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1 Solidification Processing Merton C. Flemings Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, U.S.A.
List of Symbols and Abbreviations 1.1 Solidification Mode 1.2 Plane Front Solidification and Crystal Growing 1.3 Heat Flow in Solidification of Castings and Ingots 1.4 Alloy Solidification - Traditional and Rapid Solidification Processes 1.5 Equiaxed Structures 1.6 Heat Flow and Mechanical Properties 1.7 Microsegregation in Novel Near-Rapid Solidification Processes 1.8 Alloy Solidification - Columnar Growth 1.9 Alloy Solidification - Heat Flow into the Bulk Liquid 1.10 Mixed Cases of Rapid Solidification 1.11 Macrosegregation 1.12 Deformation of Semi-Solid Dendritic Structures 1.13 Grain Refinement 1.14 Semi-Solid Slurries 1.15 Flow Characteristics of Semi-Solid Slurries 1.16 Semi-Solid Composite Slurries 1.17 Processing Non-Dendritic Semi-Solid Slurries 1.18 References
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
2 4 4 8 12 16 20 24 26 29 31 33 38 42 44 46 50 52 54
2
1 Solidification Processing
List of Symbols and Abbreviations A a0 C C* CL, C o cm9 cs d D, D s , DL
Km9 Ks L l0 mL n n P R, RT S T t, tf To TL, T{ TM V v, vx z
surface area length scale related to interatomic spacing constant composition of solid at the interface composition of a liquid, composition of the initial liquid specific heat of the mold, specific heat of the solidified metal dendrite arm spacing solute diffusion coefficient, solute diffusion coefficient of a solid, solute diffusion coefficient of a liquid fraction liquid, fraction solid volume fraction liquid gravitational acceleration temperature gradient in a solid, temperature gradient in a liquid heat of fusion casting surface heat transfer coefficient permeability consistency partition ratio, effective partition ratio, equilibrium partition ratio thermal conductivity, thermal conductivity of a solid, thermal conductivity of a liquid thermal conductivity of a mold, thermal conductivity of a solid length one-half of the dendrite arm spacing slope of equilibrium liquidus line power law index rate of nucleus formation in growth direction pressure growth rate, isotherm velocity thickness solidified temperature time, total solidification time of casting mold temperature equilibrium liquidus temperature, initial temperature melting point of the metal being cast casting volume velocity, velocity perpendicular to isotherms distance in growth direction
a, as P y y 5
thermal diffusivity, thermal diffusivity of solid metal solidification contraction constant shear rate boundary thickness
/ L , fs gL gr Gs, GL H h K K k, k\ k0 fc, /cs, kL
List of Symbols and Abbreviations
S g ji £s> QL> Qm T
distance between nucleation events cooling rate viscosity density of a solid, density of a liquid, density of a mold shear stress
KGT LKT M.I.T SIMA U.T.S.
Kurz-Giovanola-Trivedi model Lipton-Kurz-Trivedi model Massachusetts Institute of Technology strain-induced melt activation ultimate tensile strength
1 Solidification Processing
1.1 Solidification Mode One way to categorize solidification processes is by their "solidification mode." For the primary phase of usual, nonfaceting binary alloys which solidify over a temperature range, there are six of these (Fig. 1-1): columnar dendritic, cellular, equiaxed dendritic, equiaxed non-dendritic, single-phase plane front, and two-phase plane front. For alloys which freeze over a temperature range, and in which thermal gradient is sufficiently steep and convection low, the Equiaxed dendritic
Equiaxed non-dendritic
usual structure is columnar dendritic. For steeper thermal gradient and slower growth rate, the structure may become cellular. Lower thermal gradient, agitation, or grain refinement alters the structure from columnar dendritic to equiaxed dendritic. Vigorous agitation or more effective grain refinement results in equiaxed non-dendritic solidification. Sufficiently steep thermal gradient at slow growth rate results in plane front solidified alloys that are either singlephase or two-phase, depending on the number of phases present at the equilibrium solidus of the alloy. The three structures on the left of Fig. 1-1 are the most common in usual casting and crystal growing processes. The structures on the right belong to processes of emerging or potential commercial importance.
1.2 Plane Front Solidification and Crystal Growing Cellular
Plane Front (Single-Phase)
Plane Front (Two-Phase)
Figure 1-1. Types of solidification structure that can be obtained in directionally solidified binary alloys (of the non-faceting type).
Solidification with a plane front is obtained in one of three ways: (1) with an ideally pure metal, (2) with an alloy at sufficiently high temperature gradient, G, and low growth rate, R; or (3) at sufficiently high R. The first way is of little interest (except as a physical approximation for treating heat flow in solidification or casting of ingots which solidify in a narrow freezing range). (This topic is treated in Vol. 5, Chap. 10, Sees. 10.2.2 and 10.2.3.) The third is of emerging interest in "rapid solidification processing." The second is the basic technology of crystal growing. The basic heat flow objectives of all crystal growing techniques are to (1) maintain a positive thermal gradient across a liquidsolid interface, and (2) independently control this gradient so that the liquid-solid interface moves at a controlled rate. A heat balance at a planar liquid-solid interface in
1.2 Plane Front Solidification and Crystal Growing ooooooooo
Solid
I
Liquid
To inert gas source or vacuum
o o o o oQoooco o
Heating coils Crystal (a)
To inert gas source or vacuum Crystal withdrawal and rotation Crystal "Floating" liquid zone
To inert gas source or vacuum
Heating coils o
Heating coils
(b)
(c)
crystal growth from the melt is written (Flemings, 1974)
where ks is thermal conductivity of the solid metal, kL is thermal conductivity of the liquid metal, Gs is temperature gradient in the solid at the liquid-solid interface, GL is temperature gradient in the liquid at the liquid-solid interface, QS is density of the solid metal, and H is heat of fusion. Note from Eq. (1-1) that growth velocity R is dependent, not on absolute thermal gradient, but on the difference between ksGs and /cLGL. Hence, thermal gradients can be controlled independently of growth velocity. This is an important attribute of single-crystal-growing furnaces since growing good crystals of alloys requires that the temperature gradients be high and growth rate be low.
Figure 1-2. Examples of crystal-growing methods, (a) Boat method; (b) crystal pulling; (c) floating zone (Flemings, 1974, courtesy of McGraw-Hill Book Company).
The basic feature of all crystal growing furnaces is, therefore, the ability to obtain a controlled flux of heat across the liquidsolid interface. Fig. 1-2 shows schematically several types of furnaces to accomplish this (Flemings, 1974). Principles of crystal growing will be illustrated in the following sections with reference to the type of furnace illustrated in Fig. 1-2 a, in which metal in a crucible of some length, L, is fully melted and then solidified by "normal solidification" from one end to the other. In the limiting ideal case of "complete diffusion in the liquid" (or very vigorous convection), no solid diffusion, and equilibrium interface kinetics, solute redistribution in crystal growth occurs as shown schematically in Fig. 1-3. The liquid composition during solidification is given by the well-known non-equilibrium lever rule
1 Solidification Processing LIQUID
LIQUID
2 O
2 c0
Co
cs kC 0 0
L DISTANCE • (b)
DISTANCE—*(a)
Figure 1-3. Solute redistribution in solidification with no solid diffusion and complete diffusion in the liquid. (a) At start of solidification; (b) at temperature T*; (c) after solidification; (d) phase diagram (Flemings, 1974, courtesy of McGrawHill Book Company). kC( DISTANCE -
COMPOSITION • (d)
(c)
which, for constant partition ratio, fc, is written —c f^
(1-2)
where CL and fL are liquid composition and fraction liquid, respectively, and C o is initial liquid composition. This equation, also termed the Scheil equation, may be written in terms of the solid composition at the interface, Cs*, and fraction solid, / s : Cg* =
fcC0(l-/,)
(b) TEMPERATURE ACROSS DROPLET DIAMETER
1.9 Alloy Solidification Heat Flow into the Bulk Liquid When heat flows from the bulk liquid directly to the surroundings before or during solidification, conditions prevail that after solidification behavior in an important way. Heat then flows from the growing dendrite tips into the liquid, and recalescence occurs (at least locally). We sometimes see a small amount of this recalescence at the beginning of solidification in conventional castings and ingots. We can obtain much larger undercoolings in small droplet or bulk specimens, or in continuous processes, by employing clean molten metal and solidifying it without contact with materials which catalyze crystallization. In Fig. 1-34, for example, a liquid droplet is originally undercooled to a temperature T{ below the equilibrium liquidus, TL. Nucleation occurs at the left of the droplet and dendrites grow from left to right. Temperature across the droplet at this time is as shown in Fig. l-34b with heat flowing predominantly into the liquid. Movement of the dendrite front across the specimen is quite rapid at high undercoolings, and so the rate of local recalescence can be very rapid indeed. The growth velocity of dendrites into an undercooled melt is treated in a manner similar to the constrained growth discussed in the previous section. Moreover,
TIME —+(c) AVERAGE DROPLET TEMPERATURE VERSUS TIME
Figure 1-34. Solidification of an undercooled alloy droplet. 7j is initial temperature.
numerical results of dendrite tip velocity versus undercooling are very close to those calculated earlier, as shown in Fig. 1-35 for Al-4.5% Cu alloy using the LKT model (Lipton et al., 1987). Superimposed on the model is the curve of Fig. 1-31 (KGT model) which is for growth into a non-undercooled melt (constrained growth). Many workers are now studying dendrite growth in undercooled alloys, and comparing experimental results with these and other analyses. Results of one such study by Wu et al. (1987) are summarized in Fig. 1-36. Solidification of this "unconstrained" type is obtained in continuous processes when heat flow from the liquid is rapid and nucleation is hindered. Fig. 1-37, for example, shows equipment for direct casting of steel wire developed at Michelin several decades ago (Massoubre and Pflieger, 1978). The molten steel is ejected from a small orifice at speeds up to about 15ms" 1 and solidifies before Rayleigh breakup oc-
30
1 Solidification Processing I i lilMj
: :
I
Al-4 5%Cu o
KGT
•
LKT
Ni-25% Sn LKT & BC model
/
1 • &
Experimental • High-speed cinematography.-?' o Thermal measurement • Thermal measurement ° o 10° = [9 mm dia. droplet]
o o
o
8 9
~ 10"
8
8 9 o
10" II
o
10-
8
s
io " 4 r
10"
o9
l
I I i iml
o c
10
l
i
i i mill
100 Bulk undercooling, K
i i
1000
o
AT (K) Figure 1-35. Comparison of predictions of growth velocity versus undercooling for the models of Kurz et al. (1986), KGT, and Upton et al. (1987), LKT, for constrained and free dendritic growth, respectively, assuming k = k0.
Figure 1-36. Dendrite tip velocity vs. undercooling in Ni-25 wt.% Sn alloy. Experimental results and comparison with predictions of three dendrite growth models (Wu et al., 1987).
Melt Gas inlet-
curs. The wire is only about 200 |im in diameter, so radial temperature differences, even at these high velocities, are small. Solidification, in the usual case, occurs by axial dendritic growth, Fig. 1-38, and so, at steady state, dendrite growth velocity is just equal to the ejection speed. Fig. 1-39 shows results of actual experimental temperature measurements in wire spinning for a range of ejection velocities. Dendrite tip undercooling is seen to increase with increasing tip velocity and to be significant at these tip velocities of some meters per second. The undercoolings, in fact, are quite close to those of the Ni-25% Sn alloy of Fig. 1-36.
Induction coil
Crucible — Pressurised vessel (Maxi pressure: 30bars) ~0rifica
Gas inlet —*•
>
Cooling vessel
.Take-up device
Figure 1-37. Apparatus for spinning steel wire from the melt (Massoubre and Pflieger, 1978).
1.10 Mixed Cases of Rapid Solidification
Dendritic growth is treated in detail in Vol. 5, Chap. 10, Sees. 10.4 and 10.5.4.
1.10 Mixed Cases of Rapid Solidification The classes of rapid solidification cited above are not necessarily mutually exclusive with respect to any given casting oper-
LIQUIDUS
AT
TEMPERATURE
\
I DISTANCE
Figure 1-38. Solidification of spun cast wire. At steady state, wire moves to right with velocity R and dendrites grow at constant velocity R into liquid metal undercooled an amount AT.
T°C
31
ation. For example, consider the wire spinning operation shown schematically in Fig. 1-38 at steady state, and suppose that at a time, t, a large number of effective heterogeneous nuclei are continuously introduced into the molten stream. The "upstream front" then moves quickly up to the liquidus and subsequent solidification is by heat flow through the liquid-solid zone, comparable to the schematic example of Fig. 1-30. In the unsteady state, there remain two additional solidification fronts which grow together as shown schematically in Fig. 1-40. This phenomenon is observed in melt spinning (Massoubre and Pflieger, 1978). Mixed types of solidification can also occur when a thermal boundary layer reaches the surface of a casting, as can occur in solidification of atomized powders or in melt spinning. Fig. 1-41 illustrates this for melt spinning. Growth is assumed to occur only by columnar growth of existing grains, with no nucleation at the growing interface. Hence, substantial undercooling must occur in the melt to propagate growth upstream, and growth is rapid. But if the strip thickness is small compared with the thermal boundary layer, then this type of solid-
C =0.4% Si = 3.5%
j
'LIQUIDUS 1500
\ 1400
AT= 190°
AT= 2301°
V= II.I m s - 1 ^ V=l3.8ms-' ' 0~* V = l 6 . 4 m s " ' :=r ^ ^ - ^ _ 4 - * - V = 19ms"
'
265
^ 4 ~ o i
i-t \A
c
3 -
c=0.42Ks"1-^ AH
-
i
cm
1 0 6 K s " 1 . The overall fiber thickness is between 20 and 25 jim. Details of this process can be found in the literature (Gaspar et al., 1986; Boulby and Wood, 1986; Wood and Boulby, 1986). 2.4.10 Comparison of Rapid Solidification Techniques
Table 2-3 presents a summary of the various rapid solidification techniques and their product parameters (Savage and Froes, 1984).
2.5 Laser Surface Treatment (b)
Figure 2-23. (a) Schematic illustration of the melt overflow technique, (b) Shows details of the melt pool shape and nature of the shear region at the overflow lip-wheel contact point.
All the techniques described in the preceding sections involve complete melting of the alloy prior to rapid solidification. An alternative is to locally melt the surface (the depth ranging from 10 to 1000 \im) of bulk material followed by rapid solidification and subsequent solid-state cooling (Breinan and Kear, 1976; Breinan et al., 1976). This process has also been referred to as self quenching, laser annealing, laser glazing, layer glazing, etc. However, in order to avoid possible confusion with other similar terms used in metallurgy, the term laser surface treatment has been suggested by Cahn (1983) (see also Chapter 3).
94
2 Rapid Solidification
Table 2-3. Rapid solidification techniques and product parameters. Technique
Product tpye
Typical dimensions (um)
Typical cooling
Comments
Gas atomization
Smooth, spherical powder
50-150 dia.
10 2 -10 3
Water atomization
Rough, irregular powder Smooth, spherical powder Smooth, spherical powder Elongated splats
75-200 dia.
10 2 -10 4
Inert gas (nitrogen, argon) used where oxidation is a problem Used on tonnage scale
10-50 dia.
up to 106
25-80 dia.
10 5
40-100 thick
10 4 -10 7
125-200 dia.
10 2
< 50 dia., possible 1000-5000 long x 1000 dia. 20-100 dia.
10 4 -10 6
Powder, flake or coating Spherical or irregular Variable, powder to flake Foils Thick deposit
0.01-100 dia.
up to 107
0.5-30 dia.
10 5 -10 6
200 thick flake
10 5 -10 6
0.1-10 thick > 1 mm thick
106_108
Plasma spray deposition Chill methods
Coherent deposit
> 1 mm thick
3.2 Fundamental Considerations
i
— Excimer
|
Reduction
| |
j
(4-10)
Blending
|
i
I Soft grades | | Hard grades |
Figure 4-6. Flowsheet for the manufacture of carbonyl iron powder.
metallic compounds have also been used to produce metal powders by decomposition. Decomposition of the hydride is also an effective method for producing titanium and zirconium powders via the hydridedehydride route. The ductile metal or its alloy is first converted to its hydride by reaction with hydrogen at 700-900 K under pressure. The friable hydride is easily crushed to powder of the required fineness and then decomposed to the metallic powder by heating under vacuum. 4.2.2.3 Precipitation
Copper powder is sometimes produced by displacing the copper ion in the salt solution (generally copper sulfate) by iron. The extent of precipitation is controlled by factors such as the pH value of the solution. Precipitation of metals from salt solutions can also be achieved with gases such
]p H 2
(4-11)
Both nickel and copper powders are produced directly from the leached ores using this route. Various organic surface-active agents are used as additives to control the powder characteristics. An extension of this process is the precipitation of composite particles by suitably seeding the second phase particles in the solution. Precipitation from the vapor phase is also sometimes used to produce metal powder. A case in point is the production of fine, spherical powders of the refractory metals W and Mo from their gaseous hexafluorides. 4.2.2.4 Self-Propagating High Temperature Synthesis
Self-propagating high temperature synthesis of powders of ceramic and refractory compounds and alloys is a recent innovation. In this process, a porous compact made from a mixture of the reagents is brought into contact with a hot tungsten coil. This initiates an exothermic reaction which continues as a self-sustaining combustion wave propagating through the porous mass and converting it into the reaction products. The scheme of the reaction synthesis is shown in Fig. 4-7 (Crider, 1982). Depending on the temperature of the reaction, synthesis can be entirely in the solid state as gasless combustion, partly in the gaseous state as filtration combustion, or entirely in the gaseous state as condensed combustion. Of these, gasless combustion can be used for the production of powders suitable for PM applications (Munir and Anselmi-Tamburni, 1989).
4.2 Production of Powders
Rate of thermal release
Direction of wave
Initial substances
n
k y IK Zone of heating
151
\J 1 j I
Zone of synthesis
s— Temperature
\ - D e p t h of transformation Figure 4-7. Equilibrium adiabatic structure of a self-propagating high tem perature synthesis wave (Crider, 1982). Final product
The synthesis can be designed on the basis of the adiabatic temperature of combustion, the combustion wave velocity and activation energy for the compound formation. For a useful reaction, the adiabatic temperature Tad must be lower than the melting temperature of the reaction product (Munir, 1988). The value of Tad of a compound can be computed on the basis of its enthalpy of formation {AH0) and its heat capacity Cps and compared with the melting temperature to evaluate the feasibility of the reaction. The process has relatively low energy requirements and is highly cost-effective. With an exothermic reaction, the processing time at high temperatures is short and the purity of the powder can be maintained. Metastable phases such as cubic TaN and composites such as MoS 2 /Nb can be made by this process. The process is already in use in the USSR for the production of TiC abrasive powders, TiNi memory alloys and MoSi2 heating elements. 4.2.3 Electrochemical Methods
Metals of high purity can be precipitated from aqueous solutions on the cathode of an electrolytic cell in a spongy form to produce powder by subsequent comminution.
This method is mainly used in the production of copper and iron (Willis and Klugston, 1959). Fused salt electrolysis has also been used for the production of tantalum and beryllium powders (Miller, 1958). The factors that promote powdery deposits are high current densities, weak metal concentrations, low temperatures, and surfactants to promote high viscosities. All these factors also lead to low deposition rates and high costs. With increasing energy costs, electrochemical methods of powder production are being phased out (see also Chapter 11). 4.2.4 Physical Methods
Atomization is a process of breaking up liquid metal or alloy into fine droplets and allowing them to solidify as powder. Because of the versatility, purity and the control of powder shape inherent in the process, atomization is becoming increasingly popular as a route for large scale manufacture with attendant reduction in costs. Many techniques are available for breaking up a liquid metal stream into fine droplets which are then allowed to solidify by exchange of heat with the surroundings. Most common among these are the impingement of high speed jets of gas or wa-
152
4 Powder Metallurgy
ter on the liquid metal stream. This technique is limited to metals and alloys that do not chemically react with the impinging gas or water. There are also variations where the liquid metal stream is directly fragmented by centrifugal forces. These are used for producing powder from reactive metals and superalloys which are sensitive to gas contamination. There are also other techniques like vacuum atomization and ultrasonic atomization which are used in special cases. 4.2.4.1 Principles of Atomization
In conventional atomization, a liquid metal stream is produced by pouring molten metal through a tundish which is then broken into droplets by the impingement of high pressure gas or water. This disintegration of the liquid is shown schematically in Fig. 4-8. The interaction between the jets and the liquid stream begins with the initiation of small disturbances at the liquid surface which grow into shearing forces that fragment the liquid into ligaments. The energy of the jets is so large that the broken ligaments are further fragmented into droplets which can reach very
Stage I Growth of waves on liquid sheet
Stage II Fragmentation and formation of ligaments
small sizes (Shinde and Tendulkar, 1977; Lawley, 1977). The liquid metal stream has a velocity v given by =
A[2g(Pl-Pg)/Q] 0.5
(4-12)
where A is a geometric constant and g, the acceleration due to gravity; Px is the injection pressure of the liquid metal, Pg the pressure of the atomizing atmosphere and Q is the density of the liquid. The shearing forces in atomization that lead to the formation of ligaments from the liquid metal depend on the Reynold's number, Re, which in turn, is related to the size and velocity of the stream and the density and viscosity of the liquid metal. There are several empirical equations for calculating the average particle size in atomization. The most frequently used one for determining the average particle size d is given by d=A
y
0.45
/•M.5
1000 y
Stage III Breakdown of ligaments into drops
Figure 4-8. Mechanism of droplet formation in atomization (Lawley, 1981).
(4-13)
4.2 Production of Powders
where Q is the density of the liquid, y, the surface tension, rj, the coefficient of viscosity and v, the relative velocity between the liquid and gas jets; /, is the flow rate of liquid, / a , the flow rate of air and A and B are constants. Another empirical equation for the particle size is
153
for instance, even with high surface tension, aluminum and zinc tend to solidify as irregular particles because of oxidation effects. The mechanism of centrifugal atomization is different because of the process design. In this technique, the molten pool is rotated at high speed till the liquid flows over the rim of the container and is frag0.5 mented by the centrifugal force acting on (4-14) it. As the cooling rate in this process is slow Wr,. in the absence of gas jets, centrifugally atomized powders tend to be spherical. It where Wis the Weber number of the metal may also happen that the time of flight of stream, vg, the velocity of the atomizing the liquid droplet to hit the chamber walls medium, du the diameter of the liquid metal stream; rjx and r\% are the kinematic is smaller than the time required for solidification. In such instances, the particles viscosity of the liquid metal and gas, and appear as flat discs solidified on impact K, a constant. with the walls. Both these equations show the particle Because of the rotation of the molten size to decrease with decreasing surface pool, the liquid metal spreads towards its tension of the liquid metal and increasing periphery and forms a toroidal rim. Owing velocity of the atomizing medium. In practo instability at the rim, the sheet of the tice, for a given nozzle design, the average liquid breaks up into fine threads, which in particle size is controlled by the pressure of turn break into droplets surrounded by the atomizing medium and also by the smaller droplets known as satellites. The apex angle between the axes of the gas jets. mean diameter d of the main drop can be Higher apex angles lead to smaller particle estimated by balancing the surface tension sizes. force against the centrifugal force and is The particle shape in gas or water atomgiven by (Hodkin et al, 1973) ization depends largely on the surface tension and the solidification rate (Lawley, 1977). While the surface tension of the drop (4-15) tends to spheroidize it, the cooling rate limits the time available for this process. If, for instance, the time for solidification is larger where co is the rotation rate, y, the surface than the time required for spheroidization, tension and D, the melt pool diameter. The above equation is strictly valid only for the then spherical particles will result. For promain droplets, and it is difficult to calculate ducing fine spheres, it is necessary for the either the particle size or the distribution of solidification to be as late as possible bethe satellite sizes as the mechanisms underfore the droplets hit the chamber wall. Belying their formation are not fully undercause of this condition, iron and copper stood. solidify readily as fine spherical powders, Since the flight of the atomized droplets while lead and tin solidify as irregularly is entirely dictated by friction and gravity shaped powders. There are also other facopposing the centrifugal momentum, the tors that contribute to the particle shape:
154
4 Powder Metallurgy
trajectory can be easily calculated. The droplet cooling AH in time At is given by AH=-nKdNu(Td-Tg)At + T(t-T*)At
(4-16)
where Td, Tg and Tw are the temperatures of the droplet, the gas and the chamber wall respectively; e is the emissivity of the droplet, s the Stefan-Boltzmann constant and Nu the Nusselt number of the cooling gas flow. On the basis of Eq.(4-16), it is possible to design the cooling parameters and chamber size appropriately for centrifugal atomization. 4.2.4.2 Gas and Water Atomization
Inert gas atomization plant
Vacuum melting
A typical atomization unit consists of a melting facility, an atomizing chamber, and powder drying and collection unit (Gummeson, 1972) as shown in Fig. 4-9. Typical atomization parameters are given in Table 4-2, and some atomized powders are shown in Fig. 4-10. Any of the standard melting furnaces is acceptable for producing the liquid metal. However, complex alloys prone to contamination are usually melted in a vacuum induction furnace or by skull melting with an electron beam. The molten metal is then poured into a tundish with a top ceramic filter and a bottom nozzle which controls the shape and size of the falling metal stream. This stream passes through an atomizing nozzle sys-
Table 4-2. Typical atomization variables. Parameter Powder collection
Figure 4-9. Inert gas atomization unit (Courtesy DMRL).
Flow rate Flow velocity, m/s Pressure, MPa Superheat, °C
Liquid metal Water jet 4.5-90 kg/min — — 75-150
Gas jet
100-400 1-14 1/min m3/min 70-230 20-supersonic 5.5-21 0.3-8.5 -
4.2 Production of Powders
155
Figure 4-10. Atomized powder particles: (a) bronze, water atomized, (b) aluminum, water atomized, (c) high speed steel, water atomized, (d) aluminum, ultrasonic gas atomized, (e) Nimonic 80 A, argon gas atomized, and (f) Astroloy, argon gas atomized.
156
4 Powder Metallurgy
tern, in which the high velocity jets of the atomizing medium (gas/air/water) strike and disintegrate the stream into fine droplets. These droplets are carried at high velocity with the atomizing gas stream inside the chamber and solidify owing to heat loss by convection. It is possible to increase the solidification rate by cooling the atomizing gas, or even by pumping additional precooled gas from the bottom of the chamber. The selection of the atomizing jet medium is based mainly on the reactivity of the metal and the cost of the medium. Air and water are inexpensive, but react with many molten metals. Inert gases can be expensive and it may be necessary to recycle the gas when helium is used as the atomizing medium. The heat transfer characteristics of the gases are different as shown in Table 4-3 and these also determine the particle size and other characteristics; but the mechanism of atomization is independent of the medium. Nozzle design controls the efficiency of disintegration and thus dictates the final characteristics of the powder. The nozzle can be an annular concentric ring around the metal stream, or can be a set of discrete jets (Klar and Fesco, 1984). The nozzle design also incorporates the choice of a "free fall" or "confined" atomization. In the free fall atomization, disintegration takes place some distance ahead of the tundish orifice, while in confined atomization the disintegration is at the tundish orifice itself. Confined atomization with its higher efficiency of energy transfer is used for gas atomization. The apex angle for water atomization is smaller than for gas and is designed for free fall atomization. Spherical and fine powders are difficult to produce in water atomization and particles generally tend to be irregularly shaped. The process is also lim-
Table 4-3. Heat transfer coefficients for convective cooling of liquid metal droplets by different gases. Cooling gas
Argon Nitrogen Helium
Heat transfer coefficient, W x 10 3 /m 2 K for droplet diameter (in jim) 1
10
100
1000
49.0 70.8 350.0
11.8 16.8 60.0
3.3 4.7 10.0
1.02 1.45 3.00
ited only to metals and alloys from which the surface oxide can be easily removed by mechanical or chemical methods. 4.2.4.3 Centrifugal Atomization
The driving force for the development of centrifugal atomization processes has been the cleanliness of the product. These processes avoid gas jets and atomization nozzles, and therefore the liquid metal continues to remain pure during the entire process. Thus this method is eminently suited for atomizing reactive metals such as titanium and zirconium. Several centrifugal atomization processes have been developed, as listed in Table 4*4. On the Table 4-4. Centrifugal atomization processes. Mode of Mode energy of transfer melting Direct
Arc
Process
References
Rotating electrode Friedman process (REP) (1970) EB 'Pulverisation Decours sous vide' (PSV) (1976) Rotating rod Arunachalam process (RRP) etal. (1975) Plasma Plasma rotating Roberts rod process (PREP) (1984) Indirect Arc Centrifugal shot Hodkin casting (CSC) (1973) EB Electron beam Stephan rotating disc and Fischprocess (EBRD) hof(1976)
4.2 Production of Powders
basis of the mode of centrifugal energy transfer, the processes can be broadly divided into direct energy transfer processes where the liquid metal pool itself is rotated, and indirect transfer processes where the liquid metal is poured on to a rotating surface. Among the processes listed, only the rotating electrode process (REP) and plasma rotating electrode process (PREP) are commercially well developed. These are direct energy transfer processes, where a rod is rotated at high speed and simultaneously melted at one end. The melting is carried out with a tungsten electrode as in a vacuum arc furnace or with another electrode of the same material. The centrifugally atomized liquid droplets are cooled by convection with the helium gas present in the atomizing chamber and the powder is collected at the bottom. A schematic diagram of a REP atomization chamber is shown in Fig. 4-11. There are many variations to the design shown in the figure. In one variant, a long rod to be atomized is fed through a vacuum seal into the chamber, with the rotating mechanism kept outside. In another variant, small electrodes are kept within the chamber itself and are substituted into the rotating spindle as and when the molten electrodes are consumed. A glove compartment is provided to effect this substitution without breaking the furnace atmosphere. In an indirect energy transfer process, liquid metal is poured through a tundish on to a fast rotating disc which acts as a rotary atomizer. The centrifugally atomized droplets are cooled by precooled helium gas before solidification. By this, it is possible to solidify the droplets rather rapidly, generally with a rate higher than 105 K/s. Rapidly solidified nickel base alloy powders have been produced by this process and subsequently formed by iso-
Water cooling
157
Rotating consumable electrode
0 Stationary electrode Inert •£ gas (He)
Vacuum Collection port
Figure 4-11. Schematic of rotating electrode process (Lenel and Ansell, 1982).
thermal forging for the manufacture of high-temperature turbine discs for gas turbines. On the other hand, REP and PREP powders are generally large-sized and spherical with a cooling rate of about (102 K/s). It is therefore not possible to produce rapidly solidified powders by these routes. 4.2.4.4 Ultrasonic Gas Atomization Ultrasonic atomization is used for the production of powder with particle size finer than those obtained in conventional atomization. The process is similar to conventional gas atomization except for the discrete gas jets impinging on the metal stream in a pulsed fashion, with frequencies of 40-100 kHz. The high speed gas jets are accelerated by a shock wave tube to speeds up to Mach 2. The shearing action results in fine droplets, usually less than 30 jim and with very high cooling rates (up to 106 K/s) as well. Ultrasonic atomization has so far been used for low-melting alloys based on aluminum and is yet to be widely applied.
