Advances in Electronics and Electron Physics, Volume 18

ADVANCES IN ELECTRONICS AND ELECTRON PHYSICS VOLUME 18

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Advances in

Electronics and Electron Physics EDITEDBY L. MARTON National Bureau of Standards, Washington, D. C .

Assistant Editor CLAIREMARTON EDITORIAL BOARD W. B. Nottingham T. E. Allibone E. R. Piore H. B. G. Casimir M. Ponte L. T. DeVore W. G. Dow A. Rose L. P. Smith A. 0. C . Nier

VOLUME 18

1963

ACADEMIC PRESS

New York and London

COPYRIGHT

@ 1963, BY AcAuvniic

P R E S S INC.

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LIBRARY OF

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CONTRIBUTORS TO VOLUME 18 MANFRED A. BIONDI,Physics Departnzent, University of Pittsburgh and Westinghouse Reseawh Laboratories, Pittsburgh, Pennsylvania

F. P. BROOKS, JR., International Business Machine Corp., Pouyhkeepsie, N e w Yorli DAVIDP. KENNEDY, International Business Afachine COTp., Poughkeepsie, New York F. LENZ,Institute of Applied Physics, University, Tubingen, Germany G. MOLLENSTEDT, Institute of Applied Physics, Unilrersity, Tubingen, Germany

F. E. ROACH,Central Radio Propagation Laboratory, National Bureau of Standards, Boulder, Colorado

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For the best part of a year now your editor and associate editor have been in Europe, where many opportunities arose to establish new contacts and renew the old ones. The result is twofold: we gained new insight into contemporary European research in electronics and electrophysics and were able t o secure the collaboration of many colleagues to future volumes of Advances. A hearty welcome to our new contributors! As in the past years I should like to list here the authors of future reviews and the tentative titles of their contributions : G. Broussaud and J. C. Simon G. Birnbaum K. L. Bowles J. F. Dennisse M. Knoll and R. W. Schon J. L. Jackson and R. A. Piccirelli K. G. Emeleus R. G. Fowler L. S. Chernov S. H. Autler L. A. Russell J. W. Herbstreit J. Kistemaker and C. Snoek G. K. Wehner P. Grivet, and L. Malnar D. B. Medved M. Nalecz H. Raether D. de Klerk

Endfire Antennae Light Optical Masers Scattering in the Upper Atmosphere Radioastronomy Biological Effects of Atmospheric Ions Cooperative Phenomena Plasma Oscillations Electrons as a Hydrodynamical Fluid Microwavc Applications of Plasma Cryogenic Magnets High Speed Magnetic Core Memory Technology Tropospheric Propagation Atoms Produced in Sputtering Experiments Cathode Sputtering Weak Field Magnetometers Electron Ejection from Solids by Atom and Ion Impact Hall Effect and its Technical Applications Gas Discharge Phenomena High Magnetic Field

Other subjects, on which conversations are more tentative, comprise : magnetohydrodynamics, thermionic emission, noise in semiconductors, superconductivity, and others. I wish to express again my heartfelt thanks to all those whose collaboration makes these volumes possible.

L. MARTON

Sorbonne, Paris, July, 1963

vii

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CONTENTS CONTRIBUTORS TO VOLUME 18.

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V

FOREWORD . .

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vii

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The Nightglow F. E . ROACH

I . Definitions . . . . . . . . . . . . . I1. Units of Brightness . . . . . . . . . . . I11 General Spectroscopic Description of the Night Airglow IV . Nightglow Instrumentation . . . . . . . . . . V. Nightglow Observatories . . . . . . VI . Nightglow Heights . . . . . . . . . . . VII . The Hydroxyl (OH) Nightglow . . . . . . . VIII Oxygen 5577 . . . . . . . . . . . . . I X . Oxygen6300 . . . . . . . . . . . . . X . Sodium 1)in the Nightglow . . . . . . . X I . Nightglow from the O2 Molecule . . . . . . . XI1. Hydrogen Emission in the Nightglow . . . . . XI11. Excitation Mechanisms . . . . . . . . . . XIV . Concluding Remarks . . . . . . . . . . References . . . . . . . . . . . . .

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13 14 22 28 29 29 29 42 42

Recent Developments in Computer Organisation F. P. BROOKS.JR. I . Introduction . . . . . . . . . . . I1. Metaprograms . . . . . . . . . . I11. Multiprogramming . . . . . . . . IV. The Content-Addressed Memory . . . . . V. The One-Level Memory . . . . . . . VI . Last-In-First-Out Register Stacks . . . . . VII . The Fixed-Plus-Variable-Structure Computer . References . . . . . . . . . . .

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45 46 49 52 55 59 62 64

Atomic Collisions Involving Low Energy Electrons and Ions MANFREDA . BIONDI List of Symbols . . . . . . . . . . . . . . . . . I . Introduction . . . . . . . . . . . . . . . . . . 11. Theoretical Developments . . . . . . . . . . . . . . I11. Low Energy Elastic and Inelastic Collisions . . . . . . . . . ix

67 68 72 75

X

CONTENTS

IV . Attachment and Detachment of Electrons . . . . . . . . . 116 V. Recombination of Positive Ions with Electrons and with Negative Ions . 137 References . . . . . . . . . . . . . . . . . . 158

Semiconductor Device Evaluation DAVIDP. KENNEDY

I . Introduction . . . . I1. The p-n Junction Diode I11. The Junction Transistor References . . . . List of Symbols . . .

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. 167 169 216 248 249

Electron Emission Microscopy

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I. I1. I11. IV . V. VI .

G MOLLENSTEDT AND Introduction . . . . . . . . . Electron Optics of a Cathode Lens . . Photo Emission Microscopy . . . . Secondary Emission Microscopy . . . Ion Induced Emission Microscopy . . Thermionic Emission Microscopy . . . References . . . . . . . . .

AUTHORINDEX .

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SUBJECT INDEX.

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F. LENZ . . . .

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254 262 283 298 . . 320 . . 326

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The Nightglow F. E. ROACH Central Radio Propagation Laboratory, National Bureau of Standards, Boulder, Colorado Page ...

................................................ 111. General Spectroscopic Description of the Night Airglow. , . IV. Nightglow Instrumentation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................... ....................................

glow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

IX. X. XI. XII. XIII.

XIV.

.................................... B. Statistical Distribution of 5577 Intensities C. Distribution of 5577 Intensity with Latitude.. . . . . . . . . . . . . . . . . . . . . . . D. Covariance of 5577 and other Radiations.. . . . . . Oxygen 6300 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Midlatitude 6300 Arcs during Times of Magnetic Activity. . . . . . . . . . . . B. 6300 Activity in the Tropics .................................. Sodium D in the Nightglow. . . . ................................. Nightglow from the 0 2 Molecule.. . . . . . Hydrogen Emission in the Nightglow. . . ........................... Excitation Mechanisms.. . . . A. Photochemical Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . B. Excitation by Electrons Accelerated by C. The 5577 Nightglow-Aurora and Trapped Electrons.. . . . . . . . . . . . . . . . Concluding Remarks.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 6 9 9 13

15 19 22 23 27 28 29 30

35 42 42

I. DEFINITIONS The word “airglow” was introduced by Elvey (1) in 1950, following a suggestion of 0. Struve, to designate optical emissions other than the polar aurora originating in the earth’s upper atmosphere. Subsequently, the word “nightglow” came to mean that part of the airglow emitted during the night. A t the time that the word “airglow” came into common usage, it was considered that the aurora was caused by particles (electrons or protons) proceeding from the sun to the earth’s dipole magnetic field, then spiraling down along the magnetic field lines to the upper atmosphere causing excitation and ionization en route with resulting optical emis1

2

F. E. ROACH

sion. The discovery of energetic particles in the exosphere trapped by the earth’s magnetic field has turned the attention of auroral theorists to problems involving the physics of trapped particles, their release from the magnetic tubes and their relationship with auroral excitation (see for example, Chamberlain, 2 ) . The center of attention has shifted somewhat from the interaction of moving charged particles with the earth’s magnetic field to the mechanism of trapping of charged particles and their release into the atmosphere. Since the original definition of the word “airglow” involves the idea of a n aurora by its exclusion, and, since auroral mechanisms are currently under debate, it is difficult to be precise in delineating just what should be included in a general discussion of the nightglow. The basic idea in the original concept was that the night airglow is due to resident properties and events in the upper atmosphere and that the aurora is due to extraneous imposed effects. I n the present discussion, we prefer not to be bound too tightly by this concept and will describe observed phenomena which seem a priori to be resident phenomena but which may later prove to be affected by extraneous events such as trapped particles. We exclude from this survey discussion of the twilight glow and the day airglow each of which is distinguished from the night airglow or nightglow by the fact that the direct sunlight is operative in the former cases and not in the latter.

11. UNITS OF BRIGHTNESS Two units of brightness or intensity will be used: (a) ergs . ~ r n - ~ (column) * sec-l and (b) rayleighs. I n a later section we shall discuss the absolute brightness of the several night airglow components. Here we shall mention a little of the history and usefulness of the rayleigh as a unit. I n 1930 ( 3 ) Lord Rayleigh2 performed a remarkable observational feat. Working out of a window in the cellar of his home in London, he observed the night sky with a photometer which had a n optical filter centered on the nightglow emission line a t a wavelength of 5577 A. He then turned the photometer around to catch the light of a standard lamp diffused by a magnesium oxide screen. His purpose was t o satisfy the urging of Sydney Chapman for a n estimate of the absolute intensity of the 5577 A night airglow line (at that time the phenomenon was not called airglow-many used the expression “permanent aurora”). Lord Rayleigh describes in his paper his calculations involving the calibration of the standard lamp, the properties of the magnesium oxide diffusing 1 Purely thermal emission from the lower atmosphere would not be included as airglow according to current usage. 1 The Lord Rayleigh referred to is R. J. Strutt, the fourth Lord Rayleigh.

3

THE NIGHTGLOW

screen, the correction for astronomical light coming through his filter in addition t o the upper atmosphere emission, and allowance for a correction of his reading from the slant angle by which he was forced to observe out of his basement window to what it would have been in the zenith. He announced that the absolute intensit>yof the 5577 A line was 1.81 X 1OI2 quanta . m e t e r 2 (vertical column) second-1

or

-

181 X lo6 quanta cm-2 (vertical column) second-).

It is of interest t o compare this classical measurement with current measurements. The median value for the zenith intensity of 5577 A based on 21,088 measurements during ICY-IGC is 254 X lo6 quanta * cm-2 (column) * sec-1 ( . b ) . For some time authors used the expression “megaquanta * cm-2 (column) . sec-I” in referring to nightglow iiitensities but this has now, by general acceptance, been called the “rayleigh.” The formal definition is as follows: “If the surface brightness, B, is measured in lo8quanta * cm-2 . sec-I . steradian-I then the intensity in rayleighs is 4aB” (see Hunten et al., 5 ) . Thus, the classical measurement by Rayleigh indicates a n intensity of the green 5577 nightglow line of 181 rayleighs and the IGY-IGC value is 254 rayleighs. A practical advantage of the unit is that the volume emission rate in the upper atmosphere can be estimated if the effective thickness of the emitting layer is known. I n many applications the thickness is approxiTABLEI.

R E L A T I O N S H I P BETWEEN THE R A Y L E I G I I AND

ERGS. CM-~(COLUMN) . SEC-1 Wavelength A 100 1,000 3,000 3,914 5,000 5,577 5,893 6,300 10,000 45,000

One rayleigh [in ergs cm-*(column) . sec - l ] 199 19.9 6.62 5.07 3.97 3.56 3.37 3.15 1.99 0.441

x x

10-6 10-6

X X

x

10-8

X

x

10-6

X

x X

10-8

F. E. ROACH

4

mately 10 km (los cm). Cancelling out the losin the definition thus leads to the useful approximation Intensity in rayleighs = the volume emission rate in quanta

*

CM-~

sec-’

A disadvantage of the unit arises in connection with discussions of energetics in that its energy content varies with wavelength. I n Table I some typical one-rayleigh energy fluxes are listed for several wavelengths. 111. GENERAL SPECTROSCOPIC DESCRIPTION OF THE NIGHT AIRGLOW As we shall see later, there are several “nightglows” occurring a t different atmospheric heights, and probably caused by different mechanisms. They have in common their origin somewhere in the earth’s upper

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

WAVELENGTH IN MICRONS FIG.1. Above: Distribution of intensities and wavelengths of the rotation-vibration bands of OH in the nightglow; observed to about 1.5 p and predicted for wavelengths longer than 1.5 p. Also, the absolute intensity of the thermal radiation from the lower atmosphere for a temperature of 275”K, a slit width of 0.1 p , and a n emissivity e of 0.3. Below: The transmission of the lower atmosphere versus wavelength.

atmosphere. As observed from the ground, they are affected by absorption and scattering from the lower atmosphere, The vertical transmission of the lower atmosphere a t sea-level is shown in Fig. 1. The thermal emission of the lower atmosphere is also shown for a band width of 0.1 micron. Figure 1 illustrates the spectral distribution of the by far most intense

5

THE NIGHTGLOW

nightglow feature (see Table II), the rotation-vibration bands of hydroxyl

(OH). . . We are restricted in our ground observations to a relatively small spectral region from about 3000 A to 25,000 A (0.3 p to 2.5 p ) with heavy absorptions near 1.4 p and 1.9 p. For wavelengths longer than 2.5 p the thermal emission from the lower atmosphere overwhelms even the very intense OH bands which extend out to 4.5 p (note the logarithmic scale for the upper part of Fig. 1). TABLE 11. NIGHTGLOW EMISSIONS Absolute zenith intensity Source

Wavelength

Rayleighs

0 . 3 8 to 4 . 5 I./ 8645 A G5G3 A 0300, 6364 A 5890, 5896 A

5,000,000 500 15 200 30 (summer) to ‘LOO (wintcr) 01 5577 A 250 4861 A 3 H I (HB) O2 (Herzberg Bands) 3000 to 4000 A 1500 N z+ 3914 (40).

OH O2 (0, 1 atm) H I (Ha) 01 NaI

Continuum (Nightglow) Continuum (Astronomical)

4000-7000 A

I500 (0.5R/.4 Mean) 4500 (1.5Rl.4 Mean)

Ergs . cm-2(column)

. sec-1

3.6 I . 1 x 10-3 4 . 5 x 10-5 6 . 2 x 10-4 1.0 X to G.8 X lo-‘ 8.9 x 1.2 x 8.8 x 2.0 x

10-4 10-5 10-8 10-6

x

10-3

5.0

1 . 5 X lo-*

a The presence of Nz+ 3914 A as a “nightglow” emission is uncertain. It is a prominent feature of the aurora.

A list of the observed spectral features from longer to shorter wavelengths is given in Table 11. It is apparent that the hydroxyl (OH) emission is energetically predominant. Historically, on the other hand, it is a latecomer. A partial chronological listing of nightglow discoveries including the identification of specific airglow emissions is given in Table 111. The reader is referred to Chapter 9 of Chamberlain’s ( 6 ) excellent book for a detailed description of the airglow spectrum shown both as a reproduction of original spectrograms and as microphotometer tracings. Such representations are invaluable to the specialist who is interested in details. 3 Recently a n Atlas of the Airglow Spectrum, XX3000-12,400 A ( 7 ) has been compiled by Krassovsky et al. It contains detailed listings of lines, microphotometer tracings and measured absolute intensities. Much of the material of Table I1 was taken from the Krassovsky Atlas.

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F. E. ROACH

TABLE111. CHRONOLOGY OF SOME NIGHTGLOW DISCOVERIES Date

Author

Discovery

A. J. Rngstrcm

The green line, 5577, present in absence of visual aurora. 5577 present a t all times and in all parts of sky. 1895 W. W. Campbell Established existence of “Permanent aurora” or 1909 L. Yntema earthlight. 1919 V. M. Slipher Numerous spectrograms showing 5577. Demonstration of formula for increase of airglow 1921 P. J. Van Rhijn toward horizon (in absence of lower atmosphere). Interferometer measurement of green line in night 1923 H. D. Babcock sky. Wavelength = 5577.350; upper limit of width = 0.035 A. 1927 J. C. McLennan and Interferometer measurement of green line. J. H. McLeod Measurement of polarization of zodiacal light. 1928, 29 J. Dufay Midnight maximum of 5577. 1928 J. C. McLennan, J. H. McLeod and H. J. C. Ireton 6300,6364 (unresolved) and Na D line first recorded 1929 V. M. Slipher in nightglow spectrum. First absolute measurement of 5577 intensity. 1930 Lord Rayleigh Confirmed spectroscopic identification of green line. 1930 R. Frerichs Assigned it to atomic oxygen. Identified ‘Dzand ‘So levels of atomic oxygen. Predicted red lines: 6300, 6364 (‘Dz ‘ P z , ~ ) . Suggested that excitation of green nightglow (5577) 1931 S. Chapman is due to association of oxygen atoms via a 3-body collision. Quantitative separation of blue nightglow, zodiacal 1937 C. T. Elvey and F. E. Roach light and integrated starlight. 1941, 47 J. Dufay Identification of Heraberg bands of 0 2 in nightglow. 1943 P. Swings 1945, 47 D. Barbier Identification of strong rotation-vibration bands of 1950 A. B. Meinel hydroxyl (OH) in near infrarcd. Discovery of subvisual arcs of 6300 A in midlati1958 D. Barbier tudes. 1959 V. S. Prokudina Discovery of H a in the nightglow.

