. (From Ref. [10], where the quoted authoTs and methad·g are discussed in detail.) , TABLE
7i-3.
COMPARISON OF MULTIPLET IN SOME DOMINANT
+
+
1)8 - {n l)p . ..... 'S_'po . ............ " .. l)s - np(n l)p .. np(n 'po_3D ................. apo_aP .......... ....... 'po_'S . ........ ........ 'po_'D .. ........ ....... ,po_'S .......... ....... 1)8 - np2(n l)p np'(n 4P_'Do .. ............... 4P_'PO .. ............... 4P_4S0 . ................ 'P_2PO . ................ l)p np'(n l)s - np'(n 'SL5P ..... .. .. . . . . . . . . ,so_'P . ................
+
* The
f
+
+
+
+
+
VALUES FOR HOMOLOGOUS ATOMS
TRANSITION ARRAYS*
Uncertainty, %
f value
Transition
{n
s-p
Boron (n = 2) 1.21 25 I Carbon (n = 2) 0.50 50 0.31 50 0.10 50 0.42 50 0.11 50 Nitrogen (n = 2) 0.36 25 0.23 25 0.088 25 0.318 25 Oxygen (n = 2) 0.922 10 0.898 10
data are the adopted "best" values.
I
Uncertainty, %
f value
Aluminum (n = 3) 1.41 25 I Silicon (n = 3) 0.61 50 0.39 50 0.13 50 0.67 50 0.12 50 Phosphorus (n = 3) 0.57 50 0.36 50 0.13 50 0.39 50 Sulfur (n = 3) 1.1 50 1.1 50
I
Data from experimental sources are in italics.
7-206
7-207
ATOMIC TRANSITION PROBABILITIES
5.0,.---,--,----y----,-....,-----.-----,
OI 3p - ns SERIES
.4.0
I:J. Triplet (3pO_3S )
o
Quintet(~Po_5S)
3.0
2.0
o 4.0
5.0
6:0
7.0
n*-':' FIG. 7i-5. Oscillator strengths multiplied by n*3 vs. effective principal quantum number n* for the 3p-nsseries of 0 I: The solid' circles and triangles indicate that experimental values are involved in the data. (From Ref. [10], where the quoted authors and methods are diseu~sed in detail.) ,
more, in all homologous atoms the breakdown of the ,total strength of a transition array into multiplets and individual lines remains the same as long as the coupling scheme remains constant. It follows therefore that for all lines of dominant transition arrays in ho:moiogous atoms the f yal~esshould stay Il-pproximately constant. An example is given in Table 7i-3. More extensive comparisons are found in [10]. References 1. Wiese, W. L., M. W. Smith, and B. M. Glennon: Atomic Transition Probabilities, vol. 1,
Hydrogen through Neon, Natl. Standard Ref. Data Ser. NBS 4, 1966. : 2. 'Wiese, W. L., M. W. Smith, and B. M'. 'Miles: Atomic Transition Probabilities, vol. 2, Sodium through Calcium, Natl. Standard Ref. Data Ser. NBS 22, 1969. a.Moore, C. E.:A Multiplet Table 'of Astrophysical Interest, rev. ed., NBS Teen. Note ~lM~ , ' " , 4: Moore, C. E.: An Ultraviolet Multiplet Tahle, NBS Cire. 488, sec. 1, 1950. ,,' 5. Moore, C. E.: Selected Tables of Atomic Spectra, sees. 1 and 2, Si I, n, III, IV, Naa. Standard Ref. Data Ser. NBS 3, 1965, 1967. , ,6. Kelly,R. L.: "Atomic Emission Lilies Below 2000 A," Government Prmting Office, Washington, D.C., 1968. 7. Bethe, H.A., and E. E. Salpetet: "Quantum Mechanics of One- and Two-electron Atoms," Academic Press, Inc., New York, 1957.
u:s.
7-208
ATOMIC AND MOLECUl.AR PHYSICS
8. Naqvi, A. M.! Thesis, Harvard University, 1951; G. Shortley, L. H: Aller, J. E. Baker, and D. H. Menzel: Astrophys. J. 93, 178 (1941). 9. Wiese, W. L.: "Beam Foil Spectroscopy," vol. 2, p. 385, S. Bashkin, ed., Gordon and Breach, Science Publishers, Inc., New York, 1968. 10. Wiese, W. L., and A. W. Weiss: Phys. Rev. 175, 50 (1968). 11. Wiese, W. L.: Appl. Optics 7, 2361 (1968).
Explanations for Main Data Tables 7i-4 and 7i-6. A dagger (t) before a row of data indicates that m1LltipZet values are given, for example, the averaged multiplet wavelength. WAVELENGTH COLUMN: The wavelengths are given in angstroms. Values in square brackets [ ] are calculated and are likely to be less accurate than observed ones. MULTIPLET COLUMN: The numbers refer to the multiplet numbers of C. E. Moore, "A Multiplet Table of Astrophysical Interest," revised edition, Nat. Bur. Standards Tech. Note 36, 1959; or, if "uv" is added, to C. E. Moore, An Ultraviolet Multiplet Table, Natl. Bur. Standards Cire. 488, sec. 1, 1950; or, for Si I, II, III, and IV, to C. E. Moore, "Selected Tables of Atomic Spectra," NSRDS-NBS 3, secs. 1 and 2. (Preceded by "UV," if in the ultraviolet.) All are available from the U.S. Government Printing Office, Washington, D.C. 20402. STATISTICAL WEIGHTS COLUMN: The statistical weight gk of level k is related to the inner quantum number J by
The J's are listed in C. E. Moore, Atomic Energy Levels, Nail. Bur. Standards Cire. 467, vol. III, 1958, U.S. Government Printing Office~ Washington, D.C. 20402. TRANSITION PROBABILITY COLUMN: Normally, the Aki's are listed in units lOB S-I. But for hydrogen and the forbidden lines, they are listed in units S-1 and the number given in parentheses ( ) indicates the power of ten by which the transition probability values have to be multiplied. ACCURACY COLUMN: The accuracy ratings are to be understood in the sense of "estimated extent of possible errors." Since it is at present not feasible to give specific numerical error limits for each cvaluated f value, the Jata are assigned tu une of several levels of accuracy which differ by about factors of three.. Further details are found in [1,2]. SOURCE COLUMN: The numbers refer to the references given below. n indicates normalization to an absolute scale different from the one in the listed reference. References for Tables 7i-4 and 7i-5 1. Wiese, W. L., M. W. Smith,and B. M. Glennon: Atomic Transition Probabilities, vol. 1, Hydrogen through Neon, Natl. Standm'd Ref. Data Ser. NBS 4, 1966. 2. vViese, W. L;, M. W. Smith, and B. M. Miles: Atomic Transition Probabilities, vol. 2, Sodium through Calcium, Natl. Standard Ref. Data Ser. NBS 22, 1969. 3. Green, L. C., N. C. Johnson, and E. K. Kolchin: Astrophys. J. 144, 369 (1966). (Central field approximation with exchange and configuration mixing.) 4. Cohen, M., and P. S. Kelly: Can. J. Phys. 45, 1661 (1967). (Self-consistent field calculation.) 5. Cohen, M., and P. S. Kelly: Can. J. Phys. 45, 2079 (1967). {Self-consistent field calculation.) 6. Weiss, A. W.: Phys. Rev. 188, 119 (1969) and to be published. (Self-consistent field calculation with configuration mixing.) 7. Bergstrom, 1., J. Bromander, R. Buchta, L. Lundin, and I. Martinson: Physics Letters 28A, 721 (1969). (Lifetime measurement.) 8. Froese, C.: J. Chem. Phys. 47, 4010 (1967). (Self-consistent field calculation.) 9. Pfennig, H., P. Steele, and E. Trefftz: J. Quant. Spectr. & Radiative Tran8fer 5, 355 (1965). (Self-consistent field calculation.) 10. Lawrence, G. M., and B. D. Savage: Phys. Rev. 141, 67 (1966). (Lifetime measurement.)
ATOMIC TEANSITION .PROBABIJ;,ITIES 11. Hese, A., and H. P. Weise: Z. Physik 215,95 (1968). (Lifetillje measurement.) 12. Warner, B.: Monthly Notices Roy. Astron. Soc. 139, 1 (1968) . . (Scaled Thomas-Fermi approximation with limited configuration mixing.) 13. Weiss, A. W·.: Phys. Rev. 162, 71 (1967). (Self-consistent field calculation with eonfiguration mixing.) 14. Roberts, J. R., and K. L. Eckerle: Phys. Rev. 153, 87 (1967). (Relative emission measurement.) 15. Steele, R., and E. Trefftz: J. Quant. Spectr. & Radiative Transfer 6, 833 (1966). (Selfconsistent field calculation with configuration mixing.) . 16. Curnette, B., W. :S: Bickel, R. Girardeau, and S. Bashkin: PhYs. Letters 27A, 680 (1968). (Lifetime measurement.) 17. Warner, B.: Monthly Notices Roy. Astron. Soc. 141, 273 (1968). (Scaled ThomasFermi approximation.) 18. Heroux, L.: Phys. Rev. 153, 156 (1967). (Lifetime measurement.) 19. Bickel,W. .s.,R. Girardeau, and S. Bashkin: Phys. Letters 28A, 154 (1968). (Lifetime measurement. ) 20. Lewis, M. R., T. Marshall, E. H. Carnevale, F. S. Zimoch, and G. Wi" Wares: Phys. Rev. 164,94 (1967). (Lifetime measurement.) 21: Gaillard, M., and J. E. Hesser: Astrophys. J. 152,695 (1968). (Lifetime'Ineasurement.) 22. Lawrence, G. M.: Bull. Am. Phys. Soc. II, 13, 424 (1968). (Lifetime measurement.) 23. Bickel, W. S.: Phys. Rev. 162,7 (1967). (Lifetime measurement.) 24. Bickel, W. S., and S. Bashkin: Phys. Leiters, 20, 488 (1966). (Lifetime measurement.) 25. Bridges, J. M., and vy. L. Wiese: Phys. Rev. A2, 285 (1970). (Emission measurement.) 26. Lilly, R. A., and J. R. Holmes:J. Opt, Soc. Am. 58, 1406 (1968). (Relative emission measurement.) . 27. Hesser, J. E.: Phys. Rev. 174, 68 (1968). (Lifetime measurement.) 28. Hoimann,.W.: Z. Naturforsch, 24a. 990 (1969). (Emission measurement.)
TABLE
Wavelength,
A
Statistical weights Transition (J'
(Jk
I
7i-4.
TRANSITIO~ PROBABILITIES FOR ALLOWED LI
Average transition probability Aki*,
Source*
Wavelength,
A
Transition
8- 1
I
Hydro(Jen
Hy
914.039 914.286 914.576 9H.919 915.329
1-20 1-19 1-18 1-17 1-16
2 2 2 2 2
800 722 648 578 512
3.928(+3) 5.077(+3} 6. 654( +3} 8. 858( +3} 1. 200( +4}
1 1 1 1 1
8467.26 . 8502.49 8545.39 8598.39 8665.02
3-17 3-16 3-15 3-14 3-13
915.824 916.429 917.181 918.129 919.352
1-15 1-14 1-13 1-12 1-11
2 2 2 2 2
450 392 338 288 242
1. 657( +4} 2.341(+4) 3. 393( +4) 5.066(+4) 7. 834( +4)
1 1 1 1 1
8750.47 8862.79 9014.91 9229.02 9545.98
3-12 3-11 3-10 3- 9
920.963 923.150 926.226 930.748 937.803
1-10 1- 9 1- 8 1- 7 1-. 6(L.)
2 2 2 2 2
200 162 128 98 72
1. 263( +5} 2. 143(+5} 3. 869( +5) 7. 568( +5) 1. 644( +6)
1 1 1
949.743 972.537 1025.72 1215.67 3682.81
1- 5(L.) 1- 4(Dy)
2 2 2 2 8
50 32 18 8 800
4. 125( +6) 1. 278( +7) 5.575(+7} 4. 699( +8) 2.172(+3)
1- 3(LfJ) 1- 2(La) 2-20
3- 8(P,) 3- 7(P.)
1
10049.4 10938.1 12818.1 16407.2 16806.5
1 1 1 1 1
17362.1 18174.1 18751. 0 19445.6 21655.0
4-10 4--9
3~
6(?y}
3- 5(PfJ}
4-12 4-11
3- 4(Pa)
4- 8 4--7
3686.83 3691. 55 3697.15 3703.85 3711.97
2-19 2-18 2-17 2-16 2-15
8 8 8 8 8
722 648 578 512 450
2.809(+3) 3.685(+3) 4. 91O( +3) 6. 658( +3) 9.210(+3)
3721. 94 373.4.37 3750.15 3770.63 3797.90
2-14 2-13 2-12 2-11 2'-10
8 8 8 8 8
392 338 288 242 200
1. 303( +4) 1. 893(+4) 2.834(+4) 4.397(+4) 7 .122( +4)
3835.38 3889.05 3970.07 4101.73 4340.46
2- 9 2- 8
8 8 8 8 8
162 128 98 72 50
1. 216( +5) 2.215(+5) 4.389(+5) 9.732(+5) 2.530(+6)
4861.32 6562.80 8392.40 8413.32 8437.96
2- 7(H.)
2- 6(Ha) 2- 5(H'() 2- 4(HfJ) 2- 3(Ha)
3-20 3-19 3-18
* For references see pp.
8 8 18 18 18
7-208 and 7-209;
32 18 800 722 648
8.419(+6) 4.41O( +7) 1.517(+3) 1. 964( +3) 2.580(+3)
1 1 1 1 1
1
1 1 1 1
II ! I
! 1
I
I
1 1 1 1 1
1 1 1 1 1
26252.0 27575 28722 30384 32961
4-6 5-12 5:"'11 5-c1O 5-9
37395 40512.0 43753 46525 46712
5- 8 4- 5 6-12 5- 7 6-11
51273 59066 74578 75005 123680
6-10 6-9 5-6 6-8 6- 7
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
Oi
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Transition probability Aki, 10' S-1
Accuracy,
Source*
%
Wavelength,
A
Multiplet no.
Ok
5_37.030 584.3_34 t2763.S t2829_07. t2945_10
8 7 6 5 4
uv uv uv uv uv
3 uv 2 uv -
12 uv 11 uv
1 1 1 1
1
He
3 3 3 3 3
0.306 0.454 0.722 1.25 2.46
--
10 10 10 10 3
3 3 3 3 ---1
1 3 3 3
3 3 9 9 9
5.66 17.99 0.0132 0.0204 0.0339
1 1 10 10 10
_0.0505 0.0102 0_0150 0_0233 0.0393
10 10 10 10 10
1 3 3 3 3
1
1 1
3 3 3
t3187.74 3296_77 3354.55 3447.59 3613.64
3 9 8 7 6
3 1 1 1 1
9 3 3 3 3
t3634.2 t3705.0 t3819.6 t38SS.61') 3926.53
28 25 22 2 58
9 9 9 3 3
15 15 15 9 5
0_0273 0_0415 0.0671 0_09478 0_0194
10 10 10 10
3 3 3 1 3
3964.7.3 4009.21 t4026_2 _ 4120,g4143.76
5 55
1 3 9 9
3 5 15 3 5
0.0717 0.0296 0 . 121 0.0436 0_0488
3 10 10 10 10
1 3 3 3 3
- -
IS 16 53
:3
St w
O'
Helium 508.643 509.998 512.098 515,617 522.213
(C
1_ •.
1
18555.6 tI8686 18696.9 -
-
----
19089.4 t19543 20581. 3 t21120 21132_0 [33299] t[37.026] t[40365] [40396] [41216] t[42947] [46053] t[46936] t[1088DOl LiI: t2394,36 t2425,41 t2475_06 t2';;62.31 t2741. 19
.- .,-
-
-
-
-
-
-
5-uv 4-uv 3 uv· 2'uv 1 uv
-- --
5 15 5
-
3 15 1 9 3
1 9 15 5 3
3 3 9 3
2 2 2 2 2
, 4168.97 4387.93 4437.55 t4471.5 4713.2
52 51 50 14 12
3 3 3 9 9
4921. 93 5015.68 5047.74 t5875.7 6678.15
48 4 47
t7065.3 7281. 35 t9463.57 9603.42 t9702.66 t10311 t10667.6 10830.3 t10912.9 10917.0
1 5 1 15 3
0.0181 0.089.9 0.0322 0.257 0.0934
10 10 10 10
3 3 3 3 3
.3
5
P
46
1 3 9 3
1 15 5
0.199 0.1338 0.0670 0.706 0.638
10 1 10 3 3
3 1 3 1 1
10 45 67 71 75
9 3 3 1 9
3 1 9 3 3
0.278 0.181 0.00561 0.00586 0.00871
3 3 10 10 10
1 1 3 3 3
74 73 1 79 84
9 9 3 15 5
15 3 5 21 7
0.0201 0.0145 0.1022 0.0212 0.0212
10 10
3 3 1
11
10
1
10 10
1
1
70 88 87 72 -
1 3 3 9 3
3 5 1 15 9
0.00928 0.0184 0.0113 0.0349 0.00608
10 10 10 10 10
3 3 3 3 1
il2785 12790.3 '112846 12968.4 [13411.8]
-
15 5 9 3 3
21 7 3 5 1
0.0462 0.0461 0.0274 0.0336 0.0205
10 10 10 10 10
1 1 3 3 3
15083.7 '117002
-
11013.1 11045.0 11225.9 '111969.1 '112528
-
-
-
1 9
3 15
" For references see pp. 7-208 and 7-209.
0.0137 0.0664
10 10
1 3
t3232.63 t3985.5' t4132.6 t4273.1 t4602.9
2
6
2 6 6 6 6
t4971.7 t6103.6 t6707.8 t8126.4 t1051O.6
5 4 1 3 -
6 6 2 6 6
t11032.1 t12237.7 t12793.3 t13557.8 tl7546.1
-
6 6 10 6 6
t18703.1 t19274.8 t24464.7 t[25197] t26877.8
-
t[284F] '1[38081] '1[41791] '1[54633] '1[68592]
-
Li II: 178.015 199.282 t[944.72] [1093.2] '11132.1
-
'-
-
-
-
-
2 uv 1 uv -
10 10 6 6 2
6 6 10 6 2
1
1
3 1 9
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
Oi
7i-4. TRANSITION ]'ROBABILTTIES FOR ALLOWED LINES (Co
Transition probability AM, 10' 8- 1
Accuracy,
Source*
%
Wavelength,
A
Muftiplet no.
Ok
St w
Oi
r
Lithium (Continued) t1166.4 t1198.09 [1237.4] 1253.3 1420.89
-
tl493.0 t1653.1 1681. 66 1755.33 t2674.43
-
[2952.5] t[3029.1] t[3155.4] t[3195.8] [3199.4] [3250.1] [3306.5] t368.4.1 4156.3 t4.325.7 '1[4671.8] [4678.4] [4787.5J '1[4840.8] t4881.3
-
-
-
4uv
.-
2 3 5.
'-
-
4
9 3 3 3 1
3 9 5 1 3
1.07 2.88 3.16 0.784 2.82
10 3 10 10 3
5
9 9 3 3 3
15 3 5 1 9
11.2 2.96 10.1 2.03 0.192
3 10 3 10 10
1 5 1 5 1
1 9 9 15 5
3 15 3 21 7
0.202 0.549 0.318 0.739 0.736
10 10 10 10 10
1 1
1
5 5 1
1
1 1
3 3 3 1 9
5 1 9 3 15
0.528 0.252 0.295 0.351 1.11
10 10 10 10 10
1 1 5 5 5
15 5 3 15 9
21 7 5 9 3
2.21 2.21 1: 17 0.0895 0.738
10 10 10
1 1 5 5 5
10 10
BI: t1826.2 t2089.3 2496.77 2497.72 8667.2 8668.6 t11661 15625 15629 t16243
B II: 1362.46 t1624.0 [1842.8] 3451. 41 t4121. 95 BIll: t518.25 t677.09 t758.60 t2066.3 t4243.60 t4487.46 t7838.5
3 uv 2uv 1 uv 1 uv
6 6 2 4
-
2
-
4 2 2 4 6
-
1uv 3.uv
1 2
-
1 9 3 3 15
1
2 6 6 2 6
2
10
-
-
-
2
15038.7] t5484.8 [9562.2] tL57324]
-
3
-
3 1
1
~
1 9 3 15
~
0.533 0.228 0.0518 0.00110
10 3
5 1 1 1
3 3
Beryllium ··Be I: '2348.61 t2494 , 6 t2650.6 t3321.2 [3455.2]
1 uv 3 uv 2uv 1
-
3515.54 3813.40 Be II: t1036.31 t1512.4 t1776.2 t3130.6 t3247.7 t3274.64 t4360.9 t4673.46 t5270.7 t12094
"
~
25 50 25 50 2q
6,7 9 6,7 7, 8 1, ·7
0.13 0.23 .
50 50
1 1
10 10 10 3 10
1 1 1 1 1 4 4 1 4 1
[)
1 uv 4uv 3 uv 1 5
2 6 6 2 6
6 10 2 6
2
1.66 11.4 4.22 1.15 0.410
2 6 10 6 2
6 10 14 2 6
0.133 1.12 2.21 1.00 0.128
10 10 10 10 10
-
1 1 1 3 3
3 3 3 9 .. 9
362 1220 42.8 16.5 0.342
3 3 3 3 3
1 1 1 1 1
-
1 ... - _._..,
3
_1...
3
-
-
"
5.3 1.4 4.29 1.6 2.09
3
-
[6141. 2J
3 15 9 3 1
7 5
2 4 6 3
Be III: 88.314 100.254 [398.19] t[5B3.01] t[3721.8]
1 9 9 9 3
5
.
For references see pp. 7-208 and
.-
3
-_. ,--
7~209.
-
-
._
"
0.0877
..
.""
..
EIV: 52.682 60.313 t[344.19] [381.13] t2823.4 [4499.4]
C I: t1261. 3 t1277.5 1279.25 t1280.4 t1329.3.
-
1 1
-
3
-
-
1 3 1
9uv 7 uv 6 uv 5 uv 4uv
9 9 5 9 9
1431. 60 1432.12 1432.54 1459.05 1463.3::\
65 65 65 38 37
uv uv uv uv uv
5 5 5 5 5
1467.45 1481. 77 t15in.0 t1657.2 1751. 9
36 34 .3 2 62
uv uv uv uv uv
5 5 9 9 1
1930.93 2478:-564268.99 4371.33 4932.00
33 uv 6i uv" 16 14 13
5 1 3 3 3
5052.12 5380.24
12 11
3 3
'0
--- -
-
TAllLE
Wavelength.,
A
Multiplet no.
Statistical weights
Oi
7i-4.
TRANSITION PROBAllILITIES FOR ALLOWED LINES
Transition probability Aki. 10 8 8- 1
Accuracy. %
Source*
Wavelength.
A
Multiplet no.
(C
St w
O
Ok
r
Ca
Carbon (Continued)
6587.75 8335.19 9061.48
22 10 3
3 3 3
3 1 5
0.024 0.32 0.065
50 50 50
1 1 1
9062.53 9078.32 9088.57 9094.89 9111.85
3 3 3 3 3
1 3 3 5 5
3 3 1 5 3
0.083 0.062 0.25 0.19 0.11
50 50 50 50
1 1 1 1 1
9603.09 9620.86 9658.49 10124 10548.0
2 2 2
20
1 3 5 3 3
3 3 3 3 3
0.024 0.074 0.12 0.171 0.010
50 50 50 25 50
1 1 1 1 1
10683.1 10685.3 10691. 2 10707.3 10729.5
1 1 1 1 1
3 1
5 3 7 3 5
0.13 0.10 0.18 0.072 0.043'
50 50 50 50 50
1 1 1 1 1
111602.9 ·11609.9 11619.0 11631. 6 11638.6
25 25 25 25 25
5 3 7 5 3
0.00Q9~
25 25 25 25 25
1 1 1 1 1
-
Ii
3 5 3
g
5 5
5
0.0492 0.0073 0.0453 0.0163
50
4371.59 4372.49 4374.28
45 45 45
2 4 6
t4411.4 5143.49 5145.16 5151.08 5640.50
39 16 16 16 15
10 4 6 6 2
5648.08 5662.51 t5890.4 6578.03 6582.85
15 15 2 2
4 6 10 2 2
6783.75 6787.09 6791.30 6800.50 7231,12
14 14 14 14 3
6 2 4 6 2
C III: 386.203 t459.57 977.026 tH75.7 1247.37
{)
2 uv 6 uv 1 uv 4uv 9 uv
1 9 1 9 3
[11653] 11656.0 11677.0 11747.5 [11778]
29 29 25 24 24
11801. 8 11849.3 11863.0 1:1.880.4
24 23
12551. b
3(r
3
3 7 3 5
23"~
2:>'
1 3 5 5 5
0.157 0.158 .0.0101 0.202 0.0375
25 25 25 25 25
1 1 1 1 1
7 5
25 50 50 50 25
1
25 25 25 25
1 1
7 5 3 3 1
1 3
0.0266 0.017 : 0.029 0.11 0.0352
3 5 5 5
5 3 5 7
0.0262 0.0435 0.078 0.123
3
i
1 1
1
,,~
12582.3 12602.6 12614.8' 16890
30 30 30 -
1
1
elI:'
t687.25 t904.09 tlOlO.2 t1036.8 tl323.9
5 uv 3 uv 11 uv
t1335.3 2509.11 2511.71 2512.03 2836.71
1 14 14 14 13
2837.60 t3876.7 3918.98 . 3920.68 4074.53
7. uv 2 uv
12 (:; 10
."',,)tor'
2.65 0.63 0: 126 0.75 0.359
25 25 25 25 25
10, 13 13, 14 13, 14 13,14 13, 14
25 25
13, 14 1
'2 8
0.359 2.66 0.62 1. 24 1. 96
10 14
2.28 2.46
6 2
10
UV UV
4 4
4
uv
2
13 uv 33
2 28
~
36 6
4
2 ~
4 6 "
28.0 41. 6 34.3 22.2 5.3
6 4
2
4 36 .>
407{).bo 1'4267.2
13 i3 13
uv
~4
UV
25 25 25 25 25
10 6 4 2 10
6 6
.---
8 10
~
36
2~
----
ieferencei~se;;pp.~ 7~~20~r and 7~209.
...
~25
25 25 25 25
13
13
I,~
14
1, 14 1 1
1
2296.89 3170.16 t3f~09. 3 3703.52 t3887.1
8 uv 8 10 12 15
4056.06 4122.015 4325.70 4388.24 t4516.5
24
))
17
3 3
4647.40 4663.53 46.65.90 467.3.91 5249.6
1 5 5 5 23
3 5
5253.55 5272.59 67'27.1 6730.7 6744.2
4 4 3 3 3
3 5 1 3 5
C IV:· t244.907 t259.52 289.143 296.857 296.951
3 10 9 8 8
7~
3
i
9
3 15
7'
14 9
9
3 5
5
uv uv uv uv uv
2 6 2 2 4
uv uv uv uv () uv
2 2 2 2 4
--.- -
312.418 312.455 384.032 419.525 419.714
2 2 7 6
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
(Ii
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Ttanllition probability ..:hi, 10 8 S-1
Accuracy,
Source*
%
Wavelength,
A
Multiplet no.
(Jk
1 tlV 1 tlV 14 uv 13 uv 12 uv
2 2 10 10 2
2698.70 t3936 5021 5023 5801. 51
12 uv 2 3 3 1
4 2 2 4 2
4
Nitr
14 6 2
2.65 2.63 6.62 0.673 1.17
3 3 10 10 10
1 17 17 17
2 6 2 2 4
2.33 0.330 0.464 0.930 0.319
10 10 10 10 10
17 17 17 17 1
4
1
2
2
34.973 40.270 t186.72 197.02 t227.22
-
1
1 9 3 3
3 3 15 5
[247.31] t248.71 267.26 t2273.9 , [::1540.8]
-
1 9
5812.14 CV:
-
~
3 1
9
3 15 5 9 3
Sta w
(Ji
Carbon (Continued)
1548.20 1550.77 t2524.40 t2595.14 2697.73
(Co
0.316 2550 8870 142 124 136· 128 425 396 0.565 0.160.,
1
6945.22 7442.30 7468.31 8184.85 8188.01
29 3 3 2 2
6 4 6 4 2
8216.32 8223.12 8242.37 8590.01 8629.24
2 2 2 8 8
6 4 6 2 4
1 1 1 1 1
10
1
8680.27 8683.40 8686.16 8703.26 8711.71
3 10 10 3·
1 1 5 5 1
8718.84 9028.92 9045.88 9060.72 938&.81·
1 15
3 3 3 3 3
1
1 1 1 1
9392.79 9822.75 9863.33 10105.1 10108.9.
7 19
3
-
15 7
l\}
18 18
6
4
2 2 4
6 2 6 2 2
4 6 8 2 4
Nitrogen
N I: 1134.17 1134.42 1134.98 t1164.0 t1167.9
2 uv 2 uv ,2 uv 7 uv (iuv
4 4 4 10 10
2 4 6 10 14
1.82 1.82 1. 60 0.;343 0.87
25 25 25 25 25
10 10 10 10 111• .10
1199.55 1200.22 1200.71 tl24::i.3 nHO.7
1 uv 1 uv 1 uv 5 uv 13 uv
4 4 10 6
6 4 2 10 10
4.01 3.86 4.01 3.35 0.95
25 25 25 25 25
In, In, In, In. In,
t1411. 94 1494.67 ti743.6 4099.95 4lO9.96
10 uv 4 uv 9 uv lO 10
6 4 6 2 4
10 2 6 4 6
0.379 3.65 1.46 0.034 0.040
25 25 25 50 50
In, 10 In, lO In. 10 1 1
4214.73 4215.92 4230.35 4914.90 4935.03
-5 5 5 9 9
4 2 6 2 4
6 4 4 2 2
0.022 0.031 0.033 0.00759 0.0158
50 50 50 10 10
[5197.8] [5201.8] 5281.18 5328.70 5401.45
-
2 6 6 2
0.023 0.023 0.00282 0.00254 0.00369
50
14 13
2 4 6 8 2
5411.88 6644.96 6646.51 6653.46 6656.51
20 20 20 20
4 8 2 6 4
2 6 2 4 2
0.0075 0.0311 0.0194 0.0244 0.0193
25 25 25 25 25
-
-
* For references see pp.
4,
2
7-208 and 7-209.
50
25 25 25
In, In, In, In.
10 10 10
10 10
1
1 1
1 1 1 1 1 1 1 1 1 1
1 1
10112.5 10114.6 10128.3 10147.3 10164.8
18 18 18 18 18
6 8 4 6 8
10500.3 10507.0 10513.4 10520.6 10539.6
28 28 28 28 28
2 4 2 4 6
10549.6 10591.9 10644.0 10653.(') 10713.6
28
6 6 4 2 4
-
-
-
10718.0 10757.9 11291. 7 11294.2 11313.9
17 17 17
6 6 8 2 6
11997.9 12074.1 12186.9 [12330] [12384]
37 37 27 34 34
4 6 6 4 4,
12461.2 12467.8
36 36
4 6
N II: 644.825 645.167 t671.48
4uv 4uv 3uv
3 5 9
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
(fi
-
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Sta Transition probability Aki, 10' S-l
AccuSource*
racy,
%
Wavelength,
A
Multiplet no.
(fk
~e
(Ii
Nitro(fen (Cuntinued)
25 25
18 10, 18
0.52 0.49 0.353 0.35 0.54'
50 50 2.5 50 25
1
5 1 3 1 5
0.93
25 25 25 25 25
1 1 1 1 1
3 5 5 3, 5
0.228 0.175 0.52 1.58
25 25 25 25 25
1 1
12
3 3 5 3 3
4026.08 t4040.9 4124.08 4133.67 4145.76
40 39 6565 65
7 21 3 5 7
9 27 5 5 5
0.90 2.64 0.276 0.458 0.64
25 25 25 25 25
4176.16 4.227.75
42 33
5 5
7 3
2.19 1.06
25 25
t916.34 t1085.1
2 uv 1 uv
9 9
9 15
1886.82 2206.10 2461. 30 2709.R2 3006.86
14 uv 15 uv 23 uv 22 uv 18
3 3 5 5 3
3 5 3 7 3
3328.79 3330.30 .. 3331. 32 3437.16 3593.60
22 22 22 13 26
7. 3 5 3 3
3609.09 3829.80 3838.39 3919.01 3995.00
26 30 30 17
(Con
10.4 3.56
1.11
0.83 2.40 0.231
LOO
I I
1 1 1
1
1
1 1 1
Nitro
5940.25 5941.67
28 28
3 5
6167.82 6170.16 6173.40 6242.52 ·6340.57
36 36 36 57 46
9 g 7 7 7
6356.55 6357.57 6482.07 6504.61 6532.55
46 46 8 45 45
5 3 3 7 5
6610.58 6629.80 6809.99 6834.09 6941. 75
31 41 54 54 53
5 5 5 3 5
N III: 685.513 6S5.816 t990.98 1804.3 1805.5
3 uv 3 uv 1 uv 22uv 22 uv
2 4 6 2
1
-1 : 1
1 1 1.
4
t4239.4 4447.03 4530.40
48 15 59
15 3 7
21 3 9
2.14 1.30 1. 69
25 "25 25
1 1
4552.54 4601.48 4607.16 4613.87 4621.39
58 5 5 5 5
7 3 1 3 3
9 5 3 3 1
0.76 0.270 0.340 0.196 0.90
25 25 25 25 25
1 1 1 1 1
4630.54 4643.09 4677.93 4779.71 4788.13
5 5 62 20 20
5 5 3 3 5
5 3 5 3 5
0.84 0.466 1. 65 0.269 0.248
25 25 25 25 25
1 1
4803.27 5104.45 5338.66 5340.20 5351. 21
20 34 69 69 69
7 1 5 7 7
7 3 7 5 7
0.313 0.189 0.139 0.194 0.275
25 25 25 25 25
5478.13 5480.10 5495.70 5526.26 5530.27
29 29 29 63 63
3 5 5 3 5
5 3 5 5 7
0.100 0.167 0.298 0.198 0.377
25 25 25 25 25
1 1 1
5543.49 5666.64 5676.02 5679.56 5686.21
63 3 3 3 3
5 3 1 5 3
5 5 3 7 3
0.327 0.423 0.310 0.56 0.231
25 25 25 25 25
1
1 1 1 1
5710.76 5927.82 5931. 79
3 28 28
5 1 3
5 3 5
0.137 0.315 0.425
25 25 25
1
* For references see pp. '1-208 and 7-209.
1
1
1 1 1
1 1 1 1
1 1
1 1
t1885.25 t1908.11 2063.50 2063.99 2972.60
24 27 30 30 25
uv uv uv uv uv
10 10 6
[2977.3) [2978.8) 2983.58 3365.79 3367.36
25 uv 25 uv 25 uv 5 5
4 2 4 4 6
8
2
3374.06 3745.83 3754.62 3771.08 3934.41
5 4 4 4 8
6 2 4 6 2
3938.52 3942.78 4097.31 4103.37 4195.70
8 8 1 1 6
4 4 2 2 2
4200.62 4215.69 4348.36 4514.89 4518.18
6 6 10 3 3
4 4 8 6 2
4523.60 4861. 33 4873.58 4884.14 6445.05
3 9 9 9 14
4 6 6 8 2
6450.78 6453.95
14 14
2 4
TABLE
Wavelength,
A
Multiplet no.
Statistical weights gi
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Transition probability Aki 10 8, S-1
gk
Accuracy,
Source*
%
Wavelength,
A
Multiplet no.
14 14 14
4 6 6
4 8 6
NIV: t225.17 247.05 t283.53 335.050 765.140
6 uv 2uv 5 uv 10 uv 1 uv
9 1 9 3 1
15 3 15 5 3
.921. 982 922.507 923.045 923.211 923.669
3 uv 3 uv 3 uv 3 uv 3·uv
3 1 3 5 3
5 3 3 5 1
924.274 1718.52 3463.36 3478.69 3482.98
3 uv 7 uv 7 1 1
5 3 5 3 3
3
3 3 3 5 3
3484.90 3747.66 4495 4528 [4685.4]
1 8 6 6 11
St w
gi
Nit'rogen (Continued)
6463.03 6466.86 6478.69
(Co
0.232 0.432 0.129
Nitro
25 25 25
1 1 1
25 50 25 25 25
1 9 9 18 15
3.57 4.82 3.58 10.7 14.4
25 25 25 25 25
18 18 18 18 18
5 5 5 3
5.9 3.23 0.94 1.09 1.09
25 25 25 25 25
18 19 1 9,20 9, 20
1 5 3 3 3
1.07 1.0(} 0.189 0.305 0.089
25 25 25 25 25
9,20 1 1 1 1
92 110 264 200 20.5
[185.09] 1896.82 1907.34 11)07.87 [2914.6]·
-
-
3 3 3 3 1
6 uv 2'uv 2 uv 2uv 3
5 5 3 1 5
01:
11.52.16 1302.17 1304.87 1306.04 t3947.29 t4368.30 t5330.0 5435.16 5435.76 5436.83
5 12 11 11 11
3 15 3 5 7
t6046.4 t6157.3 t6259.6 6453.64 6454.48
22 10 50 9 9
9 15 21 3 5
6456.01 6653.78
9 65
7 3
4733 4752 5236 5245 5734
11 11,
5. 5 9
6383 7109.48 7123.10
2: 4 4.
NV: tHi2.562 t186.13 t209.28 247.563 266.192
3 uv 6uv Zuv 5 uv 4uv
i
! i
i
5. 7 3 5 3:
5 7 5 7 5
0.081 0.102 0.261 0.345 0.178
25 25 25 25 25
1 3 5
3 5 7
0.193 0.107 0.142
25 25 25
1 9 9
2
6
6 2
17 17
2
10 6 4 2
10 10 10 10 10
4 2 2 6 2
2 4 2 2 6
60.6 3.38 3.36 3.06 0.368
10 3 3 10 10
1 1 1 17 17
2 2 6 10 6
4 2 10 14 2
0.415 0.411 0.958 1. 62 1.40
10 10 10 10 10
1 1 17 1 17
2
57.2 142 120 357 30.2
'.'
2(}6 .• 375
1238.81 1242.80 t3l61 t4335
4uv l.uv 1 uv 2 3
4603.83 4619.9 t4751 t4933 t5273
1 1 5. 7 4
NVI:
24.898 28.787 t161.22 [173 .341 tl73.92
, i J
i
1
1 1 1 1
1
1 1
-
-
-
1 1 3 1 9
3 3 9 3 15
5160 18100 285 269 876 i
* For referenoes see pp. 7 ·208 and 7-209.
3 3 3 3 '3
1 1 1 1 1
,
I
t7002.1 7156.80 t7254.4
21 38 20
7471.36 7473.23 7476.45 7477.21 7479.06
55
55 55 55 55
5 5 5 3 3
7480.66 7771.96 7774.18 7775.40 7886.31
55 1 ;1 1 64
1 5 5 5 3
7939.49 7943.15 7950.83 7952.18 7995.12
35 35 35 35 19
7 7 5 3 5
8227.64 8232.99 8235.31 t8446.5 8508.63
34 34 34 4
5 3 3 3 3
8820.45 t9263.9 t11287 11295.0 11297.5
37 8
11302.2 t13164
J
-
~
7 7 I
7
-
9 5 9
);
15 9 3 5 7 9
TABLE 7i-4. TRANSITION PROBABILITIICS FOR ALLOWED LINES (C
Wavelength,
A
Multiplet no.
Statistical weights
S Transition probability
10 8,
Aki (Ii
I
8- 1
Accuracyo %
Source*
(
OXY(len (Continued)
20 uv 20 uv 14
14 14
"
2 2 6 4 2
4 2 6 4 2
0.37 0.36 0.278 0.493 0.77
50 50 25 25 25
1 1 1 1 1
3134.82 3138.44 3139.77 3277.69 3287.59
14 23 23
8 6 4 4 6
6 4 2 6 6
1.23 0.96 0.76 0.259 0.60
25 25 25 25 25
1 1 1 1 1
3290.13 3305.15 3306.60 3377.20 3390.25
23 23 23 9 9
2 6 4 2 2
4 4 2 2 4
0.356 0.379 0.70 1. 88 1.86
25 25 25 25 25
1 1 1 1 1
3470.42 3470.81 3712.75 3727.33 3739.92
27 27 3 3 31
4 6 2 4 4
2 4 4 4 6
1. 24 1.12 0.280 0.59 0.267
25 25 25 25 25
1 1 1 1
3749.49 3762.63 3777.60
3 31 31
6 4 4
4 4 2
0.90 0.269 0.252
25 25 25
1 1
14 14
A
Multiplet no.
(lk
o II: 2733.34 2747.46 3122.62 3129.44 3134.32
Wavelength,
OX
4650.84 4661.64 4676.23 4861.03 4871. 58
1 57 57
[4872.2] 4890.93 4906.88 4924.60 4941.12
57 28 28 28 33
4943.06 4955.78 5160.02 5176.00 5190.56
33 33 32 32 32
5206.73 6640.90 6721.35 6895.29 6906.54
32 4 4 45 45
6908.11 6910.75
45 45
1 1
1
1
1
34 17
4 4
4 2
0.55 1.40
25 25
1 1
6
2 2 4 4 14
4 2 4 2 18
0.217 0.95 1'.27 0.447 2.20
25 25 25 25 25
1 1 1 1 1
6 6 6
97 lO
10 10
19 19 19 36 101
8 10
4 6 4
1. 70 1. 98 0.55 0.77 0.157
25 25 25 25 25
1 1 1 1 1
25 25 25 25 25
1 1 1 1 1
19 21 20 20 23
3 7 5 3 3
uv uv uv uv uv
2983.78 2996.51 3004.35 3017.63 3035.43
10 10 10
3043.02 3047.13 3059.30 3083.65 3084.63
4 4 4 26 26
3 5 5 7 7
26 12 12 12 31
9 3 3 3 3
6
4
i
I
3 3 5 7 3
6
6
6
26
18 2 6
8 22 6 6
0.220 2.43 2.63 1.08 0.398
5 5 35 35 35
4 2 6 6 8
6 4 6 8 6
1.15 0.95 0.57 0.0212 0.0282
25 25 25 25 25
1 1 1 1 1
35
8
5 86 86 15
4 2 .. 4 6
8 4 4 6 8
0.57 0.154 1. 51 1.81 1.11
25 25 25 25 25
1 1 1 1 1
3207.12 3215.97 3260.98 3265.46 3267.31
31 31 8 8 8
5 7 5 7 3
93 93
4 6 2 4 6
6 8 4 6 8
1. 70 1. 82 0.422 0.79 1.04
25 25 25 25 25
1 1 1 1 1
3382.69 [3383.5] 3383.85 3384.95 3394.26
27 27 27 27 27
5 5 5 7 7
1
1 1
i
1
';
6 8 4 4 6
o III: 2454.99 2558.06 2597.69 2605.41 2695.49
- --
.. For references Bee pp. 7-208 and 7-209.
_._ .. _ - _ . _ - -
3088.04 3115.73 3121.71 3132.86 3200.95
I'
TABLE
Wavelength,
A
Statistical weights
Multiplet no.
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Transition probability Aki, 10 8 S-1
AccuSource*
racy,
%
OXY{Jen (Continued)
OXY{
5 3 1 3 5
0.096 0.493 1. 47 0.367 0.366
25 25 25 25 25
1 1 1 1 1
24 24 35 35 35
5 5 5 5 3
3 5 7 5 5
0.60 1.08 1.40 0.347 1.04
25 25 25 25 25
1 1 1 1 1
3650.70 3653.00 3961. 59 [4072.3] 4073.90
35 35 17 23 23
3 1 5 1 3
3 3 7 3 5
0.58 0.77 1. 28 0.52 0.71
25 25 25 25 25
1 1 1 1 1
4081.10 4440.1 4447.82 4461. 56 5268.06
23 33 33 33 19
5 5 5 5 1
7 3 5 7 3
0.94 0.495 0.492 0.486 0.311
25 25 25 25 25
5500.11 5592.37
19 5
5 3
5 3
0.112 0.328
25 25
[3555.3] 3556.92 3638.70 3645.20 3646.84
I
Sta w
(}i
I
7 1 3 3 3
27 24 24 24 24
A
Multiplet no.
(}k
(}i
[3395.5] [3520.7] [3530.7] [3532.8] [3534.3]
Wavelength,
(Co
i i I
I
1 1 1 1 1 1 1
4783.43 4794.22 4798.25 4813.07 5305.3
9 9 9 9 11
4 4 6 6 4
5362.4
11
6
o V: t192.85 220.352 629.732 760.445 1371. 29
5 10 1 3 7
uv uv uv uv uv
9 3 1 5 3
3058.68 3239 3275.67 3717 3747
6 5 5 8 8
3 3 5 5 7
4135.9 4158.76 4554.28 5114 5343
11 11 7 1 13
3 3 3 1 1
5352 5376
13 13
3 3
o IV: 787.710 790.103 790.203 [2494.8] [2511.4]
1 uv 1 uv 1 uv 5 5
2 4 4 2 4
4 4 6 2 2
4.87 0.97 5.8 1.02 2.01
25 25 25 25 25
23 23 23 1 1
3063.46 3071. 66 3194.75 3209.64 3348.08
1 7 7 4
2 2 6 8 2
4 2 6 8 4
1.48 1.47 0.194 0.286 1.03
25 25 25 25 25
1 1 1 1 1
3349.11 3354.31 3362.63 3375.50 3385.55
4 8 8 8 3
4 4 4 4 6
6 2 4 6 8
1.23 0.69 0.69 0.68 1.06
25 25 25 25 25
1 1 1 1 1
3390.37 3396.83 3411.76 3489.84 3560.42
3 3 2 14 12
2 4 4 4 4
2 4 6 6 6
0,88 0.56 1.15 0.99 1.08
25 25 25 25 25
1 1 1 1 1
3563.36 3729.03 3744.73 3758.45 3995.17
12 6 6 6 10
6 6 6 8 6
8 8 6 8 6
1. 15 0.69 0.194 0.112 0.215
25 25 25 25 25
1
1 1 1 1
t4568 [4652.5] [4685.4]"" 4772.57 4779.09
15 13 13 9 9
14 2 2 2 2
10 2 4 4 2
0.124 0.301 0.295 0.128 0.254
25 25 25 25 25
1 1 1 1 1
1
"Forreferences Bee pp. 7-208 and 7-209,
5417 5432 5473
13 13 13
3 5 5
5573 5582· 5600 6329 6790
3 3 3 14 12
1 3 5 5 3
12 17
5 3
6830 t7438
o VI: uv uv uv uv uv
6 2 2 2 4
1031. 95 1037.63 t3068 t3314 t3426
1 uv 1 uv 2 4 6
2 2 2 6 10
t3509 t3622 3811.35 3834.24
5 3 1 1
10 6 2 2
t129.84 t150.10 172.935 183.937 184.117
5 2 4 3 3
o VII: 18.627 21. 602 t120.331 [128.25] t128.46
1 1 3 1 9
7i-4.
TABLE -Wavel~ngth,
--
- -
Multiplet :no.
A
TRANSITION PROBABILITIES FOR ALLOWED LINES
-_ ..- Statistical weights Transition probability Aki, 10' 8- 1 gi gk
- _ ..
Accuracy, %
Source*
Multiplet no.
Wavelength,
A.
-
._-
I
--
-
:
3
-
5 5 3 1 3
Ii 3
-
3 1
1530 0.805 , 0.784 0.781 0.246
i
3 3
3 3 3
1 i
i
:
i
3 3 3 2 ·'2
I
i
6 4 2-
6, 4
4 4 4 6 4
I
8 2
i
~
I
,
0.29 0.18 0,090 0.14 0.24.
r
6
6856.{)2 6870.22 11902.46 6909 ..82 6966.35
2 ..2 '2 6
2
7037'.45 7127.88 7202.37 ' 7311.02 7331. 95
_6 6 6 5 1
4 2 2 4 6
7398.68 7425.64 7489.14
~2
:
4 2. 4
l' ~l
5
i
Ii 4: 2
! i
4 2 4
2 4
2 4,
i
,
1
50 50 50 50 50
1 1 1-
50
1 1 L
1
1 -
,
0.45 0."38 0.31 0.18 0.16 0.38 0.30 0.072 0.27 0.17 .
50 50 50 50
,
3039.75 3113.58 3115.67
3 1 1
3121. 52 3124.76 3134.21 3142.78 3145:54
1 ·1 1 4 1
3146.96· 3154.39 3156.n 3174.i3 3174.73
cf
1
Fluorine ,F I:' 6239.64 6348.50 6413.66 6773.97 6834.26
L L
,
i
L
,
56
i
1 1 1: 1
NeI: 735.89 743.70 3454.19 3472.57 3520.47
1 1 1
5433.65 5852.49 5881. 90
, 50
2
3213.97
,
50 50 50
-
'4 '4 2' ·2
,
-2uv 1 uv 2 2 7
I
6 2 2
0.25 0.30 0.13
g
Flu
Oxygen (Continued) [135.77] 1623.29 1637. \)6 1639.58 [2475.4]
(C
- - - -_ S
."_ .. -.- .- ..
------.---
50 50 50
,
i
6 i
-
5
1
5
5975.53 6030.00 6046.13 6064.54 6074.34
1 3
5 3 3 3 3
6096.16 6118.03 6128.45 6143.06 6163.59
3
6217.28 6266.50 6293.74 6304.79 6313.69
1 5
7552.24 7573.41
1 1
4 2
6 4
0.10 0.14
50 50
1 1
5939.32 5944.83
7754.70 7800.22
4 4
4 2
6 4
0.35 0.29
50 50
1
F II: 3202.74 t3504.0 !3535.2] 3536.84 {3538.6]
8 3 6 6 6
5 15 3 5 3
5 25 1 3 3
1.4 2.86 2.1 1.5 0.51
50 25 50 50 50
1 1 1 1 1
6 6
5 5 21 7 5
1.7 0.31 0.147 1.3 1.3
50 50 25 50 50
1 1 1 1 1
1
3541.77 l3544.5] t3641. 7 3847.09 3849.99
11
1 1
7 5 21 5 5
3851. 67 4024.73 4025.01 4025.50 [4103.4
1 2 2 2 4
5 3 3 3 9
3 5 1 3 15
1.3 1.2 1.2 1.2 2.05
50 50 50 50 25
1 1 1 1 1
4109.17 4116.55 [4117.1] 14118.8] 4119.22
5 5 5 5 5
7 5 5 3 3
7 5 3 5 3
1.6 1.2 0.45 0.27 1.3
50 50 50 50 50
1 1
t4246.16 4299.18 t4446.9
9 7 10
25 5 15
35 7 21
2.47 1.7 2.35
25 50 25
1
FIll: 3034.54 3039.25
3 3
6 6
6 8
0.184 2.75
25 25
1
'* For references see pp.
7-208 and 7-209.
1 1 1
3
-
3 1 5
-
3
-
-
3 5 3 5 1
5 1 3 3 3
6328.16 6334.43 6351. 86 6382.99 6402.25
3 1
6421. 71 6506.53 6532.88 6598.95 6678.28
3 5 6 6
-
3 3 1 3 3
6717.04 6929.47 7032.41 7173.94 7245.17
6 6 1 6 3
3 3 5 3 3
1
5 5 1 3 5
1
1
1
TABLE
w avelength, A
Statistical weights
• Multiplet no.
.7i-4.
I
10'
8- 1
Accu· racy,
%
Multiplet no.
,W a veloength, I:Source* A
{I
{lk
Neon .(Continued)
-
7304.82 7438.90 7488.87 8377.61 8495.36
5 12 18
8654.38
33
Ne II:
-
!
N
1 3 7 5
3 3 5 9 7
0.0030 0.0242 0.349 0.51 0,357
50 10 25 25 25
5
7
0.445
25
1
26n
,
25 1 1 1 1
2
0.91 0.11 0.46 0.43 0.52
50 50 50 50 50
1 1 1 1 1
2
4 4 8 4 2
1.2 0.78 3.1 2.0 2.5
50 50 50 50 50
1 1 1 1 1
8 8 16 16 15
4 2 8 6 4
6 4 6 4 4
1.8 0.93 0.11 0.17 0.14
50 50 50 50 ,1;0
1 1 1 1 1
23 15
6
4 4
0.12 0.36
50 50
1 1
[2858. OJ [2870.0] [2873 :0] [291O.4J [2925.71
-
[2955.7] 3Q01.65 3034.48 3037.73 3045.58
4 4 8 8 8
3047.57 3054.69 3118.02 3169.30 3248.15 3255.39 3263.43
-
I
,
6 6 6 2 2 6 4
6 4
:3
6 6 4 4
(C S
: Transition :probability . Aki,
{Ii
TRANSITIONPROllABILITImS FOR ALLOWED LINES
[4292.4] [4346.9]
57 57
4379.50 4385.00 4391. 94 4397.94 44Q9.30
56 56 57 56 57
i
4413.20
1
1
57
Ne III:
i
2086.96 2087.44 2088.92 2089.43 2095.54
!