158
4 Powder Metallurgy
4.2.4.5 Vacuum Atomization
4.2.4.6 Rapid Solidification
Vacuum atomization, or soluble gas atomization, employs the difference in solubility of gas in liquid metal at different pressures to fragment the liquid into fine droplets. In this process, the molten metal is first supersaturated with a soluble gas under high pressure and the liquid stream is then suddenly exposed to vacuum. The supersaturated gas almost explodes out of the liquid fragmenting it into very fine droplets. A schematic diagram of the process is shown in Fig. 4-12. Alloys of iron, cobalt, nickel, copper and aluminum have been vacuum-atomized with hydrogen as the dissolved gas. The powders are generally fine and spherical. As this process depends exclusively on dissolved gases, it has only limited applicability and is not being used extensively.
Many techniques have been developed employing the advantages of rapid solidification processing (RSP) for utilizing metastable phase structures to advantage (see Chapter 2). Most of the conventional atomization processes discussed in the earlier sections lead to a normal cooling rate of 103 K/s. With some enhanced heat transfer techniques, several atomization techniques have been developed to achieve cooling rates of over 104 K/s. Such techniques with increased cooling produce rapidly solidified powders, flakes, wires and strips (Grant, 1983; Savage and Froes, 1984). Rapid solidification techniques developed (Table 4-5) are based on atomization, continuous casting, melt extraction and melt extrusion (Jones, 1981, 1982). In rapid solidification rate centrifugal atomization (Fig. 4-13), liquid metal is centrifugally atomized off a disc rotating at very high speeds (35 000 rpm) and the droplets cool by flight through high velocity helium gas streams to give powders in the size range 25-100 \im (Cox et al., 1976). An impinging melt stream contacts a moving chill surface in chill block melt spinning, planar flow casting and free jet casting to produce tapes with thickness 10-100 |im and widths 3-250 mm. In melt extraction processes, a rotating disc is brought into contact with a liquid metal pool for producing rapidly solidified fibers and tapes (see Chapter 2). While the rapidly solidified atomized powders can be consolidated directly, in the case of tapes and fibers, some comminution or shredding is necessary for further PM processing. Often the RS powders see application in the form of powder itself. For applications that call for consolidation of the RS powders, suitable consolidation techniques are employed with minimum
Vacuum
— Powder collection tank
Melting crucible
|— Powder drain Induction heater Vacuum
— Container
Figure 4-12. Schematic of vacuum atomization unit (Lawley, 1986).
4.3 Characterization of Powders
159
He gas input
H t
Figure 4-13. Schematic of rapid solidification rate atomization process (Joensson and Hohmann, 1987).
Air out
Table 4-5. Rapid solidification techniques. Process
Atomization Centrifugal Atomization Splat Extraction
Technique
Product type
Powder size, urn
Cooling rate, K/s
Application
Water atomization Ultrasonic gas atomization Rapid spinning cup Rapid solidification rate Electron beam splat quench Twin roll atomization CBMS PFC/MD CME/PDME
Irregular Spherical Variable Spherical Splat Flaky Tape < 3 mm Tape, wide Filament /Fiber
75-200 10-50 50 at. % Si) the lattice parameters fell on the linear extrapolation between the lattice parameters for pure Ge and Si (Vegard's "law"). However, in Ge-rich alloys (>50 at.% Si) the lattice parameters of the as-milled powders were larger than predicted for Vegard's law. Annealing the alloys with the expanded lattice parameters serve to decrease them in the direction of the Vegard's law line - i.e. partial "recovery" was observed. Impurities are apparently not responsible for the expanded lattice parameters in Ge-rich MA Ge-Si alloys. The possibility of nonequilibrium (e.g., partially interstitial) solid solutions is being explored with further study of the recovery of the lattice parameters by annealing (Leonard and Koch, NCSU, work in progress). Another example of an apparent nonequilibrium solid solution due to MA was noted during MA of pure Nb and Sn powders to form initially the A15 intermetallic compound, Nb 3 Sn, which then was found to transform to the amorphous structure on further milling (Kim and Koch, 1987). The lattice parameter measured for the A15 phase which was MA with tungsten carbide milling media under
217
argon was 0.529 + 0.001 nm, in excellent agreement with literature values for bulk A15 Nb 3 Sn. The powder milled with steel media, however, exhibited expanded lattice parameters. The oxygen levels in both sets of samples were similar, but the samples milled with the steel balls and vial contained significant quantities of iron impurities incorporated from the milling media. The apparent expansion of the Nb 3 Sn lattice by Fe impurities is in contrast to the results of Caton (1985) who measured a small contraction of the A15 Nb 3 Sn lattice with iron additions in sintered material. The latter result is consistent with the smaller atomic radius at Fe (0.127 nm) compared to Nb (0.147 nm) and Sn (0.155 nm) (Pearson, 1972). Since it appears that the lattice expansion in MA Nb 3 Sn is due to incorporation of Fe, it is concluded that Fe must be present in the Nb 3 Sn lattice in a non-equilibrium, perhaps partly interstitial, arrangement. 5.5.2 Intermediate Phases
Intermediate phases and intermetallic compounds have been synthesized from the pure components by MA in several alloy systems. The equilibrium Hume-Rothery electron compounds, p'-brass (McDermott and Koch, 1986), y-brass, and e-brass (McDermott, 1988), were synthesized by MA of pure Cu and pure Zn powders mixed in the proper proportions. Thus the equilibrium intermediate phases were synthesized by MA of the elemental components. In the case of P'-brass, evidence for f.c.c. deformation-induced martensite was observed by X-ray diffraction as a minor phase in the p'-brass matrix. A nonequilibrium phase was therefore also present as a result of the plastic deformation which is an integral part of MA. Lee et al. (1990) have shown that the y-brass (Cu5Au8)
218
5 Mechanical Milling and Alloying
phase is very stable to milling. Milling for 60 h in a planetary mill only served to broaden the X-ray diffraction lines but did not alter their positions. Similar milling conditions easily lead to amorphization in other compounds such as NiZr 2 . The stability of Cu 5 Zn 8 was attributed to the modest value of stored energy of cold work obtained by milling (2 kJ mol" 1 ) compared to the free energy difference between the Cu 5 Zn 8 compound and its supercooled liquid at 300 K (9 kJ mol" l ). Kim (1987) and Koch and Kim (1985) synthesized the intermetallic compounds Nb 3 Ge, Nb 5 Ge 3 , and NbGe 2 by MA of elemental Nb and Ge powders. In the cases of Nb 3 Ge and Nb 3 Sn, continued milling eventually resulted in the formation of an amorphous phase. The topic of amorphization will be discussed in more detail in Sec. 5.6. Ivanov et al., 1988, studied the synthesis of Ni and Co aluminides and amorphous alloys by MA of the elemental powders. They showed the formation of the intermetallic compound Ni 2 Al 3 from mixtures of Ni and Al powders at a composition of Ni 40 Al 60 . Continued milling produced a metastable P'-NiAl phase which reverted to the rhombohedral Ni 2 Al 3 phase after annealing. Powder of composition Ni 30 Al 70 formed a metastable Ni 2 Al 3 intermetallic on MA that decomposed to two-phase Ni 2 Al 3 and Al3Ni by annealing. Ni 75 Al 25 powder composition formed an f.c.c. solid solution which ordered to the Ll 2 , Ni3Al compound on annealing. The formation of an amorphous alloy was observed in a narrow range of composition (27 to 35 at.% Al). Atzmon (1990) has made very interesting observations relevant to the mechanism for MA during the synthesis of Al3Ni and NiAl intermetallic compounds by MA of elemental Ni and Al powder in a SPEX shaker mill. In a powder mixture of
composition Al 75 Ni 25 MA produced the Al3Ni compound in a gradual manner consistent with layer diffusion. The reaction at 60 °C (ambient conditions) was faster than at 35 °C (cooling with a fan) presumably because of the higher interdiffusion coefficient. The formation of the NiAl compound was found to depend on the vial temperature, the atmosphere in the vial, and whether milling was interrupted or continuous. Gradual transformations to NiAl occurred for continuous milling (2.5 h) in pure argon at 35 °C and at 60°C in argon (2 h). Transformation to NiAl was seen at somewhat shorter milling times at 35 °C in a mixture of air and argon. The fascinating observation occurred after milling in pure argon at 35 °C for 1.7 to 2 h. Milling was then stopped for periods of 1 to 12 h, allowing the vial to cool to room temperature. Separate experiments showed that the powder at this stage was still elemental Al and Ni mixed lamellae. Shortly (30 to 60 sec later) after resumption of milling after such a pause, an exothermic reaction occurred. A thermocouple mounted in the vial bottom indicated temperature rises of 27 °C within about 1 sec while a thermocouple in the side wall showed a rise of 20 °C in 7 sec. Atzmon estimated that under adiabatic conditions this exothermic heat released from the sample as 49 kJ mol" 1 which is comparable to the heat of formation of NiAl (59 kJ mol" 1 ) given the approximate nature of the measurement. In fact, again assuming adiabatic conditions, it was estimated that the heat of formation of NiAl was sufficient to bring solid NiAl from 25 °C to 1738 °C (100 °C higher than its melting point). Atzmon speculated that the interruption and subsequent cooling (and possibly oxidation?) result in lower ductility and therefore resumed milling leads to energy concentration in smaller volumes, re-
5.5 Synthesis of "Equilibrium" Phases by Mechanical Alloying
suiting in higher local temperature upon impact. This explanation seems unlikely since Al and Ni do not normally exhibit ductility losses at low temperatures, and the average temperature difference (35 °C to 25 °C) is so small. More research is needed to understand this important experiment. Kumar and Mannan (1989) observed a similar rapid phase formation during MA of a mixture of pure Nb and Si powders at an average composition corresponding to Nb 5 Si 3 . After milling for 73 min in a SPEX mill the powders remained elemental Nb and Si as determined by X-ray diffraction. Only two more minutes of milling (perhaps less), i.e. X-ray examination at a total milling time of 75 min, resulted in complete transformation to crystalline Nb 5 Si 3 in three tetragonal allotropic forms: oc-Nb5Si3, the stable room temperature form; p-Nb 5 Si 3 , the high temperature form; and y-Nb 5 Si 3 , believed to be stabilized by the presence of impurities. Further milling increased the amount of P-Nb5Si3 at the expense of ot-Nb5Si3 and y-Nb 5 Si 3 . No temperature measurements were made, but since Nb 5 Si 3 is a high-melting point intermetallic with an estimated heat of formation o f - 5 4 kJ mol" 1 (de Boer et al., 1988) an exothermic reaction as in the case of NiAl is likely. A much larger exothermic heat effect has been observed during the reduction of CuO by Ca by mechanical alloying (Schaffer and McCormick, 1990). This will be discussed later in the Chapter. Therefore, it appears that in the case of compound formation or chemical reactions with large exothermic heats of reaction, significant heat input leading to high temperatures and even explosive reactions can occur by mechanical alloying. This is in contrast to the very modest ( < 1 0 0 200 °C) temperature rises usually attributed to the heat generated from the kinetic energy of the milling media.
219
Morris and Morris (1990) used mechanical alloying in a Fritsch Mini-Planetary ball mill to synthesize the Cr 2 Nb intermetallic compound from elemental Cr and Nb powders. After about 15 h of milling X-ray diffraction lines of the hexagonal Laves phase, Cr 2 Nb, were observed. This is the stable phase at high temperatures but it undergoes an allotropic transformation to the cubic Laves phase at about 1600°C which is the room temperature equilibrium phase. Further milling to 20 and 25 h resulted in the disappearance of the hexagonal Cr 2 Nb Laves phase and the reappearance of b.c.c. lines of Cr and Nb. Such "demixing" reactions due to milling will be discussed further in Sec. 5.6. However, Kumar (1990) did not observe the formation of the Cr 2 Nb intermetallic compound on milling elemental Cr and Nb powder at compositions from 49 to 52 wt. % Cr (within the Cr 2 Nb phase field). He observed the evolution from the elemental components to an amorphous structure during milling in a SPEX shaker mill. The differences in these results can not be assessed without more information. Kumar carried out his milling in an argon atmosphere in the milling vial while the milling atmosphere in the work of Morris and Morris was not reported. Vial temperatures were not reported for either experiment. These very different results on milling the same components point out how critical the milling variables such as atmosphere, vial temperature, and mill energetics must be with regard to the end products of the solid state transformations induced during milling. A number of intermetallic compounds have been produced with MA as the first step in a synthesis procedure. Benn et al. (1988) have reviewed several intermetallic compound systems where an intimate mixture of the elemental components was at-
220
5 Mechanical Milling and Alloying
tained by MA, as well as partial compound formation in some cases. The intermetallic synthesis was then completed during the thermomechanical treatments carried out for compaction of the powders. Larson et al. (1977) have produced the A15 structure intermetallic Nb 3 Al by MA of stoichiometric mixtures of Nb and Al powders followed by heat treatment. Similarly, (Benn et al., 1988), Ti3Al and TiAl have been synthesized by milling in the presence of a process control agent under inert atmosphere. Subsequent heat treatment at 540 °C (Ti3Al) or 600 °C (TiAl) produced the given intermetallics. The compound Al3Ti is difficult to prepare by conventional ingot metallurgy because of the high Al vapor pressures, the large differences in melting points between Al and Al3Ti, and the peritectic solidification behavior. It has, however, been synthesized by MA followed by annealing (Benn et al., 1988). 5.5.3 Immiscible Alloy Systems Mechanical alloying offers one of the few methods for producing a homogeneous mixture of two or more immiscible phases. This is the case for the ODS alloys where the oxides are essentially insoluble in the metallic matrices. More generally, MA may be applied to binary alloy systems that exhibit solid, or even liquid, immiscibility. Benjamin (1976) described the synthesis by MA of homogeneous mixtures of Fe-50 wt. % Cu, a system that exhibits limited solid solubility, as well as Cu-Pb alloys for which there is a liquid miscibility gap. Patel and Diamond (1988), have used MA, sometimes in conjunction with rapid solidification methods, to synthesize fine homogeneous phase distributions in immiscible alloys such as Cu-Cr, Al-In, CuW and in immiscible Cu-base bearing alloys such as Cu-Pb-Sn.
Green et al. (1984) have developed a novel electrical contact material by MA of Cu-15 vol.%Ru mixtures. Copper and ruthenium are mutually insoluble. A CuRu composite was produced by MA the elemental powders, annealing the MA powders, cold-pressing, and warm rolling the composite. Cold-rolling and annealing were used to obtain the final strip dimensions. Scanning electron microscopy (SEM) revealed the final size of the Ru particles to be about 1 to 2 jim in diameter. Removal of surface copper by etching produced a structure in which the hard, refractory, and conductive Ru particles protrude from the surface and serve as the electrical contacts, supported by the Cu matrix that provides electrical continuity. Iron and magnesium are immiscible in the solid state and form a large miscibility gap in the liquid state (Kubaschewski, 1982). Konstanchuk et al. (1987) studied the hydriding properties of a Mg-25 wt. % Fe composite produced by MA. The microstructure after MA consisted of a laminated mixture with iron dispersed in a magnesium matrix. Clean metallic contact was achieved at the Mg/Fe interfacial boundary; surface oxides of iron being reduced by magnesium to form a clean metallic surface. A separate experiment was conducted to show that the magnesium did indeed reduce Fe 2 O 3 to Fe during the MA process. The Mg-25 wt. % Fe composite exhibited a large hydrogen storage capacity (5.1 to 5.8 wt. %) and the rate of hydriding was considerably higher than that for pure magnesium. At hydriding temperatures above 625 K, a ternary hydride, Mg 2 FeH x , formed which inhibited dehydriding reaction rates. Thus, a temperature of about 615 K was deemed to be optimum for the hydriding reaction. A question regarding the phase distribution in mechanically alloyed immiscible
221
5.5 Synthesis of "Equilibrium" Phases by Mechanical Alloying
of the system, i.e., large positive heat of mixing. With sufficient mobility, the like atoms will segregate together. An order of magnitude estimate for this segregation, using *jDt as the characteristic diffusion distance, and ambient temperature diffusion coefficients, was consistent with the microstructural observations. A particularly interesting observation from the study of MM immiscible Ge-Sn and Ge-Pb systems was the depression of the melting point of Sn or Pb with milling time and Ge concentration. The first observation of the melting point depression was noted in DSC scans for a Sn-45 vol. % Ge mixture as a function of milling time (Koch et al., 1989). The magnitude of the melting point depression, ATm, increased with milling time, that is, with refinement of the dispersion. Melting point depressions were defined from the DSC endotherms as A7^ eak and A7^ail as illustrated in Fig. 5-16. The magnitudes of the AT^'s were found to reach constant values after 32 h of milling. After 32 h of milling the average diameters of the hard Ge particles embedded in the Sn (or Pb) matrix were
-rtail 1 M
T peak 1
M
T
t
uni
(f)
-
flow larbit
systems is: what is the lower size distribution limit to which immiscible particles can be milled? Since in solid solution alloys, MA can result in alloying at the atomic level, very fine particle distributions might be attainable by MA immiscible components. Mechanical alloying has recently been applied to the immiscible systems Ge-Sn, Al-Ge, and Ge-Pb with the goal of determining the limits of phase refinement (Gross, 1988). Mechanical alloying was carried out for milling times up to 60 h under an air or argon atmosphere in a SPEX mixer/mill. Some tests were conducted with the milling vial cooled with a stream of liquid nitrogen. X-ray diffraction of powder taken at various milling times showed the systems remained as twophase pure components and their precise lattice parameters remained constant with milling time, which indicated no alloying or contamination to the accuracy of the lattice parameter measurements. Optical microscopy, SEM, and transmission electron microscopy (TEM) were used to follow the progress of the microstructural refinement with milling time. The average center-to-center nearest neighbor distance between dispersed Ge particles was measured by the above metallographic techniques. The logarithm of Ge interparticle distance exhibits an inverse linear dependence on milling time. After 32 h of milling, the average Ge interparticle distance was about 20 nm. Stereology techniques determined that the Ge particles had a random Poisson distribution throughout the Sn matrix. Further milling did not appear to significantly change the particle sizes or distributions so the limit of refinement was attained for the given milling conditions in this system. The mixing of these insoluble components by mechanical attrition is balanced by the demixing driven by the thermodynamics
^
\
/
V
X
180
200 220 Temperature in °C
240
Figure 5-16. DSC scan for the melting of Sn in Sn45.5 vol.% Ge powder milled 32 h. 7geak and T£il are defined as shown (Jang and Koch, 1990 a).
222
5 Mechanical Milling and Alloying
approximately 10 nm. As Ge concentration was increased in each system, for a constant milling time of 32 h, the melting point of Sn (or Pb) decreased (Jang and Koch, 1990a). ATm for Sn is plotted against vol. % Ge in Fig. 5-17. The melting point depression increases with vol. % Ge. No ATm data are shown for Ge concentrations > 80 vol. % because no endothermic peak could be seen for the melting of Sn for samples containing > 80 vol. % Ge. This is not a problem of resolution. Unmilled powder of 88 and 95 vol. % Ge clearly showed a well-defined endothermic melting peak in the DSC at the Tm of pure Sn, and with the enthalpy of fusion for pure Sn, 60 J g" 1 . The enthalpy of fusion for Sn, determined from the area of the melting endotherms, is plotted against vol. % in Fig. 5-18. The enthalpy of fusion, A// m , decreases with Ge concentration and finally disappears for the Ge-rich mixtures (88 and 95 vol. % Ge). Only minor changes in Tm and AHm were observed after heating the samples in the DSC through the melting point, cooling to room temperature, and re-heating. These experimental results suggest that the premature melting is nucleated at the Ge/Sn interfaces. As the fraction of Sn atoms adjacent to the Ge particle surfaces increases, the melting point and enthalpy of fusion decreases. When the density of Ge particles becomes so large that all the Sn atoms are within a few atomic layers of the interface, the Sn may assume a disordered or amorphous structure. Selected area electron diffraction patterns were obtained on samples of 76.5 vol.% Ge and 88 vol. % Ge. The electron diffraction pattern for the 76.5 vol. % Ge sample shows a ring and discrete spots for the (101) reflection of crystalline Sn. This reflection is not seen for the 88 vol. % Ge sample but a ring of diffuse intensity is observed near the
50 m
40
• •
•
A
O
30
•
o
:20
•
9
A
o
•
10
20
o
o
•
A
40 60 vol.% Ge
80
100
Figure 5-17. Melting point depressions, A7^ eak and AT^ail for Sn as a function of vol.% Ge after milling 32 h. ATNJeak is also shown for samples milled 32 h and then cycled once to a temperature >505 K. • Ar,Jail: o ATfPeak: A A7^eak after heating cycle to >505 K (Jang and Koch, 1990 a). 70.0
40
60
80
100
vol.% Ge Figure 5-18. Enthalpy of fusion of Sn as a function of vol.% Ge after milling 32 h. Data for samples cycled once to above 505 K are also shown, o as-milled: A after heating in DSC to > 505 K: A unmilled Sn88 vol.% Ge (Jang and Koch, 1990a).
position where the (101) Sn line should appear. The electron diffraction data suggest that an amorphous structure has been induced in the Sn layers trapped between the Ge particles by milling for the 88 vol. % Ge sample. That mechanical milling of powder of immiscible components can result in a very
5.5 Synthesis of "Equilibrium" Phases by Mechanical Alloying
fine dispersion at the level of nanocrystalline dimensions has been demonstrated by Schlump and Grewe (1989) in systems such as Fe-W, Cu-Ta, TiNi-C, and W-NiC. Similarly, Shingu et al. (1989) found a fine grain structure in immiscible Ag-Fe powders at the nanometer level. Nanocrystalline structures prepared by ball milling will be discussed in more detail in Sec. 5.6.6. Fukunaga et al. (1990) give evidence for at least the partial amorphization of the immiscible system Cu-Ta. Iron impurities from steel milling media accelerated the amorphization reaction, but amorphization was still observed when milling was carried out with Cu-Be balls and vial. This experiment will also be discussed further in the Section 5.6.3 on amorphization by milling. 5.5.4 Synthesis of Materials for Special Applications Mechanical alloying/milling has been used to prepare unique materials for a variety of special applications. The excellent permanent magnet material, Nd 1 5 Fe 7 7 B 8 (see Vol. 3A, Chap. 5), has been prepared by MA of the elemental powders followed by annealing (Schultz etal., 1987). The milling was carried out under argon in a cylindrical steel chamber in a planetary ball mill. The Fe and Nd particles are milled (30 h) until the Nd Xray diffraction peaks are no longer visible and only broadened peaks for Fe are observed. Amorphous boron particles do not mechanically alloy with the Fe-Nd matrix. After annealing 1 h at 600 °C, the boron does dissolve in the Fe-Nd powder and the Nd 2 Fe 14 B phase is formed. The magnetically isotropic particles so formed have a very fine microstructure comparable to rapidly quenched samples, exhibit a do-
223
main wall pinning behavior and have excellent hard magnetic properties such as Hc up to 13 kOe and BHmax up to 12.8 MGOe. Ivanov and coworkers (Ivanov et al., 1987; Song et al., 1987; Stepanov et al., 1987; Konstanchuk et al., 1987) have developed Mg-base alloys for hydrogen storage by mechanical alloying. Mechanical alloying of Mg with either Ni, Fe, Co, or Ce was carried out in a planetary mill under an inert or hydrogen atmosphere for short times (3 to 15 min). X-ray diffraction of the powders after MA showed only Mg and the given metal. Hydrogen absorption and desorption experiments were then carried out on the MA powders. All the samples demonstrated relatively high reactivity with hydrogen. The elements added to Mg could be classified with regard to their hydrogenation behavior as follows (a) those, e.g. Ni, forming an intermetallic compound (Mg2Ni) capable of absorbing and desorbing hydrogen, (b) those, e.g. Ce, forming hydrides that can function as hydrogen pumps due to stoichiometric variations, and (c) those systems (Mg-Co, MgFe) that do not form hydrides. The intermetallic compound Mg2Ni was formed from the mechanically alloyed Mg-Ni powder during hydriding and dehydriding cycles. The reaction temperature was 583 K, and the hydrogen pressure during hydriding was 0.8 MPa, and 0.15 MPa during dehydriding. The volume fraction of Mg 2 Ni increased with hydriding/dehydriding cycling. The compound formation by interdiffusion of Mg and Ni at 583 K was presumably enhanced by the defects created by the expansion and contraction of the lattice during the process of hydriding/dehydriding cycling. Mechanical alloys, composites of Mg with 5 to 20 wt. % Fe (or Ni, Ti, or Cu), have also been used as supercorroding alloys. These alloys, developed by the Naval
224
5 Mechanical Milling and Alloying
Civil Engineering Laboratory, operate as short-circuited galvanic cells to react rapidly and predictably with seawater to produce heat and hydrogen gas (Black, 1979; Sergev et al., 1981) for several marine applications. Mechanical alloying provided the appropriate microstructures for these cells to function, which could not easily be attained by other, more conventional methods. Mechanical alloying has been used in the past to synthesize certain high magnetic field A15 superconductors such as Nb 3 Al (Larson et al., 1977) and Nb 3 Sn (White and Nix, 1979). It was used because of the difficulty in preparing such compounds by standard solidification techniques due to the very large differences in the components melting points and the peritectic solidification behavior. The mechanically alloyed powders formed the A15 compound during compaction and the resulting material exhibited good homogeneity. Inoue and Masumoto (1989) have prepared the new high Tc oxide superconductors by MA followed by oxidation heat treatment. They studied the possibility of forming a homogeneous phase in immiscible Ba-Ln-Cu alloys (Ln = Y, Gd, Ho, or Er) as a precursor to the high Tc oxides. Mixed powders of Ba, Cu, and Ln 80 Cu 20 (Ln = Y, Gd, Ho, or Er) were milled in a conventional laboratory ball mill with an argon atmosphere in the milling vial. After 10 h of milling the X-ray diffraction peaks of the starting powder mixture (Ba, Cu, Ln 80 Cu 20 ) disappear and are replaced by peaks for a non-equilibrium f.c.c. Cu solid solution phase. Thus, it was possible to produce a homogeneous metallic phase precursor for subsequent oxidation. However, the LnBa 2 Cu 3 O 7 _ 8 (Ln = Y, Gd, Ho, or Er) material formed by oxidation (920 °C in oxygen) had superconducting
properties no better than material prepared by the conventional sintering process.
5.6 Mechanical Milling/Alloying as a Nonequilibrium Processing Tool The application of high energy ball milling that has stimulated the most research interest in recent years is its use as a nonequilibrium processing tool. It has been realized that mechanical alloying/ milling can be used to synthesize metastable structures, in analogy to other nonequilibrium processing methods such as rapid solidification and physical vapor deposition. However, the precursor phase in the case of MA/MM is typically a crystalline solid, or solids, rather than liquid or vapor. The thermodynamics and kinetic factors which govern metastable phase formation can therefore be very different. In this section the various, often competing, metastable structures that have been made by the high energy ball-milling of powder will be reviewed. 5.6.1 Extended Solid Solutions Equilibrium solid solubility limits are often exceeded by nonequilibrium processing methods such as rapid solidification. This is also true for MA. There are a number of examples of this effect in the literature, but, with the exception of recent work by Polkin et al. (1990), no systematic studies have been reported, to the author's knowledge, on solid solubility enhancement by MA. Extended solid solubilities have been noted in the process of studying amorphization in several alloy systems. Schwarz et al. (1985) found that the solubility limit of Ti in f.c.c. Ni was approxi-
5.6 Mechanical Milling/Alloying as a Nonequilibrium Processing Tool
amorph.cryst.- &
0)
c 0) CD if)
.a
mately 28 at. % on MA of Ti and Ni powders. This may be compared with a predicted solubility limit from the equilibrium phase diagram of only a few percent (Hansen, 1958). It was suggested (Schwarz et al., 1985) that this increased solid solubility could be explained by the metastable equilibrium between the oc-Ni f.c.c. solid solution and the Ni-Ti amorphous phase as opposed to the stable equilibrium between oc-Ni and Ni 3 Ti. The common tangents to the free energy curves calculated for these phases at 235 K (the milling temperature used) are consistent with the observed solubility limits. This is illustrated in Fig. 5-19. A similar result was obtained by Lee and Koch (1987) in a study of amorphization of Ni-Nb alloys by MA. The terminal Ni f.c.c. solid solution and the Nb b.c.c. solid solution were found to
225
Figure 5-19, Free energy of alloys of Ni and Ti. The heavy solid curve is the free energy of the amorphous phase. The thin curves are the free energies of the crystalline terminal solid solutions. The dotted curves are the free energies of the crystalline intermetallic compounds. The dashed lines are tangents common to the crystalline solid solutions and the amorphous phase. These define composition regimes a, b, c, and d. Regime (a) is the crystalline Ni-amorph. rich terminal solution. Regime (c) is the single-phase amorphous alloy. Regimes (b) and (d) are two_ ^ % -cryst. phase mixtures of amorphous alloy and the terminal solid solution of the major element. The symbols near the bottom of the figure denote the products obtained by MA of pure Ni and Ti powders: Solid and half-solid symbols denote single-phase and two-phase products, respectively (after Schwarz et al., 1985).
be approximately 10 at. % Nb and 10 at. % Ni respectively. This may be compared with solubility limits determined by Duerden and Hume-Rothery (1966) of 4.2 at. % Nb (at 987 °C) and 3.5 at.% Ni (at 1000 °C). The solubility limits at the milling temperature (nominally 60 °C) are expected to be much lower. Hellstern et al. (1988) found an extended solid solubility of Al in b.c.c. Nb of about 30 at. % for MA of elemental Nb and Al powder. The stable equilibrium diagram (Lundin and Yamamoto, 1966) for Al-Nb indicates Al solubility of 1021 ions/m2 are often needed with implantation. Thus, high concentrations are achieved with less accelerator time. Heavy ions like Xe create numerous atomic displacements and mix more efficiently. The configuration in Fig. 6-6 a was used to alloy Al and Pt (Mayer et al., 1981) as shown in Fig. 6-7. With Xe ion mixing, RBS analysis indicates that the initial sharp interface between the layers (the nearly vertical solid lines at the right edge of the Pt signal and left edge of the Al signal) becomes graded as a Pt-Al alloy forms. In this example, a stoichiometric compound (PtAl2) forms, and the mixing proceeds at constant composition with increasing Xe fluence, as indicated by the steps in the two signals. The ion-beam mixed phases can differ from those produced by thermally reacting the layers, and
Ion Induced Phase Transformation Sample Configurations A)
Bilayer
j Substrate B)
Multilayer, Planar
3
2Z2
Fd/2EdN
(6-2)
where Nd is the average number of displacements per target atom (dpa), 0 is the ion fluence (ions/m2), Fd is the energy deposited into elastic collisions, Ed is the energy needed to displace an atom from its lattice site (~ 20 eV), and N is the atomic density. TRIM also keeps account of Fd during the simulations, and uses this relation to calculate the number of displacements. The number is substantial: ~1000 vacancies are expected along the ion track in Al for each 100 keV Ni ion, but most of these recombine with interstitials so that far fewer are retained. The host atoms are nonetheless displaced many times; for 1020 Ni/m 2 , calculated to produce a peak concentration of 2.6at.%Ni, individual atoms in the implanted layer are displaced 10-24 times. For the 40at.%Ti in 304 steel in Fig. 6-9, the damage varies from -1000 to 2000 dpa. TRIM also determines the depth distribution of displacements, which peaks closer to the surface than jRp. The distribution of lattice damage in Ni-implanted Al (see Fig. 6-3) was found
with ion channeling to peak closer to the surface than the concentration (Picraux et al., 1980), as expected. An important aspect of lattice displacements is that they are not uniform along an ion track. Instead, an ion displaces a host atom which recoils and produces a dense cascade of displaced atoms; it then travels in a straight line until it has another such collision. These localized displacements are termed collision cascades, and are believed to be well-defined entities in sufficiently heavy (Z > 20) materials irradiated with heavy ions (Johnson et al., 1985); the density of displaced atoms increases with ion and target masses. The collision cascade is a state of high kinetic energy (several keV), small size ( WITH
O 0
\ \#
o
o
o
X)
^OCo 1
250
300
350 TEMPERATURE(K)
\
\ \
•
•
•
400
b) Figure 6-16. a) Calculated implantation profiles for 4 x 1O20 He/m2, 10 keV, and 1.25 x 1020 D/m2, 10 keV, and nuclear cross section for D( 3 He,p) 4 He as functions of depth in Ni. b) Fraction of D retained in traps during ramping of temperature at 2 K/min. (Myers et al., 1989).