1868

-

1

IV. NIGHTGLOW INSTRUMENTATION The choice of instrument for the study of the nightglow is influenced by the absolute intensity of the phenomenon. T o illustrate, a comparison is made between the speed of a spectrograph widely used for nightglow (and aurora) research during the International Geophysical Year (IGY) and a birefringent type photometer used a t the Fritz Peak Observatory

7

THE S I G H T G L O W

for sevcral years. For convenience, comparative calculations will be shown for the recording of a n emission feature of 100-rayleigh intensity. Such a n intensity delivers a flux to the observer a t the surface of the earth of 108 F = - quanta cmd2 sec-I . steradian-I 477

- - lo* quanta - cm-2 . sec-I . (square degree)-'. 41,253

I n order to produce a spectrum line of photographic density 0.6 a total of 1.50 X 10'" quanta . cm-2 is r e q ~ i r e d . ~ TABLE Iv. COMPARISON

OF SPEEDS OF IGk' SPECTROGRAPH BIREFRINOENT PHOTOMETER

IGY spectrograph

AND

FRITZP E A R

Birefringent photometer

Aperture of lens: 6.0 in. = 15.24 cm Area of lens: 182 cm2 Field of view: Circular 5" diamcter = 10.6 square degrees. Transmission of system = 0.1 0.1 X 19.6 X 182 X lo8 F = 4.1253 X lo4 (12.8)2 = 8.65 X 105 quanta second-1 = 7.95 X l o 6 quanta * * sec-' Quantum efficiency = 0.1 1.5 X 1 O l o Exposure time for Electron flow 0.6 density = 7.95 x 106 = 8.65 X 104 electrons.second-1 = 1.89 X 104sec Let N = total number of electrons pro= 5.2 hr duced in time, 1 ; let p = precision of measurement = fi Precision of measurement of such a spectrum line = 2.5%

Slit width: 0.03 cm = 2" of sky focal length collimater = 12.8 Ratio: focal length camera Assunicd transmission of system = 0.5 F/cm2 of emulsion . , X lo8 - 0.5 X 22 X (0.03)* (0.03)2 4.1253 X lo4 X

-

-

~

N 1

0.2 0.1 0.018

8.65 1.7 8.65 1.62

X lo4 X lo4 X los X lo8

0.3 0.8 1.1 2.5

It is obvious from an inspection of Table IV that the two instruments, the spectrograph and the photometer, are useful in separate and complementary roles. For the study of spectroscopic details the long exposures 4 For a discussion of the properties of the photographic emulsion upon which this figure is based, the readcr is referred to Hiltner (8) and t o Baum (9).

00

TABLEV. IGY AIRGLOW STATIONS Geographic Number

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

Name Thule Loparskaya Zvenigorod Bialkow Ondrejov Lomnicky-Stit Simferopol Rapid City Haute Provence Memambetsu Abastumani Fritz Peak Sendai Niigata Kakioka Gifu Maruyama Shodo-Jima AS0

Sacramento Peak Mount Abu Tamanrasset Poona Zamboanga City Lwiro Huancayo Camden Mirnyj

Country Greenland USSR

USSR Poland Czechoslovakia Czechoslovakia USSR USA France Japan USSR USA Japan Japan Japan Japan Japan Japan Japan USA India Sahara India Philippines Congo Peru Australia Antarctic

Latitude

Longitude

76"33' 68"38' 55'42' 51"29' 49"55' 49"12' 44"50' 44"02' 43"55' 43"55' 41 "45' 39"54' 38'06' 37"42' 36"14' 35"27' 35"Ol' 34"33' 32"53' 32'43' 24"36' 22"48' 18"31' 6"54' - 2"16' -12"03' -34'04' -66"33'

68'50'W 33'22'E 36"44'E 16'40'E 14'59'E 20'13'E 34'04'E 103"03'W 5'43'E 144'12% 30"50'E 105'29'W 140'33'E 138'49'E 140"ll'E 137"02'E 139'58'E 134"16'E 131"Ol'E 105"45'W 72'43'E 5"31'E 73"52'E 122'04% 28"49'E 75"20'W 150'38'E 93" E

Sheet Parameter L (250 km)

88 5.36 2.60 2.27 2.13 2.05 1.73 2.91 1.75 1.58 1.58 2.35 1.37 1.36 1.32 1.29 1.28 1.27 1.22 1.80 1.07 1.09 I .oo 0.97 1.07 1.08 1.91 20.18

Magnetic Latitudes -

Dip

soy9 66?3 54?0 49 ?2 47 :3 46'13 42?5 57?0 41 '10 37% 38'17 51'11 32 ?2 31 P7 30 ?O 29 y9 29 ?O 29?3 28?0 41 ?7 20 ?6 14'19 12?7 - 0?65 -16Yl - 1:3 -45P7 -64:s

Geomagnetic 88 ?l 63?7 51?1 50 ?9 49% 48: 1 41 '12 53Pl 4523

34?0

36?7 48?7 27?9 27P4 26:O 25PO 24% 23?9 22 ?O 41 ?6 15?5 25 ?4 9 P3 - 4:4 - 3?8 - OP6 -4236 -77:O

r m

*

THE NIGHTGLOW

9

required for the spectrograph in order to bring out faint details are not serious. However, for a rapid survey of variations of intensity over the sky the photometer5 is the better instrument. Recording spectrometers in which a photoelectric pickup is used behind a second analyzing slit have been useful in auroral and twilight research but are, in general, too slow for the lower intensities encountered in the nightglow. Some significant and useful work has been done with interferometers (see, for example, the classical measurement of 5577 A wavelength and width by Babcock, 12). V. NIGHTGLOW OBSERVATORIES During the IGY-IGC some twenty-eight observatories were active in the observation of the nightglow. They extended from Thule in the north to Antarctica (see Table V). The heaviest coilcentration of effort was on the green line (5577 A) for which more than 20,000 individual zenith observations were reported. A discussion of some of these results will be given in a later section. VI. NIQHTGLOW HEIGHTS Triangulation on nightglow patches by a method comparable to that used to determine heights of auroral features is not possible because of the generally amorphous character of the phenomenon. An exception occurs for some of the 6300 A features such as midlatitude or tropical arcs. The deduction of heights from measured emission temperatures on the basis of the upper atmosphere’s temperature-height profile has been used with some success. The direct measurement of airglow heights has been accomplished by filtered photometers on rockets. A summary of some measurements is shown in Table VI according to work done chiefly by NR L experimenters (13).

For many years efforts were made to estimate heights of airglow features from the general increase of intensities toward the horizon, the so-called Van Rhijn method. In principle, the method is sound, in practice the deduced height is strongly affected by many uncertainties so th a t the method may now be considered as of only historical interest. The reader interested in a critical discussion of this method is referred to Roach et al. (10). The formula introduced by Van Rhijn (14) although of limited practical usefulness in determining nightglow heights, is helpful in underA general description of the birefringent photometer is given by Roach et aZ. (10). The essential unit, the birefringent filter, is described by Dunn and Manring ( 1 1 ) .

10

F. E. ROACH

standing a prime observational fact, namely, the general increase of nightglow intensities from the zenith to the horizon. If h is the mean height of a nightglow layer above the earth's surface, R is the radius of the earth, z is the zenith distance,6 I0 is the intensity of the layer overhead, and I , is the intensity a t zenith distance x, we then have

V , " 1, I0

1

,/I

- (+)'sin2

x

The function V is listed in Table VII. Figure 2 illustrates how the function varies with zenith distance. TABLEVI. PROBABLE HEIGHTSOF NIGHTGLOW EMISSIONMAXIMA From model atmosphere ~~~

~

Number density Height" Temperature Eniission (km) (OK)

N?.

0 2

0

Total

1 . 0 0 (14) 4 . 4 7 (12) 2.34 (13) 6 . 9 5 (13) 2.04 (12) 3 . 5 5 ( 8)

3 . 9 8 (13) 1 . 4 1 (12) 9.55 (12) 4 . 4 7 (13) 4.57 (11) 5.75 ( 7)

3.80 (11) 1 . 5 1 (12) 9 . 5 5 (11) 4 . 2 7 (11) 1.12 (12) 2.63 ( 9 )

1.40 (14) 7.39 (12) 2.45 (13) 11.46 (13) 3 . 6 2 (12) 3 01 ( 9)

~~~~~

01% 5577

85 98 0 2 94 5893 a7 Continuum 103 6300 (250)

150 185 168 150 230 1210

From Packer (IS) excepting for 6300 which is estimated from correlation with F-layer parameters.

It must here be noted that the increase indicated in the left side of Fig. 2 refers to the case of no interference by an intervening lower atmosphere. Such a condition may be realized from a satellite or even from a balloon. The intervention of the lower atmosphere has two effects: (a) the line of sight pencil of light is absorbed causing a progressive weakening toward the horizon as greater air masses are traversed; (b) there is a general scattering (primarily molecular scattering) which increases toward the horizon. These two factors together with the increasing function, V , result in a distribution toward the horizon as shown in Fig. 2 (right side). The interpretation of such curves in terms of height t o the emitt)ing layer is strongly dependent on the assumed extinction (and scattering) The angle from the zenith toward the horizon along a vertical circle is called zenith distance by astronomers. It is the complement of the altitude.

THE NIGHTGLOW 1

TABLE VII. THEFUNCTION V = Ji

\h z \

0 20 40 50 60 70 75 83 85 90

11

-

(h)zsinzz

50

100

150

200

250

1.000 1.063 1.2'38 1.539 1.955 2.766 3.503 4.701 6.594 8,027

1.000 1.062 1.293 1.523 1.914 2.635 3.234 4.085 5.128 5.709

1.000 1.061 1.285 1.508 1.876 2.523 3 023 3.669 4.355

1.000 1.060 1.27'3 1.493 1.841 2.426 2.853 3,365 3.861 4.084

1.000 1.059 1.273 1.480 1.80'3 2.341 2.710 3.130 3.511 3.672

4.088

coefficients of the lower atmosphere. The spotty nature of the nightglow dictates the use of a large quantity of data from all parts of the sky and over a long period of time. Thus, effective coefficients with similar space and time coverage are needed. In practice the finesse with which these can be attained is a severe limitation on the precision with which the height can be estimated.

( 1 1 1 1 1 1 1 1 1 1

'0

20

40

60 80 0 20 40 ZENITH DISTANCE

60

80

100

FIG.2. Variation of nightglow intensities with zenith distance. Left: predicted from Eq. (1) for no lower atmosphere and three assumed heights. Right: Comparison of predicted (no lower atmosphere) and observed for 5577 from Fritz Peak. Difference betwecn curves illustrates the effect of the lower atmosphcre.

F. E. ROACH

12

TABLE VIII. CALCULATED VIBRATIONAL LEVELSOF OH Energy 0

0 1

2 3 4 5 6 7 8 9 10 ~

TABLEIx. LrST Wavelength X air (A) 3,816.6 4,172.9 4,418.8 4,640.6 4,903.5 5,201.4 5,273.3 5,562.2 5,886.3 6,168.6 6,256.0 6,496.5 6,861.7 7,274.5 7,521.5 7,748.3 7,911.0 8,341.7 8,824.1 9 ,373.0 9,788.0 10,010 10,273

~~~

OF

cm-1

ev

0 3,570 6,974 10,214 13,291 16,207 18,958 21,543 23,957 26,194 28,145

0.00 0.44 0.86 1.27 1.65 2.01 2.35 2.67 2.97 3.25 3.49

~

~

OH BANDSI N

Absolute intensity Transiin rayleighs tion (Chamberlain and (0’ - d’) Smith, 15) 0-0 8-0 9-1 7-0 8-1 9-2 6-0 7-1 8-2 5-0 9-3 6-1 7-2 8-3 4-0 9-4 5-1 6-2 7-3 8-4 3-0 9-5 4- 1

~~

0.023 0.12 0.73 0.71 3.8 11.o 4.4 22 57 33 110 130 310 520 280 710 930 1800 2800 3400 3100 3600 7600

~

ORDER OF WAVELENGTH

Wavelength X air (A) 10,828 11,433 12,115 12,898 13,817 14 ,336 15,047 15,824 16,682 17,642 18,734 19,997 21,496 28 ,007 29 ,369 30,854 32,483 34,294 36,334 38 ,674 41,409 44,702

Absolute intensity Transiin rayleighs tion (Chamberlain and (v’ - 0”) Smith, 16) 5-2 6-3 7-4 8-5 9-6 2-0 3-1 4-2 5-3 6-4 7-5 8-6 9-7 1-0

2-1 3-2 4-3 5-4 6-5 7-6 8-7 9-8

12,000 15,000 17,000 16 ,000 13,000 46 ,000 74,000 88,000 90,000 82,000 71,000 54 ,000 37 ,000 920,000 820 ,000 640 ,000 490,000 360 ,000 260 ,000 180,000 110,000 65,000

13

THE NIGHTGLOW

VII. THE HYDROXYL (OH) NIGHTGLOW The hydroxyl nightglow is quantally more than 1000 times as intense as all other known nightglow emissions. Energetically it corresponds to an aurora between IBC' I1 and IBC 111. If the hydroxyl emission were concentrated in the visual region of the spectrum, the night sky would glow like midtwilight, the Milky Way would be invisible and only the brightest stars would stand out against the competing background. TABLEx. THE S T R U C T U R E O F T H E 6-2 BANDO F OH (FROM (ASSUMEDTEMPERATURE: 225°K) R1

branch

Wavelength Intensity

R2 branch

K"

(A)

(R)

Wavelength (A)

1 2 3 4 5 6 7

8299.0 8288.7 8281.7 8278.3b 8278.5 8282.5 8290.4

87 101 77 44 21 8 2

8311.4 8296.8 8287.0 8281.5 8280.3 8283.5 8290.7

z

340

P I

Intensity (R)

Wavelength (A)

32 42 36 23 12 4 1

8399.3 8430.2 8465.4 8504.8 8548.6 8596.8

150

-

branch

CHAMBERLAIN,

6)a

PObranch

Intensity (R)

Wavelength (A)

Intensity (R)

155 179 136 78 36 14

8382.9 8415.7 8452.6 8493.6 8538.8 8588.1

57 75 64 41 20 8

598

265

a Q branch a t 8341.7; intensity 439 rayleighs; intensity of entire band = 1800 rayleighs. b Band head.

The hydroxyl nightglow bands are due t o rotation-vibration transitions in the lowest electronic state of OH, the 2?r state. The pertinent vibrational levels are listed in Table VIII. Transitions have been observed up to and including the ninth vibrational level. A complete list of all the bands either observed or predicted is given in Table IX together with the predicted absolute intensities from Chamberlain and Smith (15). The rotational structure of the individual bands may be illustrated by a specific example, the 6-2 transition (see Table X and Fig. 3). Three branches (P, R, and Q) can be identified. The P-branch has been nicely resolved and includes about six double lines extending toward longer wavelengths. The Q- and R-branches cannot be resolved with the resolution used in nightglow studies. 7 IBC refers to International Brightness Coefficient. The faintest visible aurora is IBC I and the steps go by powers of 10 t o IBC IV, the brightest.

14

F. E. ROACH

The intensities increase rapidly toward the infrared. I n the visible part of the spectrum the OH bands are relatively weak. However, it should be noted that the 9-3 band a t 6256 A (intensity 110 rayleighs) is a source of contamination in the case of observations of the 6300 A atomic oxygen line when coarse filters are used for isolating the line. Also the 8-2 band a t 5886 A (intensity 57 rayleighs) can cause trouble in the observation of the sodium-D lines a t 5890 and 5896 A especially in the summer

FIG.3. A portion of t h e nightglow OH spectrum showing in particular the 6-2 band. Compare with t h e detailed structure of the 6-2 band in Table X. The predicted position of the 10-5 band would place it in t h e same general region but sufficiently displaced to distinguish it from the 6-2 band. The absence of the 10-5 band and any other bands involving the 10th or higher vibrational levels is a n important observational fact. The original spectrogram is due to Meinel ( 1 6 ) .

when the D lines are extremely weak. The 7-1 band a t 5562 A is quite weak (22 rayleighs) and only a minor source of contamination in the observation of 5577 A (atomic oxygen).

VIII. OXYGEN5577 The three lowest spectroscopic levels of atomic oxygen are shown in Fig. 4. One of the prime observational facts that applies quite generally to the nightglow and also to some extent to the aurora is that the two radiations, 5577 (green) and 63008 (red) are independent of each other. This independence is apparent even to a casual observer after only a single night of observations. Characteristically, in midlatitudes, 6300 decreases rapidly in intensity in the early evening, reaehes a low value

* In general, we refer t o t h e 6300 emission and intend it to be understood t h a t 6364 is included. The latter is about 55 the intensity of the former.

15

THE NIGHTGLOW

then may rise slightly with the dawn. On the other hand 5577 only occasionally shows a twilight and/or dawn effect but frequently has broad periods of elevated brightness. The general behavior is illustrated in Fig. 5. The 5577 A nightglow has received a great deal of attention by observers, partly due to its early discovery and partly to the fact that its ev

J

0.74 SEC

-0

TERM

‘s

‘D

3P

FIG.4. The low lying energy levels of atomic oxygen.

wavelength is one that facilitates observations whether by photographic, photoelectric or visual methods. Out of the large body of published material on the emission, mention will be made of (a) evidence for cellular patterns in the 5577 nightglow, (b) statistical distribution of intensities, (c) geographical distribution of intensities and (d) covariance of 5577 with the Herzberg bands and the nightglow continuum.

A . Cellular Patterns The diurnal (or nocturnal) variations of the intensity of 5577 at a given observing station have been the subject of many investigations. A generalization is often found in the literature to the effect that, characteristically, there is a local midnight maximum of intensity. Although this seems to be statistically true, a maximum may actually occur at any time during the night. If the entire sky is under observation, there may be some

16

F. E. ROACH

800

I

I

20

21

I

I

I

I

22 23 0 I 105OW STANDARD TIME

2

3

4

I

I

I

700 600 rn I (3

5 G

500

(L

f

400

> k w

300

k

z 200

100

0 19

Fro. 5. Zenith intensity variations of the oxygen en?.hions, 5577 and 6300, at Fritz Peak during the night of September 6/7, 1961.

degree of simultaneity of intensity change over the sky. But there is also an element of independence especially for regions of the sky far from each other. The practical limit for observing is to a zenith distance of 80" (altitude lo"). For an emission height of 100 km this corresponds to a distance along the earth's surface of 466 km. In Table XI the distances correspondTABLEXI. DISTANCE ALONG EARTH'S SURFACE CORRESPONDINO TO ZENITH DISTANCE, z(h = 100 KM) z

Distance (km)

0 40 60 70 75

0

258 338

80

466

83 167

THE NIGHTGLOW

17

ing to other zenith distances are shown. The examples chosen in Table XI correspond to the zenith distances customarily used in the Fritz Peak observing. I n a systematic survey of the sky, it is thus possible to map the intensities over a region corresponding to a circle of radius 466 km (assuming a height of 100 km). The observations a t Fritz Peak, for example, result in an isophotal map over a region indicated in Fig. 6.