-
-
t2413 . 0 2590.04 2593.60 2595.68 2610.03
11 uv 11 uv 11 uv -
2613.41 2615.87 t2678.2
12 uv
-
3
3297.74 3323.75 3453.10
2 7 21
6 4 4
6 4 4
0.53 1. 56 0.59
50 25 50
1 In, 27
3456.68 3503.61 3551. 52 3557.84 3561. 23
28 28 24 6 31
2 2 2 2 4
4 2 4 2 6
1.0 1.9 0.055 0.51 0.11
50 50 50 25 50
1
In, 27 1
3565.84 3568.53 3571.26 3590.47 3594.18
34 9 31 32 34
4 6 4 4 4
4 8 4 6 2
0.82 1.14 0.43 0.087 1.3
50 25 50 50 50
1 In, 27 1 1 1
3612.35 3628.06 3632.75 3659.93 3664.09
26 41 33 33 1
2 4 4 4 6
4 4 4 6 4
0.22 0.57 0.090 0.11 0.51
50 50 50 50 25
1 i. 1 1 In, 27
3679.80 3694.22 3697.09 3701. 81 3709.64
41 1 41 40 1
4 6 2 4 4
2 6 2 6 2
0.36 0.73 0.34 0.25 0.84
50 25 50 50 25
1 In, 27 1 1 In. '27
3713.09 3766.29 3800.02 3818.44 3829.77
5 1 39 39 39
4 4 4 2 4
6 6 4 4 6
1.19 0.245 0.35 0.69 0.88
25 25 50 50 50
In, 27 In, 27 1 1 1
4219.76 4231. 60 4290.40
52 52 57
8 6 10
8 6 12
0.33 0.22 2.5
50 50 50
1 1 1
* For references see pp.
7-208 and 7-209.
1 1 1
Ne IV: 541.124 542.076 543.884 2018.44 .2022.19
1 uv 1 uv l"uv
4 4
4,
4 6
[2174.4] [2116.-1J 2203.88 [2206.4] 2220.81
2 4 6 4 6
2258.02 2262.08 2264.54 2285.79 2293.49
6 6 6 6 4
2350.84 2352.52 2357.96 2372:16 2384.95
2 4 6 4 6
NeV: 568.418 569:759 569.830 572.106 572.336
2227.42 2232.41 2259.57 2263.39 2265.71
1 uv 1 uv 1 uv 1 uv 1 uv
1 3 3 5 5
5 7 3 1 5
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
Oi
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
S Transition probability Aki. 10 8 s-1
Accu·· racy,
Source*
%
Wavelength,
A
Multiplet no.
Ok
So
Neon (Continued)
2282.61 2306.31 Ne VI:
t122.62 2042.38 2055.93 [2213.1] Ne VIII:
t88.1l t98.20 t103.00 770.409 780.324 t[2860.1] t[8454.3] Ne IX:
[11.558] 13.44 t74.4 [82.010] t[1297.5] [1901. 51
-
3 5
3 5
0.89 0.52
50 50
1 1
22083.7 23348.4 [91380]
-
6 2 2 2
10 4 2 4
1400 2.73 2.68 1.54
50 25 25 25
1 1 1 1
Na II:
-
2 6 6 2 2
6 10 2 4 2
853 2760 462 5.72 5.50
10 10 10 10 10
1 1 1 1 1
-
2 6
6 10
10 10
1
300.151 301. 432 372.069 Na III:
-
-
-
-
-
1 1 3 3 3 1
(C
3 3 9 5 9 3
0.696 0.0214 24800 88700 1460 4180 0.980 0.329
3 3 10 3 3 3
1
1 1 1 1 1
1
-
-
-
4 uv 3 uv 2 uv
1752.65 1849.58 1856.73 1935.54 1939.32
-
1951. 21 1965.04 [1976.4] 1985.58 1995.62
-
[2004.8] [2011.9] [2028.6] [2036.9] [2045.5)
-
-
-
-
Sodium NaI: t2852.8 33.02.37 33.02.98 4494.18 4664.81
[2.067.4] [2107.7] [2151.2] [2174.5] [218.0.8]
1 uv 2 2 15 12
2 2 2 2 2
6 4 2 4 4
.0 . .0.06.0 .0 . .029.0 .0 . .0293 .0 . .0126 .0 . .0214
25 25 25 25 25
2 2 2 2 2
4747.94 4751.82 4978.54 5148.84 5153.4.0
11
9 8 8
2 4 2 2 4
2 2 4 2 2
.0 . .0.059 .0 . .0119 .0 . .0418 .0 . .011.0 .0 . .022.0
25 25 25 25 25
2 2 2 2 2
5682.63 5889.95 5895.92 6154.23 616.0.75
6 1 1 5 5
2 2 2 2 4
4 4 2 2 2
.0.1.09 .0.63.0 .0.628 .0 . .0241 .0 . .0482
25 3 3 25 25
2 2 2 2 2
8183.26 t865G.3 t9465.94 t9961. 28 10749.3
4 19 24 23 18
2 2 10 10 2
4 6 14 14 2
.0.413 .0 . .00231 0.0079 0.0127 0.0074
25 25 25 25 25
2 2 2 2 2
Na IV: 319.638 360.761 410.3'71
22 3 3
10 2 4 2 10
14 2 2 4 14
0.0224 0.084 .0.167 0.0108 0.0471
25 25 25 25 25
2 2 2 2 2
Na V: 307.152 360.319 360.367 367.557 t445.14
2 2 4 10 2
4 2 2 14 4
.0.0217 0.0058 O. .0115 0.140 0.062
25 25 25 25 25
2 2 2 2 2
t10834.9 11381. 5 11403.8 12311.5 t12679.2
11
21
14767.5 16373.9 16388.9 t18465.3 22056.4
* For references see pp.
7-208 and 7-209.
-
-
4 2 2 4 4
[2194.8] [2222.8] [223G.3J [2232.2J [2246.7J
-
[2278.5J [2310 . .oj [2367.3J [2459.4J [2468.9]
-
--
2 4 2 4 2
[2497.0]
-
6
-
5 1 5
-
4 2 4 4 6
459.897 461. 051 463.263 511.193
-
-
-
-
-
-
-
4 4 6 4 4
4 4 4 4
TABLE
Wavelength,
A
Multiplet
Statistical weights
no~.
7i-4.
Transition probability Aki,
(Ii
I
TRANSITION FROB ABILITIES FOR ALLOWED LINES
10'
8- 1
Accuracy,
-
Source*
%
Wavelength,
A
Multiplet no.
(lk
Ma(lne8ium
Ma
Mg I:
2025.82 2736.54 2776.69 2778.27 2781. 42
Mg III:
2 9 6 6 6
2782.97 2846.72 2938.47 2942.00 3091. 07
6 5 3 3 5
3329.92 3332.15 3336.67 3829.35 4351. 91
uv uv uv uv uv
1 5 3 1 3
3 7 5 3 1
l.2 0.207 l.31 l. 76 5.3
50 25 25 25 25
2 2 2 2 2
186.510 187.194 23l. 730 Mg IV:
[1230.3] [1245.2] [1246.6] [1253.7] [1375.4]
4 uv 3 uv 2 uv
-
5 1 3 5 1
3 3 3 3 3
2.16 0.15 0.052 0.086 0.313
25 50 50 50 25
2 2 2 2 2
4 4 4 3 14
1 3 5 1 3
3 3 3 3 5
0.034 0.10 0.17 0.940 0.21
50 50 50 10 50
2 2 2 2 2
1459.52 1490.41 [1525.2] [1548.1] 1658.92
-
4702.99 5167.32 5172.68 5183.60 5528.40
11 2 2 2 9
3 1 3 5 3
5
50 10 10 10 50
2 2 2 2 2
1680.02 1698.83 [1703.4] 1874.59 1893.87
-
3 3 5
0.16 0.116 0.346 0.575 0.14
t7657.8 8806.76 8923.57
22 7 25
3 3 1
9 5 3
0.0148 0.14 0.011
25 50 50
2 2 2
1906.71 1946.20 1956.58
uv uv uv uv
(C
3
-
-
-
-
-
-
-
9"255.78 9414.96
27 38
5 15
7 21
0.089 0.022
25 25
2 2
tl0811.1 10953.3 11828.2 12083.7 tl4877.6
37 35 6 26
15 1 3 5 15
21 3 1 7 21
0.0452 0.025 0.26 0.170 0.105
25 50 50 25 25
2 2 2 2 2
t15031 17108.7
-
3 1
9 3
0.139 0.094
25 25
2 2
-
MgV:
276.581 312.311 351. 089 352.202 353.094
-
353.300 354.223 355.326
-
-
Mg II:
t2660.8 2790.77 2795.53 2802.70 2928.63
4 uv 3 uv 1 uv 1 uv 2 uv
10 2 2 2 2
14 4 4 2 2
0.38 3.94 2.68 2.66 1. 07
50 10 10 10 25
2 2 2 2 2
2936.51 t3104.8 4384.64 4427.99 4433.99
2 uv 6 10 9 9
4 10 2 2 4
2 14 4 2 2
2.15 0.81 0.14 0.107 0.214
25 25 50 25 25
4481. 2 t5264.3 t6346.8 7877.05 8213.99
4 17 16 8 7
10
10 10 2 2
14 14 14 4 2
2.25 0.125 0.216 0.66 0.260
8234.64 9218.25 9244.27 9632.2 10951. 8
7 1 1 15 3
4 2 2 10 4
2 4 2 14 2
0.52 0.359 0.356 0.413 0.166
---
9 4 4 4
uv uv uv uv
2 2 2 2 2
2567.98 2575.10 2652.48 2660.39 3082.15
2 2 1 1 3
uv uv uv uv
10 25 25 25 25
2 2 2 2 2
3944.01 3961. 52 6696.02 6698.67 7835.31
1 1 5 5 10
25 25 25 25 25
2 2 2 2 2
8772.87 10873.0 10891. 7 11253.2 13123.4
9 12 12 8 4
--
• For references see pp. 7-208 and 7-209.
Al I:
2145.56 2168.83 2367.05 2373.12 2373.35
TABLE
Wavelength,
A
Multiplet no.
Statistical weights (Ii
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
I Transition probability Aki, 10' S-1
,I AC'3u-
Wavelength,. Multiplet Source*: A no.
raey, 0' 10
(lie
I
1
Aluminum (Continued)
13150.8 16719.0 16750.6 16763.4 Al II: tU91. 0 1539.74 1670.81 1719.46 1760.10
4
2 2 4 4
-
-
2 4 6
4
0.181 0.085 0.101 0.017
2.5 2.5 2.5 50 ,
I ,
2 2 2 2
9 3 1 1 3
15 5 3 3 5
1.7 8.8 14.6 6.79 3.30
1761. 98 1765.81 1767.60 1855.95 1858.05
5uv 5 uv .5 uv 4 uv 4 uv
1 3 5 1 3
3 1 3 3 3
4.38 13.1 5.4 0.832 2.48
25
1862.34 t1908.7 1931. 05 t1963.0 1989.85
4 uv
5 9 3 9 3
3 9 1 15 5
4.12 8.1 10.8 12 14.7
10 50 25 50 2E1
2 2 2 2 2
t2193.8 2816.19 t2996.8 3088.52 t3653.0
-
15 3 9 3 9
21 1 15 5 15
3.1 3.83 0.11 0.15 0.27
50 25 50 50 50
2 2 2 2 2
-
8 uv
14 20 12
!
,
uv uv uv uv
10 2 6 5
A
I
2 2 2 2 2
50 50 10 10
2"d
2 2 2 2 2
'J"
~"
25 10
10 ,
3713.10 3980.56
4
12
:,
,
t4150.1 4357.24 4512.54 4903.71 5696.47
5 9 3
i
11
2
5722 ..65 AllV: . 129.729 [130.37 160.073
2 ,
-
Si I: . 1255.28 1256.49 1258.80 1637.01 1638.28
UV UV UV UV UV
1640.27 1675.21 1845.52
UV 104 UV 23 UV 10
41.12 41. 12 41.12 104 104
i
3703.22 3733.91 3738.00 3866.16 5593.23
18 11 11 17 16
3 3 5 3 3
5. 3 3 1 5
0.38 0.13 0.21 0.37 2.3
50 50 50 50 50
2 2 2 2 2
5613.19 t5859.7 t6237.4 6335.74 6816.69
77 41 10 22 9
5 15 9 5 1
7 21 15 3 3
0.070 0.24 1.1 0.14 0.11
50 50 50 50 50
2 2 2 2 2
6823.48 6837.14 6917.93 6919.96 7042.06
9 9 75 15 3
3 5 5 3 3
3 3 7 1 5
0.34 0.57 0.16 0.96 0.59
50 50 50 50 25
2 2 2 2 2
7056.60 7063.64 7449.42 7471.41 7624.48
3 3 98 21 91
3 3 3 5 1
3 1 5 7 3
0.58 0.58 0.12 0.94 0.050
25 25 50 50 50
2 2 2 2 2
t8358.2 8640.70
40 4
15 1
21 3
0.50 0.286
50 25
2 2
AI III: 1379.67 1384.14 1605.7 1854.72 1862.78
t1935.88 3612.35 3702.09
1 uv 1 uv 1 4
2 4 2 2 2
2 2 4 4 2
4.51 8.9 12.1 5.67 5.60
25 25 10 10 10
2 2 2 2 2
10 4 2
14 2 2
12.2 1.48 1.14
25 25 25
2 2 2
* For reference. Bee pp. 7-208 and 7-209.
1847.47 1848.15
UV 10 UV 10
3 3
1850.67 1852.47 1901. 34 1977.60 1979.21
UV 10 UV 10 UV 57 UV 7 UV 7
5 5 5
1983.23 1988.99 2054.84 2061.19 2065.52
UV 7 UV 7 UV 103 UV 103 UV 103
3 5 5 5 5
2124.12 2207.98 2210.89 2211. 74 2216.67
UV 48 UV 3 UV 3 UV 3 UV 3
5
3 3 5
2435.15 2506.90 2514.32 2516.11 2519.20
UV 45 UV 1 UV 1 UV 1 UV 1
5 3 1 5 3
2524.11 2528.51 2881.58 3905.52 4102.94
UV 1 UV 1 UV 43 3 2
3 5 5
4782.99 4947.61 5006.06 5645.61 5665.55
11.06 17.09 17.08 10 10
3
1
5 3 3 3 1
TABLE
Wavelength,
A
Multiplet no.
Statistical weIghts ~
I w
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
S
I
Transi~i?n probabIlIty Aki, 10' S-1
Silicon (Cont~nued) 5 3 0.039 3 1 0.031 5 5 0.025 3 1 0.080 1 3 0.011
Accuracy,
(C
. Wavelength, Source*, A
Multiplet no.
%
, Si
5684.48 5701.11 5708.40 5772.15 5780.38
11 10 10 17 9
50 50 50 50 50
12 12 12 12 12
5793.07 5797.86 5948.55 6721. 85 6976.52
9 9 16 38 60
3 5 3 3 3
5 7 5 5 5
0.014 0.014 0.044 0.034 0.023
50 12 50 12 50 12 502 50 2
7003 57 7005: 88 7680.27 7918.39 7932.35
60 60 36 57 57'
5 7 3 3 5
7 9 5 5 7
0 024 0: 027 0.062 0.054 0.054
'502 50 2 50 ~2 502 50 2
7944.00 809.3.24 9413.51 10288.9 10371.3
57 34 14 6 6
7 3 3 1 3
9 3 1 3 3
0.049 0.012 0.29 0.027 0.081
50 50 50 50 50
2 12 12 2 2
3856.02 3862.60 4128.07 t4621.5 504l.03
1 1 3 7.051 5
10585.1 10603.4 10661.0 10689.7 10694.3
6 5 5 53 53
5 3 1 3 5
3 5 3 5 7
0.19 0.048 0.089 0.12 0.12
50 50 50 50 50
12 12 12 2 2
t5466.6 5957.56 5978.93 6347.10 6371.36
7.031 4 4 2 2
I
1250.43 1251.16 1260.42 1304.37 1309.27 1526.72 1533.45 t2072.4 2500.93 2904.28 3203.87 3333.14 3339.82
UV13.05 UV 8 UV 4 UV UV UV UV UV
3 3 2 2 9
UV 18 UV 17 7 6 6
10727.4 10749.4 10786.9 10827.1 10843.9
53 5 5 5 31
7 3 3 5 3
9 3 1 5 5
0.12 0.10 0.24 0.19 0.098
50 50 50 50 50
2 12 12 12 12
10869.5 10979.3 11984.2 1199l. 6 12031.5
13 5 4 4 4
3 5 3 1 5
5 3 5 3 7
0.24 0.042 0.15 0.11 0.18
50 50 50 50 50
12 12 12 12 12
Si III: 883.398 994.787 997.389 1108.37 1140.55
UV UV UV UV UV
27 6 6 5 32
12103.5 12270.7 15557.8 15884.4 15888.4
4 4 42.21 42.jll ' 11.12
3 5 5 3 3
3 5 5 3 3
0.061 0.033 0.013 0.020 0.082
50 50 50 50 50
12 12 2 2 12
114l. 58 1142.28 1144.31 1144.96 1155.00
UV UV UV UV UV
32 32 32 32 31
15960.0 16060.0 16094.8
42.21 42.21 : 42.21 .I
7 3
5 1 3
0.070 0.083 0.060
50 50 50
2 2 2
1155.96 1156.78 1158.10 1160.26 116l. 58
UV UV UV UV UV
31 31 31 31 31
1207.52 1294.54 1296.73 1301.15 1303.32
UV UV UV UV UV
22 4 4 4 4 48 38 9 61 59
Si II: 989.867 1190.42 1193.28 1194.50 1197.39
UV UV UV UV UV
6 5 5 5 5
,
1223.91 1224.25 1227.60 1229.39 1246.74
UV UV UV UV UV
8.02 8.02. 8.02 8.01 8
1248.43 1250.09
UV 8 UV 13.05
5
6818.45 7113.45 7125.84 7848.80
7.20 7.19 7.19 7.02
2 4 4
4 4 2 4 2
6.7 7.2 29 35 14
50 50 50 50 50
2 2 2 2 2
4 4 6 6 2
2 4 6 8 4
20 11 24 36 6.3
50 50 50 50 50
28 28 28 28 2
1328.81 1362.37 1417.24 1435.78 1588.95
UV UV UV UV UV
4 4
4 4
13
38
50 50
2 28
1778.72 1842.55
UV 35 UV 20
2 2
• For references see pp. 7-208 and 7-209.
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
(Ji
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
Transition probability Aki, 10 8 8- 1
AccuraCj",
Source*
%
Wavelength,
A
Multiplet no.
(Jk
Silicon (Continued)
t2449.48 2528.47 2546.09
UV 78 UV 81 UV 56
2559.21 3233.95 3241.62 t3486.91 3590.47
UV 55 6 6 8.06 7
3681. 40 3791. 41 4338.50 4341. 40 4494.05
10.09 5
S
15 5 5
21 7 5
1.2 0.81 0.61
50 50 50
2 2 2
5 5 15 3
7 3 3 21 5
7.7 1.3 2.3 1.8 3.9
50 50 50 50 50
2 2 2 2 2
46 15
5 1 1 3 3
3 3 3 1 3
0.33 2.0 0.147 1.8 0.46
50 50 25 50 50
2 2 2 2 2
4552.62 4554.00 4567.82 4574.76 4619.66
2 15 2 2 13
3 5 3 3 3
5 3 3 1 5
1.26 0.76 1. 25 1. 25 0.33
25 50 25 25 50
2 2 2 2 2
4638.28 4665.87 4683.02
13 13 13
1 3 5
3 3 5
0.43 0.32 0.95
50 50 50
2 2 2
S
3
(
2120.18 2127.47 t2287.04 t2675.2 t2723.81
UV UV UV UV UV
18 18 22 25 32
3149.56 3773.15 4088.85 4116.10 t4212.41
2 3 1 1 5
4314.10 4328.18 t4403.73 6667.56 t6998.36
4 4 14
7068.41 7630.50 7654.56 t8240.61 8957.25
4.01 9 9 15 3.01
9018.16
3.01
3.02 12
4683.80 4716.65
13 8.09
3 5
'7
1.3 2.8
50 50
2 2
4730.52 5473.05 5490.11 5539.93 5696.50
13 12.08 12.08 12.08 8.17
5 5 3 5 5
3 7 3 5 3
0.52 0.79 0.33 0.19 0.20
50 50 50 50 50
2 2 2
5704.60 5716.29 5739.73 6169.84 6314.46
8.17 8.17 4 22 10.02
7 9 1
0.18 0.19 0.47 0.12 1.2
50 50 50 50 50
2 2
3
5 7 3 7 1
6521. 49 6831. 56 7612.36 8262.57 8265.64
17 10.07 10 .. 01 10.06 10.06
3 5 3 5 5
5 3 5 7 5
0.32 0.74 1.1 0.91 0.23
8269.32 8341. 93 9799.91
10.06 44 8.08
3
3 5
5 5 3
0.70 0.26 0.39
5
1
PI: 1774.99 1782.87 1787.68 t1859.2 2136.18
1 1 1 5 4
uv uv uv uv uv
4 4 4 10 6
2 2
2149.14 2152.94 2533.99 2535.61 2553.25
4 9 8 8 8
uv uv uv uv uv
4 2 2 4 2
50 50 50 50 50
2 2 2 2 2
2554.90 8046.79 8090.08 8637.62 8741. 54
8 uv -
4 8 6 2 2
50 50 50
2 2 2
9175.85 9304.88 9525.78 9563.45 9593.54
3 3 3 2 2
2 4 6 4 2
9750.73 9790.08 9796.79 9903.74 9976.65
2 4 4 2
4 2 6 2 6
4 4 1 1 1
4 4 2 4 6
2
2
2
Si IV: "1645.759 t~149. 941 815.049 818.129 t1066.63
UV UV UV UV UV
15 13 4 4 11
10 10 2 4 10
14 14 2 2 14
7.0 14.5 12.3 24.4 39.1
50 25 25 25 25
2 2 2 2 2
1122.49 1393.76 1402.77 t1533.22 1727.38
UV UV UV UV UV
3 1 1 24 10
2 2 2 10 4
4 4 2 14 2
22.2 9.20 9.03 3.57 5.5
25 10 10 25 25
2 2 2 2 2
* For references see pp. 7-208 and 7"209.
P
10084.2 10204.7 10511.4 10529.5 10581. 5
-
2
TAilLE 7i-4. TRANSITION PROBABILITIES FOR ALLOWED LINES (Co
Wavelength,
A
Multiplet no.
Statistical weights
Transition probability AM, 10 8
(Ii
I
8- 1
AccuSource*
racy,
0/0
Wavelength,
A
Multiplet no.
(Ii
(lk
Phosp
Pho8phoru8 (Continued)
10596.9 10681.4 10813.0
1 1
2 4
1
6
2 4 6
0.17 0.11 0.060
50 50 50
2'
2 2
P II: 1301. 87 1304.47 1304.68 1305.48 1309.87
2 2 2 2 2
uv uv uv uv uv
3 3 3 5
3 1 3 5 3
0.53 1. 57 0.392 0.392 0.65
25 25 25 25 25
2 2 2 2 2
1310.70 1535.90 1542.29 4385.35 4402.09
2 uv 1 uv 1 uv -
5 3 5 3 1
5 5 7 3 3
1.17 0.096 0.127 0.40 0.73
25 25 25 50 50
2 2 2
-
3 3 3 3 5
5 3 1 1 5
0.18 0.55 1.6 0.73 0.54
50 50 50 50 50
1 5 3 5 3
3 7 3 7 5
0.25 1.3 0.19 1.4 1.0
50 50 50 50 50
4414.28 4417.30 ,4420.71 4424.07 4463.00 4467.98 4475.26 4483.68 4499.24 4530.81
-
-
-
-
-
1
St w
2'
2 I
, i
2 2 2 2 2 2 2 2 2 2
5583.27 5588.34 5727.71
-
6024.18 6034.04 6043.12 6055.50 6087.82
-
6165.59 7735.06 7845.63
-
-
-
5 3 3
3 1 5 5 3
-
5 1 3
PIlI: 3219.32 t3280.22 3717.63 3744.22 3802.08
4 6 10 10 10
2 10 2 4 6
3895.03 3904.79 3951. 51 3957.64 3997.17
9 9 9 9 9
4 2 4 6 6
4057.39 4059.27
1 1
4 6
-
-
4533.1)6 4554.83 ,4565.27 4582.17 ;4588 . .04
"
-
-
,~
-
4589.86 46.02 . .08 4626.7.0 4628.77 4658.31 4864.42 4927.2.0 4935.62 4943.53 , 4954,.39
,
-
,-_.
-
•
!
-
i
'
'
I
-
,
-
"5 I 1 :
..
-
,~
-
3 :"
!
,
-
.-'~
5.0 5.0 5.0 5.0 50
.0'.11 0.19 0.63 ; .0.63 .0,.78
i I i
3
'.-
* For references see pp. 7-208 and 7~2tl9.""
I
!
0'.58 ' .0.4.0 ' .0.12 "0.35 1, . .0
50 5.0 5.0 50 5.0
i ,, ;
.0.55 0.24 ' 0.32 ' 0.11 .0.23
'5 , ' i I ",
2
,2
t4587.91
2 2 2
PIV: 628.983 ,629.914 : 631. 765 776.366 823.181
2 2 2
2
846.999 849,.764 : [855.05] , 866.84 95.0.662 '
2 2
50 '50 50
i I
:00
i
i
5.0
2 2 i
2 2 2 2 2 2 2 2
'
0.'93 .0.69 .0.33
;
::.,gIJ~,
, ,
~
., !
.0:11 .0.45
5.0 5.0 5.0 5.0
,
~G
,.
5.0 50
2
'--2 '
2 2 2 2 2
1 3 3 ,
4 2 2
7
14
,
'2
5.0 5.0 5.0 50 50
:
408.0 . .04 4222.,15 4246.68
2 2 2
!
3 5 3 3 ' 5 ! " ! 3 '
'3:" : ,,' "I
-
1.6 1.9 .0.3.0 0.9'7 .0,.21
.0 96
" !
"-
.0 33 1 7
5.0 50 50 5.0 5.0
.0 \/6
3
'3 5 '3 3 3 '.0'1\'(\'3" ./. ,,',: ':1" 5' I ' '5 ! ,5 : 5 1 , 3 .. 5 ' _ ,3 i
,
-
,
7 3
.0 31
3 '
3 1.
I
-
-
.
5
5
-
-~--
54.09.72 5425.91545.0.74 5483.55 5499.73
5 3
3 3
--
'
5 '9 5 3 7
1 ,
-
/>296.13' 5316 . .07 5344.75 5378.20 5386.88
3 7 5 '3 7
5 5
"
-
,3 5 1 5 7
'i
,
-
49il9.71 -5.04.0:8.0 -5152.23 5191.41 ,5253.,!'2
55.07.19 5541.14
-
5 3 3 5 5
!
' " 9,63.993 1025.58 1028.13 , 1033.14 1035.54
4uv 4 uv 4uv -
3 uv
-
5uv
-
1 uv
,
-
2 uv 2 uv 2 uv 2uv
-
' ,1 1 1 I i
,
3
3 2 --
.1
3 1 3 5
-
:
.,r·,
3 5 3 5 1
-
-
t109G.G 1118.59 [1847.5] 3347.72 3364.44 3371.10 ' [3719.·3] 3728.67 4249.57
1 3 5 3 1
'
,
,
15 3 5 3 3
3 7 5 1
-
+---
.---
J
,
Wavelength,
A
Multiplet no,
.._..
Sta ti~tical weights
I
fJi
7i-4.
TABLE
I
TRANSITION PROBABILITIES FOR ALLOWED LINES
S Transition ' probability ,Aki, 10 8 8- 1
Accuracy,
%
Wavelength, \ Multiplet : Source* no. A
(Jk
!
(
I
Phosphorus (Continued)
Su
I
PV: 542.567 544:914 t673.90 865.435 1997.53]
---. -
997.641 10'00.36 i117.98 1128.00 [1379.7] 1385.11 [2424.3] [2440.8] [2441.1] 3175.16 3204.06
2 4 10 2 4
2 2 14 4 4
25 49 97 31.0 1.7
25 25 25 25 25
2 2 2 2 2
---".. -
6 4 2 2 2
4 2 4 2 2
15 16 12.0 11.6 6.6
25 25 25 25 25
2 2 2 2 2
-
-
1
4 2 4 4 2
2 4 6 4 4
13 6.4 7.4 1.2 2.34
25 25 25 25 25
2 2 2 2 2
1
2
2
2.28
25
2
4.8 2.4 1.3 1.1 4.8
50 50 50 50 50
2 2 .2 2 2
~--.,-
-
I
-.
S I: 1295.66 1~96.17
1302.34 1302.87 1303.11
9,11V
9-uv 9,uv 9-uv 9,uv
Sulfur 5 5 3 3 3
(C
5 3 5 3 1
t8684.2 t9036.7 9212.91
6 13 1
9228.11 9237.49 10455.5 10456.8 10459.5
1 1 3 3 3
S II: 1124.39 1125.00 1131. 05 1131. 65 1234.14
8 8 8 8 7
1
uv uv uv uv uv
1250.50 1253.79 1259.53 3567.17 3616.92
1 uv 1 uv 1 uv 56 56
3892.32 3933.29 4032.81 4142.29 4145.10
50 55 59 44 44
1303.42 1305.89 1'1320.0 l401. 54 1409.37
9 uv 8 uv 6 uv 6 uv
5 1 9 5 3
3 3 15 3 3
1.9 1.7 0.94 0.91 0.50
50 50 50 50 50
2 2 2 2 2
4153.10 4162.70 4165.11 4259.18 4294.43
44 44 64 66 49
1412.90 t1429.1 1448.25 1474.01 1474.39
6 5 12 3 3
uv uv uv uv uv
1 9 5 5 5
3 15 3 7 5
0.16 3.6 6.9 1.6 0.57
50 50 50 50 50
2 2 2 2 2
4463.58 4483.42 4552.38 4656.74 4716.23
43 43 40 9 9
1483.04 1483.23 1485.61 1487.15 1666.69
3 3 4 3 11
uv uv uv uv uv
3 3 1 1 5
5 3 3 3 5
1.2 0.75 0.023 0.89 5.8
50 50 50 50 25
2 2 2 2 2
4792.02 4815.52 4824.07 4885.63 4917.15
46 9 52 15 15
1687.49 1782.26 1807.34 1820.36 1826.26
uv uv uv uv
1 1 5 3 1
3
13 2 2 2
3 3 3 3
0.94 1.5 4.1 2.2 0.73
50 50 25 25 25
2 2 2 2 2
4924.08 4925.32 4942.47 4991. 94 5009.54
7 7 7 7 7
4694.13 4695.45 4696.25 t5278.7 6403.58
2 2 2 4 9
5 5 5 3 3
7 5 3 9 5
0.0076 0.0074 0.0072 0.0038 0.0057
50 50 50 50 50
2 2 2 2 2
5014.03 5027.19 5032.41 5047.28 5103.30
15 1 7 15 7
6408.13 6415.50 t6751. 2 7679.60 7686.13
9 9 8 7 7
5 7 15 3 5
5 5 25 5 5
0.0095 0.013 0.079 0.012 0.020
50 50 50 50 50
2 2 2 2 2
5142.33 t5208.0 5320.70 5400.67 5428.64
1 39 38 61 6
7696.73 t8451. 6
7 14
7 9
5 3
0.028 0.050
50 50
2 2
5432.77 5453.81
6 6
-
* For references see pp. 7-208 and 7-209.
1
TABLE
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES (C
, Wavel~ngth,
Stati&tical weiihts
Multiplet no.
A
gi
I;
S , Transition probability : Aki, 10 8 S-l
AccuSource*
racy, :
Wavelength,
A
%
g,
Multiplet 'no.
I'
i
:
!
Sulfur i(Contin'!led) I
i
5473.59 5509.67 5526.22
6 6 11
5536.77 5564.94 .5578.85 5606.i1 .5616.63
Ii
I
I
i
4 6
6 11 11 11
:
.5639.96 .5646.98 .5659,.95 5664.73 6305.51
14 14 11 11 19
6312.68 7967.43 :8314.73
26 12 12 .'
SIll: . 2460.50 2489.59 2496.,24 2499.08 2508.15
!
17 17 17 17 17
(;
10 4 i
uv' uv uv uv uv
2 4 8
2 4 8
4 2 6 4 8 6 2' 4;
5 3
i
3
5
!
6 6 6 8 4
:
:
0.74 0.39 0.081 0.066 0.16 0.074 0:30 0.083
4 2 6
0.75 0.68 0.34 ' (U,8 0.18
4 2 2
0.20 0.080 0.16
6
4
5, ,3 [)
.45 .77 .5 '
1 3
.3
.i
50 50 50
2 2 2
50 50 50 50
2 2 2 2 2
50
50
;
!
50 50 50 50
2 2 2
2 !
2 2 2
50 50 50
50 50 50 50 50
2
i
2 2 2 2 2
4,
4332.71 434Q.30 4361.53
4
4
S IV: 551. 17 3097.46 3117.75
I
-
1 1
SV: 437:37 438.19 439.65 658.262 786.47:6
4uv 4uv 4uv '3 uv r uv
849:241 852.185 857.872 860.,462
'2uv 2 uv 2 uv 2 uv
--
S VI: t464.654 706.480 712.682 ,712 .. 844 933.382 , 94,L517
,
!
I
5 3 3 3 1
uv uv uv uv uv
'i
uv
!
S
2636.88 2665.40 2680 .. 47 269.1.68 2702.76
19 19 19 19 19
uv uv uv uv uv
5 1 3 3
5 5 3 3 1
0.45 1.4 0.62 0.46 1.9
50 50 50 50 50
2 2 2 2 2
3
I
2718.88 2721. 40 2'726.82 2731.10 2741. 01
16 19 20 16 16
uv uv uv uv uv
3 5 3 5 5
3 3 5 5 3
1.2 0.77 0.60 1.1 0.39
50 50 50 50 50
2 2 2 2 2
2756.89 2775.25 2785.49 2856.02 2863.53
16 16 20 15 15
uv uv uv uv uv
7 7 3 5 7
7 5 3 7 9
1.4 0.,24 0.61 5.1 5.7
50 50 50 50 50
2 2 2 2 2
2872.00 2904.31 2950.23 2964.80 2985.98
15 15 18 18 18
uv uv uv uv uv
3 7 5 5
5 7 5 7 5
4.7 0.61 3.0 4.0 0.99
50 50 50 50 50
2 2 2 2 2
3662.01 3717.78 3778.90 3831. 85 3837.80
6 6 5 5 5
3 5 3 1 3
3 3 5 3 3
0.64 1.0 0.44 0.56 0.42
50 50 50 50 50
2 2 2 2 2
3838.32 3860.64 3899.09 4253.59 4284.99
5 5 5 4 4
5 3 5 5 3
5 1 3
1.3 1.6 0.67 1.2 0.90
50 50 50 50 50
2 2 2 2 2
* For references see pp.
3 ,
7
5
7-208 and 7-209.
Cl I: 1201.36 1335.72 1347.24 1351. 66 1363.45
2 2 2 2
4323.35 4363.30 4369.52 4379.90 4438.48
9 8 8 7 6
2
4469.37 4475.31 4526.20 4601. 00 4661. 22
15 7 15 15 15
4 4 4 2 2
4691. 53 4976.62 5099.80 7256.63 7414.10
-
4 4 2 6 6
-
5 4
uv uv uv uv
2 4 4 2 '2
4 4
4 6
7547.06 7717.57 7744.94 7769.18 7821. 35
5 4 5 -
-
4 4 2 6 6
7830.76 7878.22
3
4 6
TABLE
Wavelength,
A
Multiplet no.
Statistical weights
7i-4.
I
10'
S-1
Accuracy %
Source*
Wave~ength,
A
Multiplet no.
(Jk
Ch
Chlorine (Continued)
7899.28 7915.09 7924.62
-
-
4
-
4 2 2
6 2 4
0.058 0.061 0.021
50 50 50
2 2 2
8
4 4 4 6
0.046 0.041 0.021 0.38 0.40
50 50 50 50 50
2 2 2 2 2
7935.00 7976.95 7997.80 8085.54 8086.67
3
-
6 2 4 4 6
8212.00 8333.29 8375.95 8428.25 8550.46
2 2 2 2 13
6 4 6 2 4
6 4 8 2 2
0.079 0.16 0.28 0.24 0.019
50 50 50 50 50
2 2 2 2 2
8575.25 8948.01 9073.15 9121.10 9191.67
2 1 12 1 1
2 6 4 6 4
4 4 2 6 2
0.12 0.12 0.19 0.17 0.21
50 50 50 50 50
2 2 2 2 2
1
4 4 2 2 2
6 6 2 4 4
0.066 0.24 0.083 0.091 0.19
50 50 50 50 50
2 2 2 2 2
9584.77 9592.20 9632.37 9702.35 9875.95
11
12 1 11
(C
S Transition probability Aki,
(Ii
TRANSITION PROBABILITIES FOR ALLOWED LINES
4130.86 4132.48 4133.66 4147.09 4208.03
60 29 60 60 43
4224.92 4241.38 4253.51 4261. 22 4270.61
83 24 24 66 66
4276.51 4291. 76 4304.07 4307.42 4336.26
66 19 19 19 19
4343.62 4399.14 4569.42 4768.68 4778.93
19 46 35 40 40
4785.44 4794.54 4810.06
40 1 1
GIll: 1063.83 1071.05 1071: 76 1079.08 2546.,94
1uv Iuv Iuv 1 uv 13uv
5 5 3 3 3
13 uv 14uv 57
5 3 3 7 -3
2'549.85 2906.25 3022;93 3231. 75 3315.44
37
3329.12 3522,14 3568.04 3618.88 3639.19
37 64 78; 77 77
378L23 3798.80 3805.24 3809.51 3850.97
72 62 62 62 25
3854.75 3868.6-2 3883.80 3913.92 3916.70
84 84 55 68 68
3
3917.57 3954.21 3990..19 40 40.064036.53
6-8 82 76 76 ' 76
I;i
73
;5 7 ·5
5 3 7 '5
7 3 5 7 3 9
'7
5 5 3 1
0.482 0.85 0.285 0.277 0.58
25 25 25 25 50
2 2 2 2 2
0,76 0.86 0:60 0.12 1.1
50 50 50 50 50
2 2 2 2 2
7 7 5 3 3
1.5 1.4 1;2 1.2 0.72
50 50 50 50 50
7 7 9 5 7
(i.87 1.6 1.8 1.5 1.8
5 9 5 9 7 5 5
3 5 3 5 5
2 2
2 2 2
50 50 50
2 2 2 2 2
2.2 2.7 0.33 ,0.82 0.74
50 50 50 50 50
2 2 2 2 2
0.78 1.1 0.84 0.62 0.46
50 50 ,.50 50 50
2 2 2 2 2
50 50
4811.57 4857:04 4896.77 4904.76 4907.17 4914.32 4917;72
74 74-
'
17
17 39
'1
IT 17
4922.14 5068.10 5078.25 5098.34 50.99.30
f7 16 f6
16' 16
7
5103,04 5104.08 5113.36 5221. 34 5392.12
16 16 16 3 28_
-
5443.42 5444.25 5444.99 5456.27 5568.81
2 2 80-
6094.65
26
2-2-
01 I-ri:
'7
5 3
* For references- see 1'1'. 7-208 &nd 7-209; -- -
2253.07 2268.95 2278.34 2283.93 2298.51
15 uv 15 uv 15uv 15 :tlN. 19 uv
,
4
8
4
TABLE
Wavel~ngth, A
I Multiplet I,
Statistical weights
no.
, ,
(}i,
Ii
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES
S , Transition ' probability Aki, 10 8 S-l
Acc~,racy,
Source*
%
Wavelength, • Multiplet ,no. A
(Jk
Ch
'Chlorine (C;ontinued) , i
2340.64 2370.37 2403.32 2416.42 2484.27
19 uv 24'uv 17uv 17 uv 13 uv
6 8 6 2 4
6 6 6 4 4
4.2 2.8 104 0.88 0.73
50 50 50 50 50
2 2 2 2 2
2486.91 2504.23 2510.92 2519.45 2531. 76
21 uv 13uv 13 uv 13 uv 22uv
4 6 6 8
2
6 6 4 8 4
0.68 1.0 0.63 1.5 4.4
50 50 50 50 50
2 2 2 2 2
[3071.4] [3076.7] [3106.0] [3167.9]
2532,48 2577.13 2580.67 2601. 16 2603.59
22uv 18uv 18,uv 12 uv 12uv
4 4 6 2 4
6 6 8 4 6
5.3 4,3 4.7 4.6 5.0
50 50 50 50 50
2 2 2 2 2
AI: 866.80 876.06 1048.22 1066.66 4044.42
2609.50 2616.97 2618.78 2624.71 2651.19
12uv 12,uv 12 uv 23 uv 12 uv
6 8 4 6 8
8 10 4 4 8
5.7 6.6 1.8 0.44 0.92
50 50 50 50 50
2 2 2 2 2
4158.59 4181.88 4198.32 4200.67 4259.36
2661. 65 [2662.3] [2663.2] 2665.54 2669.6]
16 uv 16uv 16uv 16 uv 16 uv
4 2 2 6 4
6 4 2 8 4
3.4 2.0 4.0 4.8 2.6
50 50 50 50 50
2 2 2 2 2
4266.29 4272.17 4300.10 4333.56 4335.34
C1 V:
I
(
390.148 392.433
4
50 50 50 50 50
2 2 2 2 2
1.2 0.41 1.6 0.68 0.93
50 50 50 50 50
2 2 2 2 2
4 2 4 4 6
1.9 0.76 0.93 1.9 1.9
50 50 50 50 50
2 2 2 2 2
8 6 8 6 4
1.8 1.7 1.7 1.2 0.70
50 50 50 50 50
2 2 2 2 2
3 3
6 4 2 4
6 4 2 4 4
3.5 2.7 3.0 0.44 0.86
3191. 45 3244.44 3259.32 3283.41 3289.80
3 6 6 2 2
6 2 2 4 2
4 4 2 6 4
3320.57 3336.16 3387.60 3392.89 3393.45
6 6 2 11 11
4 4 6 4 6
3530.03 3560.68 3602.10 3612.85 3622.69
10 10 1 1 1
6 4 6 4 2
2710.37 2965.56 2991. 82 3104.46 3139.34
3656.95 3670.28 3682.05 3720.45 3748.81
20 uv 11 uv 11 uv
1 1 . 1 . 5 5
2 4 6 4 2
Cl IV:
1532.19 1539.30 1617,43 [2782.4] [3063.1]
* For references
7 5 5 5 3
2 4 6 6 4 5 3 5 5 5
see pp. 7-208 and 7-209.
1.4 0.86 0.48 1.7 1.3 6.3 5.6 3.5 2.3 1.7
I
50 50 50 50 50 50 50 50 50 50
2 2 2
2 2 2 2 2 2 2
4345.17 4510.73 4887.95 4894.69 5151.39
-
5162.29 5187.75 5495.87 5558.70 5606.73
-
5650.70 5882.62 5888.58 5912.09 5928.81 5971.60 6032.13 6043.22 6105.64 6416.31 6752.84 6871. 29 6965.43 7030:25 7067.22
-
-
-
-
-
-
-
-
7068.73 7158.83 7206.98 7311.72 7316.01
-
7350.78 7372.12
-
-
-
TABLE ~
~
... _ ..
Wavelength,
A-
Multiplet no..
Statistical weights gi
I
7i-4.
TRANSITION PROBABILITIES FOR ALLOWED LINES -
Transitio.n pro.bability AM, 10 8 S-l
~
Accuracy,
.- .
So.urce*
%
Wavelength, Multiplet no.. A-
Ok
Argon (Continuetl)
7383.98 7435.33 7503.87
~
-
7514.65 7635.n 7723.76 7724.21 7948.18
-
8006.16 8014.79 8103.69 8115.31 8264.52
-
-
-
-
8408.21 8424.65 8521.44 860l'k 78 8667.94
--
8761. 69 9122.97 9194.64 9224,50 9291. 53
-
-
--
-'
2
3 5 3
5 5 1
0.087 0.0094 0.472
25 50 25
3 5 5 1 1
1 5 3 3 3
0.430 0.274 0.057 0.127 0.196
25 25 25 25 25
2 2 2
3 5 3 5 3
5 5 3 7 3
0.0468 0.096 0.277 0.366 0.168
25 25 25 25 25
2 2 2 2 2
3 3 3 5 1
5 5 3 5 3
0.244 0.233 0.147 0.0108 0.0280
25 25 25 25 25
2 2 2 2 2
3 5 3' 3 3
5 3 3 5 1
0.0099 0.212 0.0198 0.059 0.0366
50 25 25 25 25
2'
~
2
2 2
13499.2 13504.0 13573.6 13599.2 13622.4 13678.5 13825.7 14093.6 :: 14596.3 14634.1 14786.3 15046.4 15173.3 15302.3 15402.6 15899.9 15989.3 16436.9 ' 16549.8 16940.4 ' 23844.8
2 2' 2
09] ..
P; JI:: : 4669.5 4736.6 7869.5 H483.2· 11898.2
!
4 4 4 4 6
4 2 6
4 4 4
:4
2
6
2
2F 2F
3
3F
5
IF IF
1 1 1
25
2
1.0.8(-1) 4.26(-2) 2.0. (-4) 2.97(-4) 7.5 (-2)
25 25 50. 25 25
2
1.13( -1) LO.l( -1) 5.3. (-2)
25 25 25
2
25 50. 50. 25 25
2
3
P,XV:. [2681 .. 7]
.25
2
5
5
2.20.(-1) 6.3 (-3) 2.0. 6.3 (-3) l. 70.( -2)
.1
3
7.8 (-2)
5
5
2 2
2 2
2 2
2
2 2
2
, Sulfur!
S.I: . 450..6.9 4589.26 7725.0.4 10.819.8 1130.5,:8
2F 2F 3li'
IF lJi'
5 3 ;'i 5 3
1 1
1 5 ;'i
7.3 (-3) 3.5 (-1) l. 78 2.77(-2) 8.0. (-3)
,
50. 25 25 25 25
2 2
2 2
2
.B U: 40.68.60. 40.76.35
.11i'
IF
it
4
4
2
3.M(-1) l. 34( -1)
Sta w Uj
Chlo
l. 82( -2)
Phosphorus '·P·I: 5332.4, 5339.7 87.87.6 8799.1' [13533] .
(C
PROBABILITIES FOR FORBIDDEN LINES
·25 25
2 2
Cl IV: 3118.3 320.3.3 5323.29 7530..54 80.45;63
2F 2F 3F
IF
IF
3 5 5 3 5
·Cl V: [67QO.O]
2
Ar II: [69842]
4
Ar III: 30.0.5.1 :3109.0. . 51111. 82 7135.80. 7751.0.6 [898\l6]
2F 2F 3F
IF IF
Ar IV: [285;'1.6]
5 3
5 5 3 5
4740..20.
7170~62
IF IF 2F
4 4 4 4 4
7237.26 7262.76 7332:0.
2F 2F 2F
6 4 ·6
[2868.~] 471L33
A; v: [26!) 1. 1] [2:;':86.1] 41>25.54
3
€i
·2F
5
6716.42 6730.78 10284.3
2F 2F 3F
4 4 4
6 4 4
4.7(-4) 4.3 (-4) 1.75(-1)
50 50 25
2 2 2
6435.10 7005.67 [78905)
10317.7 10336.0 10369.7
3F 3F 3F
6 4 6
4 2 2
2.14(-1) 1.98(-1) 8.7 (-2)
25 25 25
2 2 2
KIll: [46240)
SIll: 3721.8 3796.7 6312.1 9069.4 9532.1
2F 2F 3F IF IF
3 5 5 3 5
1 1 1 5 5
8.5 (-1) 1.6 (-2) 2.54 2.49( -2) 6.4 (-2)
25 50 25 25 25
2 2 2 2 2
KIV: [2593.5) [2711.2) 4510.9 6101.83 6794.8 [59757J
S V: [2268.0)
-
1
3
2.36(-1)
25
2
Chlorine ClII: 3583.2 3675.0 6152.9 8579.5 9125.8
2F 2F 3F IF IF
5 3 5 5 3
1 1 1 5 5
1. 8 (-2) 1.34 2.29 1. 04( -1) 2. 94( -2)
50 25 25 25 25
2 2 2 2 2
2F 2F
4 2 6 4 4
9.6 (-1) 3.74(-1) 1.0 (-3) 7.1 (-3) 3.90(-1)
25 25 50 25 25
2 2 2 2 2
4 2 2
3.64(-1) 3.51(-1) 1.08(-1)
25 25 25
2 2 2
C1 III: 3342.7 3353.4 5517.66 5537.6 8433.7
IF 3F
4 4 4 4 4
8481.6 8501.8 8550.5
3F 3F 3F
6 4 6
IF
* For references Bee pp. 7-208 and 7-209.
t For this line the frequency in megahertz iB liBted.
I
IF IF
-
I
3 5 3
-
4
-
5 3 5 5 3 5
-
2F IF IF -
KV: [2495.3) [2515.3] 4122.63 4163.30 6223.4
IF IF 2F
4 4 4 4 4
6316.6 6349.5 6446.5
2F 2F 2F
6 4 6
CaIV: [32090)
-
4
Ca V: [2280.0) [2412.3] 3996.3 5309.18 6086.92 [41551]
-
2F IF IF -
5 3 5 5 3 5
-
Section 8
NUCLEAR PHYSICS J. B. MARION, Editor ,
-
The University of Maryland
CONTENTS 8a. 8b. 8c. 8d. 8e. 8f. 8g. 8h. 8i. 8j.
Nuclear Constants and Calibrations ........................ , ....... " Properties of Nuclides ....... ; ............. , .. , ..................... Atomic Mass Formulas .................... '.' . . . . . . . . . . . . . . . . . . . . .... Passage of Charged Particles through Matter .......................... Gamma Rays .......................... , ................... , ...... , Neutrons ....................... , ................................... Nuclear Fission ...................... " ... , ......................... Elementary Particles and Interactions .............................. " Health Physics ................................... : . . . . . . . . . . . . . . .. Particle Accelerators .............. , ; ...............................
8-2 8-6 8-92 87142 8-190 8-218 8-253 8-277 8-291 8-316
Sa. Nuclear Constants and Calibrations JiERRY B. MARION
University of Maryland
This section collects the various nuclear quantities that are useful in designing or analyzing experiments in nuclear physics. For an extensive collection of graphs and tables, the reader is directed to Marion and Young [1]. 8a-1. Nuclear Constants in the MeV System. A complete list of fundamental physical constants and d~rived quantiti~sis. to be found inside the front cover oUhis volume .. For .many nuclear physics calculations, however, it' is convenient to have certain of these quantities already .expressed in. MeV energy units. The following list has been generated by using the fundamental constants of Taylor, Parker, and Langenberg [2]. moc 2 . = 0.5110043 Me V M p c 2 =938.2595 MeV M n c2 =939:5529MeV . c2 = 931.481 MeY/amu h = 4.135705 >< 1O- 2i Me V~se~ -h = 6.582180 X 10- 22 MeV-sec 'hc = 1.973288 X 10-11 Me V-cm -h 2c2 = 389.387 Me V2-barn e = 3.794-703 X 10-7 (MeV-cm)! e2 = 1.439977 X 10-13 MeV-em e/-hc = 1.923036 X 10' (Me V-cm)-! (e/-hc) 2 = 3.698066 X 10 8 (Me V-cm)-I -h/moc 2 = 1.288087 X 10-21 sec 8a-2. Natural Units.
If -h
= 1 and c = 1, then
Mass, energy, and impulse are in units of cm-1 Angular momentum is dimensionless e = l/V137 1 MeV = 0.506 X 1011 em-I If fL = 1, c = 1, and mo = 1, then 1 sec = 7.764 X 10 20 natural units 1 cm = 2.58 X 1010 natural units 1 Me V = 1.96 natural units Sa-S. Alpha-particle Calibration Energies. Listed in Table 8a-l are the values for alpha-particle momenta and energies recommended by Wapstra [3]. The energies have been calculated for Wapstra's Bp values by using the expression
E
= a(Bji)2
+ b(Bp)4 + C(Bp)6 8:'2
NUCLEAR CONSTANTS AND CALIBRATIONS
8-3
where a, b, andc are [1] a = 4S225.33 X 10-12 keY (G-cm)-2 b = -311.9S X 10-24 keY (G-cm)-4 c = 4.04 X 10- 36 ke V (G-cm)-6
Sa-I.
TABLE
ALPHA-PARTICLE CALIBRATION ENERGIES
Source P0210 ............... Bi2l1 ........... : ... P0211 ............ : .. Bi212(ThC ao) Bi212(ThC al) Po212(ThC') ........ Bi'!4 ............... P021' ............... P021' ...............
Bp, G-cm
. . .
*... : .. . *...... . . . . .
PO'I' ............... . P021S ............... Rn 21 ' .............. Rn220 .............. Rn 222 ...... " ......
. . . .
Ra''' .............. . Ra 22 ' .............. . Ra 226 • • . • • • • • • • . • • . • Th227 .............. . Th 228 • • • • • . • . • • • • • . • Th 230 • • . • • • • . • " . • . •
* Intensity ratio: ao/a!