In Fig. 6-16 b, the fraction of D remaining at the implanted depth is plotted versus temperature during warming of the specimen at 2 K/min. Also plotted are results for the same experiment but with no He. With He, D migrates from the implanted zone at 370 K, which is clearly higher in temperature than found when no He is present (310 K). This shift demonstrates the trapping of D at the He bubbles. In fact, the release temperature in the absence of He is higher than that at which D would leave due to diffusion alone, 200 K, which indicates that D is also trapped (but more weakly) by lattice damage created during the implantation. Nickel is well suited to these experiments because its surface is known to be quite permeable to hydrogen isotopes; thus when D is thermally released from the traps, it can diffuse to the surface and leave the specimen. The transport of D out of the implanted zone is treated by numerically solving a set of coupled differential equations which treat the binding to He traps, diffusion in the matrix, and release at the surface. The binding enthalpy is adjusted to fit the observed release, as shown by the theoretical curve through the data with 0.55 eV trap strength. This binding enthalpy and that of D to He in other metals agree with values expected for chemisorption on the walls of the He bubbles (Myers et al., 1989). The chemically inert He is insoluble in metals and forms cavities whose surfaces chemisorb hydrogen like those of a bare metal. The surfaces are attractive sites for D because of their low electron density. The binding of D to vacancies in metals has also been extensively characterized using similar methods. This trapping and other solute reactions in metals determined with ion-beam methods are reviewed by Myers etal. (1987 and 1989).
6.5 Surface Alloys with Improved Macroscopic Properties
6.4.3 Search for Cold Fusion: Pd-D In 1989, it was reported that electrochemical charging of Pd electrodes with D was able to induce D-D fusion, even at a level capable of significant heat output (Fleischmann and Pons, 1989). The reported work linked high densities of D to fusion; D/Pd ratios >1.0 were desirable. Ion implantation of D into Pd was identified as a method to explore high D concentrations based on previous work which achieved a D/Pd ratio of 1.3 + 0.2 by implanting at 35 K where D is immobile (Moller, 1982). The implantation produces a hydride phase, with D ordered in octahedral sites of an f.c.c. Pd lattice at D/Pd = 1.0 (Traverse and Bernas, 1987); electrochemical charging also forms the hydride, but with D/Pd ^ 0.9 (Knapp et al., 1990). In the recent investigation (Myers et al., 1990), D was implanted at 10 keV to 3.9 x 1022 D/m 2 at 41 K. The amount of D retained in the specimen was measured with the D(d,p)T (T-triton) reaction. The yield from the reaction was accounted for with a mathematical model which used the implanted depth profile from TRIM (Ziegler et al., 1987), the nuclear cross section variation with depth in the sample, and a saturated D concentration of D/Pd = 1.6±0.3. After implantation, the specimen was maintained at 41 K and the charged particle detector left on to count protons and tritons from possible fusion events. After 8 hours, only one count was observed against an expected background level of 1.4 counts. This negligible yield places a limit on the possible fusion rate of ^ 2 xlO~ 2 1 events/D-s. Fusion was also not observed at 81 K, nor during warming to room temperature. Similar work with Zr and Ti placed comparable limits on their fusion rates. This limit on the fusion rate in Pd is not as low as that of other work (e.g., ^ 10~ 24
275
events/D-s; Knapp et al., 1990), but the experiment is unique in examining such high D/Pd ratios. The D in excess of D/Pd = 1.0 could also be identified during warming of the specimen by its release at 120 K, as compared with the release of the remaining D at ~ 200 K. This superstoichiometric D is thought to occupy tetrahedral sites and to diffuse more rapidly due to its avoiding the tightly binding octahedral sites, which are filled for D/Pd > 1.0 (Richards, 1989).
6.5 Surface Alloys with Improved Macroscopic Properties This section examines ion-beam alloys with improved surface-related macroscopic properties. Two general areas being widely examined are mechanical properties and corrosion resistance. Important examples of alloys with reduced friction and/or wear, increased hardness and strength, reduced aqueous corrosion rates or with combined reductions in corrosion and wear rates are discussed below. These and other surface-related properties modified with ion beams have been reviewed (Herman, 1981; Picraux, 1984; Clayton, 1987). Benefits observed in both areas are promoting the commercial ion-beam treatment of components made of several steels and alloys of Be, Ti, Zr, Co, or Ni (Armini, 1986; Dearnaley, 1987; Sioshansi, 1987). Ion implantation has several attractive features for use on engineering components. The treatment can be applied to finished products with no change in dimensions. It modifies only a surface layer and not the bulk alloy. Components can be implanted at room temperature to avoid changing the mechanical properties of the substrate, unlike some coatings which require elevated temperatures. The implant-
276
6 Ion Implantation and Ion-Beam Mixing
ed layer is formed by injecting atoms beneath the surface and is thus more adherent than a coating. However, there are also negative aspects: implantation is usually a line-of-sight process, forms a very thin alloy, and becomes more limited by sputter erosion for glancing incident angles. The process is also relatively expensive. Treated components are therefore usually highercost, precision parts which must closely retain their dimensions in mild-wear or corrosive environments. 6.5.1 Nitrogen Implantation to Reduce Wear of Steels
The implantation of N is widely used to reduce wear rates for a variety of steels and components (Picraux, 1984; Hirvonen, 1984). In general, N implantation is believed to harden the surface and thus increase wear resistance, but in some cases other mechanisms are important. The phases observed in N-implanted Fe and steels form a basis to interpret the wear behavior. The phases of N-implanted pure Fe have been identified with TEM and Mossbauer spectroscopy (Rauschenbach and Kolitsch, 1983; Moncoffre, 1987). For concentrations up to 11 at.%, N stabilizes the austenitic y phase of Fe (f.c.c), which replaces the ferritic a (b.c.c.) phase. With increased N content, a' martensite (b.c.t.) and oc"-Fe16N2 (b.c.t.) form, while at the highest fluences, e-Fe2N (hex) forms. The e phase was found to contain 25-33 at.% N, which is in the concentration range often used to improve mechanical properties. For Fe, the implanted concentration saturates at 33 at.% N (Singer, 1984b). The microstructures of N-implanted steels are similar to those of Fe but differences in depth profiles and compositions result from other elements in the steels. In stainless steels with >10at.%Cr, the N
profiles have the expected gaussian shape (Singer, 1984 b), but in Fe and low-alloy steels, N can migrate toward the surface, especially if the temperature rises (> 50 °C) during implantation (Moncoffre, 1987). This difference is believed due binding of N to Cr, which immobilizes it, whereas N can redistribute during implantation in the absence of Cr. Nitrogen also stabilizes austenite (Carbucicchio et al., 1981) and forms nitrides at high concentrations, including the e phase. However, the phases may be carbonitrides which incorporate C from the steel into their lattice structures (dos Santos et al., 1983). The reduction in wear obtained with N implantation is generally thought to result from its strengthening of the metal near the wearing surface. Several mechanisms have been considered, but the observed microstructures noted above and other experimental comparisons identify two as being applicable (Hubler, 1982): 1) strengthening by interstitial N, which can be expected to accumulate at dislocations and impede their motion, and 2) strengthening by nitride precipitates, which inhibit dislocation motion. Furthermore, at high N concentrations, the surface layer may also be almost completely converted into the hard nitride phase. Thus the benefits are believed to be directly related to phases containing N, as opposed to lattice damage or compressive stresses which would also be present when other elements are implanted. Type 304 stainless steel has a metastable f.c.c. structure which transforms to b.c.c. when the surface is mechanically polished (Singer et al., 1988) or undergoes sliding wear (Follstaedt et al., 1983), and requires special consideration. The transformed surface layer is brittle, and breaks away during sliding wear. Implanting N at low concentrations stabilizes austenite, which
6.5 Surface Alloys with Improved Macroscopic Properties
results in a softer surface that wears more quickly during abrasive testing (Singer et al., 1988), but nonetheless reduces sliding wear (Fayeulle and Treheux, 1987). High concentrations (45 at.%) can be implanted into 304 to form a layer with predominantly £-(Fe,Cr)2N; reduced sliding wear is also observed with this treatment (Yostetal., 1983). In summary, wear reductions are observed by many workers for N implantation into steels. It is notable, however, than benefits are not obtained for fully hardened bearing steels (Carosella et al., 1980; Pope etal., 1984). The benefits for softer steels are generally believed to result from strengthening the surface. However, questions remain about one aspect of the treatment: reduced wear rates are observed at depths beyond the implanted thickness (Lo Russo et al., 1979). It was initially proposed that N migrates deeper into the steel ahead of the wearing surface (Hartley, 1979), but evidence for such migration is disputed (Singer et al., 1984 a). It has also been proposed that N implantation initiates a mild, oxidative wear mode between the contacting parts, which persists even after the implanted layer is worn away (Hale et al., 1987). Although extended wear reduction is not fully understood, its existence seems not to be in question. 6.5.2 Implantation of Ti + C to Reduce Friction and Wear
A second treatment used to improve the tribological properties of steels is the implantation of Ti and C at the same depth. This treatment has some significant advantages over the more widely used implantation of N (Follstaedt, 1985 a). However, Ti is more difficult to implant, and its heavier mass (Fig. 6-8) results in thinner surface alloys. One advantage is that Ti + C im-
277
plantation reduces both friction and wear, whereas N generally reduces only wear. Secondly, the Ti + C treatment provides these reductions for all steels examined to date, whereas N provides no benefits in hard bearing steels like 52100 and 440 C. Implantation of Ti + C is being evaluated for treatment of 440 C ball bearings in the U.S. Space Shuttle's main rocket engines (Ng and Naerheim, 1987). The results for 440 C with Ti + C are illustrated in Fig. 6-17, which compares (a) maximum wear depths (MWD) and (b) friction coefficients for pin-on-disk tests of implanted disks with those of unimplanted disks (Pope et al., 1984). At the top of Fig. 6-17 a, the calculated maximum Hertzian stresses exerted on the disk are given for the pin loads on the horizontal axis. Reduced friction and wear are found to persist for 1000 cycles at loads as high as 600 g and Hertzian stresses up to 1.5 times the yield strength of 440 C steel at maximum hardness (1840 MPa). For 304 steel, benefits are obtained even at 3.5 times the yield stress (Follstaedt, 1985 a). In addition to improving the performance of steels, Ti + C reduces friction and wear of Co alloys (Dillich et al., 1984), and such benefits are expected for Ni alloys (Follstaedt et al., 1989 b). These benefits have been closely linked to the amorphous phase which forms when Fe is implanted with Ti and C. All the steels are amorphized, and the amorphous layer has been observed intact across wear tracks (Follstaedt et al., 1984 c). The amorphous phase in Fe implanted with Ti and C is a ternary phase for typical implanted concentrations; e.g., for 20 at.% Ti, 4 at.% C is required to form the phase (Knapp etal., 1985). The benefits and amorphous phases were observed in steels with > 20 at.% of both Ti and C, which are within the ternary composition limits. For
278
6 Ion Implantation and Ion-Beam Mixing
HERTZIAN STRESS (MPa) 1850 2300 2650 2900 3150 1.00 0.50
0.05 A,T -IMPLANTEp 200 a)
400 600 800 NORMAL LOAD (g)
1000
1.0
0.8
h
W
FFl
o
LJJ
0.6
ION
o o
0.4
hO
£
0.2 ^•-IMPLANTED
200
b)
400 600 800 NORMAL LOAD (g)
1000
Figure 6-17. a) Average maximum wear depth (MWD) and b) friction coefficient at the end of 1000 cycle pin-on-disk test of unimplanted 440 C and implanted with 2xlO 2 1 Ti/m 2 , 180-90 keV, plus 2x x 1021 C/m2, 30 keV, plotted versus load on 440 C pin (Pope et al., 1984).
high Ti concentrations, small precipitates (10-20 nm) of mixed Ti + Cr carbides are found within the amorphous layer on stainless steels (Follstaedt et al., 1989 a) and may contribute to improved performance.
Two recent studies indicate the essential roles played by both Ti and C in providing extended tribological benefits. At high Ti concentrations (50at.%), binary amorphous Fe-Ti alloys can be formed by ionbeam mixing (Hirvonen et al., 1986), as expected from irradiation studies (Brimhall et al., 1984). The friction and wear behavior of amorphous Fe-Ti on 304 was compared to that of the same alloy implanted with a high fluence of C (3 x 10 21 C/m 2 , 50 keV), and the C was found to significantly increase the number of cycles with low friction (Hirvonen et al., 1987 and 1990). Second, the implantation of C into stainless steels has recently been found to produce an amorphous alloy, in which Cr acts like Ti to stabilize the amorphous phase instead of the £-Fe2C phase that forms in pure Fe (Follstaedt et al., 1989 c). Benefits are observed with C alone, but do not persist for as many cycles and are not observed at the high pin loads as with Ti + C. These two comparisons indicate that tribological performance is improved somewhat for amorphous layers with either Ti alone or C alone, but extended benefits require both elements. Comparisons with other amorphous alloys indicate that the Ti + C treatment gives superior performance (Follstaedt et al., 1989 b). Current research is aimed at identifying how the amorphous Fe(Ti,C) layer reduces friction and wear, and two factors appear to be important. First, the phase is harder than the steel substrates. Hardness was inferred from earlier work (Follstaedt, 1985 a), but has now been directly observed for the layer on 440 C steel with indentation at depths of ~100nm (Bourcier, 1990). Second, oxidation of the wear surface appears to be important in determining friction levels and wear rates (Pope et al., 1988; Fayuelle and Singer, 1989).
6.5 Surface Alloys with Improved Macroscopic Properties
279
6.5.3 High-Strength A1(O) Alloys
Implantation of O into Al has recently been shown to produce hard surface layers with very high flow stresses (Bourcier et al., 1990 a and 1990 b). In this work, O was implanted at five energies (200-25 keV) to give a nearly constant composition of 20 at.% O extending to a depth of 500 nm. An ultra-low load indenter was used to obtain penetration-versus-load curves at depths ^lOOnrn. The curves were fitted with numerical simulations obtained by large-strain, finite-element modeling of the deformations. The simulations took account of the indenter shape, the compressive yield strength of the pure Al substrate (41 MPa) and the higher flow stress of the implanted layer, which was adjusted to obtain agreement with experiment. The penetration depths observed in the implanted specimen were only ~ 1/12 of those in Al at the same loads, and required a flow stress of 2900 + 400 MPa for the layer. A smaller but still quite high value, 1200 + 400 MPa, was found after annealing the alloy 1/2 hour at 550 °C. The flow stress of the asimplanted alloy exceeds the yield strength of fully hardened 440 C bearing steel, 1840 MPa, and is several times those of the strongest commercial Al alloys. The microstructure of the as-implanted alloy is shown in Fig. 6-18. Electron diffraction patterns must be tilted off the zone axes in order to detect low-intensity, diffuse spheres surrounding each (sharp) Al matrix spot, as seen in Fig. 6-18 a. Darkfield imaging with a diffuse sphere shows a high density of fine precipitates 1.5-3.5 nm in diameter, as seen in Fig. 6-18 b. Annealed alloys have also been examined (Myers and Follstaedt, 1988; Bourcier et al., 1990 a), and their microstructures are useful for understanding the crystal structure of the precipitates in the as-implanted
Figure 6-18. a) Diffraction pattern of Al implanted with 20 at.% O, tilted off the zone axis, b) dark-field image of oxide precipitates imaged with the diffuse reflection circled in a) (Bourcier et al., 1990b).
alloy. Annealing 1/2 hour at 550°C produced larger (4-10 nm diameter) precipitates of y-Al2O3, a cubic spinel phase. The cubic axes of y-Al2O3 align parallel to those of the f.c.c. Al matrix, and a spinel reflection almost overlaps each Al reflection. The phase has a f.c.c. sublattice of O~ 2 ions, with Al + 3 ions ordered on {111} planes. This ordering doubles the sublattice cell size to 0.790 nm, and gives addi-
280
6 Ion Implantation and Ion-Beam Mixing
tional reflections which are isolated from those of Al and readily observed. These ordering reflections are absent for the asimplanted alloy, implying that its precipitates are disordered y-Al2O3 with Al + 3 ions at random interstitial sites in an f.c.c. O ~2 lattice of nearly the same spacing as AL The precipitate sizes and coherency have been used in well established models of hardening, with the assumption that all of the O was precipitated (Bourcier et al., 1990 a and b). The unusually high strengths are well accounted for, even though the models are being applied at very high precipitate densities and volume fractions (20%). The higher strength of the as-implanted alloy is due to the smaller size and correspondingly higher precipitate density. Aluminum has previously been found to be hardened by implanting O or N (Ohira and Iwaki, 1987). The above studies extend earlier work by quantifying the strength of the layers and accounting for it with conventional hardening mechanisms. The numerical modeling is an essential part of the evaluation; the increase in strength to 80 times that of Al is not fully reflected in the reduced indentation depths because the soft substrate influences deformation, even for penetrations less than 1/5 of the implanted layer thickness. 6.5.4 Aqueous Corrosion of Fe-Based Alloys
The use of ion implantation to reduce the corrosion rates of Fe and its alloys in acidic or chloride solutions has been examined by many workers, and is summarized in recent reviews (Clayton, 1987 and 1989). Anodic polarization of metals in these solutions is often used to examine the formation of passivating surface layers which reduce further dissolution of the metal, and also to measure the degree of protection
against pitting corrosion offered by the passivating layer. Increased corrosion resistance has been obtained by implanting Cr, Cr + Mo, Cr + P, Ta, N, P or B, but in some cases improvements depend upon the composition of the bulk alloy. Ion-beam mixing is also being used to form corrosion-resistant surface layers. Increased corrosion resistance is widely observed for Cr implantation of Fe, and the concentration dependence agrees with that observed for bulk Fe-Cr alloys. Implantation thus creates a surface layer with the corrosion resistance of a stainless steel. The effect of Cr concentration was more pronounced than any other effects of the implantation, such as those due to lattice damage. These benefits are also found with Cr for bearing steels (Wang et al., 1979) and dual implantations of Cr + Mo or Cr + P are even more protective, again in agreement with bulk alloy results. The increased protection against pitting corrosion for these two steels has potential for application to jet engine bearings, which corrode during operation at sea as well as during shelf storage. The benefits obtained with implantation of bearing steels led the U.S. Navy to initiate a program to adapt the treatment to the balls and races of bearings (Smidt et al., 1987). Facilities have been developed for rotating and heat-sinking these curved pieces during implantation while mitigating the effects of sputtering. The cost of treatment on a production scale was projected to be $ 82.50/bearing. An additional consideration favoring surface alloying is that costly or strategic elements like Cr which are needed only to improve surface properties can be used in much smaller quantities instead of being distributed throughout the bulk. Some of the more corrosion-resistant Fe-based alloys are metallic glasses con-
6.5 Surface Alloys with Improved Macroscopic Properties
taining both Cr and P. Sorenson et al. (1986, 1988) have used P implantation of bulk Fe-Cr alloys to form passive surface alloys and to study the effects of P content and alloy structure on corrosion behavior. The results with Fe 6Cr, Fe-lOCr and Fe-18Cr illustrate the mechanisms responsible for improved electrochemical properties when P and Cr are present together. The alloys were implanted with 100 keV P to form layers - 1 0 0 nm thick. Corrosion currents were examined for 600 mV polarization in 0.1 N H 2 SO 4 solutions with 500 ppm Cl. The implantation of P decreased the corrosion current of Fe-lOCr, increased the current of Fe-6Cr and increased pitting, and had essentially no effect on Fe-18Cr. These seemingly contradictory results are understood with current models of passi vating film formation. The Fe-6Cr alloy has marginal Cr for forming a protective passivating layer. The P is believed to enhance the Cr dissolution rate and speed the formation of the layer for solutions without Cl, but in more aggressive Cl solutions, it also increases the rate of pitting. The Cr content of Fe-18Cr alloys is sufficient to form passivating layers readily, and P has little effect for this alloy, which is already very corrosion resistant. Implantation of P improves the intermediate alloy, Fe-lOCr, because it has enough Cr to form a protective layer, and Cr dissolution from the metal into that layer is enhanced by the P. Examining several P fluences indicates that maximum benefits are achieved at high concentrations (20-30 at.% P), where the alloy is transformed from the crystalline b.c.c. phase to an amorphous phase. At these P concentrations, a thicker passivating layer is formed which reduces the corrosion current by ~ 10 ~ 4 relative to the bulk Fe-lOCr alloy to produce behavior like that of Fe-18Cr.
281
The P-implantation results are the first to show implantation-enhanced passivity of low Cr Fe-based alloys. The studies use ion implantation to alter composition near the surface in a controlled manner and to form an amorphous surface alloy. The mechanisms identified are applicable to bulk alloys, and these studies thus also fall in the category of Sec. 6.4. 6.5.5 Reduced Corrosion and WearofTi-6AI-4V The implantation of N also significantly improves the mechanical properties of Ti alloys. Substantial reductions in friction and wear of the engineering alloy Ti-6 Al4 V (weight percentages) have been found (Oliver et al., 1984): the friction coefficient was reduced from 0.48 to 0.15, and the wear volume by a factor of more than 100. The strong chemical reaction of Ti and N produces TiN precipitates in N-implanted Ti-6A1-4V (Vardiman and Kant, 1982); improved fatigue properties were also observed with the treatment. Titanium alloys are generally thought to wear poorly, and N implantation is thus of interest for treating such components. One of the more successful commercial applications of ion beams is N implantation of hip and knee replacement joints made of Ti-6A1-4V, which are treated on a production basis (Sioshansi, 1987). The prostheses use a Ti component, for instance, to replace the ball of the femur, which moves against a mating component made of ultrahigh molecular weight polyethylene (UHMWPE). The Ti alloy was chosen for its biocompatibility and bulk mechanical properties; N is also an acceptable element for components placed in the body. Basic research investigating the use of N implantation for this wear couple has been done by Williams and Buchanan
282
6 Ion Implantation and Ion-Beam Mixing
(1985). They devised an electrochemical cell with a cylindrical Ti-6A1-4V electrode rotating between two UHMWPE pads pressing against it. The electrolyte is a 0.9%NaCl solution with 10% bovine serum added to simulate body fluids. The corrosion currents observed during the sliding wear with the electrode at — lOOmV anodic potential are shown in Fig. 6-19 for unimplanted and 20 at.% Nimplanted electrodes. Despite scatter, the data separate clearly and show that the corrosion current is reduced more than a factor of 100 with N implantation. Examination of the sliding surfaces indicates that wear is also reduced by the treatment (Williams, 1985). Unimplanted electrodes are heavily blackened and scored by the rotating contact with the pads, while implanted ones have a smooth, mirror finish like that before the test. Profilometry of ORNL-DWG 8 3 - 4 8 3 8 2
10
Figure 6-19. Corrosion current vs. time for unimplanted and N-implanted (20 at.%) Ti-6A1-4V electrodes. I M. Williams and R. A. Buchanan, Ion Implantation of Surgical Ti-6Al-4V Alloy, Materials Science and Engineering 69 (1985) 237-246, Figure 2.
the worn electrodes shows that the maximum depths of wear grooves are reduced from 30-80 jim to ^ 1 Jim. Moreover, the UHMWPE pads also show reduced wear when the electrode is implanted. The Ti-6A1-4V and UHMWPE elements of the prostheses are eroded by a combination of mechanical wear and chemical corrosion. Nitrogen implantation reduces both mechanisms in this example.
6.6 Concluding Remarks Many aspects of surface-alloy formation by ion implantation and ion-beam mixing are relatively well understood, as are the basic atomic processes occurring during these treatments. The microstructures of new alloys can be interpreted against a broad background of accepted results. Frequently, the initial materials are transformed into metastable solids, including supersaturated solutions, disordered crystalline phases, metallic glasses and quasicrystals. Systematic trends are found for the occurrence of these phases and have been formulated into predictive guidelines. In this chapter, additional guidance for predicting phases was obtained by examining ion-irradiated alloys. The microstructures of irradiated alloys are also of interest for radiation damage studies, for instance, to determine the evolution of alloys used in reactors. By combining the special capabilities of ion implantation with the depth resolution of ion beam analysis (often ~ 0.01 ^m), submicron-scale alloys can be tailored to exhibit solute phenomena, such as trapping, precipitation and dissolution, and diffusion. These processes can be quantified to provide basic information of interest for bulk alloy phenomena at temperatures lower than may be otherwise inves-
6.8 References
tigated. The methods presented in Sec. 6.4 can be extended to other alloys, for instance, to study solute trapping at dislocations, or to obtain solid solubilities for phase diagrams, including ternary systems (Myers, 1978). The ability of ion-beam treatments to improve tribological and electrochemical properties has led to their being applied to commercial products. A number of service companies in the U.S.A., the U.K. and Europe now offer ion-beam treatments for engineering components, and the industry can be described as steadily growing. Commercial acceptance of ion-beam treatments depends upon technical merit and economic considerations with respect to competing treatments. In general, the processes are being accepted for specialized applications, such as treatment of medical components placed in the body. Two recent developments appear important for the future of ion-beam alloying. First, ion beams are being combined with vapor deposition in a process termed ionbeam assisted deposition (IBAD) (Hubler, 1989). Implantation is carried out during deposition to produce a layer which is more adherent and can have new properties derived from the ion beam. Second, a new technique termed plasma-source ion implantation (PSII) is being developed for gaseous species (Conrad, 1989). A plasma is formed around the target, which is biased to accelerate the ions into it. This method injects ions into the target from all directions and at normal incidence to curved surfaces. The sputtering of curved surfaces is thus reduced, and the process is stated to be substantially less expensive. Both developments are likely to find commercial uses. This chapter has focussed on metallic alloys formed by implanting into metal substrates or by ion-beam mixing two
283
metals. In addition to the well-known uses of ion beams with semiconductors, other materials are being modified. Ion-beam treatment of ceramics is now being examined (White etal., 1989) for improvement of surface-mechanical properties and optoelectronic properties. Polymers are also being treated to form new materials with different optical and electronic properties (Davenas et al, 1989). These examples demonstrate that ion-beam treatments are not limited to metal and semiconductor applications, but find uses in the full range of modern materials.
6.7 Acknowledgements The author wishes to thank his many colleagues who have contributed to this chapter through valuable discussions of their work or by collaborating with him. This work was supported by the U.S. Department of Energy under contract number DE-AC04-76DP00789.
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7 The Epitaxy of Metals Donald W. Pashley Department of Materials, Imperial College of Science, Technology and Medicine, London, U.K.
List of 7.1 7.2 7.3 7.3.1 7.3.1.1 7.3.2 7.4 7.4.1 7.4.1.1 7.4.1.2 7.4.1.3 7.4.2 7.4.2.1 7.4.2.2 7.5 7.5.1 7.5.2 7.5.3 7.5.3.1 7.5.3.2 7.5.3.3 7.6 7.6.1 7.6.2 7.6.2.1 7.6.2.2 7.6.2.3 7.6.3 7.7 7.8
Symbols and Abbreviations Introduction Deposition Methods General Characteristics of Epitaxy Orientation Relationships Deposition Conditions for Obtaining Epitaxy The Role of Lattice Misfit The Modes of Growth of Epitaxial Metal Films The Nucleation Modes of Growth Monolayer Growth The Volmer-Weber Nucleation Mode The Stranski-Krastanow Mode of Growth Post-Nucleation Growth Processes Liquid-Like Coalescence Reorientation and Recrystallization Effects Elastic Strains and Misfit Dislocations Changes in Elastic Strain with Increasing Thickness Misfit Dislocations The Formation of Misfit Dislocations Formation During Monolayer Growth Formation During Volmer-Weber Growth Formation During Stranski-Krastanow Growth Lattice Imperfections in Layers Grown by Epitaxy Imperfection Structures Observed Modes of Formation of Lattice Defects Copying from the Substrate Defects Linked with Misfit Dislocations Defects Resulting from Coalescence of Nuclei Changes in Imperfection Structure as Growth Proceeds Summary and Conclusions References
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
290 291 292 293 293 294 295 296 296 299 301 302 303 303 306 308 309 310 312 312 317 319 320 320 320 320 321 322 325 326 327
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7 The Epitaxy of Metals
List of Symbols and Abbreviations a a0 b b
K
9 I m n N
spacing of atom (or ion) rows in the substrate surface lattice constant spacing of atom (or ion) in the parallel rows in the deposit total Burgers vector of the dislocation edge component in the interface spacing of the parallel planes in the deposit film spacing of the substrate planes perpendicular to the surface and parallel to the misfit dislocations reciprocal lattice vector length of misfit dislocations lattice misfit in % integer number of threading dislocations spacing of the parallel array of dislocations periodicity of the moire pattern critical thickness growth temperature melting temperature
Ay
surface energy of the deposit film interfacial energy surface energy of the substrate surface energy of materials A and B change in surface energy
2D,3D AES CVD MBE RHEED TEM UHV
two-, three-dimensional Auger electron spectroscopy chemical vapour deposition molecular beam epitaxy reflection high energy electron diffraction transmission electron microscopy ultra-high-vacuum
7 A > 7B
7.1 Introduction
7,1 Introduction The subject of epitaxy has its origins in observations made well over a century ago, when mineralogists became interested in the natural intergrowth of two different mineral species, in such a way that the two had a clear crystallographic orientation relationship. Such observations caused mineralogists to study the growth of one substance on another in the laboratory, mainly by growth from solution. The first known paper on the subject concerned the growth of sodium nitrate on calcite (Frankenheim, 1836). Initially, most observations were made by optical microscopy but once X-ray diffraction techniques became available the scope of such studies was much increased, and by the 1930's many examples of epitaxy had been reported. The term epitaxy was introduced by Royer (1928) to denote the phenomenon, and was derived from the Greek to mean "arrangement on". The scope for studying epitaxy was again increased once electron diffraction techniques became available, allowing extremely thin surface growths of substance B on a single crystal of substance A to be examined for orientation. As a result, it was found that well defined epitaxy occurs for a wide range of combinations of substrate and deposit. There has, over the years, been controversy concerning the correct form of the adjective and adverb to be used in connection with epitaxy, in view of its Greek derivation. Whilst words such as epitactic can be fully justified on this basis, the adjective epitaxial is now so widely used that it is impractical to attempt to bring about any change, even though epitaxial cannot be justified on etymological grounds. Therefore epitaxial is used as the accepted adjectival form in this chapter.