FIG.6. Extent of observational coverage for three assumed heights of the nightglow.

The discerning reader will here realize that there is a difficulty in making such isophote “maps.” The difficulty arises from the fact that there is a general increase of intensity toward the horizon [Eq. (l)] associated not with intrinsic changes of upper atmosphere emission but with the accident of observing from the earth’s surface. Numerical methods for eliminating this effect are discussed by Roach and Pettit (I&), and here it will suffice to say that reasonable approximations to local zenith intensities seem to be possible. An example of a series of isophote maps prepared in the manner indicated is shown in Fig. 7. It appears that there are distinct changes of structure through the night. Such maps have been made corresponding to close spacings of time (5 min). When they are projected by cinema techniques there is a strong impression of a large scale dynamical phe-

18

F. E. ROACH

nomenon rather suggestive of movements of the “weather” on successive weather maps. Thus, the idea of dynamical nightglow cells has developed. The estimation of the size of the nightglow cells is made difficult by the fact that they are frequently larger than the field of view from a single station. Using indirect methods, Roach et al. (17, 18) came to the conclusion that a typical cell has a size of about 2500 km ( ~ 2 . times 7 the observer’s field of view) and a speed of about 90 meters/second (200 miles/hr) . Smaller scale cellular structure can occasionally be detected on the records. It will not be surprising if it develops that there is a spectrum of

FIG.7. An example of hourly changes of 5577 intensity patterns a t Fritz Peak for the night of October 1/2, 1956. Darker shadings correspond to more intense regions of the sky.

cells from small scale turbulent irregularities to the gross phenomena mentioned here.

B. Statistical Distribution of 5577 Intensities We have indicated that the median intensity of 5577 for the IGY-IGC ensemble of data is 254 rayleighs. I n Table XI1 we show a statistical summary of the entire body of information. One of the general characteristics of all published statistical surveys of this radiation is that, when the intensities are plotted in histogram form they always show a positive skewness. This is not particularly surprising since on the low side there is a definite bound, namely zero intensity, whereas on the high side there is not necessarily a bound since a priori any intensity is possible.

19

THE NIGHTGLOW

TABLEXII. STATISTICAL DISTRIBUTION OF 55778 INTENSITIES Intensity in rayleighs Number of Lower observations decile

Station Airglow (25 stations) Mirnyj Thule (6) College (5) a

21,088 96 9,732 3,968

Lower quartile

Median

Upper quartile

Upper decile

176 300 490 1290

254 560 630 2400

360 820 812 6020

490 1,050 1 ,120 11,500

128 195 380 740

Taken from Yao, Table 8 (4).

w 2o 0

z

W

oz oz I>

0 0

0 10 I-

Z

W 0

200

400

600 800 1000

Q IN RAYLEIGHS

0

2

4

3sa

6

8

10

FIG.8. Statistical distribution of 5577 zenith intensities based on 21,088 observations during the IGY-IGC. Left: plotted with respect to t h e intensity. Right: plotted with respect to the cube root of the intensity.

The skewness in the distribution may be empirically removed by using a root of the intensity or its logarithm. The fact that the use of the cube root (Fig. 8) leads to an essentially “normal” distribution has led to the suggestion (Barbier, 19) that this is in support of the Chapman triple collision reaction as the source of excitation (see Section XIII, A ) . As examples of intensity distributions a t various locations, Fig. 9 shows some for Fritz Peak, Rapid City, College, and Thule-four stations ranging in latitude from outside, to and inside the auroral zone.

C . Distribution of 5577 Intensity with Latitude I n Table XI11 is assembled a large quantity of data on the absolute zenith intensity of 5577 for stations grouped according to latitude. Most

F. E. ROACH

20

8 lo z w

K K

3 0

0

0

0.5

%j w K

2 LOG

3

4

Q IN RAYLEIGHS

FIG.9. Distribution of 5577 intensities a t four stations: Rapid City, Fritz Peak, Thule, College.

TABLE XIII. COMPILATION OF OBSERVATIONAL MATERIAL FOR 5577

Number Q (5577) of obser- Rayleighs Station vations (median) I

I1

4932 5278 7252 3500

111 IV Yerkes Ithaca 0 Saskatoon Meanook College 3968 Mirnyj 96 Hallett 1374 0

0 0

Thule

9732

Lb for 100 km

Corresponding

x

Reference

220 235 280 315 250 600 1500 2000 2400 560 630

1.052 1.289 1.728 2.431 3.008 3.157 4.292 4.617 5.449 19.74 23.13

10"O 27"2 29"5 49"3 54"7 55"5 60Y90 62"3 64y42 76"s 77"O

630

87.81

83"3

Yao (4) Yao (4) Yao (4) Yao (4) Sandford (21) Sandford (21) Sandford (21) Sandford (21) Roach and Hees (22) Yao (4) M. A. Gordon (unpublished material) Roach et al. (23)

From spectrographic studies by Sandford (21). The absolute calibration for these four entries was obtained by forcing agreement between the spectrographic intensities a t Yerkes and the IGY photometric results for Rapid City. b L is the sheet parameter (in earth radii) of McIlwain (20); is the corresponding latitude (see text). 0

21

THE NIGHTGLOW

4

Ib

;0

$0 40

$0

sb

;0

eb gb

INVARIANT MAGNETIC LATITUDE

FIG.10. Distribution of 5577 intensities according to geomagnetic latitude (from Table XIII).

of the information comes from the IGY-IGC program with other sources as noted. A plot of the ensemble of data is shown in Fig. 10. Discussion of the interpretation of the observations is deferred until later.

D. Covariance of 6677 and other Radiations Barbier has been the leader in inve'stigations of simultaneous observations of several emissions. With his photometer a t the Haute Provence Observatory (France), he systematically observes in eight colors : 6700 (OH), 6300 (narrow, chiefly the 01 line), 6300 (broad including the 9-3 band of OH), 5893 (Sodium D),5580 [OIJ, 5260 (continuum), 4400, and 3670 (chiefly O2 Herzberg bands). On the basis of similar temporal changes in intensity, Barbier has grouped the emissions as follows: 5577

\

5260 4400 3670

[The 5580 group

!:::

1 )The 5900 group

6300 broad The quality of the correlations may be judged from Fig. 11 taken from Barbier (24). Of particular interest is the fact that the atomic oxygen emission, 5577, and the molecular oxygen emission (the Herzberg bands through the 3670 filter) are so closely correlated. This covariance supports

F. E. ROACH

22

/

900

700

36701

600

300

526-

f

20 0

100

I

0

1

500

I

1000 I(5580)

1 1500

FIG.11. Correlations between (a) 3670 (Herzberg bands) and 5580 (actually 5577 of atomic oxygen) and (b) 5260 (significant nightglow continuum plus astronomical components) and 5577. According t o Barbier (24) from observations a t Haute Provence.

the hypothesis that the atomic 557'7 and the molecular (Herzberg band) oxygen emissions result from a common excitation mechanism. IX. OXYGEN6300

It is extremely difficult to present a unified description of 6300 nightglow because of its many different manifestations. It has already been mentioned that there is no apparent covariance with 5577. From this fact we deduce: (a) after the emission of each photon of 5577 the oxygen atom must either emit a photon of 6300 or leave the lD state by collisional deexcitati~n~; (b) the lack of covariance between 6300 and 5577 shows that the second alternative is followed; (c) therefore, the 6300 emission that we do observe must be due to some mechanism not associated with 5577 and must be emitted at a n atmospheric height where collisional deexcitation is less than it is in the 100-km region where 5577 occurs. The emission of 6300 a t higher altitudes (say 250 km) and the nonemission of 5577 at these altitudes can occur only if the source of excitation is restricted to less than 4.2 ev-at least it must very strongly favor the 2.0 ev of the 'D state over the 4.2 ev of the 1X state. Barbier (25) has given a general summary of several morphological 6300 A features which he has observed and isolated a t the Haute Provence 9 It should be noted that the mean lifetime of the ID state is 110 see compared with less than 1 second for the IS state (see Fig. 4).

T H E NIGHTGLOW

23

Observatory (HP) in France and a t the tropical station a t Tamanrasset (T) in Sahara. These include the the the the the the

polar aurora (HP) twilight phenomenon (HP, T ) western sheet (HP) subpolar sheet (HP, T) tropical arc (T) “para” twilight phenomenon (T)

These phenomena are frequently superimposed photometrically aiid are distinguishable only by their concentration in particular directions or a t particular times. The 6300 A line has a very strong twilight and dawn enhancement caused by the direct action of sunlight on oxygen atoms in the upper atmosphere. The effect is especially prominent near the horizon in the azimuth of the sun but is also observable up to the zenith. There is no discontinuous change right at the moment of twilight although the intensity is rapidly decreasing. The twilight and night phenomena merge photometrically into each other. A logical discussion of the 6300 nightglow melange might hopefully be based on the excitation mechanisms, but such a criterion is iiot available to distinguish the several phenomena listed by Barbier. As a matter of fact, a definitely auroral phenomenon-midlatitude arcs which occur during times of magnetic activity-have been considered to be auroral in the morphological sense and possibly nightglow (photochemical origin) in the microscopic.

A. Midlatitude 6300 Arcs during .Times of Magnetic Activity During the IGY, a n interesting 6300 effect was discovered by Barbier (26). Almucantar sweeps revealed evidence for the existence of well-

defincd arcs going across the sky in a general east-west direction. They occur during times of significant magnetic activity. The properties of the arcs are here enumerated: (1) They are oriented along invariant latitudes,’O (Fig. 12). On one occasion, a t least, a n arc coincided in space and time with a region of high energy particles observed from a satellite (27) (Fig. 12). lo The invariant latitude, A, is deduced from the so-called sheet parameter, L, introduced by McIlwain (90) according to cos2 X = r / L where r is the geocentric distance to the emitting layer in earth radii. L is approximately the geocentric distance to the equatorial crossing of the pertinent magnetic line of force also in earth radii.

F. E. R O A C H

24

(2) They occur a t heights of about 400 km (Roach et al., 28; Moore and Odencrantz, 29; Rees, SO). (3) A typical cross sectional representation is shown in Fig. 13 (31). The great extent both horizontally and vertically is apparent.

6300A ARC

‘i

F. F?

FIG.12. A 6300 arc observed over western United States parallel to the locus of sheet parameter, L, = 2.5. Extension of arc coincides with region of maximum counts of high energy particles observed from Explorer VII.

0 2

0

2

I

’ NORTH

SOUTH

DISTANCE IN km

FIG.13. IsophotaI section of a typical 6300 A arc ($1).

(4) They have been frequently observed over ranges of some 3000 km in longitude. On occasion, they have been observed almost simultaneously in France and the United States suggesting that they may extend a t least one-third of the way around the world (32, 33) (Fig. 14).

FIG.14.6300 A arc of September 29/30, 1957, observed near the same sheet parameter, L (2.38), in Europe and t,he United States. Insert shows that the typical arc has a width approximately the size of the State of Colorado.

26

F. E. ROACH

12

I

I

I

I

I

I

I

I

I

I

-

$

+ 0

6

4

2

200

I50 v)

I (3

w

d

100

K

a” 50

0 350

I

I

I

I

I

1

I

1

I

I

20

21

22

23

00

01

02

03

04

05

300 E

Y

LL

r

250

200

-

I

19

06

HST, HOURS FIQ.15. Variation of 6300 A nightglow intensity over Maui (Hawaii) during the night of June 5/6, 1961 (center). Simultaneous variations of the ionospheric parameters foFe (upper) and h’F (lower).

27

THE NIGHTGLOW

( 5 ) There is evidence that there are conjugate arcs in both the northern and southern hemispheres (33). (6) They are significantly correlated with magnetic activity (Barbier, 34). (7) They have been observed predominantly in midlatitudes. (8) Two independent investigations indicate that radio frequency beams which traverse red arcs show strong scintillation effects (35, 36). (9) There is evidence that oblique radio echoes are reflected from the arcs (37).

B. 6300 Activity in the Tropics The temporal history of 6300 intensity in the tropics frequently exhibits a dramatic increase typically over a two-hour period (Fig. 15). 300

250

200 v)

I

i2

> a u

6

150

100

..

.

50

. ..t---INTERCEPT = 18 '

0

10

20

30

(foF2f exp

40

[-1-

50

60

FIG. 16. Observed intensity of 6300 A a t Maui (Hawaii) versus the function (foF2)*exp - [(h'F - 200)/41.3].

Associated with the increase is a concurrent change in the F-region of the ionosphere-the F-region increases its electronic density and/or moves to a lower part of the atmosphere. A semiempirical formula has been introduced by Barbier (38), and by A. and D. Delsemme (39) to describe the relationship between the absolute zenith intensity of 6300 and the

28

F. E. ROACH

parameters of fopzand h’F”

The quality of the correlation between Q and Eq. (2) is shown in Fig. 16. A possible significance will be discussed later a s we consider excitation mechanisms.

X. SODIUM D IN THE NIGHTGLOW The sodium D lines seem to be omnipresent in nature. The spectrochemist may inadvertently find them on his spectrograms due to contamination from a n operator’s hands. They occur in the spectrum of

JAN FEEI h

MONTHS

FIG.17. Mean seasonal variation of sodium D nightglow a t Cactus Peak (California) during period 1948-1951.

meteors as they become incandescent on entry into the upper atmosphere. They are prominent features of the spectrum of the sun,12 a s well as of many other stars. Interstellar lines of sodium were discovered years ago by astronomers. The sodium D lines flash up briefly during twilight and dawn. And finally they are present in the nightglow spectrum. The outstanding characteristic of the sodium D lines in the nightglow is their annual variation. As shown in Fig. 17 they display a maximum during winter and a minimum (close to zero, actually) during summer. At one time, it was conjectured that the maximum might be due to the passage of the earth through a meteoric cloud of material but the fact that the seasonal variations in the two hemispheres are six months out of I1 In ionosphere parlance f0F2 is the maximum frequency reflected by the F-layer and h’F is the lowest apparent atmospheric height from which the F-layer reflects. I2 The designation “D” lines was attached to them in the catalogue of prominent spectral features in the sun’s spectrum made by Frauenhofer in the 19th century.

29

THE NIGEIT(:LOW

phase does not support the idea. Another conjecture is that the source of the high atmosphere sodium is elevated sea-water salt. The covariance of the nightglow sodium D emission and OH emissions has been pointed out by Barbier (24). These two nightglow components seem to occur in approximately the same regions of the atmosphere.

XI. NIGHTGLOW FROM

THE

O2 MOLECULE

The following band systems of 0, have been observed in the nightglow : (a) The Herzberg bands ( A 3 2 , ++ X3&-). Most of the observed bands are in the 3600 A region. (b) The Atmospheric Sygtem (D'2,f + X3Z0-). The 0-1 band is a t 8645 A. The 0-0 band a t 7619 A is reabsorbed by the lower atmosphere. (c) Infrared Atmospheric System (ulAg+ X3Zu-). The 0-1 band is a t 1.58 p. The 0-0 band a t 1.27 p is reabsorbed; it should be observable from rockets. The total emission from these band systems is of interest. In Table I1 an estimate of 1500 rayleighs was made for the Herzberg bands. The 0-0 bands of the two atmospheric systems will have to be observed above the lower atmosphere (e.g., from rockets) in order to get reasonable measurements. Chamberlain (6) has estimated that the atmospheric system has a n intensity between 8000 and 30,000 rayleighs and the infrared atmospheric system not more than 50,000 rayleighs.

XII. HYDROGEN EMISSION IN

THE

NIGHTGLOW

Three separate hydrogen emissions are distinguishable in the light of the night sky : auroral, nightglow, and astronomical. The hydrogen lines Ha and HB, when of auroral origin, are broad and asynimetrical which has been interpreted as evidence for a significant radial velocity of incoming protons, which velocity is reflected in the movements of the hydrogen atoms after the protons have been neutralized by the acquisition of electrons. The nightglow and astronomical hydrogen lines are very narrow and quite faint. They can be disentangled from each other by the increase of astronomical hydrogen in the vicinity of the Milky Way.

XIII. EXCITATION MECHANISMS In Section 111we mentioned the absolute intensitics of some nightglow features. It is of interest to compare these with other energy fluxes in and through the atmosphere (Table XIV) as an orientation to a discussion of excitation mechanisms that may be responsible for the nightglow

30

F. E. ROACH

emissions. The very intense hydroxyl emission corresponds to a rate of temperature change of only 1.7 X 10-4"K second-' or 1°K in 6 X lo3 seconds (less than 2 hr). Such a change is possibly significant in the overall energy balance. The normal intensity of the 5577 radiation, on the other hand, is so low that its participation in the energy balance is trivial. It is necessary to keep in mind that there may be different types of excitation for the several nightglow species. The very fact that they occur a t different atmospheric heights strongly suggests such a conclusion. It is even possible that a given emission may have a multiple origin. In TABLEXIV. SOME ENERGY FLUXES Energy density, E , (erg . cm-8 . sec-l) Flux, F (for lo8 em thickness (erg . cm-a (col) sec-1) of layer)

-

Source Solar constant Nightglow OH (total) IBC I11 aurora (known optical radiations) Nightglow 5577 (250 rayleighs) 3 x 1Olo electrons . . sec-1 (7.5 kev each)

-

1 . 4 X lo6 3.2 18

3.2 X 1.8 x 10-6

0.0009 360

9 x 10-10 3.6 x 10-4

particular, 6300 A with its slow decrease in intensity during the post twilight period followed by other phenomena during the night suggests the possibility of multiple excitation mechanisms. Approaches to the general problem of nightglow excitation have included : (a) photochemical reactions, (b) electrical currents, and (c) release of magnetically trapped particles.13 These will be discussed in order.