=
331,722 370,720 393,190 354,326 355,475 427,060 338,170 399,488 391,490 375,050 352,870 376,160 361,260 337,410 349,010 343,450 314,990 354,070 335,570 311,960
± 15 ± 40 ± 50 ± 20 ± 20 ± 20 ± 70 ± 16 ± 40 ± 40 ± 70 ± 40 ± 60 ± 70 ± 50 ± 40 ± 80 ± 60 ± 60 ± 160
Energy, keY
5304.5 6621.9 7448.1 6049.6 6088.9 8785.0 5510.9 7688.4 7383.9 6777.3 6000.1 6817.5 6288.5 5486.2 5869.6 5684.2 4781.8 6040.9 5426.6 4690.3
± 0.5 ± 1.4 ± 1.9 ± 0.7 ± 0.7 ± 0.8 ± 2.3 ± 0.6 ± 1.5 ± 1.5 ± 2.4 ± 1.5 ± 2.1 ± 2.3 ± 1. 7 ± 1.3
± 2.4
± ± ±
2.0 2.0 4.8
2.57.
8a-4. Gamma-ray Calibration Energies. Listed in Tables Sa-2 to Sa-4 are the weighted mean values of the energies of gamma rays frequently used as calibration standards [4] .. (A more comprehensive list may be found in ref. 4.) Also, relative intensities are given for C 0 56 since the gamma rays from this nucleus span such a wide energy range and are therefore of great value for both energy and efficiency calibrations. Gamma rays from both radioactive sources and nuclear reactions are given. 8a-5. Accelerator-energy ;Calibration Points. In order to know with precision the energy of the beam from an accelerator, unless an absolute instrument of some type is available, the beam-analyzing system must be calibrated against some accurately known energy points. One,method frequently used to calibrate such analyzers is to measure a number of gamma-ray resonances and neutron thresholds to establish several points of the energy seale. Listed in Tables Sa-5 to Sa-7 are a number of energy points suitable for calibration purposes. Only the weighted mean values are given; more complete details can be found elsewhere. [5].
8-4
NUOLEAR PHYSICS TABLE
8a-2.
GAMMA RAYS FROM RADIOACTIVE SOURCES
Half life
Energy, keY
Source
511.006 moc 2 . • • . • 477.57 Be 7...... Na 22 ••••• 1274.55 {136S.526 Na 24 ..... 2753.92 320.080 Or" ..... 834.81 Mn 64 .... C06 •..... { 1173.23 1332.49 Zn 65 • • • • • 1115.40 898.04 Y" ...... { 1836.13
± ± ± ± ± ± ± ± ± ± ± ±
0.002 0.05 0.04 0.044 0.12 0.013 0;03 0.04 0.04 0.12 0.04 0.04
TABLE
± ± ± ± ± ± ± ± ± ±
O. 19 . O. 15 0.05 0.13 0.07 0.13 . 0.09 0.09· 0.10 0.45
TABLE
15.0 h 27.8 d ·314 d 246 d
Nucleus
F17 .......... F18 .......... 0 '7 ........... Bu ........... B'2 .......... N14 .......... Be'· ...... : .. N'4 ... ·....... Be'· ......... C12 ..........
Bp·7 ..... Tl'·' ..... (ThO") ..
Am'H ....
661. 635 411. 795 { 569.62 1063.44 1769.71 { 510.723 583.139 2614.47 26.348 59.543
{
± ± ± ± ± ± ± ± ± ±
0.076 0.009 0.06 0.09 0.13 0.020 0.023 0.10 0.010 0.015
Half life 30 y 2.70 d 30 y (1. 91 y) 433 y
106.6 d
Sa-3. GAMMA RAYS FROM C0 66
0.1 ± 0.40 ± 100 1.52 ± 13.02 ± 1.86 ± 69.35 ± 4.38 ± 15.30 ± 0.72 ±
·8a-4.
OS'37 ..... Au l9 ' • . • •
5.26 y
Relative intensity
Energy, keY 733.79 787.92 846.76 977.47 1037.97 1175.26 1238.34 1360.35 1771.57 1964.88
53 d 2.60 y
Energy, keY
Source
0.05 0.11 0.16 0.35 0.23 1.47 0.16 0.53 0.08
Energy, keY 2015.49 2035.03 2113.00 2598.80 3009.99 3202.25 3253 . 82 3273.38 3452. 18 3548.11
± ± ± ± ± ± ± ± ± ±
Relative intensity
0.20 0.12 0.10 0.12 0.24 0.19 O. 15 0.18 O. 2:;l 0.25
2.93 7.33 0.37 16.77 0.84 3.15 7.70 1. 55 0.88 0.18
± ± ± ± ± ± ± ± ± ±
0.16 0.30 0.08 0.57 0.16 0.16 0.34 0.11 0.10 0.10
GAMMA RAYS FROM NUCLEAR REACTIONS
l'~ray
energy', keY
.Nucleus
l'-ray energy, keY
495.33 ± 0.10 C." ....... , .. 4945.46 N14 ... , ..... 658.75 ± 0.7" 5104.87 870.81 ± 0.22 016 ........... 5240.53 953.10±0.60 N16 ......... 5268.9 N16 .......... 1673.52 ± 0.60 5297.9 016 ......... 2312.68 ± 0.10 b 6129.3 2589.9 ± 0.25c Be'· ........ 6809.4 2792. 68 ± O. 15" . 0" ..... , ... 7117.02 3367.4 ± 0.2' 7367.5 Pb'··........ " 4439.0 ± 0.21 N'4 ......... 9173 N16 ......... 10829.2
± 0.178 ± 0.18 ± 0.52 ± 0.2 ± 0.20 ± 0.4 ± 0.48 ± 0.49 ±1" ± 1h ± 0.48
From 1.70-1.04 MeV decay. Doppler shifted unless formed in O"(I'/+)N". 'From 5.96-3.37 MeV decay (thermal neutron capture). d From 5.10-2.31 MeV decay. e From thermal neutron capture. J Doppler shifted unless formed in B12(I'/-)C12. • Doppler shifted unless formed in 015(I'/-)N16 or by thermal neutron capture. • Calculated from C13(p,'Y)N'4 resonance energy (1747.6 ± 0.9 keV) and 1964 masses; value given for observation at 0 deg to beam direction. a
b
NUCLEAR CONSTANTS AND CALIBRATIONS TABLE
Sa-5.
PROTON RESONANCE ENERGIJDS
r, keY
Reaction
F19(p,a')')016 .... .. . F19(p,a'Y)016 .... .. .
A12'(p,')')Si
28 • • • • • • •
CI3(p,'Y)NH ..... .. . 016(p,p)016 .. ..... . C12(p,p)C12 . ...... . a
8-5
340.46 872.11 991.90 1747.6 12714 14233
± 0.04 ± 0.20 ± 0.04 ± 0.9 ± 8a ±8
2.4 4.7 0.10 0.077
± ± ± ±
0.2 0.2 0.02 0.012
,' the latest of which is the ninth edition [10]. 8-6
NUCLEAR CONSTANTS AND CALIBRATIONS
8-7
References 1. Mattauch, J. H. E., W. Thiele, and A. H. Wapstra: 1.li64 Atomic Mass Table,Nucl. Phys. 67, 1 (1965), as revised by N. B. Gove and A. H. Wapstra, to be published. 2. Wapstra, A. n.: 1967 Mass1'able for· A = 212;.Proc.3d Intern. Can!. on Atomic .)ll~§..~es~lhJ()3, R. C. Berber, ed., University of Manitoba Press,. Winnipeg, 1967. 3. Nuclear Data Sheets published as sec.B of the journal Nuclear Data, K. "Vay, ed. This is a continuing series, with properties of the isotopes given in complete detail, which appears periodically. Before 1965 this series was published by the National Academy of Sciences. . 4. Lederer, C. M., J. M. Hollander, and I. Perlman: "Table of the Isotopes," 6th ed., John Wiley & Sons, Inc., New York, 1967. 5. Fuller, G.H.,and A. O. ·Nier: Appendix 2, "Relative Isotopic Abundances," Nucl . .Data Sheets. 6. Fuller, G. H., and V. W. Cohen: Nucl. Data A5(5), & (1968). 7. Ajzenberg-Selove, F., and T. Lauritsen: Energy Levels of Light Nuclei A = 11-12, N ucl. Phys. A114, 1 (1968). Other references in this series are contained herein. 8. Endt, P. M., and C. Vander Leun: Energy Levels of Z = 11-21 Nuclei, Nucl. Phys. - - ·Al0S, 1 (1967). 9. Goldman, D; T., P. Aline, R. Sher, and J. R. Stehn: Twenty-two Hundred Meter per Second Neutron Absorption Cross Sections, submitted for publication. 10. Goldman, D. T., and J. It. Roesser: "Chart of the Nuclides," 9th ed., General Electric Co., 1966.
TABLE (1)
I
I
(2)
Atomic Symnumber bol Z
(3)
(4)
Name
Mas. number A
n
2
I He
Li
IHydrogen Neutron IHelium
I Lithium
(7)
(8)
Number of neutrons N
Mass excess, amu X 10-'
Spin and parity
% abundance or half life
1
3 4
6
4 5 6
8 6652 t+ 7.8252 H 14.1022 H 16.0497 H 16.0297 H 2.603 0+ 18.89 0+ 34. 0+ 15.123 H 3 16.004 ]l"22.487 2+ ('})26.80
11m 99.985% 0.015% 12.3 y 0.00013% 100~r,
0.802. 0.122. 7.42% 92.58% 0.85 s 0.172 •
00
PROPERTIES OF NUCLIDES
(6)
o
7
8b-1.
(5)
-I-
--- -H
I
(9)
Magnetic Quadrupole moment, moment, nuclear barns magnetons
-1. 9131 +2.79278 +0.85742 +2.9789 -2.1276
(11)
(12)
(13)
Mode of decay, energy, and intensity. MeV(%)
I'/-decay Q values, MeV
Energy and intensity of 1'-ray transitions, MeV(%)
!l0)
(14)
2,2oo-m/s neutron~
absorption cross section, barns
1'/-0.78 ..........
+0.0028 ........... ...........
..................... 0.332 · . . . . . . . . . . . . . . . . . . . . 0.00052
.................... ....................
0.01861
p-0.0186 ....................
.
........... · . . . . . . . . . . . . . . . . . . ........... . . . . . . . . . . . p-3.51(lOO) P-1O, .•. ,n · . . . . . . . . .. .. -0.0008 .................... +0.82202 -0.04 .................... +3.2564 P-13, a1.6 +1.6532 ........... ........... p-11.0(75), 13.5(2),
· ... .. . . . ..
3.51 10.7
· . . . . . . . . . . .. . . . . . . . . · . . . ... .. .. .. . . . . . . . .
5327
· . . . . . .. . . . . . . . . . . . . . 950 ....................
I Be
I Beryllium
7
16.929 12.183 13.534 21.67
10 11
B
I Boron
12 8
27. 24.609 12.9385 9.305 14.354
10 11
12
.:;'}-
53.37 d
]l"-
3
100%
0+ (t)+
2.7 X 10' y 13.6.
0+
H
0.011 s 0.7Us 19.78% 80.22% 0.0204.
0+
0.019s 0.0127s 19.4 s
I'}-0+
20.4 m 98.89%
(2+)
3+ 3
]l"-
........... .(100) -1.1776 +0.05 ........... ........... p-0.555(100) ........... p-11.5(61), 9.3(29), · . .. . . . . . . . 4.7(6), 3.6(4) ........... ........... (J, n ........... . . . . . . . . . . . PH, a21.6 ................. +0.08 +1.8007 · .. . . .. . .. . .. . . . . .. . +2.6885 +0.04 p-13.37(98),9.0(1), ±1.oo2 ...........
0.037
16.0 13.61 0.862
10
4
17.78 31.04 16.86
11 12
5 6
11.432 O.
I Carbon
t"' I?"J
P. l:d t,j
::r:
0.478(10)
51,000
~ Ul H
Q Ul
0.555 11.61
':;0.001 2.12(32),6.79(4),5.86(2), 4.64(2), 7.97(2)
18.0 . .................... 1 3836
13.370
..................... 4.43(1), •..
0.005
· .. , aO.195(1.5)
13 C
Z q Q
0.99(88)
nO.7, . . . 4
I 00
........... .......... (J13.4(93), . . . , n 13.437 ........... p, p8.2(60).1.1(40), 2a 1'/+1.87(0.98), 0.85(1.6), ........... ........... 1.87 1.98 ±1.03 ±0.031 pO.97(99+), .(0.2) ........... . ................... ...........
3.67(7) 0.717(100) 1.023(1.6) •..............•..... 10.0034
N
'I Nitrogen
13 14 '15 16 12
3.354 3.2420 10.600 14.70 18.62
9 10
1
jJ-
0+
H 0+
H
+0.7024 ........... .................... ........... ........... ~0.156
1.11% 5730 Y 2.4 s 0.74 s ·0.0110s
........... , ........... ........... ........... ±0.46
...........
~4.51(68),
9.82(32)
~,n
tJ+16.38, . . . , (100)
......... 1 ..................... 10.0009 0.1561 9.77 :1 5. 299 (68) 8.0 4.43(2.4) 17.36
3uO.195(3) 10_
13 14 15 16
17
5.738 . 2 3.0744 H 1 jJ0.108 6.101 ·210
8.45
I (!)-
10.0 m 99 .• 3% 0.31% 7.2 s 4.16 s
I
±0.3221 tJ+L19(100) +0.4036 ........... , ....... , ........... -0.2831 ' ........... .................... ........... ~4.3(68), 10.4(26), . .. , aU(O.OOl) ........... ···········1 In.1(95),7.81(3),
2.22
10.422 8.68
.............. : ....... 11.89 ...................... 0.000024 6.13(69), 7.11(5),2.75(1) 0.87(3), 2.19(0.5)
8.68(2), nO.40(45),
18
8 10
F
10
I Oxygen
I Fluorine
I Ne I Neon
13 14 15 16 17 18 19 2G
11
14.25
(0,1,2)-
0.6·3 s
'17
10 11 12 8
18 19 20 21 22 17
10 11 12 13 7
24.81 , (!-) 8.597 0+ 1 3.070 jJ-5.0850 , 0+ -0.867 -0.8400 0+ 3.578 4.08 0+ 2.096 0.937 H -1.595 -0.017 2+ -0.049 (H) 3.04 (!-) 17.7
18 19 20 21 22 23
9 10 11 12 13
5.711 0+ 1.881' -7.560 0+ -6.1S3 -'8.615 ' 0+ -5.529
1.5 s 17.4 s 90.92% 0.257% 8.82% 37.6s
24
14
-6.39
3.38 m
t+
i+ i+
H
i+
, 0.0087 s 71.0 s 124 s 99:759% 0.037% 0.204% 27 H 14tl 66 tl 109.7 m 100% 11.4 s 4.4 s 4.0 s 0.10 s
........... ........... ........... ...........
........... ...........
±0.7189 :
........... ........... -1.8937
-0.026
........... , . ........... ........... ........... ...........
+2.6288 +2.094
13.9
{J+, p6.40(80), 6.97(20) 1l+1.81(99.4), 4.12(0.6) tJ+1.74(100)
17.8 5.1443, 2.312(99) 2.760
~
1.98(100), 0.82(59), 1.65 (59), 2.47(41)
0 'tI
trJ
~
>-3
H
. .................... . .. . . . .. . . .. .. . .. .. . . . ....................
.................... .................... . . . . . . . . . . . . . .. . , . .. {J-3.25(62), 4.60(38)
4.819 3.81 2.759 0.655
tr
{J+1.74(100) tJ+0.635(97), .(3)
±4.722
...........
'tI
1.2(45), 1.81(5) tr9.4
........... ........... ... .................. ........... tr5.42(100) ........... tr5.4(87), 4.0(13)
0.000178 0.235 0.00021
0.197(97), 1.37(59) 1.06(100)
0.0098
bj
cj 0 t"' ......
t:I
trJ
7.030 1.63(100) 5.68 . 0.350(100), 1.38(13) 12 1.28(100), 2.06(67)
........... ........... ........... tr11 ........... ........... {J+, p4.59, 3.80, 5.08,
0
Z
. ....................
-
trJ m
7JJ.
6.95, . . .
H
H (i+)
........... ........... -1.887
........... -0.6618
{J+3.42(93), . . • ........... tJ+2.22(100) • ••.•.• : .•.•••••. , ••
I
4.45 3.238
, •.•.•• :
11. 04(7) ••••••. c.; •.• c •• ; ••••
.. :. : i: OS .. · :::::::::::! ';:4.38'(67;: 3:95(32):' .! .. 4:3S0' .! 0'.439(33;: i:64'(ii: .,. : .•. 10.036 2.4(1), . . .
I
10+
10.038
+0.09
........... ........... tr1.99(92),1.10(8)
2.47
0.472(100),0.88(8)
I
,00
I
('.0
TABLE
(1)
I
(2)
I
I
(3)
(4)
I
I
Mass Name
number
excess,
neu-
omu X 10-'
trons
N
12
13
1 Na 1Sodium
1 Mg I Magn..ium
IAI
I Aluminum
20
1
9
-7-.4
I
21 22
10 11
23 24 25
12 13 14
26 20 21
15 8 1 8 1-19.. 11.71
-2.35 -5.563
10 . 229 1--9.036 -10.05
22
10
-0.41
23 24 25 26 27 28
11 12 13 14 15 16
-5.875 -14.956 -14.161 -17.407 -15.657 -16.121
24m
24 25 26m 26
11 12 13 13
% abundance
-1-..-.. -.
.- 11
Spin and parity
Mass
ber of
A
(8)
1 ,.....
(14)
(11)
(12)
(13)
Mode of decay, energy, and intensity,
B-decay Q yalues, MeV
Energy and intensity
neutron~
. of ,,-ray trans'itions,
absorption cross section, barns
(10)
(9)
00
(Continued)
0
2,2oo-m/s
Num-
Atomic sYm-1 number bel Z
PROPERTIES OF NUCLIDES
(7)
(6)
(.5)
8b-i.
0.5
I!+ I!+ 3+
4+
5-2+
12:
~r:~~:.
0.402 s
..........
22.8 s 2.1i02 y
+2.386 +1. 746
100% 14.98 h 60 s
+2.2175 +1.690
1.04 B 0.6 B 0.12 s
...
MeV(%)
fl+l1.25, 5.55, . . . , a2.14, ..•
/l+2.52(98),2.17(2) fl+0.544(90), 1.82(0.05), .(9.5) +0.14
13.91 3.54 2.843
...........
tJ-1.39(99), .•. tJ-3.8(65), 3.3(30). 2.2(5)
5.515 3.83
...........
/l'-6.7(100), . . .
8.5
...........
fI+,
p3.4, 4.0, 4.3, 4.8,
5.9, 6.45 fl+3.16(59), 3.23(36), 1.88(5) fl+3.04(91), 2.60(9)
0+
H
0.1~ B
...........
/l+13.3(4.4), 11.9(1.9),
14.32
14+
2.0\! B
. .. .. . .... .
fl+3.40(48),4.42(41),
13.88
0+
i+
5+
7.2-1
7Jl
...........
%+
0.35(2.2) 1.274(99.5)
13.1
12.0 s 78.70% 10.13% 11.17% 9.49 m 21.3 h
0+
1.63, . . .
0.534
...........
!+
MeV (%)
....................
4.00 s
10+
I. ~9:568··1 t: -13.106
or half life
Magnetic Quadrupole moment, moment, nuclear barns magnetons
2.61 1. 836
4.26 4.232 4.003
0.073(59), 0.583(100), 1.28(5) 0.439(9) . .......... 1 0 . 05 .. ....... .. 0.18 ........... 0.030 0.84(70), 1.0(30), 0.18(1) 0.032(96), 1.35(70), 0.40(31), 0.95(29) IT0.439(93), 1.369(1.9) 1.37(40),2.73(32), 4.22(15), 7.1(7), 5.4(6)
11.81(100), 1.2(2), .. ,
H (')
7Jl
14
I Si
I Silicon
27 28 29 30 25
14 15 16 17 11
-18.459 -18.088 -19.552 -17.1 4.1
h
26 27 28 29
12 13 14 15 16 17 18 13
-7.66 -13.297 -23.071 -23.504 -26.228 -24.636 -25.86 -8.2
0+
3+
h (2,3)+ (h)
100% 2.27 ill 6.52 :n 3.3 s 0.22 :,
+3.6414
+0.15
...........
... , ................ p-2.87(100)
........... · . . . . . . . . .. ........... · ... .. . . . . .
p-2.5(93), 1.5(7) p-3.8(84), 5.1(16) [J+, p4.25, 1.95, 3.47,
...........
[J+3.83(66), 3.00(34)
........... · ...... ...
[J+3.8(100), ...
. '4:634"1 3.68 8.5 12.7
i.779(iooi· ...........
10.232
1.27(93),2.43(7) 2.23(58),3.51(42)
2.31, 2.18, 0.97, ...
30
15
16
IP
I S
I Phosphorus
I Sulfur
31 32 28
29 30 31 32 33 34 29
14 -18.19 15 -21.68 16 -26.235 . 17 -26.091 18 -28.272 19 -26.7 13 1-3.
h
0+
H
2.1 s 4.17,j 92.21% 4.70%
0+
3.09%
H
2.62" 650 y 0.27,
0+ (3)+
H
4.23 s 2.50 m
H H (i)+
100%
H
H (i+)
14.2~
d 25.3 d 12.4 3 0.193
........... ........... -0.5553 ........... · . . . . . . . . . . ........... · . . . . . . . . . . ........... ~
............ · . . . . . . . . . . ...........
. . ... .. . . .. . . . .. . . . . .................... ....................
P-1.49(99.9), 0.21(0.1) p-0.21 (100) [J+11.5(52), 6.96(16),
5.25(13), 3.94(13), 8.80(7) [J+3.94(98), 2.68(1), ...
.
· . . . . . . . . . ........... ........... · . . . . . . . . .. [J+3.24(99.5), 1.01(0.5) +1.1317 · . . . . . . . . . . .................... -0.2523 · . . . . . . . . . . P-1. 710(100)
........... ........... · . . .. .. . . . . · . .. .. .. .. . . .......... ...........
p-0.248(100) p-5.1(75),3.2(25) [J+, p3.5, 3.73, 5.0, 5.2,
5.07 4.81
0.82(34)
. ....................
. .................... . . . . . . . . . . . . . . . . . . .. .
0.16 0.28 0.10
1.492 0.21 14
1.266(0.1) 1.78(100),4.50(29), 3.04(8),7.50(7),2.84(6),
!:d
4.95 4.24
1.27(1) 2.23(0.5)
!:d
'"d
0
'"d
t;1
1. 710 0.248 5.1
.....................
1-3 ,....
0.19
0
2.1(25), 4.0(0.2)
"'.I
0.
~
~14
q
5.4, ... 30
14 1-15.10
31 32
15 16 17 18 19
33
34 35 36
17
I
Cl
I Chlorine
37 38 32
-20.39 -27.926 -28.541 -32.130 -30.967
20 1-32.91 21 -28.88 22 -28.8 15 -14.24
0+
1.253
........... ...........
[J+4.43(80), 5.10(20),
6.13
0.68(80), . . .
1+
2.613 95.0% 0.76% 4.22% 87.0 d
........... ........... · . . . . . . . . . . ...........
[J+4.39(99), •••
5.44
1.266(1)
............... ..... ........... ........... ....................
0.014% 5.06 m 2.87 h 0.30.
0+
H
0+
H 0+ (i-)
0+
2+
+0.6433
-0.055
+1.00 or -1.07
+0.04
· . . . . . . .... ......... .. ........... .. -........
........... ........... .......... -. · ... ... ... .
-
. . . .. . . .. ... . ... .. ..
. .................... . .................... . ....................
-
1l+0.167(100) .
4.8 3.0 12.8
7.5(14),6.2(10),11.6(1) ·33
16 1-22.56
IH
12.52 s
I.......... ·1· ......... ·1 [J+4.5(99.7),
•••
0.53 0.18 0.02
t"' >-< t::I t;1 m
0.167
.................... P-1.6(94), 4.8(6), •.. P-l.l(95), 3.0(5) [J+9.5(60),4.7(25),
t;1
m
5.57
..................... 10.14 3.11(94),3.7110.4) 1.88(95) 2.23(89), 4.77(25), 2.46(5),1.65(5), 3.31(4), 2.9(0.3)
I
00 I
I-' I-'
TABLE (1)
I
(2)
I
Atomic \ sYm-\ number b I Z ' o·
(3)
Name
(4)
\ :
,I
Mass nU~ber:
(5) Number of neutrons N
(6)
8b-1.
PROPERTIES OF NUCLIDES
(8)
(7)
Mass excess, amu X 10-3
Magnetic Spin and i parity
% abundance 0:
hal! life
(Continued)
moment,
-nuclear magnetons
(14)
(13)
(11)
(10)
(9)
···cr ,.... I\:)
2,200-mj, Quadrupole moment,
/l-decay
Mode of decay,
energy, and intensity, ' Q_values,
MeV
MeV (%).
barns
Energy irid intensity of l'-ray. transitions, MeV (%).
neutron~
absorption cross section, barns
._-- .-- - - - - - - - - - 17
18
I Cl
IAr
191 K
I Chlorine
H
·34m 34 35 36
171-26.250 18 : -31.146 10+ 19 -31.693
37 38m 38
20 21
-32.00
2-
39
22
1-31. 99
Ih
I Argon
40 33
23 15
'-29.6 -10.
16 17 18 19 20 21 22 23 24 25 26 17
-19.7 -24.75 -32.453 -33.223 -37.267 -35.683 -37.616 -35.500 -36.95
;I Potassium
34 35 36 37 38 39 40 41 42 43 44 36 37 38m
18
-26.64
~:
\~34:o97p~
(2-) (H)
0+
i+ 0+
H 0+
7 z-
D+ 7
20+
-18.6
H
D+
32.'1 m 1.57 s 75.53% 3.07 X 10' y 24.47% 0.74 s 37.2 m
+0.82133 +1.285
-0.079
+0.6R411
~0.062
-o.rm
0.9 H 1.80 s 0.337% 34.8 d 0.063% 269'Y 99 .. 60% 1.83 h 33 y 6m 14m 0.27 s 1'.23 s 0.95 s
6.63
/l+4.5(lDO)
5.48
/l-0.71(98.3), ,(1.7), Wo.12(0.002)
0.712 1.14
. . . .. . . . . . . . .
. ...........
-
4.9 3.44
+0.63
/l+, p3.27, 2.17, 2.54, 3.93,; .. /l+5.05 /l+4.95(93), . . .
+0.95
,(100)
7.5 12 6.06 5.96
44
Z ,q .....................
............. t>~7.5, ~3.2 ......
ITO-. 146 (45), 2.13(41), 3.30(14); 4.12(0.4) .
....................
1"4.9(53), 1.1(36), 2.8(11) 1"1.91(85), 2.18(8), 3.44(7)
. 55'.0 m 1.42 m 0.18 s
11+2.5(28),1.3(27), . . .
0.43
..
••••••••••••
-1.3
........
.................... ...........
I
0.565
1"0.565(100) 1"1.198(99), 2.489(0.8) /l-
. 2.49 0.60
(3-
... , ....... ...........
I" /l+9.9(70), 5.3(25)
+0.204 . W5.12(98), . ;. .................... W5.03(100)
. ........
12.9 6.15 6.05
t:-
, 2.17(47),1.64(36). 3.81(0.02) 1.27\50), 1;52(43), 0.25(42) ' 1.45,3.1,0.33, 2.85, ..
~
'"0
.ll:i '>-< 10' y 0.0118% 6.88% 12.36 h
43
24
1-39.27
I~+
21.8 It
+1.374 ........... /3+2.7(99.8), ..• +0.3914 +0.055 · . . , . . . . . . . . . . . . . . . . -1.298 -0.07 1>1.31(89.4), ........... ........... ,(10.6), /3+(0.001) +0.2149 +0.067 .................... -1.141 ........... 1>3.52(87), 2.00(18), ±0.163
........... /3-0.82(83), 0.46(10),
5.93 1.314 1.505
1.52(18), ...
1.82
0.372(85), 0.616(60), 0.396(20), 0.593(13), 0.222(3), 1.02(2), .•. 1.16(65),
20
I Ca
I Calcium
I Scandium
20m 1158
±0.173 ........... 1>2.1(70),1.1(20),4(10) · . . . . . . . . . . ........... /3-6.3(50), . . .
4.19 7.72
17.5. 0.1738
...........
1 (2-)
22.0
45 46
26 27
1-39.3 -38.0
1%+ 2(-)
47 37
281-38.3 17 -14.2
38
18
-23.74
39 40 41
19 20 21 22 23
-29.29 -37.408 -37.721 -41.372 -41.223 -44.510 -43.807 -46.31 -45.46
43 44 45 46 47
I Se
5.2
1-38.44
42
21
........... ........... 1>5.2(35), 2(30), 4(9),
25
2~
25 26 27
I::. · · H
0+ 7
20+ 7
Jr-
0+
(iJ0+ 7
Jr-
III
0.58
/3-4.1(99), 6(1) · . . . . . . . . . . ........... /3+, p3.16, 1.74, 2.77, 1.98, 2.54, ... ........... · . . . . . . . . . . J3+5.59(79), 4.02(21),
0.88 " 96.97% 7.7 X 10' y 0.64% 0.145% 2.06% 162.7 d 0.00.3% 4.56 :I
· . . . .. . . . . · . . . . . .. . . . · .. . . .. .. .. -1.595 · . . . . . . . . . . ........... ........... -1.317 ........... · . . . . . . . .. . ........... ........... · . . . . . . . . . · . . . . . . . . . ........... ........... ........... ...........
.
...........
.
.
6.65 11.56
· .. . . .. .. . . .. . . .. . . . .................... 1>0.256(100), ...
~
"d
t."2.13(94),1.50(6)
...........
2.46
...........
-45.76 -51. 79
55 56
0+
....................
' 1.1 s 23 h 41.9 m
25 26
54
D+
t-
+0.24
0.605 2.22 1.03
D+ ,,-
53
-1.1039
· .. . . . . . . .,
.(100) ±0.06 .(70) ........... ........... 1>"(30) -0.05 .................... +5.149 · . . . . . . . . . . ........... 1>"2.47(99), .•• ........... ........... 1>"2.5(100) 1l-3.3(100) ...........
-53.951 -55.229 -'59.490 -59.349 -61.12 -59.17 -59.4
52
....................
330 d . 6 X 10" Y 0.24% 99.710% 3.73 m 2.0 m 55 s
26 27 28 29 30 31 32
7
· .. ... . . .. .. .. . . .. . .
1. 97 7.05 2.92 4.013
D+
51
+0.29
...........
........... ........... 1>"1.8 ........... ........... 1l+6.0(100) · . . . . . . . . . . ........... tJ+1.90(96), .(4) ........... ........... tJ+0.694(60), .(40)
1.7m :0.426 s 33m . 16.0 d
-46.0 -48.73
(~)-
-0.7883
7.-28% 73.94% 5.51% 5.34% 5.8 TIl
22 24 25
50
I Mn I Manganese
D+
,,-
48 49
25
,,7
51
54 Cr
5
D+
26 1-51. 482 1%27 -52.836 6+
53
'I
,,-
50
52
24
-48.232 -52.051 -52.128 -55.216 -53.40
25 26 27 28 29
47 48 49
4.31% 27.8 d 83.76% 9.55% 2.38% 3.5 ill 5.9n 2m 0.281\ s 46m 21 m 5.7"
,
±4.5 +3.3470
...........
±0.48
........... ±0.94 ........... -0.4743 ........... ........... · . . .. ... ..
tJ+ ........... .(100) · . . . . . . . . . . tJ+1.54(65), 1.42(29),
...........
·. . . . . . . . . .
~7
1.4 2.56
· . . . . . .. . . . ... .. .. .. .(100)
0.752
........... · . . . . . . . . . . . . . . . . . . . .................... ±0.03 · . . . . . . . . . . . ................... ........... 1>"2.59(99+) ........... 1>"1.5(100) ........... ........... tJ+(99), .(1) · . . . . . . . . . · . . . . . . . . . tJ+6.6 ±3.57 · . . . . . . . . . . tJ+2.17(97); .(3) ±0.0076 ........... tJ+2.63(92), .(8) ........... .(62), tJ+O.58(38) ±3.05
.
. .
±5.01 ±3.29 +3.444
3.97
........... .(100) ........... .(100) · . . .. . ... .. .. +0.4
1.5(0.7), 1.8(5), 0.983(100), 1.312(98), 2.24(3), 1.55(70) 0.783(30) . . . . . - . . . . . . . . ... .. . 1.43(100), ... 1.0(100) 2.21(100),0.99(100), 0.84(100)
.
0.116(100), 0.31(100) 0.090(30),0.063(29), 0.153(4), . . . . .................... 0.320(9) . .............
. .................... . ....................
2.59 1.6
100
'"d
!:d 4.8
0 '"d
trJ
!:d 1-3 .....
trJ
Ul
0 "'J 16 0.76 18.2 0.38
:z:q 0 t"'
.....
tI trJ
Ul
1.52, 2.24 0.083(100), 0.026(100) 0.79, 1.11,
7.63 3.19 4.708 0.598
... . . . .
.................... '11.7 ................... 83 ................. .. 1 9 ... ............. 0.14 0.320(95),0.928(5), 0.605(1) 0.125,0.17
1.38
. l.435(100), 1.435(100), 0.938(100), 0.747(99), ...
~.~~~:1~~)::'-:::::: .::: I~~r
'f
i-'
:;J
2l q 0
t"
I-
3.50(50), 2.40(25), 1.50(25)
I.......... ·1 ........... 11>0.93,1.51, .•. ............. 1>1.4(lOO) ........... ............
1.576
0,276(2), 0.290(1), 0.565(1), .. ~ ......... . . ............ ......... 1.031(22), 0.356(16), . 0.989(14), 0.676(13), ~
... 3.58
1.8
0.05
~
Z
I
q
C
0.356(73), 0.512(45), 0.226(34), 0.729(22),
t" l"!l
> ::0
0.408(100)
I> I>
'ctI ~
~
11-, n [:1+, p2.5 .. 1l+4.7 [:1+1.72(51), 1.1(10), 0.65(3), .(30) 1l+3.58, 0.93, 1.80, • ±0.25
5~7
3.02
+2.lO6 +1.317 ±0.514
+0.31 +0.71 ±0,18
+2.270 ...........
+0.26
.(99), 1l+0.36(1)
1.371
[:1+2.52(82), ..• ,.(7)
3.57
. . . . , .. . . . . . .
...........
............
....................
1>1.66, 2.36
0.630,0.720, . . . 0.620, 0.285
2.02 1.873
l/2
0.56, 0.65, . . . ITO.1076(lOO) .0.239(27), 0.298(8), 0.578(7), . , , 0.614(13) ITO.208(100) ..........
........... : .........
11-2.02(84),1.38(7), ... , ,(6), [:1+0.866(3)
H i;lj '"C
iIi
>
,1>5.5, •••
~2.5
5.5 ~2
p+2.0 .(100)
...........
........... ....................
...........
.•.•.......• (100)
-0.642
t>.:I
118,700
3.4 ~.4
1.99
0.56
0.305(73), 0.390(11), 0.68(3), .•• 0.434(43),0.62(22), 0.51(10), ••• ITO.ll tu9,O.31 0.374 0.132"1 0.140, 0.275, 0.420, 0.67 0.084(49),0.074(34), 0.126(16),0.159(4) 0.296(30),0.590(24), 0.566(7),0.723(5), .•• .................•.•. 14.8 0.040(100) •.••
+0.8
~7X10'y
........... ........... .................... ••....... 1 •.......•••.•.••••••• 10.28 0.035 ........... ........... ,1>0.035(100)
26.71% 4.7m
. . ......... ...........
....................
Z q Q
t:'
t>:J
1.51
0.49(0.5) 102
w1
barns
1-92.72
108
cross section,
(12)
• •.•.•.........•.•.... p-0.92(66),O.70(22), 1.31(3), .••
22·m
MeV(%)
(11)
130 m
(!)+
of ,,-ray transitions,
2,200-m/B :neutronabsorption
(10)
1.......... 1 .....•.•
62 1-93.25
(14)
(13)
........... ........... . ..................
107
00
(Continued)
45 s 35.Gh
(i+)
-94.31
IH
46
(9) Magnetic
Mass
-=/(t-)
106m
106
8b-1.
. ........ 1 ITO.188(60),
0.11(40)
0.08(40),
:>
p:j
~
~ .....
Q
U1
111 H2 113 114 115 117 118 99
65 66 67 68 69 71 72 52
-81.7
100 101
53 54
-84. -87.0
9m 11m
63 64
-94.046 -94.84
H
13.47h 11.81% 5.5 h 22 ill 21 h 1.4m 2.4 ill 40 s 5s 3.1 s 2.8m
109 110
0+
111m
47
I Agi Silver
-92.33 -92.61
0+ 0+ 0+
102m
7. 'I
102 102
4m 13 ill
55
103m 103
104m 104
105
+4.4
57
1:":9i5;,"I~!
130 ill 67 ill
+3.7 +4.0
I'
58
1-93.48
I i-
±0.101
I..
1
10+
-91.0
H .......... 1H -94.909 +:....
591-93.32 60
.... : ..... (0+)
61
1-94.047
IH
0.088(89), . . .
2.2 0.30
ITO.17(75), 0.07 . 0.38, 0.58, ..• 0.0185(20)
1.04(45), 1.70(40), 1.53(32), •.• . .. 0.728 0.26,1.16,0.65,0.67,0.58, 4.4 0.86, 0.73, 1.60, 0.558,
5.56
.............
1 40d
8.4 d
...........
24.7 ill 44.3 s 51.82% >5y
+2.9
2.42
+2.80
ill
........... .(50), tJ+1.7, 1.3
2.7
I
4.10
.1
1. 34.
,(100) tJ+1.96(50), . . . , _(30)
2.97
..............
-0.1135
. . . . . -. . . . . . . . . . . . . . _(90)
........... 111.6(96), . . . _(2), 1l+0.88 (0.28)
0.55, 0.78, 1.27, 2.06 0.558(85),0.727(65), 1.80(42), 2.07(20), . . . ITO.138 0.27(34),0.12(26), 0.15(23), 0.24(10), 1.16(9), . . . ITO.02(30), 0.556(70) 0.556(84),0.764(48), 0.854(30), 1.34(8), 1.62(8), . . . 10.344(42), 0.280(32), 0.064(10), 0.443(10), 0.644(10),1.088(4), . . . 0.115(55), 0.061(15), 0.153(9), 0.752(7), •.. 0.512(20) ITO.093(100) ..................... 135 ITO.03(9), 0.08(9), 0.722(90),0.614(90) 0.632(2) 0.434(0.45)
I' ....... I
tJ+2.7(60), _(10) _,11'"0.99
1 _(100),11'"
I 0.4
6.0
1l+2.4(40), 2.9, 3.3, 3.6 tJ+2.26(37), 1.90(13), 1.50(3), . . . ,_(45)
...........
H
56
108m 108
+4
1.115
............
11(25) 112.2(100) 1l-0.28(100) II .. IlII~4.5(73), ~4.4(27) II Il.... ........ 13+3.32(53), 1.7(24), 2.45(23) Il+ 5:8 ,6+2.73(44),2.18(23), 1.56(17), . . . , _ ........... 11'"3.4, 4.06, 3.07, _(13)
5.7 s 66 In
106m 106 107m 107
1:":;';':4" .. I.. · .... · (i-)
II
........... ........... 111.03(99+), .•. . ........... '"
1.64 1. 92
'"0" !;:d 0 '"0"
t
!;:d
>-3 t
H
U2
0
"'1
Z 0
(')
t"'
H
tI i:'1
(fl
00
I
C>.:> C>.:>
TABLE
(1)
(3)
1 (2) :1
AtOmiC! 8!
nU~ber '~:- •
(4)
(5)
8b-1.
(8)
(7)
(6)
I Ag
Name
Mass number A
I Silver
Number of neu-
trons N
Mass excess, amu X 10-'
109m 109
....
62
-95.244
Spin and parity
139.8 s 48.18% 253 d
63
1-93.886 I H
24.4 s
111m 111
64
!'··········I(H)
74 B 7.5 d
112
65
1-92.94
2-
3.2 h
i-
1.2m 5.3 h
(1-)
5 s· 49 B 21m
-94.70
66
-93.44
114' 115m 115
67
-91.
68
-91.1
116 117 118 101 102 103 104
69 70' 71 53 54 55
-89.
56'
-81.0 -85. -86. -90.
0+ 0+
Magnetic Quadrupole moment, moment, nuclear barns magnetons
% abundance or half life
110
113m 113
I Cd I Cadmium
H 1-
.... 6+
110m
48
(11)
(12)
(13)
(14)
Mode of decay, energy, and"iiltensity, MeV(%)
'Il-decay Q vallies,
Energy aridiiJ.tensityof ')'-ray transitions, MeV(%)
2,200-m/s . neutron.. absorption cross section, barns
(10)
~
H>-
1
--- -- --- --47
(9)
cr
(Continued)
PROPERTIES OF NUCLIDES
2.5m LIm 5.3 B 1.2m 5.5m 10m 57m
I
±4. 3
+~: !~~5
I· .........
MeV
..
·1· .................. '1' ....... '1 ITO.088(100)
:::::::::::
~O.087(6;';: O:53(3'li:' ::::::::: O.658(90i:o.885·(7ii:··· 0.937(32),0.764(213), 1.384(21), .•. , ITO.116(1) 0.658(4), ~ ~ :
tr2.88(96), 2.2(4), ... 2.88 .(0.3) 0.87 . ................... .......... ITO.OB5(100) ........... . --- . 0.34(6), 0.25(1) 1.05 -0.145 . . . . . . . . . . tr1.05(93),0.n(6), 0.80(1), ... 0.617(41), 1.40(5), 3.96 ±0.054 ........... 1l-3.96(54),3.35(22), 1.63(3),2.11(3). 1.96(10), ... 2.55(2), ... . _ ....... 0.14,.0.60,0.39,0.56,0.70 ...................... tr
l;tI
'"d
p:j
~ H (')
Ul
105
57
106 107 108 109 110 111m 111
58 59 60 61 62
I
In
1 Indium
1%
-93.537 -93.388 -95 811 -95.050 -96.990
0+
H
0+
H
0+
"-!+ 11
63 64
112
49
1-91.
.-95 814 -97.238
0+
~1._
1.22% 6.5 h 0.88% 453 d 12.39% 48.'3 m 12.75% 24.1)7% 14y 12.26% 28.36% 43 d
113m 113 114 115m
65 66
115
67
1~94.57
116 117m
68
1~9~:238
117
69
1-92.76
I!+
118 119m 119 121
70
-93.08
0+
-9004
100
71 73 57
-86.30
50 m 2.7 m 10m 13 s 5.3 In
107
58
-89.6
59
-90.3
0+
11 -2--
108m 108 109m, 109ml 109
!+
-95.592 -96.637
... I
60
I!+ .1
~;_
2,3+ (6,H)
1"I(~l-+) ........ . (2-) -92.88
!+
-0.74
55.m
. ...........
-0 6144
+0.8
~2.8
1.417
0.31, 0.34, 0.35, 0.43, 0.61, 1.9, 2.0, 2.3 ..............•...... 11.0 0.093(100) •••.
0.182
0.088(100) . : . : : : : : : : . .\
.................... • (99.7), IJ+0.302(0.3)
.................... ·-0.8270
+0.8
-1.11 -0.5943
-1.0
-1. 087 -0.6217
-0.8
-1.040
-0.6
.(100)
.
. . . . . . . . . . . . . . . . .. . .................... . .. . . , ... . . . . .. . . . . .
..................... 10.06 IT? ..................... 20.000 ..................... 0.34 0.935(2), 1.29(1), . . .
1r0.58(100) ....................
/l-1.62(97), 0.68(1.6), /l"·I.11(60), 0.58(31),
-0.6477
1.45
. .. .
1r0.67, 0.41
[.
.[.. .. . ... ..[ 1r0.65, 0.79, 2.23, •.. [ 2.52
,
. 0.077
O.27P(18), 1.998(15), 1.21(11), 0.880(10), 1.433(10),1.408(8), . . . [ 0.213(31), 1.303(19), 0.34.5(18), 1.577(17), 0.314(16),0.897(7), •.. 0.8?
1r3.5 1r3.5
3.5
32 m
1'1+2.2, ..• , •
3.5
3n m 56 TIl
11+3.50, 2.66, 2.28, • 13+1.29, •
5.15 5.11
...........
. ...................
.............
+5.53
+0.86
.(94), /l+0.79(6)
2.02
>-:3
H
l':j
W
0
I>j
:z:
Ci
0
t'
H
I:J
l':j W
.. Ir 6.7
0
"d
~0.8
Ir
IJ+4.89, 2.7
0.21 s 1.3m 4.3 h
.. .. . . . . ..
"d
[:lj
l':j [:lj
0.336(95), 0.526(26), 0.492(10), . . .
..................
7.58% 3.4 h
~O~
ITO.150. 0.247
....................
53.iih
[2.4 h
IJ+1.69, .••
+0.5
0.53, 0.63. 0.86, 1.66, 0.99, . . . 0.22(46),0.32,0.73,0.84, 0.94, 1.05. 1.25, . . . 0.383, 0.633, 0.842 0.633,0.842,0.872,0.243, 0.150, . . . ITO.68(lOO), 1.44(80) ITO.658(100) 0.205, 0.28, 0.35, 0.65, 0.91
00
I
~
C.;1
TABLE (1)
I
(2)
I
IsYm-1 nU~ber bol Atomic
(3)
(4)
Name
M.... number A
I
(5) Num-
I berneu-of trons
IIndium
(8)
Mass excess, omu
Spin and parity
% abundance or half life
--
i13m 113 114m 114 115m 115
7(+) -92.77 -94.93
2+ . 9
fi
H 63
-94.46
.1+
·1
64
-95.91
H
5+
65 1-95.10
66
11+
t1~96:i3' .. .H
4..9h
~7m 7.3.m 2.81 d 20.7m 14m 100m 4.28% 50.0 d 72 s 4.50b .6 X 10" y ~5.72%
116m, 116ml
(9)
(Continued)-
(10)
Magnetic Quadrupole moment, moment, nuclear barns magnetons
~
(11)
I:::::::::: .5+
C/.:) ~
2,200-m/s Mode of decay, energy, and intensity, MeV(%)
/l-decay Qvalues, MeV
f1Bs S4.0m
+4.36
-0.21 or +0.22 +0.36
+5 ..53
+0.85
.(100)
+2.81
+0.089
1'0.66(44) .(34), p+1.56(21)
.+10.4or
-10.7
" /IT? .. '
Energy and intensity of -y-ray transitions, 'MeV (%)
neutron-
absorption crOSB seetion, barns
0.66,0.91
/l+2.20(71), •.. , (29)
............ ........... ..................... ........... ........... .................... -0.210 +5.523 +4.7
· . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . +0.82 . . . . . . . . . . . . . . . . .. . . . ........... .«0.02-) .
........... ........... -0.244 5.534
· .. ... .. .. . +0.83
/l-1.986(98), ..• .(2), /l+0.4(0.004) /l-o.83(5) 1'0.49(100)
~.93
'. 0.83 0.65 ·2'.59
1.986 1.44 0.49
........... · ... . . . . . . . ... ... .. '. '. '. '. '. . .... +4.3 ............ /l-c1.00(49), 0.87(40), '-
~
-94.74
1+ 1
140
-95.p
f~ •+
1. 93 h 44m
...........
8j~
116 i17m 117 118m, 118m
67
118 119m
69 1-93.9 1H .......... (i-)
.......... (4,5+)
.............. · . . . . . . . . ..
~
.~
c::t
(')
:t" 0.617(6) lTO.393(100) _.................... ITO.1916(96.5), 0.724(3.5), 0.556(3.5) 1.30(0.2)
t;l ~
10.7
~
-
3.27
4.4m
1'3.3(99), ". , ... (H.77(37), 1.62(16) />,0,74(100) /l-1.8E1) ',," /l"1.3(53j, 2.0(32),., .•
5s 18m
.............. · . . . . . . . . . . ...........
/l-4.2(80),.3;0(16), ••• 1'2.7, . . . , (95)
4.2
1.47
iti
Iii
J:Q
g Q
.. .. ...... ...... .. "
;
"
ITe.16!(100,l 1.293(80.), 1.09(53), 0.417(36), 2.H1(20l.· 0.819(17), 1.508(li),
'
........... ........... ............ ........... . .......... ........... ........... -0.2515
0.658(99), ..• ITO.539 0.247(94),0.173(89), ..• TTO.156(100)
rp.
ITO.335(95)
0.60(11), . . .
68
(14)
(13)
, .(12)
,---
110m 110 111m 111 112m 112
PROPERTIES OF NUCLIDES
(7)
X 10-'
N
.49 .1 In
8b-1.
(6)
1.293(1), . . . ' ." . ITO.314(47),0.158(16) 0.56(100),0:158(100.) ITO.138(99) 1.23(97), '1.05(80), 0.69(4p,.... L23(15) 0.023,0.91, ITO.30(5)
198
119 120m? 120
50
I Sn I Tin
121 121 122 123 124 108 109". 109
70 1-94.2 1 (!+) .......... (1)+ 71 -92. (4,H)
72 73 74 75 58
-92.1 -89. -89. -86.8 -88.
59
-8.9
0+
.......... ..........
110 111
60 1- 92 . 13 61 -92.24
0+
112 113m 113 114 115 116 117m 117 118 119m 119 120 121m 121 122 123m 123 124 125m 125
62
-95.17
0+
63 64 65 66
-94.81 -97.24 -96.65 -98.252
i+
67 68
-97.039 -98.387
t+
126 127
. . . . .. . . ..
-96.684 -97.793
4.0b 35m
........... ........... ........... ...........
........... ........... .................... ........... ........... .(9) ±0.88 ........... .(100)
~250d
t+
8.58% 32.85% 76y 27 h 4.72% 40m 129 d 5.94% 9.7 ni 9.6d
0+
¥11
0+ (1-J!:t_)
H 0+ (H)
-95.762 -96.549
73 74
-94.26 -94.717
¥-
75
-92.21
J.l--
76
........... ........... ........... ........... ........... · . . . . . . . .. . ........... ...........
0+
i+
71 72
.. .. . .. .. .
3.1 m 30 s 8. 36 s 4. 9m 1.5m 18.1 m
0+ (i+)
1~~~:~4 ... 10:......
~!O'Y
4m
........... ........... ........... ........... ........... ........... ........... ...........
~2.2(41),
2.35
10.82(95),0.73(5)
. ......•. 1.17(~15)
" " ..................
T-
0+
I
I"..•................... ....... "I' ··········1 P-'~5.6(,..;85) ~1.6(100)
46.
0.96% 20m 115d 0.66% 0.35% 14.'80% H.Od 7.61% 24.03%
(1+)
..........
2 4m . 13.2.
3.1(27), • •.
5.6
1.171(100), 1.02(61) 1.28(14), 0.090(12), 0.71(12),0.94(12), •••
3.4
0.94 0.99,1.14
n.7 ~ ~5
~7
/1-404
4.4 7.4
~5
~2
/1+ .(80), /1':1.52(20)
~4
0.59 2.52
.(70), p+1.51(30)
1.13, 0.99, 3.21 0.28,0.42 IT 1.12(50), 0.65(44), 0.33(26), 1.55(18), . . . 0.283(95) 1.14(2), 0.75(1), 1.89(1),
. .................... 0.76
'"d
~
0 '"d ~
1.15
~
"(f.l
0
-0.918
· . ... ... .. .
........... .................... ........... ........... . ...................
. ....................
"':J 0.006
ITO.158(100)
-1.000
........... ........... . ................... ........... .................... o
•
•
•
•
•
•
•
•
•
. ....................
±0.08
~0.383(100)
........... ........... ......................
~ ~2.7
0" • • • • • • • • •
~
0.14
"(f.l
0.037(100) 0.383
........... ........... .................... ......... · ... . . . . . . . ........... ~1.26(100) ......... ........... ........... ~1.42(99), ... 1.42 ........... ........... . ........ ........... ........... />2.04(97), ... ......... · . . .. . . . . . . ........... 1>2.34(95), ... 2.34 •••••••
t"'
1-1
ti
+1.046
. ....................
Z q Q
0.01
ITO.065(100), 0.024
•
........... ........... .................... ........... . . . . . . . . . . . /1-0.3.5(100) ±0.70
~
1-1
ITo.o79(91) 0.393(100), 0.255(1)
~ ••
~.3
. ........
..................... 10.15 0.16(100) 1.09(1), ... ..................... 10.14 0.325(97), ... 1.067(4), 0.822(1.5), 0.915(1.4), ... 0.060, 0.067, 0.092 0.495
Cf
CIj
'1
8b-1.
TABLE
"""(i) 1(2)"1
(3)
(4)
Name
Mass number A
1
(5)
(5)
NumAtomic 1 sYm-1 nu~ber bol
PROP]DRTIES OF NUCLIDES
(7)
(8)
Spin and parity
% abundance oj' half life
(9)
Mass
I ber of
excess,
neutrons N
amu X 10-'
(Continued)
(10)
Magnetic Quadrupole moment, moment, nuclear barns magnetons
00
I
(11)
(12)
(13)
Mode of decay,
I'l-decay Q values, MeV
Energy and intensity of l'-ray transitions, MeV(%)
energy, and intensity,
MeV (%)
(14)
CJ,:l
00
2,200-m/s neutronabsorption cross section,
barns
----50
I Sn
I Tin
127
77
-90.