291
A new tool was applied to the study of epitaxy when high quality transmission electron microscopes became available in the 1950's. Detailed studies of the mode of growth and internal structure of epitaxial deposits provided much new knowledge, and theoretical approaches to the understanding of epitaxy could be initiated and developed with much more realism than hitherto. Considerable progress was made towards scientific understanding, resulting from studies which included many on epitaxial growth of metals. Until about 20 years ago most work on epitaxy was carried out as a piece of basic scientific research, but then strong interest developed in the possibility of using epitaxy as a means of making single crystal thin layers of semiconductor materials for use in electronic devices. In the last 15 years, and particularly the last 10 years, considerable effort has been devoted to studies of the epitaxy of semiconductors, and epitaxial growth is now established as a unique processing step in the manufacture of electronic and opto-electronic devices. The demonstration by Esaki and Tsu (1970) that artificial superlattice structures of semiconducting materials can be produced by epitaxial growth has stimulated much new research. Studies of the epitaxial growth of other substances has diminished over the same period. The epitaxy of single and multilayer semiconductor layers is treated in Vol. 4, Chap. 8. Interest in the epitaxy of metals has been revived in recent years by the developments with artificial metallic superlattice structures. These have applications as gratings for soft X-rays, but current interest centres on their potential as magnetic materials or as superconducting materials. A recent review of the properties of artificial metallic superlattices has been given by Jin and Ketterson (1989) (see also
292
7 The Epitaxy of Metals
Vol. 3, Chap. 6). Metallic superlattices are treated in Chapter 8 of this Volume. It is clear that epitaxial growth now has the potential of becoming an important processing route for certain specialised metallic materials, hence the justification for the inclusion of this chapter in a volume on processing. The purpose of this chapter is to provide a summary of the most important aspects of the epitaxial growth process relevant to the growth of single crystal metal films. Inevitably, because of the dominance of work on semiconductor epitaxy during the last decade, some of the recent understanding of epitaxy is based upon such work. Thus it is necessary to refer to some of the semiconductor research, but as far as possible examples are restricted to epitaxial deposits of metals. Further discussion of ultrathin films and superlattices of both metallic and ceramic systems will be found in Vol. 3 of this Series. The first important area of the subject concerns the conditions which have to be satisfied if epitaxial growth is to take place. In practice, experimental conditions can be found to allow many materials to be grown epitaxially on a range of different substrates. Ever since Royer (1928) put forward his rules for epitaxy, the role of the lattice misfit, or mismatch, between the substrate and the deposit at their interface, has been considered to have an important influence. However, although it is commonly believed that a small percentage misfit is essential for epitaxy to occur, it is well established that very large percentage misfits do not necessarily prevent epitaxy. The misfit does have an important influence on both the initial stages of growth of an epitaxial deposit and the way in which the structure of the deposit changes as deposition continues. Much has been learned about the modes of growth involved in epi-
taxy, from both theoretical and experimental studies. These modes of growth determine the structure of an epitaxial deposit, including the degree of structural perfection. Transmission electron microscopy has been of great importance in providing evidence of the nature of the lattice imperfections present in epitaxial deposits, and because a number of applications of these deposits require low densities of such imperfections, great interest centres on how the imperfections are formed, and how their formation can be prevented or their existence eliminated.
7.2 Deposition Methods Any technique which provides a means of depositing a thin metal film on a substrate surface, in a well controlled manner, can be used for producing epitaxial deposits on a single crystal surface. It can be important to prepare a clean flat surface of the substrate, with a particular crystal plane parallel to the surface, and to maintain the cleanness of the substrate surface during the initial stages of the deposition. For this reason, growth under conditions of a good clean vacuum is commonly used, either by the simple method known as vacuum evaporation or by its more modern version known as molecular beam epitaxy (MBE) (see this Volume, Chap. 8). Nevertheless good epitaxy can also be achieved by the simpler technique of electrodeposition (e.g. of one metal upon another) provided the substrate is electrically conducting and is stable in the required electrolyte. (Epitaxy in electrodeposited metallic coatings is treated in this Volume, Chap. 11, and in Chap. 10, Sec. 10.4.5.) A further technique is known as chemical vapour deposition (CVD). The substrate is heated in an atmosphere containing a
7.3 General Characteristics of Epitaxy
gaseous compound which decomposes as its molecules impinge on the substrate surface causing metal atoms to stick onto the surface. The technique is used widely for the growth of epitaxial layers of semiconductors. An example is the formation of a layer of silicon by the decomposition of SiH 4 . Alternatively, metal atoms are released onto the heated substrate surface by the chemical interaction between two different gaseous species which are passed over the substrate. The interaction only occurs on, or in close proximity to, the substrate surface. An example is the formation of gallium arsenide by the interaction between (CH 3 )Ga and AsH 3 : (CH 3 ) 3 Ga+AsH 3 -*GaAs + 3CH 4 With both of these CVD techniques, the rate of deposition can be varied by changing the substrate temperature or by changing the gas pressures or the gas flow rates. There is commonly only a limited range of substrate temperatures which can be used for a given rate of deposition of metal atoms. Undoubtedly the most common method used for metal epitaxy is that of vacuum evaporation. The source of metal vapour is simply a small volume of molten metal, the temperature of which is varied to control the rate of deposition of metal atoms on a substrate surface placed at a distance of a few centimetres away. The substrate temperature can then be varied quite independently of the rate of deposition of metal atoms. Whilst good epitaxy can be obtained if the deposition is carried out in a relatively poor vacuum, e.g., 10~ 3 Pa, much work is now carried out in a much higher vacuum (e.g., 10 ~9 Pa) in order to ensure that the substrate surface remains clean during the deposition process. The MBE deposition method also benefits from a clean vacuum environment, and
293
additionally uses metal sources consisting of Knudsen cells which allow highly stable rates of deposition to be used. This is of considerable importance for the formation of alloy layers of particular compositions from two or more sources as well as for the growth of artificial superlattices, where alternating layers of two metals, or alloys, are required with accurately controlled thicknesses. One important advantage of both the vacuum evaporation and the MBE techniques is that a reflection high energy electron diffraction (RHEED) system can be incorporated in the growth chamber to allow the structure of the epitaxial deposit to be observed during its growth.
7.3 General Characteristics of Epitaxy Epitaxy covers a range of deposits with wide variations in their characteristics. The essential requirement is the occurrence of preferred orientation in the deposit, directly related to the three-dimensional orientation of the substrate. The deposit crystals vary from large facetted crystallites, readily visible to the naked eye, such as were observed by the mineralogists, to thin uniform films of deposit which are only detectable by techniques such as electron diffraction or electron microscopy. 7.3.1 Orientation Relationships
It is normal, although not always observed, for a plane of atoms or ions in the deposit to be parallel to such a plane in the substrate, usually including the surface plane of the substrate. The parallel planes are usually aligned in such a way that a row of atoms or ions in one plane is parallel to a similar row in the other plane. Symmetry matching at the interface plane (i.e.
294
7 The Epitaxy of Metals
the substrate surface plane) is common, resulting in all atom rows in the substrate surface having a parallel row in the deposit. Since matching at the interface plays a dominant role in determining the orientation relationships, it follows that epitaxy can occur even if the substrate and deposit do not have the same crystal structure. Thus face-centred cubic (f.c.c.) metals such as gold and silver can be deposited epitaxially on the cleavage surface of mica, which has a monoclinic structure. The (001) cleavage face of mica contains a hexagonal network of ions, and the (111) plane of the face-centred cubic metals which also consists of a hexagonal network of atoms grows parallel to the mica cleavage surface. The control of epitaxy by alignment at the interface plane also results in the threedimensional orientation relationship between substrate and deposit being different for growth on different crystallographic surfaces of the substrate. This normally applies in all cases except where the substrate and deposit have the same crystal structure (e.g., both are face-centered cubic), and where the two are in parallel orientation on all substrate plane. Thus f.c.c. metals tend to grow on each other in parallel orientation, for all substrate surface planes. Comprehensive compilations of observed epitaxial orientations have been published by Seifert (1953) and Pashley (1956). More recently, Grunbaum (1975) has produced an updated and much more extensive list of known epitaxial systems, including references to all of the sources of information, but space limitations prevented inclusion of the details of the epitaxial relationships. It does not always happen that only one deposit orientation occurs on a given sub-
strate plane under a particular set of conditions of deposition (e.g., rate of deposition, substrate temperature). Often, a mixture of apparently unrelated orientations is observed. For example, Honjo et al. (1977) observed mixtures of (001) and (110) orientations of nickel and copper on (001) faces of magnesium oxide. Sometimes, a mixture of orientations occurs in the early stages of growth, but only one of these persists in thicker layers. Thus Matthews and Grunbaum (1965) found that, under certain conditions of deposition, (111) orientations of gold formed initially on the (001) cleavage face of rocksalt, but did not persist into thicker layers (but see Sec. 7.4.2.2). The (001) parallel orientation of gold, also present initially, dominated the thicker layers. Another form of multiple orientations is known as multiple positioning. This arises in situations where there are two or more equivalent ways of arranging a particular deposit orientation on the substrate surface, due to differences in symmetry. The simplest example is double positioning which occurs with (111) orientations of face-centred cubic metals (e.g. silver) on substrates such as mica (see Fig. 7-1 a). The two distinct orientations are: (111) Ag//(001) mica, with either [lTO] or [110] Ag//[100] mica. These are related to each other by a rotation of 180 degrees about the [111] axis, i.e., they are twin related orientations. In the case of (111) gold orientations on (001) rocksalt, as quoted above, there are the eight orientations made up of two sets of four equivalent orientations as shown in Fig. 7-1 b. 7.3.1.1 Deposition Conditions for Obtaining Epitaxy
In many of the reported cases of epitaxy, good quality orientation has been ob-
7.3 General Characteristics of Epitaxy
[110]
Figure 7-1. (a) Double positioning represented by the two twin-related orientations which occur for f.c.c. structures on a substrate of hexagonal symmetry, such as the mica cleavage surface, (b) The eight orientations of gold on the (001) rocksalt cleavage surface. Four equivalent (111) orientations have directions parallel to NaCl directions and the other four equivalent orientations have directions parallel to NaCl directions.
tained only over a limited range of deposition parameters. The relevant parameters appear to be: 1. The cleanness of the substrate surface 2. The smoothness of the substrate surface 3. The presence of contamination in the deposit 4. The rate of deposition 5. The substrate temperature during deposition. Because, in many experiments, there is inadequate information on items 1 and 3, and how they are influenced by items 4 and 5, it is not possible to draw any firm general conclusions. This applies particularly to much of the older evidence which relates to growth in poor quality vacuum systems. It is generally assumed that the presence of contamination is detrimental to the occur-
295
rence of good quality epitaxy (i.e., good alignment of all of the deposit in one single orientation). This is probably so, although Matthews and Grunbaum (1965) found that contamination can favour the establishment of good quality epitaxy of gold on rocksalt. Many investigators have found that substrate temperature has an important influence on the occurrence of epitaxy, following the early work of Bruck (1936), who found that a minimum temperature was required for the epitaxy of metals on rocksalt. This became known as the epitaxial temperature. When growth is carried out by the vacuum evaporation or MBE techniques, it is normal for the substrate to be held at an elevated temperature during deposition. Apart from the obvious possibility that substrate temperature is likely to modify the state of cleanliness of both the substrate and the deposit, it will also influence the various kinetic factors in film growth such as the surface mobility of the atoms arriving on the substrate surface. The rate of deposition will also influence the kinetic factors. 7.3.2 The Role of Lattice Misfit Ever since the classic work of Royer (1928), lattice misfit, or mismatch, at the interface between the substrate and the deposit has been considered as having an important influence on whether or not epitaxy occurs. The percentage misfit is simply defined as: 100 (b- a) m=
(7-1)
where a is the spacing of atom (or ion) rows in the substrate surface and b is the equivalent spacing in the parallel rows in the deposit. For some orientations, m varies with direction in the interface. Royer put forward a number of rules for the oc-
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7 The Epitaxy of Metals
currence of epitaxy, mainly based upon the extensive studies of his school on the growth of surface deposits from solution. The most widely quoted rule is that epitaxy only occurs if the misfit is less than about 15%. Extensive observations since have shown quite clearly that a small misfit is not a necessary requirement for epitaxy. This has been shown particularly well by systematic studies of the growth of a series of similar compounds (e.g., alkali halides), with a range of lattice parameters, by evaporation onto the same substrate. For a review of this evidence see Pashley (1956). Frank and van der Merwe (1949 a, b, 1950) introduced the idea that the growth of an epitaxial deposit depends upon the initial growth of a monolayer of the deposit which is strained elastically to match (i.e., have zero misfit with) the substrate surface. This was based upon the concept of pseudomorphism introduced by Finch and Quarrell (see Sec. 7.5). Frank and van der Merwe calculated that the pseudomorphic monolayers would only form for natural misfit values less than some limiting value in the region of 10-15%. Whilst this criterion for epitaxy is not sufficient, because other growth modes occur (see Sec. 7.4.1), the ideas introduced by Frank and van der Merwe have had a profound influence on the understanding of epitaxy, especially in relation to lattice strain and misfit dislocations (see Sec. 7.5). Because good quality epitaxy can occur with large misfit values, and because the orientation which occurs in a particular case is not necessarily that which has the best possible fit between the deposit and the substrate, it is difficult to provide a systematic framework for describing the role of misfit in epitaxy. However, there are some systematic studies which provide convincing evidence. Thus, Honjo et al. (1977) have carried out extensive observa-
tions on the orientation of three series of materials, including f e e . metals, on a magnesium oxide substrate in (001) orientation. They find that several distinguishable orientations of the f e e . metals occur with (001), (110) or (111) planes parallel to the surface, and that there is a systematic dependence of these orientations on the ratio of the lattice parameters of the substrate and the deposit, as summarized in Table 7-1. The best fit of the (001) orientation requires the ratio to be unity. For the other two orientations there are good onedimensional fits, corresponding to parallel rows of atoms having the same spacings in the substrate ^nd the deposit, when the ratio has the value v ^3/2 for the (110) orientation and 2/^/3 for the (111) orientation. The three orientations seem to occur for those f e e . metals which have lattice parameters giving ratios fairly close to these values. Thus there are examples where good lattice matching does appear Table 7-1. Epitaxial orientations of metals on MgO (from Honjo et al., 1977). Metala
Ni Cu Pd Pt Al Fe Au Ag In Pb a
Ratio R b
0.84 V3 ^0.85 2 "^0.92 0.93 0.96 0.96 0.97 . 0.97 ^ 1.091 2 ^ 1.17 j y 3 ~^ i.i8
Orientations (110)
(001)
**c **
*d * ** ** **
(111)
*
**
all metals are f.c.c. except In, which is face-centred tetragonal and Fe which is b.c.c. and is referred to its f.c.c. base. b R = ratio ametal/aMgO. c **: strong preference. d *: less strong preference.
7.4 The Modes of Growth of Epitaxial Metal Films
to determine particular epitaxial orientations, but this is not generally true. The misfit does seem to have significant influence on the details of the growth of an epitaxial layer.
7.4 The Modes of Growth of Epitaxial Metal Films Extensive studies by electron microscopy and electron diffraction and Auger electron spectroscopy have shown that there are wide variations in the way in which thin expitaxial deposits grow on a substrate. The initial stages of growth have received particularly strong attention because it has often been considered that epitaxy is determined during the initial stages, although post-nucleation processes are now known to have an important influence in some cases. It is generally recognised, following the work of Bauer (1958), that the initial stages can be classified into three idealised kinds of nucleation as described by Bauer and Poppa (1972). A useful historical summary of the basis for this classification has been given by Markov and Stoyanov (1987). 7.4.1 The Nucleation Modes of Growth The three distinct modes are illustrated in Fig. 7-2. The first mode follows from the theory of Frank and van der Merwe (1949 a, b, 1950) (and hence is called the Frank-van der Merwe mode, or monolayer mode) and consists of monolayer or twodimensional (2D) growth. The deposit grows monolayer by monolayer. Once one monolayer has been completed, a new monolayer is nucleated on top of it and when this monolayer is completed the process repeats itself.
297
(a)
(b)
(0 Figure 7-2. The three modes of growth of epitaxial layers (a) The Frank and van der Merwe monolayer (2D) mode; (b) the Volmer-Weber (3 D) mode; (c) the Stranski-Krastanow mode involving monolayer (2 D) growth followed by 3D growth.
The second mode involves the initial formation of a surface distribution of threedimensional (3D) nuclei, separated by uncovered regions of the substrate surface. The size and number of these three-dimensional nuclei changes as further deposition continues, until the nuclei coalesce and eventually form a continuous deposit film. This mode is normally known as the Volmer-Weber mode of growth. The third mode of growth is a combination of the other two. 2D growth occurs first, but after a few monolayers have formed the mechanism changes and 3D nuclei form on the uppermost layer. Further growth then occurs as for the VolmerWeber mode. This third mode is known as the Stranski-Krastanow mode. Whether 2D or 3D growth occurs initially can be considered in terms of surface energies, as has recently been summarised by Bauer and van der Merwe (1986). If the surface energy of the substrate is ys, the surface energy of the deposit film is yf and
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7 The Epitaxy of Metals
the interfacial energy is yin, monolayer growth is expected if the change in surface energy Ay, resulting from the deposition, is given by:
Table 7-2. The surface energy of various substances (from Kern et al., 1979). Substance
Face
Ay = yf + y i n - y s ^ 0
KBr KC1 NaCl CaCO 3 LiF CaF2 Cd Mg Zn Pb Pb MgO Si Al Al Ag Ag Au Au Cu Cu Cr Cr a-Fe a-Fe Ni Ni Pt Pt W Diamond
(100) (100) (100) (1010) (100) (111) (0001) (0001) (0001) (111) (100) (100) (111) (111) (100) (111) (100) (111) (100) (111) (100) (110) (100) (110) (100) (111) (100) (111) (100) (110) (111)
(7-2)
If this continues to apply as deposition continues, monolayer growth will continue. Since the Frank and van der Merwe theory involves the elastic straining of the monolayers, the elastic strain energy is included in these y values. If the strain energy contribution is large and increases as the number of monolayers increases, a point can be reached where Eq. (7-2) no longer applies and 3D nucleation takes place. This is the Stranski-Krastanow mode. If Eq. (7-2) does not apply at the beginning of growth, the Volmer-Weber 3 D nucleation process takes place. The main difficulty in applying the surface energy criterion represented in Eq. (72) is the lack of reliable data on the three surface energies. The problems have been considered by Kern et al. (1979), who tabulate a limited amount of data including surface energies of particular crystal faces of some alkali halides and some metals. An extract from these data is given in Table 7-2. In addition to the difficulty of making measurements, there is the problem of ensuring that measured values are not seriously influenced by the presence of contamination. It is well known that small traces of impurities can have a significant effect on surface and interfacial energies. Kern et al. (1979) have also given some values for the interfacial energies between a few pairs of metals. These values are small in comparison with the majority of the surface energies given in Table 7-2. Thus if ys is significantly greater than yf, 3 D nucleation is expected. If the materials of the substrate and deposit film are interchanged, ys becomes significantly less than
Surface energy ys (nJ mm ~ 2) 137 152 170 230 340 450 624 739 909 774 892 1200 1240 1692 1941 1693 1944 2218 2547 2554 2932 2775 3644 3032 4010 3246 3720 3294 3781 ^3000 5650
yf with the result that 2D nucleation is expected. When the values of ys and yf are nearly equal, the type of nucleation is determined by yin. If yin is small in comparison with ys and yf, it is possible for Eq. (7-2) to be satisfied, or nearly satisfied, both for growth of a particular deposit on a particular substrate and when the substrate and deposit are interchanged. Bauer and van der Merwe (1986) suggest that close to monolayer growth could then occur in both cases.
7.4 The Modes of Growth of Epitaxial Metal Films
7.4.1,1 Monolayer Growth
The interfacial surface energy yin is dependent upon the nature and the strength of the bonding at the interface. It also depends upon the value of the misfit, through the contribution of the elastic strain energy. Thus sufficiently low values of yin to allow Eq. (7-2) to be satisfied are likely to be confined to substrate/deposit combinations for which the misfit is small, although there are some exceptions to this. In accordance with the Frank and van der Merwe theory, pseudomorphic monolayer growth will normally only apply to cases of low misfit, although it would not be expected that a small misfit is a sufficient condition for monolayer growth. Many examples of strained pseudomorphic monolayer growth have been reported, and these generally involve misfits of no more than a few percent, perhaps up to values approaching ten percent. Because the surface energies of metals tend to be high in relation to many nonmetals (see Table 7-2), growth of metals on non-metals commonly occurs by the Volmer-Weber 3 D mode. The known cases of monolayer growth of metals are largely confined to the growth of metals on each other, although monolayer grown on some other substrates has been observed. The detection of monolayer growth can be achieved by several techniques. Reflection high energy electron diffraction (RHEED) (Milne, 1990) distinguishes monolayer growth from 3 D nucleation, but it can only be done with certainty if the growth is carried out simultaneously with the diffraction analysis by an appropriate in-situ technique. For growth of semiconductor layers by MBE, it is now common practice to include a RHEED system in the growth chamber. This has had particular value following the observation of oscillations in
299
the intensity of the specular reflected electron beam, as well as the diffracted beams, from surfaces on which monolayer growth is taking place (Harris et al., 1981a, b). These RHEED oscillations are interpreted (Neave et al, 1983) in terms of the changes in reflected intensity which occur as each monolayer of the growth is completed, to be followed by the nucleation of monolayer islands which coalesce to form the next monolayer. Although there is not complete agreement as to the detailed interpretation of the intensity oscillations, it is generally accepted that the periodicity does correspond to a thickness increase of one monolayer. Also it is generally accepted that the occurrence of the oscillations is direct evidence of monolayer growth. The technique has been applied to a number of metal depositions. For homoepitaxy, i.e., the growth of a metal on itself, RHEED oscillations have been observed (Steigerwald and Egelhoff, 1987) for copper grown on copper and f e e . iron grown on f e e . iron, When, however, f e e . iron is grown on copper there are no RHEED oscillations initially, but they do occur after the first few layers are deposited. This is explained as due to the initial growth of 3 D nuclei of iron followed by monolayer growth once a continuous layer of iron has formed. Jalochowski and Bauer (1988 a, b) have observed RHEED oscillations for silver and lead grown on silicon at 100 K. Auger electron spectroscopy (AES) can be used to detect monolayer growth (see Sec. 7.4.1.3 and Fig. 7-4), if in-situ observations are made during the growth of the deposit. Transmission electron microscopy also allows monolayer growth to be identified, if in-situ growth is carried out inside the electron microscope. Alternatively, if transmission electron microscopy is carried out after the growth of a deposit below the critical thickness tc (see Sec.
300
7 The Epitaxy of Metals
7.5.3.1), the absence of any misfit dislocations at the interface is evidence of pseudomorphic monolayer growth. There is now considerable interest in the growth of artificial superlattices of metals, such as are formed by the alternate epitaxial deposition of two different metals, or alloys, on a substrate. It is possible to grow the superlattice as effectively a single crystal if the two components have the same structure and the same lattice parameter. In the case of semiconductor III-V compounds this is commonly achieved by adjusting the lattice parameters of the two components by alloying between two or more III-V compounds. This approach can be extended by using two components with only a small lattice parameter difference, giving a misfit of perhaps one percent or less. The pseudomorphic strain associated with the monolayer growth mechanism then results in the superlattice also effectively being a coherent single crystal. This is then known as a strained layer superlattice. The periodicities in the interface plane match perfectly, but the periodicity perpendicular to the interface will be different in the two components since each component will be elastically strained in the direction away from the average of the natural periodicities. Such strained layer superlattices can be grown provided the thickness of each pseudomorphic component does not exceed the value of the critical thickness tc at which strain relief occurs (see Sec. 7.5.1; see also Chap. 8 of this Volume). Bauer and van der Merwe (1986) have considered the requirements for the growth of metallic superlattices, including the need for just one orientation to occur for growth of both A on B and B on A. For growth of superlattices with a small periodicity it is necessary for monolayer growth, or near monolayer growth, to take
place. This can be achieved with the appropriate combination of surface and interfacial energies (see Sec. 7.4.1). When Eq. (7-2) is nearly, but not completely, satisfied, the formation of a layer of uniform thickness can be achieved if a high rate of deposition and a low substrate temperature are employed. This results in a high density of thin plate-like nuclei which join together with the minimum of liquid-like coalescence (see Sec. 7.4.2.1), similar to the case illustrated in Fig. 7-8. Superlattices of metals have been grown by MBE for a number of different combinations. Durbin et al. (1982) prepared superlattices of niobium and tantalum which are both b.c.c. structures with a lattice mismatch of less than 0.2%. They were grown on single crystal sapphire substrates, with superlattice periodicities of 2-100 nm. Kwo et al. (1985) succeeded in growing good quality superlattices of gadolinium and yttrium, which are rare earth metals with hexagonal structures. Since both of these metals react chemically with many possible substrates, such as sapphire, a buffer layer of niobium on sapphire was used as the substrate. The structures of the two components do not have to be the same. Thus Cunningham and Flynn (1985) have grown superlattices of f.c.c. iridium and h.c.p. ruthenium. One of the problems in making superlattices of metals is to avoid significant alloying of the two components at the interfaces by being able to keep the temperature of the substrate sufficiently low during the deposition. Hsieh and Chiang (1986) have shown that it is possible to maintain sharp interfaces of silver and gold. Flynn (1988) has considered both the effect of alloying, and the maintenance of a smooth surface during growth, on the allowed growth temperatures. He maintains that RHEED oscillations are associ-
7.4 The Modes of Growth of Epitaxial Metal Films
ated with periodic surface roughening (see, e.g. Pautikis and Sindzingre, 1987), which is undesirable for the formation of a good superlattice. As the growth temperature is raised, the RHEED oscillations disappear, and this is explained as due to the increased surface mobility of the deposited atoms leading to ledge growth at steps (Fig. 7-3 a) with no formation of isolated monolayer nuclei or other clusters (such as shown in Fig. 7-3 b) on the ledges in between steps. He concludes that the growth temperature Tg must be greater than about 3/8 Tm, where Tm is the melting temperature of the metal being deposited, to avoid roughening. However, to avoid interdiffusion or alloying at the interfaces he estimates that the value of Tg needs to be less than 3/8 Tm. Thus there is only a very narrow range of possible values for Tg, if good quality superlattices are to be produced. He concludes, taking account of the limited accuracy of his estimates, that this optimal range is Tg = 0.35-0.40 Tm. This also means that it is not likely that good metal superlattices can be grown for two metals with very different melting temperatures, unless they are immiscible.
(a)
(b)
Figure 7-3. (a) Atoms diffusing to surface steps, resulting in growth of ledges without formation of new ledges, (b) Nucleation on ledges in between steps leading to periodic variation in surface roughness, causing RHEED oscillations.
301
7.4.1.2 The Volmer-Weber Nucleation Mode
A considerable amount of experimental study of 3 D nucleation has been made by transmission electron microscopy (TEM). Much of this work has involved deposits of metals on non-metallic substrates for which yf is generally much greater than ys. Gold and silver grown by vacuum evaporation onto rocksalt surfaces were by far the most widely studied systems before studies of semiconductor epitaxy became widespread in recent years. This arose because of the ease of making clean smooth surfaces by cleavage, and because the deposit layers could readily be detached from the substrate, for examination in the electron microscope, by dissolving the sodium chloride substrate in water. However, it is important to take into account a wide range of systems in order to obtain a balanced view of the nucleation mode of growth. The size and shape of the initial nuclei will also be determined by surface energies. This can be considered in terms of an extension of Wulff s theorem which determines the equilibrium shape of an isolated three-dimensional crystal (see Kern et al., 1979). For low values of the interfacial energy, the nuclei forming on a foreign substrate will have small ratios of height to width, and will therefore tend to be platelike. For high values of the interfacial energy, the nuclei will be much more equiaxed. Often they will have well developed crystallographic shapes. Nuclei are observed down to the smallest size which can be detected in the electron microscope, approximately 10 A in diameter. They are commonly distributed randomly over the substrate surface, with average separations which can be up to about a hundred diameters during the initial stages of deposi-
302
7 The Epitaxy of Metals
tion. However, particularly for metals deposited onto alkali halide surfaces, the initial nuclei form preferentially at surface steps on the substrate, even when those steps are only one atom layer in height. This was first observed by Bassett (1958), and many examples of the use of this decoration technique to provide information about the arrangement of steps on alkali halide surfaces, treated in different ways, have been reported by Bethge et al. (1968). Considerable efforts, both experimental and theoretical, have been devoted to the understanding of the kinetics of nucleation in the Volmer-Weber mode. Good reviews have been published by Venables and Price (1975) and Venables et al. (1984). Interest has centred upon topics such as (i) the smallest size of stable cluster, which would determine the initial nuclei; (ii) the rate of formation of stable nuclei for given deposition conditions; (iii) the geometrical distribution of nuclei over the substrate surface; and (iv) the change in size and numbers of nuclei as deposition continues, particularly to take account of the onset of the coalescence of nuclei leading to a reduction in numbers. Although these factors have considerable scientific interest, they do not seem to have had any major impact on the understanding of the factors controlling the occurrence of epitaxy. Some attempts have been made to determine the most energetically favourable orientation of a small stable nucleus on a single crystal substrate, in the hope that this could provide a means of developing a theory of epitaxy which would predict which orientation(s) will occur in a given situation. The best known treatment is that of Walton (1962), who considered two mechanisms by which a particular orientation may be favoured. Either a nucleus of a critical size, and in a particular orientation, is adsorbed more strongly than any other, or it is more able
to grow because nuclei or clusters of atoms in other orientations require the addition of atoms in unfavourable positions in order to grow. Whilst this approach helped to explain the orientation of f.c.c. metals on alkali halides, even though the misfit values are very high (e.g., 27%), it has not resulted in the prediction of orientations in many other systems. For this reason, no further consideration is given to the nucleation kinetics, and the reader is referred to the above-mentioned reviews for further information. It is important to consider how growth proceeds beyond the early nucleation stage, and how both the orientation and the structure of a deposited thin film are influenced. This is discussed in Sec. 7.4.2. 7.4.1.3 The Stranski-Krastanow Mode of Growth
Following the classification of the growth modes by Bauer and Poppa (1972), and their identification of the StranskiKrastanow mode as intermediate between the other two modes, various examples of the Stranski-Krastanow mode have been observed. In addition to examples involving the growth of semiconductor films, there are now an increasing number concerning epitaxial metal deposits. These seem to occur mainly either on substrates of molybdenum and of tungsten or on substrates of silicon and of germanium. The deposits include f.c.c. metals such as silver, gold and lead. Extensive reviews of the evidence have been published by Kern et al. (1979) and Venables et al. (1984). Much of the early evidence was based upon the application of Auger electron spectroscopy because the Auger signal originates from only the top few atom layers of a surface, so that monolayer growth causes the signal from the substrate to be reduced strongly
7.4 The Modes of Growth of Epitaxial Metal Films
for growth of just a few monolayers (Fig. 7-4b). For 3D nucleation, the Auger signal from the substrate remains strong for relatively large amounts of deposit (Fig. 7-4 a). The intermediate StranskiKrastanow mode causes the Auger signals to change as shown in Fig. 7-4c. The initial
(a)
No. of monolayers
(b)
No. of monolayers
(c)
No. of monolayers
Figure 7-4. The effect of different modes of growth on the Auger signal from the surface during AES analysis, (a) Three-dimensional nucleation according to Volmer-Weber mode, (b) Monolayer growth, (c) Stranski-Krastanow growth, with three-dimensional nucleation occurring after the formation of two monolayers. S = substrate; D = deposit film.