A . Photochemical Reactions A listing of several photochemical reactions which are currently under discussion as possible contributors to the observed nightglow is given in Table XV. Historically, the first proposal of a photochemical origin for the excitation of nightglow is due to S. Chapman who in 1931 (40) suggested that the atomic oxygen in the upper atmosphere combining to form molecular oxygen constitutes a significant energy reservoir. The energy gained by the combining of two oxygen atoms into a molecule is 5.08 ev which is sufficient t o excite most of the observed nightglow features. 13 According t o present usage, excitation by release of trapped particles would be considered as a n auroral rather than a n airglow mechanism.

31

THE NIGHTGLOW

Chapman's suggestion that the energy of association of oxygen is responsible for the green line (5577 A) via a three-body collision has grown in general acceptance over three decades.

0

+ 0 + 0-t 02 + 0 ('Dl 0 (ID)+ 0 +-hv (5577 A) (IS)

Indirect evidence supporting the reaction is that it predicts covariance of 5577 and the Herzberg bands of molecular oxygen, in agreement with TABLEXV. SOMEPROPOSED PHOTOCHEMICAL REACTIONS Excitation energy (ev.) Reaction

Available

Required

+ +0

3.32 3.33

>3.25 but 0). Further, they justify the use of Born approximation a t low electron energies on the basis that the principal contribution to the excitation takes place a t large electron-molecule distances, where the wave function of the incident electron is only slightly distorted from a plane wave. Their calculations indicate that, while the electron energy loss in this case is smaller than for molecules with permanent dipole moments, it is still substantially in excess of the elastic losses, especially for Nz. These theoretical results are compared with experiment in Section 111, B. The general formalism for the calculation of the probability of radiative capture of a n electron by a positive ion (recombination) or by a neutral atom (attachment) predates the development of quantum theory, and both classical and quantum calculations have been shown to lead t o the same results (see for example Eddington, I r a ; Morse, 1%; Massey and Burhop, 1 ) . However, application to atoms or ions more complicated than hydrogen has suffered from the lack of knowledge of the appropriate wave functions. Recently, considerable effort has been devoted to the calculation of radiative capture of electrons by hydrogen atoms (or its inverse, photodetachment from H-), Here the original calculations of Bates and Massey (18), involving a plane wave representation of the free electron and an unperturbed hydrogen atom in its ground state, have been successively improved. The first improvement was made by Chandrasekhar arid colleagues (19), who modified the free electron wave function by the static Hartree field of the hydrogen atom. The bound state H- function in these calculations was determined through variational calculations involving energy minimization. More recently, John (20) has included electron exchange between the incoming and the atomic electron, with a n attendant improvement in the agreement with experiment (see the detailed description by Branscomb, 3'1; and see Section IV, A ) . An alternative free electron function has been variationally calculated by Geltman and Krauss (22)) using a linear combination of 1, 2, and 3 s hydrogenic wave functions a t short range, and results very similar to those obtained by Johns have been obtained. Internal consistency tests of these various theoretical calculations, involving use of the matrix element for the dipole moment in length, velocity, and acceleration forms (.%'I), indicate that there are still significant errors in the free and/or bound state wave functions in use, although the most recent calculations (22) indicate considerable improvement over the original work (18). Comparison of the various theories with experiment is made in Section IV, A .

LOW ENERGY ATOMIC COLLISIONS

75

Recently, calculations of three body recombination between a n electron and a positive ion in the presence of a second electron (the inverse of electron impact ionization of an excited atom) have been carried out for hydrogen (23-26) and for helium (27'). These calculations are of interest at rather substantial electron and ion densities (>, 1012 0111-9, where the three body recombination process begins to outweigh two body processes such as dissociative recombination (28). An electron in the vicinity of a positive ion makes a transition from the continuum into a bound state of the resulting atom following a collision with a second electron. Whether the electron is permanently captured or later reemitted depends on the rates of excitation and deexcitation of the particular level formed in this initial phase of the process. In addition to the spontaneous radiative decay from this level (if it is not metastable) there are excitations, ionizations, and deexcitations as a result of inelastic and superelastic impacts of other plasma electrons with the excited atom. On the basis of a number of simplifying assumptions (such as a Maxwellian energy distribution for the plasma electrons) and assumed values for the cross sections for excitation and deexcitation, calculations are made of the rates of loss of electrons i n hydrogen and helium plasmas. The results are compared with available measurements in Section V, C , 2.

111. L O W ENERGY ELABTIC A N D I N E L A S T I C COLLISIONS I n this section we consider the experimental determinations of collisions of slow electrons and ions with neutral atoms or molecules and with each other and compare the measurements with available theory. The classes of collisions covered here include elastic (no change of the internal state of the atom or molecule) and low energy inelastic collisions leading to rotational or vibrational excitation of the struck molecule.

A. Elastic Collision of Electrons with Atoms and Molecules i. Electron-Hydrogen A t o m Scattering. Although a number of theoret,ical calculations of the elastic scattering of low energy electrons by hydrogen atoms had been in existence for more than twenty years (,5'9), the formidable difficulties in producing a known density of hydrogen atoms had discouraged experimental investigations of this problem. I n 1957, Bederson, Malamud, and Hammer (BMH) (30) reported on atomic beam measurements of e-H total scattering cross sections for electron energies a t or below -10 ev. The hydrogen atoms were produced by means of a radio frequency discharge, and up to 65% dissociation of the molecular hydrogen was achieved. The hydrogen atoms in the beam were separated from the molecules by a Stern-Gerlach magnet. The angular resolution of the experiment was sufficient to determine the cross section

76

MANFRED A. BIONDI

for scattering through angles greater than 7". At the lower ( Q > cm2, the high sensitivity trapped electron method was used, a t some sacrifice in electron energy resolution. Figure 21 presents the cross sections for excitation of the various vibration states by giving their values at 0.16 ev above the threshold energy for each particular state. The absolute values of the cross sectioiis are &% only known within a factor of two; however, the 15 20 25 30 3 5 relative values are quite accurate. The symbols Electron Energy (ev) ]Ag and I&+ on the figure indicate the positions FIG.19. Dependence on of these electronic excited states on this scale electron energy of the relaand suggest rather small cross sections tive cross sections for indicm2) for excitation of these states a t 0.16 ev rect excitation of nitrogen above their threshold. molecules initially in the I n contrast to the case of nitrogen, where v = 0 state to various strong vibrational excitation was achieved by vibration states. electrons of several ev energy, oxygen exhibits rather small excitation cross sections, which, however, occur a t electron energies equal to the vibration threshold ( A z L ,= 0.2 ev). At present, it has not been possible to determine experimentally whether the vibration excitation in O2 is via a direct process or whether, as an intermediate state of a n indirect process, a vibrationally excited state of the 02ion is first formed. There is evidence from analyses of swarm experiments (81) that the total

id&

Electron Energy lev1

FIQ.20. Comparison of the several experimental determinations of the cross section for inelastic scattering of electrons by nitrogen molecules. The peak cross section, cma. determined in the trapped electron method, is ~3 X

10 x

9

*(: 7

Vibrational Quantum Number

FIG.21. Cross section, a t 0.16 ev above threshold energy, for electron impact excitation of the various vibration states (v = 1 , 2 , 3 , etc.) of oxygen molecules initially in the v = 0 state. The symbols 1~~ and %,+ indicate the positions on this “energy,’ scale of these electronically excited configurations of 02. 100

101

L O W ENERGY ATOMIC COLLISIONS

effective cross section for vibrational excitation of oxygen by electrons of mean energy -0.5 ev is of the order of lo-’’ cm2.

D. Scattering of Electrons by Ions The rate of scattering of slow ( T , ‘v 300’K) electrons by ions in a plasma has been deduced by Anderson and Goldstein (51) from their microwave conductivity measurements. By measuring the dependence of the average collision frequency of the electrons in a low pressure helium afterglow on the electron (ion) concentration they were able to separate the electron-ion scattering contribution from the electron-atom contribution. The values of the average electron-ion momentum transfer

Maximum Ion Density l ~ r n - ~ l

FIQ.22. Dependence of the average electron-ion collision frequency on ion (electron) density a t 7’. = Ti = 300°K, as determined from microwave conductivity measurements in helium.

collision frequency, V,,,,, deduced from their measurements are shown in Fig. 22. It will be noted that Cmr varies almost linearly with the electron (ion) density. Theoretical calculations (82-84) of electron scattering by ions in a plasma, which consider the Coulomb forces between the electron and ion cut off a t the Debye shielding radius, yield expressions for V,, of the form V,,

=

An,T,-” In [BTe3*/n,],

(18)

for the case T, = T,. Anderson and Goldstein deduce the values

A

=

3.6 ~ m ~ - ( ~ K ) % e c - ~and

B

=

3.7

x

lo3 C ~ - ~ - ( O K ) - $ ~

from their experiment. The calculated values of Ginsburg and Vilenski (82) are A = 3.59 and B = 3.32 X lo3, in excellent agreement with the

102

MANFRED A. BIONDI

experimental observations. The theory of Burkhardt et al. (83)gives substantially different values; namely, A = 2.25 and B = 8.4 X lo3, while Spitzer and Harm's (84) calculations also lead to a substantially smaller predicted value of the electron-ion collision frequency. Similar studies of mixed electron-atom and electron-ion scattering have been carried out by Lin et al. (85) using dc conductivity determinations in isothermal argon plasmas (10,000-15,000"K) a t rather higher degrees of ionization (> These measurements agree rather well with the dc conductivity predicted by Spitzer and Harm (84).

E . Ion-Atom Collisions at Low Energies I n this subsection we shall consider the collisions of low energy positive and negative ions with atoms or molecules insofar as such collisions lead to simple elastic scattering, charge transfer, and ion-molecule reactions. The experimental methods used for studying these processes involve largely ion mobility, ion beam, and afterglow-mass spectrographic apparatus. The means of determining the desired cross sections or reaction rates from the measured quantities are described next. 1 . Methods of Measurement. A principal means of determining the very low energy ( 5 0 . 1 ev) scattering or charge-transfer cross-sections is the ion mobility tube. For ions in thermal equilibrium with the gas in which they move (Ti = Tg,,) the Chapman-Enskog formula (86) gives for the ion mobility, p i ,

where e is the ionic charge, N the gas density, m7 the reduced mass of ion and atom, and E is a small correction to the first order mobility theory (86). The quantity is the momentum-transfer cross-section averaged over the Maxwellian velocity distribution of the ions and atoms. Thus, from ion mobility measurements carried out over a range of gas temperatures and in sufficiently small applied fields so that the ion energy is thermal, one can determine, in principle, the energy dependence of Qm. For simple potential scattering of the ion and atom, the momentum transfer cross section Qm is related to the differential scattering cross section, I ( @ ,as given in Eq. (2). However, for charge transfer processes of the symmetrical type, i.e.,

am

the original ion is neutralized and an identical new ion is formed. One may define a critical impact parameter, b,, inside which half of the ions colliding with atoms are neutralized and outside of which essentially no

L O W ENERGY ATOMIC COLLISIONS

103

charge transfer O C C U ~ S Viewed .~ in the center of mass system, for b < b,, the emerging ions are symmetrically distributed about the scattering angle 0 = go”, even if potential scattering takes place during the transfer collision. Thus, one can show (87) that the momentum-transfer crosssection appropriate to mobility measurements involving charge transfer is Q m ‘V nbC2 (21) Unfortunately, it appears very difficult to extend, by mobility measurements, the determinations Qm for potential scattering and for charge transfer to substantially higher energies than can be achieved in temperature studies of ion mobility. In the electron case, measurements of p and D / p a s functions of E / p were coupled with calculations of the electron velocity distributions to extend the cross section analyses well beyond the thermal range. However, ion velocity distributions, in even moderate electric fields, are extremely difficult to calculate. Wannier (88) has shown that, as a result of velocity persistence when ions collide with atoms, the velocity distribution becomes highly distorted in the applied field direction (he characterizes the velocity distribution a s “onion” shaped), and hence the spherical harmonic expansion to first order, which has been successfully applied to Boltzmann transport calculations of electron velocity distributions, breaks down completely. For nonMaxwellian distributions, only in the case of particularly simple ionmolecule interactions such as pure polarization attraction, have simple expressions equivalent to Eq. (19) been obtained (8,0), relating the mobility t o the interaction parameter (e.g., the atomic polarizability). A second means of studying the very low energy behavior of ions is provided by studies of electrons and ions during the afterglow following creation of a plasma in a gas. Often, the electron concentration during the afterglow is observed by microwave techniques (see for example Biondi, Rose, Goldstein et al., 90) while the ions are studied by monitoring, with a differentially pumped mass spectrometer, the currents of ions reaching a wall of the container boundiiig the plasma (91-95). During thermal equilibrium in the late afterglow, studies of the electron loss by ambipolar diffusion to the walls provide a means of determining the positive i o n diffusion coefficient D, (or mobility p l ), since the electrons’ ambipolar diffusion coefficient D , under these circumstances is simply,

D,

‘v

2Di

=

2p;kT/e.

6 Actually, the charge transfer probability oscillates rapidly between 0 and 1 as one decreases b below the value b,, and the transfer probability rapidly drops to zero outside of b,.

104

MANFRED A. BIONDI

Studies of the time dependences of the various ion currents reaching the wall of the plasma container permit deduction of the rates of the important ion-molecule reactions. Finally, ion beam apparatus has been refined to the point where it is possible to study ion-molecule collisions for rather slow ions ( 5 1 0 ev energy). I n some experiments the ion beam is made to cross a n atomic beam, permitting studies of collisions with atoms such as H and 0 (94). 2. Studies of I o n - A t o m Potential Scattering. In some cases measurements of the temperature dependences of thermal ion mobilities have provided a convenient, although not particularly precise, means of examining the low energy portions of the interaction potential curves between ions and atoms or molecules. I n general, the procedure followed in such studies has been t o assume a more or less realistic approximation to the long range attractive and short range repulsive interactions between ion and atom and then to calculate the variation of mobility with temperature for comparison with experiment. I n 1905 Langevin (95) pioneered in this area by calculating the mobility of a n ion colliding with polarizable atoms on the assumption that the long range attraction could be represented by a polarization interaction, V,( R ) = - cre2/2R4,where a is the atomic polarizability and R the internuclear distance between ion and atom, and that the short range repulsion could be represented by a rigid sphere behavior, i.e., V , ( R ) = 0 for R > Ro and V,(R) = 00 for R 6 Ro. Later, H a d and Cook (96)subsituted a softer repulsion term, V,(R) = C / R 8 ,for Langevin’s rigid sphere interaction. It has been recognized that these two forms for the repulsion bracket actual atomic behavior, the one being too hard, the other too soft, and the applicable experimental observations often lie intermediate between the predictions of the two theories (97’). Margenau (98) suggested the more complete form for the long range attraction,

A R

R C +-R6 ++.. R7

to include higher order interactions between ion and atom; however, from his estimates of the various coefficients it appears th a t the polarization term provides an adequate representation of the attractive potential in most cases. Meyerott (99) used a more realistic, exponentially falling repulsion term, V,(R) = C exp ( - cR), in his calculations of the mobility of Li+ in helium as a function of temperature, obtaining fair agreement with measurements. Recently, Dalgarno et al. (100) have given a n excellent survey of the theory involving potential scattering and the applicable experimental information up t o the year 1958. They show, for example, th a t a single

105

LOW E N E R G Y ATOMIC COLLISIONS

interaction, given in atomic units by

V ( R ) = 74.2 exp (-2.75R)

-

1.39/R4,

(23)

obtained by trial and error modification of Meyerott's interaction, satisfactorily predicts the observed values of mobility a s a function of temperature for Lif and Naf in helium ( I C I I ) , although the observations for Cs+ require a modification of the repulsive interaction coefficients. The substantial number of recent measurements of thermal positive and negative ion mobilities and diffusion coefficients (97, 102-108) have added little t o our knowledge of the applicable interatomic forces, although they have provided considerable information concerning the resonant charge transfer interaction (see Section 111, El 3 ) . Many of the studies were carried out at a single temperature and comparisons made with t,he mobility values predicted for a pure polarization attraction. Except in cases of highly polarizable gases, e.g., Ar, the agreement was found to be rather poor, as one might expect. However, in many of the temperature studies, e.g., Nez+/He, He+/Ne, Nez+/Ne, Ar2+/Ar (97, 106), the observed mobilities6 (see Table I) were TABLEI. EXPERIMENTAL VALUE6 O F THERMAL I O N MOBILITIES'I N U N L I K E ION/GAS CASESCOMPARED TO THE POLARIZATION (0°K) LIMIT.THE GAS DENSITY MOBILITIES ARE REFERRED TO A STANDARD OF

2.69

x

loi9 CM-3

Ion mobility (cni2/volt-sec) Ion/gas

0°K (theory)

77°K

195°K

300°K

Hez+/He Nez+/He He+/Ne Nez+/Ne Arz+/Ar

(19) (16.0) (12.2) (6.1) (2.1)

18.0 16.5 13.1 6.6 2.7

21.7 17.1 16.7 7.0 2.9

20.3 17.3 17.2

6.3 2.7

I,. M . Chanin and ht. A. Biondi, Phys. K P Z )106,473 . (1957); G. E. Courville and M. A. Biondi, J . Cheni. Phys. 37, Gl6 (1962). a

consistent with the low temperature limits determined by long range polarization attraction using the measured polarizabilities of the atoms. At finite temperatures the behevior often lay intermediate between the Langevin and Hass6-Cook theories, suggesting that a n interaction of the general form of Eg. (23) could be made to fit the observations by adjusting the repulsion parameters. 6 Beaty (105),has observed three distinct ion mobilities in argon at 300°K (PO = 1.5, 1.8, and 2.6). While the assignment of PO = 1.5 to Ar+ is probably correct, our conclusion t h a t the highest mobility ion is Ar2+ remains to be verified by mass analysis.