12.1 h
· . . . . .. . . . .
128
78
1-89.5
59 m
...........
2m 9m 2.6 :n 1.3m 2.2m 0.9 :n 5.7m 3.3 m 32m
. . . . . . . . . . · . . . . . . . . . . rr·... .. ... . . rr........... . . . . . . . . . . I'l-
10+
129m
51
I Sb
I 'Antimony
129 130 131 132 112 113 . 114 115
79 78 79 80 51 52 53 54
116m
0+
-87.87 -90.53 -91.12 -93.40
I ........
........
%(+)
rr-1.5
........ ,
...........
, . . . . . . .. . . . .......... -0.27
+3.46 ...........
13(+)
16 m
· ... .. . . .. .
· . . . . . . ... .
rs;-
2.71. 5.0 h
+2.67
-0.4
1-93.42
117 118m
66
1~95.16 ...
118 119 120
67 68
1-94.43
1H
120 121 122m'
69 70
1-
94 92 .
1H
~96:07 ...
it!
~96:188 .. ~~)
1.15, ..•
·
........... ...........
50 rr.
55
1.3
,
1.......... 1 (8-)
116
rr-0.08, 0.7
0.44, O.4G, 0.82, 1.10,2.00, 2.32, ... 0.50(51), 0.57(22), 0.072(19), 0.044(7)
±2.5 +3.45
'16.5 ill 57.25% 4:2m
±2.3 +3.359
...........
t-
1.9 /,>0.90(35), 1.12(24), 0.81(17), ..•
I' ......... "] . . · · · 1
/'>1 ...................... /'>2.6 . . . . . . . . . .. ........... /'>0.58(32), 1.55(22), 1.82(12), 1.06(9), . . . /'> /'> /'> /'> · ........... /'> · ., ........ 13-, n
0.564(66), 0.686(3), 1.26(1), 1.14(1)
1. 61
....................
/'>.62(50), 2.31(22), 0.24(11),1.60(5), . . . ±2.6
1.972
3.7 1.60
4.3 2.4
.................. 13.4 ITO.025(100) ITO.Ol(80),0.505(20) 0.644(20), 0.603(20) 0.603(97), 1.691(50), 16.5 0.722(14), 2.091 (7), 0.644(7), . . . 0.427(31),0.60(24), 0.634(11), 0.463(10), 0.176(6), . . . 0.41, 0.67, . . . 0.29,0.41,0.58,0.69,0.85, 0.99, . . . 0.685(35), 0.473(22), 0.784(13),0.253(9), 0.604(5),0.543(3), . . . 0.314, 0.53, 0.64, 0.75 . 0,75(200),0.32(83), 1.07(4) 0.916, 1.03, 0.683, 1.73,
'"d
t:d
0 '"d (:I:j
t:d >-3 H
~ 0
l:;J
2i
... 0.20, 0.82, 1.03, 1.16 ~5
~3
0.19, 0.33, 0.82, 0.94 0.95(48),0.64(37)
q 0
t-< H t::I
~6
(:I:j
~4
[J1
/'> a3.28 1~1O a3.1, {J'", p2.6, 3.4, 3.7 ~7 {J'", p ~9 {J'", p2.46, 2.67, 2.82 13+ ................ ......... ITO.275 . " ........... 13+2.8, . . . , ,(20) 4.5 1 0.72(34), 1.28(32), 1.38(32), 1.08(24), 0.96(6), 1.58(6)
...
..........
1~3
00
I w
~
8b-1.
TABLE (1)
I
(2)
Atomic Symnumber Z
bol
I
(3)
(4)
Mass Name
number A
I
(5)
52
Te
(7)
(6)
(8)
(9)
(Continued)
(10)
(11)
(12)
(14)
(13)
Cf .... 0
Number of
neutrons
N
----
PROPERTIES OF NUCLIDES
Mass
Magnetic
excess,
Spin and
amu X 10-'
parity
% abundance 0: half life
Quadrupole
moment,
moment,
nuclear magnetons
barns
Mode of decay, energy, and intensity, MeV(%)
/l-decay
Q values, MeV
Energy and intensity of 1'-ray transitions, MeV(%)
2,200-m/s neutronabsorption
cross section I barns
-- --- --Tellurium
116 117 117m 117 118 119m
64
-91.7
0+
65 66
-91.40 -94.
H
.-0+ 11
IH
119
67
1-93.60
120 121m
68
1~95:98 ... 1¥_
121 122 123m 123
69 70
-95. -96.944
71
-95.718
124 125m 125 126 127m 127
72
-97.170
75
-94.79
128 129m
76
-95.532
129
77 [-93.40
130
78
H 0+ 11 -2--
H 0+
11 -t--
73 74
-95.574 -96.688
H
0+ (1"'--) (H)
0+
-"-11
-93.768
[H 0+
2.50 h 1.9h 0.1 B 61 Dl 6.0d 4.7d
15. ~ h 0.089% 154 d
............ ...........
. . . .. . . . . . .
...........
...........
...........
...........
±0.25
............
...........
~
~
""f
rJl H
orJl
117 118 119 '120 121 122
63 64 65 66 67 . 68
-,80. -84. -84.8 -88. -88.5 -91.
123
69
-91.6
124 .125m 125
70
-93.9
0+ 0+ 0+
0+
(J.~_)
71
-93.5
(H)
126 127m 127
72
-95.71
0+
73
-94.8
(H)
128 129m 129 130 131m 131 132 133m 133 134 135m 135 136 137 138
74
-96.468
0+
75 76
-95.216 -96.491
77 78
-94.915 -95.843
79 SO
-94.19 -94.602
81 82 83 84
139
85
140
86
141 142
87 88
(J.21.-)
1._.1._ 2
t+
0+
1.i-1+ 0+
(J.2:l-)
-92.86 779
~92.
(1+) 0+
(J.'l-~) (h)
0+
~88:26 ~86:
0+
-81.6
/-79. ..........
L1m 6m 6m 41 m 39m 20 h
..........., •.•...•.... E, fi+ ........... ........... f3+ ........... fi+ · . .. . . . . . . . • •••.•.••.• , E ·.. . . . . . . . . ........... f3+2.8 ........... ........... «100)
2.1 h
...........
0.096% 558 17 h
........... ........... · . .. . . . . . . . ... -.-....... ..........., ...........
0.090% 70 B 36.4 d
...........
1.92", 8.0 d 26.44% 4.08", 11.8 d 21.18% 26.89% 2.261 5.,27 j 10.44% 15.6n 9.2h 8.87% 3.9 Ul 14m
............... ................. -0.7768 ........... ............... ........... ........... . . . ... . . . . . . . . . .. ........... . . . . . . . . . . . . . . . . . . . . -0.12 +0.6908 ... . . . . . . . . . . . . . . . . . ............ .....................
........
I .......... 1 ........
1148 1. 78 1.15 ,
4.7
......... I> .... I>
~
0
>,j
toJ
l:O 'd
P::
~ I-
oj
Z q
(")
t' .....
t1 l':J
rJl
...
0.303(15), 0.384(7), 0.276(6), ... ..................... 12 ITO.268(100) ..................... 15.8 ITO.164, 1.05, 0.82 ..................... 1~4 ITO.6616(100) . .................... 5.1
'fI>.fJ
c.n
TABLE (1)
I
(3)
Atomic Syml!Iumber hoI Z
I
(3)
Mass Name
B.
57
I:
L.
(5)
I
Number of
n~~ber
neutrons N
A
- - -. - 5fi>
(4)
8b-1.
PROPERTIES OF NUCLIllES
(6)
(7)
(8)
Mass excess, .mu X 10-3
Spin and parity
% abu'ldance
(9)
co \
(Continued)
~
(14)
(11)
(12)
(13)
Mode of decay,
Il-decay Q values, MeV
Energy and intensity
neutron-
of l'-ray transitions,
absorption cross section,
(10)
0':>
2:200-m/s
or half life
Magnetic Quadrupole moment'; moment, nuclear barns magnetons
--- -- ---
energy. and- intensity, M"V(%)
MeV(%)
barns
..
Barium
1Lanth.num
-94.76 -91.17 -89.36
138 139 140
82 83 84
141
85
\-85.8
142
86
1-83.5
143 144 124 125 126
87 88 67 68 69 70
-71t. -77.
127
(~-) 10+ 0+
71
-84.
129 130
72 73
~87.
131
74
1-89.9
~~'-3(72i:2:~i23): ' - :..
I: ::: :: :::::
12.8 d
I ........
18 m
........... ...........
tr3;O, 2.8, 2.6, 2.4, 2.0,
3.0
10+
11m
· . . .. . . .. . .
tr1.0, 1.7
2.2.
12 s 11.4 s 7m ;:0
~
2;1 H
C"l 172
62
63
1 Sm ·1 Samarium
1 Eu 1 Europium
140 141
78 7~
-82.
142 143m 143
80
-84.9
0+
81
-85.26
(¥-) (H)
144 145 146 147
82 83 84 85
-87.93 -86.52 -8,6.90 -85.08
0+
148 149 150 151 152 153
86 , -85.15 87 -82.79 88 -82.70 89 -80,04 90 -80.24 91 -77,88
0+
154 155 156
92 1-77.78 93 -75,35 94 ..,.74.46
14m 23m
...
(t)-
0+
]1-
.,.
]1-
0+
CH-) 0+
1+ 0+
!H
0+
157 142 143 144 , 145
95 79 80 81 82
-79,9 -81.13 -83.61
(i+)
146
83
1-82.74
1 (4-)
(Hi H (!+)
........... · . . . . . . .. . ........... ............
(J+ '~4.4
" (J+
72.5m 65.• , 8.83 m
........... ........... .(94), (J+1.03(6) ........... ............ . ................... ........... ·. . . . . . . . . . P+2.47(50), .(50)
3,09% 340 d 1.00 X 10' Y , 1.07 X 10" Y , 14.97% 11.24% 13.83% 7.44% 90 Y 26.72% 47 h
............ ........... ..................... ........... ........... .(100) '........... · .... - .. -. ,,2.50
22.71% 23m 9.4 h
0.5m 1.2m 2.6m 10.5 s 5.8 d
14.6 d
2.05 3.49
ITO.750(100) 1.055(3),1.51(1),1.17(1),'
0.638
o.o6i4(i3): :.: :....... ,I :~i~
~
-0.813
-0.20
,,2.232
. ... , ... ; ...•...... ,. '175
... ........ ........... .................... . .................... -0.670 +0.058 ...................... . .................... .......... · . . . . . . . . . . •••...•• ·.r •.•••••••. . .................... ........... ........... P-0.076 (98) 0,076 0.021.7(2) ........... ........... . ................... ......... ...................... -
-0.022
+1.2
P-0.70(48), 0.63(32), . 0.80(20), ... :
0.801
148
84 1-83.18
85
1-81.81
I(H) 1(5-)
4.73 ,40,000 102 15,000 210
0.103(28), 0.070(5), •.•
. . . . . . . . . . . · . . . . . . . . . . . ....... ............. ......... . .................... ....... .... ±O. 9 P~1:54(92), 1.4(6), .••• ·1.65 (U04(93), 0.246(5), ••• ........... ......... " p-0.72(51), 0.43(44), . 0.72 0.088(30), 0.204(20), ~
........... ........... ........... ........... ...........
........... · ... .. ... . . ........... ............
P-
1l+4.0(100) (J+5.2, ..• .... , ..... ' .(96), P+1.72(1.5), 0.79(5)
I. ...... , ... 1........... 1.(96), (J+1.467(3.5),
5.0 6.33 2.72
3.872
122d
I........... 1, .......... 1.(99), (J+0.747(0.6),
1. 767
l54d
0.622(0.4), 0.548(0.3), «2.90(0.002) I........... 1..... , ..... 1.(100)
3.10
1.659, 0.820, 2.481 0.894(67), 0.654(15), 1.658(14), 1.997(7), 0.543(5), •.. 0.747(100), 0.633(40), 0.634(37), 0.704(9), 0.666(7), 1.53(6)•..• 0.1212(46),0.1974(32), 0.678(12), 0.602(8), 0.799(7), .•. 0.550(100), 0,630(72),
0.611(20),0.553(17), 0.726(12),0.414(8), •.•
to1
~
>-
:J
Z
cj ~
. 0.11 'C 0.386, .. ·i.ilz, 2.0 .
t"
1.32, 1.66,
H
t::;1
t>:J rJ2
. 0.072, 0.067, 0.315, 0.387, 0.296,. 0.627, 1.20, 1.89, 2.60,
~0.8
~
.(99); /1'"1.2(1)
2.0
1.21
«100)
0.826(63), 0.211(9), 0.592(8), 1.17(8), 1.37(5), 0.305(3), •• ..................... 1160· 0.44(0.06), 1.11(0.05),
...
.................... ±2.2
ITO.046, 0.052, 0.037 0.091(5) 0.073(5) ..................... 165 0.184(90), 0:810(60), 6.711(58),0.081(12), 0.412(~~), 0.532(12),
I
i.
29 h 3.1 h
±O.65
-
p-o.07, ...
...........
IT0.0578, 0.383(6,s) 0.081(8) . ITO.30(100)
..................... 0.37
r13 .
00
I
01
'"
TABLE
(1)
(2)
(3)
(4)
(5)
N.me
Mass number A
Number of neutrons N
Atomic
Symnumber bol Z
--- -68
Er
Tm
8b-1.
PROPERTIES OF NUCLIDES
(7)
(8)
Spin and parity
% abulldance or half life
Mass excess,
amu X 10-'
Magnetic. Quadrupole moment, moment, nuclear barns magnet'()Ds
166 167m
ThujiuJI:
98
-69.69
(11)
(12)
(13)
(14)
Mode of decay, energy, and intensity, MeV (%)
Il-decay Q values, MeV
Energy and intensity ot 1'-ray transitions, MeV(%)
2,200-m/s neutronabsorption cross section, barns
fl-
D+
49 h
0+ 1
.......... fl-
170 171
99 100 101 102 103
-67.92 -67.60 -65.38 -64.51 -61. 94
172
104
-60.63
173
105
-57.3
H 0+ 1
fl-
0+ 5
........
.
........
........... . .......... . ... .. . . ... . ..........
93 94
.......... (3) -66.0 ........ -67.33 t(+)
77m 22m 1.8li
........... . .......... .(100) ........... . .......... !fi"3.82, 2.3, . . . " ........... " !fi"1.1, 0.40 ±0.08
95
-66.51
1.9m
........... ........... .(61), !fi"2.94(26),
...
151 161
85 92
162 162 163
...
164
-51. ..........
-58. -66.2
........ ........ ........
12m
........... ........... .................... ......... ........... ........... . ................... . ........ -0.564 .................... ......... +2.8 ........... ........... .................... ......... +0.513 ........... p-0.34(58), 0.33(42) 0.340 ........... ........... .................... ......... ±0.70 P-1.065(91), 0.58(4), ±2.4 1 490 1.49(2) . . . . . . . . . . ........... p-0.36(44), 0.29(42), 0.9 0.9(10), ... ........... ........... p-2.3(70), 1.8(30) 2.8
1.6. 3.0 s 5. 30 m
84
ill!
(H)
. .......... ........... ........... ...........
a5.11 a5.04 a4.96 .(100)
96
-67.56
t+
30.1 h
...........
...........
,(99+), t/+0.30(0.007)
..................... ITO.2078(100) . .................... . .................... 0.00842
30
. . . . .. . . . . . . .. . . . . .. .
6
0.308(63), 0.296(28), 0.112(25), 0.124(9), ... 0.407(40),0.610(40), ... 0.20(60), 0.40(30), 0.18(20), 0.52(20), 0.36(19), 0.16(18), ..•.
~8
3.5
... .. . .. 4.89 2.42 3.95
1.57
700 1.9
zq Cl
t"'
l'J
>-~
~
~ H
Cl U1
~7
2.85(13) 165
00
--33.41% 2.3 s 22.94% 27.0'1% 9.4 d 14.88% 7.6 b
...
153
Cf c.n
(Continued)
(10)
(9)
-- --Erbium
167 168 169
69
(6)
.
0.0456, 0.0595, 0.1061, 0.1126, 0.0845, 0.147, 0.172, •.. 0.102(100), 0.236(13) 0.102 0.104(8),0.24(5),0.29(3), 0.24(3), ... 0.091(4), 0.356, 0.39, 0.77, 0.86, 1.16, 1.31, 1.67, ... 0.243(50), 0.297(35), 0.807(15), 0.34(10), 1.13(5).0.70(2) . . . .
97
1-1J6.42
12+
7.7 h
167
98
1-67.12
IH
9.6 d
168
99
1-65.77
I ........
85 d
...........
169 170 171 172
100 101 102 103
1-65.76 -64.17 -63.54 -61.39
2111
100% 129 d 1. 92 Y 63.7 h
-0.232 . . . . . . . . .. .................... ±0.246 f3-0.97(77),O.885(23) ±0.57 ±0.229 ........... 1'0.098(98),0.03(2) · . .. . . . . ... ........... 1'1.80(39), 1.88(23), 0.41(14), 0.28(10), 0.71(8), . . .
173
104
1-60.35
174
174 175 176
70
I
Yb
I Ytterbium
2-
18.2 h ... 1
105 106 107
166 167 168 169
961-66.14 97 -65.02 98 -66.08 99 -64.78
100 101
155 15 mm
1-52.9
84 85 92 93 94 95
5.2 m
1-57.8 -56.1
154 155 162 163 162.25(100) 1>1.34(87), 1.1(13) ,8""3.3 a5.68 a5.27
0.497
2.25 1.34 3.3
0.113(14), 0.208(7), •••
t
'-l
8b-1.
TABLE (ll
(2)
Atomic Symnumber bol Z
(4)
(5)
(6)
(7)
(8)
Name
Mass number A
Number of neutrons N
Mass excess, amu X 10-3
Spin and parity
% abundance or half life
OF
NUCLIDES
Magn~ti:c moment, nuclear .m~.gp.eton~
'f
(CiJiitinued)
0;,
(10)
(11)
(12)
(13)
(14)
Quadrupole moment, barns
Mode of deeay, . energy, ann intensity, MeV(%)
/l-decay Q values, MeV
Energy and intensity of l'-~ay transitions, MeV (%)
2,200-m/s neutron· absorption cross section,
(9)
Ir
Iridium
192m, 192ml
... ...
...... .......
9(+) 1(+)
>5y lAm
192
115
-37.36
4(-)
74.2 d
11
193m
...
.. .
193
116
-37.04
194m 194
...
...
117
-34:88
~
..
barns
. ......... ......... .... (3-1.2(0.008), 1.5(0.007), .. .
......
±L8
12 d 62.7% 171 c' 17.4 h
-'2.--
H 1-
195m
..........
+0.158
4.0 h
+1.2
...........
ITO.161(100) ...... ITO.058(9H ), 0.317(0.008), . . . 1,100 1'0.672(49), 0.53(42), . 0.317(81), 0.468(49), 1.4'57 0.24(5), . . . 0.308(30), 0.296(29), ,(4) 0.604(9), 0.612(6), . . . 1.2 .................. 0.05 ......... ITO.080(100) 120 .............. ... 1l-"2.19, 2.49
1.......... ll,?--
3.9"
193m
",6.12 ",5.92 ",5,85 ",5.62(55), 5.48(45) ",5.34
1.3 s 2,6 s 7.2 s 11. f; s 50 S 1.0m 4,3 ill 12 m 8m 8m 4.7 m 30 m
E,
...
(3+
" 1>", ",5.07(0.01)
... " ",4.69
~3
1-36.
IH
16 h
±0.139
.(100)
194
115
1-34.58
11-
39.5 h
±0.074
.(97), 1>"1.5(2), 1.2(1)
195 196m
116
I, ........ 112t.-
31 s
34 . 95 1-.......... I12(-) ~+
183 d. 9,7 h
~4.4 ~2.0
3.5
.(0.03)
114
~1
2.51
....................
±0.147 ...........
.(100)
q
0.16, 0.22, 0.30, 0.10
t" t9
0.25, 0.33, 0.63 0168(80) 0.713,0.448,0.813,0.168,
il1
~4 ~5
............
0.163,0,273,0.362
~5 ~6
193
195m
Z
~7
0.229
0.29,0.60, . . . 0.030, 0.048, 0.091, 0.278, 0.133, . . . 0.316,0.157,0.{)451, 0.295,0.105,1.140, . . . ITO.0323, 0.258, 0.220, 0.291, . . . 0.18(11), 0.26(9), 0.114(5), 0.440(3), . . . 0.328(68), 0.294(12), 1.469(8), 1.887(4), 2.044(4), 1.596(3), ••. ITO.0567, 0.2615(97), 0.200(2), ..• 0.0985,0.0308, . . . ITO.148(42), 0.188(32), 0.285(5),0.316(5)
0
> ~ '"ti
><j Y.l H
@
196
117 1-33.44
I. ....... I-\L
197m 197
80
I Hg
I Mercury
IH
16.18 d
........... .(94)
+0.58 or -0.62
+0,14486 +0.590
...........
1-31.23
H
3.15 d
+0.270
...........
121
1-29.3
1(1-)
48.4 m
12.2 q3 124 125 99
-28.1 -2,5.6 -24. -21.7 -17. -2'1. ':
0+
26 m 30 s 5,5 s 4s 3.5 B 5.. 9 s 3'.6 B .. 10.5 s 8.8 s 32 B 52 B 1.4n 3m 3.3 Iol 9m 20 m
199
120
200 201 20.2 203 2.04 179 180 lSI 18'2' 183 184 185 186 187 188 189 190
ioo 101 102 103 104 105 106 107 108 109 110
-22. -24. -25. -27. -28. -30. -30. -32. -32. -33.
111 1-3,. 112 -34.
I.
193m
193
113
1-33.
194 195m
114
1~34:.
+0.58
...........
i-·······,···
·
..........
........... ........... .............. ..... .........
· ..........
1>1.5 1l-3.5(90), 3(10) 1>1.9 1>4.5 a6.08 0'1.17(2)
0.368(24), 1.227(23), 1.593(1), ... 0.54 0.44(10), 0.52(0.3) '0.69 '0.43
98.8 25,800
>-'3 >-< i?'.J
'-'2
....... - ...
0.412(99), 0.676(1), 1.088(0.2) 0.1584(73), 0.2082(21)
i:d
!~4
I .•.•
ITO.130, 0.279, . . . , (100) .................
i"
,.,0.961(99), 0.29(1),
"'0.30(73), 0.25(2), 0.45 0.46(6) · ........... 1>2.2(70), 0..7(25), . . . ' 2.2
55 m
. ..ll(+)
• • • • • • • • • • • • • ••
0.356(94), 0.333(25), 0.426(6),1.091(0.2)
0.684
............... '....
100% 2.697d
118 1-33.45 119 -31. 769
1.48
1>0.259(6) 7.4.~ ,
2-
198
191 192
12-
:0.12,0.27,0.35,0.44 0.175,0.255, Q.400 0.140 '0.165,0.240,0.320,0.500 , 0.0288, 0.143, 0.130, 0'.155, ••. 0.26, ... 0.274(100), 0.157(20), 0.114(10), . . . ITO.0395, 0.1012(16), 0.257, 0.218, 0.574, 0.220, ... 0.038, 0.187, 0.564, 0.762, 0.855, 1.040, ...
Z
tj 0 t
-
-< Cl
Ul
(7+)
196m 196
115
1-29.
191m
'+1.55
7+
2-:-
5.3 h
± tI
~
o
11.0 .22
43 ...................... ,&-1.80(49),1.29(24), .'. 4 . 9.94 1-.52(23), 1.04(5), • . . . ........... , ......... :: ~1.99(100) 'a.98
1.3m 11.1lj 17m 37m
~2.4,
o
':z;I
Z
gd >-
4
Ul
202m
1.......... 19-
I
202 203m
120 1-27.97 H .......... (¥-+)
203
121
1-26.60
122 123 124
-26.96 -25.52 -25.53
204m 204 205 206
....
207m 207 208
209
I(~-)
90+ (~-)
0+
.-
J24
125 126 127
-24.097 -23.34 -18.90
1
13.62 h
~3X105y
...........
...........
6.1
...........
...........
B
52.1 h 66.gm 1.43% 3 X 10 7 y 23.$% 0.71 B
.
22.~%
0+
52_3% 3.30 h
(H
· .. .... .... ........... .(10)
........... ...........
.(100)
.................... «100)
.. ....... IT0.422(90), 0.961(90), 0.787(45),0.658(35), 0.490(10),0.460(8), . . . 0.05 . . . . . . . . ITO.825(92), 0.820(10),
·
...
0.98
0.279(81),0.401(5), q.680(1) ........... . .......... . ................... · . . . . . . . ITO.9Q, 0.3.75" •.. ........... ........... .................... ......... ..................... 10.66 · . . . . . . . . . . .. , . , ...... .(100) 0.04 , ...... ... . . . . . . . . . . . . . . . . . . . ......... 1 ..................... 10 . 30 ........... . . . . . . . . . . . . . . . . . . . · . . . . . . .. ITl.064, 0.570(100) +0.5895 .................... .............................. 0.71 ...... , .... .., ...... , .......... ......... ..................... 10.015 ........... ,s-0.635 0.64
.
,
.
.
H
0
Ul
210
128
-15.80
0+
22 Y
129
-11.23
(H)
36.1 m
130
-8.11
0+
10.64 h
131 132
-0.16
(l4>D)
211 (AcB)
212
........... ........... /1""0.017(81),0.063(19) ..3.72 ........... ........... /1""1.37(92),0.53(6), 0.95(1),0.25(0.7), ..• ........... ........... /1""0.34(81), 0.58(14),
0.063
10.0465
1.37
I
........... ........... /I"" ........... · . . . . . . . . . . /1""0.69(42),0.74(36), 1.03(6), .••
2 1.04
0.57
0.400(3), 0.832(3), 0.427(2), 0.766(1), ••• ' 0.239(47), 0.300(3), .••
(ThB)
213 214
-304
10.2 m 26.8m
(RaB)
83
1 Bi
1Bismuth-
1190 191m 191 192 193m 193 194 195m 195 196? 197 198 199 200 201m 201 202 203
107 108 109 110 111
-13. -14. -16. -16.
112 113 114 115 116 117
-19. -19. -21. -21. -22. -22.
118 119 120
-23. -22. -23.17
15.
40. 3.2. 70. 85. 50. 2.5m .......... 7.8m 8m 11.9m 9 24.7m 2 7 35m 59, n 9 1.8 h 5 95m 11.8 b 2-
..
•
........... ........... . .......... ........... ........... . .......... ........... ........... ........... . .......... ........... ........... ........... ........... ........... ........... ........... +4.59
204
121 1-22.
16+
111.2 h
+4.25
205
122 1-22.62
I!-
15.3 d
+5.5
206
123 1-21.61
16+
16.24d
+4.56
207
1 124 1-21.52
I(H
130 y
........... ........... ........... ........... ........... · . . . . . . . . .. ........... ........... ........... ........... ........... ........... ........... ........... ...........
I
-0.41
..6.31 a6.06
"d
~
a6.50 a5.90 a5.61 a6.10 ",5.42
0
"d
-.l:;j
~ >-:3
E, a:5.~
~8
«99+), a5.81(0.05) .................... «99+), a5.48(0.01)
~5.li ~7
>-
< 10- 4 s
........... ........... a8.38(100), ..• ........... ......... " a7.688(100), .•.
131
-0.55
(i,H)
1.78 X 10-' B
132
1. 92
0+
0.15 s
........... ........... ,,8.384(100), ••• 1>(0.0002) ........... ........... ",6.777(100), ..•
133 134
6. 9.01
0+-
-~
2.237
0.563 1.40
6.13 h
........... ...... ..... ty-L19(35), 1. 76(20), 2.10(13), 0.62(6), •...
66 m +p'.~
............
(0.-)
'1.17 m
~
43.35
(H)
:6.75 h
:-
234 (UZ)
143
, 235 236 237
144 145 146
45.4 49.0. 52:22
22i 228
135 1.36
31'. 31'.38
;o.f:
229
137
33.50.
'(if)..
2~.7m .
... 12m 39m
.
:1.3 III 9.2m 5~m
..
............., ,.....
,'7~.,O,
., 11-0..26(55),,0..15(40.) •. 6.5~(5) . .-. ... ,... ,......... ,. ,1i~2.. ~9(98) ,., .
.... ,..,.. ...... .......... ..... ... ........... ......... ............ ....... ...... -.,. ;. .......... , ,
1.29 0..5.6
0..954(,,0.), 0..91(24), 0..45(18), 0..51(8), •••
Fission 1,50.0.
0..0.27(6),0..29(6), •.•
20.0. Fission O.Di
~.
0..87(51).0..971(40.). 0..150.(12). 0..46(9). , 0..1;7(8). 0..107(5) • ••• 0..31(34). 0..30.0(6); i 0..341(4) • .. : ITo..D7(o..l).o..043(2). 1.0.0.(0.,6); •.. 0..90.(70.). 0..10.0.(50.). D.126(2~). D.7D(24}, 0..56(15). 0..22(14) ••
760.
1# >-< t::J
m 0 "'l
:z: tJ
(")
...........
...........
ITO. 048(99.5), •.. 0.042 0.045 0.075(61), 0.044(5), . . . 0.043, ...
0.91
...........
0.98(SO), 1.35(76), 0.58(29), 0.36(12) 0.228(lS),0.278(17), 0.209(5), 0.06S, 0.057, 0.049, . . . 1.00(77), 0.90(23), lAO 0.060(36), 0.026(3), . . . 787 Fission 3.3
(fJ.
/l-0.91(78),0.65(17), 0.60(5) /l-
.. . . . . . . . . .
1,371 Fission 1,011 20 271 Fission 196 1.8 260
1.5 ~2.3
. . . . .. .. . . .
TIl
ill
0.020S
.................... 1.2, ... /l-0.15(90), 0.33(10)
1. 9 h (%-)
,/l-0.0208(9H), a4.90(0.002), . . . .. a4.90(76), 4.S6(24) /l-0.58(61),OA9(38),
~0.93(48),
~1.8h
5(-) 1(-)
......
+5.6
8 X 107 Y 10.5 h 10.9 d
55.
244m
. 245
(H)
-0.73
t" t:I
H
1:9
(fJ.
-3 0
;s::
....0
;s::
~ l/l l/l
"'1
0
~
;s:: q
t"
~ l/l
Cf
Q)
:::;:
>-
(!)
0:: W
Z. W
(!)
Z
o
..
Z
In
~
~
..J ::J
~
-5
5 z
0::
o
0::
f5
,
c.-
2
...
-2
2
0
. ..
d.
0
-2 + 40
60
100
140
160
MASS NUMBER A
8c-1. Errors of calculated binding energies versus mass number A: (a) for mass la:w with volume term and Coulomb energy only, fitted with 1 parameter to odd-A binding energies; (b) for 4-parameter liquid-drop mass law; (c) residual errors for odd-A nuclides, far Ef1~ (8c-3) fitted to 1,148 odd-~and even-A nuclides; (d) same mass law, residual errors of eveneven (+) and odd-odd (0) nuclides.
FIG.
8-95
ATOMIC MASS FORMULAS
The expansion of Eq. (8c-2) is accurate only to the extent that the discrete levels occupied by nucleons can be represented by a smooth distribution, and the structure apparent in Fig. 8c-1b is due principally to the breaking down of this assumption. A correction term to the liquid-drop mass law .can be constructed by comparing a single-particle-Ievel diagram such as that of the Nilsson model to a smoothed average of the same levels. The method used is that of Strutinsky, extended by Tsang [13], who has shown that the results reach a limit which is independent of the details of the smoothing. The calculations [9] yield two functions IJUN(N,.) and oUz(Z,.), where. is a measure of the spheroidal deformation of the nucleus. The coefficients of these functions in the mass law depend only on the radii of the neutron and proton distributions, rNAt and roAt, respectively. The parameter rN is new, but ro is the same radius constant which describes the proton charge distribution in the Ooulomb energy. Pairing correlation energy cannot be included in an average nuclear potential. It is calculated by applying the Bardeen-Oooper-Schdeffer (BOS) formalism to the single-particle levels, using as the average pairing matrix element G N 1/A. For a given value of the one adjustable parameter GNTN 2 = Gpr02, the BCS ground-state energy for each particle number is found, and the difference in binding energy between it and the sum of the Nilssonlevels is called PN(N,.) or P z(Z,.) [9]. Since the presence of an unpaired particle decreases the binding energy of the BOS. solution, the evenodd mass difference is calculated directly with no additional parameters. (A simple alternative phenomenological form for the even-odd difference is ± 0/At, where the + sign is for even-even nuclides, - for odd-odd, and the term is omitted for odd A. ,The least-squares determined value for 0 is 10.6 ±1.1 MeV.) It is known that many nuclei, e.g., the rare earths and actinides, have nonspherieal equilibrium shapes which are represented approximately in the Nilsson model by spheroids. The terms 0U and P are explicit functions of the deformation paramete'f E; the surface and Coulomb terms in the liquid-drop mass law can also be expanded in powers of t. Then by maximizing total binding energy with respect to E, the equilibrium deformation '0 is found; the results [9] agree qualitatively with experiment. Several, uther small terms ::tTe included in th" m""" 19w. In the Ooulomb energy there arlO an .exchange term [2] and a correction for the diffuseness .of the nuclear surface [8J. A first-order term in (A - 2Z) / A seems to be required to represent extra binding of nuclei with N = Z; a rapidly decreasing exponential is used [8]. The binding of the atomic electrons [14] is included, although small, to prevent falsification of other terms. The complete formula is, in MeV, B(Z,A) =
a
A _ !3(A - 2Z)2 _ [
A
I'
Ai _1/(A A,- 2Z)2] (1 +~45
'0
3 2 Z' (1 0.76361 2.453 4. 2 92 - (; e roAt Zi - r02Ai - 45 EO - 2,835
+ 7 exp ( - 61A ~ 2ZI) + 14.33 X 10-6zz.39 + oUN(A -:-: Z, '0) + OUZ(Z,Eo) + PN(A - Z,
EO)
2+~ 3) 2,835 EO
3) '0
+ PZ(Z,Eo)
(8Q-3)
The value used fbr !e is 0.864 MeV-fm. 8c-4. Determination and Testing of Coefficients. The principal method used to determine coefficients is least-squares fitting to tables of experimentally derived bind:ing energies. From a statistician's [15] point of view, this is not a valid procedure :because there arecorrelatiG>ns among the data of the mass table. Therefore Eq. -(8c-3) has been fitted both to the mass table and to the raw experimental data. Other methods, e.g., fitting the Ooulomb radius to a fission barrier [8], have also been used. In this m::tss la'lv, the four p9xameters of the Nilsson model were chosen [9] by trial and error to .reproduce known level structures as well as possible. The value for the BOS 2
8-96
NUCLEAR PHYSICS
parameter was found by solving the problem with several values of the BCS parameter, iterating to find the solution which minimized the sum of residuals. The least-squares solution fitting the remaining six parameters to 1,148 binding energies from the 1964 [10] and 1967 [11] mass tables is given in the second column of Table 8c-l, and the solution fitted to 552 mass-spectroscopic doublets [16] and 957
TABLE
Parameter
MeV ........ MeV ........ /" MeV ........ '1, MeV ........ a, (3,
. . . .
ro, fm ... ....... . TN,
fm ......... .
Gp T02. lVIe V -fm 2 ••• Ul,
U2,
MeV ........ . MeV ........ .
8c-1. MASS-LAW
COEFFICIENTS
Fitted to mass table
Fitted to doublets and reactions
15.8089 ± 0.0170 30.157 ± 0.142 20.230 ± 0.052 47.66 ± 0.94 1.18729 ± 0.00229 1. 2285 ± 0.0070 28.70 0.805 0.464
15.8570 ± 0.0322 31.402 ± 0.168 20.337 ± 0.105 53.52 ± 0.92 1.17641 ± 0.00376 1.1983 ± 0.0078 27.67 l. 916 0.449
nuclear reaction Q values [11,16] is given in the third column. The standard deviation is the fit to total binding energies, and U2 is the fit to the doublets and reaction energies. The quoted errors in Table 8c-l are the square roots of the diagonal elements of the error matrix adjusted to force x 2 = degrees of freedom. For the first column they show only the relative uncertainties in the determination of the parameters; for the second column they are a more accurate estimate of statistical uncertainties. The values of the cocfficients are slightly diiTel'enL from those in the "Winnipeg Proceedings" [9] because of the elimination of the free parameter in the Strutinsky smoothing and the addition of a neutron radius different from the proton radius. The residual errors of the calculated binding energies with the coefficients of the first column are Showl1 for odd-A nuclides in Fig. 8c-le, and for even-A in Fig. 8c-ld. The systematic errors remaining above A = 200 are due to undercorrection for the doubly closed shell at 208Pb and to higher-order shapes of deformation [13]. Figure 8c-ld indicates systematic differences between even-even and odd-odd nuclides, demonstrating that the even-odd mass difference as calculated by BCS theory in this mass law is not accurate. Different forms for the A dependence of the pairing matrix element, e.g., G '" 1/A 0.8, were found to give a qualitatively better fit to even-odd mass differences, but always with a considerably larger sum of residuals than the solution presented here. The first test of a mass law is its ability to fit the known binding energies. In this case the rms deviation is 805 keY. Much better fits have been obtained, e.g., 168 keY by Zeldes [7], but generally by using a large number of phenomenological terms to represent shell, pairing, and deformation effects. Since the probability of successful extrapolation decreases with increased number of parameters, a "figure of merit" is sometimes applied which is the product of the rms deviation and the number of parameters. The mass law presented here has only 11 adjustable parameters, including all model parameters. To test interpolation the data were placed in random order and divided into two groups of 574 binding energies each; to test extrapolation the 622 data with NIess UJ
8-97
ATOMIC MASS FORMULAS
than the stability line were placed in one group and 526 neutron-rich data in another. A separate determination of the parameters was made for each of the four groups, and the sums of residuals were compared to the sum of residuals for the mass law fitted to all the data by applying the variance-ratio or F-distribution test.! The respective values of F obtained for the four groups are 1.04, 0.95, 1.03, and 1.01; since the. F distribution for this number of clegrees. of freedom is approximately normal about 1.00 with standard deviation ±0.07, the statistical test is well satisfied both for interpolation and for extrapolation from either side of the beta-stability line to the other. There is, of course, no guarantee that the extrapolation continues accurately beyond the known nuclides. Wing [17] has developed and used tests for comprehensive comparison of various mass formulas-based on alpha-decay energies asa function of N, neutron-pair separation energies as a function of Z, local roughness of beta-decay energies, the betastability line and the steepness of the valley of beta stability, separation of even and odd mass surfaces, and delayed neutron and proton precursors. No mass laws tested to date satisfy all tests. The ultimate test is use. Two examples of problems involving extrapolation to neutron-rich isotopes which have been used to compare formulas are the r process 6f nucleosynthesis [18] and the study of delayed neutron emitters [19]. In both these cases the mass law presented here behaved well. 8e-5. Table of Binding Energies. Binding energies for 2,827 nuclides calculated from Eq. (8c-3) with the coefficients of the second column of Table 8c-I are given in Table 8c-2. From 16 to 34 isotopes of each element from Z = 20 to Z = 114 are given. The isotope nearest to Green's [20] approximation of the beta-stability line, N·~ Z = 0.4A2/(A + 200), is indicated by a star. The four data columns give, in MeV: the spherical liquid-drop part of the binding energy [first three lines of Eq. (8c-3), with. = 0]; the shell correction oUN(N,.o) + OUZ(Z,EO); the BOS pairing energy PN(N,EO) + PZ(Z,EO); and finally the total binding energy. The deformation energy of the liquid drop is the difference between the final column and the other three columns. Particle separation energies (binding energies of the last particles) for nucleus (Z,A) can be found as follows: Sp(Z,A) = B(Z,A) - B(Z - 1, A-I) Sn(Z,A) = B(Z,A) - B(Z, A-I) Sa(Z,A) = B(Z,A) - B(Z - 2, A - 4) - 28.3 MeV
The energy available for ground-state negative beta decay is Q/l(Z,A)
=
B(Z
+ 1, A)
- B(Z,A)
+ 0.8 MeV
and the end point of the positron energy for decay to the ground state is Q/l+(Z,A) = B(Z- 1, A) -'- B(Z,A) -'- 1.8 MeV
References 1. von Weizsacker, C. F.: Z. Physik 96, 431 (1935). 2. Bethe, H. A., and R. F. Bacher: Rev. Mod. Phys. 8, 82 (1936). 3. Johnson, W. H., Jr., ed.: Proc. 2d Intern. Con/. on Nuclidic Masses, Springer-Verlag OHG, Vienna, 1964; referenced. as "Vienna Proceedings," 4. Forsling, W., C. J.Herrlander; and H. Ryde, eds.: ·"Nuclides Far Off the Stability Line," Almqvist and Wiksell, Stockholm, 1967; also Arkiv Fysik 36; referenced as "Lysekil Proceedings." 5. Barber, R. C., ed.·: Proc. 3d Intern. Con!. on Atomic Masses, University of :Manitoba Press, Winnipeg, 1967; referenced as "Winnipeg Proceedings." .
.
.'
(References continued on
p.
8-142.)
Application of the F distribution is correctly described in report LA-3751 [91; comments concerning it in the corresponding paper in the "Winnipeg Proceedings" are not accurate. 1
TABLE
8c-2.
co' I
CALCULATED BINDING ENERGIES IN MEV
'"
00,
Number of neutrons N
Mass number A
Liquid drop
Z
20 21 22 23* 24 25 26 27 28 29 30 31 32 33 34 35
40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55
20 21 22 23 24* 25 26 27 28 29 30
41 42 43 44 45 46 47 48 49 50 51
BCS pairing energy
Total binding energy
Number of neutrons N
Mass number A
= 20: Calcium
339.1 350.0 360.3 369.9 379.1 387.7 395.7 403.2 410.3 416.8 422.9 428.5 433.7 438.5 442.8 446.8 Z
Shell correction
-1.3 -2.7 -3.6 -3.5 -3.3 -2.3 -1.1 1.0 3.2 1.4
o.
-0.9 -1.3 -2.8 -4.2 -4.9
Z
2.6 2.1 5.1 3.4 5.6 3.4 4.7 1.9 1.9 1.8 4.0 2.6 4.3 3.3 6.1 4.3
340.4 349.3 361.8 369.9 381.3 388.8 399.3 406.1 415.4 420.0 426.9 430.2 436.6 438.7 444.6 446.2
= 21: Scandium
343.2 356.8 367.8 378.2 388.1 397.4 406.1 414.4 422.1 429.3 436.1
-2.5 -3.6 -4.1 -3.7 -3.2 -1.9 -1.3 0.3 2.0 0.5 -0.6
1.2 0.6 3.1 1.3 3.1 0.9 2.5 0.4 0.5 0.4 2.2
341.8 353.6 366.7 375.7 387.8 396.0 407.2 414.9 424.6 430.1 437.7
28 29 30 31 32 33 34 35 36 37 38 39 40
51 52 53 54 55 56 57 58 59 60 61 62 63
Liquid drop
44 45 46 47 48 49 50 51 52 53 54 55 56 57
BCS pairing energy
Total binding energy
= 23: Vanadium (Continued) 442.6 451.2 459.3 466.9 474.1 480.9 487.1 493.0 498.5 503.6 508.3 512.7 516.7 Z
20 21 22 23 24 25 26 27 28* 29 30 31 32 33
Shell correction
1.2 0.2 -1.6 -2.6 -3.0 -3.4 -5.4 -5.7 -6.1 -6.6 -6.4 -6.9 -6.8
2.1 1.4 4.0 2.6 4.3 2.4 5.6 3.6 5.6 4.0 5.6 4.2 6.1
445.9 452.7 461.6 467.0 475.4 479.6 487.4 490.9 498.0 500.9 507.5 509.9 515.9
-3.0 -3.1 -5.1 -4.4 -4.9 -3.7 -2.8 0.9 1.5 0.7 -1.6 -2.4 -2.9 -2.9
t"'
1:9
:> P:I
fot:i
~
;JH o
= 24: Chromium
350.2 366.0 381.1 395.4 409.1 420.5 431.3 441.6 451.3 460.6 469.4 477.7 485.5 492.9
z
q
o
U1
5.2 3.5 7.5 5.3 8.0 5.7 7.2 3.0 4.4 3.4 6.4 4.9 6.6 4.2
352.5 366.3 383.5 396.3 412.2 422.4 435.7 445.3 457.2 464.6 474.2 480.2 489.2 494.0
31 32 33 34 35 36
52 53 54
55 56 57
442.4 448.3 453.7 458.7 463.3 467.6 Z
20 21 22 23 24 25 26* 27 28 29 30 31 32 33 34 35 36 37 38
42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
20 21 22 23 24 25 26 27*
43 44 45 46 47 48 49 50
1.1 3.0 1.8 3.9 2.3 4.4
441.6 448.8 451.7 458.2 460.4 466.3
4.8 3.6 7.0 5.1 7.4 5.0 6.6 3.2 4.0 3.4 6.0 4.5 6.2 4.4 7.8 5.8 8.0 6.0 7.6
347.9 360.3 376.1 385.7 398.5 407.3 419.3 427.5 438.1 444.2 452.4 457.1 464.8 468.3 475.5 478.3 484.8 487.2 493.1
2.8 1.4 4.8 2.7 5.0 2.4 4.4
348.3 361.4 377.9 390.1 403.6 413.1 425.7 434.7
= 22: Titanium
346.4 360.7 374.3 385.5 396.0 406.0 415.5 424.5 432.9 440.8 448.2 455.2 461.7 467.8 473.5 478.7 483.6 488.1 492.2 Z
-1.8 -2.4 -3.5 -4.2 -5.0 -5.4
-3.3 -3.9 -5.3 -4.9 -4.9 -3.7 -2.9
O. 1.2 0.1 -1.7 -2.6 -3.1 -3.7 -5.8 -6.2 -6.7 -6.9 -6.7
= 23: Vanadium
348.7 363.8 378.1 391.8 403.0 413.7 423.9 433.5
-3.3 -3.7 -5.1 -4.4 -4.5 -2.9 -2.6 0.3
1.1
58 59 60 61 62 63 64 65
34 35 36 37 38 39 40 41
499.8 506.3 512.4 518.1 523.4 528.3 532.9 537.2 Z
20 21 22 23 24 25 26 27 28 29 30* 31 32 33 34 35 36 37 38 39 40 41 42 43
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68
21 22
47 48
350.9 367.4 383.2 398.2 412.6 426.3 437.8 448.7 459.1 469.1 478.5 487.4 495.8 503.9 511.4 518.5 525.2 531.5 537.4 543.0 548.1 552.9 557.4 561.5
I
8.4 6.3 8.6 6.2 7.9 6.3 8.0 6.1
502.4 506.5 514.3 517.8 524.9 527.9 534.5 537.1
2.6 1.0 4.7 2.4 5.0 2.2 4.5 0.6 1.9 1.0 3.8 2.4 4.1 1.9 5.7 3.5 5.6 3.8 5.4 3.9 5.7 3.9 6.0 4.4
351.6 366.2 384.0 397.6 414.2 426.8 440.7 450.9 463.5 471.6 481.8 488.4 498.1 503.6 512.6 517.4 525.7 529.8 537.5 541.2 548.3 551.5 558.1 561.0
2.3 6.1
369.4 387.9
= 25: Manganese
Z
I
-5.8 -6.0 -6.7 -6.5 -6.4 -6.7 -6.4 -6.1
368.0 384.5
-1.9 -2.1 -3.9 -3.0 -3.4 -1.7 -1.6 1.8 2.4 1.6 -0.5 -1.4 -1.8 -1.9 -4.5 -4.6 -5.1 -5.4 -5.2 -5.7 -5.4 -5.2 -5.3 -4.9
I>
"3
o
~ H
Q
~
I>
Ul Ul
6 ~
c:j
~
= 26: Iron
I
-0.9 -2.6
b ~
TABLE
Number of neutrons N
Mass number A
Liquid drop
Z
23 24 25 26 27 28 2.9 30 31* 32 33 34 35 36 37 38 39 40 41 42 43 44
49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
49 50 51 52 53
Shell correction
CALCULATED BINDING ENERGIES IN MEV
BCS pairing energy
Total binding e,nergy
Number of neutrons N
400.2 415.3 429.6 443.4 455.0 466.0 476.6 486.6 496.2 505.2 513.9 522.0 529.8 537.1 544.0 550.4 556.6 562.3 567.7 572.7 577.4 581.7
-2.3 -2.5 -1.5 -0.4 2.9 3.8 2.8 0.7 -0.1 -0.6 -1.0 -3.5 -4.0 -4.6 -4.4 -4.3 -4.6 -4.4 -4.1 -4.5 -4.1 -3.6
402.2 419.4 432.7 448.8 459.6 472.9 481.5 492.4 499.7 510.0 516.0 525.7 531.0 539.9 544.7 552.9 557.1 564.8 568.6 575.7 579.1 585.7
2.1 0.5 2.1 0.1 1.5
387.3 402.3 420.2 434.2 450.8
= 27: Cobalt
385.0 401.4 417.1 432.2 446.6
0.4 0.7 1.2 2.2 3.0
Liquid drop
Z
4.2 6.6 4.5 5,8 1.9 3.1 2.3 5.1 3.6 5.3 3.2 7.1 5.2 7.4 5.1 6.8 5.1 6.9 5.1 7 .. 6 5.8 7.6
39 40 41 42 43 44 45 41l 47 48
67 68 69 70 71
72 73 74 75 76
53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69
Shell correction
BCS pairing energy
Total binding energy
oo
= 28: Nickel (Continued) 580.8 587.7 594.2 600.3 606.1 611.5 616.6 621.4 625.9 630.0 Z
24 25 26 27 28 29 30 31 32 33 34 35* 36 37 38 39 40
f.....
(Continued)
Mass number A
= 26: Iron (Continued:)
Z
22 23 24 25 26
8c-2.
-0.7 -0.6 -0.9 -0.9 -0.5
o.
0.9 2.1 3.9 5.5
2.4 4.2 2.8 5.0 3.3 4.9 3.2 4.2 1.7 2.5
582.5 591.3 596.1 604.4 608.9 616.5 620.7 627.7 631.5 638.0
0.8 1.8 2.5 4.0 5.5 4.1 3.0 1.9 1.3 0.2 -0.6 -1.4 -1.7 -2.4 -2.6 -3.0 -3.1
t;;; po ~
.~
== 29: Copper
418.6 434.9 450 .. 6 465.6 480.0 41)3.9 505.8 517.1 528.0 538.4 548.4 557.9 566.9 575.6 583.8 591.6 599.0
zq
o
.::.1 2.1 0.2 1.6 -0.3 -0.2 -0.3 1.4 0.3 2.2 1.0 3.1 1.6 3.6 2.1 4.0 2.7 4.6
421.3 436.6 454.6 469.0 485.4 497.5 510.1 519.3 531.4 539.4 550.7 557.9 568.6 575.1 585.1 591:0 600.3
;1 H
o
1Jl
27 28 29 30 31 32* 33 34 35 36 37 38 39 40 41 42 43 44 45
54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72
460.4 472.0 483.2 493.9 504.0 513.7 523.0 531.7 540.1 548.0 555.4 562.5 569.2 575.5 581.4 587.0 592.2 597.1 601.7
4.3 5.8 .. 4.5 3.4 2.2 1.5 0.5 -0.2 -1.0 -1.4 -2.1 -2.4 -2.8 -2.8 -2.6 -2.2 -1.5 -0.4 0.5
-0.4 -0.2 -0.4 1.4 0.3 2.3 1.0 3.1 1.5 3.5 2.0 4.2 2.8 4.7 2.9 4.5 2.4 3.6 1.7
464.1 477.6 487.1 498.5 506.4 517.4 524.2 534.3 540.3 549.8 555.1 564.0 568.8 577.1 581.4 589.1 593.0 600.1 603.7
Z = 28: Nickel
23 24 25 26 27 28 29 30 31 32 33 34* 35 36 37 38
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
401.8 418.2 433.9 449.0 463.4 477.2 489.0 500.2 511.0 521.3 531.1 540.5 549.4 557.9 565.9 573.6
1.6 1.7 2.6 3.8 5.9 7.9 6.2 4.8 3.9 3.5 2.0 0.6 -0.2 -0.7 -0.7 -0.5
1.5 3.5 1.6 2.7 -0.2
O. -0.2 2.1 0.7 2.3 1.2 4.1 2.5 4.6 .2.5 4.0
404.9 423.5 438.1 455.5 469.0 485.1 495.0 507.1 515.6 527.1 534.3 545.2 551.8 561.8 567.7 577.1
41 42 43 44 45 46 47 48 49
70 71 72 73 74 75 76 77 78
606.1 612.7 619.0 625.0 630.6 635.9 640.9 645.5 649.9
26 27 28 29 30 31 32 33 34 35 36 37* 38 39 40 41 42 43 44 45 46 47 48 49 50 51
56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81
451.4 467.1 482.1 496.6 510.5 522.4 533.9 544.9 555.4 565.5 575.1 584.3 593.1 601.4 609.4 617.0 624.2 631.0 637.5 643.7 649.5 654.9 660.1 665.0 669.5 673.8
-2.9 -2.5 -1.8 -0.8
O. 1.2 2.7 3.9 5.9
2.9 4.5 2.5 3.7 1.9 2.9 0.9 1.8 -0.3
605.8 614.5 619.6 627.7 632.4 639.9 644.3 651.2 655.4
5.9 2.3 3.2 2.6 5.2 3.8 5.4 3.6 7.1 5.4 7.5 5.3 6.9 5.3 7.0 5.4 7.7 6.0 7.7 6.1 7.1 4.4 5.4 2.4 2.9 2.5
456.7 471.6 488.7 501.4 516.1 525.8 538.4 546.9 558.9 566.7 577.8 584.9 595.4 601.9 611.8 617.8 627.1 632.7 641.3 646.6 654.6 659.5 667.0 671.5 678.3 680.8
Z = 30: Zinc
-0.6 2.3 3.4 2.2 0.4 -0.4 -0.9 -1.5 -3.7 -4.2 -4.7 -4.6 -4.5 -4.8 -4.6 -4.5 -4.8 -4.3 -3.9 -3.2 -1.9 0.2 1.4 4.2 5.9 4.6
~
o ~ a
~
rJl
I:;J
o
~
~
rJl
cr
I-'
o .....