303
rapid decrease in the Auger signal from the substrate ceases immediately the 3D nucleation stage is reached. The scanning electron microscope, in conjunction with Auger electron spectroscopy and reflection high-energy electron diffraction, has also been used to provide direct evidence on the Stranski-Krastanow mode (Venables et al., 1980), by in-situ deposition. The nuclei, or islands, of the deposit could be observed in the microscope, and the presence of monolayer growth remaining between the islands could be determined by means of the Auger signals. A further electron microscope technique which has been applied to studies of this growth mode is that of reflection electron microscopy (Osakabe et al., 1980). The images are formed from diffracted beams obtained when the surface of the sample is illuminated by an electron beam at a glancing angle, and the resolution is adequate to allow monatomic surface steps to be seen. The technique has been applied to studies of copper, silver and gold on silicon surfaces (Takayanagi, 1985). For example, the growth of gold is seen to occur by the nucleation of monolayers at steps on the silicon surface and, after these had grown to complete one monolayer, the formation of 3D islands was observed. Detailed information was obtained on the reconstruction of the silicon substrate surface (see Vol. 1, Chap. 8) and on the superlattice structures of the deposited monolayers and the associated domain arrangements. 7.4.2 Post-Nucleation Growth Processes 7.4.2.1 Liquid-Like Coalescence Once a two-dimensional distribution of three-dimensional nuclei has been established by the Volmer-Weber mechanism (see Sec. 7.4.1.2), further deposition results in the growth in size of these nuclei. The
304
7 The Epitaxy of Metals
shape of the nuclei will remain the same if the surface diffusion of the newly arriving deposit atoms over the surfaces of the nuclei is sufficient to allow equilibrium shapes of the nuclei to be maintained. The nuclei, or islands, will continue to grow in size, in this way, until they grow sufficiently large to cause neighbouring islands to touch each other, and coalesce. The coalescence process has been observed when the epitaxial deposition process has been studied by in-situ electron microscopy. Bassett (1960) was the first to observe the so-called liquid-like coalescence behaviour of silver islands on a thin film substrate of molybdenite (MoS2). Two islands were shown to coalesce just as though they were liquid droplets, with the apparently instantaneous shape changes illustrated in Fig. 7-5. Pashley et al. (1964) extended the studies to include deposition of gold on molybdenite, and showed that the material in two coalescing islands remained solid, giving normal electron diffraction patterns, during the entire liquid-like coalescence. The initial observations were carried out in the normal poor vacuum conditions of electron microscopes of the day, leading to some doubts concerning the validity of the observations. Significantly improved vacua were used subsequently for in-situ microscopy of epitaxial deposition (Valdre et
Figure 7-5. The sequence of shape changes during the liquid-like coalescence of two non-crystallographic nuclei.
al., 1970; Poppa, 1969; Takayanagi et al., 1978 a), and the general characteristics of the initial observations were confirmed. The liquid-like coalescence is explained as due to self-diffusion of the deposit metal, e.g., gold, driven by surface energy. It seems likely that surface diffusion provides the predominant process, and Pashley et al. (1964) made some estimates of the times required to form necks between coalescing spheres of a range of different sizes, based upon the theory of particle sintering given by Kingery and Berg (1955). The results showed that the time required to produce a neck (e.g., as shown in Fig. 7-5b) of a given proportion of the initial size of the coalescing spheres is proportional to the fourth power of the initial radius of the spheres. Hence, in accord with the observations, smaller islands coalesce very much more rapidly than larger islands, although the effect of the non-spherical shape of the islands would need to be considered in any exact quantitative comparison. The general characteristics of the liquidlike coalescence depend upon the rate of surface diffusion, and the two extreme cases are illustrated schematically in Fig. 7-6 and Fig. 7-8. For fast surface diffusion and small islands (say less than about 100 nm across, in the case of gold at 300 °C), the sequence shown in Fig. 7-6 applies. Although the example illustrated is for triangular-based islands, the same kinds of sequence occur for islands of other crystallographic shapes. As soon as the two islands of Fig. 7-6 a touch, surface self-diffusion provides the possibility of rapid transfer of material to bring about a shape change in the compound island. In the initial stages of coalescence, rapid changes in total surface energy are brought about by significant rounding at the edges of the islands, due to the transfer of material from regions most remote from the neck to the
7.4 The Modes of Growth of Epitaxial Metal Films
Figure 7-6. The sequence of shape changes during the liquid-like coalescence of two triangular-based nuclei.
neck region which forms at the point of contact between the two islands (Fig. 76 b). This results in a dumb-bell shaped island which has lost its crystallographic shape (Fig. 7-6 c). Further reduction in surface area, coupled with a general thickening of the compound island, causes a more equiaxed island to form. A final reduction in total surface energy is brought about by the formation of a crystallographically shaped island (Fig. 7-6 d) which is just a larger version of each of the initial islands before coalescence commenced.
305
This coalescence process continues in the same way, thereby causing a continuous decrease in the number of islands per unit area, until a stage is reached when the total process of Fig. 7-6 is incomplete before a compound island is involved in coalescence with a neighbouring (compound) island. This changed situation arises because (i) the coalescence time increases rapidly as the average island size increases and (ii) the longer is the coalescence time the more do newly arriving deposit atoms cause an increase in the size of a compound island before the coalescence process is completed. Consequently, a deposit which starts off as nuclei with well developed crystallographic shapes develops into a distribution of much larger and fewer islands with rounded shapes. These rounded islands become joined together to form a network structure, the holes in which eventually become filled-in to produce a continuous hole-free deposit film. Fig. 7-7 illustrates the general characteristics of the growth sequence. When the surface self-diffusion, together with any volume self-diffusion, of the deposit material is sufficiently small, no significant change in the size and shape of islands can take place by the mechanisms
Figure 7-7. Transmission electron micrographs showing the stages of growth of a continuous epitaxial film by the Volmer-Weber 3 D mode, when pronounced liquid-like coalescence takes place (from Pashley etal., 1964). (a)
306
7 The Epitaxy of Metals
given in Fig. 7-6. Shape changes are then dependent upon the selective deposition of newly arriving deposit atoms, as illustrated schematically in Fig. 7-8. The extent to which the newly arriving atoms, diffusing over the uncovered regions of the substrate surface, deposit in the re-entrant regions, such as R in Fig. 7-8 b, determines how large the compound island grows before an equilibrium shape is re-established. Even with strong selective deposition at R, such as is shown for the sequence of Fig. 7-8, the compound island will be much larger than results from the coalescence of two islands of equal size by the mechanism of Fig. 7-6. A feature of the latter mechanism is that the area of coverage of the substrate surface is reduced by the liquid-like coalescence, but this does not happen in the selective deposition mechanism of Fig. 7-8. In general it is to be expected that for the coalescence of two islands, a combination of selective deposition and liquid-like coalescence will be involved in the shape changes which take place. The precise sequence of shape changes which occur, when two crystallographically shaped is-
lands coalesce, will depend upon just where they contact. For example, if the two islands contact at their apices, the sequence will be quite different from that which occurs when the apex of one touches the mid-point of the side of the other. The case illustrated is intermediate between the two. The liquid-like coalescence, resulting from surface self-diffusion of the deposit material, occurs commonly with a number of metals and it is mainly of significance when 3D nucleation takes place. During the early stages of the growth sequence, the liquid-like coalescence delays the formation of a continuous deposit film, since it causes a decrease in the actual area of coverage of the deposit, as shown in Fig. 7-5 and Fig. 7-6. During the later stages of the sequence a network structure is formed, as illustrated in Fig. 7-7. Further deposition occurs preferentially to fill in re-entrant regions such as that at R, driven by the reduction in surface area and hence surface energy. Hence, surface diffusion aids the formation of a continuous hole-free deposit film during the later stages of the sequence. 7.4.2.2 Reorientation and Recrystallization Effects
Figure 7-8. The sequence of shape changes during the coalescence of two triangular based nuclei, in the absence of liquid-like behavior and involving only selective deposition of newly arriving atoms.
In a number of systems, notably the growth of f.c.c. metals on alkali halides such as rocksalt, the initial nuclei can occur in a mixture of different orientations. In other systems the initial nuclei, although in the same nominal orientation, have deviations from exact alignment so that there is a spread of up to several degrees in orientation of the nuclei. In at least some of these latter cases it is believed that the poor alignments are related to contamination. When either mixed orientations or misalignments occur, it is possible for con-
7.4 The Modes of Growth of Epitaxial Metal Films
tinuous deposit films, resulting from further deposition, to be good quality single crystal films. The reorientation or recrystallization involved can take place either during coalescence of nuclei or following coalescence. The basic recrystallization process has been observed by in-situ transmission electron microscopy. Jacobs et al. (1966) studied the double positioning structure (see Sec. 7.3.1 and Fig. 7-1 a) in gold deposited on molybdenite, and found that reorientation occurred on coalescence. When two nuclei, or islands, in the two twin-related (111) orientations (or positions) coalesced to form a compound island containing a twin boundary, not necessarily a coherent twin boundary, the boundary sometimes migrated out of the island to leave an island in one single orientation (Fig. 7-9). Clearly, the driving force for this migration is the reduction and removal of the energy of the boundary. When the two coalescing islands were very different in size, the smaller island converted to the orientation of the larger island as the rapid liquidlike coalescence took place. The equivalent processes can occur for any general misorientation between two coalescing nuclei or islands. The epitaxial growth of gold on rocksalt cleavage surfaces contains a mixture of nuclei in eight different (111) orientations and nuclei in the parallel (001) orientation. As growth proceeds there is considerable recrystallization, but the result depends upon whether the rocksalt surface is exposed to air before the deposition is carried out (Matthews and Grunbaum, 1965). If growth takes place on a surface cleaved in ultra-high vacuum (UHV), the (111) oriented nuclei consume the (001) nuclei which recrystallize so that the continuous gold film contains a mixture of (111) oriented grains. If the rocksalt surface is ex-
307
posed to air before deposition of gold is carried out in UHV, the (001) nuclei consume the (111) nuclei and the continuous gold film is a single crystal in (001) orientation. Matthews (1965) explains this as due to the more numerous and larger (001) nuclei gaining over the smaller, less numerous (111) nuclei. When the substrate is not exposed to air, fewer nuclei form during the deposition of gold and the (111) nuclei grow quite large before coalescence takes place. Consequently the (111) nuclei seem to gain over the (001) nuclei during coalescence. Once a continuous deposit film is produced, there is still the possibility that any small grain of one orientation, which has become surrounded by material in another orientation, can be removed by grain boundary migration. Just as for the effect illustrated in Fig. 7-9, the driving force for the migration is the reduction in grain boundary area. This process would allow any remaining isolated grains of (111) orientation, in the example of the previous paragraph, to be eliminated. The important conclusions from the above evidence are: (1) significant changes
Figure 7-9. The liquid-like coalescence of two twinrelated triangular-based nuclei, leading to a double positioning twin boundary which then migrates out of the compound island which is formed. I and II represent the two positions.
308
7 The Epitaxy of Metals
in orientation can occur as a result of the coalescence of nuclei having different orientations; and (2) the final orientation of an epitaxial layer grown by the VolmerWeber 3D nucleation mechanism can be determined during the post-nucleation growth processes, rather than being completely determined by the orientation of the initial nuclei. Conclusion (2) is well illustrated by the fact that considerable grain growth can be achieved in polycrystalline films deposited onto single crystal substrates, so that large grains with well defined epitaxial orientations are produced (Thompson et al., 1990). The effect was obtained for the growth of f.c.c. metals deposited on alkali halides or mica, at relatively low temperatures for normal epitaxial growth, followed by annealing at higher temperatures. In this situation, the recrystallization is not related to coalescence since it takes place in a continuous film of uniform thickness. The technique provides a possible alternative method for growing epitaxial thin films, especially for film thicknesses lower than the minimum thickness for growth of continuous films by the normal Volmer-Weber mechanism.
the interface between them. This strain is accompanied by strain of the opposite sign normal to the interface, so as to maintain a nearly constant atomic volume. Their evidence was shown (Pashley, 1956) to be invalid, but their idea has proved to be correct for many substrate/deposit combinations studied during the last 25 years. The idea was incorporated into the classic theoretical treatment of Frank and van der Merwe (1949 a, b, 1950), in which the effect of the magnitude of the misfit on the formation of pseudomorphic monolayers was considered. It was shown that such monolayers would form for misfits below a certain limiting value (see Sec. 7.3.2). It was suggested that thickening of the deposit by successive growth of monolayers would lead to relaxation of the elastic strain and the formation of edge dislocations at the substrate/deposit interface. The way in which these dislocations accommodate the misfit between the substrate and the deposit is illustrated in Fig. 7-10. These are what are now well known as misfit dislocations. The above use of the term 'pseudomorphic' must be distinguished from its sometimes other use to denote the occurrence of Deposit
7.5 Elastic Strains and Misfit Dislocations The existence of elastic strains in epitaxial deposits is most commonly related to the formation of layers which are pseudomorphic. The term basal plane pseudomorphism was introduced by Finch and Quarrell (1933 and 1934), who interpreted observations on thin films of zinc oxide on zinc, and aluminium on platinum, as demonstrating that oriented deposits are strained elastically so that their lattice spacings match those of the substrate at
T
f
1F 1 1
Substrate Figure 7-10. The formation of misfit dislocations between the substrate and the epitaxial deposit to accommodate the misfit between the two.
7.5 Elastic Strains and Misfit Dislocations
an abnormal crystalline structure in an epitaxial deposit, to match the structure of the substrate (e.g., a normally h.c.p. material growing as f.c.c. on a substrate of f.c.c. material). 7.5.1 Changes in Elastic Strain with Increasing Thickness
For sufficiently small misfit values, the lowest energy state of a monolayer is a pseudomorphic monolayer. As further monolayers are added a stage is reached at which the deposit film should revert to its normal crystal spacings. This occurs at what is commonly known as the critical thickness, tc, and various approaches have been taken to the calculation of the critical thickness. The first treatment was published by van der Merwe (1963), and extended by Ball (1970) and Ball and van der Merwe (1970), who considered the minimum total strain energy by taking account of both the pseudomorphic elastic strain and the strain field of misfit dislocations. They defined the critical thickness as that at which it becomes energetically favourable for misfit dislocations to be present at the interface. This approach has been extended by taking account of the possible mechanism which can lead to the formation of misfit dislocations once tc has been exceeded. These mechanisms are summarised in Sec. 7.5.3.1. Jesser and Matthews (1967, 1968 a, b) and Matthews and Crawford (1970) considered the critical thickness as being determined by the misfit strain being adequate to exert a sufficient force on a threading dislocation to cause it to move according to the mechanism illustrated in Fig. 7-13. Thus, on this basis, the value of tc is determined by a force balance rather than an energy balance. The approach was extended to the case of the generation of
309
half-loops by the mechanism of Fig. 7-14, and the force required for their nucleation was calculated by Matthews (1975 a). He suggested that a dislocation loop will have a critical radius for expansion under the action of epitaxial stresses, and produced expressions for this. Cherns and Stowell (1976) extended this approach and included consideration of the nucleation and expansion of partial dislocation loops together with the associated stacking fault. A detailed theoretical discussion of the interpretation of the critical thickness has been provided by Willis et al. (1990) and Jain et al. (1990), with particular reference to semiconductor epitaxy. In the case of epitaxial metals, it is generally found that the theoretical values for tc agree fairly well with the observed thicknesses at which the onset of formation of misfit dislocations occurs, whereas epitaxial semiconductor layers commonly remain strained for thicknesses much greater than the theoretical values. This is believed to be due to the difficulty of nucleating misfit dislocations in these materials. An interesting confirmation of this conclusion has been provided by Hull et al. (1988) who annealed, in-situ in the transmission electron microscope, a layer of germanium-silicon alloy grown on silicon. They showed that there was a large increase in the number of misfit dislocations when the annealing temperature was well above the growth temperature, illustrating that such epitaxial layers have a metastable structure above tc. A good example of the determination of tc for a metallic system is that of gold grown on (111) palladium surfaces (Kuk et al., 1983). Low energy electron diffraction was used to measure the lattice constant of the gold as a function of thickness for growth which was shown to occur by the monolayer mechanism. Fig. 7-11 shows
310
7 The Epitaxy of Metals
Lattice
No. of monolayers
Figure 7-11. The change in the lattice parameter of an epitaxial gold layer on a (111) palladium surface as a function of the amount of deposit, as determined by low-energy electron diffraction (Kuk et al., 1983).
the result, with pseudomorphism extending only for the first two monolayers, to give a tc value of about 0.45 nm, followed by the gradual relief of the pseudomorphic strain during the growth of the next eight monolayers. This strain relief was assumed to be due to the gradual formation of misfit dislocations. 7.5.2 Misfit Dislocations The most efficient dislocations for accommodating the misfit between an epitaxial deposit and its substrate are pure edge dislocations with their Burgers vector in the plane of the interface. For the common situation of a two-dimensional misfit in the plane, a two-dimensional dislocation network is required. For metal deposits, the examples where the misfit dislocations have been observed and their Burgers vector determined is rather limited, but it is normally found that the Burgers vectors are of the same kind as those found within bulk crystals. However, they are not free to move by slip unless the interface plane happens to be a slip plane. Thus for cubic structures having (111) slip planes, the ideal misfit dislocations cannot slip unless the
deposit is growing in (111) orientation, and then slip can only occur in the interface plane. Such misfit dislocations cannot cross-slip and pass through the thickness of the film. The spacing of these misfit dislocations can be determined with reference to the spacing of the moire patterns obtained from two overlapping crystals. Examples of moire patterns are given in Fig. 7-26. Let the spacing of the substrate planes perpendicular to the surface and parallel to the misfit dislocations be ds9 and the spacing of the parallel planes in the deposit film be df. The misfit is m in %, where 100(d f -d s ) m=-
(7-3)
These two parallel sets of planes will go in and out of register with the periodicity of the Moire pattern, Sm. This is given by Bassett etal. (1958): d{ds d(-ds
100 d{
(7-4)
m
If the component of the Burgers vector of the misfit dislocations, parallel to the interface and perpendicular to the dislocation line, is be (i.e., the edge component in the interface), this will be given by be = ndf
(7-5)
where the dislocation is assumed to be in the deposit film. This assumption is based upon the substrate being thick so that all elastic and/or plastic strain resulting from the misfit occurs in the deposit. For perfect dislocations n is an integer, which is given by n=g b
(7-6)
where b is the total Burgers vector of the dislocation and g is the reciprocal lattice vector perpendicular to the planes of spacing d{. Thus if these are the (hkl) planes g
7.5 Elastic Strains and Misfit Dislocations
311
is given by ghkl. It follows that the spacing Sd of the parallel array of dislocations which completely accommodates the misfit is given by 100 ndf 100 (g • o
(7-7)
(a)
m m For the common situation of f.c.c. metals growing in parallel orientation on the (001) face of another f.c.c. metal, the normal arrangement is a square network of misfit dislocations along [110] and [110] with Burgers vectors of [f \ 0]and[f \ 0] respectively. The spacing of the dislocation network required to accommodate all the elastic strain is given by putting when g • b = 2 in each case and S, = l00aL/2m Eq. (7-7) is more commonly given in the form 100 be
(b) Figure 7-12. A schematic representation of the slip involved in forming misfit dislocations at the interface between a substrate and an epitaxial deposit which forms initially by the pseudomorphic monolayer mechanism, (a) Positive misfit producing pseudomorphic compressive stresses, (b) Negative misfit producing pseudomorphic tensile stresses.
(7-8)
m In general, as implied above, it is not necessary that the misfit dislocations have their Burgers vectors in the interface plane. If the interface contains an array of dislocations which have Burgers vectors with significant components lying in the interface plane, the misfit can be accommodated. However, the Burgers vector components normal to the interface plane results in the interface also being a small angle tilt boundary (see Sec. 7.5.3.1 and Fig. 7-12). Any Burgers vector components parallel to the misfit dislocation lines, giving them a screw component, result in the interface being a low-angle twist boundary. It is therefore possible that the interface plane is a low-angle boundary consisting of a mixture of tilt and twist components. The consequences of this can be illustrated by reference to the above example of the par-
allel orientation of one f.c.c. metal crystal on another. A possible alternative to the ideal misfit dislocations is dislocations along [110] and [110] with, for example, Burgers vectors of [\ 0 \] and [0 \ \\ respectively. Such misfit dislocations are commonly observed with the epitaxy of III-V semiconductor compounds on each other, where they are called 60° dislocations because their Burgers vectors are at 60° to the dislocation line. These dislocations are free to slip on (111) and (111) planes respectively. The edge component of their Burgers vector within the (001) interface plane is a/y/8, giving an effective value of n as 1, so that their spacing is halved relative to that of the ideal misfit dislocations, and is 100 a 2 . /2 m
312
7 The Epitaxy of Metals
The edge component perpendicular to the (001) plane is a/2, which would cause each of the two perpendicular sets of misfit dislocations to give a tilt of a/2
i00a/{2^2m)
2m
100
radians
2m The net result is a tilt of ^j- radians about [100]. This angle increases linearly with m and has a value of 1.1 degrees for ra = l%. Such tilt angles should be observable but none appear to have been reported. The screw component of the Burgers vector along the dislocation lines is a/y/8, and the square network results in a twist of the deposit lattice, about [001], of m radians
Too
i.e., 0.55 degrees per 1% misfit. 7.5.3 The Formation of Misfit Dislocations
The way in which misfit dislocations are formed in an epitaxial deposit depends upon (i) whether or not the deposit is elastically strained (i.e., pseudomorphic), and at what stage the elastic strain is relieved by misfit dislocations, and (ii) the mode of growth of the film, i.e., monolayer growth or nucleated growth. 7.5.3.1 Formation During Monolayer Growth
Generally, Frank-van der Merwe monolayer growth is confined to the lower range of misfit values, say m < 1 0 % , and nucleation will commonly occur for higher misfit values. If monolayer growth occurs for the higher misfit values, the theory indicates that pseudomorphism will not occur and the first monolayer will have close to its natural spacing, so that misfit disloca-
tions are expected to form at the interface right from the earliest stages of growth. The most energetically favourable dislocations would be expected to have the same Burgers vectors as those which normally occur in bulk material of the deposit. If the contact plane of the deposit contains required directions for these Burgers vectors, the formation of ideal misfit dislocations with their Burgers vectors parallel to the interface is likely. However, if the contact plane of the deposit does not contain these directions, either misfit dislocations with abnormal Burgers vectors would form or the misfit dislocations would have normal Burgers vectors not parallel to the interface plane. Most systematic evidence, including the relatively extensive observations on semiconductor epitaxy, has been obtained on low-index surfaces which do contain the directions along which normal Burgers vectors occur (i.e., the (100) and (111) surfaces of f e e . materials). Thus there is little evidence on what happens when there are no normal Burgers vectors parallel to the interface, or when there are insufficient (i.e., there is only one in the {110} surface off.ee. materials). The most important consideration is how dislocations are introduced once a film of large area growing by the Frank and van der Merwe monolayer mechanism exceeds its critical thickness tc. Spontaneous nucleation of misfit dislocations at the interface, without any passage of dislocations through the film, is neither likely nor an adequate requirement. In order to relieve the elastic strain of m in % which is present in the plane of the film, and which exists uniformly through the thickness of the film, it is necessary to bring about plastic deformation. This can be done either by slip or by climb, or by a combination of the two. The basic requirement for slip is that it occurs on an inclined slip plane, with the
7.5 Elastic Strains and Misfit Dislocations
Burgers vector of the dislocation having a non-zero component parallel to the interface and perpendicular to the line of intersection between the interface and the slip plane. This ensures that the misfit dislocation formed at the interface has an edge component in the interface and that linear plastic strain occurs in the plane of the film. Fig. 7-12 a illustrates the requirement for a film initially under elastic compression, since it involves plastic elongation of the film. Fig. 7-12 b illustrates the requirement for a film initially under elastic tension, which is compensated by plastic compression. The diagrams of Fig. 7-12 illustrate that a tilt boundary is produced as a result of the slip occurring on a parallel set Of regularly spaced slip planes. Thus the deposit layer would become detached from the substrate in the absence of an accompanying tilt. Two basic kinds of mechanism for introt
. ~
,. .
.
,
, - i
ducing misiit dislocations by slip have been proposed, and supported by experimental evidence, The first, proposed by Matthews (1975 b) to explain some observations on the growth of certain f.c.c. metals on each other, involves the movement of dislocations which thread continuously through the substrate and the deposit (see Fig. 7-13). Glide of the dislocation on an inclined slip plane, through the deposit only, leaves a trailing dislocation in the interface. This results in a non-ideal misfit dislocation being formed, provided the above basic requirement for the Burgers vector is fulfilled. The mechanism is likely to apply mainly for cases of rather small misfits, perhaps significantly less than 1%, because large numbers of threading dislocations with appropriate Burgers vectors would be needed to provide the high density of misfit dislocations required to accommodate larger misfits. Also, it is necessary to consider mech-
313
Deposit Substrate i t
I ~T
Figure7 . 13>
The formation of a misfit dislocation by the glide of a dislocation which threads through both the substrate and the epitaxial deposit. The Burgers vector of the dislocation must contain a component n o r m a l t0 the i n t e r f a c e t h e r e f o r e the misflt disloca ' " tion produced is not an (ideal) edge dislocation.
anisms which apply in the absence of threading dislocations, as would be likely for growth up to the critical thickness on a dislocation free substrate, Such a mechanism was also proposed by Matthews (1975 a and 1976 b), and involved the nucleation of dislocation loops at the growing surface of the epitaxial deposit. The loops expand by glide (see Fig. 7-14) and provide the misfit dislocations as they reach the interface, together with a pair of threading dislocations. If this mechanism operates so as to produce the complete interface misfit dislocation network required to relieve all of the epitaxial elastic strain, it results in the interface also being a low-angle boundary, and twist and/or tilt will occur as discussed in Sec. 7.5.2. There is little experimental evidence that such tilts or twists do actually occur in practice, even though the angles
314
7 The Epitaxy of Metals
Substrate
Figure 7-14. The nucleation of dislocation loops at the surface of an epitaxial deposit, and their expansion to form misfit dislocations at the interface, together with a pair of threading dislocations AB and CD.
involved for misfits of 1 % or more should be detectable. In fact, almost none of the papers dealing with the occurrence of misfit dislocations which are not ideal misfit dislocations contain any reference to the angular tilts and twists, which seem to have been largely ignored. One exception is the observation of a rotation of about 2 Vi degrees of an epitaxial deposit of cadmium selenide on germanium (Gejji and Holt, 1978). These authors showed that this rotation is consistent with the presence of a network of misfit dislocations having a screw component. Observations of small angular misorientations of cadmium sulphide grown on several different substrates have been made by Igarashi (1971), who explains them as due to the misfit dislocation arrangements. One possible reason for the lack of much evidence for tilts or twists is that the occurrence of non-ideal misfit dislocations is not common, at least for metal deposits. Alternatively, it is possible to avoid the tilts or twists by a suitable combination of non-ideal misfit dislocations of different Burgers vectors. Any mechanism for introducing ideal misfit dislocations must involve at least some elements of dislocation climb. This was first demonstrated by Yagi et al. (1971) who observed the formation of ideal misfit
dislocations during the growth of gold films on palladium inside the electron microscope. The simplest mechanism is for Frank dislocation loops to nucleate at the surface, and to move to the interface by climb, as shown in Fig. 7-15. If the plane of the loop is perpendicular to the interface, ideal misfit dislocations are produced. More generally, the plane will be inclined at some other angle and the dislocations will have Burgers vectors with a component normal to the interface, resulting in the interface becoming a tilt boundary. Also, for f e e . metals the Frank sessile dislocation forms on a (111) plane where it produces a stacking fault, so that a regular arrangement of stacking faults would extend through the epitaxial layer, on (111) planes. Cherns and Stowell (1975 a) have made a detailed study of the growth of palladium on (001) gold, by evaporation inside an electron microscope, and find that Frank sessile dislocations do climb as loops generated at the palladium surface. However, this follows the nucleation of Shockley partial dislocations, see Fig. 716, which produce stacking faults on the inclined (111) plane. These faults are removed as the Frank dislocation follows on the same (111) plane, and the two dislocations join together at the interface to pro-
Deposit
Figure 7-15. The relief of compressive pseudomorphic strain by the nucleation of a dislocation loop which expands by climb, to produce a misfit dislocation at the interface.
7.5 Elastic Strains and Misfit Dislocations
Frank partial Deposit
Stacking fault
Ideal misfit dislocation
Shockley Partial
Substrate Figure 7-16. The nucleation, and expansion by climb, of a half-loop of a Shockley partial dislocation in an epitaxial layer of palladium on gold. This produces a stacking fault on the (111) slip plane which is removed by the nucleation, and expansion by slip, of a half-loop of a Frank partial, which combines with the Shockley partial at the interface to produce an ideal misfit dislocation.
duce an ideal misfit dislocation:
- [1 1 2] + \ [1 1 1] -> i [1 1 0] o
Shockley
3
z
Frank
The misfit dislocation forms along [110] in the (001) interface, and is a pure edge dislocation with its Burgers vector in the interface. This particular sequence applies only for a negative misfit (i.e., the lattice parameter a0 for palladium is 4.7 % smaller than a0 for gold), where the Frank dislocation must produce an extrinsic stacking fault since it must introduce an extra (111) plane of atoms to relieve the elastic tension in the palladium. If the Frank dislocation were to nucleate first, followed by the Shockley partial, an ideal misfit dislocation would form at the interface but an arrangement of overlapping stacking faults would remain on the (111) plane. However, for a positive misfit, it is necessary to nucleate a Frank dislocation (involving an intrinsic fault) first followed by a Shockley partial, although this particular mechanism does not appear to have been reported. Reversal of this order is not possible since it would
315
involve a non-allowed stacking sequence on the (111) plane. Thus a combination of slip and climb, involving two (or more) dislocation loops, provides a mechanism for introducing ideal misfit dislocations at the interface, without any remaining planar faults. It seems that in some cases, at least, more complex slip and climb sequences apply. Cherns and Stowell (1975 b) find that when palladium is grown on a (111) gold surface, trigons of ideal misfit dislocations are produced by a sequence of interactions following the simultaneous nucleation of Frank partials on the three inclined {111} planes. Similar trigons of misfit dislocations have been observed by Honjo et al. (1977), who studied the in-situ growth of iron on a gold (111) surface. In this case the iron has the f.c.c. structure (y-phase) and is pseudomorphic up to a thickness of about 0.3 nm, after which the misfit dislocations are nucleated. The splitting of these dislocations into partials was revealed by a detailed contrast analysis. More recently, evidence for the mechanisms by which misfit dislocations are introduced during the growth of some epitaxial semiconductor films has been sought. For the growth of germanium-silicon alloys, a new misfit dislocation source has been observed by Eaglesham et al. (1989). This involves the formation of a diamond-shaped stacking fault which acts as a source for loops of 60° dislocations which can glide into the interface. No climb is involved in this mechanism. It is necessary for more careful experimental studies to be made for a range of substrate/ deposit combinations which result in pseudomorphic monolayer growth. Improved understanding can only follow from more direct evidence of the actual mechanisms which occur, and the conditions under which they operate.