106

M A N F R E D A. B I O N D I

There are, however, two rather puzzling features which have emerged from these types of studies. For the case of Hez+in helium, the mobility a t 77°K has decreased from its 195°K value to a point where it is already below the pure polarization limit appropriate to T = O°K (97). Since corresponding effects are not observed in the more polarizable gases, neon and argon, it is difficult to see how “clustering” of Hez+ with helium to form a heavier ion complex can explain the results. Also, in studies of negative ion mobilities, e.g., 0 2 - and 0- in O2 (108), and low energy scattering cross section measurements for H- in He and in Ne ( l o g ) , scattering in excess of that predicted by the polarization forces is observed. Thus, a t 77°K the observed mobility of 0 2 - in 0 2 is 35% below the pure polarization limit, and a t energies of -10 ev and less the H- scattering by He and by Ne is roughly twice the polarization value and increases more rapidly with decreasing energy than for a pure polarization interaction. I n addition, studies a t 300°K of the thermal mobilities of negative oxygen ions in both atomic and molecular gases (107) yield values below the polarization limit, even if one assumes the ions are 0 3 - rather than OZ-. For scattering by atoms it does not appear that either addition of the higher order attractive terms or the partial cancellation resulting from consideration of the repulsive interaction can lead to the observed behavior.6a I n the case of molecular gases the inclusion of a longer range interaction resulting from the permanent electric quadrupole moment of the molecule may conceivably explain the observations (110). However, since the pronounced deviations in the negative ion scattering are observed in both atomic and molecular gases, it may be that the large extent of the negative ion wave function relative t o that of a positive ion is responsible for the additional interaction required to explain the negative ion observations. 3. Ion- Atom Charge Transfer. Processes of charge transfer, such a s

+ B-+ A + Bf C + D--+ C- + D, A+

and

involve the transfer of one or more electrons from one atomic species t o another a t a collision. Under certain circumstances-especially resonant charge transfer between identical atomic species, i.e., A+/A-charge transfer can be the dominant ion-atom interaction. I n this subsection 6* Note added in proof: S. Geltman (private communication, 1962) has pointed out that, for He2+/He,inclusion of the R-6 term in the interaction permits the mobility to rise from its value at 77°K to the pure polarization value a t 0°K. It seems doubtful that this added interaction term can similarly account for the 01-/0~,H-/He, and H-/Ne results.

LOW ENERGY ATOMIC COLLISIONS

107

we shall be chiefly concerned with single electron transfer froin neutral atoms t o singly charged positive ions for three different cases; (a) true resonance, (b) nonresonance, and (c) accidental resonance. (a) Resonant charge transfer. For the case of He+ in He, Massey and Mohr (111) (MM) calculated that the ion mobility a t ordinary temperatures and above should be determined largely by the charge transfer process rather than by the polarization attraction or short range repulsion interactions considered in the previous subsection. Unfortunately, owing to confusion of ion identity involved in contemporary (-1930’s) mobility measurements (112), MM’s calculation was considered to have overestimated seriously the charge transfer contribution, since it predicted a mobility half the observed value. Morc than a decade later the apparent discrepancy was resolved by the suggestion of Meyerott (113) that the mobility measurements had referred to He2+ in helium aiid by new diffusion ( l l 4 , 9 1 ) and mobility (103,115)measurements, which showed the presence of two ionic species in helium, one of which had the mobility predicted by M M for He+ in He and t8hcother of which agreed with earlier measurements ( 1 1 2 ) . More recently, the calculatioiis of ion mobilities in their parent gases under conditions where the charge transfer interaction dominates have been extended by Holstein (87) to other gases for which the wave functions a t large distances from the nucleus are reasonably well known. I n addition, the case H+/H has been calculated exactly by Bates (116), while the case H+/H* has been treated by Boyd aiid Dalgarno (117) for the excited state, n = 2. For the case of true resonance, A+ A + A A+, a t infinite ionatom separation the extra electron can occupy either ion core site with equal energy; however, as a result of the atomic interactions a t finite separation, the degeneracy is removed and a n energy difference, AIL, occurs between the two stationary states of the system. The frequency a t which the extra electron jumps back and forth between localization around each of the ion sites is simply v = Au/h. By calculating Au as a function of the internuclear distance of the ion cores, the critical impact parameter inside which the transfer probability during a collision has a n average value one half can be determined. Using Eq. (21) one can then calculate the momentum-transfer cross section. The theoretical treatments of ion mobilities in parent gases, together with comparisons with experimental measurements, have recently been reviewed by Dalgarno (118). In addition, a detailed review of calculations of charge transfer, with the notable exception of Holstein’s work, has been given by Bates and McCarroll (119). The observed temperature dependences of thermal ion mobilities for the resonant charge transfer case determined by Chanin and Biondi (9?’),

+

+

108

MANFRED A. BIONDI

together with their calculations using Holstein’s (87) theory, are given in Table 11. The lower temperature (77 and 195°K) theoretical values include appreciable contributions to the momentum transfer cross section by the long range polarization attraction. Agreement between experiment and theory is poorest for helium, which paradoxically should be the most accurately calculable case, since helium’s outermost shell is an s-shell, for which the Hartree-Fock wave functions used in the theory are applicable. One may investigate the general accuracy of the theory used in these calcuIations by comparing Holstein’s values with exact calculations of Bates OF THEORETICAL AND EXPERIMENTAL VALUES TABLE11. COMPARISON OF THERMAL IONMOBILITIES FOR ION/PARENTGAS CASES. THEMOBILITYVALUESARE REFERREDTO A STANDARD GAS DENSITYOF 2.69 x 1o’O CMV3

Ion Mobility (cm2/volt-scc) Temperature (OK)

TheoryG

Experiment*

77 195 300

17.1 13.8 12. 2

13.5 12.1 10.8

Ne+/Ne

77 195 300

5.5 4.6 4.1

5.2 4.5 4.2

Ar +/Ar

77 195 300

2.2 1.9 1.7

2.2 2.0 1.6

Ion/gas He+/He

a T. Holstein, J. Phys. Chem. 66, 832 (1952) and Research Report 60-94698-3-R9, Westinghouse Research Laboratories, Pittsburgh 35, Pa. (1955) unpublished. * L. M. Chanin and M. A. Riondi, Phys. Rev. 106, 473 (1957).

(116) for H+/H. It is found that, a t the critical interaction distances which determine the charge transfer cross section, the Au values computed by the two methods differ by only a few per cent, leading to even smaller differences in the computed mobilities. Thus, although better agreement between the experimental mobilites for He+ in He and semiempirical (118) or less exact theoretical (120) treatments has been obtained, one must regard the situation in helium as rather unsatisfactory. It turns out that the discrepancy between theory and experiment for both He+ and Hez+ ions in helium can be removed by using an atomic polarizability one third larger than the measured values; however, there is no apparent basis for such an adjustment of the long range attractive. interaction.

109

LOW ENERGY ATOMIC COLLISIONS

I n addition to the temperature dependence studies cited, measurements have been made a t 300°K for Kr+/Kr, Xe+/Xe (103, 104, 121, 122) and for Hg+/Hg (102). I n these cases the mobilities agree reasonably well with approximate, unpublished calculations by Bernstein (102, 103).

The charge transfer process has been investigated from moderate (-10 ev) energies to rather high energies (> lo3 ev) by ion beam techniques. Here the cross section for charge exchange is approximately the area (rrbC2)over which the probability for charge transfer oscillates between 0 and 1, multiplied by the average probability, %. Dalgarno (118) and, later, Sheldon (123) have shown that the theoretically predicted energy dependence (87) permits one to match the charge transfer cross section, Q C t , deduced from mobility studies a t very low energies ( 100 ev) processes ( 5 ) has demonstrated a rapidly decreasing cross section with decreasing velocity in the adiabatic region, i.e., Q,.t exp (-CAu,/v), for H+/We. Further, he has shown a striking correlation between the energy defect, Au,, of the reactions and the energy a t which a maximum cross section is observed, not only for charge transfer but also for ionization and excitation processes. Hasted points out that departures from the “adiabatic” energy dependence, yielding substantially larger cross sections a t low energies, are sometimes observed, possibly as a result of intrusion of other processes in the experimental measurement. It should be noted, however, that as one brings the two atoms A and B together, the energy difference between the two configurations A+-B and A-B+ may decrease, a s a result of differing polarizabilities of atoms A and B, to the point where (Au/ti)(R/v) does become small compared to unity. If, a t this separation, the charge transfer interaction is sufficient, transfer may take place with large probability, leading to the larger-than-expected transfer cross section. It is clear that in “nonresonant” cases no uniform predictions

-

111

LOW ENERGY ATOMIC COLLISIONS

can be made concerning the variation of the charge transfer cross section with energy. Unfortunately, the very low energy region, where the adiabatic condition should lead to small charge transfer, has not been investigated extensively experimentally, since ion beam techniques cannot reach these low energies and ion mobility studies cannot observe the drift velocity of A+ in B if A+ loses its charge to B by transfer. However, the technique of measuring the time dependence of mass analyzed currents of ions reaching the walls from the afterglows of plasmas (93, 133) has permitted the determination of two body rate coefficients and the corresponding averaged cross sections a t -0.04 ev (2’ = 300’K). Dickirisoii and Sayers (133) have studied charge transfer in He0 2 gas mixtures and obtain a value for the two body rate coefficient, P = 2.5 X lo-” cm3/sec, for the process Of

+

0 2 +

0

+ Oz+,

(27)

corresponding to Get1: 3 X cm2 a t an average energy of -0.04 ev. This cross section is more than an order of magnitude smaller than the values for resonant atomic cases such as Ne+/Ne and may involve a quite different process, i.e., atom, rather than electron, transfer (see Section 111, E, 4 ) . Fite et al. (93) obtain a value in this range from their measurements of afterglows in 0, and He-02 mixtures. However, very recent (134) studies by Langstroth and Hasted, using similar techniques, yield a n order of magnitude smaller value, P ‘v 1.8 X cm3/sec, for this process. The various studies are all in rather early stages, and it is not, as yet, possible to decide which is the correct value. Fite et al. (93) report a preliminary value for the transfer process,

-

Nz+

+ Oz+

Nz

+ Oz+,

-

act

(28)

which is rather large, P 2 X cm3 sec, corresponding to 3 X 10-15 cm2. These measurements, a t either a single afterglow temperature (300°K) or over a very narrow range of temperatures, do not permit deduction of the energy dependence of Q L I in the low energy region. However, these types of studies are first comiiig into extensive use (99, 93, 133, l&), and it is expected that information on energy dependences will be forthcoming. Recently, studies of nonresonant charge transfer and atom transfer reactions involving low energy ( < 1 ev) negative ions have been carried out in mass spectrometers employing “high” pressure ion sources (135, 136). Surprisingly large cross soctions, ~ 1 0 - < I ~QCt < lo-’* cm2 were observed for charge transfer reactions such as O-/NOz, SF6-/NOz,

112

MANFRED A. BIONDI

and C1-/N02, in view of the fact that substantial energy discrepancies exist if the reactions involve formation of NOz- without excitation of the internal degrees of freedom of the molecules. Some evidence for quite different behaviors in the variation of Qct with energy has been obtained in much higher energy (2100 ev) beam experiments (94, 131, 137, 138). It is found that the cross sections are of the order of cm2 and show only moderate energy dependences; QCt for N+/Oz, 02+/N2, and N2 +/N0 increases with decreasing energy around 100 ev; Qct for O+/Oz, N2+/02, O+/Nz and N+/NZ exhibits essentially no variation with energy in this range, while for Oz+/O and N2+/0 the cross section decreases with decreasing energy. (c) Accidental resonance charge transfer, If the ionization potentials of atoms A and B are very nearly equal, one has a n accidental resonance and “asymmetrical resonance” (159) charge transfer can occur. Bates and Lynn (119, 139) have argued that for sufficiently slow encounters the probability of charge transfer should be very small. Given that the energy difference a t very large separations of the two configurations A+-B and A-B+ is arbitrarily small, i.e., Au, ‘v 0, as the separation between A and B is decreased, the value of Au arising from the electrostatic potential interactions may become finite (for example, as a result of differing atomic polarizabilities for A and B), and hence electronic excitation will be required to change from the one molecular ion state to the other. Thus, unless the colliding particles have sufficient energy, the adiabatic condition rules out such transitions, and charge transfer will not occur. However, as a result of complexities in calculating the detailed shapes of the potential curves, Bates and Lynn do not provide a n estimate of the critical collision velocity below which charge transfer can no longer occur. One can obtain an estimate of the critical velocity by inquiring whether, before reaching a range Rp a t which the adiabatic condition rules out appreciable transitions between the two states, the total phase for charge transfer is already appreciable. If it is, then charge transfer occurs with high probability. To illustrate, a t a given relative velocity, v, the critical distance for appreciable charge transfer, R,, is given by (Auct/fi)(RJv)

-

1,

(29)

wherePAuct is the level splitting due to the charge transfer interaction in the absence of differing polarizabilities of A and B. The range R, a t which the adiabatic condition rules out, for the given velocity, electronic transitions between the molecular ion states split by the differing polarization interactions is given by

113

LOW ENERGY ATOMIC COLLISIONS

since, at the large values of R with which we are concerned, the polarization interaction is the only important c1ect)rostatic i n t e r a ~ t i o n .Since ~ AucLvaries much more rapidly (- exp - aR ) with separation than does Aupol there is a value of separation, R1, a t which the twosplittings are equal. For R < R1, we haveAurt > Au,,,Land charge transferoccursfreely, while for R > R1, we have nu,, < A U , , ~ ,that , ; is, the adiabatic condition inhibits charge transfer. For a given velocity, if Eq. (29) yields a value of the critical charge transfer distance, It,, which is less than R1, then the charge transfer is not inhibited. However, as the velocity is decreased, R, increases, until finally R, > R1 and we have reached the region in which the charge transfer cross section diminishes with decreasing velocity, a s discussed by Bates and Lynn. For the usual values of atomic polarizabilities, these velocities are very low, corresponding to energies V,I, then some excited levels of the configuration 2 lie above the continuum of configuration 1. The process of dielectronic recombination (1) involves as a first step the radiationless transition, 1Xf e 2X*, (62)

+ *

where the ion in configuration 1 captures an electron of the proper energy to form the excited state of configuration 2 without change in total energy of the system. The excited state may decay by autoionization [reaction ((32) going to the left] with a lifetime of lO-'4 sec, or it may be stabilized against autoionization by a radiative transition to a level below Vil, i.e., zX* + zX'* hv. (63) However, since radiative lifetimes are considerably longer (210-lo sec) than autoionization times, there is only a small probability of stabilizing the initial recombination event. The little experimental evidence concerning the importance of this process comes from studies of the inverse, photoexcitation, process. For example, Pery-Thorne and Garton (218) have measured the far uv absorption of krypton. They find a series of strong, broad lines (Beutler lines) corresponding to transitions from the ground state to excited states between the 2P$aand 2P56series limits of krypton. The breadth of the lines is the result of the short excited state lifetime against auto0.04), they ionization. From the measured f-values of these lines (f were able to show that a n earlier estimate by Garton et al. (219)for argon of (Ydiel. 1O-l" cm3/sec at T , = 300°K is considerably too large, perhaps by two orders of magnitude. I n the earlier work a value off 1 had been assumed, leading to the high estimate. Thus, it appears that dielectronic recombination, for the noble gas ions a t least, is somewhat less important than ordinary radiative recombination. 3. Dissociative Recombination. The previous discussion has pointed out that electron capture by radiative and dielectronic recombination processes leads, a t T , = 300°K, to values of a < lo-" cm3/sec. The inference from ionospheric measurements and the observations in microwave afterglow studies of electron-ion recombination coefficients of the

s

+

-


, 100) were attained, one finds that the actual recombination coefficients lie rather close to the values deduced from a n analysis in terms of Eq. (57). Additional evidence th at the electron removal is by volume

-

L O W ENERGY ATOMIC COLLISIONS

145

recombination has been provided by the observation of the phenomenon of “afterglow quenching” in neon (228) and in helium (227, 229, 230). Here it is observed that, when the electron eiiergy during the afterglow is momentarily increased slightly by application of microwave energy to the plasma, the afterglow (recombination) radiation intensity decreases, and the loss rate of electrons decreases. Both of these observations are consistent with recombination control during the afterglow, since recombination rates generally decrease with increasing energy, while atomic excitation processes and ambipolar diffusion loss arc both expected to increase with increasing electron energy. Attempts have been made to determine whether these large recombination coefficients observed in microwave afterglows are indeed the result of the dissociative process by examining two of its characteristic features. Referring to reaction (G4), it will be seen that (a) a molecular positive ion is required, and (b) the excited atom formed a s a result of this process has a n additional kinetic energy of dissociation over the usual thermal eiiergy of the ions and atoms in the plasma. The first of these points has been investigated (227, 231) by studying electron loss during afterglows where first molecular positive ions (Arz+) and then atomic ions (Ar+) are expected to dominate. At moderate (p 10 mm Hg) pressures in pure argon the afterglow ions are all converted to Arz+ in a time short compared to the measuring In this case the “recombination” solution, Eq. (57), is followed over a n electron density range of a factor of 40, and a value of a ‘V 7 X lop7cm3/ sec is obtained. If, on the other hand, a small amount (1 : 1000) of argon is added to pure helium, then Ar+ is the predominant ion, formed by the Penning ionizing reaction, HeM Ar + He Ar+ e. On the time scale of the measurements, appreciable conversion to Arz+ does not occur, since the Ar atoms necessary for the coilversion are present in such a small concentration. I n this case, after an initial afterglow period showing evidence of the Penning ionization process, the final decay is by fundamental mode diffusion [Eq. (58) with a, = 0 for j # 11 over the measured pressure range, 2-7 mm Hg, and a t electron densities equal to the values attained in pure argon. Analysis of scatter in the data indicates that if recombination is present in this case, it must occur a t < times the rate it did in pure argon. Thus, the large two body recombination requires the presence of molecular positive ions. The second point, that dissociative recombination leads to the

-

+

+

+

8 Mass spectrographic studies of microwave afterglows in noble gases, e.g., references 91 and 93, have confirmed the predominance of the molecular ion at moderate pressures.