TABLE 8c~2. CALCULATED BINDING ENERGIES IN MEV I
NUUlber of neutrons N
Mass number A
Liquid drop
(Continued)
BCS pairing energy
Sheil correction
f i3
1:-'.
i
Total bi~ding
energy
. Number of ~eutro~s N
Mass number A
Liquid drop
Shell , correction
BCS pairing energy
Total binding energy
3.4 7.1 5.4 7.1 5.5 6.5 3.8 4.9 2.0 2.4 2.1 4.0 3.2 4.4 2.9 3.9
641.9 652.6 659.8 670.0 676.8 686:3 692.7 701.6 707.7 715.9 719.9 725.6 728.9 734.0 736.6 741.4
6.0 4.7 6.6 4.7 6.4 5.0 6.9 5.2 7.0 4.8 6.9
519.1 532.6 548.8 561.1 576.4 586.5 599.8 609.2 621.9 630.6 642.5
i' Z "" 31: Gallium
27 28 29 30 31 32 33 34 35 36 37 38* 39 40 41 42 43 M 45 46 47 48 49
pO
51. 52
58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83
467.9 483.5 498.5 513.0 526.9 539.0 550.5 561,6 572.3 582.4 592.2 601.5 610.4 618.9 627.1 634.8 642.2 649.2 655.8 662.1 668.1 673.8 679.1 684.2 688.9 693.4
i 29 30
61 62
:1
7'
Z = 33, Arsenic (Continued)
LO
1.1 1.9 1.0 -0.9 -1.7 -2.2 -2.5 -4.5 -4.8
469.7 487.4 500.7 515.9 527.6 540.8 550.0 562.5 570.8 582.6 590.3 601.3 608.4 618.8 625.4 635.2 641.3 650.5 656.2 664.8 670.2 678.1 683.2 690.5 693.5 698.3
2.0 1.3 3.8 2.5 4.1 2.2 5.4 3.5 5.5 3.9 5.4 4.0 5.9 4.2 6.1 4.5 6.0 4.7 5.6 3.0 4.2 1.2 1.8 1.4 3.4
~5.2
-5.7 -5.5 -6.0 -5.9 -5.7 -5.6 -5.3 -4.7 -4.3 -3.0 -0.9 0.2 3.0 4.5 3.3 1.5
32': Germanium,
499.81 514.8 ,
0; -2.3
1
8.6 6'.5
I
503.2 519.0
41* 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56
,
74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89
644.7 653.4 661:8 669.8 677.5 684.8 691.8 698.5 704.8 710.8 716.5 721.9 727.0 731.8 736.4 740.6 Z
30 31 32 33 34 35 36 37 38 39 40
64 65 :66 67 68 69 70 71
72 73 74
-5:2 -7.9 -'-7.4 -7.0 -6:3
,,i ,
~5:0
-2.9 -1:7 1.0 2.7 1.4 -0.3 ~1.3
-2.2 -2.6 -3.1
= 3"/,: Selenium
516.3 531.9 547.0 561.5 575.5 587.8 599.6 611.0 622.0 632.5 642.6
-'3;2 -4.0 -4.5 -4.4 -4.8 -5.8 -5.9 -5.8 -6.0 -5.0 -5.9
,
I
2o t"I
t;:j
p., ~
~ ~ H
oW.
31 32 , 33 34 35 36 37 38 39 40* 41 42 43 44 45 46 47 48 49 50 51 52 53 54
63 64 &5 66 67 68 69 70 71 72
:
: :
:
73
74 75 76 77 78 79 80 81 82 83 84 85 86
i
529.:3 543.2 , 555.4 567 '0 578 i2
'588:9 599.2 609.1 &18.6 627.6 636.3 644.5 6.52.4 659.9 667.1 673.9 680.4 686.5 ' 692.4 697.9 703.1 708.1 712.7 717.1
-3.0 -3.5 -3.3 -6.3 -5.6 -6.0 -6:8 -6.4 -6.2 -6.8 -6.'6 -6.7 -6.4 -6.1 -5.6 -4.4 -2.0
5:0 6.7 4.4 8.4 5:6 7.6 '6.2 7.6 5.9 8.1 6.4 8.3 6.8 8.7 7.3 8.3 5.3 -6.6 3.4 4.1 3.5 5.7 4.8 6.1
-LO
2.0 3.4 2.3 0.3 -0.6 -1.5
•
531. 3 546.4 556.1 569.1 578.1 590.3 598.6 610.2 617.8 6.28.7 635.8 646.1 652.8 6t\2.5 668.7 677.8 683.6 692.1 697.7 705.4 708.9 714.1 716.9 721.6
Z= 33: Arsenic
29 '30 31 32 33 34 35 36 37 38 39 40
,
62 63 64 65 66 67 68 69 70 71 72 73
600.3 515.9 530.9 545.4 559.5 571. 6 583.4 594.7 605.6 616.0 626.0 635.5
-1.2 -3.0 -3.7 -4.2 -'-3.8 -6.9 -5.1 -5.3 -5.4 -5.8 -5.2 -5.7
I
2.1 4.6 3.·2 4.8 2.7 6.5 3.1 5.1 3.5 5.3 3.3 5.3
501.1 517.5 530.4 546.1 557.7 1;71.2 580.7 593.6 602.5 61.4.6 622.8 634.2
41 42* ' 43 '14 45 , 46 47 48 49 50 51 52 53 54 55 56 57
75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91
,
652.3 661. 5 670.4 678.9 687.1 694.9 702.4 709.5 716.3 722.8 729.0 734.8 740.4 745.7 750.7 755.4 759.'9
-'5.5 -6:3 -5.5 -6.3 -6.5 -5.3 ~3.0
-2.0 0.4 2.4 0.9 ~0.6
-1.6 -2.4 -2.9 -3.4 -4.5
5.1 7.3 5.4 7:8 7.0 7.9 5.1 6.3 3.8 3.8 3.7 5.4 4.6 5.8 4.4 5.3 4.9
650.7 661.9 6()9:6 680.3 687.5 697.:6 704.4 713.'8 720.4 729.0 7-33.5 739.7 743.4 749.0 752.1 757.3 759.8
67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
85
547.8 562.9 577.5 591.6 603.9 615.9 627.3 638.4 648.9 659.1 668.9 678.3 687.2 695.9 704.2 712.2 719.8 727.1 734.0
-4.8 -4.2 -4.3 -4.4 -4.7 -3.4 -'4.5 -3.3 -4.2 -4.0 -4.8 -'1.4 -6.3 -5.7 -4.8 -3.2 -2.4 -0.1 1.'7
o
.~ H
o ~
Z "" 35: BTomine
32 33 34 35 36 37 38 39 40 41 42 43 44* 45 46 i 47 48 49 50
P>
8
4.7 2.8 4.4 2.9 4.6 2.3 4.5 2.2 4.1
2.5 4.6 2.9 5.7 4.0 5.3 3.2 4.5 2.1 2.3
547.3 560.2 576.1 588.1 601.9 612.0 625.1 634.5 646.8 655.5 667.1 675.3 686.4 694.1 704.6 712.0 721.9 729.0 738.0
P> w
w
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o
~q t"
P> w
! b
CN
-,-
i Number of neutrons N
TABLE
Mass number A
Liquid drop
8c-2.
f-
~
~ ~ H (') [f).
51 52 53 54 55 56 57 58 59 60
751.5 758.3 764.8 771.0 776.8 782.5 787.8 793.0 797.9 802.4
72
594.5 609.0 623.2 635.6 647.7 659.3 670.5 681.2 691.6 701.5 711.1 720.4 729.3 737.9 746.1 754.0 761.6 768.8 775.7 782.4 788.7 794.8 800.7 806.2 811.5 816.5
Z 35 36 37 38 39 40 41 42 43 44 45 46 47* 48 49 50 51 52 53 54
55 56 57 58 59 60
0.2 -1.6 -2.4 -3.3 -3.7 -4.2 -5.4 -3.5 -1.5 -1.1
87 88 89 90 91 92 93 94 95 96
73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 .93 94 95 96 97
=
3.6 5.6 4.6 5.8 4.4 5.4 5.1 5.1 2 ..9 3.7
755.2 762 ..3 766.9 773.5 777.4 783.6 787.0 793.0 796.4 802.0
1..9 3.1 1.2 2.4 1.2 2.9 1.4 3.5 2.3 5.3 4.4 5.6 3.2 4.4 2.0 2.2 2.0 3.7 2.8 3.9 2.7 4.3 1.9 2.9 1.0 1.7
590.7 606.7 619.1 633.1 643.6 656.8 666.6 679.0 688.2 700.1 708.7 720.2 728.6 739.4 747.4 757.4 763.4 770.9 776.0 783.0 787.4 794.0 798.0 804.5 808.5 814.5
37: Rubidium -2.8 -2 ..5 -1.8 -1.5 -1.9 -2.4 -2..4 -3.6 -3.7 -6.0 -6.8 -5.7 -3.9 -2.9 -0.6 1.2 -0.1 -1.6 -2.5 -3.3 -3.9 -4.4 -2.5 -2.4 -0.9 -0.3
60 61 62 63 64
98 99 100 101 102
829.7 834.9 839.8 844.4 848.8
Z 37 38 39 40 41 42 43 44 45 46 47 48 49 50* 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66
76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105
=
625.5 640.1 654.3 666.8 678.9 690.6 701.9 712.8 723.4 733.6 743.4 752.9 762.1 770.9 779.3 787.5 795.3 802.9 810.1 817.0 823.8 830.1 836.3 842.2 847.8 853.0 858.1 862.9 867.4 871.7
0.3 0.9 0.9 1.2 1.2
2.5 1.3 2.3 1.2 2.0
829.0 833.2 839.1 842.7 848.1
0.3 1.2 0.1 2.1 0.7 2.3 1.9 5.0 2.7 4.7 3.0 4:0 2.2 2.2 2.1 3.4 2.6 3.6 2.8 4.8 1.7 2.7 0.5 1.0 0.2 1.3 0.2 0.9 0.2 1.2
621.6 637.7 650.4 664.3 675.1 688.3 698.4 711.2 720.9 733.2 742.5 754.2 763.2 774.0 781.0 789.3 795.4 803.3 808.6 816.1 821.0 828.4 833.3 840.2 844.8 851.1 855.2 861.0 864.5 869.7
39: Yttrium 0.3 0.8 0.8 -0.6 -0.7 -1.7 -3.3 -5.6 -4.1 -4.8 -3.6 -2.6 -0.9 0.9 -0.4 -1.6 -2.3 -3.0 -4.1 -5.1 -2.4 -2.1 0.1 1.0 1.2 1.2 1.4 1.6 l.2 0.9
~
o
!S Q
~
~
6
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t"'
>-
U1
w w
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o
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q
t"'
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Z = 48: Cadmium
4.0 5.2 2.0 2.8 2.2
---_ .. _ - _ . _ - - - - - - - - - - -
774.2 ,/'89.0 801.0 815.0 825.0 --- - - - - - - - -
40 50 51 52 53
07 98 00 100 101
799.2 811. 9 824.3 836.4 848.1
6.3 8.3 6.8 5.4 4.4
Cf'
I--'
o
CD
C'lO'
t-
· TAilLE-~c=2.-CALCULATED-BINbiNG ENERGIES iN- MEV {Conlinued) ..... ,
Number of neutrons N
Mass number A
I'
Liquid drop·
Shell correction
BO$ pairir,lg
energy
Total binding energy
Number, Mass of neunumber A trons N
Liquid drop'
Shell correction
BOB pairing energy
Totalbinding energy
'f-' """" o
"
Z
54 55 56 57 58 59 60 61 62 63 '64* 65 66 67 138 69 10 71
72 73 74, 75 76 77 78 79 80 81 82
102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130
= 48: Cadmium (Continued) 859.4 870,,4 881.1 891.5 901,5 911.3 920.7 929.9 938.8 947.4 955.7 963.8 971.5 979.1 986.3 993.3 1000.1 1006,6 1012.9 1018.9 1024.7 1030.3 1035,,7 1040.9 1045.9 1050.6 1055.2 1059.5 1063.7
3,6 3,1 2.7 1.1 -:-0.6 -1.5 -2.9 -3.7 -:-4.1 -4.6 -4.4 -3.4 -3,5 -2.5 -2.7 -:-1.8 -2.1 -1.3 -1.8 -,-0.8 -1.3 O. O. 1.9 3.1 4.5 6.0 7.8 9.6 .-
.-
Z
S,n 1.7 2.5
2.0 4,5 3.4 5.6 4,6 5.9 4.7 5.9 3.7 5,0 3.0 4.5 2.6 4.2 2,6 4.S 2.6 4,6 2.9 4.6 2.5 3.2 1.9 2.3 0.9 1.0
866.0 875.2 886.3 894.5 90,5,5 913.1 i 923.5 930.8 9·10.6 947.5 956.9 9133.5 972.5 918.8 987.4 993.4 1001. 6 1007.2 1015.a 1020.S 1027. 9 1033.D 1040.3 1045.2 1052.2 1057.0 1063.5 1068.2 107'4.3
54 55 56 57 58 59 60 61 62 63 64: 65 66 67* 68 69 70 71
72 73
74 75 76 77 78 79 80 81
104 105 106 1Q7 108 109 110 111 112 l1S 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131
= 50: Tin (Continued) 864,7 876,,6, 888.0 899,2 910.1 920.6, 930.8 940.8 950.4 959.8 968.8 977.13 9813.1 994.4 1002.4 10lD .1 1017,6 1024,9 1031. 9 1038,6 1045.2 1051.5 1057.5 1063.4 1069.0 1074,5 10-79.7 1084.7
6.7 6.2 5,8 4.2 2.6 1.5 a.3 -0.5 -1.1 -1.5 -1.6 -2:.2 -=2.7 -2.8 -3.1 -2.7 -=2.7 -=2.3 -1.5 ":':0.6 a.4 1.9 2.9 4.6 6.1 7.4 9.0 10.7
2.0 0.7 1. 5, 0.9 3.,5 2.5 4.6 3.5 5.0 3.7 5.0 3,9 5.7 4.4 6,2 4.6 6,2 4.7 5.7 4,0 4.8 2.8 3.7 1.7 2.2 1..0 1.3 -0.1
873-.5 883.4 895,4 904.3 916.1 924.,6 935.8 943.8 954.,4 962.0 972.2 979.3 989.2 996.0 1005.4 1012,a 1021. 0 1027,3 1036.0 1042,() 1050-.4 1056,11064.1 1069.7 1077.4 1082.9 1090.0 1095.3
zc::j (')
t:-
!;:d
~
~ ....
C
rJ2
81 82 83 84 85 86 87 88 89
133 134 135 136 137 138 139 140 141
1107.3 1112.8 1118.0 1123.1 1128.0 1132.7 1137.2 1141. 6 1145.7
7.1 8.8 7.7 6.3 5.5 4.5 3.9 3.4 3.3
1.5 1.7 1.5 2.8 2.2 3.2 2.5 3.1 1.7
1115.9 1123.3 1127.2 1132.2 1135.8 1140.5 1143.6 1148.1 1150.8
1.7 4.2 2.7 4.5 2.5 4.4 2.4 3.6 1.8 3.2 1.7 2.9 1.5 2.6 1.3 2.8 1.3 2.9 1.7 3.6 2.2 3.3 2.2 2.4 1.0 1.2 1.0
907.3 920.2 929.9 942.2 951.4 963.2 972.2 983.5 992.1 1002.9 1011.1 1021.4 1029.3 1039.2 1046.6 1056.1 1063.2 1072.4 1079.2 1088.1 1094.7 1103.3 1109.8 1117.9 1124.3 1132.0 11:,6.2
Z = 53: Iodine
57 58 59 60 61 62 63 64 65 66 67 68 69 70
110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136
71
72* 73 74 75 76 77
78 79 80 81 82 83
I
906.2 918.2 930.0 941.3 952.5 963.2 973.7 983.9 993.9 1003.5 1012.9 1021.9 1030.7 1039.3 1047.6 1055.6 1063.4 1071.0 1078.3 1085.4 1092.3 1098.9 1105.4 1111. 6 1117.6 1123.4 1129.0
-0.5 -2.2 -2.6 -3.6 -2.9 -4.0 -3.1 -3.3 -2.5 -2.8 -2.2 -2.4 -1.8 -1.8 -1.3 -1.7 -0.7 -1.2 -0.5 -0.9 . 0.4 1.1 2.2 3.9 5.7 7.3 6.3
I
78 79 80 81 82 83 84 85 86 87 88 89 90 91 92
132 133 134 135 136 137 138 139 140 141 142 143 144 145 146
1107.6 1114.4 1120.9 1127.3 1133.4 1139.3 1145.0 1150.6 1155.9 1161. 0 1166.0 1170.7 1175.3 1179.7 1183.9
IZ
-0.3 0.9 2.5 4.4 6.0 5.1 3.6 2.9 1.9 1.3 0.8 0.8 0.2 -0.8 -3.0
=
55: Cesium
957.4 968.9 980.2 991.1 1001.7 1012.1 1022.1 1031. 9 1041. 4 1050.7 1059.7 1068.4 1076.9 1085.1 1093.1 1100.8 1108.4 1115.7 1122.8 1129.7 1136.3 1142.8
-2.2 -2.3 1.7 -2.1 -1.6 -1.8 -1.7 -2.0 -1.8 -1.7 -1.5 -1.4 -1.4 -1.5 -1.3 -2.4 -1.6 -1.3 -0.1 1.5 3.4 4.9
4.8 3.6 3.9 2.4 2.6 2.3 3.6 3.0 4.1 3.3 3.9 2.5 3.2 2.5 5.2
1112.1 1118.9 1127.4 1134.1 1142.1 1146.7 1152.3 1156.5 1161. 8 1165.6 1170.7 1174.0 1178.8 1181. 3 1186.1
~
o
lS: J-< Q
61 62 63 64 65 66 67 68 69 70 71
72 73 74 75 76* 77 78 79 80 81 82
116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137
1.8 2.8 1.4 2.7 1.3 2.3 1.3 2.5 1.3 2.2 1.0 1.9 1.1 2.2 1.4 3.5 2.5 4.0 2.8 3.1 1.6 1.9
955.0 967.5 977.5 989.5 999.0 1010.4 1019.5 1030.4 1039.0 1049.4 1057.6 1067.5 1075.3 1084.9 1092.4 1101.8 1109.1 1118.3 1125.5 1134.3 1141. 3 1149.6
lS:
po.
U1 U1
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o
i:d
lS: q
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U1
w w
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o
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63: Europium 0.1 -0.7 -0.8 -1.5
'r
I-' I-'
-,J
TABLE 8c-2.CALCULA~·ED BINDING ENERGIES IN MEV
t1
P::
;:;1 H o U).
Z !",.64: (ladolini'/Am
1.1.0
Ill,
76 7'l 78 79 80 81 82 83 84 85 86 87 88 89 90 91* 92 93
94 Q5. \16,
97 98 99100 101 102 loa 104 105 106 107 108 109
145
114i.4 1151.8 1162.0 1171. 9 1181.6 1191.2
146 14,( 148 149 150 151 152. 153 154 1;55 );56 157 15.8 1;59 160 161 162 163 164 165 166 167 168 169 170 171 172 173
1209.5. 1218.4 1.227.0. 123.5.5 1243.7 1251.7 1259.(1 1267.2 1,274.7 1281.9 1288.9 1295.8 1302.4. 1308.8 1315.1 1321.2 1327.1 1332.8 1338.3 1343.7 1348.9 1353.9 1358.8 1363.5 1368.1 1372.4 1376.7
140 I'll 142 143. 144
143 144
-1.8 O.
~200.5
Z
78 79
-0.6. -1.4 -2,.2 -3.. 0 -3.5 -1.1 -2'.3 -1.8 -2.1 -2.5 -2.0 -1.4 -0.5 0.1 0.7 1.2 1.6 2.0 2.4 2.9 3.3 3.3 3.:3 3.4 3.:6 3.7 3:8 3.1 2.8 2.4 2.1 1.5
0.5 0.90.3 0.5 .0.3 1.0 0.6 1.1 0.7
1140.9 1150.7 116-2.1 1.171.9 1183.4 1193.3 1204.4 1212.2 122.1.0 1228.4. 123(i.8 124a.9 1252.0 1258.6 1266.. 8 1,273.4 1281.4 1287.8 1295.5 1301.6. 1308.91314.7 1321.61327.0 1333.4 133.8.5 1344.4 1349.. 2 1354.6 1358.8 1363.9 1367.7 1372.5 1376.0
1.5 2.0.
1163.6 lI73.7
1.9~.6
3.-1 3.4
Q.2 4.0, a.9 3.9 4.·9; :;1.4 3.8 3.0 3.1 1.9 2.1 1.0 1.5 0.7 1.4 0.7 1.2 0.4; 0.8 0,.4
LO
= 65: Terbium
1164.4 1174.6
I
-1.1 -2 .. 3
I,
175 176 1;.46 14.7 148 149 150
1.3 139.2.3, 1 • 1396 ..5 . 0."9 Z =; 6.6: 'pysprosi;um 1187 ..0 -3 ..4 1197.2 -1.6 1207.1 -0.1 121.6.8 -0 ..8 1226.3 -2.3 1235.5 -0.9 1244.6 -1.0 1253.4 -1.7 1262.0 -~ .. 2
1
80 81 82 83 84 85 86 87 88 89 90 91 92. 9a 94 95* 96 97 98 99100 Hi!. 102 103 104 105 106 107 108 109 110 III 112 113
178 179
1278.7 1286 .. 7 1294 .. 61302 .. 1 1309.5 1316.7 1323 .. 7 1330.6 1337.2 1343.6 1;349.9 1356.01361 .. 9 1367.7 1373.2 1378:6 1383.9i388.91393.9 1398.6 140;L2 1407.7 1412.0 1416.,2
81 82
148 1.49
Z ? 1199.4 1209,6
lSI
152 153 154 155 156 157 iS8 159 1;60 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176
177
-0·7
~270.4
-0.1 0:4 0 .. 9 1..3 1..7 2.0 2.4 2 .. 9 3 .. 3 3... 3 3 .. 3. 3.4 3.:5 3.7 3.8 3.2 2.9 2 .. 5 2.2 1.7 1:4 0.9. 0.6 0.3, 67: Holmium
I
-1.1 0.1
Ii
0.9 0.4
1391.6 1395.0
i?3
1188.9 1199.4 1211.1 1219.6
3.8 4.2 3.7 5.0 207 2.9 2 ..5 2.6 1.4 1..9 0 .. 9 1.5 0. 7 1 .. 4 0.7 1..2 0.4 0.8 0) 1..0 0. 5 0 .. 9 0.3 0.5 0 .. 3 1.0 0.5 1.0 0.6 1.3 0.8. 1.4 0,.9
1301.2 1309.5 1316.2 1324.0 1330.3 1337.7 1343.7 1350 .. 7 1356.3 1362.8 1368.0 1374.) 1378.8 1384.4 j388;8 1394.1 1398.1 1403.2 140.6.. 8. 1411.6 1415.1
2.6 3.2
1200.9 1212.9
~228.9
1237.0 1246.1 1253. .. 7 12(12 .. 5 1269.7 1278.5 1285.7 12.94.~
~
":3
~ ""
C'l
~
~ UJ.
m J:;j
0
~.
~. Q t"'
~ UJ.
'f
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TABLE
8c-2.
CALCULATED BINDING ENERGIES IN MEV
(Continued)
cr
~
Number of neutrons N
Mass number A
Liquid drop
Shell correction
Total binding energy
BOS pairing energy
Number of neutrons N
Mass number A
Z = 67: Holmium (Continued)
83 84 85 86 87 88 89 90 91 92 93 94 95 96* 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114
150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181
1219.6 1229.4 1239.0 1248.3 1257.4 1266.4 1275.1 1283.6 1291.9 1300.0 1307.9 1315.6 1323.1 1330.4 1337.5 1344.4 1351.1 1357.7 1364.0 1370.2 1376.2 1382.1 1387.7 1393.2 1398.6 1403.8 1408.8 1413.6 1418.4 1422.9 1427.3 1431. 6
I
-0.2 -2.0 -0.2
O. -0.9 -0.6 -0.2 0.2 0.7 1.1 1.5 1.8 2.1 2.5 2.9 3.3 3.3 3.3 3.4 3.5 3.7 3.8 3.2 2.9 2.5 2.3 1.8 1.5 1.0 0.8 0.4 0 .. 2
Liquid drop
Shell correction
BOS pairing energy
Total binding energy
t-:)
o
Z = 69: Thulium (Continued)
2.3 3.9 1.3 1.3 1.1 1.6 0.6 1.2 0.3 0.9 0.2 0.9 0.2 0.8
O.
0.3
O. 0.6 0.1 0.5 -0.1 0.1 -0.1 0.6 0.1 0.6 0.2 0 ..8 0.3 1.0 0.4 1.0
:
1221.7 1231.3 1239.7 1249.1 1257.0 1266.2 1273.8 1283.0 1290.5 1299.4 1306.6 1315.2 1322.1 1330.3 1336.9 1344.6 1350.8 1358.0 1363.9 1370.7 1376.2 1382.5 1387.5 1393.4 1398.0 1403.6 1407.8 1413.2 1417.1 1422.1 1425.8 1430.6
87 88 89 90 91 92 93 94 95 96 97 98 99 100* 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118
156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187
1263.9 1273.4 1282.7 1291.8 1300.7 1309.4 1317.8 1326.1 1334.1 1342.0 1349.7 1357.1 1364.4 1371.5 1378.4 1385.1 1391.7 1398.0 1404.2 1410.3 1416.1 1421.8 1427.3 1432.7 1438.0 1443.0 1448.0 1452.7 1457.3 1461.8 1466.1 1470.3
O. -0.2 -0.3 -0.1 0.2 0.4 0.8 1 .. 1 1 ..4 1.7 2.2 2.6 2.6 2.6 2.7 2.8 3.0 3.1 2.7 2.4 2.1 1.9 1.4 1.2 0.9 0.7 0.3
O. -0.2 -0.2 -0.3 -0.4
0 .. 7 1.4 0.8 1.4 0.6 1.2 0.4 1.1 0.4 0.9 O.
0.4
O. 0.7 0.1 0.6 -0.1 0.2 -0.1 0.5
O. 0.6 0.1 0.7 0.2 0.8 0.3 1.0 0.4 0.9 0.3 0.8
1264.2 1273.8 1281. 9 1291.5 1299.5 1308.8 1316.6 1325.6 1333.1 1341.7 1348.8 1357.1 1363.8 1371.6 1378.0 1385.3 1391.4 1398.3 1403.9 1410.3 1415.5 1421. 6 1426.5 1432.3 1436.8 1442.4 1446.6 1452.0 1456.0 1461.1 1464.9 1469.9
z
q
o
~ :.-
~
~
~ .....
C
rJl
Z
83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98* 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116
1221.9 1232.0 1241.9 1251.5 1260.9 1270.1 1279.1 1287.9 1296.6 1304.9 1313.1 1321.1 1328.9 1336.5 1343.9 1351.0 1358'.0 1364.8 1371.5 1377'.9 1384.2 1390.3 1396.3 1402.0 1407.6 1413.1 1418.3 1423.5 1428:4 1433.2 1437.9 1442.4 1446.8 1451.0
151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 i76 177 178 179 180 181 182 183 184
,Z
85 86
I
154 155
= 68: Erbium
I
Z
0.2 -1.5 0.2
3.2 4.6 2.1 2.3 1.8 2.4 1.7 2.0 0.9 1.4 0.6 1.2 0.5 1.0 0.2 0.5 0.1 0.8 0.2 0.7
O. -0.6 -0.7 -0.8 -0.3 0.4 0.9 1.4 1.7 2.1 2.5 3.0 3.4 ,3.4 3.4 3.5 3.6 3.8 3.9 3.3 3.0 2.6 2.3 1.8 1:5 1.1 0.9 0.4
O. 0:3 0.1 0.7 0.3 0.8 0.4 1.1 0:6 1.2 0.7 1.5 1.0 1.7
O. -0.3 -0.6
1225.2 1235.2 1243.9 1253.5 1261.7 1271,0 1278.8 1288.1 1295.8 1304.9 1312.4 1321.2 1328.4 1336.8 1343.7 1351.6 1358.1 1365.6 1371.8 1378.8 1384.6 1391.2 1396.5 1402.6 1407.5 1413:4 1417.9 1423:5 1427.8 1433.1 1437.0 1442.1 1445.8 1450.7
157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190
1266.3 1276.1 1285.7 1295'.1 1304.3 1313.2 1322.0 1330.5 1338.9 1347.0 1355.0 1362.7 1370.2 1377.6 1384.8 1391'.8 1398.6 1405.2 1411'.7 1418.0 1424.1 1430.0 1435.8 1441.5 1447.0 1452.3 1457.4 1462.5 1467.3 1472.1 1476.6 1481.1 1485.4 1489.5
1245.7 1255..7
89 90 91
160 161 162
1288.2 1297.9 1307.3
I
1.0 0.8
0.4 0.2 -0.2 -0.4 -0.3
O. 0.4 0.7 1.1 1.3 1.8 2.3 2.2 2.2 2.3 2.4 2.6 2.7 2.4 2.2 1.8 1.6 1.3 1.1 0~8
0.6 0.2
O. -0.1 -0.2 -0.1
O. O. O.
1.5 1.9 1.3 2'.1 1.3 2.0 1.1 1.7 1.0 1.5 0.7 1.0 0.7 1.3 0.8 1.3 0.6 0.8 0.5 1.0 0.6 1.1 0.6 1.1 0.6 1.2 0.8 1.5 0.9 1.5 0.8 1.4 1.0 l.8
1267.9 1277.8 1286.0 1295.7 1303.8 1313.4 1321.3 1330.6 1338.3 1347.2 1354.6 1363.1 1370.1 1378.1 1384.8 1392.4 1398.7 1405.9 1411.7 1418.5 1423.9 1430.4 1435.5 1441. 6 1446.4 1452.3 1456.8 1462.5 1466.8 1472.3 1476.4 1481.7 1485.9 149l. 0
0.8 1.7 1.0
1288.3 1298.3 1306.5
~
o
f5
o
~
Ul I:;j
o
~
q
~
Ul
' 'z = 71: Lutetium
= 69: Thulium
1244.3 1254.2
= 70: Ytterbium
87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102* 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120
I
0.9 1.1
I
O. -0.4 -0.5
~
I-'
t>:l
I-'
TABLE
Number of neutrons N
l\lass number A
Liquid drop
Sc-2.
Shell correction
CALCULATED BINDING ENERGIES IN
BCS pairing energy
II
Total I binding I energy
Number of neutrons N
cr......
MEV (Continued) Liquid drop
Mass number A
Shell correction
BCS pairing energy
Total binding energy
~ ~
I.
Z
92 93 94 95 96 97 98 99 100 101 102 103 104* 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122
163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193
= 71: Lutetium 1316.6 1325.6 1334.4 1343.1 1351.5 1359.7 1367.7 1375.6 1383.2 1390.6 1397.9 1405.0 1411.9 1418.6 1425.2 1431. 5 1437.7 1443.8 1449.7 1455.4 1461.0 1466.4 1471. 7 1476.8 1481.8 1486.6 1491. 3 1495.8 1500.2 1504.5 1508.6
Z
(Continued)
-0.5 -0.2
O. 0.5 0.8 1.3 1.7 1.8 1.7 1.8 1.9 2.2 2.2 1.9 1.7 1.4 1.2 0.9 0.9 0.6 0.4
O. -0.2 -0.2 -0.2
O. 0.2 0.4 0.7 1.0 1.1
1.8 0.9 1.5 0.6 1.2 0.3 0.7 0.3 1.0 0.4 0.9 0.2 0.5 0.1 0.6 0.2 0.7 0.2 0.7 0.3 0.9 0.5 1.2 0.6 1.1 0.4 0.9 0.4 0.8 0.6 1.3
1316.3 1324.4 1334.0 1341.9 1351. 0 1358.6 1367.4 13"14.7 1383.0 1389.9 1397.8 1404.4 1411.8 1418.0 1425.0 1430.8 1437.5 1M2.9
1449.4 1454.5 1460.6 1465.4 1471.4 1476.0 1481. 7 1486.1 1491.7 1496.1 1501.5 1505.9 1510.8
94 95 96 97 98 99 100 101 102 103 104 105 106 107* 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125
167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198
= 73:
Tantalum (Continued)
1340.7 1349.9 1358.9 1367.7 1376.2 1384.6 1392.8 1400.8 1408.6 1416.2 1423.6 1430.9 1437.9 1444.9 1451. 6 1458.2 1464.6 1470.8 1476.9 1482.8 1488.6 1494.2 1499.6 1505.0 1510.1 1515.2 1520.0 1524.8 1529.4 1533.9 1538.2 1542.4
-0.4
O. 0.3 0.7 1.0 1.1 1.0 1.1 1.1 1.4 1.5 1.4 1.3 1.1
0.9 0.8 0.8 0.6 0.4 0.2 0.1 0.1 0.2 0.6 1.0 1.6 2.1 2.5 2.8 3.3 3.7 4.1
1.8 0.9 1.3 0.5 0.9 0.4 1.2 0.6 1.2 0.3 0.7 0.3 0.8 0.3 0.9 0.4 0.8 0.4 1.0 0.6 1.3 0.7 1.2 0.4 0.9 0.1 0.6 0.2 0.8 0.5 1.1 1.0
1340.7 1349.0 1358.7 1366.7 1376.0 1383.8 1392.6 1400.1 1408.5 1415.5 1423.6 1430.3 1437.9 1444.3 1451. 6 1457.6 1464.6 1470.2 1477.0 1482.3 1488.9 1494.0 1500.3 1505.3 1511.5 1516.5 1522.5 1527.4 1532.9 1537.6 15!2.9 1547.5
zq Q
t"' t'Ol
". ::0 "d
iI1
~ H Q
U1
Z
90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105* 106 107 108 109 110 111 112 113 114 115 116 117 118
un 120 121 122 123
92 93
162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 In1 192 193 In4 1n5
165 166
= 72: Hajni1,m
1300.1 1309.9 1319.4 1328.7 1337.8 1346.8 1355.4 1363.9 1372.2 1380.4 1388.2 1396.0 1403.5 1410.9 1418.0 1425.0 1431.8 1438.5 1444.9 1451.2 1457.4 1463.4 1469.2 1474.9 1480.4 1485.8 1491.0 1496.0 1501.0 1505.8 1510.4 1514.9 151n.3 1523.5
l
Z
Z
-0.6 -0.5 -0.7 -0.5 -0.2 0.2 0.5 0.9 1.3 1.4 1.3 1.4 1.4 1.7 1.8 1.6 1.5 1.2 1.0 0.8 0.8 0.5 0.3
2.6 1.7 2.5 1.6 2.2 1.3 1.8 1.0 1.4 0.9 1.7 1.1 1.6 0.8 1.2 0.8 1.2 0.8 1.4 0.9 1.3 0.9 1.6 1.1 1.9 1.3 1.9 1.1 1.6 0.9 1.5 1.2 1.9 1.6
O. -0.2 -0.2 -0.2 0.1 0.4 0.9 1.2 1.6 1.8 2.3
1301.6 1310.0 1320.0 1328.3 1338.1 1346.2 1355.6 1363.5 1372.5 1380.0 1388.6 1395.8 1404.0 1410.7 1418.5 1425.0 1432.3 1438.3 1445.3 1451.0 1457.8 1463.1 14(\9.6 14,'4.7 1480.9 1485.8 1491.8 14n6.5 1502.5 1507.1 1512.n 1517.5 1522.n 1527.3
I
-0.6 -0.5
168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 1n5 1n6 1n7 1n8 Inn 200 201
1343.1 1352.6 1361. 8 1370.9 1379.7 1388.4 1396.8 1405.1 1413.2 1421.1 1428.7 1436.3 1443.6 1450.8 1457.7 1464.6 1471.2 1477.7 1484.0 1490.2 1496.2 1502.1 1507.8 1513.3 1518.8 1524.0 1529.2 1534.2 153n.0 1543.7 1548.3 1552.7 1557.1 1561.2 Z
= 73: Tantalum
1321. 7 1331.4
94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109* 110 111 112 113 l14 115 116 117 l18 119 120 121 122 123 124 125 120 127
I
1.9 1.2
I
1322.2 1330.7
n6 n7 98
171 172 173
= 74: Tungsten -0.4
O. 0.3 0.6 0.9 1.0 0.9 1.1 1.0 1.3 1.4 1.4 1.3 1.2 1.0 1.0 1.0 0.8 0.7 0.5 0.4 0.6 0.8 1.0 1.3 1.8 2.6 3.3 3.3 4.3 4.7 5.3 5.n 5.3
2.3 1.3 1.8 1.0 1.4 0.9 1.7 1.0 1.7 0.8 1.3 0.7 1.2 0.7 1.3 0.7 1.2 0.7 1.4 0.9 1.6 1.0 1.5 0.9 1.6 0.9 1.2 0.7 1.7 1.0 1.5 1.3 1.4 1.2
1343.9 1352.4 1362.3 1370.6 1380.2 1388.1 1397.3 1405.0 1413.7 1420.9 1429.3 1436.3 1444.2 1450.8 1458.4 1464.7 1472.0 1477.9 1484.9 1490.6 1497.4 1502.9 1509.5 1514.8 1521.4 1526.6 1532.9 1538.1 1544.0 1548.n 1554.5 1559.4 1564.4 1567.7
1.4 0.4 1.0
1364.6 1373.0 1382.9
P>
>-3
o
~
H
o
~
P>
~
"'1
o
~
~
cj
f;:
U2
= 75: Rhenium
1364.3 1373.6 1382.7
0.2 0.6 0.8
cr
F-' t-:) ~
TABLE
Number of neutrons N
Mass number A
Liquid drop
Z
99 100 101 102 103 104 105 106 107 108 109 110 111 * 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129
174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204
Shell correction
= 75: Rhenium 1391.7 1400.4 1408.9 1417.2 1425.4 1433.3 1441.1 1448.7 1456.1 1463.4 1470.5 1477.4 1484.1 1490.7 1497.1 1503.4 1509.5 1515.4 1521.2 1526.9 1532.4 1537.8 1543.0 1548.1 1553.1 1557.9 1562.5 1567.1 1571.5 1575.8 1579.9
8c-2.
CALCULATJDD BINDING ENERGIES IN MEV
BCS pairing energy
Total binding energy
Number of neutrons N
Mass number A
1391.0 1400.5 1408.3 1417.4 1424.9 1433.6 1440.8 1449.1 1455.9 1463.8 1470.4 1478.0 1484.2 1491. 5 1497.4 1504.5 1510.3 1517.3 1523.0 1529.8 1535.3 1541.8 1547.2 1553.3 1558.4 1564.2 1569.2 1574,,5 1578.0 1582.2 1585.5
101 102 103 104 105 106 107 108 109 110 111 112 113 114* 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132
178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209
Z
(Continued)
1.0 0.7 0.9 0.8 1.2 1.2 1.5 1.4 1.3 1.1 1.2 1.2 1.0 0.8 0.7 0.4 0.6 0.9 1.3 2.1 2.9 3.8 4.4 5.0 5.5 6.3 6.8 7.5 6.7 6.0 5.. 5
Liquid drop
0.3 1.2 0.5 1.2 0.3 0.8 0.1 0.6 0.1 0.8 0.2 0.7 0.2 1.1 0.6 1.4 0.7 1.4 0.7 1.0 0.1 0.4 -0.1 0.2 -0.1 0.1 -0.1 -0.1 -0.1 0.5 0.2
Shell correction
= 77: Iridium 1415.0 1423.9 1432.5 1441. 0 1449.3 1457.4 1465.4 1473.2 1480.8 148S.2 1495.4 1502.5 1509.4 1516.2 1522.8 1529.2 1535.5 1541.7 1547.7 1553.5 1559.2 1564.8 1570.2 1575.5 1580.6 1585.6 1590.5 1595.2 1599.8 1604.3 1608.6 1612.8
f
(Continued) BCS pairing energy
Total binding energy
0.9 1.6 0.7 1.3 0.3 0.7 0.2 1.0 0.2 0.8 0.3 1.5 0.9 1.5 0.8 1.5 0.6 0.8 0.1 0.4
1414.9 1424.5 1432.5 1441. 8 1449.4 1458.4 146.5.7 1474.2 1481. 3 1489.5 1496.2 1504.1 1510.6 1518.4 1524.7 1532.4 1538.5 1545.9 1551.9 1558.9 1564.8 1571.3 1577.0 1583.2 1588.8 1594.5 1598.5 1603.1 1606.8 1611.3 1614.8 1619.0
GJ
~
(Continued)
0.4 0.3 0.6 0.7 1.2 1.4 1.4 1.3 1.4 1.6 1.4 0.7 0.9 1.1 1.5 1.9 2.6 3.5 4.2 5.0 5.7 6.2 6.9 7.7 8.3 8.9 8.1 7.3 6.8 6.3 5.9 5.5
O. 0.4 -0.1 0.1 -0.1 -0.1 -0.1 0.6 0.3 0.8 0.3 0.7
Z d o
~.
t-
i:d
>tI
::c:
~ H
o
if>
=
76: Osmium
1385.2 1394.5 1403.4 1412.2 1420.8 1429.2 1437.4 1445.5 1453.3 1461. 0 1468.5 1475.9 1483.0 1490.0 1496.8 1503.5 1510.0 1516.4 1522.5 1528.6 1534.5 1540.3 1545.9 1551.4 1556.7 1561.9 1566.9 1571.8 1576.6 1581. 2 1585.7 1590.1 1594.4 1598.5
1.0 1.2 0.9 1.1 1.0 1.3 1.4 1.8 1.8 1.7 1.5 1.6 1.5 1.3 0.8 0.7 0.8 1.1 1.5 2.4 3.5 4.0 4.6 5.3 6.0 6.8 7.7 8.3 9.0 8.1 7.3 6.6 6.0 5.5
=
77: Iridium
Z 98 99 100 101 102 103 104 105 106 107 108 109 110 111
112 113* 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131
174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207
Z 99 \
~-
176 177
1396.7 1405.9
I
0.4 0.1
Z 1.3 0.5 1.5 0.7 1.4 0.5 1.1 0.2 0.7 0.2 1.0 0.3 0.9 0.5 1.6 1.2 1.8 1.0 1.5 0.4 0.6 0.2 0.8 0.2 0.6
O. 0.1
O. O. O. 0.7 0.4 1.1 0.7
1386.0 1394.4 1404.1 1412.3 142.1. 6 1429.3 1438.3 1445.8 1454.3 1461.4 1469.6 1476.4 1484.3 1490.7 1498.4 1504.6 1512.0 1518.1 1525.5 1531.4 1538.6 1544.5 1551. 3 1556.9 1563.3 1568.7 1574.8 1580.1 1585.6 1589.3 1593.7 1597.2 1601.4 160·i.7
101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116* 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134
179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212
=
1417.3 1426.4 1435.4 1444.1 1452.7 1461.1 1469.3 1477.3 1485.1 1492.8 1500.3 1507.7 1514.8 1521. 8 1528.7 1535.4 1541.9 1548.3 1554.5 1560.6 1566.6 1572.4 1578.0 1583.5 1588.9 1594.1 1599.2 1604.2 1609.0 1613.7 1618.3 1622.7 1627.0 1631.2 Z
0.8 1.8
1396.6 1406.6
103 104
182 183
78: Platinum
1437.7 1446.7
-0.1
O. 0.2 0.4 0.9 1.2 1.3 1.2 1.5 1.7 1.5 1.4 1.6 1.8 2.2 2.5 3.1 3.8 4.6 5.4 6.0 6.3 7.1 7.8 8.3 9.0 8.2 7.3 6.8 6.1 5.7 5.2 5.2 4.7
=
1.3 2.1 1.1 . 1.8 0.6 1.1 0.5 1.3 0.4 1.0 0.6 1.6 0.9 1.6 0.8 1.5 0.7 1.1 0.2 0.5 0.1 0.7 0.1 0.4 0.3 0.4 0.2 1.1 0.7 1.3 0.9 1.4 0.6 1.2
1417.6 1427.6 1435.7 1445:3 1453.2 1462.4 1470.0 1478.9 1486.2 1494.7 1501.7 1510.0 1516.7 1524.7 1531. 3 1539.1 1545.4 1553.0 1559.2 1566.5 1572.6 1579.4 1585.2 1591.8 1597.5 1603.5 1607.7 1612.6 1616.5 1621. 2 1624.9 1629.4 1632.8 1637.1
1.2
14m.S 1447.4
~
>-3 0
a::...... Q
a::
~ Ul Ul
'"J
0
!:d
a::
c1 t
1
'1-'-
Number of neutrons N
Mass number A
I
Liquid Shell drop .:: correction
BCS pairing energy
Total binding energy
Number of neutrons N
Mass number A
, Z. = 79: G,!ld (Continuefi)
105 106 107
108 1:09 110 111 112 113 114 115 iL16
117 U8* .119
120 121 '122
.123 '124 12'5 '126
.127 ,128 ;129 :130 ;131 -:132
133 1M 135 136
184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206
207 208
209 .210
211 2:12 !2t;3
214 215
1455.6 1464'.2 1472'.7 t480':9 1489'.1 1497.0 1504.7 1512'.3 , 1519.7 1527.0 , 1534.1 1541'.0 1547.S 15Q4A 1560.9 1567.2 1573.4 J579'.5 1585'.3 1591.1 ,1596.7 1602.;1 1607.·5 i1612.6 1617.7 ,1622'.6 16;n·.4 . ;1632'·1 ! .1636.6 ,l64LO
1645.2 164'9>4.
-~.2 ~1
~3 ~3
0.8 ~8 ~S
0.7 1.0 1.4 1.8 2~3
2.9 ~9
~6 ~4 6~O
8.6 7~3
0.8 1'.4 0'.6 1.5 0.5 1.2
0.7 1.7 0.9 1.6 0.9 1.5 0'.6 0.8 0'.1 0.4 O. ,004 -0.1
0'.1 -0.1
~4
-0.1
.0.
7.6
0 ..6
~l
5.8
0.3 O.S 0.3 0.8
8~
0.2
~.2
B.2
Shell 'correction
BiGS pairing energy
Total binding energy
t-:l
.0;,
Z = 81: 'Thallium (Continued)
~O ~6 ~3
8.5
Liquid drop
0.6
5.0
-0.1
. '4~9
0.1
1455.4 1'.1065.0 1472.8 1482 .. 0 .1489.5 1498.4 1505.6 1514.2 1521.3 1529.6 1536.4 1544'.5 .1551.2 1559'.0 1565.5 1'573'.0 1579.3 1586.4 1592.5 1599.2 1605.2 1611.4 1615.S 1620.9 .1625.1 1630.0 l633.9 l638.6 1642.3 1,646.8 1650.2 1654.4
109 110 111 112 113 114 115 116 117 118 119 120 121 122* 123 124
204 205
125
206
126 127
207
128
129 130 131 132 133 134 135 136 137 la8 139 140
190 191 192 193 194 195 196 197 198 199 200 201 202
203
ZOS '209 210 211 212
213 214
215 216 217
218 219 220 221
1495.4 1503.8 1512.1 1520.2 1528.1 1535.8 1543.4 1550.9 155S.1 1565.3 1572.2 1579.0 1585.7 1592.2 159S.5 1604.7 1610.8 1616.7 1622.5 1628.1 1633.6 l639.0 1644.2 1649'.3 1654.3 1659.1 1663.8 lQ68A 1674.7 1561.8 1570.2 1577.2 158!>.2 ,1592.0 1599.6 1606 . .1 M13.3 161f}.8 1626.5 1631.3 1636.9 164l.5 1646'.8 ,1651.2 1656.4 1660.5 .1665.4 .1669.;2 .1j)73'.9 1676 .. 9
1.7 1.3 2.9
1684.5 1688.9
.1.2 2.'p
-.0 .. 6
1.4
-0.8
2.S 1.5 2'.4 1.2 1.'5
0'.
0.4 1.3 2.3 3.3
4.4 4'.9 5.5 6.1 6.8 7.7 8.!> 9.1 9.8 8.9 8.1 7.5
6.9 .6.4 6'.0
O·a
0.6 0.1 0.7 0.2 0.6 -0.1 0.1 -0.1 -:0'.1 -0.1
D.7 0.4 1'.0 0 .. 6 1.1
5.8 5.5
0'.4
5.5
-0.1 0.;1
5.4 4'.1
,. 2.7 1.8 .0.'5
0' ..8
iL681'.p
~
g
t-
'"'
0 ~ H 8 ~-
>
7JJ 7JJ
"'l 0 ~
~
q
t
7JJ
Z = 83: Bismuth
I
L4 2.7
1477.7 1487.5
111 112
I
194 195
1517.7 1526.2
I
-1.3 -1.4
)
00 I
f-' Gj
'l-
TABLE
Number of neutrons N
Mass number A
Liquid drop
8c-2.