316
7 The Epitaxy of Metals
The existing evidence on misfit dislocations and their formation during monolayer growth has been obtained predominantly with deposits of either (a) f.c.c. metals or (b) silicon and germanium and their alloys or (c) III-V semiconducting compounds with the cubic zinc sulphide structure. These three classes of material have similar slip systems and dislocations, involving dislocations with < | \ 0> Burgers vectors slipping on {111} planes. The growth of deposits in (001) orientation has featured strongly, with growth of metal layers in (111) orientation also having been fairly extensively studied. Little work has been done on deposits in other orientations, including (110). In the case of (001) deposits, the situation is simple because a square network of misfit dislocations along the [110] and [lTO] directions can be formed, either of ideal misfit dislocations or of the so-called 60° dislocations. In either case, complete relief of the pseudomorphic elastic strain is possible by this network, although tilt or twist should occur with the 60° dislocations (see Sec. 7.5.2). Likewise, for deposits in (111) orientation, misfit dislocations along [110], [101] and [011] form a triangular network of either ideal or 60° type. For most other orientations the pos-
[110]
[110] Figure 7-17. The slip planes on which dislocations can glide into the interface between an epitaxial layer of a f.c.c. metal and the (110) surface of another f.c.c. metal, to form misfit dislocations along AB. ABCD is the (111) plane and ABEF is the (111) plane.
sibilities are more limited, with no more than one direction in the interface plane. Therefore the pseudomorphic strain can be relieved by ideal misfit dislocations, either in one direction only in the interface plane, or not at all. Complete relief of the elastic strain requires the formation of non-ideal misfit dislocations with their Burgers vectors inclined to the interface plane. The lack of much reported experimental evidence on misfit dislocation formation in deposits in orientations other than (001) and (111) makes it difficult to come to any firm conclusions, but what evidence there is highlights the need to study such orientations further. Postnikov et al. (1976) have studied the formation of misfit dislocations in thin layers of platinum on (001), (110), (102), (103), (111), (112) and (123) surfaces of gold. They show an example where all of the misfit dislocations in (110) interfaces lie along the [110] direction, with inclined Burgers vectors of < | \ 0> type (see Fig. 7-17). These are assumed to have formed as a result of slip on the (111) and (111) planes. Slip on the (Til) and (111) planes would not relieve any of the pseudomorphic elastic strain because these planes are perpendicular to the interface. Therefore the observed misfit dislocations relieve strain only in the [001] direction, and it is not possible to relieve strain in the [110] direction by slip involving the normal {111} i\ \ 0> system. Growth of platinum on the (102) gold surface demonstrates another important aspect. The first misfit dislocations, produced as strain relief commences, lie along the [211] and [2TT] directions, with inclined Burgers vectors (see Fig. 7-18). These two directions are at an angle of 48 degrees to each other, and it is not possible to relieve the strain equally in all directions in the interface with such an arrangement. Such an-
7.5 Elastic Strains and Misfit Dislocations
isotropy arises unless the two sets of dislocations are perpendicular. This probably explains why further relief of strain involves the formation of misfit dislocations along [23T] and [23T], since these do help to reduce the strain anisotropy. These two examples demonstrate that strain relief by pure slip will result in an anisotropic strain distribution in the plane of an epitaxial layer, for most orientations of the interface. There is little experimental evidence as to how complete strain relief can be achieved in such cases. On the basis of known mechanisms, it seems that either abnormal slip systems must operate or dislocation climb must take place. It is also of interest to note that whilst there are many examples of TEM images of misfit dislocations produced following the formation of pseudomorphic layers, there is a lack of systematic evidence showing the increase in density of the misfit dislocations as the deposit layer is thickened and elastic strain is fully relieved. The first misfit dislocations which form tend to be in small groups, or clusters, such as is shown in Fig. 7-18. The non-uniform spacing is often much greater than that required to relieve all of the misfit strain. Further increase in thickness is required to raise the stress to a level at which further misfit dislocations are formed, so that complete relief of stress occurs at a thickness well above tc, as shown in Fig. 7-11. It seems to be a common experience with semiconductor epitaxial layers, such as those of the III-V compounds, that pseudomorphic layers often grow to thicknesses considerably greater than the theoretical critical thickness tc (see Sec. 7.5.1), and that the reduction in strain occurs gradually as growth continues. It is widely believed that this arises because of the difficulty of nucleating and moving dislocations in these structures. Since dislocations
317 [211]
[211] Figure 7-18. Groups of misfit dislocations formed in the interface between a platinum deposit film and a (102) gold substrate, as observed by Postnikov et al. (1976).
move easily in many of the metal deposits under consideration, especially at the elevated growth temperatures, it seems likely that the main reason for any lack of misfit dislocations with the deposits of these metals relates to the difficulty of nucleation. Jesser and van der Merwe (1989) have recently reviewed the theory involved in predicting the critical thickness in epitaxy. 7.5.3.2 Formation During Volmer-Weber Growth
For many examples of the Volmer-Weber growth mode (e.g., metals deposited on non-metallic substrates), the misfit is sufficiently high to prevent growth of pseudomorphic nuclei. Consequently misfit dislocations can form during the initial stage of nucleation simply by the local distribution of the misfit at the interface in accord with the classic diagram for the formation of misfit dislocations (see Fig. 7-10). For very high values of the misfit, requiring misfit dislocations very closely spaced together (say by three atomic spacings or less), the concept of misfit dislocations becomes meaningless. But for smaller values of misfit requiring spacings of dislocations of (say) 5 atomic spacings or more, the local concentration of misfit is likely to occur so
318
7 The Epitaxy of Metals
that misfit dislocations are produced. Once the misfit dislocations have been formed at the interface between the nuclei and the substrate, further increase in the lateral size of the nuclei automatically causes the misfit dislocation network to extend as the interface extends. Once a continuous holefree deposit film is formed, a continuous misfit dislocation network is present, although the coalescence of nuclei can result in irregularities in the network coupled with the formation of threading dislocations (see Sec. 7.6.2). In some systems, the initial nuclei of an epitaxial deposit can be pseudomorphically strained. An example is the growth of tin on tin telluride (Vincent, 1969). In analogy with the monolayer growth mechanism, the elastic strain of the nuclei should be relieved by the formation of misfit dislocations. This can occur by the nucleation of dislocations at the edge of the nuclei (Fig. 7-19), and their movement along the interface. This limited amount of interfacial slip seems possible even if the interface plane is not a normal slip plane, because the nuclei are not constrained by any surrounding material from moving slightly as slip occurs, so that the stresses required for such slip could be significantly less than for bulk material. Vincent (1969) produced evidence, based upon the spacing of moire patterns, that the residual elastic strain in the tin nuclei varied in a sawtooth manner with the lateral dimension of the nuclei (Fig. 7-20). He interpreted this as due to
•l/i Substrate (a) (b) ' Figure 7-19. The nucleation of ideal misfit dislocations at the edge of nuclei, and their movement along the interface as in (a), resulting in the formation of an array of misfit dislocations as in (b).
build-up of elastic strain as the nuclei increased in size, followed by a significant drop in the residual strain as a new misfit dislocation moved into the interface from the edge of the nucleus. Takayanagi et al. (1975) pointed out that the tin nuclei should be molten at the growth temperature of 200 °C, raising doubts as to the validity of this interpretation. They failed to reproduce the sawtooth variation found by Vincent, but by carrying out in-situ deposition in the electron microscope they did obtain evidence for a sawtooth variation in the moire pattern spacing in images of individual solid nuclei during growth at 80 °C. A different explanation for this sawtooth variation was put forward (see also Honjo and Yagi, 1980), partly because no direct evidence could be found of the presence of misfit dislocations. This explanation is based upon the existence of linear atomic chains of tin, which are strained uniformly without the concentration of misfit required for the model of Fig. 7-10. The sawtooth variation is explained as a result of the changes of the linear chain between two different stable configurations. The movement of dislocations from the edge of a nucleus to provide misfit dislocations to relieve elastic strain was observed in the early work of Matthews (1966), for example with the growth of gold nuclei on platinum. Cabrera (1964, 1965) concluded that the amount of pseudomorphic elastic strain in a nucleus should decrease as the size of the nucleus increases, and that this would be accompanied by an increase in the number of misfit dislocations. This decrease is illustrated in Fig. 7-20, for tin on tin telluride which has a misfit of 7.8 % in the direction in which the measurements were made. The important difference between the mechanisms for introducing misfit dislocations at the interfaces of nuclei,
7.5 Elastic Strains and Misfit Dislocations
Strain
No. of misfit dislocations 4
5
6
7
8
9
10
3.0-
20
30 40 Island width (nm)
Figure 7-20. The sawtooth variation in the strain in nuclei of tin grown on a substrate of tin telluride, as a function of the width of the tin nuclei and as measured from the spacing of moire patterns (Vincent, 1969).
319
and those mechanisms required with deposits formed by monolayer growth, is that there is no requirement for any plastic deformation through the thickness of a nucleus. When misfit dislocations are introduced at the interface of the nucleus with the substrate, the elastic strain in the nucleus automatically becomes relaxed, whereas no such relaxation is possible in a continuous deposit film without associated plastic deformation (see Sec. 7.5.3.1). A further mechanism, which involves no plastic deformation through the thickness of the nucleus, is the introduction of misfit dislocations by existing grown-in threading dislocations, illustrated in Fig. 7-21, as proposed by Jesser and Matthews (1968 b). 7.5.3.3 Formation During Stranski-Krastanow Growth
Substrate
Figure 7-21. The stages in the generation of non-ideal misfit dislocations at the interface with nuclei, due to the motion of a substrate dislocation which is extended into the nucleus. The dislocation remaining in nucleus A can move out of the nucleus to complete the formation of a misfit dislocation below nucleus A.
There seems to be little or no experimental evidence on the mode of formation of misfit dislocations following the monolayer growth stage of the Stranski-Krastanow mechanism. This is because little electron microscopy has been carried out on metal deposits produced by this mode. Possibilities can be deduced by analogy with what occurs during Frank van der Merwe growth and Volmer-Weber growth. If relaxation of pseudomorphic elastic strain occurs before the 3D nucleation stage commences, the introduction of misfit dislocations should occur by the mechanisms discussed in Sec. 7.5.3.1. If nucleation occurs on top of a pseudomorphic layer, it seems likely that misfit dislocations will nucleate at the edges of the nuclei, as in Fig. 7-19, either immediately the nuclei form or during their subsequent growth. These misfit dislocations would have to propagate through the continuous layer beneath the nuclei, perhaps in the form of expanding dislocation loops.
320
7 The Epitaxy of Metals
7.6 Lattice Imperfections in Layers Grown by Epitaxy 7.6.1 Imperfection Structures Observed In addition to any misfit dislocations, epitaxial layers commonly contain a variety of lattice defects, although the layers can be largely defect free under ideal conditions of growth. The most common defect is the dislocation line which starts at the interface with the substrate and ends at the free surface of the layer. This is known as a threading dislocation, which can either follow a fairly straight path joining the two surfaces of the film or follow a more complex path between the two surfaces. In the latter case, there is likely to be an intersection between two or more dislocations giving rise to some kind of irregular network, although such arrangements have been more commonly observed in semiconductor films. This is partly because more electron microscope observations have been carried out on thick (say > 1 jim) semiconductor layers than on metal films. Dislocation densities up to 108 mm~ 2 have been reported. Stacking faults are found in many epitaxial layers, especially in f.c.c. metals grown on non-metallic substrates such as alkali halides. These planar faults normally extend through the thickness of the film
Partial Partial
Stacking fault Figure 7-22. A stacking fault of limited length produced by coalescence, and bounded by two partial dislocations.
and are terminated within the film by partial dislocations as shown in Fig. 7-22. Overlapping stacking faults can also occur, as well as microtwins. 7.6.2 Modes of Formation of Lattice Defects The main modes of formation of lattice defects can be classified as follows: (1) copying of defects from the substrate; (2) formation of defects linked with misfit dislocations; (3) introduction of defects during the coalescence of nuclei. In addition, it is known that defects can be introduced as a result of contamination of the substrate surface, but what follows relates to mechanisms which can operate under nominally clean conditions. 7.6.2.1 Copying from the Substrate If the substrate contains lattice imperfections which emerge at the surface on which the epitaxial growth takes place, extension of those imperfections into the epitaxial layer can occur. It would not be expected that imperfections would extend into a layer which has its own lattice spacings and is not pseudomorphic with the substrate, whether it grows as monolayers or as 3 D nuclei. This is because the relative positions of atoms in the deposit, at the interface, should be determined largely by their binding with the deposit. If, on the other hand, the epitaxial layer is pseudomorphic, it would be expected that imperfections would extend into the deposit, because the positions of the deposit atoms (e.g., in monolayer growth) should be determined entirely by the position of the atoms in the substrate surface. Whilst it is known that copying, or extension, of substrate dislocations into the deposit does oc-
7.6 Lattice Imperfections in Layers Grown by Epitaxy
cur in some cases (e.g., Matthews, 1975 b) and not in others, there is no systematic experimental evidence to support the kind of arguments given above. It would be helpful to know whether the occurrence of copying depends upon other material properties, in addition to pseudomorphism in the deposit, or upon the Burgers vector of the substrate dislocation. 7.6.2.2 Defects Linked with Misfit Dislocations Whether or not the formation of misfit dislocations involves the formation of defects threading through the deposit thickness, depends upon the mechanism by which the misfit dislocations are formed. For ideal pseudomorphic monolayer growth the formation of misfit dislocations, as the deposit film increases in thickness beyond the critical thickness tc, occurs in one of two ways (see Sec. 7.5.3.1). The first way involves the movement of threading dislocations copied from the substrate, and this mechanism introduces no new threading dislocations although rearrangement of the existing threading dislocations is involved. The second, and more important, class of mechanisms involves the nucleation of dislocation loops at the surface of the growing pseudomorphic deposit film. The basic process is illustrated in Fig. 7-14, which shows that as the loop expands and causes a misfit dislocation to form at the interface it leaves two threading dislocations AB and CD. These move apart as expansion of the loop continues, but they remain as threading dislocations unless they move to the edge of the film. In general, this is unlikely to happen since loops would be nucleated at many points on the surface of the film and each would produce a misfit dislocation of a limited length. Further expansion would cease ei-
321
ther as a result of the reductions in local stresses due to the generation of other misfit dislocation loops in neighbouring regions of the film, or possibly as a result of an obstacle such as a local region of impurity or another dislocation. Thus the number of threading dislocations produced per unit area will be given by twice the number of loops generated per unit area. This, in turn, will depend upon (a) the misfit, and the extent to which it is relieved; (b) the Burgers vectors of the dislocation loops, and (c) the average length of the misfit dislocations produced. On this simple basis, the number of threading dislocations, N is given by: N=
4/cmlO 10
per
(7-9)
where m in % is the misfit, a fraction k of which is accommodated by a square array of misfit dislocations of length / in nm and edge component of Burgers vector in the interface plane b e in nm. This is derived from Eq. (7-8). However, in practice, there is likely to be considerable interaction between the different expanding dislocation loops. For two loops on the same inclined plane, the interaction would result in annihilation of a pair of threading dislocations, as illustrated in Fig. 7-23. For two loops on near neighbouring parallel inclined planes, separated by a distance less than the spacing of misfit dislocations required to relieve all of the elastic strain, a pair of close dislocations of opposite sign would be produced. In general they would have mixed edge and screw character, and there would be a force of attraction between them. They could therefore annihilate each other by a combination of climb and crossslip. Consequently N might be very considerably reduced from the value given by Eq. (7-9). In fact, there is little experimental evidence of the number of threading dislo-
322
7 The Epitaxy of Metals
/\
~7
Deposit
J
Substrate
j Figure 7-23. The interaction between two expanding dislocation loops, of the same Burgers vector and on the same slip plane, resulting in the reduction of the number of threading dislocations.
cations remaining in a thin epitaxial layer, due to this mechanism of formation. This includes studies on epitaxial semiconductor layers, although it is generally assumed that the mechanism does lead to the formation of threading dislocations. In the same way, the more complex mechanisms summarised in Sec. 7.5.3.1 would also be expected to result in the formation of threading dislocations, and possibly also stacking faults.
lier, Matthews (1959) had proposed that stacking faults can be produced as two nuclei coalesce and Matthews and Allinson (1963) concluded that the often extensive formation of microtwins in f.c.c. metals grown on rocksalt result from coalescence. The effects can be considered by reference to Fig. 7-24, which represents the displacement misfit between three coalescing nuclei in terms of just one set of crystal planes normal to the substrate surface. According to the model, as each of the three pairs of nuclei join together as they grow larger, the planes shown will join so as to minimise the elastic strain energy. For certain values of the displacement misfits between the coalescing pairs of nuclei, such as for the example of Fig. 7-24, the joining will occur so as to produce an incipient threading dislocation in the hole between the nuclei (Jacobs et al., 1966). As the hole becomes filled in, a real threading dislocation is produced. Whilst the compound nucleus, or island, remains free from any further coalescence it is possible for the dislocation to move out of the island. Once a
7.6.2.3 Defects Resulting from Coalescence of Nuclei When nuclei form with their natural crystal spacings, and there is a misfit at the interface with the substrate, it follows that a line joining an interface atom in one nucleus to an interface atom in a neighbouring nucleus will not necessarily be an integral multiple of the normal interatomic distance. This arises because the substrate and deposit lattices are not commensurate, so that there will be a small random displacement of the lattices of the two nuclei. Jacobs et al. (1966) were the first to propose that these displacement misfits can lead to the formation of dislocations. Ear-
Figure 7-24. The formation of a threading dislocation by the coalescence of three nuclei which are not pseudomorphic with the substrate, so that a random displacement misfit exists between adjacent nuclei. The vertical lines represent a parallel set of crystal planes.
7.6 Lattice Imperfections in Layers Grown by Epitaxy
continuous network structure is formed, following further coalescences (see Sec. 7.4.2), any threading dislocations moving out of the islands effectively result in incipient threading dislocations in the holes into which they move. It follows that real threading dislocations are inevitably created once the holes become filled in. Liquidlike coalescence might prevent the formation of threading dislocations by the mechanism of Fig. 7-24 during the early stages when the nuclei and islands are quite small. It would not, however, prevent the mechanism operating during the later stages leading up to the network stage. Thus displacement misfit between islands, which is a necessary consequence of the misfit between substrate and deposit, does lead to the formation of threading dislocations. The experimental evidence in support of this conclusion has been obtained by insitu transmission electron microscopy and examples have been presented in earlier reviews (Pashley, 1965; Honjo and Yagi, 1980). The mechanism shown in Fig. 7-24 applies where there is a misfit between substrate and deposit, and no pseudomorphism. It applies irrespective of the presence of misfit dislocations. If the misfit is not too large for the formation of misfit dislocation (see Sec. 7.5.3.2) an alternative, and largely equivalent, mechanism of the formation of threading dislocations can be put forward, in terms of the joining up of misfit dislocations (Fig. 7-25). The misfit dislocations at the interface of neighbouring nuclei with the substrate will not necessarily be aligned in register with each other, so that as such nuclei coalesce some local bending of the misfit dislocations is required to allow them to join together. Depending upon the extent of disregistry between the misfit dislocations associated with each pair of the three coalescing is-
323
Figure 7-25. The formation of a threading dislocation as a result of the joining of misfit dislocations at the interface with three adjacent nuclei. The vertical lines represent a parallel set of misfit dislocations.
lands, one of the misfit dislocations (e.g. pq in Fig. 7-25) can be left terminating at the centre of the coalescence. Since dislocations cannot terminate inside a crystal, the misfit dislocation pq must be linked at q to a threading dislocation which forms during coalescence. In this situation the threading dislocation must have the same Burgers vector as that of the misfit dislocation pq. Thus, by this mechanism, the threading dislocations produced would be confined to those with Burgers vectors matching the Burgers vectors of the misfit dislocations, and there is no evidence as to whether or not this is normally the case. Subsequent interactions between threading dislocations could lead to the formation of dislocations with other Burgers vectors. Coalescence between two nuclei or islands can lead to the formation of a stacking fault if the displacement misfit between them has an appropriate value. For the f.c.c. system the exact displacement required is | . With parallel growth occurring on a (001) substrate there is no such vector in the surface plane, but there are directions at angles of 24 degrees to the surface, so that the appropriate dis-
324
7 The Epitaxy of Metals
placements in the surface plane can have large components parallel to a direction. In the most favourable situation a displacement misfit of d along the [210] direction in the (001) surface has a component of 0.91 d along [211], so that an appropriate value of the displacement d would be largely accommodated by the formation of a stacking fault on coalescence. For growth on a (111) substrate there are directions in the surface, so that appropriate displacements can be completely accommodated by stacking faults being formed during coalescence.
These examples demonstrate that some of the random displacements of nuclei due to misfit are likely to result in the formation of stacking faults during coalescence, as is actually observed (Jacobs et al., 1966; see Fig. 7-26). The evidence shows that such stacking faults can be eliminated by slip, whilst the deposit continues to consist of isolated nuclei or islands. During the later stages of growth the elimination of stacking faults results in the formation of incipient threading dislocations, just as for the above case of the removal of dislocations at the network stage.
Figure 7-26. The growth of gold on MoS 2 , inside the electron microscope, showing the formation and elimination of stacking faults, F 1 , F 2 , F 3 , F 4 , following coalescence (From Jacobs et al., 1966). 25nm
7.6 Lattice Imperfections in Layers Grown by Epitaxy
In addition to the formation of thin microtwins threading through an epitaxial deposit, and also believed to result from coalescence of nuclei (Matthews and Allinson, 1963), the presence of multitwinned particles of f.c.c. metals formed during the early stags of epitaxial deposition has been observed by transmission electron microscopy. They have been identified by several workers for growth on alkali halide cleavage surfaces (e.g., Ino and Ogawa, 1967), and have also been observed for growth on mica cleavage surfaces (Allpress and Sanders, 1964). In their simplest form they consist of a tetrahedron bounded by (111) surfaces together with a primary twin and a secondary twin on each of two of the faces of this tetrahedron, as illustrated in Fig. 7-27. This produces a compound particle which has five-fold symmetry when viewed along OA. More complex particles, involving larger numbers of tetrahedral components, appear to have hexagonal symmetry. Other particles containing five tetrahedral components appear as rhombic shapes. The number of multiply twinned particles present in the early nucleation stages decreases as growth continues. It is believed that this is largely due to recrystallization occurring during coalescence (see Sec. 7.6.3). The size of the remaining particles increases during continued deposition. There is some evidence that the multiply twinned particles are formed initially by coalescence, although they can also be considered as originating from earlier stages of nucleation, in the form of spontaneously strained structures (Ogawa and Ino, 1972). 7.6.3 Changes in Imperfection Structure as Growth Proceeds
Once a continuous hole-free and largely strain free epitaxial layer has been formed,
B
325
C (a)
(b)
Figure 7-27. A model for the formation of five-fold multiply twinned particles, (a) OABC is the basic (111) oriented tetrahedron, on two faces of which the primary twin tetrahedra OACL and OABF are formed. The secondary twin tetrahedra are OALD and OAFE. Closing of the gap ED gives the five-fold symmetry of the particle when viewed along OA, as shown in (b).
further growth can proceed by continuing the orientation of the deposit by a monolayer process. It is of interest to consider how the lattice defects present in the layer will develop as the layer thickness increases. It would not be expected that any formation of new independent defects would take place, since none of the mechanisms discussed in Sec. 7.6.2 should apply to homoepitaxy or growth with a zero misfit.
326
7 The Epitaxy of Metals
There seems to be little evidence, in the case of metal epitaxy, as to how the imperfection structure changes with increasing thickness. Many studies have been made of thicker layers of epitaxial semiconductors, since layers of 1 jim to 5 jam in thickness are commonly used for the investigation of optical and electronic properties. It is commonly found that the dislocation density in the epitaxial layer decreases with distance from the interface, and that the surface regions of such layers can be relatively perfect. Existing threading dislocations must extend into the epitaxial layer as growth proceeds but, under the action of local stresses, they can change their direction as they extend in length. In so doing, they can interact with other dislocations, joining with them and possibly forming irregular networks as several dislocations join together. As this joining process occurs, the further propagation of the joining dislocations into the growing layer ceases. In this way the number of threading dislocations reduces with thickness, and irregular networks containing dislocations running approximately parallel to the surface are left below the growing surface. These networks can be modified, and simplified, by slip and/or climb processes if growth continues at a suitably high temperature. This general picture seems to be consistent with the observations made on semiconductor layers, and it seems likely that similar changes will occur with epitaxial metal layers, so that a reduction in defect density occurs as thickness increases.
7.7 Summary and Conclusions Epitaxy has been observed with a range of metals, but much emphasis has been put on the growth of f e e . metals. When f e e . metals are grown on single crystal metals
as substrates, the pseudomorphic monolayer growth mechanism applies in a number of cases, whereas the formation of 3 D nuclei by the Volmer-Weber mechanism occurs in others. For a few cases the Stranski-Krastanow mechanism applies. When f e e . metals are grown on non-metallic single crystals the most common mode of growth is 3 D nucleation. Much of the existing evidence relates to growth on alkali halide substrates. It seems likely that epitaxy of metals can be obtained on a wide range of substrates, under appropriate deposition conditions. A recent summary of some of the factors which are inadequately understood, together with a discussion of the present understanding of epitaxy, has been published by Bauer et al. (1990). In common with other epitaxial thin films, especially those of semiconductors which have been studied rather extensively over the last 10 to 15 years, epitaxial deposits of metals commonly contain high densities of lattice defects threading through the thickness of the films. This applies generally for growth by the YolmerWeber 3 D nucleation mechanism, and only for growth by the Frank van der Merwe monolayer mechanism do the epitaxial metal films contain really low defect densities. In these latter cases the defects extending through the thickness of the film appear to be formed mainly as a result of the mechanisms which operate to provide the interfacial misfit dislocations required to accommodate the misfit between the substrate and deposit. There is a lack of systematic evidence on the development of both interfacial misfit dislocations, and defects extending through the thickness of an epitaxial deposit, as the growth of an epitaxial layer proceeds. Various models exist for explaining and predicting how the various kinds of defect structure are formed, and these
7.8 References
models are supported by much experimental evidence, but a number of detailed aspects are not covered by the models and the limitations and range of applicability are not adequately understood. If, as seems likely, the use of epitaxial deposits of metals and alloys for studies of, for example, magnetic and superconducting properties increases there will be need for an increase in knowledge on defect structures and their formation. This need would increase further as technological applications of epitaxial metal layers develop. One area of considerable current interest is the growth of superlattice structures, including strained layer superlattices (see this Volume, Chap. 8). The MBE technique has allowed such superlattices to be grown successfully, but there are likely to be limitations on the metallic pairs which can be used because monolayer growth will often not occur both for metal A on metal B and for metal B on metal A. It will be interesting to see whether the use of alloys, rather than pure metals, increases the scope for growth of good quality superlattices.
7.8 References Allpress, J. G., Sanders, I V. (1964), Phil. Mag. 10, 645. Ball, C. A. B. (1970), Phys. Status Solidi 42, 357. Ball, C. A. B., van der Merwe, J. H. (1970), Phys. Status Solidi 38, 335. Bassett, G. A. (1958), Phil. Mag. 3, 1042. Bassett, G. A. (1960), in: Proc. Eur. Conf. Electron Microsc. Delft: Houwink, A. L., Spit, B. J. (Eds.). Nederlandse Vereniging voor Electromenmicroscopie, p. 270. Bassett, G. A., Menter, J. W., Pashley, D. W. (1958), Proc. Roy. Soc. A246, 345-368. Bauer, E. (1958), Z. Kristallogr. 110, 372. Bauer, E., Poppa, H. (1972), Thin Solid Films 12,167. Bauer, E., van der Merwe, J. H. (1986), Phys. Rev. B33, 3657. Bauer, E., Dodson, B. W., Ehrlich, D. X, Feldman, L. C , Flynn, C. P., Geis, M. W, Harbison, J. P., Matyl, R. I , Peercy P. S., Petroff, P. M., Phillips,
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J. M.? Stringfellow, G. B., Zangwill, A. (1990), J. Mater. Res. 5, 852. Bethge, H., Keller, K. W., Ziegler, E. (1968), /. Cryst. Growth 3, 184. Bruck, L. (1936), Ann. Phys. 26, 233. Cabrera, N. (1964), Surf. Sci. 2, 320. Cabrera, N. (1965), Mem. Sci. Rev. Mat. LXII, 205. Cherns, D., Stowell, M. J. (1975a), Thin Solid Films 29, 107. Cherns, D., Stowell, M. J. (1975 b), Thin Solid Films 29, 127. Cherns, D., Stowell, M. J. (1976), Thin Solid Films 37', 249. Cunningham, J. E., Flynn, C. P. (1985), J. Phys. F: Met. Phys. 15, L221. Durbin, S. M., Cunningham, J. E., Flynn, C. P. (1982), J. Phys. F: Met. Phys. 12, L75. Eaglesham, D. J,, Kvam, E. P., Maher, D. M., Humphreys, C. I , Bean, J. C. (1989), Phil. Mag. A 59, 1059. Esaki, L., Tsu, R. (1970), IBM J. Res. Develop. 14, 61. Finch, G. I., Quarrell, A. G. (1933), Proc. Roy. Soc. A 141, 398.
Finch, G. L, Quarrell, A. G. (1934), Proc. Phys. Soc. Lond. 46, 148. Flynn, C. P. (1988), J. Phys. F: Met. Phys. 18, L195. Frank, F. C , van der Merwe, J. H. (1949a), Proc. Roy. Soc. A 198, 205. Frank, F. C , van der Merwe, J. H. (1949b), Proc. Roy. Soc. A 200, 125. Frank, F. C , van der Merwe, J. H. (1950), Proc. Roy. Soc. A 201, 261. Frankenheim, M. L. (1836), Ann. Phys. 37, 516. Gejji, F. H., Holt, D. B. (1978), J. Mater. Sci. 13, 2048 Grunbaum, E. (1975), in: Epitaxial Growth: Matthews, J. W. (Ed.). New York: Academic Press, pp. 611-673. Harris, J. X, Joyce, B. A., Dobson, P. X (1981 a), Surf. Sci. 103, L90. Harris, J. X, Joyce, B. A., Dobson, P. X (1981 b), Surf. Sci. 108, L444. Honjo, G., Takayanagi, K., Kobayashi, K., Yagi, K. (1977), /. Cryst. Growth 42, 98. Honjo, G., Yagi, K. (1980), in: Current Topics in Materials Science Vol. 6. Amsterdam: North Holland Publishing Company, pp. 195-307. Hsieh, T. C , Chiang, T. C. (1986), Surf. Sci. 166, 554. Hull, R., Bean, X C , Warder, D., X, Leibenguth, R. E. (1988), Appl. Phys. Lett. 52, 1605. Igarashi, O (1971), J. Appl. Phys. 42, 4035. Ino, S., Ogawa, S. (1967), J. Phys. Soc. Japan 22, 1365. Jacobs, M. H., Pashley, D. W, Stowell, M. X (1966), Phil. Mag. 13, 129 Jain, S. C , Willis, X R., Bullough, R. (1990), Adv. Phys. 39, 127. Jalochowski, M., Bauer, E. (1988 a), Phys. Rev. B37, 8622. Jalochowski, M., Bauer, E. (1988 b), Phys. Rev. B38, 5272.