146

MANFRED A . BIONDI

formation of excited atoms with kinetic energy of dissociation, has been investigated by Rogers and Biondi (23W),who examined the shapes of the afterglow lines for excess Doppler broadening. Although, as the discussion a little later will make clear, the evidence for the large two body recombination loss in helium is confused by conflicting experimental evidence, this gas was chosen for the line broadening studies because, a t low pressures, the afterglow lines are well separated in the spectrum and some of the lines originate from states of short lifetime. The former consideration is of value in the low-intensity, high resolution Fabry-Perot interferometric techniques (233) used in these afterglow studies; the latter point is required in order that the fast atoms radiate a broadened line before they either transfer their excitation to a slow atom or dissipate their excess kinetic energy in collisions. At the low pressures at which the afterglow radiation consists predominantly of the helium line spectrum, the electron and ion loss is diffusion controlled; however, the temporal dependence of the late afterglow radiation has been found to be consistent with the predicted behavior of the product, ne n(He2+), considering the fact th a t the early afterglow ions are He+, and the He2+is formed by three body collisions of He+ and two helium atoms. I n addition, the line is very slightly broader than thermal (2' = 30OoIi) during the discharge, decreases t o thermal width during the early afterglow and then increases in width during the late afterglow, when the radiation is expected to originate from recombination. This observation should be considered rather convincing proof that dissociative capture is the origin of the observed, large recombination coefficients; yet the inferred dissociation kinetic energy of the excited atom is rather smaller (-0.1 ev) than originally expected. Also, one wishes the line broadening had been observed for a case, such as neon, where the recombination loss is well established, rather than for helium, where considerable uncertainty exists. As a result, the problem has been reexamined for neon, and it appears that the necessary conditions for observing line broadening can be met; therefore studies are presently underway. Having established that the dissociative process is probably the cause of the observed recombination, it is still difficult to state the dissociative recombination coefficients for the noble gases and some of the diatomic gases, since one finds large variations in the detail with which a given gas has been studied and in the degree to which the obstacles to achieving quantitative determinations have been avoided. The case of helium is particularly puzzling since, following the early preliminary recombination studies, there have been several detailed studies (229, 230, 232) whose results are, to some degree, conflicting. The line broadening studies (23.2)

L O W E N E R G Y ATOMIC COLLISIONS

147

described earlier, although carried out in a diffusion controlled region, were consistent with a recombination coefficient for helium in the range 10-9-10-* cm3/sec. Chen, Leiby, and Goldstein (CLG) (Zd9), working a t rather high (-30 nun I-Ig) pressures in a long cylinder 1.G4 cm in diameter, achieved a value of y > 10, which from Gray and Kerr’s analysis should lead t o reasonably accurate (-25%)) determinations of a from the slopes of the l/n, vs t curves. The corrected value of a obtained from their data is cm3/sec, essentially independent of pressure over the -7 X range 15-30 mni Hg. Both CLG and Iierr and his students (230)’who carried out painstaking studies of helium afterglows, observed a proportionality between the emitted afterglow intensity and ne2at high ( > 15 mm Hg) pressures, indicating recombination contr01.~However, it appears that CLG’s inference, by the use of narrow band interference filters, that thc high pressure afterglow radiation consisted of lines such as A5876 and A3889 is incorrect, since spectographic studies ($30, 23.2)indicate that, a t these pressures, the radiation is almost entirely band spectra of Hez*. Kerr and co-m-orkers (280) have carried out very careful absolute intensity measurements of the various helium bands, which all decay with the same time dependence, and find that, by summing th e contributions within the spectral range of their apparatus, a > 7 X cm3/ sec, with a n absolute accuracy of a factor of two. Further, they find that a t late (12-40 nisec) times in the afterglow a t 15 mm Hg pressure the decay is exponential in character, i.e., diffusion controlled. I n the intermediate (-4-12 msec) region a more rapid decay than by diffusion alone is observed, and on the assumption that a solution of the form of Eq. (59) gives a n upper bound on CY they estimate a 2 < X lop9 cm3/sec. However, in this same time interval, other of their curves a t the same pressure indicate non-negligible metastable-metastable ionization, which, if also present in the analyzed curves, could lead to a substantial underestimation of a. Thus, it is not clear whether I<err and co-workers’ results contradict CLG’s early afterglow value of a ‘v 7 X cm3/sec. Even if Kerr et al. have not underestimated the later afterglow value of a, it may be that the decay time of vibrational excitation of Hezf, which is estimated to be rather long (231), perhaps of the order of several milliseconds, leads 9 It should be noted that a t the high electron densities, ~ 1 0 e/cc, ” used by CLG the predicted magnitude of the three-body (ion plus two electron) recombination rate is the same as the observed value, except that a quite different time dependence for the t4ectron loss is predicted. In addition, the afterglow intensity should not be proportional to ns2 if this process is of importance (see discussion in Section V, C, 2).

148

MANFRED A. BIONDI

to a progressive diminution of a with afterglow time. It is reasonable t o assume that the Hez+ is most probably formed in a high vibration state as a result of the three body conversion from He+. If, as a result of the curve crossing in the dissociative recombination process, reaction (64), the higher vibration states He2+ exhibit larger values of a, then the required dependence of a on time in the afterglow can result. Even granting the foregoing hypothesis to bring the two high pressure helium studies into harmony, we are unable to account for the dissociative process leading to emission of Hez* band radiation. There have been no serious proposals that He3+ ions are sufficiently stable to occur in appreciable concentrations in the afterglow studies1° and so permit dissociative recombination to form He2* He. If we start from He2+,the excited states of He* formed by recombination are expected to decay by emission of radiation long before conversion to Hez* by three body collisions can occur. Thus, in spite of painstaking studies of helium afterglows, we are unable to satisfactorily account for a number of the observations in terms of a unified set of atomic collision processes; in particular, the precise nature of the recombination process and its magnitude have not, as yet, been determined. Of the other noble gases, only neon, and to a lesser extent argon, have been studied in sufficient detail and under well enough controlled experimental conditions to permit quantitative conclusions concerning the magnitude of a. I n neon (145, 223, 227), the afterglow spectrum consists only of line radiation and the emitted intensity is accurately proportional to me2. These observations, coupled with the fact that measurements were carried out in a recombination dominated region (y >, loo), suggest that the value given in Table I11 is a reasonably accurate measure of recombination between electrons and Nez+ ions, presumably in their ground vibration state (231). I n argon, for which it is somewhat more difficult to obtain or prepare extremely pure gas samples, the afterglow radiation studies are less complete, although once again I ne2 is found (231). I n addition, measurements of a are carried out in y > 100 regions, so that accurate values are obtained. Although the noble gases krypton and xenon have been recently restudied by Lemon and Sexton ( 2 3 3 , substantial impurities of the one gas in the other, together with rather poor ranges of linear l/n, vs t data, especially for the case of krypton, prevent quantitative conclusions 2 X cm3/sec, in agreement being drawn. For xenon a value of a

+

-

-

lo The appearance of mass 12 ions in maw spectographic studies of helium afterglows is usually under conditions where C+ is a readily suspected impurity (234, 236). To clarify this point studies using the mass 3 isotope of helium are contemplated.

149

LOW ENERGY ATOMIC COLLISIONS

with earlier work by Richardson (237), who had similar impurity problems, is obtained. The quantitative determinations of recombination coefficients in the diatomic gases are even more sparse, as a result of the fact that, unlike noble gases where a diatomic ion is the most complex expected, polyatomic molecular ions are known to occur. At present, the technique of simultaneous mass analysis of the ions reaching the walls of the microwave afterglow cavity, together with the usual electron density determinations, is just coming into extensive use. A preliminary report of studies of recombination of electrons with nitrogen ions and with oxygen ions has been given by Kasner, Rogers, and Biondi (KRB) (92). I n these microwave afterglow studies, using a differentially pumped, Boyd-type rf mass spectrometer to monitor the ions reaching the wall of the microwave cavity, it was observed that, at pressures > mm Hg, N3+ and N4+ions in nitrogen and Oaf in oxygen became significant. Thus, earlier studies (222, 226) of these gases do not, in all probability, refer to N2+and Oz+ ions, as originally supposed. I n order t o reach a recombination controlled region (y > loo), K R B added a relatively high (-20 mm Hg) pressure of neon to the nitrogen and the oxygen to reduce diffusion loss to a negligible value. Ionization of O2 and N2 by neon metastables assured that the neon remained “inert,” with only oxygen and nitrogen ions appearing in significant quantities during the afterglows. Recent extensions (234) of the N2-Ne mixture studies, with improved determinations of time-resolved afterglow ion currents and use of the most recent Gray and Kerr correction factors, lead to a value of CY

=

(3 f 1) x

cm3/sec

for N2+ ions and electrons a t 300°K. I n these studies, gated photomultiplier scans of the spatial distribution of afterglow radiation in the rectangular microwave cavity showed no vertical or lateral asymmetries. On the assumption that I ( s , y, z ) [n,(z, y, z)12 the inferred electron distribution appears to be slightly more centrally concentrated than for a fundamental diffusion mode distribution. However, in the high y region attained in the studies, the resulting higher diffusion modes have orily a small effect on the deduced recombination value. If the Nz+ ions under study are produced by the reaction NeM N Z + Ne Nez+ el then energy considerations require that they be in a vibration state, v 6 3, while if they are produced by electron impact on ground state, v = 0, N z molecules, the Frank-Condon principle requires that they be in the v = 0 state. At higher nitrogen partial pressures in the N2-Ne mixtures the N4+ion, together with some N3+, predominates. Here

-

+

+

+

150

MANFRED A. BIONDI

-

a tentative value a(N4+) 1 x crn3/sec is obtained. It is interesting to note that this value is approximately the same as the corrected value obtained from the earlier work (222). A preliminary value for Ozf ions, obtained a t low (-lop3 mm Hg) partial pressures of oxygen in neon and for y > 100, is a =

(1.7 5 1) X

cm3/sec (92, 234).

The oxygen studies have not proceeded sufficiently far to assign the vibration state of the Oaf ion, nor has a value of a! for the 0 3 + ion been obtained. Results for other diatomic gases are not presented, since there is contradictory evidence from the various microwave afterglow studies, many of which have not been carried out in recombination controlled regions, and all of which have omitted mass identification of the ions under study. For example, for hydrogen it is not a t present possible to reconcile Persson and Brown’s (224) “higher diffusionmode’’ explanation of electron decay from their short duration (-1 psec), asymmetrically distributed plasmas with the results of Varnerin (54),who obtained a value of a cm3/sec at high (>40 mm Hg) pressures, where y 3 10 was attained. Since H3+ ions, rather than Hz+ ions have been found to predominate in moderate pressure (greater than a few mm Hg) hydrogen afterglows (235) it is clear th at mass analysis of the ions is one of the essential steps in the study of recombination and other afterglow processes in diatomic gases, and is of considerable assistance in studies of noble gases and their mixtures. I n this review, many of the studies of recombination carried out in the last decade have been omitted from consideration because of space requirements and because some of them failed to meet the conditions for quantitative recombination determinations. I n most of the studies for which recombination coefficients are presented, the experimental conditions have been such that the assumption that T , = TgBs= 300°K during the measuring interval should be valid. There is little reliable information concerning the dependence on electron energy of the recombination coefficients. For reasons which by for now should be obvious, the quoting of an energy dependence of l’-o.8 hydrogen from the early studies (222) is not valid, while from the same paper the finding of essentially no dependence on temperature over the range 77°K T , 410°K for electron-ion recombination in neon should be reliable. Here the electron temperature was varied by changing the gas temperature. Chen et al. (229) studied the energy dependence of a a t higher pressures in helium, using microwave energy to heat the electrons and gauging the effect on the recombination rate by the decrease in

-


10 variation of vapor pressure. This is somewhat surprising since, from the data presented, it appears that volume recombination loss a t charge densities of < 2 X 10” ions/cm3 only slightly outweighed fundamental mode diffusion loss, leading to values of y which were not always large compared to unity. Thus, one must consider the possibility that higher mode diffusion was responsible for much, or all, of the inferred recombination. Yeung quotes values of the mutual neutralization coefficient a t = 1.5 X lo-* cm*/sec for iodine “molecular” ions and -290°K of aI1put. aneut. = 1.9 X lop8 cm3/sec for bromine and assigus a n uncertainty of - 5 % . I 1 However, these values should be considered as indicating the possible order of magnitude of this process, rather than accurate determinations, in view of the criticisms raised in the previous paragraph and also of a n absolute ion density error of 50% stemming from a mass assignment error. It is known that I- is formed in the thermal electron attachment reaction, rather than Iz-, as Yeung assumed (see, for example, 177). This work, while as yet hardly definitive, represents a very important step in positive ion-negative ion studies, avoiding a s it does the ambiguities of probe determinations of charged particle densities. These techniques, together with mass analysis of the ions reaching the walls of the afterglow container, should be of value in the study of mutual neutralization reactions iiivolving 0 2 + and &-, Nz+ and 0 2 - , etc., which are of considerable interest for ionospheric analyses.

+

C. Three-Body Recombination Processes 1. Neutral Molecule Stabilized Recombination. The excess energy of recombination between a positive ion and a negative ion or a n electron 11 In the recently published chapter on “Ionic Recombination” in Atomic and Molecular Processes, ref. 6 , Sayers points out that, in a continuation of Yeung’s work, Greaves has found a serious error in an electronic calibration which suggests that a ten timcs larger value of CY is to be inferred from the data. The value of y, however, remains unchanged and the criticisms in the text, remain valid, even with these larger a values.

154

MANFRED A . BIONDI

may be removed by a neutral atom or molecule acting as a third body, i.e.,

+ +N+X*+Y+N + + N + X * + N.

X+ YX+ e

(66) (67)

There is not a great deal of experimental information concerning these three body processes. However, for ion-ion recombination, reaction (66), the classical theories of Thomson (241) for medium and low pressures (51 atmosphere) and of Langevin (242) for high pressures ( > 1 atm) have been, for many years, regarded as providing adequate treatments of the capture probability. For the low pressure case, one calculates the probability of occurrence of a collision with a neutral molecule which removes sufficient kinetic energy from the positive or negative ion to cause the orbit in the coulomb field of the other charged particle to become closed. I n this region the capture probability increases linearly with increasing neutral particle density so that one may assign a three body coefficient to describe the capture rate. I n the high pressure case, where the necessary energy removing collisions occur frequently, the recombination rate is limited by the speed with which the one ion can drift toward the other under the attraction of its field. This mobility limited motion, therefore, varies inversely with gas density. Quite some time ago Machler (243) investigated ionic recombination in air a t high pressures (>>1 atm) and found the pressure dependence of the Langevin theory. Sayers (244) investigated the range from tenths of an atmosphere to a few atmospheres and found a t first the increase in recombination with pressure predicted by Thomson theory, followed by a decrease with further pressure increase above -1 atm. Natason (245) recently developed a single treatment valid over the whole range from low pressures to very high pressures and obtains excellent agreement with Machler’s and Sayers’ data. I n the low pressure range Sayers’ data and the Natason theory lead to a three-body ionic recombinatlion coefficient for air a t 300°K of K,i N 3 X cm6/sec. Similar values were obtained in studies by Gardner (246) of pure oxygen over the pressure range 100-760 mm Hg. These large coefficients suggest that a t pressures of 2 1 0 mm Hg the three body process becomes more important than the mutual neutralization process. An alternate process leading to three body ionic recombination has been examined theoretically by Fueno et al. (247). Here the recombination occurs via a two stage process,

+ N 5 (XN)+, (XN)+ + Y-+ X Y + N. Xf

followed by

LOW ENERGY ATOMIC COLLISIONS

155

An alternate process involving formation of a weakly bound complex with the negative ion rather than the positive ion may also be possible. On the assumption that formation and decay of the complex by reaction (68a) is essentially in equilibrium, while reaction (68b) is highly exothermic, they calculate the over-all three body coefficient for the process. For “air” ions they obtain a value a t 2 I ) O O I i of K,, 1 X 1 O V 6 cm6/sec, with values for other gases such as 0 2 , CO, COZ, NzO lying within a factor of two, except for Hz, whose value is -4.5 times larger. It thus appears that this process is more than a n order of magnitude less effective in causing ionic recombination than the Thonison process. However, the authors compare their calculated values for the most part with very old ( > 50 years) measurements, which suffered from serious impurity effects and measuring problems, and conclude that their calculated values are in satisfactory agreement with measurements. There is even less information concerning neutral atom stabilized, electron-ion recombination, reaction (67). Massey and Burhop ( 1 ) have modified the Thomson ion-ion theory by considering the fact that, unlike a negative ion, a n electron loses only a very small fraction of its kinetic energy on making a momentum transfer collision with a neutral atom. Thus, the electron-ion recombination coefficient is reduced by a factor of the order of (m/2M)fh, where m is the electron and n l the ion mass, relative to the corresponding ion-ion process. They point out that, if the third body is a molecule rather than an atom, the total energy loss per collision, including losses to rotational and vibrational excitation, replaces the usual 2 m / M factor in the calculations. Using the measured energy loss and collision cross sectioii data for air, they calculate a value, K,, 11 6 X cm6/sec at 300°1i, approximately 50 times smaller than the ion-ion value. Unfortunately, there appear to be no measurements of the neutral stabilized, electron-ion recombination to which the theoretical values can be compared. 2. Electron Stabilized Recombination. Recently, in order to explain volume loss of electrons and positive ions from moderate and high density plasmas, a three body recombination process has been invoked which is essentially the inverse of ionization by electron impact on excited atoms. Using hydrogen as an example, one has

-

H+

+ e + e S H * + e.

(69)

Since the process does not require the presence of molecular ions, it can lead to recombination rates in excess of radiative values when only atomic ions are present, provided that the plasma charge densities are sufficiently high. D’Angelo (24) has proposed this process to explain electron-ion re-

156

MANFRED A. BIONDI

combination rates greater than the radiative values and has calculated the rate of reaction (69) for 10I2 < ne < loL3e/cm3 and 1000°K < T , < 10,OOO"K on the assumption th at radiative cascading to lower levels stabilizes the recombination. Bates and Kingston (25), McWhirter (26), and Hiniiov and Hirschberg (27) have improved on these calculations for hydrogenic ions and for He+ by inclusion of the effect of superelastic electron collisions on the stabilization. An important point stressed in these calculations is the fact th a t simple capture of a plasnia electron into a high-lying state of H* does not 14.