Shell correction
CALCULATED BINDING ENERGIES IN MEV
BeS pairing energy
Total binding energy
Number of neutrons N
Mass number A
Z = 83: Bi8muth (Continued) 113 114 115 116 117 118 119 120 121 122 123 124 125 126* 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144
196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227
1534.6 1542.9 1550.9 1558.8 1566.6 1574.2 1581.6 1588.9 1596.0 1603.0 1609.8 1616.4 1623.0 1629.3 1635.6 1641.7 1647.6 1653.4 1659.1 1664.6 1670.0 1675.3 1680.4 1685.5 1690.3 1695.1 1699.7 1704.3 1708.6 1712.9 1717.1 1721.1
-0.6 -0.3 0.6 1.4 2.2 3.3 3.8 4.5 5.1 5.8 6.6 7.4 8.0 8.7 7.8 7.0 6.5 5.9 5.5 5.1 4.8 4.5 4.4 4.3 3.0 1.8 0.8 -0.3 -0.9 -1.7 -2.0 -2.5
(Continued) Liquid drop
Shell correction
BeS pairing energy
Total binding energy
1.9 1.0 1.3 0.8 1.3 0.8 1.3 0.7 1.0 0.8 0.9 0.8 1.5 1.2 1.8 1.3 1.8 1.2 1.6 0.7 1.0 0.8 2.6 2.0 3.4 2.6 3.7 2.5 3.0 0.9 1.3 1.0
1566.0 1574.1 1583.4 1591.4 1600.3 1608.0 1616.5 1624.0 1632.1 1639.5 1647.1 1652.8 1659.3 1664.8 1671.1 1676.3 1682.4 1687.4 1693.2 1697.9 1703.4 1707.3 1712.9 1716.6 1721. 9 1725.9 1730.5 1734.0 1738.8 1742.4 1747.2 1750.8
cr
I-'
t-.:l 00
Z = 85: A8tatine (Continued) 1.2 2.1 1.0 1.4 0.4 0.6 0.1 0.6 0.1 0.5 -0.1 0.1 -0.1
O. -0.1 0.6 0.3 0.8 0.4 0.9 0.3 0.7 -0.1 0.1
O. 1.6 1.3 2.6 2.0 3.1 2.3 3.3
1535.0 1544.6 1552.4 1561.5 1569.1 1578.0 1585.5 1593.9 1601.2 1609.2 1616.3 1623.9 1630.8 1637.9 1643.3 1649.3 1654.4 1660.1 1665.0 1670.6 1675.1 1680.5 1684.8 1689.8 1693.3 1698.5 1701.8 1706.6 1709.7 1714.3 1717.4 1721.8
116 117 118 119 120 121 122 123 124 125 126 127 128 129* 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147
201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232
1564.9 1573.2 1581. 2 1589.1 1596.8 1604.4 1611.9 1619.1 1626.3 1633.2 1640.1 1646.8 1653.3 1659.7 1665.9 1672.1 1678.0 1683.9 1689.6 1695.2 1700.6 1705.9 1711.1 1716.2 1721.1 1725.9 1730.6 1735.2 1739.7 1744.1 1748.3 1752.5
-0.7 0.1 0.9 1.5 2.1 2.8 3.4 4.2 4.9 5.4 6.1 5.3 4.5 4.0 3.4 3.0 2.5 2.4 2.0 2.0 1.8 0.6 -0.8 -1.5 -2.7 -3.0 -3.8 -3.6 -3.6 -1.9 -1.6 -1.4
z
c:l Q
~
i>
~
~ ;3 ....Q rJJ
Z = 84: Polonium
-
112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127* 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145
196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229
1528.5 1537.2 1545.6 1554.0 1562.1 1570.1 1577.9 1585.6 1593.1 1600.4 1607.6 1614.7 162l. 6 1628.3 1634.9 164l.4 1647.7 1653.9 1659.9 1665.8 167l. 6 1677.2 1682.7 1688.0 1693.3 1698.4 1703.3 1708.2 1712.9 1717.5 1722.0 1726.4 1730.6 1734.7
-l.9 -l.3 -l.5 -0.5 -0.1 l.0 l.9 2.5 2.9 3.6 4.3 5.3 6.0 6.6 7.3 6.5 5.6 5.0 4.3 3.9 3.4 3.3 3.0 3.1 2.9 l.7 0.2 -0.6 -2.0 -2.4 -3.5 -3.5 -4.3 -3.2
Z = 86: Radon
2.7 l.7 3.1 l.8 2.6 l.4 1.8 l.2 1.9 l.4 1.8 l.0 l.3 l.1 l.2 l.1 l.9 l.6 2.3 l.9 2.4 l.7 2.1 l.0 l.3 l.1 3.0 2.4 4.1 3.3 4.8 3.6 4.8 2.8
1529.1 1537.4 1547.1 1555.1 1564.6 1572.4 1581.6 1589.3 1598.0 160E;.5
1613.7 1621.0 1628.9 1636.1 1643.4 1648.9 1655.2 1660.5 1666.5 1671. 5 1677.4 1682.1 1687.7 1692.2 1697.5 170l. 2 1706.6 1710.0 1715.1 1718.4 1723.2 1726.4 1731.1 1734.2
Z = 85: Astatine
114 115
199 200
-l.5 -l.1
11548.0 . . 1556.6 1
2.0 l.3
1548.2 1556.5
117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 * 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148
203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 '231 232 233 234
1575.8 1584.0 1592.2 1600.1 1608.0 1615.6 1623.1 1630.5 1637.7 1644.7 165l. 6 1658.4 1665.0 1671.5 1677.8 1684.0 1690.1 1696.0 170l. 8 1707.5 1713.0 1718.4 1723.7 1728.8 1733.9 1738.7 1743.6 1748.3 1752.9 1757.4 176l. 7 1765.9
119 120 121 122
206 207 208 209
1594.8 1603.0 1611. 0 1618,9
-0.7
O. 0.5 0.9 l.7 2.1 3.1 3.7 4.3 4.9 4.2 3.3 2.8 2.1 l.7 l.2 l.1 0.7 l.0 0.6 -0.4 -2.1 -2.6 -4.1 -4.0 -5.0 -4.0 -2.2 -1.9 -l.7 -l.5 -1.2
l.7 2.2 l.7 2.4 l.8 2.4 l.6 2.1 l.9 2.0 l.8 2.7 2.3 3.0 2.6 3.1 2.3 2.8 l.7 2.1 l.7 3.8 3.0 4.8 3.5 4.8 2.9 2.1 l.5 2.0 l.8 2.2
1576.6 1586.2 1594.4 1603.5 1611.4 1620.2 1627.9 1636.3 1643.9 165l. 7 1657.6 1664.4 1670.1 1676.6 1682.0 1688.3 1693.5 1699.6 1704.5 1710.2 1714.3 1720.1 1724.1 1729.5 1733.3 1738.5 1742.3 1747.4 175l.4 1756.5 1760.5 1765.3
l.1 l.5 1.0 1.8
1595.6 1605.0 1613.2 1622.1·
p,. >-3
o
~
I-
:;j
o
l:d
~ cj t"'
p,.
m
Z = 87 : Francium
-0.2 0.5 1.2 1.4
~
f-'
I\:)
~
't1 ~
;:;l >-I
o
Ul
171 172 173 174 175 176 177 178 179 180 181 182
276 277 278 279 280 281 282 283 284 285 286 287
2008.8 2013.8 2018.8 2023.8 2028.6 2033.3 2038.0 2042.5 2046.9 2051.3 2055.5 2059.7
1.1 1.0 0.9 1.1 0.7 0.6 0.5 0.6
O. -0.1 -1.2 -1.4 Z
160 161 162 163 164 165 166 167 168 169 170* 171 172 173 174 175 176 177 178 179 180 181 182 183
266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289
1948.0 1954.6 1961. 0 1967.3 1973.5 1979.6 1985.5 1991.4 1997.1 2002.7 2008.2 2013.6 2018.9 2024.1 2029.2 2034.2 2039.2 2044.0 2048.7 2053.3 2057.8 2062.2 2066.5 2070.8
=
0.3 0.6 0.3 0.4 0.4 0.8 0.5 0.7 0.9 1.1 1.8 2.0
2009.4 2014.9 2019.6 2025.0 2029.5 2034.5 2038.8 2043.6 2047.6 2052.2 2056.1 2060.3
106 3.2 3.2 3.4 3.1 3.1 2.8 2.6 2.3 2.1 1.7 l.3 1.1 1.2 1.2 1.5 1.2 1.2 1.0 1.0 0.4 0.3 -0.6 -0.9 -1.1
0.7 0.1 0.3 0.1 0.4 0.1 0.5 0.2 0.6 0.4 1.0 0.6 1.0 0.7 0.8 0.8 1.1 0.9 1.2 1.4 l.7 2.3 2.7 2.5
i
1950.8 1956.8 1963.6 1969.5 1975.9 1981. 5 1987.7 1993.0 1999.0 2004.1 2009.9 2015.0 2020.8 2025.8 2031.3 2036.1 2041.3 2045.8 2050.7 2055.1 2059.8 2063.9 2068.3 2072.2
167 168 169 170 171 172 173 174* 175 176 177 178 179 180 181 182 183 184 185 186 187
275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295
1998.6 2004.7 2010.7 2016.5 2022.3 2028.0 2033.5 2039.0 2044.4 2049.6 2054.8 2059.8 2064.8 2069.7 2074.4 2079.1 2083.7 2088.1 2092.5 2096.8 2101.0
2.4 2.1 2.0 2.0 2.1 2.2 2.3 2.6 2.4 2.3 2.2 2.0 1.6 1.3 1.0 0.6 0.4 0.4 0.1 -0.6 -0.6 Z
166 167 168 169 170 171 172 173 174 175 176* 177 178 179 180
275 276 277 278 279 280 281 282 283 284 285 286 287 288 289
1995.2 2001.6 2007.9 2014.1 2020.1 2026.1 2031.9 2037.6 2043.3 2048.8 2054.3 2059.6 2064.8 2070.0 2075.0
=
0.2 0.8 0.4 0.8 0.4 0.8 0.5 0.6 0.6 0.9 0.8 1.2 1.3 1.8 1.8 2.4 2.1 2.3 2.0 3.0 2.3
2000.6 2007.0 2012.7 2019.0 2024.5 2030.7 2036.2 2042.0 2047.2 2052.7 2057.6 2062.9 2067.7 2072.7 2077.2 2082.0 2086.2 2090.8 2094.6 2099.1 2102.8
~ H
o ~
i>
U1 U1 "';j
o
109 2.9 2.6 2.5 2.4 2.5 2.6 2.8 3.0 3.3 3.1 3.1 3.0 2.8 2.5 2.2
~
1-3
o
0.1
O. 0.4 0.1 0.4
O. 0.3
O. 0.1 0.1 0.3 0.1 0.5 0.6 1.0
1997.7 2003.7 2010.3 2016.2 2022.7 2028.4 2034.8 2040.4 2046.5 2051.8 2057.5 2062.6 2068.0 2072.9 2078.2
~
c:j t
U1
f
i-' C;.?
'-0
TABLE
8c-2.
CALCULATED BINDING ENERGIES IN
Cf'
MEV (Continued)
I-' ~
i
Number of neutrons N
Mass number A
Z
181 182 183 184 185 186 187 188 189
Shell
Liquid drop
correction
= 109
290 291 292 293 294 295 296 297 298
2079.9 2084.7 2089.5 2094.1 2098.7 2103.1 2107.5 2111. 8 2115.9
278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295
2010.7 2017.0 2023.2 2029.4 2035.4 2041.3 2047.2 2052.9 2058.5 2064.0 2069.4 2074.7 2079.9 2085.0 2090.0 2094.9 2099.7 2104.4
168 169 170 171 172 173 174 175 176 177 178* 179 180 181 182 183 184 185
Number of neutrons N
Mass number A
=
1.1 1.6 1.3 1.5 1.2 2.2 1.6 2.2 1.5
2082.8 2087.8 2092.2 2096.9 2100.9 2105.6 2109.4 2113.8 2117.5
0.5 0.2 0.4 0.3 0.5 0.3 0.4 0.4 0.7 0.6 1.1 1.4 1.4 1.4 1.8 1.6 1.7 1.5
2013.7 2019.8 2026.6 2032.6 2039.2 20·15.1 2051. 3 2056.9 2062.8 2068.1 2073.8 2078.9 2084.3 2089.2 2094.3 2098.9 2103.8 2107.9
110 2.9 2.9 3.2 3.1 3.4 3.6 3.9 3.7 3.7 3.5 3.4 2.8 3.0 2.8 2.5 2.4 2.4 2.0
Liquid drop
Z
(Continued)
1.9 1.5 1.3 1.3 1.0 0.3 0.3 -0.1 0.1 Z
Total binding energy
BCS pairing energy
I
177 178 179 180 181 182* 183 184 185 186 187 188 189 190 191 192 193 194
289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306
288 289 290 291 292 293 294 295 296
= 112
5.1 5.0 5.0 5.3 5.1 4.8 4.7 4.7 4.3 3.7 3.5 3.1 3.0 2.8 2.7 2.6 2.8 2.6
0.5 0.9 0.8 0.8 0.7 1.1 0.8 1.0 0.8 1.7 1.3 1.9 1.4 1.9 1.4 1.8 1.2 1.6
2077.2 2083.3 2088.8 2094.6 2099.8 2105.3 2110.2 2115.4 2119.9 2125.1 2129.4 2134.3 2138.5 2143.3 2147.2 2151.9 2155.7 2160.2
6.1 6.2 6.2 6.3 6.4 6.6 6.4 6.2 6.1
-0.1 0.1
2068.6 2075.1 2080.9 2087.2 2092.9 2098.8 2104.2 2109.8 2114.8
o
(Continued)
2071.6 2077.4 2083.0 2088.6 2094.0 2099.3 2104.6 2109.7 2114.8 2119.7 2124.6 2129.4 2134.0 2138.6 2143.1 2147.5 2151.8 2156.0
2062.7 2068.8 2074.8 2080.8 2086.6 2092.3 2097.9 2103.4 2108.8
Total binding energy
Shell correction
Z
175 176 177 178 179 180 181 182 183
BCS pairing energy
=
113
O. 0.2 -0.1 O. -0.1 0.2 -0.1
zq
o
t" ~
P>
::d
"C
lJ1
;3 H
o
C/2
186 187 188 189 190 191
296 297 298 299 300 301
2109.1 2113.6 2118.0 2122.4 2126.6 2130.8
1.3 1.2 0.8 0.8 0.6 0.6
2.4 1.9 2.6 2.0 2.4 1.9
2112.8 2116.7 2121.. 4 2125.2 2129.6 213il.3
3.6 4.0 4.2 4.4 4.4 4.4 4.3 4.3 4.1 4.2 4.0 3.6 3.5 3.5 3.1 2.4 2.4 2.0 2.0 1.9 1.9 1.6
0.1 0.3 0.2 0.1 0.3 0.2 0.5 0.4 0.5 0.5 0.9 0.7 0.9 0.6 1.5 1.0 1.6 1.0 1.4 0.9 1.4
2035.9 204.2.7 2048.7 2055.1 2060.9 2066.9 2072.4 2078.3 2083.5 2089.1 2094.2 2099.5 2104.2 2109.3 2113.5 2118.6 2122.7 2127.5 2131.5 2136.1 21il9.9 21,14.4
4.8 5.0 5.1 5.1
0.4 0.6 0.4 0.7
2052.7 2059.3 2065.2 2071.5
Z = 111
171 172 In
174 175 176 177 178 179 180* 181 182 183 184 185 186 187 188 189 190 191 192
282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303
2032.3 2038.5 2044.6 2050.6 2056.5 2062.3 2068.0 20n.6
2079.1 2084.4 2089.7 2094.9 2100.0 2104.9 2109.8 2114.6 2119.3 2123.9 2128.4 2132.8 2137.1 2141.3
O.
Z = 112
173 174 175 176
285 286 287 288
2047.5 2053.7 2059.8 2065.8
-- -- - - - - - - - - - -
184* 185 186 187 188 189 190 191 192 193 194 195 196
297 298 299 300 301 302 303 304 305 306 307 308 309
2114.2 2119.4 2124.5 2129.5 2134.4 2139.3 2144.0 2148.7 2153.2 2157.7 2162.0 2166.3 2170.5
6.0 5.5 5.2 4.9 4.7 4.5 4.4 4.3 4.2 4.2 4.2 4.2 4.4
0.1
O. 0.6 0.3 0.8 0.4 0.8 0.3 0.7 0.2 0.5 -0.1
O.
2120.3 2124.9 2130.3 2134.7 2139.9 2144.2 2149.1 2153.3 2158.1 2162.1 2166.7 2170.5 2174.9
~
>'3
o ls: ......
Z = 114
177 178 179 180 181 182 183 184 185 186* 187 188 189 190 191 192 193 194 195 196 197 198
291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312
2077.7 2083.7 2089.7 2095.6 2101.4 2107.1 2112.7 2118.2 2123.6 2128.8 2134.0 2139.1 2144.1 2149.0 2153.8 2158.5 2163.2 2167.7 2172.1 2176.5 2180.7 2184.9
7.4 7.7 7.7 7.9 7.7 7.5 7.4 7.5 6.9 6.4 6.1 5.8 5.6 5.4 5.3 5.2 5.3 5.3 5.5 5.8 4.9 4.1
O. 0.1
O. O. O. 0.3
O. 0.1
O. 0.8 0.5 1.1 0.7 1.1 0.7 1.0 0.4 0.7
O. O. O. 1.2
Q
2085.1 2091. 6 2097.5 2103.6 2109.1 2114.9 2120.1 2125.7 2130.5 2136.0 2140.6 2145.9 2150.4 2155.5 2159.8 2164.8 2168.9 2173.7 2177.6 2182.3 2185.6 2190.1
ls: ~
U1 U1 >::j
o
~
q t
2 EmlU. E2 dE JJ
_ 2PZ 2mv 2 - {32 In I
(8d-9)
e
This choice of Emin is necessary to take into account the increase of J over JI at small energies W (see Fig. 8d-I) but it will not give exact agreement with the quantum mechanical theory. To achieve this, it is necessary to choose
I.
Iav exp
=
4\' C,Z
(8d-IO)
where Ie now of course is energy-dependent. For the practical calculation of stopping power, the following, relativistically correct formula is used:
S -!T =
=
e· g: 3
08 )
(i) [f({3) -
Z2
In Iav -
I c; - n
(8d-ll)
i
Stopping power in units MeV j(g/cm 2 ) = keV /(mg/cm 2 ); and Z, {3, Z, and A are defined with Eq. (8d-l). p = density of stopping material (g/cm 3) Co = shell correction of the ith shell Ii = density correction at high energies Iav = average excitation potential per electron of stopping atom (including low-velocity density effect), a constant by definition. f({3) = In
G~2~:) - {32
(8d-lla)
(32 and f({3) are listed in Table 8d-l as functions of the kinetic energy T of several particles. f({3) is applicable for any charged particle of velocity v = (3c and mass 0.25
f--
0.2
/I
0.15 0.1
e/z 0.05
o -0.05 -0.1 0.01
V I',i"
I!/
If
ty
< ,,'\
If
Jr---- :-:--.."""'"'
V
Ai
~~ ~
~ ~~ ~
II I
/11
~ ~ ;;;;;
/I 0.1
2
4
7 10
T/Z MeV
+
. FIG. Sd-3. Practical shell correction C / Z for particles of charge 1. The abEcissa is T /Z == Ti/(mrZ); see Eq. (Sd-12). For Z 225, Walske's, and for Z > 25, Bonderup's shell corrections are modified to fit experimental data for protons and deuterons. In this procedure. deviations from the first Born approximation are included in C/Z, and the shell corrections depend on the incident particle charge z. For C/Z < -0.1, the Bonderup corrections do not fit the data well.
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
8-147
M »m. If an ion of mass Mi and kinetic energy Ti is under consideration, its velocity can be found by looking up in Table Sd-1 the value of {J corresponding to a proton energy (Sd-12) where mr = M;c 2/93S.259 MeV. In general it will be easiest to use existing tables, e.g., NS70. Due to the generalized approach used in NS70, large differences from experimental data are found, e.g., for alpha particle ranges in argon (50 percent at 1 MeV, no less than 4 percent up to 10 MeV). The shell corrections can be obtained from Fig. Sd-3, and I values from Fig. Sd-4. 6 5 14
~
3
N
.....
Jl 2 1
.
•
.
• •eo
10
•
9
o
• •
8
'.16
24
32
40
48
. . ,
56
64
72
80
88
Z
FIG. 8d-4. 'The mean excitation energy Iav for different elements. Given is IavlZ versus Z, For H 2, Iav = 19.2 eV, for He, Iav = 41.3 eV, from a-particle measurements. The values represent the author's present opinion, and may change by several percent. The strong fluctuations found for neighboring elements are significant though.
For most metals the density effect 0 is negligible for proton energies below 1000 MeV. For details see ST67, FA56, CF70, and page 69 of BK5S. Experimental confirmation is found, e.g., in NM67, and BH67. At low energies (proton energies of less than 0.5 MeV, alpha-particle energies below 2 MeV), the charged particle will not have its full charge (see Sec. Sd-6). A list of values for S computed (BJ67) from Eq. (Sd-ll) is given in Table Sd-2. For emulsion, see BD63 and BA63. For the other materials, the I values given in Fig. Sd-5 were used. The shell corrections are discussed in Sec. Sd-5. The density effect is not used. For proton energies of 0.05 to 12 MeV, the experimental stopping powers for many substances are given in Table Sd-3. Most of these numbers are read from the graphs of WH5S, and the tables of AH67, AS6S, and AV69. This seems to be the best way to average the experimental results, but see also MA6S, OR6S, WM67, JK6S, SP70. The stopping cross section in eV-cm 2 per atom can be obtained by multiplying Swith the factor (A/No) X 10' (Avogadro's nuniberN o, atomic weight A). For protons in other elements, interpolation for Z, by the method of Lindhard and Scharff (LS53) can be used, but direct computation from Eq. (Sd-H) is recommended. (A discussion of experimental results is found in BK67.) The stopping power of compounds is within a few percent an additive function of the stopping power of the elements which make up the compound (Bragg rule, see, e.g., BI6S or BT6S). Precise measurements at 300 MeV (TH52) have shown deviations of about 1 percent.from additivity. At energies between 4 and 30 MeV energy-
8-148 TABLE
NUCLEAR PHYSICS
8d-1.
RELATIVISTIC VELOCITY {3 = FUNCTION
f({3); FOR
vic,
(32, AND STOPPING-NUMBER
HEAVY IONS AS A FUNCTION
OF KINETIC ENERGY
T
Kinetic energy T for Protons. MeV
Alphas. MeV
Pions. MeV
Muons. MeV
Electrons. keV
{3
(32
fC(3)
0.50 0.55 0.60 0.65 0.70
1.9863 2.1849 2.3836 2.5822 2.7808
0.0744 0.0818 0.0893 0.0967 0.1041
0.0563 0.0619 0.0676 0.0732 0.0788
0.2723 0.2995 0.3268 0.3540 0.3812
0.032634 0.001065 0.034225 0.001171 0.035745 0.001278 0.037204 0.001384 0.038606 0.001490
6.9925 7.0877 7.1746 7.2546 7.3286
0.75 0.80 0.85 0.90 0.95
2.9795 3.1781 3.3767 3.5753 3.7740
0.1116 0.1190 0.1265 0.1339 0.1413
0.0845 0.0901 0.0957 0.1014 0.1070
0.4085 0.4357 0.4629 0.4902 0.5174
0.039960 0.041269 0.042537 0.043769 0.044966
0.001597 0.001703 0.001809 0.001916 0.002022
7.3975 7.4620 7.5225 7.5796 7.6336
1.00 1.10 1.20 1.30 1.40
3:9726 4.3699 4.7671 5.1644 5.5616
0.1488 0.1636 0.1785 0.1934 0.2083
0.1126 0.1239 0.1351 0.1464 0.1577
0.5446 0.5991 0.6536 0.7080 0.7625
0.046132 0.002128 0.048380 0.002341 0.050528 0.002553 0.052587 0.002765 0.054567 0.002978
7.6848 7.7800 7.8668 7.9467 8.0206
1.50 1.60 1. 70 1.80 1.90
5.9589 6.3562 6.7534 7.1507 7.5479
0.2231 0.2380 0.2529 0.2678 0.2827
0.1689 0.1802 0.1914 0.2027 0.2140
0.8169 0.8714 0.9259 0.9803 1.0348
0.056478 0.003190 0.058326 0.003402 0.060116 0.003614 0.061854 0.003826 0,063544 0.004038
8.0895 8.1539 8.2143 8.2713 8.3252
2.00 2.10 2.20 2.30 2.40
7.9452 8.3425 8.7397 9.1370 9.5342
0.2975 0.3124 0.3273 .0.3422 0.3570
0.2252 0.2365 0.2477 0.2590 0.2703
1.0893 1.1437 1.1982 1.2526 1.3071
0.065189 0.004250 0.066794 0.004461 0.068360 0.004673 0.069891 0.004885 0.071388 0.005096
8.3764 8.4250 8.4714 8.5157 8.5581
2.50 2.60 2.70 2.80 2.90
9.9315 10.3288 10.7260 11.1233 11.5205
0.3719 0.3868 0.4017 0.4165 0.4314
0.2815 0.2928 0.3041 0.3153 0.3266
1. 3616 1.4160 1.4705 1.5250 1.5794
0.072855 0.005308 0.074292 0.005519 0.075701 0.005731 0.077084 0.005942 0.078442 .0.006153
8.5987 8.6378 8.6754 8.7116 8.7465
3.00 3.10 3.20 3.30 3.40
11.9178 12.3151 12.7123 13.1096 13.5068
0.4463 0.4612 0.4760 0.4909 0.5058
0.3378 0.3491 0.3604 0.3716 0.3829
1.6339 1. 6884 1. 7428 1.7973 1.8517
0.079776 0.006364 8.7803 0.081089 0.006575 8.8129 0.082380 0.006786 8.8445 0.083650 0.006997 , 8.8751 0.084901 0.007208 8.9048
3.50 3.60 3.70 3.80 3.90
13.9041 14.3014 14.6986 15.0959 15.4931
0.5207 0.5356 0.5504 0.5653 0.5802
0.3941 0.4054 0.4167 0.4279 0.4392
1.9062 1.9607 2.0151 2.0696 2.1241
0.086134 0.007419 0.087349 0.007630 0.088547 0.007841 0.089728 0.008051 0.09089 40.008262
8.9336 8.9616 8.9889 9.0154 9.0412
4.00 4.10 4.20 4.30 4,40
15.8904 16.2877 16.6849 17>.0822 17 .. 4794
0.5951 0.6099 0.6248 0.6397 0.6546
0.4505 0.4617 0.4730 0.4842 0.4955
2.1785 2.2330 2.2874 2.3419 2.3964
0.09204 50.008472 0.09318 10.008683 0.09430 30.008893 0.09541 10.009103 0.09650 70.009314
9.0664 9.0909 9.1148 9.1382 9.1610
PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE
8d-1.
RELATIVISTIC VELOCITY {3 =
FUNCTION
f({3)
vic,
8-149
(32, AND STOPPING-NUMBER
FOR HEAVY IONS AS A FUNCTION
OF KINETIC ENERGY
T (Con#nued)
Kinetic energy T for Protons, MeV
Alphas, MeV
Pions, MeV
Muons, MeV
Electrons, keV
{3
(3'
f({3)
4.50 4.60 4.70 4.80 4.90
17.8767 18.2740 18.6712 19.0685 19.4657
0.6694 0.6843 0.6992 0.7141 0.7289
0.5068 0.5180 0.5293 0.5405 0.5518
2.4508 2.5053 2.5598 2.6142 2.6687
0.097589 0.009524 0.098660 0.009734 0.099718 0.009944 0.100766 0.010154 0.101802 0.010364
9.1834 9.2052 9.2265 9.2474 9.2679
5.00 5.50 6.00 6.50 7.00
19.8630 21.8493 23.8356 25.8219 27.8082
0.7438 0.8182 0.8926 0.9670 1.0414
0.5631 0.6194 0.6757 0.7320 0.7883
2.7232 2.9955 3.2678 3.5401 3.8124
0.102827 0.010573 0.107803 0.011622 0.112552 0.012668 0.117102 0.013713 0.121474 0.014756
9.2879 9.3825 9.4687 9.5480 9.6213
7.50 8.00 8.50 9.00 9.50
29.7945 31.7808 33.7671 35.7534 37.7397
1.1157 1.1901 1.2645 1.3389 1.4133
0.8446 0.9009 0.9572 1.0135 1.0698
4.0847 4.3570 4.6294 4.9017 5.1740
0.125688 0.129758 0.133699 0.137521 0.141233
0.015797 0.016837 0.017875 0.018912 0.019947
9.6895 9.7533 9.8131 9.8695 9.9228
10.00 10.50 11.00 11.50 12.00
39.7260 41.7123 43.6986 45.6849 47.6712
1.4876 1.5620 1.6364 1.7108 1.7852
1.1261 1.1824 1.2387 1.2950 1.3514
5.4463 5.7186 5.9909 6.2632 6.5356
0.144845 0.020980 0.148363 0.022012 0.151795 0.023042 0.155145 0.024070 0.158420 0.025097
9.9733 10.0213 10.0671 10.1108 10.1526
12.50 13.00 J3.50 14.00 14.50
49.6575 51.6438 53.6.301 55.6164 57.6027
1.8596 1.9339 2.008.3 2.0827 2.1571
1.4077 1.4640 1.520.3 1.5766 1.6329
6.8079 7.0802 7.3525 7.6248 7.8971
0.161623 0.026122 0.164759 0.027145 0.167831 0.028167 0.170844 0.029188 0.173800 0.030206
10.1927 10.2311 10.2!l81 10.3037 10.3380
15.00 15.50 16.00 16.50 17.00
59.5890 61.5753 63.5616 65.5479 67.5342
2.2315 2.3059 2.3802 2.4546 2.5290
1.6892 1.7455 1.8018 1.8581 1.9144
8.1695 8.4418 8.7141 8.9864 9.2587
0.176701 0.031223 0.179552 0.032239 0.182353 0.033253 0.185108 0.034265 0.187818 0.035276
10.3712 10.4032 10.4342 10.4643 10.4934
17.50 18.00 18.50 19.00 19.50
69.5205 71.5068 73.4931 75.4794 77.4657
2.6034 2.6778 2.7522 2.8265 2.9009
1.9707 2.0270 2.0833 2.1396 2.1960
9.5310 9.8033 10.0757 10.3480 10.6203
0.190486 0.036285 0.193112 0.037292 0.195700 0.038298 0.198249 0.039303 0.200762 0.040306
10.5216 10.5490 10.5757 10.6016 10.6269
20.00 21.00 22.00 23.00 24.00
79.4520 83.4246 87.3972 91.3698 95.3424
2.9753 3.1241 3.2728 3.4216 3.5704
2.2523 2.3649 2.4775 2.5901 2.7027
10.8926 11.4372 11.9819 12.5265 13.0711
0.203241 0.208097 0.212829 0.217443 0.221947
0.041307 0.043305 0.045296 0.047281 0.049261
10.6514 10.6988 10.7438 10.7868 10.8279
25.00 26.00 27.00 28.00 29.00
99.3150 103.2876 107.2602 111. 2328 115.2054
3.7191 3.8679 4.0167 4.1654 4.3142
2.8153 2.9279 3.0405 3.1532 3.2658
13.6158 14.1604 14.7050 15.2496 15.7943
0.226348 0.051234 0.230652 0.053200 0.234864 0.055161 0.238989 0.057116 0.243032 0.059064
10.8673 10.9051 10.9414 10.9763 11.0100
8-150 TABLE
NUCLEAR PHYSICS
Sd-l.
R.ELATIVISTIC VELOCITY
FUNCTION
f(fJ)
fJ
=
vic,
fJ2,
AND STOPPING-NUMBER
FOR HEAVY IONS AS A FUNCTION
OF KINETIC ENERGY
T (Continued)
Kinetic energy T for Protons, MeV
Alphas, MeV
Pions, MeV
Muons,
MeV
Electrons, keV
fJ
fJ2
f(fJ)
30.00 31.00 32.00 33.00 34.00
119.1780 123.1506 127.1232 131. 0958 135.0684
4.4629 4.6117 4.7605 4.9092 5.0580
3.3784 3.4910 3.6036 3.7162 3.8288
16.3389 16.8835 17.4282 17.9728 18.5174
0.246996 0.250885 0.254704 0.258454 0.262140
0.061007 0.062943 0.064874 0.066799 0.068717
11. 0425 11.0738 11.1042 11.1335 11.1620
35.00 36.00 37.00 38.00 39.00
139.0410 143.0136 146.9862 150.9588 154.9314
5.2068 5.3555 5.5043 5.6531 5.8018
3.9414 4.0541 4.1667 4.2793 4.3919
19.0621 19.6067 20.1513 20.6959 21. 2406
0.265763 0.269327 0.272833 0.276284 0.279683
0.070630 0.072537 0.074438 0.076333 0.078222
11.1896 11.2164 11.2424 11.2677 11.2923
40.00 41.00 42.00 43.00 44.00
158.9040 162.8766 166.8492 170.8218 174.7944
5.9506 6.0994 6.2481 6.3969 6.5457
4.5045 4.6171 4.7297 4.8424 4.9550
21.7852 22.3298 22.8745 23.4191 23.9637
0.283030 0.080106 0.286328 0.081984 0.289579 0.083856 0.292784 0.085722 0.295944 0.087583
11.3163 11.3396 11.3624 11.3845 11.4062
45.00 46.00 47.00 48.00 49.00
178.7670 182.7396 186.7122 190.6848 194.6574
6.6944 6.8432 6.9919 7.1407 7.2895
5.0676 5.1802 5.2928 5.4054 5.5180
24.5084 25.0530 25.5976 26.1422 26.6869
0.299062 0.302138 0.305173 0.308170 0.311129
11.4273 11 .4480 11.4682 11.4879 11.5072
7.4i\82
27.2315 5.6306 5.9122 28.5931 6.1937 1 29.9547 6.4752 31. 3162 6.7568 32.6778
0.314051 0.098628 11. 5261 10.321203 0.103171 11.5716 0 _i\2F1147 (I 107(\80 11.6149 0.334896 0.112155 11.6562 0.341463 0.116597 11.6956
198.6300 50.00 208.5615 52.50 55.00 1 218.4930 228.4:':45 57.50 60.00 238.3560
7.8102 8.1821 1 8.5540 8.9259
0.089438 0.091287 0.093131 0.094969 0.096801
62.50 65.00 67.50 70.00 72.50
248.2875 258.2190 268.1505 278.0820 288.0135
9.2978 9.6697 10.0416 10.4135 10.7855
7.0383 7.3198 7.6014 7.8829 8.1644
34.0394 35.4010 36.7625 38.1241 39.4857
0.347858 0.354091 0.360170 0.366105 0.371903
0.121005 0.125380 0.129723 0.134033 0.138312
11.7333 11.7695 11. 8041 11.8375 11.8696
75.00 77.50 80.00 82.50 85.00
297.9450 307.8765 317.8080 327.7395 337.6710
11 .1574 11.5293 11.9012 12.2731 12.6450
8.4460 8.7275 9.0090 9.2906 9.5721
40.8473 42.2088 43.5704 44.9320 46.2936
0.377569 0.383111 0.388534 0.393843 0.399043
0.142558 0.146774 0.150958 0.155112 0.159236
11.9005 11.9304 11.9592 11.9871 12.0141
87.50 90.00 92.50 95.00 97.50
347.6025 357.5340 367.4655 377.3970 387.3285
13.0169 13.3888 13.7608 14.1327 14.5046
9.8.536 10.1352 10.4167 10.6982 10.9798
47.6551 49.0167 50.3783 51.7399 53.1014
0.404140 0.163329 0.409136 0.167392 0.414036 0.171426 0.418845 0.175431 0.423564 0.179407
12.0403 12.0657 12.0903 12.1142 12.1375
100.00 105.00 110.00 115.00 120.00
397.2600 417.1230 436.9860 456.8490 476.7120
14.8765 15.6203 16.3641 17.1080 17.8-518
11 .2613 11.8243 12,3874 12.9505 13.5135
54.4630 57.1862 59.9093 62.6325 65.3556
0.428198 0.437222 0.445938 0.454366 0.462525
12.1601 12.2036 12.2450 12.2844 12.3220
0.183354 0.191163 0.198860 0.206448 0.213929
PASSAGEl OF CRARGElD PARTICLElS THROUGH: MATTER TABLE 8d-1.
RELATIVISTIC VELOCITY (3 =
FUNCTION
f((3)
vic,
8-151
(3', AND STOPPING-NUMBER
FOR HEAVY IONS AS A FUNCTION
OF KINETIC ENERGY
T (Continueil)
Kinetic energy T for (3
(3'
f((3)
Alph"s, MeV
Pions, MeV
Muons, MeV
125.00 130.00 135.00 140.00 145 .. 00
496.5750 516.4380 536.3010 556 .. 1640 576.0270
18.5956 19.3394 20.0833 20.827i 21.5709
14.0766 14.6397 15.2027' 15.7658 . 16.3289
68.0788 70.8019 73.5251 76.2482 78.9714
0:470431 0.221305 0.478098 0.228577 0.485539 0.235748 0.492767 0.242820 0.499793 0.249793
12.3579 12.3923 12.4254 12.4572 12.4878
150 .. 00 155.00 160.00 165.00 170 .. 00
595.8900 615.7530 635.6161 655.4791 675.3421'
22.3147 23.0586 23.8024 24.5462 25:2900
16.8919 17.4550 18.018i 18.5811 19.1442
81.6945 84.4177 87.1408 89.8640 92.5871
0.506627 0.513279 0.519756 0.526067 0.532220
0.256671 0.263455 0.270146 0.276747 0.283258
12.5173 12.5457 12.5733 12.5999 12.6257
175.00 180.00 185.00 190.00 195.00
695.2051 715.0681 734.9311 754.7941 774.6511
26.0339 26.7777 27.5215 28.2653 29.0092
19.7072 20.2703 20.8334 21.3964 21.9595
95.3103 98.0334 100.7566 103.4797 106.2029
0.538221 0.289682 0.544077 0.296019 0 . .549793 0.302273 0.555377 0.308443 0.560832 0.314532
12.6507 12.6749 12.6985 12.7214 12.7437
200.00 205.00 2iO.00 215.00 220.00
794.5201 814.383i '834.2461 854.1091 873.9721
29.7530 30.4968 31.2406 31. 9845 32.7283
22.5226 23.0856 23.6487 24.2118 24.7748
108.9260 111. 6492 114.3723 117.0955 119.8186
0.566163 0.320541 0.571377 0.326471 0.576476 0.332324 0.581464 0.338101 0.586347 0.343803
12.7655 12.7866 12.8073 12.8274 12.8471
225.00 230.00
33.4721 34.2159 34.9597 35.7036 36.4474
25.3379 25.9010 26.4640 27.0271 27 . .5901
122.5418 12.5.2649 127.9881 130.7112 133.4344
o..591128 0.349432
240.00 245.00
893.8351 913.6981 933.5611 953.4241 973.2871
0 . .59.5809 0.3.54989 0.600396 0.36047.5 0.604889 0.365891 0.609294 0.371239
12.8663 12.8851 12.903.5 12.9215 12.9391
250.00 255.00 260.00 265.00 270.00
993.1501 1013.0131 1032.8761 1b52.7391 1072.6021
37.1912 '37.9350 38.6789 39.4227 40.166.5
28.1.532 28.7163 29.2793 29.8424 30.4055
136.1575 138.8807 141. 6038 144.3270 147.0501
0.613611 0.3766i9 0.617845 0.381733 0.621998 0.386882 0.626073 0.391967 0.630070 0.396989
12.9.564 12.9734 12.9900 13.0063 13.0223
27.5.00 280 ..00 285.00 290.00 295.00
1092.4651 1112.3281 1132.19li 11.52.0.541 1171.9171
40.9103 41.6.542 42.3980 43.1418 43.8856
30.9685 31. .5316 32.0947 32.6577 33.2208
149.7733 152.4964 155.2196 157.9427 160.66.59
0.633994 0.401949 0.637846 0.406848 0.641628 0.411687 0.64.5342 0.416467 . 0.648991 0.421189
13.0380 13.0534 13.0686 13.0835 13.0982
303.00 310.00 320.00 330.00 340.00
1191.7801 :1231 . .5061 1271.2321 1310.9.581 1350.6841
44.6295 46.1171 47.6048 49.0924 .50.5801
33.7838 34.9100 36.0361 37.1622 38.2884
163.3890 168.8353 174.2816 179.7279 185.1742
0.6.52.575 0.425854 0.6.59558 0.435016 0.666304 0.443961 0.672826 0 ..452695 0.67913.5 0.46122.5
)3.1126 13.1409 13.1682 13.1948 13.2206
3.50.00 1390.4i01 '360.00 . 1430.1361 '370.00 . 1469.8621 . 380.00 1509.5881 390.00 '1549.3141
52.0677 .53.5554 65.0430 56 . .5307 .58.0183
39.4145 40.5406 41.6667 42.7929 43.9190
190.6205 196.0668 201 . .5131 '206.9.594 212.40.57
0.68.5242 0.469557 9.6911.56 0.477697 0.696887 0.48.5661 0.702442 0.49342.5 0.707830 0.501024
i3.2458 13.2703 13.2942 .i3.3176 13.3404
Protons, MeV
i
Electrons, keV
i
235.~0
8-152
NUCLn:AR PHYSICS
TABLE
8d-1.
RELATIVISTIC VELOCITY (3 =
FUNCTION
f((3)
vic,
(32, AND STOPPING-NUMBER
FOR HEAVY IONS AS A FUNCTION
OF KINETIC ENERGY
T (Continued)
Kinetic energy T for
,
(3
(32
f({3)
MeV
Alphas, MeV
Pions, MeV
:MuOTIs. MeV
Electrons, keV
400,00 410.00 420.0(l 430.00 440.00
1.589,fWll 1628.7661 16A8.4021 1708.2181 1H7.9441
59 ..5060 60.9936 62.4813 63.0689 65.4566
45.0451 46,1713 47.2074 48.4235 49.5496
217.8520 223.2083 228.7446 234.1009 230.6372
0.713059 0.5084.53 0.718135 0.515717 0.723064 0.522822 0.727854 0.529772 0.732510 0.536570
13,3626 13,3845 13.4058 13.4267 13.4473
450.00 460.00 470.00 480.00 490,00
17R7.G701 1827.3961 lS67.1221 1906.8482 1946.574:2
66.0442 68.4319 69.9195 71.4071 72.8048
50.6758 .51. 8010 52.9:280 54.0542 55.1803
245.0835 250.5298 255.9761 261.4224 266.8687
0.737036 0.741440 0.745724 0.740895 0.753956
0.543223 0.549733 0.556105 0.562342 0,568450
13.4674 13.4871 13.5065 13.5256 13.5444
.50'1.00 510.00 520.00 530.00 540.00
1986.1002 2026.0262 2065.7522 2105.4782 2145.2042
74.38"4 75.87f11 77.3577 78.8454 80.3330
,'i6.3064 57.4325 58.5587 60.8109
272.3150 277.7613 283.2076 288.6539 294.1002
0.757911 0,761765 0.765521 0.769183 0.772754
0.574430 0.580286 0.586023 0.591643 0.5971·19
13.5628 13.5809 13.5988 13.6164 13.6337
550.00 560.UO 570.00
2184.0302 2234.6562
580.00
2304.1082
590.00
2313. [:342
81. 8207 83.3083 84.7960 86.2836 87.7713
61.9371 6:i.0632 64.1893 65,3154 60.4416
299.5465 304.9928 310.4391 315.8854 321. 3317
0.776237 0.779636 0.782953 0.786191 0.789353
0.602.545 0.(j07S32 0.613015 0.61809(j 0.623078
13,6508 13.6677 13.6843 13.7007 13.7168
600.00 610.00 620.00 630.00 640.00
2333.5602 67.5fl77 326.7780 0.792441 80.2589 2423.2862 90.7466 68.6938 332.2243 0.795458 2463.0122 1 92.2M2 1 69.8200 1 337.6706 0.798406 2502.7382 93.7219 70.9461 343.1169 0.801287 2542.4642 95.2095 72.0722 34fl.5632 0.804103
0.627963 0.6327531 0.637451 0.642060 0.646582
13,7486 13.7642 13,7795 13.7947
650.00 660,00 670.00 680.00 690.00
2582.1902 2621.9162 266l. 6422 2701.3682 ;)741. 0942
96.6972 98.1848 99.6725 101.1601 102.6478
73.1983 74.3245 75.4506 76 ..5767 77.7029
354.0095 359.4558 364.9021 370.3484 375.7947
0.651018 0.655372 0.659644 0.663837 0.667954
13.8098 13.8246 13.8393 13.8539 13.8683
700.00 710.00 720.00 730.00 740.00
2730.8202 2820.5462 2860.2722 2899,9982 2939,7242
104.1354 105.6231 107.1107 108.5984 110,0860
78.8;)1)0 79.9551 81.0812 82.2074 83.3335
381. 2410 0.819753 0.671995 13.8825 386.687:3 0,822170 0.675963 13.8966 392.1336 0,824536 0.679859 13.9106 397,5199 0.826853 0.683686 13.9244 403.0262 0.829123 0.687444 13.9380
750.00 760.00 770.00 780,00 790,00
2979.4502 3019.1762 3058.9022 3098,6282 3138.3542
111.5737 113.0613 114.5490 116.0366 117.5243
84.4596 85.5857 86.7119 87.8380 88.9641
408.4725 413.9188 419.3651 424.8114 430.2577
(J,S31346 0.691136 0.833524 0.694763 0.835659 0.698326 0.837751 0.701827 0.839802 0.705268
800.00 810,00 820.00 830.00 840,00
3178,0803 3217,8063 3257,5323 3297.2588 :3336.9843
119.0119 120.4996 121. 9872 123.4749 124.9625
90.0903 9l. 2164 92.3425 93.4686 94.5948
435,7040 441.1503 446.5966 452.0429 '157.4892
0.841813 0.843785 0,845718 0.847615 0.849476
Protons,
2261.
::;~22
59.6848
0.806857 0.809550 0.812185 0.814762 0.817284
0.708649 0,711973 0.715239 0.718451
13.7328
13.9516 13.9650 13.9783 13,9915 14.0045
14.0175 14.0303 14.0430 14.0556 0.7n60\) 14.0681
PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE
8d-I.
8~153
RELATIVISTIC VELOCITY (3=V/C, (3', AND STOPPING-NUMBER
FUNCTIONf((3) FOR HEAVY IONS AS A FUNCTION OF KINETIC ENERGY
T (Continued)
Kinetic energy T for '--.
(3
(32
1«(3)
462.9355 468,3818 473.8281 479.2744 484.7207
0.851301 0.853093 0.854851 0.856576 0.858270
0.724714 0:727767 0.730770 0.733723 0.736628
14.0805 14 . 0928 14.1050 l4.1172 l4.1292
101.3515 102.4777 103.6038 104.7299 105.8561
490.1670 495.6133 501.0596 506.5059 511.9522
0.859933 0.861566 0.863170 0.864745 0.866293
0.739485 0.742297 0.745063 0.747785 0.750463
14.1411 14:1529 14.1647 14.1763 14.1879
141.3266 142.8143 144.3019 145.7896 147.2772
10B.9822 108.1083 109.2344 110.3606 111.4867
517.3985 522.8448 528.2911 533.7374 539.1837
0.867813 ·0.869306 0.870774 0.872216 0.873634
0.753099 0,755694 0.758248 0.760762 0.763237
14.1994 14.2108 14.2221 14.2334 14.2446
l48.7649
112.6128
544.6300 0.875028 0.765673 14.2556
protons,l MeV I
Alphas, MeV
Pi.ons,
850.00 860.00 870.00 880.00 890.00
MeV
Muons, MeV,
Electrop.s, keV
3376.7103 3416.4363 3456.1623 3495.8883 3535.6143
126.4502 127.9378 129.4255 130.9131 132.4008
95.7269 96.8470 97.9732 99.0993 100.22.'54
900.00 910.00 .920.00 93.0.00 940.00
3575.3403 3615.0663 3654.7923 3694.5183 3734.2443
133.888;1 135.3761 136.8637 138.3514 139.8390
950.60 960.00 970.00 980.00 990.00
3773.9703 3813.6963 3853.4223 3893.1483 3932.8743
1000.00
3972.6003
dependent deviations up to 3 percent have been observed for A1 20 3, Si0 2, and Lucite (TS67 and BToS). At sin,all e118rglb6, energy-loss IneaSUl'BInellts (SZG5, BP71) have 'also shown deviations from the Bragg rule. For the approximation' with an analytic function, the expression
S
=
CT"
maybe u$edoverJimited energy ranges; e.g" for protons with 5 < T < 20 Me V in Ge, C = 136.7 imd IX =, -0.7313 will be accurate to better than 0.4 percent (see BI68 for other values). If particles of initial energy Tare absorbed in a material of thickness 8, the mean residual energy '1', of the particles can be calcUlated directly: where
'1', = (CRTY -s)1IY C R = (C'Y)-1 and 'Y = 1
~
IX. ,
If the stopping power is used to obtain '1'1, successive approximations mUJ3t be calculated. The computer program of BJ67 produces the coefficients C, CR ) and IX, Bd-4. Range~energy Relations. As long as fewer than about 20 perce'nt of the par,ticles are removed from the incident beam by ,nuclear reactions, the median projected ,ange Rm(T) isdefineq. as the thickness of material through which one"'half of the incident monoenergetic charged 'particles of energy T are transmitted (see page 203 of BI68). The mean range of monoenergetic particles of kinetic energy T is defined by R(T)
=
ff(R)R dR
(Sd-I3)
8-154
NUCLEAR PHYSICS TABLE
8d-2.
CALCULATED MASS STOPPING POWER
Sip
IN MEV/(G/CM 2) FOR PROTONS
'"
66.6 eV Water
166 eV Al
eu
40.875 39.303 37.858 36.525 35.292
46.641 44.840 43.185 41.666 40.254
33.776 32.531 31. 385 30.325 29.343
31. 448 30.456 29.531 28.666 27.855
34.147 33.082 32.087 31.156 30.283
38.944 37.724 36.586 35.521 34.522
15.0 15.5 16.0 16.5 17.0
27.094 26.376 25.700 25.061 24.456
29.463 28.690 27.960 27.271 26.618
17.5 18.0 18.5 19.0 19.5
23.882 23.337 22.820 22.327 21.857
20.0 21. 0 22.0 23.0 24.0
475 eV
820 eV
Ag
Pb
27.169 26.218 25.341 24.528 23.773
23.213 22.435 21.714 21. 045 20.422
17.620 17.068 16.556 16.079 15.633
28.429 27.577 26.779 26.032 25.330
23.069 22.409 21. 790 21.209 20.663
19.840 19.294 18.781 18.299 17.844
15.216 14.823 14.454 14 .10.~ 13.775
33.583 32.700 31. 865 31. 077 30.331
24.669 24.045 23.456 22.898 22.369
20.148 19.662 19.202 18.764 18.348
17.415 17.009 16.625 16.259 15.910
13.463 13.167 12.885 12.618 12.363
25.999 25.411 24.852 24.320 23.812
29.623 28.951 28.312 27.703 27.123
21. 866 21. 389 20.934 20.500 20.086
17.953 17.577 17.218 16.876 16.549
15.579 15.263 14.961 14.673 14.398
12.120 11. 888 11.666 11.454 11.251
21.409 20.571 19.802 19.095 18.442
23.327 22.421 21. 590 20.824 20.117
26.569 25.534 24.584 23.710 22.902
19.690 18.949 18.268 17.640 17.059
16.237 15.651 15.110 14.609 14.145
14.134 13.639 13.181 12.756 12.362
11.056 10.688 10.348 10.032 9.738
17.837 17.275 16.750 16.261 15.802
19.462 18.852 18.284 17.753 17.256
22.153 21.457 20.808 20.202 19.634
16.519 16.017 15.548 15.109 14.697
13.714 13.312 12.936 12.585 12.254
11.995 11. 653 11.333 11. 033 10.750
9.464 9.207 8.965 8.738 8.524
30.0 31.0 32.0 33.0 34.0
15.372 14.967 14.586 14.225 13.885
16.789 16.349 15.935 15.544 15.174
19.101 18.600 18.127 17.681 17.258
14.310 13.946 13.602 13.276 12.969
11.943 11.648 11.370 11.107 10.857
10.483 10.230 9.992 9.766 9.553
8.323 8.132 7.952 7.780 7.617
35.0 36.0 37.0 38.0 39.0
13 ..562 13.256 12.965 12.689 12.425
14.823 14.491 14.175 13.874 13.587
16.859 16.479 16.119 15.775 15.449
12.677 12.399 12.135 11.884 11. 645
10.620 10.395 10.181 9.977 9.782
9.349 9.1.56 8.972 8.797 8.629
7.461 7.313 7.172 7.037 6.908
40.0 41.0 42.0 43.0 44.0
12.174 11.934 11.704 11.485 11.275
13.314 13.053 12.804 12.565 12.336
15.137 14.839 14.555 14.282 14.022
11.416 11.198 10.989 10.788 10.597
9.596 9.418 9.248 9.085 8.928
8.469 8.315 8.167 8.025 7.889
6.785 6.667 6.554 6.445 6.340
64 eV Be
78 eV Graphite
10.0 10.5 11.0 11.5 12.0
37.720 36.252 34.904 33.662 32.513
12.5 13.0 13.5 14.0 14.5
'"
I
T, '" MeV
'"
25.0 26.0 27.0 28.0 29.0
~
I
320 eV
.
I
PASSAGE OF CHARGEb PARTICLES THROUGH MATTER TABLE
8d-2.
CALCULATED MASS STOPPING POWER
IN MEV /(G/CM') FOR PROTONS
~T T, "'MeV "'-
8-155
Sip
(Continued)
64 eV Be
78 eV Graphite
66.6 eV "Vater
166 eV AI
eu
475 eV
820 eV
Ag
Pb
45.0 46.0 47.0 48.0 49.0
11. 073 10.880 10.694 10.515 10.343
12.117 11.906 11.704 11.509 11.322
13.771 13.531 13.301 13.079 12.866
10.413 10.236 10.066 9.903 9.745
8.777 8.632 8.493 8.358 8.229
7.759 7.633 7.513 7.396 7.284
6.239 6.142 6.049 5.958 5.872
50.0 52.5 55.0 57.5 60.0
10.178 9.790 9.435 9.109 8.808
11.142 10.719 10.333 9.977 9.649
12.660 12.179 11.738 11.333 10.959
9.594 9.238 8.911 8.611 8.334
8.104 7.811 7.543 7.295 7.066
7.176 6.922 6.689 6.475 6.275
5.788 5.590 5.409 5.241 5.085
62.5 65.0 67.5 70.0 72.5
8.530 8.271 8.031 7.807 7.597
9.345 9.064 8.801 8.557 8.328
10.613 10.293 9.994 9.715 9.454
8.077 7.839 7.616 7.409 7.214
6.854 6.657 6.474 6.302 6.140
6.090 5.917 5.756 5.606 5.465
4.940 4.804 4.678 4.560 4.449
75.0 77.5 80.0 82.5 85.0
7.400 7.215 7.041 6.877 6.722
8.113 7.911 7.721 7.542 7.373
9.210 8.980 8.764 8.560 8.368
7.032 6.860 6.699 6.546 6.402
5.988 5.846 5.711 5.584 5.463
5.332 5.207 5.090 4.978 4.873
4.344 4.246 4.153 4.065 3.982
87.5 90.0 92.5 95.0 97.5
6.576 6.437 6.305 6.180 6.060
7.213 7.061 6.917 6.780 6.650
8.185 8.013 7.849 7.693 7.545
6.266 6.136 6.013 5.897 5.785
5.350 5.241 5.139 5.041 4.948
4.773 4.679 4.589 4.503 4.422
3.902 3.827 3.755 3.687 3.622
100.0 105.0 110.0 115.0 120.0
5.947 5.735 5.541 5.364 5.200
6.526 6.294 6.083 5.888 5.709
7.403 7.140 6.899 6.678 6.475
5.679 5.481 5.300 5.134 4.980
4.859 4.693 4.542 4.402 4.274
4.343 4.197 4.063 3.940 3.826
3.559 3.443 3.337 3.238 3.148
125.0 130.0 135.0 140.0 145.0
5.049 4.909 4.779 4.657 4.544
5.544 5.391 5.248 5.116 4.992
6.287 6.113 5.951 5.800 5.659
4.839 4.707 4.585 4.471 4.364
4.155 4.044 3.942 3.845 3.755
3.721 3.623 3.532 3.447 3.368
3.064 2.986 2.912 2.844 2.780
150.0 155.0 160.0 165.0 170.0
4.438 4.338 4.245 4.157 4.073
4.876 4.767 4.664 4.568 4.477
5.527 5.403 5.287 5.177 5.074
4.264 4.171 4.083 4.000 3.921
3.671 3.592 3.517 3.447 3.381
3.293 3.224 3.158 3.096 3.037
2.720 2.664 2.611 2.560 2.513
175.0 180.0 185.0 190.0 195.0
3.995 3.921 3.850 3.783 3.720
4.391 4.309 4.232 4.159 4.089
4.976 4.883 4.796 4.712 4.633
3.847 3.777 3.710 3.647 3.587
3.318 3.259 3.202 3.149 3.098
2.982 2.929 2.879 2.832 2.787
2.468 2.426 2.386 2.347 2.311
I
I
I
320 eV
I
----
&:-156
NUCLEAR PHYSICS
8d-2.