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Jesser, W. A., Matthews, X W. (1967), Phil. Mag. 15, 1097. Jesser, W. A., Matthews, J. W. (1968 a), Phil. Mag. 17, 461. Jesser, W. A., Matthews, J. W. (1968 b), Phil. Mag. 17, 595. Jesser, W. A., van der Merwe, J. H. (1989), in: Dislocations in Solids. Vol. 8: Nabarro, F. R. N. (Ed.). Amsterdam: North Holland, pp. 421-496. Jin, B. Y, Ketterson, J. B. (1989), Adv. Phys. 38, 189. Kern, R., Le Lay, G., Metois, J. J. (1979), in: Current Topics in Materials Science Vol. 3. Amsterdam: North Holland Publishing Company, pp. 131-419. Kingery, W. D., Berg, M. (1955), J. Appl. Phys. 26, 1205. Kwo, J., McWhan, D. B., Hong, M., Gyorgy, E. M., Feldman, L. C , Cunningham, J. E. (1985), in: Layered Structures, Epitaxy and Interfaces, Pittsburgh: Materials Research Society; Symposia Proceedings Vol. 37, pp. 509-515. Kuk, Y, Feldman, L. C , Silverman, P. J. (1983), Phys. Rev. Lett. 50, 511. Markov, I., Stoyanov, S. (1987), Contemp. Phys. 28, 267. Matthews, J. W. (1959), Phil. Mag. 4, 1017. Matthews, J. W. (1965), Phil. Mag. 12, 1143. Matthews, J. W. (1966), Phil. Mag. 13, 1207. Matthews, J. W. (1975 a), /. Vac. Sci. Technol. 12, 126. Matthews, J. W. (1975 b), in: Epitaxial Growth, Matthews, J. W. (Ed.) New York: Academic Press, pp. 560-609. Matthews, J. W, Allinson, D. L. (1963), Phil. Mag. 8, 1283. Matthews, J. W, Grunbaum, E. (1965), Phil. Mag. 11, 1233. Matthews, J. W., Crawford, J. L. (1970), Thin Solid Films 5, 187. van der Merwe, J. H. (1963), /. Appl. Phys. 34, 117. Milne, R. H. (1990), in: Supplementary Volume 2 of the Encyclopedia of Materials, Science and Engineering: Cahn, R. W. (Ed.). Oxford: Pergamon, pp. 1231-1234. Neave, J. H., Joyce, B. A., Dobson, P. J., Norton, N. (1983), Appl. Phys. A31, 1.
Ogawa, S., Ino, S. (1972), J. Cryst. Growth 13/14, 48. Osakabe, N., Tanishiro, Y, Yagi, K., Honjo, G. (1980), Surf Sci. 97, 393. Pashley, D. W. (1956), Adv. Phys. 5, 173. Pashley, D. W. (1965), Adv. Phys. 14, 327. Pashley, D. W., Stowell, M. X, Jacobs, M. H., Law, T. X (1964), Phil. Mag. 10, 127. Pautikis, V., Sindzingre, P. (1987), Physica Scripta T 19, 375. Poppa, H., (1969), /. Vac. Sci. Technol 2, 42. Postnikov, V. S., Ijevlev, V. M., Solovjev, K. S. (1976), Thin Solid Films 32, 173. Royer, L. (1928), Bull. Soc.frang. Min. 51, 1. Seifert, H. (1953), in: Structure and Properties of Solid Surfaces: Gomer, R., Smith, C. S. (Eds.). Chicago: University Press, p. 218. Steigerwald, D. A., Egelhoff, W. F. (1987), Surf. Sci. 192, L887. Takayanagi, K. (1985), in: Layered Structures and Epitaxy, Pittsburgh: Materials Research Society; Symposium Proceedings Vol. 56, pp. 129-138. Takayanagi, K., Yagi, K., Kobayashi, K., Honjo, G. (1975), J. Cryst. Growth 28, 343. Takayanagi, K., Yagi, K., Kobayashi, K., Honjo, G. (1978 a), /. Phys. E: Sci. Instrum. 11, 441. Thompson, C. V., Floro, X, Smith, H. I. (1990), /. Appl. Phys. 67, 4099. Valdre, U., Robinson, E. A., Pashley, D. W, Stowell, M. X, Law, T. X (1970), /. Phys. E: Sci. Instrum. 3, 501. Vincent, R. (1969), Phil. Mag. 19, 1127. Venables, X A., Price, G. L. (1975), in: Epitaxial Growth: Matthews, X W. (Ed.) New York: Academic Press, pp. 382-436. Venables, X A., Derrien, X, Janssen, A. P. (1980),
Surf Sci. 95,411. Venables, X A., Spiller, G. D. T., Hanbuchen, M. (1984), Rep. Progr. Phys. 47, 399. Walton, D. (1962), Phil. Mag. 7, 1671. Willis, X R., Jain, S. C , Bullough, R. (1990), Phil. Mag. A62, 115. Yagi, K., Takayanagi, K., Kobayashi, K., Honjo, G. (1971), J. Cryst. Growth 9, 84.
8 Metallic Multilayers A. Lindsay Greer and Robert E. Somekh
Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, U.K.
List of 8.1 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.2.5 8.3 8.3.1 8.3.2 8.3.3 8.3.4 8.3.5 8.3.6 8.3.7 8.3.8 8.4 8.4.1 8.4.2 8.4.2.1 8.4.2.2 8.4.2.3 8.4.2.4 8.4.3 8.4.3.1 8.4.3.2 8.4.3.3 8.4.3.4 8.4.3.5 8.4.3.6 8.4.3.7 8.4.4 8.4.4.1 8.4.4.2
Symbols and Abbreviations Introduction Structure Classification Composition Modulation Two-Phase Multilayers Interfacial Structure Stability of Multilayer Structure Properties Origins of Special Properties X-Ray and Neutron Reflectivities Normal-State Electron Transport Superconductivity Magnetic Properties Mechanical Properties Other Properties Summary Preparation Introduction Thin Film Growth Processes General Considerations Surface Mobility Development of Microstructure and Morphology Internal Stress Deposition Technologies General Considerations Evaporation Sputtering Chemical Vapor Deposition Electrolytic Deposition Atomic Layer Epitaxy Mechanical Reduction Process Control Layer Thickness Size and Uniformity
Materials Science and Technology Copyright © WILEY-VCH Verlag GmbH & Co KGaA. All rights reserved.
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8.4.4.3 8.4.4.4 8.4.4.5 8.4.5 8.4.5.1 8.4.5.2 8.4.5.3 8.5 8.5.1 8.5.2 8.5.3 8.5.4 8.5.5 8.5.6 8.6 8.7 8.8
8 Metallic Multilayers
Deposition Rate Buffer Layers Level of Vacuum Summary, Issues and Outlook Comparison of Evaporation and Sputtering Issues in Multilayer Deposition Outlook for Ideal Multilayers Structural Characterization Introduction X-Ray Diffraction Neutron Diffraction Transmission Electron Microscopy Techniques for Chemical Profiling Probes of Local Structure Applications and Outlook Acknowledgements References
355 355 356 356 356 358 360 360 360 361 365 365 367 368 368 368 369
List of Symbols and Abbreviations
List of Symbols and Abbreviations a D D Do HC2 kB Mr, Ms Q T t Tc Tm Y
lattice parameter diffusion coefficient interdiffusivity pre-exponential term of the diffusion coefficient upper critical field Boltzmann constant remanent magnetization, saturation magnetization activation energy temperature time for growth of one monolayer superconducting transition temperature melting temperature biaxial in-plane elastic modulus
9 0 9k X v
coverage in monolayers Bragg angle rotation angle in magneto-optic Kerr effect radiation wavelength lattice vibration frequency
ALE b.c.c. c.c.p. CVD EXAFS LUCS MBE MOCVD NMR PACVD RHEED RKKY TEM UHV XHV YSZ
atomic layer epitaxy body-centered cubic cubic close-packed chemical vapor deposition extended X-ray absorption fine structure layered ultrathin coherent structures molecular beam epitaxy metal-organic chemical vapor deposition nuclear magnetic resonance plasma-assisted chemical vapor deposition reflection high-energy electron diffraction Ruderman-Kittel-Kasuya-Yosida (exchange interaction) transmission electron microscopy ultra-high vacuum extra high vacuum yttrium-stabilized zirconia
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8 Metallic Multilayers
8.1 Introduction Metallic multilayers epitomize the refinement of metal thin film deposition processes. They represent what might be called materials engineering on an atomic scale, with structures made up of layers only two to three atomic monolayers thick. From initial work half a century ago which was aimed at using metallic multilayers to calibrate X-ray wavelengths, there are now established applications in X-ray optics. There are other potential applications, notably as thin film magnetic and magnetooptic recording media. The commercial applications of metallic multilayers so far are belittled by the development of semiconductor multilayers (Volume 4, Chapter 8), which have created the new field of bandstructure engineering and revolutionized semiconductor device design. Nonetheless, the properties of metallic multilayers have been explored in a wide variety of materials research studies which can take advantage of the precise artificial, finescale layering which is possible. Metallic multilayers remain a particularly fruitful area for research because of their unique properties, and work on them is aided by recent advances in materials characterization. In this chapter we first describe the structural types of these new materials in Section 8.2, before introducing their wideranging properties in Section 8.3. Section 8.4 is the core of the chapter, covering preparation methods and highlighting the recent developments which now permit the routine deposition of these fine-scaled structures. Characterization methods which have aided the development of multilayer research are outlined in Section 8.5. Metallic multilayers, while as yet less important than semiconductor multilayers,
have great potential, and Section 8.6 briefly considers their applications and the outlook for them.
8.2 Structure 8.2.1 Classification In essence a multilayer is made by the alternating deposition of two different materials. After perhaps the first few layers, it is assumed that the structure of all the layers of one material are the same. The structure of each material is clearly of importance for the properties of the multilayer, not only in itself, but also for the influence it can have on the structure of the other material; each material acts as a substrate for the deposition of the other. In metallic multilayers, the materials may be amorphous, polycrystalline, or monocrystalline - a much wider range of structures and combinations of structures than is common in semiconductor multilayers. Yet not all combinations of structures are possible. Single crystal thin films can normally be obtained only by epitaxial growth on a monocrystalline substrate; the thin film will then have a well defined orientation relationship with the substrate (see Chapter 7). Polycrystalline deposits normally exhibit a degree of preferred orientation. A polycrystalline thin film, even on an amorphous substrate, can often be annealed to achieve a large grain size (much greater than the film thickness) with a particular crystallographic axis perpendicular to the substrate. Such a mosaic structure may have many of the properties of a monocrystalline film, though the orientations of the grains about the normal to the substrate are not defined. A monocrystalline layer will contain defects of a type and density dependent on deposition conditions and the perfection of the substrate.
8.2 Structure
Depending on the degree of preferred orientation and grain size in comparison to layer thickness, there can thus be a range of structures and properties between the random polycrystal and the single crystal. If a mosaic layer is used as the basis for successive deposition of epitaxial crystalline layers, then for most purposes the multilayer will behave as though it were monocrystalline. Thus it is possible to have multilayers of the following types: amorphous/ amorphous, polycrystalline/polycrystalline, amorphous/polycrystalline, monocrystalline/monocrystalline (including mosaic/ mosaic), and amorphous/mosaic. The other combinations are unlikely. In monocrystalline/monocrystalline multilayers it is expected that there is an epitaxial relationship between the layers defining the orientation relationship between successive layers and ensuring that all layers of the same type are in identical orientation. In amorphous/mosaic multilayers, on the other hand, there is not expected to be any orientation relationship between the mosaic layers (other than the common direction normal to the substrate). 8.2.2 Composition Modulation The simplest multilayer structures to describe and analyse are those which consist of a composition modulation imposed on a single structure. In almost all cases of this type, intermixing can lead to a uniform single phase of the starting structure. Compositionally modulated amorphous alloys do not exhibit the special effects associated with the relationship between the repeat distance of the multilayer and crystallographic spacings. Such effects can arise when a composition modulation is imposed on a single crystal (a monocrystalline film, or one grain in a mosaic film). Such multilayers, in which each layer has
333
the same structure in the same orientation, may properly be termed superlattices. Semiconductor multilayers have mostly been of this type, and often approximate to the special case in which each layer consists of an integral number of crystallographic periods. Polycrystalline/polycrystalline multilayers in which the two materials have the same crystal structure may also be regarded as compositionally modulated, though the orientations of the grains and relationship between the orientations in successive layers may not be well defined. 8.2.3 Two-Phase Multilayers While compositionally modulated multilayers may be regarded as single phase, there are clearly examples of two-phase multilayers, in which the two materials have different structures and in which simple homogenization is not possible. If twophase multilayers are annealed, one material may dissolve in the other or react with it to yield a third phase. Alternatively, the two materials may be stable in contact with each other, in which case the only possible effect of annealing would be coarsening of the layer pattern. The two materials, though of different structure, may have an orientation relationship. The resulting multilayers (monocrystalline/ monocrystalline, or mosaic/mosaic) have been termed layered ultrathin coherent structures (LUCS) (Schuller, 1980). In these there may be a full epitaxial relationship, as in a superlattice, or only the crystallographic directions normal to the substrate may be defined. The degrees of order in a multilayer have been discussed by McWhan (1985). 8.2.4 Interfacial Structure In multilayers of whatever type, the nature of the interfaces is of great impor-
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8 Metallic Multilayers
tance. Even if the average repeat distance is well defined, there may be local variations, i.e., the interfaces may be rough. While roughness can be controlled by varying production parameters, keeping it to low values is not straightforward. For a smooth thin film to be obtained on a substrate, the material must wet the substrate, or, if not, the atomic mobility in the deposit must be insufficient for agglomeration to occur. But (at least for macroscopic film thicknesses) if one material "A" wets another material "B", B cannot wet A; thus deposition of a high quality multilayer relies at least partly on lack of mobility. Simply lowering the substrate temperature to ensure lack of mobility is not acceptable, because there must be enough mobility to allow the desired structure to be achieved in both materials (unless they are both amorphous). Since the temperature scale for atomic mobility is normalized with respect to the melting point Tm of the material, problems are most likely to arise for multilayers in which the two materials have widely differing Tm. If we suppose that A wets B (and therefore that B does not wet A), then a good multilayer can still be obtained if T m (A)< r m (B). If T m (A)> Tm(B), however, a substrate temperature low enough to stifle the agglomeration of B into islands is likely to be too low to permit successful deposition of monocrystalline A. A possible solution is to change substrate temperature from layer to layer, as discussed in Section 8.4.5.2. Distinct from interfacial roughness, yet experimentally difficult to distinguish from it by many techniques, is interfacial diffuseness. This may arise from interdiffusion during deposition or subsequently. Since diffuseness corresponds to material of intermediate composition, which roughness per se does not, it can lead to distinct effects on multilayer properties.
When the two materials in the multilayer are monocrystalline, the structure of the interface is important. The considerations to be discussed here apply also to the single, layered grains in a mosaic multilayer. When the two materials are of the same phase (i.e., in a compositionally modulated single crystal), the interface may be fully coherent, or partially coherent (Fig. 8-1). In the former case, the interfaces are free of dislocations and lattice matching is achieved by having compensating average strains in the layers, compressive in one material, tensile in the other. Poisson's ratio effects lead to an accentuation of the lattice parameter difference in the direction normal to the substrate. The strains may be considerable and can substantially alter the material properties. When the interfaces are partially coherent through the presence of interfacial dislocations, there is local strain around the dislocations but the average strain in the layers is zero. There may be significant differences in multilayer properties between the coherent and partially coherent cases. For example, in a compositionally modulated alloy, the diffusional mixing which occurs on annealing is much faster in the coherent multilayer, because of the extra driving force provided by the average layer strains (Philofsky and Hilliard, 1969) (Fig. 8-2). The degree of coherency may be governed by strain energy minimization or by the critical strain necessary for dislocation nucleation or motion. Details may be found in Chapter 7. For thin layers, coherency is always preferred; in multilayers with layer thickness or repeat distance greater than a critical value, there is partial coherency. A special case of two materials with the same structure in a multilayer is when one of the materials adopts a non-equilibrium structure in order to match the other. This pseudomorphism arises because the free en-
8.2 Structure
335
Figure 8-1. Schematic drawings of (a) coherent, and (b) partially coherent layered structures. In the coherent structure the planes perpendicular to the substrate are of constant spacing and alternating layers are under tension and compression. In the partially coherent structure the strains are relieved by the introduction of misfit dislocations. [From McWhan(1985).]
ergy of the multilayer is lowered when the interfaces can be coherent or partially coherent as is possible with matching structures (and similar lattice parameters). The non-equilibrium structure can be a known metastable phase. For example, in Nb/Zr multilayers, contact with the b.c.c. niobiX (nm) 16
^E
4 3 1 1
14-
o
1 2--
N
2
1.5
1
I
1.2 1
1.0 1
-
10-
^O ?o
6-
o
4I
1
i
I
I
I
10
15
20
25
30
35
B 2 (10 18 m' 2 )
Figure 8-2. The variation of the effective interdiffusivity D at 389 °C with repeat distance X in compositionally modulated Cu/Pd mosaic multilayer. The quantity B is defined by B = (2/d2) [1 - cos(2 n d/X)], where d is the spacing of the atomic planes parallel to the substrate (in this case (111)). The layers were fully coherent for X < 2.8 nm (giving enhanced D), and incoherent for X > 3.8 nm. [From Philofsky and Hilliard (1969).]
um stabilizes the b.c.c. high temperature allotrope of zirconium (Lowe and Geballe, 1984). But in other cases, the non-equilibrium phase is quite novel: in Mo/Ge multilayers the germanium adopts a b.c.c. structure to match the molybdenum (Wilson and Bienenstock, 1988). The interfaces in a multilayer may be ordered or disordered (Clemens and Gay, 1987). An example of an ordered interface is the fully coherent interface between two layers with the same crystal structure and a small lattice mismatch. But ordered interfaces can also exist when there is epitaxy between materials with different crystal structures, e.g., b.c.c. niobium and c.c.p. copper. When the interface is ordered, the fluctuations in layer thickness must be a multiple of a crystal plane spacing, giving long-range coherence through the thickness of the multilayer. This coherence is readily detectable by X-ray diffraction (see Section 8.5.2) which shows high-angle superlattice lines. When the interface is disordered, there can be a continuous distribution of layer thickness, long-range coherence is lost, and the high-angle superlattice lines are absent (though those at low angle remain). Disordered interfaces are
336
8 Metallic Multilayers
most likely for materials with a large structural mismatch. The structure of the interfaces in a multilayer will determine their energy. The interfacial energy will in most cases be a major component of the amount by which the multilayer's free energy exceeds that of the equilibrium state of the same average composition. It is also possible that the interfaces may possess an interfacial stress, i.e., an effective tensile stress capable, in the absence of substrate effects, of holding the multilayer in a state of biaxial in-plane compression (Cammarata and Sieradski, 1989). 8.2.5 Stability of Multilayer Structure Although multilayered structures can be found in equilibrium in natural systems (e.g., dichalcogenides), most artificial metallic multilayers have free energies far in excess of equilibrium and are susceptible to some type of transformation if there is sufficient atomic mobility. Contributing to the excess free energy are the interfacial free energy, the strain energies and excess chemical energy relative to a mixed composition. Stability is clearly important if the special properties of multilayers are to be exploited. The simplest type of structural change in a multilayer is diffusional mixing at the interfaces. The increased interfacial diffuseness and the reduced amplitude of the composition modulation may affect many properties. The repeat distance can also change. The individual layer materials may show changes in structure. Amorphous layers may crystallize. The crystallization temperatures may be raised or lowered by interaction with the surrounding layers, possibly as a result of interdiffusion (Sevenhans etal., 1988). Polycrystalline layers
and mosaic layers may show grain growth. The moving grain boundaries are paths for fast diffusion, and as they sweep through the multilayer the composition modulation is destroyed. Thus for retention of a composition modulation it is essential to have a large stable grain size, or amorphous phases (Greer and Spaepen, 1985). The melting point of a material in a multilayer can be significantly depressed, as observed for example for lead layers only a few nm thick in a Pb/Ge multilayer (Willens etal., 1982). Both interfacial energy and chemical mixing can contribute to this effect. A further type of structural change is reaction between the materials of the multilayer to give one or more new phases. If the multilayer is composed of elements with a strongly negative enthalpy of mixing, the heat released when the reaction starts may be sufficient to allow it to proceed explosively. This has been observed in transition metal/amorphous silicon multilayers (Clevenger et al., 1988). The phase which forms by reaction in a multilayer may itself be metastable. Even if the two materials in the multilayer are stable in contact with each other, the multilayer configuration may not be stable. On annealing, some coarsening may be expected in which the density of interfaces will be lowered. This coarsening may take the form observed in lamellar eutectics (Graham and Kraft, 1966), but it has not been studied in artificial multilayers. While stability is essential for applications, the structural changes which can occur in multilayers are of considerable scientific interest. Multilayers are particularly useful for studies of interfacial reactions and of interdiffusion. Most of the quantitative work so far has been on interdiffusion (Volume 5, Chapter 2, Section 2.2.2.3). This has mostly been achieved
8.3 Properties
by measurement of X-ray satellite intensities during annealing. The technique is useful because interdiffusivities down to ~ 10~ 2 7 m 2 s" 1 can be measured. This sensitivity, possible because of the short diffusion distances, is at least one thousand times better than for techniques based on composition profiling (Greer and Spaepen, 1985), and permits measurement at low temperature in metastable materials and unrelaxed structures. A potential complication for determination of interdiffusivity, Z>, is the dependence of D on the repeat distance of the multilayer, an effect which becomes apparent at the very high concentration gradients achievable in deposited multilayers. Yet this dependence of D is useful, for it is related to the mixing thermodynamics of the system. Strain effects, mainly due to coherency, can also have a marked effect on D (Fig. 8-2). Interdiffusivity in both metals and semiconductors (in each case either crystalline or amorphous) has been studied using multilayers, as reviewed by Greer and Spaepen (1985).
8.3 Properties 8.3.1 Origin of Special Properties The fine repeat distances in artificial multilayers can give rise to special properties and the precise control of layer thickness leads to a wide range of possibilities for tailoring of properties. The special properties, which may be improvements of normal properties or may be unique to multilayers, are in some cases of interest for applications; in other cases they are of interest in providing opportunities to test the theory of the origin of the property. The properties of semiconductor/semicon-
337
ductor superlattices are already widely exploited. Although not so developed in their applications, metallic multilayers have aroused much interest; their physical properties are treated elsewhere in this Series (Volume 3, Chapter 6). In this chapter, however, it is important to pay some attention to the origin of the special properties of multilayers in order to assess the demands placed on processing to achieve a desired property. Most theories of physical properties contain at least one characteristic length. When the repeat distance of a multilayer becomes comparable with that length, effects due to the layering can be expected. Examples of characteristic lengths are: the wavelength of incident radiation for reflectivity; the electron mean free path and the de Broglie wavelength for electrical resistivity and other normal-state transport properties; the exchange interaction length for magnetism; and the penetration depth and coherence length for superconductivity. These lengths vary from about 5 nm to 1 jim, setting quite varied requirements for multilayer structure, particularly for the perfection of the interfaces. In detail, the possible origins of the distinctive properties of multilayers are (classification after Schuller (1988)): - thin film effects, due to the limited thickness of one or other type of layer; - interface effects, arising from the interactions between neighboring layers; - coupling effects between layers of the same type, acting through the intervening layers; and - periodicity effects from the overall periodicity of the multilayer. Without attempting a comprehensive review, some examples are given below of the properties of metallic multilayers; where possible, reference is made to published reviews.
338
8 Metallic Multilayers
8.3.2 X-Ray and Neutron Reflectivities The reflection of X-rays provided the motivation for most of the early studies of metallic multilayers. The aim was to use multilayers of known repeat distance to calibrate the X-ray wavelength, and later to develop useful monochromators. The first successful work was by Deubner (1930). A more detailed analysis followed in the work of DuMond and Youtz (1940). They produced a multilayer with a repeat distance of about 10 nm by modulating the gold content in an evaporated polycrystalline copper deposit. A first-order Bragg reflection was attributable to the modulation, but the control of repeat distance was not sufficient to be useful for calibration. An important observation was the decay of the reflection due to interdiffusion in the multilayer at room temperature. At present, metallic multilayers are quite widely used (and commercially available) as optical elements for X-rays (in particular soft X-rays with wavelength 2 = 5 nm). They extend the capabilities of conventional long-period crystals for use in spectrometers. Fig. 8-3 shows a reflectivity typ-
0
2 4 6 Grazing angle (degrees)
8
Figure 8-3. The measured reflectivity for X-rays (1 = 0.154 nm) at grazing incidence on a W/Si multilayer (200 layers, repeat distance 2.44 nm), available commercially as an X-ray mirror. [Adapted from Spiller (1985).]
ical for such multilayers. In addition, the principles of multilayer design used for visible light can now be extended to lower wavelengths. In this way, elements with controlled reflectivity (for a range of wavelengths) at normal incidence can be produced. The field has been reviewed by Spiller et al. (1980). For good reflectivity, the layers must have a large difference in scattering potential; for X-rays, materials of low artd high electron densities must be combined. In the high-electron-density layers there is strong absorption of the Xrays. (Absorption, by comparison, is hardly significant in multilayers for the reflection of visible light.) In the presence of absorption, "quasiperiodic" multilayers, in which the repeat distance is constant but the fraction of high electron density material increases with distance from the top surface, give higher reflectivities than normal periodic designs. Still better performance, both in range of reflected wavelengths and in integrated intensity, are obtained with aperiodic designs in which the repeat distance also is altered slightly with depth. Low-electron-density materials which have been used include carbon, boron, B4C and silicon, in each case amorphous. A widely used high-electron-density material is tungsten (which is polycrystalline or, with a sufficient impurity level, amorphous). The smoothness of the interfaces is very important and seems easiest to achieve when the structures are amorphous (Spiller et al., 1980). Tungsten, however, is very strongly absorbing, and better results may be obtained with a lighter element such as nickel which permits deeper penetration of the multilayer and consequently better spectral resolution. For applications it is important to know the stability of the X-ray mirror structures not only to thermal annealing but also to in-
8.3 Properties
tense irradiation (as experienced, for example in a monochromator on a synchroton source) (Kortright et al., 1991). As interdiffusion occurs it is expected that the reflectivity will decrease, with the intensities of higher order Bragg reflections particularly affected as the interfaces become more diffuse. These effects are found in W/Si multilayers, where a decrease in repeat distance is also noted. In W/C multilayers, however, all these effects are reversed, a surprising result which may be attributed to compound formation at the interfaces. Stability provides another reason for designing X-ray multilayers to be amorphous; the fast interdiffusion possible in fine polycrystals would be a problem. Kortright et al. (1991) have shown that prior thermal annealing can stabilize a multilayer structure against further changes under irradiation. Recently there has been work on using periodic multilayers as elements in larger structures to achieve higher efficiency in wavelength dispersion. With a spacer deposited between two multilayers, a FabryPerot etalon is formed (Barbee, 1985), and lateral patterning by lithography has also been used (Barbee, 1988). In a different application, Bionta et al. (1988) have used a cross-sectional slice of an Al/Ta multilayer as a linear zone plate for focussing an X-ray point source to a line. Multilayers are also of interest for the reflection of neutrons (k = 0.05 to 5 nm). There are uses as monochromators and as polarizing "supermirrors" with reflectivity over a range of angles. In the latter case aperiodic designs are used, combining a ferromagnetic and a non-magnetic material (e.g., Fe/Ge and Fe/W) (Majkrzak, 1989).
339
8,3.3 Normal-State Electron Transport
The theory of non-superconducting electron transport in multilayers is well advanced, and many novel effects have been predicted. While for semiconductor 'superlattices' there is experimental verification of the effects, some of which are now exploited in commercial devices, for metallic multilayers it is fair to say that theory has outstripped experiment. The requirements for some of the novel transport effects to be observed in metallic multilayers are particularly stringent, and producing materials of sufficient quality is one of the major challenges in multilayer deposition. There are two reasons why the effects are more difficult to observe in metallic than in semiconductor multilayers. The interface quality in semiconductor multilayers (deposited typically by MBE, see Section 8.4.3.2) seems to be higher than for metals and often approximates well to the ideal expected in a superlattice. Metallic multilayers have been made with slightly less sharp interfaces (two mixed monolayers at the interface, rather than one) as might be expected from the easier diffusion in metals. More importantly, however, for metals some of the characteristic lengths are substantially less than for semiconductors. An example of this is the de Broglie wavelength. When the thickness of a thin film approaches the de Broglie wavelength, the quantum size effect alters the transport properties. In semiconductors the de Broglie wavelength can be 5 to 10 nm, and the quantum size effect can be readily observed in multilayers of comparable repeat distance. In metals, on the other hand, the wavelength is such that the effect could be observed only for atomic monolayers. The field of semiconductor superlattices has been reviewed by Esaki (1985). The possible origins of the electron
340
8 Metallic Multilayers
transport properties of metallic multilayers have been analysed by Jin and Ketterson (1989) who also provide a review of experimental results. The main observation for metallic multilayers is the resistivity increase due to electron scattering at the interfaces. The resistivity has a component which is inversely proportional to repeat distance, and rises to the usual limit, for strongly scattering materials, of ~150|iQcm. As the resistivity rises, its temperature coefficient becomes less positive, and near the upper limit of resistivity it becomes negative (Fig. 8-4). The multilayers with a vanishing temperature coefficient of resistance can be exploited as temperature-independent thin film resistors. The anisotropy in resistivity which would be expected in a multilayer has not been observed because of the difficulty of making through-thickness measurements in a low resistivity material. The predicted negative differential conductivity in the through-thickness direction has been verified for semiconductor superlattices (Esaki, 1985), but not for metals. Other effects which should occur in metallic multilayers even when the repeat
515 0.12
distance is quite large (i.e., when it exceeds the electron mean free path) are the integral quantum Hall effect and hopping conduction; these also have not been observed, presumably because the required atomically smooth interfaces were not achieved. When a thin film thickness is comparable with the mean free path, the resistivity rises according to the classical size effect. This has proved useful in interpreting some results on metallic multilayers. On the other hand, as discussed above, the quantum size effect which would set in at lower values of layer thickness is probably not observable in metals. When the mean free path becomes very short, comparable with the atomic diameter, localization and interaction effects can arise. Metallic multilayers provide a useful probe of these effects for two-dimensional conduction (as reviewed by Jin and Ketterson (1989)) (see also Vol. 3, Chap. 6). Many of the novel transport properties of metallic multilayers remain to be demonstrated. The challenge is to produce multilayers which, in particular, have higher quality interfaces, showing better coherency, smoothness and sharpness. Even with the better materials, however, it must be doubted whether the technological potential can be as great as for semiconductor superlattices.
^0.08 o
8.3.4 Superconductivity
^0.04 ^
0 0.04 20
n /c
100 200 Temperature (K)
300
Figure 8-4. Normalized electrical resistivity as a function of temperature for a series of Nb/Cu multilayers. The individual layer thickness (in nm) is marked in each case on the curve. [Adapted from Werner et al. (1982).]