I

I

I

1

I

x Conductivity kT in ev A

m

c

-

-0

.

2

rn -

Spectroscopic kT in ev

--- Calculated kT in ev

13

.

12

11

c

A

--

0

I

I

I

1

2

3

Time lmsecl

h

-2

FIG.31. Decay of electron density and electron temperature during the afterglow in a helium plasma. The experimentally determined values are indicated by the symbols; the dashed curve is the predicted decay of electron temperature obtained from the measured electron density decay and the theory of electron stabilized, electron-ion recombination.

assure permanent recombination, since other plasma electrons may collisioiially excite the H" into higher bound or even continuum states before radiative transitions or superelastic electron collisions bring it to a lower state. Thus, it is shown that only when the bound state reached obeys the condition ( u i - u,) >> lcT, is one assured of a "permanent" recombination event. The experimental studies bearing on this process, which in fact probably inspired some of these calculations, were carried out a t the Princeton Plasma Physics Laboratory on the B-1 stellerator-a long torus with magnetic field wiiidings to reduce charged particle losses from the plasma to the walls (27, 248, 249). Motley and Kuckes (249) and Hinnov and Hirschberg (27') have determined the variation of electron density and of electron temperature, using millimeter microwave, d-c conductivity and spectroscopic techniques, during afterglows in hydrogen and helium at low pressures (-1 - l o p Hg). Hinnov and Hirschberg (27) have calculated the expected three body recombination coefficients for H+ and He+,

1Ti7

L O W E N E R G Y ATOMIC COLLISIONS

obtaining good agreement with the calculations of Bates, Kingston and McWhirter (26, 260) but rather a stronger dependence of the recombination rate on electron density and electron temperature than calculated by D'Angelo (24). It is found that the three body recombination coefficients, K,,', inferred from the observed decay of charge density and of electron temperature agree very closely with the calculated values for both hydrogen and helium afterglows over electron densities ranging from -loL2 - 6 X 1013e/cm3. The degree of agreement is illustrated in Fig. 31,

-131

1

8

I 9

I

10

I

11

I

12

I

13

I

14

1

15

I

' 9 0 "e

FIG.32. Calculated total recombination coelficient as a function of electron density and electron temperature for two-body radiative, and three-body electron stabilized recombination between electrons and positive ions.

in which the calculated electron temperature required to give the observed electroii density decay via the three-body recombination process agrees well with the observed values. The three-body recombination coefficient for low electron temperatures (IcT, 5 0.25 ev) is given by

Kre' = 5.6 X 10-27(kT,)-4.5cm6/sec,

(70)

when (kT,) is expressed in electroii volts. This recombination is in addition t o the usual two-body radiative process, so th a t one has a total effective recornbination coefficient of the form, a =

-k Kre'ne.

(71)

The values of CY calculated by Hinnov and Hirschberg for lo7 < n, < 1 O I 6 e/cms and 0.03 < kT, < 1 ev are shown in Fig. 32. It will be seen that, in studies of thermal, k!!', = 0.026 ev, plasmas at high elect,ron densities, n, 3 10" e/cc, the three-body process contributes as much to electron loss by recombination as a two-body process with a coefficient

158

-

MANFRED A. BIONDI

cm3/sec. Thus, care must be taken in analyzing volume electron loss in terms of two-body recombination processes in such investigations as those of Chen et al. (229), which are in this range (see discussion of their work in Section V, B, 3 ) . It has been suggested (24, 251) that some of the early recombination studies in arc afterglows (252, 253) a t rather high electron densities and moderate electron temperatures (determined by Langmuir probes) may have actually referred to this three body process; however, dissociative recombination of electrons in a plasma containing both molecular and atomic ions could also lead to the observed loss rates; the experimental data are too sparse to choose between the two mechanisms. From the foregoing discussion it appears that, while our understanding of such recombination processes as radiative capture and electronstabilized capture of electrons by ions is satisfactory, if limited, there are other areas, such as dissociative recombination and mutual neutralization, where considerable improvement in our state of knowledge is desirable. Fortunately, the necessary experimental techniques are available, and the interest in these subjects is sufficiently great that it is to be expected that considerable progress in these areas will be forthcoming in the next few years. a!

ACKNOWLEDGMENTS The author is greatly indebted to his colleagues, especially T. M. Donahue, T. D. Holstein, A. V. Phelps, and G. J. Schulz, for their many suggestions and criticisms which have been of great value in the preparation of this review.

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162 111. 118. 113. 114. 115. 116.

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(1953). 117. T. J . M. Boyd and A. Dalgarno, Proc. Phys. Soc. (London) A72, 694 (1959). 118. A. Dalgarno, Phil. Trans. Roy. SOC.A260, 426 (1958). 119. D. R. Bates and R. McCarroll, Advances in Phys. (Phil. Mag. Suppl.) 11, 39 (1962). 120. N. Lynn and B. L. Moiseiwitsch, Proc. Phys. SOC. (London) A70, 474 (1957). 121. R. J . Munson and A. M. Tyndall, Proc. Roy. SOC.8177, 187 (1941). 126. E. C. Beaty, Phys. Rev. 104. 17 (1956). 123. J. W. Sheldon, Phys. Reu. Letters 8, 64 (1962). 124. B. Ziegler, 2.Physik 136,108 (1953); R. M. Kushner, B. M. Palyukh, and L. A. Sena, Zzvest. Akad. Nauk S.S.S.R. 23, 1007 (1959). 115. W . L. Fite, R. F. Stebbings, D. G. Hummer, and R. T. Brackmann, Phys. Rev. 119, 663 (1960). 116. D. G. Hummer, R. F. Stebbings, W. L. Fite, and L. M. Branscomb, Phys. Rev. 119, 668 (1960). 127. A. Dalgarno and H. N. Yadav, Proc. Phys. SOC.(London) A66, 173 (1953); A. Dalgarno and M. R. C. McDowell, ibid. A69, 615 (1956). 128. M. Saporoschenko, Phys. Rev. 111, 1550 (1958); R. N. Varney, J. Chem. Phys. 31, 1314 (1059). 129. R. N . Varney, Phys. Rev. Letters 6,559 (1960). 130. W . S. Barnes, D. W. Martin, and E. W. McDaniel, Phys. Rev. Letters 6, 110 (1961). 131. R. F. Stebbings and B. R. Turner, Report No. GA-2768, General Atomic, San Diego, California, 1961, unpublished. 132. H. 8. W. Massey and E. H. S. Burhop, “Electronic and Ionic Impact Phenomena,” Chapter VIII. Oxford Univ. Press, London and New York, 1952. 133. P. H. G. Dickinson and J. Sayers, Proc. Phys. SOC.(London) 76, 137 (1960). 134. G. F. 0. Langstroth and J. B. Hasted, Discussions Faraday SOC.33, 298 (1962). 135. A. Henglein and G. A. Muccini, J. Chem. Phys. 31, 1426 (1959). 136. R. K . Curran, Phys. Rev. 126, 910 (1962). 137. R. F. Stebbings, W. L. Fite, and D. G. Hummer, J. Chem. Phys. 33,1226 (1960). 138. M. A. Fineman, A. C. H. Smith, R. F. Stebbings, and B. R. Turner, Report No. GACD-2991, General Atomic, San Diego, California, 1962. 139. D. R. Bates and N. Lynn, Proc. Roy. SOC.A263, 141 (1959). 140. M. Pahl, Ergeb. exact. Naturwiss. 34, 182 (1962). 141. J . A. Hornbeck and J. P. Molnar, Phys. Rev. 84,621 (1951). 142. M. A. Biondi, Phys. Rev. 88,660 (1952). 143. W. P. Shollette and E. E. Muschlitz, J. Chem. Phys. 36,3368 (1962). 144. A. V. Phelps and J. P. Molnar, Phys. Rev. 89, 1202 (1953). 145. H. J. Oskam, Philips Research Rept. 13, 335, 401 (1958). 146. M. Pahl and U. Weimer, 2. Naturforsch. 13a, 50 (1958). 1.47. D . P. Stevenson and D. 0. Schissler, J . Chem. Phys. 29,282 (1958). 148. G. Giomousis and D. P. Stevenson, J. Chem. Phys. 29, 294 (1958). The units for the reaction coefficient in Table I should be cm3/5 rather than m3/a.

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163

149. D. S. Burch and R. Geballe, Phys. Rev. 106, 183, 188 (1957); H. Eiber, Proc. 5th Intern. Conf. on Ionization Phenomena i n Gases, Munich, 1961 p. 1334ff. (1962). 150. A. Dalgarno, Ann. geophys. 17, 16 (1961). 151. H. 5. W. Massey, “Negative Ions,” 2nd ed. Cambridge Univ. Press, London and New York, 1950. 152. L. M. Branscomb, Proc. 5th Intern. Conf. on Ionization Phenomena in Gases, Munich, 1961 p. Iff. (1962). 153. W. Lochte-Holtgreven, Naturwi8senschaften 38, 258 (1951). 154. 0. Weber, 2 . Physik 162, 281 (1958). 165. G. Boldt, 2. Physik 164,319 (1959). 156. S. J. Smith and L. M. Branscomb, J . Research Natl. Bur. Standards 66, 165 (1955). 157. S. J. Smith and L. M. Branscomb, Rev. Sci. Instr. 31, 733 (1960). 158. L. M. Branscomb and S. J. Smith, Phys. Rev. 98, 1028 (1955). 159. S. Chandrasekhar and D. D. Elbert, Astrophys. J . 128,633 (1958). 160. S. Chandrasekhar, Astrophys. J . 128, 114 (1958). 161. L. M. Bransconib and S. J. Smith, Phys. Rev. 98, 1127 (1955). 162. L. M. Branscomb, D. S. Burch, S. J. Smith, and S. Geltman, Phys. Rev. 111, 504 (1958). 163. D. S. Burch, S. J. Smith, and L. M. Branscomb, Phys. Rev. 112, 171 (1958); 114, 1652 (1959). 164. M. L. Seman and L. M. Branscomb, Phys. Rev. 126, 1602 (1962). 165. L. M. Branscomb and S. J. Smith, J . Chern. Phys. 26, 598 (1956). 166. R. S. Berry, C. W. Reimann, and G. N. Spokes, Bull. A m . Phys. Sac. [2] 7, 69 (1962). 167. L. M. Chanin, A. V. Phelps, and M. A. Biondi, Phys. Reu. Letters 2 , 344 (1950). 168. R. K. Curran, J . Chem. Phys. 35, 1849 (1961). 169. G. H. Dunn, Phys. Rev. Letters 8, 62 (1962). 170. J. D. Cragg, R. Thorburn, and B. A. Tozer, Proc. Roy. Sac. 8240, 473 (1957); J. D. Craggs and B. A. Tozer, ibid. A247, 337 (1958); 8264,229 (1960). 171. I. S. Buchelnikova, Zhur. Eksptl. Teoret. I’iz. 36, 1119 (1958); translation, Soviet Phys-JEl’P 36, 783 (1959). 172. J. G. Schulz, Phys. Rev. 128, 178 (1962). 173. P. L. Randolf and R. Geballe, Tech. Rept. No. 6, Dept. Phys. Univ. of Washington, Seattle, Washington, 1958, unpublished. 174. M. A. Harrison and R. Geballe, Phys. Rev. 91, 1 (1953). 175. A. N. Prasad, Proc. Phys. Sac. (London) 74, 33 (1959); A. N. Prasad and J. D. Craggs, ibid. 77, 385 (1961). 176. J. T. Tate and P. T . Smith, Phys. Rev. 39, 270 (1932). 177. M. A. Biondi, Phys. Rev. 109,2005 (1958); R. E. Fox, ibid. p. 2008; M. A. Biondi and R. E. Fox, ibid. p. 2012. 178. R. Buchdahl, J . Chem. Phys. 9, 146 (1941). 179. W. E. Hickam and R. E. Fox, J. Chem. Phys. 26, 642 (1956). 150. G. J. Schulz, J . Chem. Phys. 33, 1661 (1960). 181. A. N. Prasad and J. D. Craggs, Proc. Phys. Sac. (London) 76, 223 (1960). 188. G. J. Schulz, Phys. Rez:. 113, 816 (1959). 183. R. E. Fox, J . Chem. Phys. 26, 1281 (1957). 184. R. E. Fox, J . Chem. Phys. 32, 285 (1959). 185. R. K. Curran, J . Chem. Phys. 34, 2007 (1961).

164

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J. D. Craggs and B. 2. Tozer, Proc. Roy. SOC.A247, 337 (1958). J. D. Craggs and B. Z. Tozer, Proc. Roy. SOC.8264, 229 (1960). R. K. Curran, J. Chem. Phys. 34, 1069 (1961). R. I vf(rf/f), this solid angle decreases rapidly with increasing vo. This means that the aperture has a strong filtering effect, and we can, for an estimation of the resolution limit, replace v o in Eq. (10) by v,r,/f. Thus we obtain

With 4(zf) = 40 kv, /El= 100 kv/cm, rf = 10 p, and f = 5 mm, we cm = 160 A. have 6,1 = 1.6 There is experimental evidence (17, 18) for the effectivity of the filtering action of the aperture diaphragm. The experiments show that, if a very narrow diaphragm is used, the width of the velocity distribution of the electrons passing the aperture becomes practically independent on the initial velocity distribution at the cathode [Eq. (33) does not contain c!]. Other suggestions to reduce the width ofithe energy distribution by a filter lens or an electron mirror (19) have also been made but so far no successful realization of such suggestions has become known.

ELECTRON EMISSION MICROSCOPY

261

D . The Difraction Limit Diffraction effects set a fundamental limit to an arbitrary reduction of resolving power by using correspondingly narrow apertures. It can be deduced from Eq. (3) and (4) that the inclination with which an electron ray is crossing the axis after being accelerated by the potential difference U , is given by (34)

m

If by use of an aperture at anode potential [uf = 4 ( 2 e / m ) U , ] , f o is limited to values below r f u f / f [see Eq. (29)], we have (35)

It is irrelevant for this discussion whether a real image is formed in the plane z = z1 or only a virtual image which is projected by a lens or lens system to any other recording plane. The limitation of aperture expressed by Eq. (35) will result in a limitation of resolving power by a diffraction disc of radius XI 6~ = 0.61 r/

(36)

where h =

2/2emU,

(37)

is the electron wavelength in the space at anode potential. For this reason it is of no use to make rl smaller than a value

for which 6el from Eq. (33) and 60 from Eq. (36) become equal. For U , = 40 kv, A = 0.06 A, E = lo5 volts/cm and f = 5 mm, the optimal aperture radius becomes 5 p . In this case, 6,l as well as 60 have the value

If we assume that the resolutiou limit is of the order of the sum of 6,1 and 60, we obtain for our example 6 = 80 A.

262

G . MOL L E NS T E DT AND F. L E N 2

It must, however, be kept in mind that this result has been deduced assuming a plane equipotential cathode surface, which may be an unrealistic assumption. Some theoretical investigations have been made on the reduction of the resolving power resulting from field perturbations by an uneven cathode surface, variations of surface potential (e.g., contact potentials), space charge etc. (8, 10, 20-22). Another advantage of a narrow limiting aperture is the increase in depth of focus which is reciprocal to the effective opening angle of the beam contributing to the image formation. Bartz (23) has demonstrated that in his secondary emission microscope the depth of focus is about 5 times superior to that obtained in an optical microscope. E. Consequences for the Design of Cathode Lenses From the results of the above considerations we see that the shapes and potentials of the electrodes of a cathode lens should be chosen such as to make the field in front of the cathode as strong as possible and to produce the back focal (“crossover”) plane z = zf behind the anode where a fine limiting aperture can be arranged and adjusted. The optimal choice of the lens parameters has been treated in a number of theoretical and experimental papers (24-2Sa). For cathode lens systems consisting of cathode, Wehnelt electrode, and anode which produce a real image of the cathode without using an additional lens the following general rule may be stated (27): If UA is the voltage applied between cathode and anode, the field strength in front of the cathode is always smaller than UA/cm. Since the field strength in front of the cathode is limited by electric breakdown, some authors have used high voltage pulses of a few microseconds duration for the operation of their emission microscopes (25, 28-30). 111. PHOTO EMISSION MICROSCOPY

A . Resolution Limit As shown in Section I1 the resolution limit 6,1 of a cathode lens is approximately given by 61, = e/elEl if no limiting aperture is used. Herein, e is the most probable initial energy, and E the electric field strength immediately in front of the specimen surface used as cathode. Lukirsky and Prileiaev (31) have measured the energy distribution of the photoelectrons emitted from a polycrystalline silver surface under ultraviolet irradiation with X = 2537 A. It is shown in Fig. 3. I n horizontal direction the relative kinetic electron energy is plotted in units of the maximum photon energy following from Einstein’s relation for the photoelectric effect. I n vertical direction the energy distribution

263

ELECTRON EMISSION MICItOSCOPY

function N ( e ) is shown where N ( E ) & is the relative number of electrons with energies between e and e dt. Figure 3 shows that for a thick t,arget the most probable value is about 0 . 4 ~ , , , ~This ~ . result is not only found with silver but also with all other studied target materials (-41, Zii, Cu) and different wavelengths of uv irradiation, i.e., different values of tmnX. Icor emission microscopy with photoelectrons it is interesting to note t h a t for a foil 100 A in thickness the niovt probable ~ ~ ~ higher. energy of about 0 . 6 is~somewhat The reason is evidently that in a thin foil the primary photoelectric effect can oiily 1 0 025 050 075 occur near to the surface so that on their E/Emor way to the surface the electrons have less FI(+.3 . Energy distribution opportunity to lose energy than electrons of photoelectrons eniitked under which have beeii excited in deeper layers of iiltraviolet irradiation with A = a thicker target. Since most emission micro- 2537 A from ( 1 ) a thick silver scopic specimens are thick, the most proha- target, and ( 2 ) froin a silver foil ble emission energy to be used in the expres- 100 A in thickness (Sf). sion for the resolution limit is t = 0 . 4 E i n j x . If hv is the photon energy of the exciting uv radiation, and hv, the average work futictiott of the target,, we have, according to Einstein’s relation for the photoeffect

+

t

-

hv

=

hv,

+

or where A, = C/V, is the cutoff wavelength. For a polycrystalline zitic surface A, corresponds to the average value of the work functions of the various crystallites forming the surface. This value depends most sensitively on the surface roughness, gas adsorption and surface oxidation, but according to experience the practical cutoff wavelength for zinc is about X, = 3000 .I. If an extreme pressure mercury lamp (HBO 107 of Osram, West Germany) is used, the uv radiation behitid a Hcrasil quartz lens which is used to focus the electric arc otito the specimen has a spectrum with a shortest wavelength A, = 2400 A. If we insert this value for X into Eq. (41)’ we have with hc = 1.24 . lo-‘ ev C I ~ =

0.4hc

(k k) -

=

0.4 ev

264

G. M6LLENSTEVT A N D F. LENZ

The electric field streiigth in front of the cathode in the lens used by Koch (32) was determined from measurements in the electrolytic tank to 15 kv/cxn. From this a theoretical resolution limit of (43)

would follow. A more optimistic and more realistic value of &I = 16.50 11 results if we use the wavelength of the strong line X = 2630 A i n the LIV spectrum instead of the short wavelength limit where the irltellsity is very low. Indeed, Koch (36) has, with a Zn cathode and using the HBO 107 lamp, reached a resolution limit of 61, = 2000 A even without using a limiting aperture. A considerably improved resolution of about 1000 A was attained, however, by inserting an aperture 30 I.C i n diameter in the back focal plane of the cathode lens. IJnfortunately, it has not yet been possible t o use a much smaller limiting aperture down to the optiinal diameter of about 15 I.C because of the low intensity of the uv radiation, though according to Eq. (39) this would lead to a theoretical resolution liniit helow 200 A. It seems, however, possible to increase the field strength in front of thc cathode, and to reduce the difference between X, arid X by using rorresponding uv filters. The latter measure would mean a great reductioii of intensity, so that it does not seem practicable a t the preseiit performance of uv sources. An optimistic estimation of the results of an increase of field strength, however, makes it seem possible that a limit of about 250 A should be attainable with the present methods, provided that suitable specimens with a plane surface are used.