TABLE
CALCULATED MASS ·STOPPING. POWER
I
IN MEV (G/CM 2) FOR PROTONS
Sip
(Contiriued)
--
"'-.-
""", I T, .•""
MeV
64 eV Be
.
66.6 eV Water
78 eV : Graphite
320eV
166 eV
475 eV
eu
Al
"" 3.659 3.601 3.547 3.494 3.444
200.0 i 205.0 210.0 215.0 I 220.0 225.0 230.0 '235.0 240.0 245.0
4.558 4.486 4.418 4.353 4.290
4.023
, 3.960 3.900 3.842 3.787
3.530 3.475 3.424 3.374 3.326 I
:
.
4.230 4.173 4.118 4.066 4.015
3.735 3.684 3.636 3.590 3.546 I:
3.396 3.350 3.306 3.264 3.223
3.281
I: 3.238
820.eV
.Ph
Ag ~
. ..- .. - -
_.._. '.
3.049' I: 2.744: 3.003 2.959 2.917 2.877
, : 2.838
I
i
3.967 3.920 3.876 3.832 3.791
, Z.IS1
2:556 2.523 2.492 2.461 2.432
2.i25 2.098 2.072 2 ..048 2.024
2.M8 2.638 2.609 2,581 2'.554
2:404 , 2:378 2.352 , 2:327 2.303
, 1:980
2.528 2.503 2.479 2.456 2.433
2:280 2.258 2.236 2.215 2.195
1.9'00 1.882 L864 1.,847 1.831
2.411 2.370 2.331 2.294 2.260
2.176 2.139 i , 2.104 2.071 • 2.041
3·.312 3.278 3.245 3.214 3.183
3.751 3.712 3.675 3.639 3.604
2.865 2.814 2.766 2.720 2.678
3.153 3.097 3.044 2.994 2.947
3.570 3.506 3.446 3.389 3.336
2.778 2:729 2.683 2.640 2.600
350.0 360,0 .370.0 380.0 390,0
2.637 2.599 2.564 2.530 2.497
2.903 2'.862 2.822 2.785 2.750
3.286 3.239 3.194 3.152 3.112
2.562 2.526 2.492 2.459 2.429
2.227 2.196 2.168 2.140 2.114
400.0 410.0 420.0 430.0 440:0
2.467 2.438 2.410 2:384 2.359
2.717 2.685 2.655 2.626 , 2.598
3.074 3.038 3.004 2.971 2.940
2.400 2.372 2 ..346 2.321 2,297
2.089 2;066 2.044 2.022 2.002
2.335
2.572 2.547 2.524 2.501 2.479
2.910 2:882 2.855 2.829 2.804
2.275 2.253 2.232 2;213 2.194
L983 1.964 , 1.947 1.930 : 1:914
2.458 2.438 2:419 2.400 2.383
2.780 2.758 2.735 2.715 2.595
, 2.176
1.898 1.884 1.870 1.856 1.843
300.0 310.0 320.0 330.0 340.0
450.0 460.0 470:0 480.0 490.0 500.0 510.0 520.0 530.0 540.0
2.1'52
3.081 3.045 3.011 2.978 2.946
3.010 2.979 2.949 2.920 2.892
2;916 2.886 2.858 2.830 2.804
•
2.276 2:243 .2:211
i
275.0 280:0 285.0 290.0 295.0
i;
-_.-._-
3.196 3.156 ·3.117
3.184 3.147 3.111 3.076 3.043
I
.
2.801 2.766 2.732 2.699
250.0 255.0 260.0 '265.0 270,0
I
'
2.703' 2.664 2.626 2.@90
I
3.503 3.462 3.422 3.384 3.348
_ ....
I
I
.
2:001
1.959 1.938 1.919
: i
,
, 2.313
2.291 2.270 2.250
, 2.231 2.213 2.195 2.179 2.162
-
• ,.,
2.158 2.142 2.125 2.111-
I
-
--
_ ....
I
i
I I I
. i
I
:
i i
1.-815 1.785 1. 757 1-.730 1-..705
2.012 1.984 1.958 1.934 1.911
1.681 1-.659 1. 638 1.61-8 1.599
1,889 1.868 1:848 i.829 1.811
1-.581 1-.564 1..548 1-.533 1-.518
1:794 1.7781.762 1.747 L733 1.719 1.705 1.693 1.681 1.670 - _.
I
1-.504
i 1..491
, 1-.478 I
1·.466 1.. 454
1-.443 1.432 1.422 1.412 1..403
PASSAGE OF CHARGED PARTICLES THROUGH MATTER TABLE
8d-2.
CALCULATED MASS STOPPING POWER
IN MEV /(G/CM') FOR PROTONS
'"
78 eV
66.6 eV ,Vater
166 eV
Graphite
Al
ell
550.0 560.0 570.0 580.0 590.0
2.147 2.132 2.118 2.104 2.091
2.366 2.349 2.334 2.319 2.304
2.676 2.657 2.639 2.622 2.606
2,096 2.082 2.068 2.055 2.043
600.0 610.0 620.0 630.0 640.0
2.078 2.065 2.054 2.042 2.031
2.290 2.277 2.263 2.251 2.239
2.590 2.574 2.560 2.545 2.531
650.0 660.0 670.0 680.0 690.0
2.020 2.010 2.000 1.990 1. 981
2.227 2.216 2.205 2.194 2.184
700.0 710.0 720.0 730.0 740.0
1.972 1.963 1.955 1.947 1.939
750.0 760.0 770.0 780.0 790.0
1.931 1.924 1. 916 1.909 1.903
MeV
Sip
(Continued)
64 eV Be
T, ' " ~ I
8-157
320 eV
47·:; eV
820 eV
Ag
Pb
1.830 1.818 1.807 1.796 1. 785
1.659 1. 648 1.638 1.628 1.618
1.394 1.385 1.377 1.369 1.361
2.030 2.019 2.007 1.997 1.986
1. 775 1. 765 1. 755 1. 746 1.737
1.609 1.600 1.592 1.584 1. 576
1.353 1.346 1.339 1.333 1.326
2.518 2.505 2.493 2.481 2.469
1. 976 1.966 L957 1. 948 1.939
1.728 1.720 1. 712 1.704 1.697
1.568 1. 561 1. 554 1.547 1.540
1.320 1.314 1.308 1.303 1.297
2.174 2.165 2.155 2.146 2.138
2.458 2.447 2.437 2.426 2.417
1.930 1.922 1.914 1.906 1.899
1.690 1.683 1.676 1.669 1.663
1.534 1.528 1.522 1. 516 1.510
1.292 1.287 1.282 1.277 1.273
2.129 2.121 2.113 2.106 2.098
2.407 2.398 2.389 2.380 2.372
1.892 1.885 1.878 1.871 1.865
1.657 1.651 1.645 1.640 1.634
1.505 1.500 1.495 1.490 1.485
1.268 1.264 1.260
1.248 1.245 1.241 1.238 1.235
~
I
I
I
I
1.256
I
1.252
800.0 810.0 820.0 830.0 840.0
1.896 1.890 1.883 1.877 1.871
2.091 2.084 2.077 2.071 2.064
2.363 2.355 2.348 2.340 2.333
1.859 1.853 1.847 1.841 1.836
1.629 1.624 1.619 1.614 l.tHO
1.480 1.476 1.471 1.467 1.463
850.0 860.0 870.0 880.0 890.0
1.866 1.860 1.855 1.850 1.845
2.058 2.052 2.046 2.040 2.035
2.326 2.319 2.312 2.306 2.299
1.830 1.825 1.820 1.815 1.811
1.605 1.601 1.596 1.592 1.588
1.459 1.455 1.451 1.448 1.444
1.231 1.228 1.225 1.222 1.220
900.0 910.0 920.0 930.0 940.0
1.840 1.835 1.830 1.826 1.821
2.029 2.024 2.019 2.014 2.009
2.293 2.287 2.282 2.276 2.270
1.806 1.801 1.797 1.793 1.789
1.585 1.581 1.577 1.574 1.570
1.441 1.437 1.434 1.431 1.428
1.217 1.214 1.212 1.209 1.207
950.0 960.0 970.0 980.0 990.0
1.817 1.813 1.809 1.805 l.801
2.005 2.000 1.996 1. 991 1.987
2.265 2.260 2.255 2.250 2.245
1.785 1. 781 1.777 1.773 1.770
1.567 1.563 1.560 1.557 1.554
1.425 1.422 1.419 1.417 1.414
1.204 1.202 1.200 1.198 1.196
1000.0
1.797
1.983
2.240
1. 766
1.551
1.412
1.193
8-158
NUCLEAR PHYSICS
where feR) is the experimentally measured distribution function (the "probability density" of the mathematicians) and can be determined quite readily in cloud or bubble chambers and in photographic emulsions (except for problems connected with the last bubble or grain). It is not a practical quantity for experiments in which the tracks of the particles cannot be followed. In particular, the mean projected range is difficult to determine experimentally because of the removal of particles from the beam due to nuclear reactions and multiple scattering. At energies higher than a few MeV, the number of particles is sensibly reduced owing to nuclear reactions (K064, BI60, and BA61), and appropriate corrections must be applied (see Sec. Sd-S under Nuclear Reactions). The quantity related to R(T) which can be calculated from stopping-power theory is the theoretical mean range Rt(T) in the continuous slowing-down approximation (csda) : Rt(T) =
r
T S-1 dT
JTl
(Sd-14)
In principle, Tl is the thermal energy of the particle. For small velocities the description of the stopping power, given in Sec. Sd-6 under Very Low Velocity Particles can be used. If S is not known accurately at these energies, a more accurate result for R,(T') may be obtained when Tl is chosen to be a higher energy (e.g., 1 MeV for protons), and an experimental value of R(T l ) is added to the integral to take care of the low-energy contribution to the range. For experimental measurements it will be necessary to consider the detector threshold energy as the energy Tl (BM57 and HP60). A small difference between R (T) and Rt(T) is caused by the use of the csda approximation (LE52 and TT6S). A simple relation that exists between the ranges for different particles is discussed in Sec. Sd-6. Mean csda ranges for protons in several elements have been computed (BJ67) by numerical integration of the values of Tables Sd-2 and Sd-3. They are listed in Table Sd-4. Values for R (1 MeV) are obtained from BF60, MR67, and RY55. For other elements, the method of SDGO can be used to obt.ain range-energy relations. For other particles (mesons or heavier ions) see Sec. Sd-6. Extensive tabulations can be found in JA66, BJ69, BB67, and N067. For high energies (T > 1000 MeV for protons) nuclear interactions absorb most of the particles, and range becomes a rather meaningless term. While the straggling in pathlength can be represented approximately by a gaussian (see Sec. Sd-7), the asymmetry of multiple scattering (the zigzag path taken by a particle can only be longer than the foil thickness, see Sec. Sd-S), and the residual skewness of the electron-loss straggling causes an asymmetry in the range straggling. The median range therefore, is different from the mean range. The total median range Rm(T) (equal to the foil thickness), neglecting the straggling asymmetries, can be obtained from the computed mean pathlength R,(T) by the application of the multiple-scattering correction tlR: Rm(T)
=
R,(T) - tlR
The relative correction of tlR/R for several elements is plotted in Fig. Sd-5. Further discussion is given in BU60, BF61, BZ67, and TB6S. No discussion of the relation of mean and median range seems to be available (see Sec. Sd-7). 8d-5. Shell Corrections and I Values. In principle, the stopping power S can be calculated theoretically using atomic collision cross sections [Eq. (Sd-5)J. At present, no complete sets of cross sections for all shells are available, and the expression Eq. (Sd-ll) is used for the calculation of S. The unknown functions Ex, B L , . . . ; are then replaced by one unknown constant, [ = [av, and the unknown functions
TABLE 8d-3A. LOW-ENERGY PROTON STOPPING POWER
S
IN MEV /(G/CM 2)
FOR SEVERAL SUBSTANCES: ACCURACY
2
TO
10%
!
T, Mel'
H2
--- ---
He ~~
Li ~~
--~-
N2 -~~
02
i
Ne
~~---
., . . .. .. . .. .
.. . .. . .. . .. .
.. . ... .. . .. .
690
750
600
750 680 610 550 500
700 640 570 510 460
710 650 580 540 490
780 690 610 530 480
610 600 540 500 450
600 550 510 480 450
450 420 390 360 340
430 390 370 350 330
460 430 390 370 3.50
440 400 37G 350 320
410 380 360 340 320
1020 910 810 740 680
420 380 340 310 290
320 290 260 240 230
310 280 260 240 220
330 290 270 250 230
310 280 250 240 220
30r)
260
270 250 230 220
2~(J
630 590 550 520 500
270 250 240 220 210
220 210 200 195 188
210 198 187 179 170
220 200 192 183 175
210 194 185 176 168
200 192 182 173 165
161 148 137
167 154 143
160 148 137
157 144 134
... . , ... ... . ... .
... .
1050
.. . . .. .. . .. . .. .
3800
0.10 0.15 0.20 0.25 0.30
3500 2800 2300 1990 1740
1090 960 830 740 660
0.35 0.40 0.45 0.50 0.55
1560 1410 1280 1180 1090
0.60 0.70 0.80 0.90 1.00
1.13 1.8 2.0
~~
C
440 560 640 700 720
0.01 0.02 0.03 0.04 0.05
1.1 1.2 1.3 1.4 1.5
Be
470 430 390
... . ... . ... .
200 183 1138
184 173 164
.. . .
"
.
.. . .. .
I
I
1
Al ~~
A ~~
.. .
Ni - -
Cu
Kr
-- --
.. . .. . .. . .. .
480
100 145 177 200 220
70 160 190 200 210
270
440 390 340 320 310
480 430 380 330 300
260 270 260 250 230
220 220 220 210 200
290 250 220 198 182
290 280 Z'70 250 240
270 250 230 220 210
220 210 193 182 173
192 183 175
169 159 150 143 137
350
260 360 410 440 460
440 440 420 390 360 340 320 300 290 270
.. . .. . .. .
HiS
161
Ag
Sn
Xe
Au
Pb
Air
H 2O
't:1
- - - - - - - - - - - - - - U1 U1 22 .. . .. . ... Q .. . .. . ... 44 t"l 60 .. . ... . .. 75 .. . .. . ... o 730 890 "i 85 ... . , . . .. 240 o .. , ... 230 105 122 730 910 ::r; ... . .. 210 112 127 650 830 ~ .. . ... 192 119 127 580 740 o . , . ., . 176 116 120 520 660 t"l .. . , .. 163 110 113 480 600 t:I
'" '"
'"
..
...
.
151 142 134 128
142 134 127 121
152 143 134 127 121
104 98 93 88 84
106 100 95 90 86
430 410 380 350 330
540 500 460 430 400
~ ~
H
o r
t"l
U1
105 99 94
115 107 100 94 89
115 106 98 92 87
81 75 70 66 63
83 77 71 67 63
310 280 260 240 220
380 340 310 290 260
99 94 90 87 84
89 85 82 79 75
85 81 78 75 71
82 78 75 72 69
60 57 54 53 51
60 58 55 53 52
210 198 186 177 168
260 230 220 210 197
81 76 72
72 68
68 65
136 62
49 47
50 47
1130 147
188 172
61
61
59
14
45
136
159
165 161 141 133 126
155 144 135 128 121
132
122
123 116 109 104
11:3
173
200 184 171 160 150
174 164 1.513 14ll 14,.
163 155 147 140 134
142 134 127 121 116
120 115
114 109 104 99 95
137 127 119
129 119 111
112
92 85
210 198 185
230 210 197 185
103 95
110
106 101 97 91 85
80
>-3
p:: ~
o q
§ s::
'"
>-3 >-3 t"l
~
cro
i-' Q1
CO
TABLE
T. MeV
Be
--- ---
Ai
Ca
Sc
8d-3B. Ti
EXPERIMENTAL PROTON STOPPING POWER
V
Cr
- - - - - - - - - .--- ---- - - -
Mn
---
Fe
Co
--- ---
Ni
S
Cu
cr
I-' 0;,
IN MEV/(G/CM 2)*
Zn
Zr
Ag
o
Gd
Ta
--- --- --- --- --- --- ---
Pt
Au
---
--
2.00 2.25 2.50 2.75 3.00
134.25 122.70 113.21 105.19 98.35
110.67 101. 92 94.68 88.52 83.19
107.21 98.91 92.03 86.15 81.09
96.58 89.24 83.15 77.94 73.40
93.19 86.11 80.23 75.20 70.87
90.61 83.73 78.02 73.14 68.91
89.57 82.93 77.41 72.59 68.50
86.51 80.07 74.72 70.18 65.16
87.30 80.83 75.45 70.85 65.84
83.74 77.64 72.56 58.18 64.37
86.45 80.14 74.89 70.35 56.41
81.09 75.19 70.28 66.07 62.44
80.89 7.5.02 70.13 65.92 62.32
71.49 65.56 62.44 58.83 55.70
63.74 59.63 56.18 53.16 50.46
55.31 51.65 48.58 45.87 43.51
49.27 46.20 43.62 41.35 39.35
45.43 42.85 40.67 38.71 36.97
45.78 43.12 40.87 38.89 37.11
3.25
4.00
92.42 87.24 82.65 73.57
78.56 74.51 70.94 67.76
76 65 72 76 69.30 66.18
69.45 65.97 62.87 60.08
67.11 63.78 60.81 58.15
65.22 61. 93 59.04 56.44
65.01 61. 82 58.98 56.42
62.66 59.5(1 56.80 54.40
63.32 60.21 57.45 55.00
61.04 58.09 .55.46 53.10
62.96 59.97 57.28 54.88
59.25 56.43 53.91 51.65
59.16 56.36 53.85 51.60
52.92 50.42 48.20 46.20
48.07 45.94 44.02 42.28
41.42 39.57 37.91 36.42
37.59 36.02 34.60 33.32
35.39 33.96 32.66 31.47
35.52 34.09 32.79 31.62
4.25 4.50 4.75 5.00 5.25
74.90 71.60 68.58 65.87 63.36
64.85 62.21 59.80 57.59 55.56
63.38 60.83 58.51 56.37 54.41
57.57 55.29 53.21 51.30 49.53
55.74 53.54 51.53 49.68 47.98
54.09 51. 95 50.00 48.21 46.56
54.09 51. 97 50.04 48.25 46.61
52.19 50.16 48.31 46.62 45.05
52.79 50.78 48.94 47.24 45.67
50.97 49.03 47.26 45.62 44.11
52.69 50.70 48.86 47.17 45.61
49.60 47.72 45.99 44.42 42.95
4R.55 47.69 45.99 44.42 42.97
44.40 42.74 41.23 39.84 38.55
40.70 39.26 37.93 36.71 35.58
35.06 33.83 32.69 31.65 30.69
32.15 31.07 30.07 29.15 28.29
30.39 29.40 28.49 27.65 26.85
30.55 29.56 '28.65 27.79 27.00
5.50 5.75 6.00 6.50 7.00
61.06 58.93 56.96 53.42 50.34
53.68 51.93 50.31 47.38 44.81
52.59 50.91 49.35 46.53 44.04
47.90 46.38 44.97 42.41 40.17
46.40 44.93 43.56 41.10 38.92
45.03 43.61 42.29 39.90 37.80
45.09 43.68 42.37 39.98 37.89
43.60 42.25 40.99 38.72 36.71
44.22 42.87 41.60 39.31 37.28
42.72 41.41 40.20 38.00 36.06
44.16 42.82 41. 57 39.30 37.29
41.59 40.33 39.15 37.01 35.12
41. 61 40.36 39.19 37.07 35.19
37.36 36.25 35.22 33.35 31.69
34.53 33.55 32.63 30.97 29.48
29.80 28.96 28.18 26.77 25.50
27.49 26.75 26.06 24.79 23.66
26.12 25.43 24.79 23.60 22.54
26.25 25.56 24.91 23.72 22.67
7.50 8.00 8.50 9.00 9.50
47.62 45.21 43.05 41.10 39.34
42.52 40.47 38.64 36.97 35.46
41.83 39.85 38.08 36.47 35.00
38.17 36.38 34.77 33.31 31.98
36.99 3.5.27 33.71 32.30 31. 02
35.93 34.26 32.75 31. 39 30.15
36.02 34.35 32.85 31.49 30.25
34.92 33.32 31.88 30.57 29.38
35.47 33.85 32.39 31.06 29.85
34.33 32.78 31.37 30.09 28.92
35.51 33.90 32.45 31.14 29.95
33.44
31.93 30.57 29.33 28.21
33.52 32.01 30.65 29.41 28.29
30.21 28.89 27.69 26.60 25.60
28.14 26.94 25.85 24.86 23.95
24.37 23.36 22.43 21. 59 20.82
22.65 21.73 20.89 20.13 19.42
21. 58 20.72 19.94 19.22 18.56
21.73 20.85 20.06 19.34 18.67
10.00 10.50 11.00 11.50 12.00
37.74 36.27 34.93 33.69 32.54
34.08 32.82 31.66 30.58 29.58
33.66 32.43 31.30 30.25 29.28
30.76 29.65 28.61 27.66 26.77
29.84 28.77 27.77 26.85 26.00
29.01 27.97 27.01 26.12 25.30
29.11 28.06 27.10 26.21 25.37
28.28 27.28 26.35 25.49 24.69
28.74 27.72 26.78 25.90 25.09
27.85 26.87 25.96 25.12 24.33
28.84 27.83 26.89 26.02 25.21
27.17 26.22 25.35 24.54 23.78
27.26 26.30 25.42 24.61 23.85
24.69 23.85 23.07 22.35 21.68
23.11 22.34 21. 62 20.96 20.34
20.11 19.46 18.85 18.29 17.77
18.77 18.17 17.62 17.10 16.62
17.95 17.39 16.88 16.39 15.93
18.06 17.49 16.97 16.48 16.02
3.50 3.75
'Z q (')
t:-
0.27. In gases, the values are several percent smaller (AR69). It should be noted that the approach described in the next section overlaps the range of validity of Eq. (8d-20).
8-168
NUCLEAR PHYSICS
3d-5. PROPERTIES OF CHARGED P ARTICLES* (Electron Masses to Be Divided by 1,000)
TABLE
Ion
z
Electron Muon Pion Kaon Sigma + Sigma -
1 1 1
1 1 1
-1. 60219
10 24 g 0.910956 0.188357 0.248823 0.880322 2.120318 2.134436
Mass amu 0.548593 0.113432 0.149846 0.530147 1.276895 1.285398
MeV 511.004 105.6598 139.578 493.82 1189.40 1197.32
0.544630 0.112613 0.148763 0.526317 1.267671 1.276112
1. 674920 1.672614 3.343569 5.007334 5.006390 6.644626 9.985570
1.0086652 1. 0072766 2.01.35536 3.0155011 3.0149325 4.0015059 6.0134789
939.553 938.259 1875.587 2808.883 2808.353 3727.328 5601.443
1.0013786 1.0000000 1.9990076 2.9937170 2.9931526 3.9725990 5.9700375
11.647561 7.0143581 6533.743 11.648186 7.0147345 6534.093 14.961372 9.0099911 8392.637 16.622243 10.0101958 9324.309 18.276741 11.0065623 10252.406
6.9636862 6.9640599 8.9449027 9.9378820 10.9270507
Lifetime,
Charge,
nanosec
10- 19 C
Stable 2198.3 26.04 12.35 0.081 0.164 Mass
± 1. 60219 ± 1. 60219 ± 1. 60219 ± 1. 60219
+ 1. 60219
mr
excess,
IN IH 2H 3H 3 He 4 He 6 LI
0 1 1 1 2 2 3
MeV 8.0714 7.2890 13.1359 14.9500 14.9313 2.4248 14.0884
O. 1. 60219 1. 60219 1. 60219 3.20438 3.20438 4.80658
7Ll 7 Be 9 Be 10 B lIB
3 4 4 5 5
14.9073 15.7689 11.3505 12.0522 8.6677
4.80658 6.40877 6.40877 8.01096 8.01096
O.
-5.7299 -8.0249
9.61315 9.61315 9.61315 11.21534 11.21534 12.81753 12.81753 12.81753 14.41973 16.0:1192 16.02192 16.02192
19.920910 21.587011 23.247356 23.246166 24.901771 26.552769 28.220304 29.880881 31.539247 33. U,tl963 34.851833 36.508273
11.9967084 11174.708 11.9100440 13.0000629 12109.314 12.9061502 13.9999504 13040.691 13.8988145 13.9992342 13040.024 13.8981035 14.9962676 13968.741 14.8879343 15.9905263 14894.875 15.8750105 16.9947441 15830.285 16.8719738 17.9947713116761. 791 117.8647767 18.9934674 17692.058 18.8562582 19.9869546 18617.472 19.8425685 20.9883627 19550.265 20.8367424 21.9858989 20479.451 21.8270724
-9.5283 -13.9333 -13.1907 -16.2142 -17.1961 -21.4899 - 21.8936 -24.4394 -24.4376
17.62411 19.22630 19.22630 19.22630 20.82849 22.43068 22.43068 22.43068 24.03288
38.165213 39.816981 41.478836 43.133977 44.791847 46.443813 48.103625 49.759617 51.419241
22.9837363 23.9784587 24.9792559 25.9760100 26.9744073 27.9692490 28.9688156 29.9660826 30.9655359
21408.918 22335.483 23267.707 24196.165 25126.153 26052.830 26983.907 27912.843 28843.815
22.8177014 23.8052379 24.7988053 25.7883589 26.7795437 27.7671987 28.7595444 29.7496071 30.7418404
32 S 16 ~26.0127 25.63507 33 S 16 -26.5826 25.63507 34 S 16 -29.9335 25.63507 16 -30.6550 25.63507 36 S 35 Cl 17 -29.0145 27.23726 37 CI 17 - 31. 7648 27.23726 36 Ar 18 -30.2316 28.83945 38 Ar 18 -34.7182 28.83945 40 Ar 18 -35.0383 28.83945 39 K 19 -33.8033 30.44164 40 K 19 -33.5333 30.44164 40 Ca 20 -34.8476 32 .. 04383 * From refs. BB69. TP69, and MT65.
53.076053 54.735569 56.390126 59.709903 58.051385 61.367545 59.708836 63.021900 66.342392 64.683151 66.344164 66.340910
31.9632963 32.9626845 33.9590871 35.9583126 34.9595251 36.9565725 35.9576699 37.9528533 39.9.525096 38.9532869 39.9535768 39.9516172
29773.210 30704.121 31632.251 33494.492 32564.140 34424.353 33493.894 35352.369 37215.012 36284.254 37216.006 37214.180
31.7323930 32.7245615 33.7137661 35.6985491 34.7069770 36.6895976 35.6979111 37.6786813 39.6638921 38.6718877 39.6649515 39.6630060
12 C 6 6 13 C 6 14 C 7 14 N 7 15 N 160 8 170 ·8 8 180 19 F 1 9 20 Ne 10 21 Ne 10 22 Ne 10 23 24 25 26 27 28 29 30 31
Na Mg Mg Mg Al Si Si Si P
11 12 12 12 13 14 14 14 15
3.1246 3.0198 2.8637 0.1004 -4.7365 -0.8077 -0.7824 -1.4860 -7.0415
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
8~169
For ions with 21 ::;: z ::;: 39; Hvelplund and FastruJ'l (HV68,FB68) have found a periodic dependence of the stopping cross section on z for a carbon absorber. Similar effects were found in WI68, N A69, and HA68. Fractional charges for carbon absorbers in 0067 agree with Eq. (8d-20) to better than 5 percent for most ions. The fluctuations for different absorbers found in table III of that reference could be due to shell corrections. When available, experimental data should be used. Recent papers include: Br and I ions in Be, 0, AI, Ag, Au 0 '6 ions in Ag, Au; S" ions in Au S32, 013 5, Br 79 , 1127 ions in Mylar o and 01 ions in 0, AI, Ni, Ag, Au 1127 ions in 0, AI, Ni, Ag, Au, UF 4 0, N, 0, F, Ne in Be, 0 21 ::;: Z ::;: 39 in 0 ; 3 ::;: z ::;: 13 in Ar
MB66 AH68 PB68 BG65 BN67 OB68 HV{;\8" ARQ9
Interesting results for charge-statep6IiulatioIis' (1'27 ill gas arid solid)lia,ve be~n found by Moak et a1. (ML68). Many references to earlier work ate included. . Very Low VeZocity Particles. At low velocities, (3 ::;: (3, = ;z~ /137, ions will carry a reduced charge, and for (3 «(30 = 1/137 = 0.0073,tlley_will b{) neut.raL The collisions then will be between neutral atoms, arid are commonly called nuc/~qr collisions (LS63, OH63). Even for this case, enEirgy: loss to atomic electrons is still p6~sible (LS63). From a Thomas-Fermi description of the atoms,it is expect~d that the following dimensionless parameters should result in universaI range~energy:curves: Energy: Range: .
E ,.;,
p =
32.53 X T(keV) M,j[zZ(M,
+ M vr]
1.660 X 10' X R(mg cm- 2)
1M
~
2)
i
\f'-.r. 1
~~-W)21 I
.L
(8d-21) :(8d-22)
~
where'M, ~ atomic mass of incident particle M2 = atomic mass of absorber' material .z c= atomic num:ber of incident particle.(~su~lly called' Z,) Z= atomic n~mber of absorber material" (usually callJed Z2) I = z! + Zi It is found that the stopping power consists of contributions by electronic and nuclear stopping: (8d-23) From (LS63), (8d-24) . S, = k Ve where _ rr7
k
=
0.0793 X ~,v iZZ[( , Z31
+ M2)t + Z')'M'M ']
(M,
'!
~
J2
(8d-25)
22
and ~,is approximately given byzt. This formula is valid for E 300), the approach presented here overlaps with the Bethe theory using effective charges (see under Charge-state Correction in this section),
+
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
8-171
and experimental data have to be consulted to find the more reliable approach. Useful data are found in AG69 for protons with 0.5 :S; T :S; 30 keY in 10 materials. Small Volumes. The energy losses discussed in Sec. Sd-3 are as experienced by the charged particles and are not directly related to the energy gained by the absorber material (see the discussion of LET in Sec. Sd-9). EXAMPLES
1. For an energy T = 50 MeV, in a silicon detector of the transmission type thicker than 5 mg/cm 2 ~ 20 ,um, in a vacuum, about 5 percent of all the protons will each knock out delta rays of mean energy 40 keY. The mean energy loss 3. of all protons is reduced by 2 ke V. - The most probable energy loss t. p will be changed much less, though. Contrary to expectation, the spectrum of these delta ray losses is proportional to Eo.2a. 2. In very small volumes (diameter of l,um or less of a material of density p= 1 g/cm a, corresponding to the size of living cells), the energy lost by a particle of moderate or large energy is quite_ uncorrelated, to the energy absorbed in the volume. Since the behavior of lo-w-energy electrons is not well known (energies of less than 1 keV), and since the collision cross sections are not known for low-Z materials, calculations are extremely unreliable at present (KL6S, EB70).
Channeling. In single crystals it is observed that energy loss depends on the direction of the particle path with respect to the crystal axes. A detailed discussion of various aspects of the problem is given by Lindhard (LI65). Other calculations are available in several of the experimental papers mentioned below and in BR6S. If particles travel parallel to a major axis of the lattice, some can move "in between?> the atoms, reducing the number of collisions with small impact parameters (energy loss and straggling would then both be reduced; see AE67 and DM69) while others would move close to nuclear positions, increasing the effects. For a well-collimated beam with small multiple scattering, a fraction of the beam may keep away from atoms for long distances. A number of experiments have recently been published: an especially instructive diagram is given in RI:j6'7, a study of 3- to ll-MeV protons in Si and Ge is of interest for the use of solid-state detectors (AE67). Other studies are described in DW6S, DM69, ER67, R069, SV6S. 8d-7. Straggling of Heavy Particles. Particles, in passing through an absorber of thickness s, experience a random number of collisions with a wide range of possible energy transfers. The energy losses t. of a monoenergetic beam of particles thus will fluctuate ("straggle?» about the mean energy loss 3. = sS. The straggling distribution function J(t.) depends only slightly on the properties of the incident particle ((3,z) and the material (Z,A,S). It is highly asymmetric for small 3., reaching minimum asymmetry for 3. ~ 0.5T. Straggling theories frequently are based on the use of the moments ,un of the distribution functions (SY4S, TT6S, P A(9) : ,uo
==
1
Also used are the central moments Cn: (Sd-2S)
3. = ,u1 and the moments Mn of the primary collision cross section: [dO', e.g., from Eq. (Sd-2)]
Thin Absorbers.
Simple equations relate the moments (F A53): C a = sMa C, = sM,
+ 3s M 2
22
etc.
8-172
NUCLEAR PHYSICS
IT an experimental straggllitgfunction (e.g., NI61, K06S, :MR6S, AL69) IS known to have negligible spurious contributions for large ,I). (e.g .., from slit edge scattering or delta ray escape losses) the comparison of C" with M" is much simpler than the compa:rison with theoretical straggling functions. There is no simple relation between the full-width-at-half-maximum (FWHM) andu (SB67) except for a gaussian: FWHM = 2.3550'. Landau (LA44), Symon (SY4S), Vavilov (VA57), Bichsel (BJ70) and others hav:e · discussed straggfug in ·thin' absorbers. Most of these calculations are based ol:). the :use of the free electron collision spectrum. Thus:
o=.va;
M' = .
n
J
E"du' = 0.1535 Z z· E.:;;;;:~ [1 _ fJ' (n- 1) ] r fJ2 A n - 1 n
(MeV)"cm 2Jg
(Sd-29)
,using the relativistic fcrIP. of Eq, (Sd-l): dO'; = dO" .
(1 - fJ' Emax ~_)
and
, In particular' (e.g., 1304S): M ' = (0.1569Zz 2) 1 - fJ2/2 .2 . A 1 - fJ'
(Sd-30)
The Vavilov parameter K
= 0.1503Zz 2 (1 - P) S/(AfJ4)
(Sd-31)
·is used customarily in the discussion of f(,I).). Extensive tables of. f(,I).) according to WaV'ilov are given in SB67. It should be noted that the numerical convergence of the 'Vavilov calculation J-s unsatisfactory for I; = KEm • x . < 7 I (HB6S). No complete discussions are available based on the use of Eq. (Sd-2). An. estimate of the effect can 'be obtained from Figs. Sd-7 and Sd-S. For the K-shell, the ratios are somewhat :;;maller (BI69), .and they are not expected :to be. much different for the outer shells (M, N, .. ;). Experimental data confirm this assumption (Fig. 70f 'NI6i). :' '. " Corrections to the Vavilov functions' usmgEq. (Sd-~) for L-shell electrons are · discussed in BJ70. The corrections are especially important for K < D 2 = M./ M~ - 1 (BL50,BK5S: the quantity b2 used in these papers is equal to 2 D./K). For applications in thin silicon detectors,. see Fig. Sd.:9 (taken from BI70). . Thick Absorbers; An extensive discussion for large energy losses is given by Symon ,(SY4S),by Tschalar ,(TS67, TS68, TT68), and by Payne (PA69). For experimental 'results, see TM76: Fr mod,erate ~ne:rgy losses, Tschalar's :results. for heavy particles of initia,l kinetic energy T and residual mean energy Tl can 'be approximated by the follo~ing express~on for the second moment (accurate .to about 2 percent): C 2 = sM~Q
where
Q = =
(~y 0.99
for
(.T...)!
. Tl . (T)i = 0.9S5- T;
Z '" 2.3 and
B
~ > 0.4
Z '" 3.5
B
~ > 0.4
B
Tl T
Z '" 6.9
where B is the stopping number, Eq. (Sd-S), and B
E=
\' C, f(fJ) - In I - '-' Z. i .
>0.6
PASSAGE OF CHARGED .PARTICLES THROUGH MATTER
8--173
1.10
1.05
.N
1.001---r--+-I'-h'-tf--+--..l----'-----'-..l---'---..L---'--l
,::E N
::E 0.95
0.90
0.65
FIG. 8d-7. The ratio M.IM.' of the second moments of the quantum-mechanical [Eq. (8d-2) 1 and the free-electron cross sections [Eq. (8d-l) 1for the L shell. The curves apply for silicon (Wmin = 0.093), copper (0.115) silver (0.135), and lead (0.167). . .
FIG. 8d-8. The ratio MaiM 2' of the third moments for the L shell (see Fig. 8d-8 for :the elements) . Notice that the asymmetry (skewness) is reduced at lower energies. .
For larger energy losses, TS68,should be consulted. For the asymmetry of the curves, the third moment should .be studied: Tsch~Hi.r uses the' skewness parameter = Ca/C 2! for this'purpose. From his results it is found that the expression for thin absorbers, 'Y~ = 8M;/(8M~)t, is l;LCGurate to a few percent for B/Z '" 2.3 and TdT> 0.5 and for B/Z '" 6 and TdT > 0.7. It may be noted that the distribution func-
1';
8-'-174
NUCLEAR PHYSICS
-~---;----.:.-
----I
94
92
--------so - - - -
90
138 85
75
70
p
----
60
---
50
----
40
:30 25 20
---
------1
15
12
10
---~
8 6 4 :3 2
~---
:----
----
/32=0.04 0.5 0.2
-3-2
I 0,01
-'1 I
I 0.1
0
I 0.2
I I oA- 0.7 1 I
---CO
1
I 2.
I 4
I I log X 7 10 X
r
6..
FIG. 8d-9. Contour lines for the &traggling distribution function 4> (4)(Ll u ) = } 0
feLl) dB
where feLl) is the Vavilov function] in silicon for particles of velocity (32 = 0.04 (T ~ 20 Me V for prot@)1s). The curves afe similar for other yelocitieB. The Vayiloy theofY has been
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
8-175
tions for the cases discussed above are approximately give:tl by the Vavilov functions for the value K. "" O.25'Y,-' of the Vavilov parameter Kv == UEmox (SB67). For the ranges R of particles with a mean value R, 'the second central moment, also called the mean-square fluctuation 0"2 is defined by
R,'
0"2 "" (R2) -
(8d-32)
The distribution f(R) is usually approximated by a gaussian: f(R) ""
[(R - •R,)'] -
1 _ /_ exp
(8d-33)
20"
O"V 2".
+
and the probability p of finding a particle with range' between Rand R dR is The deviations from a gaussian are small, but not negligible. They are discussed in LE52 and TT68. Their influence on the Bragg curve has not been studied yet (VK69). p dR "" f(R) dR.
7
,,
\
1\
6r
""" :~
3
•~u+ACJ
2 __ '.
I~
-...::: . . . .Ai::-
1,6
, '~ " .. ~ ',
,
'""
,~ "
, ...
"",
... B.
r.-
-
1
~
=96 perCeJ:l,t, P rov 2.0, and A = 234 80 keY = 314 keY. Thus. 4 percent of the protons lose more than 314 keY (the exact answer is 315 keY).
+
+
8-176
NUCLEAR PHYSICS
values calculated by 8ternheimer (8T60), but they are still slightly larger than experimental values (BU60), which were evaluated neglecting the skewness of the range straggling curves. The observed straggling in range-energy measurements is composed of the energy-loss straggling, and an additional asymmetric contribution caused by the multiple-scattering process (BU60, BI60). Sd-S. Coulomb and Multiple Scattering, and Nuclear Interactions. Coulomb Scattering. The differential cross section for Coulomb scattering of a charged particle of kinetic energy T (in MeV), momentum p, velocity v, and charge ze by a nucleus of charge.Ze and mass number A into the solid angle 271" sin 0 do is given by the Rutherford formula: 271"e 4 z2Z(Z + 1) . dip(8) = 4p2V2 sin 4 (0/2) sm Odo "-' 0.814z 2 Z(Z T2
+ 1)
sin 0 dO sin 4 (O/2)
(8d-35)
where 0 is the angle of scattering from the incident direction. The above formula assumes that the mass of the incident particle is negligible compared with the mass of the nucleus. Deviations from the Rutherford formula will occur at large angles as the particles begin to feel the influence of nuclear forces. An estimate of the minimum energy T m for which a deviation can be expected at 0 = 180 deg can be obtained from
T = zZ(A
+ 3)-t
(8d-36)
MeV
A detailed discussion is found in EP61 and JA68. At small angles, the cross section will be smaller than give.n by Eq. (8d-35) because the atomic electrons will shield the nuclear charge. The Rutherford cross section is reduced by 10 percent at an angle Oq given by (from M047) and by 50 percent at 0,
=
00 (2.75 0.244Zt o - pc (ll'IeV)
+ 1O.85( )!
o _
where and a: = Zz/137f3.
2
0.244Zt v' 2M oc2l'
For large kinetic energies, pc
=
CT2
+ 2TMoc2)t, and with r r +2 f3 - r (r + 1)2
=
T/Moc 2,
2 _
EXAMPLE.
00
(8d-37)
10-MeV alpha particles in Au: from Table 8d-I, f3 = 0.073, a = 15.8. X 10- 3 deg. Finally,
= 1.05/(74,600)t = 3.84 Oq
= 3.84
X 10- 3 (61.7
+ 105,000)1
=
1.25 deg.
This reduction is of great importance in the derivation of the multiple-scattering formulas. Multiple Scattering in Thin Absorbers. Multiple Coulomb scattering in thin foils will cause a parallel beam of particles to spread out into a cone. Recent discussions are found in HF68, 8C63, and GD68. Moliere's theory (M048, BE53, and M055) is a small-angle approximation to the general problem (BR59, NS61, and TM59) which is in agreement with experimental results, with the possible exception of electrons in heavy elements and also possibly at small energies (f32 < 2 X 10- 3). The characteristic quantity occurring in the theory is the angle 00 , defined by 0 0 . = (J,B! where 0 2 = 01"7 Z(Z + 1)z2_s_ (8d-38) 1 • D A· (pv)2
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
s....177
01 is in radians; 8 is the foil thickness in' glcm 2, p the momentuni, and v the velocity of the particle (pv in MeV); z, Z, and A have the same meaning as in Sec~ 8d-2. . B defined in M048i for practical purposes it can be obtained from MZ67 or from Table 8d-6, for particles with charge' 1 with an accuracy of better than 5 percent. A few values are listed for z > 1. It is not obvious whether z* or z should be used for a computation of the multiple scattering of heavy ions. The use of z*is suggested. For z 2:: 6 and Z 2:: 50, all values B(fJ,z) are larger than 0.98 X B(fJ = 0, z = 1); and for z 2:: 6 and Z 2:: 20, all values B(fJ,z) 2:: 0.95 X B(fJ = 0, z = 1), but. less than
is
B(O,l).
TABLE 8d-6. B OF MOLIERE'S THEO:ity FOR z:= 1, 2, AND 6, VAJlUABLE fJ, lAND ...THICKNESS 8*
Z
_ ..... __ . I
,I
= 1
z
=" 2
z = 6
B,.g/cm'
Z
,fJ'
=
0 0.005 0.01 0.02 0.05 0.1 0.2 0.5,I 1.0 0.1 1.0 0.1 1.0
-- -- - - - - - - --, - - - - - - - - --
--10.5 13.0 15.4 17.9
8.8 11.5 14.0 16.4
8.3 7.6 6.6 5.7 4.9 3.8 2.8 7.4 4.6 10.8 10.~ 9.2 8.5 7.7 6.6 5.7 10.0 7.4 13.3 12.8 11,7 11.0 10.3 9.2 8.5 12.5 10.0 15.8 15.2 14.2 13.5 12.8 H.8 11.0 14.9 12.6
8.2 10.7 13.3 15.7
8.0 10.5 13.0 15.4
7.7 10.3 12.8 15.2
10-' 10-' 10- 1
,1
6.8 9.4 12.0 14.4
6.6 6.5 6.2 5.8 5:2 4.2 3.5 6.5' 5.0 6.8 6.4 9.3 9.2 8.9 8.5 7.9 7.1 6.4 9.2 . 7.8 9.4 9.1, lui 11.8 11.7 11.4 11.0 10.5 9.7. 9.0 11.7 10.3 11'.9 11.6 14.4 14.3 14.2 13.9 13.5 13.1 12.2 11.5 14.2 12.8 14'.4 14.2
50
'10-' 10-' 10-' 1
4.7 7.5 10.0 12.5
4.7 7.5 10.0 12,5
4.7 4.e 4.6 4.5 4;3 3.7 3.2 4.6 4.1 4.7 4.'6 7.5 7.4; 7.4 7.3 7.2 6.6 6.0 7.5 7.0 7'.5 :7.4 10.0 10.0 10.0 9.9 9.7 9.2 8.8 10.0 . 9.6 10.1 10.0 12.5 12.5 12.5 12.4 12.2 11.8 11.3 12.6 12.1 12'.5 12:5
100
10-' 10-' 10- 1 :1
3.1 6.0 8.7 11.2
3.1 6.0 8.7 11.2
3.1 3.1 3.0 3.0 3.0 2.8 2.5 3.1 2.9 .3'.1 '3.'1 6.0 6.0 6.0 5.9 5.9 5.7 5.4 6.0 5,8 6.0 '6.0 8.7 8.7 8.7 8.6 8.6 8.4 8.2 8.7 8.5 8.7 ,8.7 11.2 11.2 11.2 11.1 11.1 10.9' 10.7 11.2 11.0 11.2 11.2
3
'10-' 10-' .10- 1
10
10- 8 10-' '10- 1
20'
1
!
1
7.4 6.7 9.9 9,25 12.4 11.8 14.8 14.3
6.0 5.2 4.2 3.2 7.2 4.9 8.1 7.2 8.7 8.0 7.0 6.2 9.8 7.7 10.6 ,9.7 11.2 10.5 9.6 8.8 12.3 10.3 13.1 12.'3 13·7 13.1 12.1 11.4 14.8 12.8 15.5 l-4.7
6.7 9.3
I
* For any value of z at f3
0, B is the same as for z. = 1. Linear interpolation for Z or f3' will give sufficient accuracy. for 8. =
The theqryja valid only.for B ,~ 4.5. Logarithmic interpolation is reQ'1-ire.d
Moliere's theory modified by Nigam et al. (NS61) gives the distribution function F(x) dx for the relative number of particles entering a coneo(angle x and width dx.
The reduced angle x is defined by
x=e;;o
An extensive discussion of the problem is given in MZ67. Table 8d-7 giving F(x) is obtained from MZ67. . Also of interest is the relative number NINo of particles entering a cone of half angle a: N (alOo No =
Jo
f(x)x dx
(8d-39)
8-178
NUCLEAR PHYSICS
Values are given in Table Sd-S. For experimental tests of the theory, see B15S M05S, L067, BN66. EXAMPLE. 2-MeV protons penetrating 3 mg/cm' of Ni foil: The average energy in the foil is I.S7 MeV. (3' ~ 3.96 X 10-3 from Table Sd-1, B 'Y 7.7 from Table 8d-6. 11,2 = 4.72 X 10- 4, 110 = 6.03 X 10- 2 rad = 3.46 deg. Thus, inside a cone of half angle 7 deg, all but about 6.3 percent of the protons will be found (see Table Sd-S). TABLE Sd-7. MULTIPLE-SCATTERING DIFFERENTIAL DISTRIBUTION FUNCTION* F(x)
B=4
5
6
7
8
9
10
12
0 0.2 0.4 0.6 0.8 1.0
1.0 0.94070 0.78389 0.58102 0.38726 0.23800
1.0 0.94546 0.79992 0.60800 0.41889 0.26632
1.0 0.94850 0.81017 0.62535 0.43939 0.28491
1.0 0.95058 0.81721 0.63731 0.45363 0.29793
1.0 0.95208 0.82232 0.64601 0.46402 0.30752
1.0 0.95321 0.82616 0.65259 0.47192 0.31486
1.0 0.95409 0.82916 0.65772 0.47811 0.32063
1.0 0.95537 0.83351 0.66520 0.48716 0.32913
1.2 1.4 1.6 1.8 2.0
0.14139 0.08650 0.05666 0.03899 0.02685
0.16116 0.09681 0.05986 0.03840 0.02506
0.17437 0.10393 0.06226 0.03816 0.02387
0.18377 0.10911 0.06410 0.03807 0.02303
0.19077 0.11304 0.06556 0.03805 0.02240
0.19616 0.11612 0.06673 0.03806 0.02192
0.20045 0.11859 0.06769 0.03809 0.02154
0.20681 0.12231 0.06918 0.03817 0.02097
2.2 2.4 2.6 2.8 3.0
0.01793 0.01164 0.00799 0.00549 0.00397
0.01628 0.01048 0.00716 0.00489 0.00349
0.01507 0.00956 0.00646 0.00438 0.00310
0.01416 0.00883 0.00589 0.00396 0.00277
0.01345 0.00824 0.00543 0.00361 0.00251
0.01288 0.00775 0.00504 0.00332 0.00229
0.01241 0.00735 0.00471 0.00308 0.00211
0.01170 0.00673 0.00419 0.00269 0.00182
3.2 3.4 3.6 3.8 4.0
0.00300 0.00232 0.00182 0.00145 0.00115
0.00259 0.00198 0.00154 0.00121 0.00096
0.00227 0.00171 0.00132 0.00103 0.00082
0.00202 0.00151 0.00116 0.00090 0.00071
0.00181 0.00135 0.00103 0.00080 0.00063
0.00164 0.00122 0.00093 0.00072 0.00056
0.00150 0.00111 0.00084 0.00065 0.00051
4.2 4.4 4.6 4.8 5.0
0.00093 0.00075 0.00062 0.00051 0.00043
0.00077 0.00062 0.00051 0.00042 0.00035
0.00065 0.00053 0.00043 0.00036 0.00030
0.00057 0.00046 0.00038 0.00031 0.00026
0.00050 0.00041 0.00033 0.00027 0.00023
0.00045 0.00037 0.00030 0.00025 0.00021
0.00041 0.00033 0.00027 0.00022 0.00019
5.2 5.4 5.6 5.8 6.0
0.00036 0.00030 0.00026 0.00022 0.00019
0.00030 0.00025 0.00021 0.00019 0.00016
0.00025 0.00021 0.00018 0.00016 0.00014
0.00022 0.00019 0.00016 0.00014 0.00012
0.00019 0.00016 0.00014 0.00012 0.00010
0.00018 0.00015 0.00013 0.00011 0.00010
0.00016 0.00013
x
--
* From J.
I
I I
0.00128
I 0.00094 0.00071
B. Marlon and B. A. ZImmerman, Nucl. Instr. Methods 51, 93 (1967).
Caution must be used with the incident particle of mass approximately equal to or larger than the mass of the scattering nucleus. In this case a considerable fraction of the energy can be lost to the recoil nucleus. This effect is, of courso, not included in the fundamental energy-loss formula [Eq. (Sd-ll)J. Multiple Scattering in Thick Absorbers. For thick absorbers the mean energy correction due to multiple scattering has been calculated in TB6S for energy losses between 0.5T and 0.11', for 10 < l' < 140 MeV, for detector angles between 0.005 and 0.5 rad for protons in AI, Ag, and Au.
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
8-179
TABLE 8d-S. MULTIPLE-SCATTERING INTEGRAL DISTRIBUTION FUNCTION (Given is the fraction of incident particles found inside a cone of half angle x.)
B=4
5
6
7
8
9
10
12
0.2 0.4 0.6 0.8 1.0
0.04617 0.16893 0.33004 0.48890 0.61973
0.04431 0.16330 0.32259 0.48427 0.62202
0.04320 0.15993 0.31815 0.48156 0.62359
0.04247 0.15773 0.31523 0.47981 0.62473
0.04195 0.15616 0.31316 0.47856 0.62554
0.04153 0.15485 0.31132 0.47716 0.62555
0.04123 0.15393 0.31008 0.47637 0.62592
0.04078 0.15253 0.30814 0.47496 0.62614
1.2 1.4 1.6 1.8 2.0
0.71612 0.78446 0.83429 0.87231 0.90166
0.72641 0.80062 0.85269 0.88987 0.91679
0.73300 0.81102 0.86473 0.90159 0.92709
0.73759 0.81829 0.87324 0.90998 0.93457
0.74088 0.82357 0.87948 0.91620 0.94016
0.74266 0.82679 0.88340 0.92011 0.94358
0.74449 0.82981 0.88704 0.92378 0.94690
0.74676 0.83380 0.89194 0.92875 0.95136
2.2 2.4 2.6 2.8 3.0
0.92375 0.93964 0.95110 0.95964 0.96607
0.93623 0.94997 0.95983 0.96714 0.97259
0.94485 0.95714 0.96584 0.97224 0.97697
0.95118 0.96242 0.97026 0.97596 0.98014
0.95591 0.96636 0.97353 0.97869 0.98244
0.95868 0.96849 0.97513 0.97985 0.98325
0.96149 0.97080 0.97700 0.98136 0.98447
0.96519 0.97375 0.97928 0.98308 0.98575
3.2 3.4 3.6 3.8 4.0
0.97115 0.97529 0.97872 0.98158 0.98398
0.97684 0.98024 0.98302 0.98531 0.98722
0.98062 0.98351 0.98584 0.98776 0.98934
0.98334 0.98584 0.98786 0.98950 0.99086
0.98528 0.98750 0.98927 0.99071 0.99189
0.98581 0.98779 0.98938 0.99066 0.99172
0.98680 0.98860 0.99002 0.99117 0.99212
0.98772 0.98924 0.99043 0.99140 0.99224
4.2 4.4 4.6 4.8 5.0
0.98600 0.98771 0.98917 0.99043 0.99152
0.98882 0.99018 0.99134 0.99233 0.99320
0.99067 0.99179 0.99275 0.99357 0.99429
0.99199 0.99295 0.99377 0.99447 0.99508
0.99288 0.99372 0.99443 0.99504 0.99557
0.99260 0.99334 0.99397 0.99452 0.99500
0.99291 0.99357 0.99413 0.99462 0.99504
0.99296 0.99359 0.99413 0.99461 0.99503
5.21 5.4 5.6 5.8 6.0
0.99247
0.99561 0.99607 0.99648 0.99685 0.99719
I 0.99603 0.99644
0.99405 0.99470 0.99530
0.99395 0.99491 0.09461 1 0.99545 0.99519 0.99594 0.99571 0.99637 0.99618 0.99676
0.99680 0.99712 0.99741
0.99541 0.99541 0.99G78 1 0.99G/3 0.99610 0.99602 0.99639 0.99628 0.99666 0.99651
7.0 8.0 9.0 10.0
0.99655 0.99736 0.99791 0.99831
0.99720 0.99785 0.99830 0.99863
0.99793 0.99842 0.99875 0.99899
0.99810 0.99854 0.99885 0.99907
0.99755 0.99812 0.99852 0.99880
x ~-
O.~~331
0.99762 0.99818 0.99856 0.99883
0.99744 0.99804 0.99845 0.99874
I 0.99541
0.99574 0.9960 4 0.99631 0.99655 0.99747 0.99806 0.99847 0.9987 6
The multiple-scattering correction for median ranges has been discussed in Sec. Sd-3. Nuclear Interactions. Heavy charged particles will be removed from beams by nuclear interactions: the beam intensity will be attenuated exponentially (8d-40) where I is the flux density, and 1: is the macroscopic cross section 1: = .T to obtain the correct kinetic energy TM of the particle. Until better information becomes available, !:>.T '" 4M (keV) ("ionization defect", BB63) can be used for TM» 6M (keV) (M = atomic mass of particle). For '" particles, the upper curve in Fig. 10 of LN63 may beused; for protons,!:>.T '" 1 - 2 keY (FS69).
PASSAGE OF CHARGED PARTICLES THROUGH MATTER
'8-185
Somewhat ,different results are given in RB69. Similar results, have beenobt~ined for germanium detectors (DB67, PR69). Several factors determine the resolutioll of solid-state detectors (BL67, AN67, TS67); some of the more important are: 1. Electronic noise and drift of amplifier system 2. Ballistic deficit 3~ Pulse pileup 4. Recombination and trapping 5. Channeling (see Sec. Sd-7) 6. Absorption in surface layers 7. Statistics of the number joy of electron-hole pairs p:roq.uced.:, ', Fano (FA47) has shown that the standard deviation of then).ean numbei N~is: AN2 = «N - N)2) = FN, where F ~ 1. Bilger (BL67) found F= 0.13 for germanium. Alkh azov et al. (AK67) obtained F", 0.1 for silicon. The problem IS also discussed in DF67, ZA70. PG70 give an upper limit F ~ O.OS. ' ',,' . ' Energy-loss tables for p, d, t, He s, He 4, and Li 6 with q.ata useful for particle identifier systems are, given in BT67 and SK67. Information about the straggling in thin silicon detectors is given in Fig. Sd-7. . References AE67. Appleton, B. R., C. Erginsoy, and W. M. Gibson:~hYs. Rev. 16i, 330,(1967). , AG68. Ait-Salem, M., H. Gerhardt, F. G6nnenwein, H. Hipp, and H. Paap: lYuel. Instr. Methods 60 45 (1968). ' AG69. Arkhipov, E. P., and Yu: V. Gott: Sqv. Phys.-JETP29, . .615(1969) [Zli,;':j§ksp. Teor. Fiz. 56, 1146 (1969)]. . . . . ' " AH67. Andersen, H. H., C. C. Hanke, H. Sj2Irensen, and P., Vajda: Phys. Rev. lila,: 338 (1967). . . . •" .. , " , .: AH68. Armitage, B. H., and B. W. Hooton: lYuel. Instr. Methods5~,,29 Q968). , . AK67. Alkhazov, G. D., A. P" Komar, and A .. A. Vorob'ev,: lYuel. Instr ..Method.* 48, 1 (1967). ' AL69. Aitken, D. W., W. L. Lakin, and H. R. Zulliger: Phys.Rev',179, 393 :(1969). AN6.7. Andersson-Lindstroem, G.: Nuel. Instr. Methods 56, 309 (1967). .' AN69. Andersen, H. H.! H. Sj2Irensen, and P. Vajda: Phys, Ret'. 180; 373'(1969) .. AR69. Andreev, V. N .., V. G. Nedopekin, andY. L Rogov: Sov. Phys.--;-JETP ~9. 807 (1969) [Zh. Eksp. Teor. Fiz., 56, 1504 (1969).]. .' '. . AS68. Andersen, H. H., C. C. Hanke, H. Simansen, H. Sj2Irensen,:anq P .. VajdIF P1I,ys. Rev. 175, 389 (1968). , ;,:. ' ; AS69. Andersen, H. H., H. Simonsen, and H; Sj2Irensen: Nuel. Rhys. A125, .171 (1969). AV69. Andersen, H. H., H. Simonsen, H. Sj2Irensen, and P. Valda: Phys.Rev. -1~G;'372 (1969). " "j BA61. Barkas, W. H:: Phys. Rev. 124, 897 (1961). . " .' , . BA63. Barkas, W. H.: "Nuclear Research. Emulsions," Academic Press, Inc., New:·Y()rk, 1963. .. BB63. Bilger, H., E. Baldinger, and W. Czaja: He/v. Rhys. 36, 405 (196?): BB67. Barkas, W. H., and M. J. Berger: Paper 7 of NA67. ". .' BB69. Barash-Schmidt, N., A. Barbaro-Galtieri., L. R. Price, A. U. Rosenfeld, P. Soq:ing, C. G. Wohl, M. Roos, and G. Conforto:Rev. Mod. Phys. 41, 109 (1969). , ' c' BC69. Bronshtein, r. M. and A. N. Brozdnichenko: Sov. Phys.~Solid State 11, ~40 (1969). BD63. Barkas, W. H., J. N. Dyer, and H. H. Heckman:Phlls. Rev. Letters 11, 26 (1.963). 'BE30. Bethe, H.: Ann. Phys. 5, 325 (1930). ' BE53. Bethe, H.: Phys. Rev. 89, 1256 (1953). . , BE63. Berger, M. J.: "Methods in Computational Physics," voL I, p. 135, Alder, Fernbach, and Rotenberg, eds., Academic Press, Inc., New 1iork,.1963.. ' BE66. Bell, R. J., and A. Dalgarno: Proc. Phys. Soc. (London): 89, 55· (1966); 86, 375 (1965). BF60. Bichsel, H., and B. J. Farmer: Bull. Am. Phys. Soc .. 5, '263. (1960),. . BF61. Barkas, W. H., and S. von Friesen: Nuovo Cimento (10) 19, supp!. I, P." 41 (19,61). BG65. Booth, W., and r. S. Grant: Nucl. Phys. 63, 481 (1965). BH54. Bortner, T. E., and G. S. Hurst: Phys. Rev. 93, 1236 (1954). BH58. Breuer, H., D. Harder, and W. Pohlit: Z. Naturforsch. 138.,567 (1958)., BH67. Bellamy, E, H., R. Hofstadter, W. L. Lakin, J. Cox, M. L. Perl, W. T . .Toner, and T. F. Zipf: Phys. Rev. 164,417 (1967).
8-186
NUCLEAR PHYSICS
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PASSAGE OF CHARGED PARTICLES THROUGH MATTER
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EP61. Eisberg, R. M., and C. E. Porter: Rev. Mod. Phys. 33, 190 (1961). ER67. Eriksson, L.: Phys. Rev. 161, 235 (1967). ES69. Ehrhardt, H., M. Schulz, T. Tekaat, and K. Willmann: Phys. Rev. Letters 22, 89 (1969). FA47. Fano, U.: Phys. Rev. 72, 26 (1947). FA53. Fano, U.: Phys. Rev. 92, 328 (1953). FA56. Fano, U.: Phys. Rev. 103, 1202 (1956). FA63. Fano, U.: Ann. Rev. Nucl. Sci. 13, 1 (1963). Reprinted in NA67. FB68. Fastrup, B., A. Borup, and P. Hvelplund: Can. J. Phys. 46, 489 (1968). FC68. Fano, U., and J. W. Cooper: Rev. Mod. Phys. 40, 441 (1968). FK67. Forgue, V., and S. Kahn: Nucl. Instr. Methods 48, 93 (1967). FL67. Flaks, 1. P.: 5th Intern. Conf. Phys. of Electron. and Atomic Collisions, Leningrad, July 17-23, 1967, Publishing House, "Nauka," Leningrad. FS69. Forcinal, G., P.Siffert, andA. Coche: IEEE Trans. Nucl. Sci. NSI5(1), 4?:5.(1969). GD68. Gnedin, Yu. N., A. Z. Dolginov, and A. I. Tsygan: Boviet Phys. JETP 27, 267 (1968). GF59. Gubernator, K., and A. Flamme.rsfeld: Z. Phys. 156, 179 (1959). HA59. Hall, H. E., A. O. Hanson, and D. Jamnik:: Phys. Rev. 115, .633 (1959). HA68. Harrison, D. E., Jr.: Appl. Phys. Letters 13, 277 (1968). HB68. Hilbert, J. W., N. A. Baily and R. G. Lane: Phys. Rev. 168, 290 (1968). HF68. Hemmer, P. C., and 1. E. Farquhar: Phys. Rev. 168, 294 (1968). HL69. Heckman, H. H., and P. J. Lindstroem: Phys. Rev. Letters 22,871 (1969). HP60. Heckman, H. H., B. L. Perkins, W. G. Simon, F. M. Smith, and W. H. Barkas: Phys. Rev. 117, 544 (1960). HR68. Hara, E.: NUBl. Instr. Methods 65, 85 (1968). HU57. Hudson, A. M.: Phys. Rev. 105, 1 (1957). HV68. Hvelplund, P., and.B. Fastrup: Phys. Rev. 165, 408 (1968). IN71. Inokuti, M.: Rev. Mod. Phys. (to be published, 1971). IS67. Ishiwari, R., N. Shiomi, Y. Mori, T. Onata, and Y. Uemura: Bull. Inst. Chem. Res. Kyoto Univ. 45, 379 (1967). JA66. Janni, J. F.: AFWL-TR-65-150 (Sept. 1966). JA68. Jackson, D. F., and C. G. Morgan: PhY8. Rev. 175, 1402 (1968). JD67. Jespersgard, P., and J. A. Davies: Can. J. PhY8. 45, 2983 (1967). JK68. Johnson, C. H., and R. L. Kernell: PhY8. Rev. 169, 974 (1968). KA67. Krulisch, A. H., and R. C. Axtmann: Nucl. In8tr. Methods 55, 238 (1967). KA68. Katz, R., and E. J. Kobetich: Phys. Rev. 170, 397 (1968). KE66. Kessaris, N. D.: Phys. Rev. 145, 164 (1966). KE68. Kessel'man, V. S.: BovietPhys. Bemicond. 2, 76, (1968). KF67. Kahn, S., and V. Forgue: Phys. Rev. 163,290 (1967). KH68. Khandelwal, G. S.: Nucl. Phys. A116, 97 (1968). KJ68. Khandelwal, G. S.: PhY8. Rev. 167, 136 (1968). KK68. Kobetich, E. J., and R. Katz: PhY8. Rev. 170, 391 (1968). KL68. Kellerer, A. M.: "Microdosimetry," GSF-Bericht B-1, Strahlenbiologisches Inst. del' Univ. Miinchen. (November, 1968). KM61. Knop, G., A. Minten, and B. Nellen: Z. PhY8. 165, 533 (1961). KM66. Khandelwal, G. S., and E. Merzbacher: Phys. Rev. 144, 349 (1966). K064. Koschmieder, L.: Z. Naturforsch. 19a, 1414 (1964). K068. Kolata, J. J., T. M. Amos,. and H. Bichsel: PhY8. Rev. 176,484 (1968). KP52. Katz, L., and A. S. Penfold: Rev. Mod. Phys. 24, 28 (1952). KP67. Khan, J. M., D. L. Potter, R. D. Worley, and H. P. Smith: hY8. Rev. 163, 81 (1967). KR71. Key, J. R., and T. A. Rabson: IEEE, Trans. Nucl. Sci. NS-18, 184 (1971). KY68. Kyle, H. L., and K. Omidvar: Phys. Rev. 176, 164 (1968). LA44. Landau, L.: UBBR J. Phys. 8, 201 (1944). LB37. Livingston, M. S., and H. Bethe: Rev. Mod. Phys. 9, 263 (1937). LE52. Lewis, H. W.: PhY8. Rev. 85, 20 (1952). LH65. Leimgruber, R., P. Huber, and E. Baumgartner: Helv. Phys. Acta 38, 499 (1965). LI65. Lindhard, Jens: Mat. FY8. Medd. Dan. Vid. Belsk. 34, 14 (1965). LN63. Lindhard, J., V. Nielsen, M. Scharff, and P. V. Thomsen: Mat. Fys. Medd. Dan. Vid. Belsk 33, No. 10 (1963). LN68. Lindhard, J., V. Nielsen, and M. Scharff: Mat. Fys. Medd. DfL1/,. Vid. Belsk. 36, 10 (1968). L067. Lassen, N. 0., and A. Ohrt: Mat. Fys. Medd. Dan. Vid. Belsk 36, 9 (1967). LP57. Leiss, J. E., S. Penner, and C. S. Robinson: Phys. Rev. 107, 1544 (1957). LS53. Lindhard, J., and M. Scharff: Mat. Fys. Medd. Dan. Vid. Selsk. 27, 15 (1953). LS63. Lindhard, J., M. Scharff, and H. E. Schijiltt: Mat. Fys. Medd. Dan. Vid. Selsk, 33, 14 (1963).
NUCLEAR PHYSICS LS67. Lehmann, L., H. Spehl, and N. Wertz: Nucl. Instr. Methods 55, 201 (1967). MA68. Morton, A. H., D. A. Aldcroft, and M. F. Payne: Phys. Rev. 165, 415 (1968). ,MB66:LMottk, C. D., and M. D. BrowIi: Rhys. Rev. 149, 244 (1966). ML58. Merzbacher, E., and H. W. Lewis: "Encyclopedia of Physics," vol. 34, SpringerVerlag OHG, Berlin, 1958. ML68. Moak, C. D., H. O. Lutz, L. B. Bridwell, L. C. Northcliffe, and S. Datz: Phys. Rev. 176, 427 (1968). M047. Moliere, G.: Z. Naturforsch. 2A, 133 (1947). M048. Moliere, G.: Z. Naturforsch. 3A, 78 (1947). M055. Moliere, G.:, Z. Naturforsch. lOA, 177 (1955). M058. Mozley, R. F., R. C. Smith, and R. E. Taylor: Phys. Rev. 111, 647 (1958). }.1'R61.' Marcinkowski, A., H. Rzewuski, and Z. Werner: Nucl. Instr. ,Methods 57, 338 (1967). MR6S. 'Maccabee, H. D., M. R. Raju, and C. A. Tobias: Phys. Rev. 165, 469 (1968). \MS65. Morbitzer, L., and A. Scharmann: Z. Phys. 185, 488 (1965). ' MT65. Mattauch, J. H. E., W. Thiele, and A. H. Wapstra: Nucl. Phys. 67, 1 (1965). MY68. Myers, LT.: "Radiation Dosimetry," vol. 1, chap. 7, Ionization,2d ed., Acadeniic Press, Inc.; New York, 1968. MZ67. Marion, J. B .. and B. A. Zimmerman: Nucl. Instr.Methods 51, 93(1967). NA67. Nat!. Acad. Sci.-Natl. Res. Council Publ. 1133, U. Fano, ed., 2d printing, 1967. NA69. Nakata, H.: Can. J. Phys. 47, 2545 (1969). NI61. Nielsen, L. P.: Mat. Fys. Medd. Dan. Vid. Selsk.33, No.6 (1961). NM67. Nicolleta, C. A., P. J. McNulty, and P. L. Jain: Phys. Rev. 164, 1693 (1967). N063. Northcliffe, L. C.: Ann. Rev. Nucl. Sci. 13, 67 (1963). Reprinted in NA67. N067. Northcliffe, L. C.: Paper 8 in,NA67. ' NS61. Nigam, B. P., M. K. Sundaresan, and Ta-You Wu: Rhys. Rev. 115, 491 (Uj59). NS70. Norlhcliffe, L., C., and R. F. Schilling: Nuclear Data Tables A7, 233 (1970). NV66. Nichols, D. K., and V. A. J. Van Lint: Solid State Phys. 18, 1;(1966). "Advances .:""-;,'" )in.RlisearchApplications," Academic'Press, Inc., New York. OH63. Oen, O. S., D. K. Holmes, and M. T. Robinson: J. Appl. Phys. 34,302 (1963). OL67. Oldham, W. J. B.: Phys. Rev. 161, 1 (1967). ' " OR68. Ormrod. J. H.: ,Can. J. Phys. 46, 497 (1968). PA69. Payne, M. G.: Phys. Rev. 185, 611 (1969). PB64. Phipps, J. A., J. W. Boring,and,R. A. Lowry: Phys. Rev. 135, A36 (1964). PB68., Pierce,T. E., W. W. Bowman, andM. Blann: Phys. Rev. 172,287 (1968). PE62. Perkins, J. F.: Phys. Rev. 126, 1781 (1962). pG68. Pehl, R. R., F. S. Goulding, D. A. Landis, and M. Lenzlinger: Nucl. Instr. Methods 59, 45 (1968). PG70. Pehl, R. H., and F. S. Goulding: Nucl. Instr. Methods, 81,329 (197D). PL69. Pivovar, L. I., Yu. Z. Levchenko, A. N. Grigor'ev, and S. M. Khazan: Sov. Phys.JETP 29, 399 (1969) [Zh. Eksp. Teor. Fiz. 56, 736 (1969)]. P067. Powell, C. J.: Health Phys. 13, 1265 (1967). PR69. Palms, J.M., P. V. Rao, R. E. Wood: IEEE Trans. Nucl. Sci. NS 16(1), 36 (1969). RB69. Ray, J. A., and C. F. Barnett: IEEE Trans. Nucl. Sci. NS-16(1), 82 (1969). RC54. Rohrlich, Fl., arid B. C. Carlson: Phys. Rev. 93, 38 (1954). R060. Roll, R. G., and F. E. Steigert: Nucl. Phys. 17, 54 (1960). R068. Roesch, Wm. C.: "Radiation Dosimetry," voL 1, chap. 5, 2d ed., F. H. Attix and WIIi. C. Hosech, eds., Academic Press, Inc., New York, 1968. R069. Robinson, M.T.: Phys. Rev. 179, 327 (1969). RS67. Remillieux,;J., J. J. SaIIiueli, and A. Sarazin: ,J. Phys. Radium 28,832 (1967). RU68. Rudge, M. R. H.: Rev. Mod. Phys. 40, 564 (1968). RY55.(RybakOv, B. V.: Soviet Phys. JETP 1, 435 (1955). SA65. Sattler, A. R.: PhUs.Rev. 138, A1815 (1965). SB67. Seltzer, S. M., and M. J. Berger: Section 9,in NA67. SC63. Scott, W.:T.: Rev. Mod. Phys., 35,231 (1963). SC66. Schiflltt, H. E.: Mat. Fys. Medd. Dan. Vid. Selsk. 35, 9, (1966). ,fBI67, Singh, J. J.: NASA Tech. Note D-3927, May, 1967. SK67. Skyrme, D. J.: Nllcl. Instr. Methods 57, 61 (1967). ,SP54. Spencer, L. V., and U. Fano: Phys. Rev. 93, 1172 (1954). SP55. Spencer, L. V.: Phys. Rev. 98, 1597 (1955). ,'.SP59: Spimcer,L. V.: Nat!. Bur. Standards (U.S.) Monograph 1. SP63. Swanson, N., and C. J. Powell: Jou'r. Chem. Phys. 39, 630 (1963). SP70 .. 'Swint, J. B., R. M. Prior, and J. J. Ramirez: Nucl. Instr. & Meth., 80,134 (1970). ST60. Sternheimer, R. M.: Phys. Rev. 117,485 (1960). ST67, Sternheimer, R.M.: Phys. Rev. 164, 349 (1967). ,'SUBO. Sternheimer" R. M.: Phys. Rev. 118, 1045 (1960).
PASSAGE OF CHARGED PARTICLES THROUGH MATTER SV68. SY48. SZ65. TB68. TH52. TH67. TM59. TM70. T071. TP69. TS67. TS68. TT68. VA57. VK69. VS68. VV68. WA51. WA52. WA56. WH58. WH33. WI68. WM67. ZA70. ZM69.
8-189
Sattler, A. R., and F. L. Vook: Phys. Rev. 175, 526 (1968). Symon, K. R.: Thesis, Harvard University, Cambridge, Mass., 1948. Sautter. C. A., and E. J. Zimmerman: Phys. Rev. 140, A490 (1965). Tschalar, C., and H. Bichsel: Nucl. Instr. Methods 62, 208 (1968). Thompson, T. J.: UCRL-1910. (Thesis, Univ. of California, Berkeley, 1952). Thomas, E. W.: Phys. Rev. 164, 151 (1967). Ter-Mikayelian, M. L.: Nucl. Phys. 9, 679 (1958-1959). Tschalar, C., and H. D. Maccabee: Phys. Rev. Bl, 2863 (1970). Toburen, L. H.: Phys. Rev. A3, 216 (1971). Taylor, B. N., W. H. Parker, and D. N. Langenberg: Rev. Mod. Phys. 41, 375 (1969). Tschalar. C.: Thesis, University of Southern California, Los Angeles, January 1967. Tschalar, C.: Nucl. Instr. Methods 61, 141 (1968). Tschalar, C.: Nucl. Instr. Methods 64, 237 (1968). Vavilov, P. V.! So'l!ietPhys. JETP 5,749 (1957). Vasilevskii, I. M., I. I. Karpov, V. I. Petrushkin, and Yu. D. Prokoshkin: So'/). J. Nucl. Phys. 9,583 (1969); [Yad. Fiz. 9, 997 (1968)]. Vriens, L., J. A. Simpson, and S. R. Mielczarek: Phys.- Rev. 165, 7 (1968) ;170, 163 (1968). Van Camp, K. J" and V. J. Vanhuyse: Z. Phys. 211, 152 (1968). Walske, M. C,: Thesis, Cornell University, 1951. Walske, M, C.: Phys. Rev. 88, 1283 (1952). Walske, M. C.: Phys. Rev. 101, 940 (1956). Whaling, Ward: "Encyclopedia of Physics," vol. 34, p. 202 Springer-Verlag OHG, Berlin, 1958. Wheeler, J, A.: Phys. Rev. 43, 258 (1933). Winterbon, K. B.: Can. J. Phys. 46, 2429 (1968). white, W., .and R. M. Mueller: J. Appl. Phys. 38, 3660 (1967). Zulliger, H. R., and D. W. Aitken: IEEE Trans. Nucl. Sci; NS-17, 187'(1970). Zulliger, H. R., L. M. Middleman, and D. W. Aitken; IEEE Trans. Nucl. Sci•. NS16, I, 47 (1969).
8e. Gamma, Rays ROB~EY
D. EVANS.
Massachuse.tts ,]nstitute of Technology ,Se-l. Attenuation of Gamma Rays and x: Rays. The Photon. Photons, are classified according to their mode of origin, not their quantum energy . Gamma rays are the electromagnetic radiations whichacconipany nuclear transitions. X rays are the electromagnetic radiations which accompany electronic transitions, including the characteristic or fluorescent line spectra of X rays, the bremsstrahlung or continuous spectra of X -rays, and the positron-negatron allnihilation radiation. By eJ>tension, the X-ray category includes all photons originating outside an atomic nucleus and due to the transitions of other elementary particles, for eJ>ample, proton bremsstrahlung, mu-mesonic X ra,ys, and ... o-decay photons. In' this section we deal ollly with the interaction of photoJ;J.s with matter. The!'lc illteractions are thought to be independent of the origin of the photon. Hence we use the term photon to refer here to both 'Y rays and X rays. The quantum energy of a photon is E = hll, where II is the frequency alld h = 4.135 X 10- 21 MeV sec is Plallck's constant. The corresponding wavelength is }.. = C/II = hc/E = 0.012397 X lO- s/E cm, when E is in MeV. Competing Interactions. A photon can interact with matter by anyone of several competing alternative mechanisms. For details, see refs. B3, El, F3, Gl, and G2. In each case the interaction is an all-or-nothing affair. The interaction can be with the entire atom (photoelectric effect and Rayleigh scattering) or with one electron in theatoin (Compton effect and pair production in the field of an electron) or with the atomic nucleus (pair production, resonance elastic scattering, photo disintegration, and meson production). The probability for each of these many competing independent processes can be eJ>pressed as a collision cross section per atom, per electron, or 'per nucleus in the absorber. The sum of all these cross sections (corrected for coherence in some low-energy cases), normalized to a per atom basis, is then the probability that the incident photon will have an interaction of some kind while passing through a very thin absorber which contains one atom per cm 2 of area normal to the path of the incident photon. Attenuation, Scattering, and Absorption. The total collision cross section per atom, when multipled by the number of atoms per cm 3 of absorber, is then the linear attenuation coefficient fJ.o per centimeter of travel in the absorber. The fraction of incident photons which can pass through a thickness x of absorber whose density is p without having an interaction of any kind is e-l'o' or e-(l'ofp)(p.), where p is the density of the medium and fJ.o/ p is the mass attenuation coefficient. The absorption coefficient fJ.a is a much more restricted concept than the attenuation coefficient fJ.o. Attenuation can be by some purely elastic process, such as Rayleigh scattering or nuclear resonance (Mossbauer) scattering, in which the photon is merely deflected and does not give up any of its initial energy to the medium. Here only a scattering coefficient would be involved. However, in a photoelectric interaction, e-190
GAMMA RAYS
the entire energy of the incident photon is truly absorbed by an atom of the medium; there is no scattered residual photon. Here the attenuation of the primary ta'diation is due to complete absorption of the energy of the incident photon. The intermediate case of greatest importance is the Compton effect, in which some energy is absorbed and appears in the medium as kinetic energy of a Compton recoil electron while the balance of the incident energy is not absorbed but is present as a Compton scattered photon. Scattering, then, involves the deflection of incident photon energy, abSorp-' tion :involves the conversion of incident photon energy into the kinetic energy of a
120
100Photoelectric effect dominant
Pair production dominant
., ao
.0
I
"-
i' 200
a
;;; 1;;
6
....... lN
'" ~
I"
4 E u :;
N
'f',i'-. f'
l"l 45°
2·
Q,
~
1\
.s
)'...,
q I
1". ~~
"0
90°
"-
5
1200~
6
'\.. I"
~" "0
1500~
:;
~ -180v"~
2
I
o. I
0.01
2
3 4
6
0.1
2
:; 4
6
2
3
4
6
10
II I 2
3
4
6
100
hvo MeV FIG. 8e-4. Collision differential cross section d(,IT) / dfJ for the number of photons scattered per unit solid angle in the direction {f. [From Evans (E2).]
8-195
GAMMA RAYS
where the scattered photon hv' goes into the solid angle dn steradians at mean angle 17and the classical radius of the electron ro has the value
e' == --. moc
ro
=
(8e-12)
2.818 X 10- 13 cm
Substituting v' j Vo in terms of 17- and the incident photon energy hvo = a (moc') gives the equivalent explicit relationship d(.u) - r • dO [ -
0
1
+ a(1 1{
1
+
J' (1 +
cos' t1-) 2 a'(1 - cos 17-)' } (1 + cos' t1-)[1 + a(1 - cos t1-)]
cos t1-)
cm' electron
(8e-13)
Table 8e-l and Fig. 8e-4 give numerical values of d(,u) Ian in 10-'7 cm' (or millibarn)j steradian per electron. The classical or Thomson differential cross section is d(.uThom) _ dO - ro
TABLE
8e-I.
,(1 + cos' t1-) 2
cm' steradian . electron
COLLISION DIFFERENTIAL CROSS SECTION 10-. 7 CM'/sTERADIAN PER ELECTRON*
(8e-14)
d(,u)/dn IN
[From Eq. (8e-13)] hJlo, MeV
t110
--- -0.01 0.04 0.1 0.2 0.4 1 2 4 10 20 40 100
79.4 79.4 79.4 79.4 79.4 79.3 79.3 79.2 78.9 78.4 77.6 75.0
50
100
20°
30°
45°
60°
90 0
120°
150 0 .180 0
- - - - - - - . - - - - - - - - ' --- --- --- --79.1 79.0 79.0 78.8 78.6 77.9 76.8 74.6 68.6 60.4 48.6 30.5
78.1 78.0 77.7 77.3 76.4 73.7 69.7 62.8 48.4 34.2 22.0 10.5
74.6 74.0 73.0 71.3 68.2 60.2 50.1 37.3 21.2 12.5 7.00 3.08
69.1 68.0 66.0 62.8 57.2 45.0 33.0 21.7 11.0 6.3 3.40 1.45
59.0 57.5 53.7 48.2 41.0 27.7 18.3 11.5 5.6 2.93 1.56 0.64
48.6 45.5 41.0 35.0 28.5 17.7 11.5 7.15 3.48 1.86 0.97 0.40
38.3 46.4 64.7 73.6 34.4 40.4 53.5 60.2 29.3 31.3 39.2 43.2 22.9 23.0 27.2 29.3 16.8 15.7 17.2 17.9 10.4 8.80 8.45 8.35 6.80 5.30 4.73 4.54 4.09 2.98 2.50 2.39 1.86 1.28 1.05 0.98 0.97 0.66 0.535 0.498 0.492 0.336 0.270 0.254 0.204 0.135 0.108 0.102
* From R. D. ·Evans, Compton Effect, in "Handbuch der Physik," vol. XXXIV, pp. 218-298, S. Fliigge, ed., .springer-Verlag, Berlin, 1958. where roo = 79.41 X 10-'7 cm' is the upper limit approached by this Klein-Nishina collision differential cross section at any t1- as a = hvolmoc' approaches zero and at any a as t1- approaches zero. Klein-Nishina Scattering Differential Cross Section. The scattering differential cross section d(.u,) refers to the amount of energy scattered in a particular direction; thus d( ) = scattered energy per sec [MeV I(sec . electron)] = cm' (8e-15) .u, incident intensity [MeV I(cm' . sec)] electron The scattered energy is the number of scattered photons times the quantum energy hv' of each, and the incident intensity is the number of incident photons per unit
$"'-1:96
NUCLEAR PHYSICS
~eatimes.thequantum
energy hpoof each. Not all the'energy hpo is scattered,but only the fraction hpl/hpo. Therefore the scattering differential cross section for, unpolarized radiation is pi
d(.rr,) = - d(,rr)
"\, d" ("1)3(·j Po +
,.\
_ ro
--
2
..
p
-
vo
p
-
•
2.0
)
(8e-16)
--SInv
,,'
110
Tables and graphs of d(,rr,) over the range 1 deg .::; iJ .::; 180 deg and 0.01 MeV::;; hllo < 100 MeV are available in ref.E2. (~:~X;;gular Distr~oution of the Number of Scattered Photons. The total solid angle available per unit scattering angle is \, i _ . . '" . (8e-17)
c· .
and approaches zero in the forward~ and backward-scattering directions. ber-vB. ·angle distribution of scattered photons is
d(,rr) _ d(.rr) 2 . diJ - ail 7r sm
The num-
.0
u
electron· radian
(8e-18)
ahli'nasafoiwafd maximum which is in the vicinity of iJ ,,; 20 deg for hllo =3MeV and is at larger angles for smaller h"o (see Fig. 20 of ref. E2). -- Angular'Distribution of the Energy of Scattered Photons. The distribution of .scattetedphoton energy in any angular interval, that is, betwee~ two cones of half tingles iJ and ..f} --t-- dt!, is~ I , .~ dC,rr,) _ d(.rr,) 2 . iJ (8e-19) ~. - '(fQ 7r sm electron . radian and is more sharply peaked than the number-vs.-angle distribution because of the variatiQn of hi,' with iJ (see fig. 24 of ref. E2) . . Angular Distribution of Compton Recoil Electrons: The ionization which 'actuates many radiation detectors is due primarily to Compton recoil electrons produced in t4e detector o~ its walls and projected between cp = 0 and cp = 90 deg. The initial nitmber~vs.~a~g?e distribution of the recoil electrons is
d(.rr) = dC.rr) [27r(1 dcp dn (1
+ cos iJ) sin iJ] + a) sin cp 2
cm 2 electron . radian
(8e-20)
F.Qr photon energies below about 0.5 MeV this distribution has two maxima, in the neighborhood of20 arid 60deg. At higher photon energies the wide-angle maximum disappears and the small-angle maximum occurs at smaller angles as hvo increases (flee fig. 21 of ref. E2 and table III of ref. J1). 'En~rgy Distribution of Compton Recoil Electrons: The number-vs.-ene~gy spectrum Compton electrons is
of
d(.rr) dn diJ :dT = ali: diJ dT d (,rr) 27rmoc2 a (.rr) 27rmoc 2 = ali: (hV ' )2 = an (hvo - T)2
d(;.r)
~
7rr 02 a'moc'
{2 + (_T_)' [..!..a 2 + h"ohvo- T _ ~a (hpo Thvo. - T
T)]} cm' keV . electron
(8e-21)
8-197
GAMMA RAYS
where ro = 2.818 X 10- 13 cm and moc' = 511.0 keV. The electron spectra for hv'o = 0.5 to 3.5 MeV, in steps of 0.5 MeV, are shown in Fig. 8e-5 (see also table II of ref. j1 and fig. VII of ref. Nl). The pronounced number maximum which occurs just at the maximum electron energy T max is called the Compton edge in -y-ray spectroscopy (see Sec. 8e-6). Energy Distribution of Compton Scattered Photons. Each recoil electron has a companion scattered photon whose energy is hI" = hllo - T. Hence the energy spectrum 1.8 0.5 1.6
1.4
c
~
1.2
CD
Gi
>CD
~
1.0
d I
~
~
E
u
...
'ncident Photon Energy hv o, MeV
'"I 0
1,0
1-.
~'0.6
/
b': :c
"
0.4
1.5 2.0 3.5
o~~§§~~~~~~jj o 0.5 I 1.5 2 2.5 3 3.5 Recoil
Electron Energy T, MeV
FIG. 8e-5. Number-va.-energy distribution of Compton recoil electrons, for seven values of the incident photon energy hvo, in 10-'7 em' (millibarn)/keV per free electron. The energy spectrum of scattered photons is' obtained by transforming the energy scale from T to hllo - T for each curve ... [From Evans (E2).J
of scattered photons is complementary to the energy spectrum of recoil electrons and is given by replacing T by (hllo - hI") and dT by d(hv') in Eq. 8e-21 and in Fig. 8e-5. Average Collision Cross Section. The average (or total) collision cross section ,u is the probability of any Oompton interaction by one photon while passing normally through a material containing one electron per cm' and is given by ,u
=
r"d(,u) 2
Jo
£In
7J"
. .od.o =2
SIn
if
if
.{1+",[2(1+",)_ln(1+2",}]
7J" r o
",'
1
+ 2«
'"
+ In (1 + 2",) _ 1 + 3D!} 2", (1 + 2",)'
~ electron
(8e-22)
8c:..198
NUCLEAR PHYSICS
Numerical values are given in Table 8e"2 (see also fig. 27 on ref. E2 :;ind fig. VIn of ref. NI). For small values of a=, hvo/moc', accuracy is, best preserved by using the expansion ,(F
8
('1 _ 2a + 265 a ,_ 133 10 a
,
:3 7r r O
~
3
+ 1,144 35 a
4 _
.544 a5 7
+ 3,784 a' 20
_
. . .)
em' electron
»
while for a
(8e-23)
1, (8e-24)
is a good approximation. Average Scattering Cross Section. The total scattered energy in photons of various energies :l;!v', scattered on the average by each electron per cm' of scattering material, is the average scattering cross section ,rr, multiplied by the incident energy expressed as (number of photons) X (energy hvo per photon), where eU 8
r
7r
= }0
d(,(F,) 2
-ctfi:
{) d,J
. 7r
SIn
_ ,[In (1 + 2",) - 7rrO a'
+ 2(1 + a)(2a' - 2", a'(l + 2a)2
-
1)
8a'
+ 3(1 + 2",)3
J
cIn'
electron
(8e-25)
For small a, use, the expansion _ 8 , (1 - 3a ,rr, - 37frO
94, + 10 a
-
28 a 3
+ 7.5.'i2 a
212 a 5
4 -
1,648 a + -3-
6 -
em' electron
(8e-26)
Table 8p~2 gives numerical values of ,(F, as well as the average energy (hv')av per scattered photon, which is (hv')av = hvo ,rr,
(8e-27)
,rr
Average Absorption Cross Section. The total kinetic energy, in recoil electrons of various kinetic energies T, produced on the average per eleetron per cm' of material is the average absorption cross section ,(Fa multiplied by the incident energy expressed as (number of photons) X (energy hvo per photon), where =,
,(Fa
_,
,(F, '
,'0'
,
=
- 3(1
2,
r
' [ 2(1
,7r O
4a'
a'(1
+ 2a)3
-
+ a)' _ + 2a) (1 + a
--;;s- -
1
(1
+ 3a
+ 2a)2
_ (1
2 - 2a + a)(2a a 2(1 + 2a)'
1 + 2a31)"In (1 + 2a) ]
2a
-
1) '
em' electroIl
(8e-28)
For small a, use the expansion ,fJ"a =
8,
,(
:3 7r r O
a -
42
'10 ",'
147, 1,616 940 + 10 a 35 a + 7 a 3 -
4
5 -
7,752
21 a'
+ .. '") em' electron
(8e-29)
Table 8e-2 gives numerical values of ,rr a as well as the average energy Tav of the Compton recoil electronS, which is (8e-30)
8-199
GAMMA RAYS
TABLE 8e-2. KLEIN-NISHINA CROSS SECTIONS FOR COMPTON INTERACTIONS IN 10- 27 CM' (MILLIBARNS) PER FREE ELECTRON AND RELATED QUANTITIES* (Calculated fmm the following equations: ,0' (8e-22) and (8e-23), ,0', (8e-25) and (8e-26), ,O'a (8e-28) and {8e-29), (hv')av (8e-27), Tav (8e-30), Tav/hvo (8e-30). Using ro = 2.818 X 10-13 em and moc 2 = 0.5110 Me VJ Photon energy hvo,
MeV
Cross sections, 10- 27 em 2 /electron Collision
Scattering
Recoil electron Scattered Average Fraction of photon Absorp- average energy energy incident tion (T)av, photon energy (hv'lav, MeV ,fTa MeV (Tl.v/hvo
,O't
,fT, t
0.010 0.015 0.020 0.030
640.5 629.0 618.0 597.6
628.5 611.6 595.7 566.5
12.0 17.4 22.3 31.1
0.0098 0.0146 0.0193 0.0284
0.0002 0.0004 0.0007 0.0016
0.0187 0.0277 0.0361 0.0520
0.040 0.050 0.060 0.080
578.7 561.5 545.7 517.3
540.1 516.2 494.5 456.7
38.6 45.3 51.2 60.6
0.0373 0.0460 0.0544 0.0706
0.0027 0.0040 0.0056 0.0094
0.0667 0.0807 0.0938 0.1171
0.100 0.150 0.200 0.300
492.8 443.6 406.5 353.5
424.8 363.1 318.6 258.2
68.0 80.5 87.9 95.3
0.0862 0.1228 0.1568 0.2191
0.0138 0.0272 0.0432 0.0809
0.1380 0.1815 0.2162 0.2696
0.4.00 0.500 0.600 0.800
316.7 289.7 267.5 235.0
218.6 190.5 169.2 138.9
98.1 99.2 98.3 96.1
0.276 0.329 0.379 0.473
0.124 0.171 0.221 0.327
0.3098 0.3424 0.3675 0.4089
1.00 1.50 2.00 3.00
211.2 171. 6 146.4 115.1
I
118.3 86.70 68.67 48.65
I \cJ2.\cJ
j
84.9 77.7 66.4
0.560 0.758 0.939 1.269
I
0.440 0.742 1.061 1. 731
I
O.4:3f)9
0.4948 0.5307 0.5769
95.98 82.87 73.23 59.89
37.73 30.83 26.07 19.93
58.25 52.04 47.16 39.96
1.57 1.86 2.14 2.66
2.428 3.140 3.864 5.338
0.6069 0.6280 0.6440 0.6672
10 15 20 30
50.99 37.71 30.25 22.00
16.14 10.94 8.272 5.563
34.85 26.77 21.98 16.44
3.16 4.35 5.47 7.58
G.835 10.65 14.53 22.42
0.6835 0.7099 0.7266 0.7473
40 50 60 80 100
17.46 14.58 12.54 9.882 8.199
4.191 3.362 2.807 2.110 1.690
13.27 11.22 9.733 7.772 6.509
30.4 38 ..5 46.6 62.9 79.4
0.7600 0.7695 0.77G2 0.7865 0.7939
4.00 5.00 6.00 8.00
9.6 11.5 13.4 17.1 20.6
* From R. D. Evans, Compton Effect, in "Handbuch der Physik," vol. XXXIV, pp. 218-298, S. Fliigge, ed., Springer-Verlag, Berlin, 1958. t These nUlnerical calculations for eU and erJ"a were done on the IBM computer at·the Massachllsettf! Institllte of Technology under the direction of Mr. W B. Thurston.
8-200
NUCLEAR PHYSICS
The fraction of the incident photon energy which is absorbed and appears as kinetic energy of Compton recoil electrons in the average of all Compton collisions is Tav/ hvo = ,Ua/,u, This fraction starts at zero for very low energy photons and increases monotonically with hvo, as shown in the right-hand column of Table 8e-2. The Compton collision (or attenuation) cross section is then the sum of the Compton scattering and absorption cross sections; that is, ,u
=
(hv')av ( ) hvo
,CT
= ,CT, (,u) efT
= eUs
+
+ hvo Tav ( ) ,CT
+ ,Ua (,CT) eU
(8e-31)
ecra
8e-3. Photoelectric Effect. The entire primary photon energy hv is absorbed by the struck atom. One electron (usually from the K or L shell) is ejected with kinetic energy T, where (8e-32) T = hv - B, and Be is binding energy of the electron before being ejected from the atom. Momentum is conserved by the backward recoil of the entire residual atom. The energy B, is emitted promptly by the residual atom as characteristic X rays and Auger electrons from the filling of the vacancy in the inner shell. Because the entire atom participates in the interaction, photoelectric interactions are described by an atomic cross section aT cm 2 /atom. No single closed formula describes aT accurately over a wide range of hv. A crude but useful guide is
Z4
aT
~ const (hv) 3
(8e-33)
The experimental and theoretical material has been summarized in refs. D1, D2, E1, G2, and H3. Numerical tables of blended theoretical and experimental "best" values of aT for 11 elements from 0.01 to 100 MeV are given in ref. H3. Mainly owing to differences in the interpretation of experimental results, H3 values of aT at small hvo «0.1 Me V) and l::trge Z are smalleT than D2 ancllargel' than G2 values. For large hvo (> 1 Me V) and large Z, aT is smaller in H3 and D2 than in G2, owing to revisions in the theoretical values. For 1 Me V and large Z there is agreement among D2, G2, and H3. Photoelectric mass absorption coefficients for air, water, Al, Cu, NaI, and Pb and interpolation formulas are given in Sec. 8e-5. 8e4. Pair Production by Photons. In the field of a charged particle, usually an atomic nucleus but also to some degree in the field of an atomic electron, a photon may be totally absorbed and a positron-negatron pair emitted. A minimum incident photon energy of hv = 2moc2 = 1.02 MeV is required for pair production in the field of a nucleus, and a minimum of hv = 4moc2 = 2.04 Me V in the field of an atomic electron. The atomic cross section aK for nuclear pair production increases with Z' (reduced somewhat at very large photon energies by electron screening of the nuclear field) and with the photon energy hv. The kinetic energies of the positron and the negatron pair electrons are continuously distributed, each from a minimum of zero up to a maximum of hv - 2moc2. Tables are given for 11 elements in ref. H3, and for 24 elements and several mixtures in ref. G2. Analytical expressions for aK are complicated (see ref. HI). Tables are given for 11 elements in ref. H3, and for 24 elements and several mixtures in ref. G2. Graphs and interpolation formulas are given in ref. E1 and in Sec. 8e-5. Se-5. Mass Attenuation and Absorption Coefficients for .Photons in Narrow-beam Geometry. Linear attenuation coefficients, a (Compton), T (photo), and K (pair), are the atomic cross sections (cm 2 /atom) multiplied by atoms/cm 3 of material and have
8-201
GAMMA RAYS
dimensions of em-I. Mass attenuation coeffieieritsare the linear coefficients (em-I) divided by the density p (g/cm'), thus cr/p, r/p, Kip, with dimensions of cm 2 /g, and have the advantage of being independent of the actual density and physical state of the.attenuator. Each mass attenuation coefficient for an element is the corresponding atomic cross section multiplied by the number of atoms per gram (Avogadro's nUIl).b~r/atomic weight). Compt.on mass attenuation coefficients are nearly inde~ pende'nt of Z because the number of electrons per gram varies only slightly am.ong' ail elements except hydrogen. The total mass attenuation coefficient }Lo/p is the sum of Compton absorption (d'a/p), Comptofiscattering (cr,/ p), photoelectric attenuation (7/p),and pair-production attenuation (Kj p), (8e-34)
In some narrow-beam attenuation situations a portion of the coher,ent, el3;stic Rayleigh scattering may also be effective. The mass absorption' coefficient relates only to the actual absorption .of photon energy. This 'is ,a two-step process inv.olving,. first, the conversion .of photon energy ,t.o kirl.,etic energy of secondary electrons and to rest energy of electron pairBand, seGond; the dissipation .of this kinetic energy mainly by ionization and e'xcitationof the,at.oms in the absorbing medium, hut to a small extent also by bremsstrahlung £rom radiative c.ollisions of the secondary electrons withatornic nuclei in the absorber. There is n.o ambiguity about the firs.tstep, but the variety of treatments of the secoRd step has led t.o a confusing. group of absorption coefficients, including the so-called "tru,e"absorption," "real-absorption," "energy-absorption," "dose-absorption," and "energy-transfer-absorption'" coefficients. I( a yol1imated,. beam contf'ining nphotons/cm 2 sec, each having energy hvo MeV, 'is IwrJ,llally inoident on an absorber of thicknessdx and density p, then the number ,d:; of photons/em 2 sec,which will have collisions is ~
,
"
•
,
,
~
,
'.
,
c ,
•
"
dn
=
'
n}Lodx
= n (~)
(p dx)
(8e-35)
:rlie :incident photon intensity is I = nhvo Me V / em 2 sec, and the energy transferred from incide'nt photons to secondary electrons, which is closely similar to the. "absorbed dose rate" in Me V /g sec, can be written as dI
or
=
nhvo pdix
(}L~'n) (pdx)
~I
C"';'n)
MeV cm 2 sec MeV, gsec
(8e-36) (8e-37)
where dI is the Aangein the intensity ofthe photons, and the mass-absorption coefficient (/1-ab,n/ p) can be .defined in a variety of, slightly different ways. Mcist generally one can ,write (8e-38) where the dimensionless factors 10. (Compton),,f, (photo), .and fK (pair) represent the fractioj1 of th\l'incident photoR energy hvo;which is considered to be absorbed in the .mediumJromeach type, of interaction. The size of the "region of interest" relative to ,the ffi\laj1 free. path of.the secondary phot.ons in the medium. plays an important role in the choice of these dimensionless faqtors. The situation is clearest for the Compton interaction. The energy of the Compton 'scattered photon is usually large enough tdperrnit it to escape from a small "region
8-202
NUCLEAR PHYSICS
of interest" without interacting. Then the photon energy transferred to electrons is simply the kinetic energy acquired by the Compton recoil electron. Then, by Eq. (8e-30)
f.
Tav
=
(8e-39)
hvo
C
Hence
p
p
(8e-40)
p
or just the Compton mass absorption coefficient u a / p. In the photoelectric interaction the kinet.ic energy of the ejected photoelectron is, by Eq (8e-32), T = hvo - Be; hence one extreme estimate of iT is (f) T
- ~ - hvo - Be hvo hvo
(8e-41)
1 -
which would be valid if the binding energy Be is not released as electron kinetic energy in the volume of interest. However the excitation energy Be may be emitted as Auger electrons or as K, L, M, . . . X-ray photons. When it is emitted as Auger electrons, the energy Be is locally present in the medium as kinetic energy of electrons and iT = 1. When Be is emitted as X rays, these photons are somewhat analogous to a Compton scattered photon and could be excluded from iT" If ip is the average fluorescence yield rip increases with Z, rising from 0.01 for Z = 10 (Ne) to about 0.4 for Z =29 (Cu) and 0.95 for Z = 82 (Pb)], then another estimate of iT is (fT)' = hvo - ipBe = 1 _ ipBe hvo hvo
(8e-42)
The correction term ipBe/hvo is negligible for light elements because ip is so small. For heavy elements, where ip approaches unity,ipBe/hvo is comparable to unity for photon energies near the absorption edge (K edge = 0.088 Me V in Pb), then decreases in importance as hpo increases. But the fluorescence radiation has a very short mean free path (for example, 0.06 cm in Pb) and is therefore reabsorbed very close to the emitting atom. The correction ipBe/hvo is therefore justifiable only if the "volume of interest" for energy absorption is very small, for example, less than Imm 3 in Pb. Therefore, in absorbers having an appreciable thickness the energy B, is all reabsorbed in a small volume and the effective value of iT would be (8e-43)
(Jr). = 1
In the pair-production interaction, the total kinetic energy of the electron pair (or of the triplet in the case of pair production in the field of an atomic electron) is hvo2moc'. Hence the fraction of hvo which appears at once as kinetic energy of secondary electrons is (fKl! = hvo - 2moc' = 1 _ 2moc2 = 1 _ ~ (8e-44) hvo
hvo
a
The energy 2moc' is reemitted as two 0.511-Me V annihilation photons at the point of annihilation of the positron member of the electron pair. This annihilation radiation is the analog of Compton scattered radiation. In Pb, it has a mean free path of about 0.6 cm. For absorbers whose dimensions are small, the annihilation radiation clearly plays the role of a scattered radiation and should be so treated as in (fK)'. For larger absorbers it has been a common approximation to ignore this correction term for annihilation radiation and to take (8e-45)
S-:-203
GAMMA RAYS
This approximation usually introduces only a small change in /Lab,n/P even for thin absorbers of heavy elements because at modest energies, say 1 to 3 Me V, the pairproduction interaction is only a small component of the total absorption while at very large photon energies, where the pair production is predominant, the correction 2moc2/hvo becomes small. The magnitude of the correction is shown in Figs. 8e-6 through 8e-11. For certain dosimetric applications in radiological physics (see chap. 1 of ref. Al for details) a value of /Labsn/ P is utilized which includes only the kinetic energy transferred to charged particles per unit mass of irradiated material in an infinitesimally small 10 8 6
AIR
4
3
-.
2
I
8 ~ 6
«4 3 "'" 2 :;!iP E u
o8.I
1'0/:
.....
\
~l'1',;.
6 t=J)\ I-"?~ .." 4 I--- ~ ~\
31---
2
'5-\1--0\
~\-~
I---
11'".1> TOTAL ABSORPTION"":
"
0.0I
~
,IP
,/-+++ ~.~ 'Y :s~
8 6
~
'1;-",
- /4&
/'Q
~~.
4 ~(Yalp
3
0\
~~'*0; Ii
TOTI'L
A8S0~PTiON /'o/p
....
0
~ ~
\
I)
8