B. Photoemissive Sensitivity The photoemissive sensitivity i.e., the ratio of emission current and incident electromagnetic power is a function of wavelength which, for most metallic cathode materials, is increasing with increasing quantum energy, see Fig. 4. C. Instruments The principle of the photo emission microscope was first described and tested by Briiche (34). Mahl and Pohl (35) constructed a microscope of improved performance and applied it to studies of a number of metallic and nonmetallic surfaces after various mechanical, chemical, and thermal surface treatments. Though the iiistrumental design arid the applications contain many most interesting features we cannot got into much detail since this review article shall mainly cover recent developments not older than 10 years,

E1,ECTHON EM1SSIC)N MICROSCOPY

3

-R

2'755

' A

2480

10-4

40

*

265

2255

I

* C d of 8 3 ' K

io

X C d af293'K

-k

5 5

A / at 293 ' K

0 Zn a/ 293' K

s;'c I

C

0

Y

u 1C

4

4.5

-

5.0

Av

cv 5.5

FIG.4. Nornial photoemissive sensitivity verniis wavelength of incident radiation (33).

kv

Frc:. 5 . Ints. a. W. Bayh, 1058 ( , ! I ) . The arrangement of thc cathode leiis is shown in Fig. 2(i. 1:roiii an elcctroii gun of the Stc~igerwaltl type (;a),a fiiie electron beam strikes the target under an obliclue aligle of about 20”. To the cathode K of thc primary clectroti gun, a I oltage of -60 kv is applied, aiid its anode A has thc sam’ poteiitial as the specimen 0, i.e., -43 kv, so that the priniary elcctmtis strike the target with ail cilergy of 1 5 kcv where they releasci seco~idaries.A part of the intermediate image is again magnified by iiiraiis of an rlcctrostatic projector lens to a total electron optical niagnificatioii of 1000. The filial iniagc is recorded photographically iiiside the inicroscope colum~l.The spcciiiieii temperature can be varied by ineaiis of rrsistaiice heating. The filial image can be directly observed on a fluorescent screeii through a powerful Zeiss eyepiece with 20-fold magriificat ion.

286

G . MOLLENSTEDT

AND F. LEXZ

b. G. Bartz, 1958 ( 5 3 ) . Figure 27 is a schematic representatiorl of Bartz’ surface microscope. The primary electrons are produced i n a n adjustable electron gun with a magnetic condenser lens. The angle of incidence is about 20’. The Wehnelt electrode which encloses the specimen like a Faraday cage is on cathode potential. I t is ail advantage of this construction that, the primary beam proceeds in a practically field free space and is consequently not much deflected. For this reason it is possible to use small primary energies (e.g., 2 kev) for which a beam deflection occurs only immediately in front of the cathode. At a primary

FIG.26. Arrangement arid alectrir rircuit of a cathode lens and primary electron source in Bayh’s secondary electron emission miczroscopc ( 5 1 ) . 0-specimen; G and W-Wehnelt electrodes of rathodc lens and primary gun, respectively; E and Aanodes of cathode lens and primary gun, respectively; K-cathode; RI-limiting aperture; I-insulator.

energy of 2 kev the secondary electron yield is not much smaller than its maximum value (see Fig. 2 5 ) . According to Bartd nieasurenients in the electrolytic tank, he attains 60 kv/cm and a focal length of 5 . 2 mm for a n acceleration voltage of 40 kv. According to Eg. ( I G ) this corresponds to a resolution limit of about I500 A when no limiting aperture is used. With a limiting aperture of optimal dimensions, a theoretical resolution limit of about 80 A should be attainable. c. U. Decker, 1961 (54). Decker’s microscope has, in addition to the primary electron source, an ion source on the opposite side. A voltage of about -40 kv is applied to the specimen. Ariothcr high voltage source supplies +30 kv for the canal ray ion gun, so that the air or argon ions which clean and etch the specimen have an energy of 70 kev. The pri-

ELECTRON E M I S S I O N MICllOBCOPY

287

Fit:. 27 I3artx' secondary electron etnission rriirrosc~ope (,55). Primary elec*trori gun: (1 1 vathode; ( 2 ) IVehnrlt elect,rodr; (3) anode; (4) niagnetir condenser lens, cbathode I c n h ; (5) sperirnrn; (6) insulator; (7) \Vrhrielt elertrotle; (8) coritart spring; (5)) uiiode; (10) liiniting :tperturr; (1I ) projector lens; (12) fluorewent screen; ( 1 3 ) speviinrn holder with precision mec*linnisin for spccinien displacement in axial and perpeiitlicwlar dirrcntion.

5.

+

FI~:.28 I k c k c r ' s niicroscope ( 5 4 ) . Besides the electron soiircc EQ, a canal ray ion soiirce IQ is iisetl in order to clean and cktcli thc spccimcn surface.

288

G. MBLLENSTEDT A N D F. L E N 2

inary electrons hit the target with an eiiergy of 20 kev. With a n electrostatic projector lens a final magnification of 700 is attained on the fluorescent screen. The photographic recording method is the same as in Bayh’s and Bartz’s microscopes. In order to prevent contamination, the speciinen is heated to about 200’. A resolution of 1000 A is attained. 2. I’rrsent I’Prformancc. a. Dependence of image quality 011 the liniitiiig aperture. In order to surpass the resolving power of the optical microscope, a liniiting aperture in the back focal plane of the cathode lens must be used. There is experimental evidence that by such a limiting aperturr thr width of the energy distribution of the image-forming electrons is coiisiderably reduced (see Section IT, B ) . Of course, thc image intensity is greatly reduced if a n aperture of small diameter is used, but Bayh has recorded ail image a t a niaguification of 850 with an rxposurc’ time of 10 src, and a limiting aperture 8 p in diameter. In order to reduce

I00

FIG.29. Improvement of iruage quality with decreasing aperture diitrrictcr (a) p, (I)) 30 p , 1.5 p, ((1) 8 11. The electron optical inagnification was 850 ( , T I ) . ((8)

the effect of lens aberrations it is important that the aperture is exactly adjusted in axial and perpendicular direction, so that the axis of the imaging beam goes exactly through the center of the aperture. The variation of iniage quality with aperture diameter is denioristrated by Fig. 29 which shows a serirs of images of the same perlitic steel specimen. With an aperture diameter of 100 p some details are poorly defined, but with reduced aperture diameter the definition of the image is gradually improved. Aperture diamrters below 8 p have also been used, arid there would still be enough iiiteusity to record the micrographs but the difficulties of precise alignment cause much trouble, and a further irnprovenient of image quality was not observed. From theoretical coilsiderations (see Section 11, C) such an improvement is not t o be expected, since for aperture diameters of this size, diffraction effects begin to play an important role. b. Resolutioii test. On two micrographs of the same specimen taken a t high electron optical magnification pairs of points are selected which appear separated on both pictures. This separation, however, is in most

ELECTRON JCMIHSION MICIWSCOPY

288

cases to be found oiily i n oiiti dirrrtion siuce the image sulfers from astigniatism. I t is not yet clear whethrr this astigmatisni is a coiisequriirc of thr preferential direction of the primary heani, of the aberratioils of the cathode leiis, or of an esceatricity of thc limiting aperture. Anyway, an improvement of iniagc qualitry may be espected froin the correcting action of a stigmator. c. Dependence of emission on cathode inaterial. The differelice in emission froin various specimen materials is sigiiificaiit only when the surface is clean. If the varuuni is of the order of tor, and there are organic vapors in the residual vacuum, the contrast of a plane specimen consisting of different materials, is greatly rcdueed after a few seconds if the specimen is held a t room teniperature. A s in the case of photo ernission, the original coiltrast can be iiiaintaiiied for some minutes if the specimen is heated to temperat,ures of about 150°C.

F I ~ 30. . Srcmtlary rlcctron emmioil micrograph of a spec*inienconsisting of A), CU, and Fe ( 6 4 ) : (a) freshly cleaned wrfarc, (h) after I nim irradiation; (I-) after bombardment with Ar ions.

After an intense irradiation with hr ions froni a canal ray source the original contrast is restored even a t room temperature. I n some casrs surprisingly high contrast appears i l l secondary eniission micrographs. As a n example, Fig. 31 shows oriented growth on austeiiitic steel. d. Xonconducting specimen surfaces. Since on a tionconducting surface the primary electron beam would produce unwanted surface charges, which would impair the image quality, nieasures must be taken to prevent such charges. Hartz (53) has evaporated a platinum layer 50 A in thicktiess on poorly conducting speoiniens such as erythrocytes, poorly coritiuctiiig coal sections and diatoms. This inethod gives a good representation of the surface embossment but a distiiiction of the substrate inaterials by their specific emission is not possible because the mean path of t>he secondary electrons is shorter than the thickness of the platiniini layer. The formation of image contrast is only detcrmined by the secondary rniission from platinum and the shadow rffert of the prirnary electrons which hit under a n oblique angle.

290

((;.

G. MOLLENGTEDT A N D F. L E N 2

FIG. 31. Austcnitic steel; orientrd growth during cooling from 1000 to 700°C Ihrtz).

FIG. 32. Nonconducting, thermally etched A1203 surface with a carbon layer 50 A in thickness (U. Decker, specimen from L. Cartz, Morganite Development and Research Ltd. London).

ELECTRON EMISSION MICROSCOPY

29 1

Recent, hitherto uiipublished results by Decker show that a carbon layer about 50 A in thickness, evaporated on a non-conducting surface by iiieans of Bradley's procedure removes the surface charges and allows t o distitiguish different materials by their specific secoiidary emission. Apparently this is due to the low secondary electron yield from carbon and the comparatively long mean path length of secondary electrons in carbon. Inclusions i n glass becoiiie well visible if a carbon layer is used, and that there is no disadvantageous effect of surface charges. Another application of this niethocl is shown in Fig. 3%where a thermally etched surface of sintered A1,0, was covered with a carbon layer 30 A in thickness. e. Iniagiiig of magnetic micro fields. We have mentioned in Section 111, 11, 2 that the magnetic domains i n a ferromagnetic material can be made visible in the photo eiiiission microscope (41). Spivak and his co-workers (S,j) have also observed such specimens with secondary electrons but the results were inferior to those obtained i n (41). Decker (see :?G) has imaged the local niagiietic fields on the surface of a iiiagnetic tape 011 which a souiid frequency of 2-200 cps was recorded. ('. Scan niny Electron A1 icroscopy with SPcondary Electrons 1. G'cncral liemarlis. In scanning niicroscopy, the specimen surface is scanned with a very fine elcctroii brain, arid the emitted secoiidary electrons are used to control the intensity of a synchrouized writing bean1 scitnnitig the scrceii of a viewing tube. This procedure whose performailre a i d applicability has heeii coiisiderably i m p r o v d by the British working group i n Cambridge i n the latest years, is not ail imaging met#hotlin the optical sense, but since the iniage is formed by secondary electrons, a i d the resolution h i i t is clearly beyond that of optical microscopy, it should be nieiitioiicad i l l a review article on emission electroii microscopy. 1:igurc 33 scrves to explain the imaging principle. In all other hitherto irieiit io1ic.d ctiiission riiicroscopical tnethods a coniplete iniage of the cathode surface is fornied i l l every rnolnetit by int'ans of the cathode lens on a fluorcscent screen or a photographic emulsion. In scanning niicroscopy, however, no lenses are used to focus the complete iniage but the procedure is similar to that used in television viewing tubes. The object surface which may be regarded as subdivided into small eleinerits whose diameter is eclual to the resolution liniit of the instrument, is scaiined by a fine electron beam with a cross section approximately equal to that of one of the elements. As the beam sweeps over a particular element, this emits a number of secondary electrons, depend-

iiig on its physical properties. These clectroiis may, by a number of ways, he employed to form i n synchronism with the beam scanning the object, a magiiified image of the object. If tJhe line distance is equal to the beam diameter, both are equal to the resolution limit. The widening of the scariiiing electron spot by diffusion of the electrons in the specimeii may be iieglected since most of the emitted secondary electrons come from the point of impact, because electroiis excited ill deeper regions have much less chance to reach the surface aiid to be emitted. The magnification V = h/a i n electroil scaiiiiing microscopy is equal to the ratio of line lengths on the viewiiig screen aiid thc scarined lilies of the specinieii. 2. Instruments. a. 1\1. IGioll, 1933 (57), aiid M.Knoll and R. Theilc, 1939 (n‘8).This type of iniagc production was first technically realized by Synchronized Scanning Beams

dB L object - 0 -A

14’1(..

It

- b Image

---

3 3 . Image foriiiation by inems of scanriiiig

Knoll and Theilc (57, 68) and by von Ardeiine (59).Von Ardennc’s instrument, however, was not used to produce images using slow secondary clectrons alone but together with fast scattered electrons, and he recorded the iniagc by a mechanical device with a rotating drum, and not on a viewing screen. We shall not describe it in more det,ail, though von Ardenne’s paper contains a number of original and interesting ideas. The principles of operation of Knoll’s first scanning microscope are explained in Fig. 34. The specimen 0 whose surface is to be scanned, is arranged in a n evacuated tube on a metallic signal plate M. If the specimen consists of a conducting material, a signal plate is not required. The electron gun S in the scanning system containing the specimen produces a very fine electron beam. By a magnetic or electric deflection system A this beam is deflected in two perpendicular directions by means of sawtooth sweep voltages or currents with two appropriate frequencies in the same way as iii a television viewing tube. By this scanning procedure

the iniage is analyzed, aud the inforinat ion ahout the secondary cmissioll froin surface elemetlt~ssituated along a scanning line is trallsmitted during consecutive time elemcnts. l’hr smaller sweep frequency corresponding to t,he tiiimber of times the complete image. is writtc~rin titiit time, is called the image freque1ic.y. 111 order to give the humaii eye thc iriipressioii of a contitiuous image, a11 image frequency of about 60 sec-1 is sufficient. The higher sweep frequcncy c*orresponditig to thc numbcr of lines scanned iri unit time is callcld lint. frc~lueucy.The ratio of both frequencies is th(3 line number which should hc chosen sufficic~iitlyhigh in order to utilize completely the resolviiig power permitted by the scanning beam diameter.

The primary electron beam releases sccoiidary electrons at thc momcutary point of impact. They arc drawn to thc c.ollcctor electrode I< which is held at a positive potential l Y pof about 10 volts with respect to the signal plate, atid the secondary ernissioii current flows through the signal resistance I?,. The voltage difierence between the ends of this resistance is the signal contaiiiiiig the itiformation 011 the secontlary emission factor of the surface c~leniciits.I t is ainplified i i i a L\ itlr-hat~dainplificr V atid used to control the einissioti of the elcctroii gull in the viewitig tube B in which the electron beam is swept over the viewiiig scrc‘eti i n synchronism with the primary beani in the spwimeli tube. Hereby the tiine modulation of the signal voltage is retransduccd to a brightness niodulation of the corrcspondiiig image elements. The resulting image cat1 he recorded photographically with a powerful optical systetn. The brightness of the image elemeiits depeiids 011 their secondary electron yield and the amplification factor. The secondary electron yield

294

c.

MOLLENSTEUT

AND F. LENZ

itself depends on the surface material, the angle of incidence and the vrlocity of the primary beam. Grooves in a surface give a n increased brightness a t thrir cdges where the inclination angles a are large, since the emission is proportional to cos-' a. Knoll and Theile have also obtained images of insulating specimens usiug an additional continuous wide-angle electron beam. In this case each surface element forms a small condenser with the sigiial-plate which is slowly charged by the additional wide-angle beam to ail equilibrium potential and suddenly discharged by the scanning primary beam. This condenser discharge current pulse which is proportional to the charge stored by the image element between two passages of the scanning brain, is used as image signal. Similar methods are now widely used in image storage tubes. b. V. I