In marked contrast, the novel superconducting behavior of metallic multilayers can be readily observed without stringent requirements for multilayer quality. The characteristic length is the superconducting (Ginzburg-Landau) coherence length in the through-thickness direction (normal to the layers), and this is often in the range 5 to 100 nm. Multilayers with repeat dis-
341
8.3 Properties
tances on this scale are relatively easy to fabricate, and furthermore the superconducting properties will often be quite insensitive to interfacial quality. Multilayers of two superconductors, a superconductor and a normal metal, and a superconductor and an insulator have been studied. There are naturally occurring layered superconductors: dichalcogenides, intercalated graphite and high transition temperature ceramics based on copper oxide. The artificial superconductor/non-superconductor multilayers are of interest for comparison with these. Thin superconducting layers in such a material exhibit the proximity effect in which the critical temperature is reduced as the layer thickness is reduced. This effect is observed in the superconducting/non-superconducting multilayers, and the critical temperature in such multilayers is reduced also if the thickness of the non-superconducting spacer material is increased. Such multilayers can show three-dimensional or two-dimensional conduction behavior, depending on whether or not there is coupling between the layers of superconductor. Coupling becomes insignificant as the thickness of the non-superconducting layers exceeds the coherence length (Volume 3, Chapter 4), and the "crossover" from three-dimensional to two-dimensional behavior can be observed by increasing the thickness of the non-superconducting layer (Fig. 8-5) or, in a single sample, by lowering the temperature to decrease the coherence length. The upper critical field in layered superconductors is anisotropic and also shows clear dimensional effects. The dependence of the parallel critical field on the repeat distance arises from the interaction of the vortex lattice and the multilayer; this is an example of an effect attributable to the periodicity (Section 8.3.1). Superconducting properties of metallic
N
bs£] NV
75 -
Nv
2-D Nb: 4.5 nm Ge: 5.0 nm
\ 2-D/3-D Crossover Nb: 6.5 nm Ge: 3.5 nm
50 -
25 -
\V \\ 3-D \\ Nb: 4.5 nm V V
^v
0.7 nm
\ 0
0.8
\
0.9 T/Tc
\ \
\ 1.0
Figure 8-5. Upper critical fields HC2 (measured parallel to the layers) of Nb/Ge multilayers as a function of reduced temperature (7^ is the superconducting transition temperature). The niobium and germanium layer thicknesses are shown in each case. As the germanium thickness is increased, there is a crossover from anisotropic three-dimensional behavior to twodimensional behavior. The solid lines are calculated from Josephson coupling theory. [Adapted from Ruggiero etal. (1980).]
multilayers have been comprehensively reviewed by Ruggiero and Beasley (1985) and by Jin and Ketterson (1989) (see also Vol. 3, Chap. 6). 8.3.5 Magnetic Properties Of all multilayer properties, the magnetic behavior is the most widely studied. Band structure calculations for quantitative ab initio prediction of magnetic properties are now becoming possible, and the control of multilayer deposition is sufficient to permit the theory to be tested. Of great interest is the exchange interaction between magnetic spins. The decay length of the interaction is of the order of 1 nm and therefore accessible, albeit with some difficulty, to experimental test. In addition to this fundamental scientific interest,
342
8 Metallic Multilayers
there is great technological potential in magnetic multilayers whose properties can be tailored in a remarkably complete way. In addition to layer thickness and repeat distance, the magnetic properties may be affected by the structure of the individual layer materials (for example, iron could be b.c.c. and ferromagnetic, or pseudomorphically c.c.p. and antiferromagnetic), by the stresses in the layers (magnetostrictive effects) and by the nature of the interfaces. Important properties susceptible to control in this way are the coercivity and the anisotropy. Technologically, the greatest current interest is in polycrystalline multilayers of cobalt and platinum or palladium. These are alternatives to rare earth-transition metal thin films for magneto-optic recording, and have the advantages of greater oxidation resistance and a larger Kerr effect at the shorter incident wavelengths with which higher density recording is possible. Careful selection of deposition conditions is necessary for these multilayers as a typical Co-layer thickness is only ~0.4 nm, with Pd or Pt layers of — 1 nm. The film in total has 0.5, respectively; Thornton introduced a transitional zone between I and II, found in his sputtering experiments. These models reflect primarily the role of atomic mobility: as the mobility increases, there is a change from very porous low-density columns in zone I, to tightly packed columns in zone II, and finally to equiaxed structures in zone III. While the concept of different zones is correct, the exact temperatures of the transitions from one morphology to another may be affected by the higher surface mobilities found nowadays in cleaner deposition systems. Recently the models for thin film morphology have been refined by Messier and Yehoda (1985). In cleaner systems the films may often be rougher. Indeed, surface smoothness is an exception rather than the rule. Special measures must be taken to produce smooth multilayers over large lateral distances. The films must be grown single crystal, or at least highly textured (mosaic structure), or if they are amorphous or polycrystalline then best results are obtained if the surfaces are bombarded in some way during deposition.
Columnar grains Recrystallized grain structure
Figure 8-8. Schematic representation of the microstructure of metallic thin films as a function of substrate temperature and working gas pressure in magnetron sputtering. [From Thornton (1977).]
349
8.4 Preparation
There appears to be a difference between growing single crystal multilayers and other types. On a single crystal surface the mobility is a strict function of temperature. In all other systems, however, the density of surface defect states is more likely to control the mobility. The effective diffusion length is then related to the original distribution of nucleation sites, and the structure that has grown as the film has thickened, rather than to a limiting ideal surface diffusional process. The effective diffusion length can usually be enhanced by bombardment. Diffusion on amorphous surfaces has still not been studied, but the similarity of observed growth morphologies suggests that the surface mobilities are not greatly different from those on microcrystalline surfaces. It is clear that there are different problems in optimizing deposition conditions for single crystal films and for other types. Single crystal films grow by a range of processes on a given substrate. The processes fall into three categories (illustrated in Fig. 8-9): Volmer-Weber (island growth, as with droplets on a non-wetting surface), Frank-van der Merwe (layer-by-layer growth), and Stranski-Krastanov (growth of islands on a thin layer). These different processes are all described in detail in Chapter 7, to which the reader is referred for a complete description. 8.4.2.4 Internal Stress A general feature of thin films is that they have an internal stress. The stress in a thin film deposited at room temperature is due to the non-equilibrium nature of the growth process. For films grown on hot substrates there may be added the stress arising from the differential thermal contraction of the substrate and the film. Two factors contribute to the deposition stress:
1 OIID
C
C CD
10^1171
k M \
20 .a \ 10 ' \ b n u
O U)
h
\c
1
1
/
A
I
A
( :
\
-10 -
\d
-20 -
6
f
y
I/. oU^
g
boundaries may be formed by a twinning process. Hatherly and coworkers (e.g. Huber and Hatherly, 1980) have shown that small twins form during recovery {recovery twins) in these materials, and that these may develop into recrystallization nuclei. Such a mechanism is fundamentally different from those discussed above because it generates new crystallographic orientations during the nucleation process. Haasen and coworkers (e.g. Berger et al., 1988) have found that the formation of multiple annealing twins often occurs at a very early stage in recrystallization, and suggest that this can be considered to be part of the nucleation process. Their insitu high-voltage TEM work has even shown such twinning to occur in metals of high stacking fault energy such as aluminium, although the possibility of this being an artefact of the experimental technique cannot yet be ruled out.
/
^
\\ •MM,I, V
\
\
Ste
P" SCQn =
Direction.ND
Figure 9-21. The orientations of subgrains in deformed and recovered aluminium measured from electron backscattering patterns. A step scan was carried out across a grain and the orientations are given relative to the Cu texture component (Hjelen et al., 1990).
ary, capable of migrating into the deformed material is produced. In order to complete the recrystallization process, the deformed material is consumed by these migrating boundaries, and we examine this process in this section. Despite the importance of grain boundary migration not only during primary recrystallization, but also during post-recrystallization grain growth (Section 9.6) and in other microstructural transformations, the details of this process are not well understood. This is partly because boundary migration involves atomistic processes occurring rapidly and at high temperatures. There is as yet, no single theory which is accepted as valid, and although there is a wealth of experimental evidence, in many cases no clear pattern emerges, although it is clear that boundary mobility depends very strongly on the purity of the material (see Babcock and Balluffi, 1989). 9.5.1 Experimental Observations
9.5 Growth of Grains During Primary Recrystallization In the nucleation stage of recrystallization discussed above, a high angle bound-
It is generally accepted that the velocity of a migrating boundary is given by Equation (9-5). If the driving force is known, then the boundary mobility can be determined. Experiments in which the velocity
9.5 Growth of Grains During Primary Recrystallization
of a boundary during recrystallization is measured are however very difficult to interpret because the driving force, arising from the stored energy, and typically 10 MPa, is not easy to measure accurately, varies throughout the microstructure and does not remain constant with time, decreasing as recovery proceeds. For this reason, many measurements of boundary mobility have been carried out on materials with a better characterized driving force, e.g., an as-cast substructure. Another commonly used technique is use the boundary energy itself as the driving force by using an undeformed bicrystal whose geometry is such that the boundary area is reduced as the boundary migrates. Further details of the available techniques may be found in the reviews by Haessner and Hofmann (1978) and Grant et al. (1984). In such experiments however the driving force is much lower (around 103 Pa). It is not clear to what extent measurements of boundary mobility in specimens with such low driving forces are directly applicable to migrating boundaries in recrystallizing material. In addition, there is evidence that boundaries interact with dislocations, and that defects affect boundary mobility, indicating that there may be a real physical difference between boundary migration in deformed and undeformed materials.
395
9.5.1.2 Effects of Orientation and Purity on Boundary Migration
As boundary migration involves diffusion processes in and across the boundary, it is not surprising that the structure of the boundary should affect its mobility. Boundaries may be classified in part by reference to the number of coincidence sites, which are atom sites common to the grains on either side of the boundary (see Volume 1, Chapter 9). Special boundaries with a large number of coincidence sites are known to have properties different from those with few coincident sites. Aust and Rutter (1959) measured the migration rate of boundaries in zone refined lead under a low driving force, as a function of both orientation and impurity level. Their results, shown in Figure 9-22, indicate that in very pure lead, the boundary mobility is almost independent of orientation. How-
r?
10.0 u
"Random" grain boundaries
9.5.1.1 The Effect of Temperature
As was the case for low angle boundaries (Section 9.3.3.1), the mobility of high-angle boundaries is very temperature dependent and is given by Equation (9-6). The activation energy for pure metals is typically about half that for self diffusion (see Haessner and Hofmann, 1978). However, the activation energy is higher for impure materials.
0.002 0.004 0.006 Weight percent of tin
Figure 9-22. The rate of grain boundary migration at 573 K into zone refined lead crystals doped with small amounts of tin (after Aust and Rutter, 1959).
396
9 Recrystallization and Recovery
ever, as the impurity level rises, the mobilities of the randomly oriented boundaries fall much more than those of the coincident site lattice boundaries, suggesting than impurities are adsorbed more easily on the more open and disordered structure of the random boundaries. Liebmann et al. (1956) found that during recrystallization of an aluminium single crystal, the boundary migration rate was highest for boundaries misoriented about a axis by about 40° (Figure 9-23). Rapid growth of grains of certain orientations will lead to the development of a recrystallization texture, and the results above have often been cited in favor of the model of oriented growth of textures (see Section 9.9.2). 9.5.2 Effect of Solute on Grain Boundary Mobility As may be seen from Figure 9-22, small amounts of solute have a very large effect
on the mobility of boundaries. Lixcke and Detert (1957) were the first to formulate a quantitative theory of the effect of solute atoms on boundary mobility. This theory has been extended by others, and the developments are reviewed by Grant etal. (1984). The theory is based on the idea that atoms in the region of a boundary have a lower energy than those in the grain interior, because the open structure of a boundary allows more relaxation of the elastic misfit stresses associated with a solute atom. Therefore there is an attractive force between boundary and solute. As the boundary moves, the solute atmosphere is dragged with the boundary. The velocity of a boundary as a function of the driving pressure is shown schematically in Figure 9-24, for three different solute concentrations C1? C2 and C 3 . For low boundary velocities the solute atmosphere is dragged with the boundary, the boundary mobility being lower for larger solute content. At large boundary velocities, the boundary
— 3
o 2 '6 o -a c
Twin orientation
•D
U O 20 40 60 Orientation difference (degs) about common
Figure 9-23. Growth rates of new grains into a deformed aluminium crystal at 888 K (after Liebmann and Liicke, 1956).
Driving Force
Figure 9-24. Schematic diagram showing the grain boundary velocity as a function of the driving force for different solute concentrations C3>C2>C1 according to the theory of Liicke and Detert (1957).
9.5 Growth of Grains During Primary Recrystallization
breaks away from its atmosphere, behaving like a boundary in the pure material. For large solute concentrations the change from a loaded to a free boundary results in a discontinuity in the curve. There is evidence that the theory is qualitatively in agreement with experiments. 9.5.3 Theories of Grain Boundary Migration
Theories of grain boundary migration need to take into account the structure of grain boundaries and the nature and kinetics of the atomistic processes involved in boundary migration. Comprehensive reviews of the structure of boundaries can be found in Haessner and Hofmann (1978) and Grant et al. (1984) and in Volume 1, Chapter 9 of this series. The structure of a grain boundary is a function of the misorientation between the grains. The coincidence site lattice model is concerned with certain special orientations in which there are a number of lattice points which are common to both of the adjacent grains. Such boundaries are defined in terms of Z, where 1/S is the fraction of atoms which occupy coincidence lattice sites. Small deviations from the exact orientation can be accommodated by imposing a network of intrinsic dislocations on the boundary. Such a theory describes the geometry of the boundary, but not the details of the atom arrangements in the boundary, which are determined by energetic considerations. Detailed calculations and computer simulations (see Haessner and Hofmann (1978) for details), have been developed to predict grain boundary structures. However, little is known about the structure of the moving boundaries, relevant to our present discussion, and in which equilibrium structures may not be present.
397
Theories of boundary migration are based on reaction rate theory in which atoms are continually detached from the grain and are able to move into the boundary. For a static boundary, the atom flux from the two adjacent grains is the same, but for a moving boundary they are different. The main differences in theoretical approach is as to whether migration occurs by single atom movement or by the collective movement of a group of atoms. 9.5.3.1 Group-Process Theories In the earliest group-process theory by Mott (1948), groups (islands) of atoms move from one grain into the boundary region and similar groups attach themselves to the other grain. Developments of the model took into account the variation of grain boundary energy with orientation. Although more recent work has concentrated on single-process theories, Haessner and Hofmann (1978) have suggested that the high mobilities of boundaries in pure materials indicate that some sort of cooperative processes, such as is envisaged in the group-process theories, may be occurring. 9.5.3.2 Single-Process Theories In the earliest single-process theories (Turnbull, 1951) it was assumed that every atom in the boundary could jump by thermal activation from one grain to the other, i.e. the boundary was narrow. Later theories have taken the boundary structure into account and considered the three steps - detachment of an atom from one grain, movement in the boundary region and attachment to the other grain. Gleiter (1969) proposed a detailed atomistic model in which boundary migration occurred by the movement of steps or kinks in the boundary in a similar manner
398
9 Recrystallization and Recovery
to that occurring during the growth of crystals from a vapor. Other models based on the movement of boundary dislocations (e.g. Smith and Rae, 1979) have also been proposed. The role of vacancies in grain boundary structure and mobility has been extensively discussed, and it is thought that boundary mobility rises with increasing "porosity" of the boundary. The vacancy concentration of a boundary is likely to be a function of the boundary velocity, and this again suggests that theories developed for static boundaries may not be entirely applicable to migrating boundaries. Accurate dynamic atomistic simulations of moving boundaries are likely to provide useful insight into many aspects of grain boundary migration. 9.5.4 Computer Modelling of Primary Recrystallization
There have recently been several attempts to simulate primary recrystallization by computer modelling (see e.g. Mahin et al. (1980); Saetre et al. (1986) Doherty et al. (1986) and Marthinsen et al. (1990)). The main advantage of such models is that they can allow for realistic spatial distribution of nuclei and for complex variations of nucleation and growth rates. Such models are capable of predicting grain size distributions as well as recrystallization kinetics. However, as pointed out by Marthinsen et al. (1990), the models are not yet sophisticated enough to give any detailed insight into the mechanisms of recrystallization.
9.6 Grain Growth After Primary Recrystallization When primary recrystallization, which is driven by the stored energy of cold work,
is complete, the structure is not yet stable, and further growth of the recrystallized grains may occur. The driving force for this is a reduction in the energy stored in the material in the form of grain boundaries. The driving pressure for grain growth is some two orders of magnitude less than that for primary recrystallization, and consequently, grain growth will be slower than during primary recrystallization and will be more affected by solutes and particles which pin grain boundaries. General reviews of grain growth have been undertaken by Higgins (1974), Doherty and Martin (1976) and Randle et al. (1986). Consider first a two-dimensional grain structure as shown in Figure 9-25. If the grain boundaries are assumed to have equal energies, then the triple points are in equilibrium when the boundaries make an angle of 120° with each other. This is possible for an array of regular hexagonal grains (Figure 9-25 a) and in this case we have achieved a metastable structure which will not coarsen. However, if we take a more realistic, less regular array of grains as shown in Figure 9-25 b, then the boundaries will become curved to achieve the required triple point angles. Curved boundaries will be unstable and tend to migrate in the direction of the arrows, so as to shorten their length. The result is that grains of less than 6 sides will tend to shrink and eventually disappear, whilst those of more than 6 sides will tend to grow, and the average grain size therefore increases with time. Extension of these ideas to a three dimensional grain structure leads to similar results except that a truly stable three dimensional array, equivalent to Figure 9-25 a, does not appear to exist. Burke (1949) showed that the velocity of a boundary during grain growth would be
9.6 Grain Growth After Primary Recrystallization
399
where the constant n has a maximum value of 0.5. However, most experimental measurements show n to be less than this (see Cotterill and Mould (1976), Haessner and Hofmann (1978) and Randle et al. (1986) for details). The highest values, typically 0.4 are found for pure metals. However, reliable experimental measurements on well characterized material are not easily obtained because of the low driving force and the strong effects of small amounts of impurities. The main problem of formulating a theory of grain growth is clear from a comparison of Figures 9-25 a and 9-25 b where it can be seen that the driving forces for grain growth are local and depend in detail on the distribution of grain sizes in the material, which in turn will depend on the history of the specimen. In a detailed study of the morphology of grains during growth, Rhines and Patterson (1982) showed that the distribution of grain sizes was determined by the strain before recrystallization, and that this distribution persisted throughout the subsequent grain growth.
Figure 9-25. Growth of a two-dimensional grain structure, a) An array of regular hexagonal grains is stable, b) In an irregular grain structure the boundaries are curved, c) Secondary recrystallization.
inversely proportional to the radius of curvature, so that: (9-15) from which it can be shown that: (9-16) Experimental measurements suggest that Equation 9-16 should really be written as: D2-D20
=
(9-17)
9.6.1 Factors Affecting Grain Growth
Grain growth is inhibited by a number of factors, and the effect of solutes on boundary migration has already been discussed in Section 9.5. The rate of grain growth diminishes when the grain size becomes greater than the thickness of a sheet specimen (Burke, 1949). This is because the grains are now curved only in one direction rather than two, and thus the driving force is diminished. Thermal etching grooves may also be formed on the sample surface by diffusion, and these will also impede grain growth.
400
9 Recrystallization and Recovery
Grain growth may also be affected by the presence of a sharp crystallographic texture (Beck and Sperry, 1949). This arises at least in part from a large number of grains of similar orientation leading to more low-angle and hence low-energy boundaries. Thus the driving force for growth is reduced. The texture may also alter during grain growth (Koppenaal et al., 1960; Abbruzzese and Liicke, 1986), thereby affecting the kinetics (see Chapter 10, Section 10.4.2). Undoubtedly the most important features affecting grain growth are second-phase particles, and their effect will be considered in Section 9.8.8. 9.6.2 Theories and Models of Grain Growth 9.6.2.1 Statistical Models of Grain Growth Topological theories of grain growth, in which a regular lattice of 6-sided grains is perturbed by "defects" such as a 7-sided and a 5-sided grain have been developed. These do not describe the behavior of individual grains, and allow only statistical averages of the behavior to be derived. However, because they are analytical, they incorporate physical models of the processes involved. Early theories were due to Hillert (1965) and by Cahn and Pedawar (1965), and these predict growth kinetics according to Equation (9-6). In a recent series of papers, Liicke, Abbruzzese and colleagues (see Abruzzese and Liicke 1986, Liicke et al., 1990) have extended this approach to allow the effects of texture, boundary energy and mobility to be taken into account. Because of the difficulty in formulating an analytical theory which will take realistic complex grain size distributions into effect, there has recently been much interest in computer modelling of grain growth and the two main approaches are de-
scribed in the following sections. For further details and references the reader is referred to the review by Anderson (1986). 9.6.2.2 The Modelling of Boundary Movement In these approaches, which have been carried out for two or three dimensional cases, an initial microstructure is assumed and the forces acting on the boundaries are calculated. The movement of the boundaries on the basis of the local topology and forces is then calculated and the boundary is moved appropriately. In this way, the development of microstructure is followed (e.g. Hunderi et al., 1979, Weaire and Kermode, 1983). 9.6.2.3 Atomistic Simulation of Grain Growth In a recent series of papers, Anderson and colleagues (e.g. Anderson et al., 1984; Anderson, 1986) have described Monte Carlo simulation of grain growth in two and three dimensions. The material is divided into a number of discrete points (at the centre of areas or volumes), each of which is given a number, corresponding to a grain orientation as shown in Figure 9-26. The grain boundary energy is then specified by the interaction between the grid sites. For example, a certain value of energy might be assigned to a 4-6 boundary and the same or a different one to a 3-9 boundary. The numbers of adjacent points are then swapped and the energy change (AE) measured. If the energy is lower, then there is a probability of exp( — AE/kBT) that the change will be accepted. Transitions occur at grain boundaries and the grains grow, showing most of the features of grain growth. If this technique is applied to three dimensions, the size of the array which can be used is
9.6 Grain Growth After Primary Recrystallization 4
4
4
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4
,
9
9
9
9
9
9
401
Figure 9-26. The type of "microstructure" used for
several millimeters or larger. This process is known as secondary recrystallization, and an example is shown in Figure 9-27. Detailed discussions of this phenomenon were published by Detert (1978) and Cahn (1983). The rapidly growing grains may be larger than the average or they may have an orientation which is more favorable for growth. If the latter is the case then a pronounced texture may result on secondary recrystallization. The best known examples of this are the iron-silicon alloys used for transformer cores. In these a pronounced (110) [001] texture is produced on
atomistic simulation of grain growth. The integers denote orientations and the lines are grain boundaries (Anderson, 1986).
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limited to around 100 x 100 x 100 points. If the discrete points are equivalent to atoms (which are the unit which jump in a real material), then this means that the technique can be criticized for dealing only with very small numbers of very small grains. Liicke et al. (1990) have also pointed out that the method does not reveal general relationships or the physical meaning of the results, thus lacking the predictive power of the statistical theories. There continues to be great interest in this area of research which is just one example of the powerful molecular modelling approach now used in many branches of physics and chemistry. 9.6.3 Secondary Recrystallization In the previous section we discussed the growth of grains after recrystallization, and such growth is relatively uniform throughout the material. However, in certain circumstances, a few grains, such as the large grain in Figure 9-25 c may grow excessively, consuming the recrystallized grains. This may lead to a grain size of
"V " ' l ^ f c l ^'
Figure 9-27. Secondary recrystallization in Fe-3 % Si during an anneal at 1373 K (Detert, 1978).
The driving force for secondary recrystallization is the energy of the grain boundaries and therefore the process is more likely to occur when pinning of boundaries by second-phase particles restricts normal grain growth (Section 9.8.8). If, during a subsequent anneal, the particles coarsen or dissolve, then secondary recrystallization commonly occurs (Detert, 1978).
402
9 Recrystallization and Recovery
9.7 The Recrystallization of Ordered Alloys
280 in
As was discussed in Section 9.5, solute atoms have a significant effect on recrystallization. If the solid solution is ordered, rather than random, then there may be further effects on the recrystallization behavior. There is increasing interest in the use of ordered intermetallic alloys as materials for high temperature structural applications, and an understanding of their recrystallization behaviour is therefore of more than academic interest. The subject has recently been comprehensively reviewed by Cahn (1990). Although there is more commercial interest in alloys which are permanently ordered, solid solutions which are ordered at low temperatures, but which become disordered at higher temperatures have been studied for many years. There are differences in behavior between various alloy systems, but some general trends and effects are now established.
9.7.1 The Interaction of Ordering and Recovery
During deformation, an initially ordered alloy becomes partly disordered. For example, in Cu 3 Au, the long range order parameter was reduced from 0.85 to 0.5 during a cold roll of 60% (Roessler et al., 1963). During a subsequent anneal, the material re-orders as well as recrystallizing, and as may be seen from Figure 9-28, there is significant hardening {strain-agehardening) during the recovery stage. This is believed to be due in part to the formation of small antiphase domains during the reordering, and also due to the rapid work hardening rate as order develops in the material.
L_ (D
"E 260 • Ordered, worked A Disordered, worked • Disordered, unworked
Q_ O O 240 C in U)
cu c
T3 i_
a 150 o
si
\ 130 r Unannealed 0.1
1
10 Time [h]
100
1000
Figure 9-28. The microhardness of rolled Cu3Au as a function of annealing time (Roessler et al., 1963).
Deformation also has an effect on the kinetics of ordering. Figure 9-28 shows that for Cu3Au, initial ordering is more rapid in the deformed than in the undeformed material. This is thought to be due to the effect of dislocations on the ordering reaction. However, in FeCo, ordering is slowed by cold work (Smith and Rawlings, 1976). 9.7.2 The Effect of Ordering on Recrystallization Kinetics
An ordered solid solution is found to recrystallize more slowly than a similar but disordered alloy. This was clearly demonstrated by Hutchinson etal. (1973), as shown in Figure 9-29. The curves have the normal sigmoidal shape both above and below the ordering temperature Tc (400 °C), but below Tc the rate of recrystallization is very much slower. In these specimens re-ordering of the deformed material is complete before recrystallization commences. These authors showed that the slow recrystallization was primarily
9.8 Recrystallization of Two-Phase Alloys
Figure 9-29. Recrystallization kinetics of rolled Cu3Au, showing a marked increase in recrystallization rate above Tc (400 °C) (Hutchinson et al., 1973).
0 -
102
10
103 Time Is]
10*
so 100 \
i\
1j 10 1.0 800
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Temperature. °C 775 750 725 700
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region, and therefore of higher relative energy than in a disordered material. There is also evidence (see Cahn, 1990) that a narrow layer adjacent to the boundary may be disordered, and that there may be solute segregation in this region. This would lead to similar dragging effects on a boundary to those discussed in Section 9.5.2. Cahn (1990) has suggested that the occurrence of equiaxed antiphase domain boundaries following recrystallization of an ordered alloy is evidence of the existence of such a disordered layer adjacent to the boundary.
1000 -
0.1
403
675 1(K
1/T(K)x10 5
Figure 9-30. Plot of the grain growth rate constant against temperature in Fe-Co-V (Davies and Stoloff, 1966).
due to retardation of grain boundary mobility. A similar effect is found in FeCo-V as shown in Figure 9-30, in which a 10-fold increase in the rate constant occurs at Tc. It is not surprising that a grain boundary is less mobile when the adjacent grains are ordered. The boundary is a disordered
9.8 Recrystallization of Two-Phase Alloys As most alloys of commercial importance are multiphase, an understanding of the recrystallization behavior of such materials is of practical as well as of scientific interest. The second phase may be in the form of dispersed particles, which are present during the deformation, or the particles may form during the subsequent anneal. There are also alloys in which the volume fractions of the two phases are
404
9 Recrystallization and Recovery
similar - duplex alloys. In this section we will be primarily concerned with alloys containing stable dispersions of particles. Particles have three important effects on recrystallization: 1. Particles may increase the stored energy and hence the driving force for recrystallization. 2. Large particles may act as nucleation sites for recrystallization. 3. Particles, particularly if closely spaced, may exert a significant pinning effect on grain boundaries. The first two effects tend to promote recrystallization, whereas the last effect tends to prevent recrystallization. Thus the recrystallization behavior, particularly the kinetics and the resulting grain size, will depend on which of these effects dominate. The final grain size tends to be small when recrystallization is accelerated and coarse when recrystallization is retarded. 9.8.1 Recrystallization Kinetics
The recrystallization kinetics strongly depend on both the particle size and the interparticle spacing, as was first clearly demonstrated by Doherty and Martin (1962). It is difficult to separate the effects of these two parameters because there are few investigations in which they have been independently varied. Nevertheless it is clear that by comparison with a single phase alloy, recrystallization is retarded or even completely inhibited by closely spaced particles, and is accelerated by widely spaced particles, as shown in Figure 9-31 (see, e.g., Doherty and Martin (1976), Humphreys (1979 a) for further discussion). The strong effect of particle size on the recrystallization kinetics, for a constant (large) interparticle spacing is shown in Figure 9-32.
Time for 50% Recrystallization (s) 10000000 1000000 100000 10000
single-phase alloy
1000
•H-+
100, 10, 0
0.5
1 1.5 2 2.5 Interparticle Spacing (^m)
3
3.5
Figure 9-31. The effect of interparticle spacing on the time for 50% recrystallization in Al-Cu single crystals. (Data from Doherty and Martin, 1964).
Time for 50% RecrystaUization [s]
10000
1000
2 3 Particle Diameter [jiml
Figure 9-32. The effect of particle size on the time for 50% recrystallization in Al-Si crystals with a large interparticle spacing. (Data from Humphreys, 1977).
The effects of both particle size and interparticle spacing on the kinetics are shown schematically in Figure 9-33. Curve A, in which only retardation is found, is typical of aluminium alloys containing particles which are below the critical size for particle stimulated nucleation (Section 9.8.3). Curve B is typical of copper alloys with small particles. Curve C shows the behavior of alloys with large particles. The reason why small particles appear to accelerate recrystallization in copper but not in aluminium may be a result of the lower recovery rate and hence larger driving force for recrystallization in copper alloys. Thus in aluminium, many of the geometri-
9.8 Recrystallization of Two-Phase Alloys
Interparticle Spacing
Figure 9-33. Schematic diagram showing the effects of both particle size and spacing on the recrystallization kinetics. See text for details.
cally necessary dislocations produced during deformation (Section 9.2.1) may be dynamically recovered, so that the stored energy of the 2-phase alloys is not significantly greater than that of single-phase alloys. 9.8.2 The Deformed Microstructure
Particles have a large effect on the microstructure developed during deformation, and this in turn affects the recrystallization behavior. If the particles deform during the deformation, then they do not significantly alter the dislocation density compared to a single phase alloy. However, they cause the slip to be inhomogeneous, and this may affect the subsequent recrystallization behavior as demonstrated by Kamma and Hornbogen (1976). These authors showed that at lower strains the inhomogeneous slip accelerated recrystallization, but at larger strains, the dispersion was refined by repeated particle cutting, leading to retarded recrystallization. If the particles do not deform with the matrix, then geometrically necessary dislocations are generated at the particles (Section 9.2.2). The form and distribution of these dislocations is primarily a function of strain and particle size, although other fac-
405
tors such as shape, interface strength and matrix are known to be important (see for instance Humphreys, 1985). The dislocations which accumulate at the particles are a result of the incompatibility between the plastically deforming matrix and the non-deforming particle, and the nature of the dislocation structures depends on how the resulting stresses are relieved by plastic relaxation. For small particles and low strains, plastic relaxation generally involves the generation of prismatic loops. However, for particles of diameter greater than around 0.1 jim, stress relaxation may also occur by local lattice rotation. The effect of strain and particle size on the relaxation mechanisms in aluminium single crystals is summarized in Figure 9-34. For small particles, at which prismatic loops are formed, the important effect on the microstructure is the increased dislocation density which was discussed in Section
Primary Prismatic Loops
Particles deform
0.2 0.3 Shear strain
(U
Figure 9-34. Deformation mechanisms at particles in aluminium as a function of shear strain and particle radius normalized with respect to dislocation Burgers vector (after Humphreys, 1979 b).
406
9 Recrystallization and Recovery
9.2.2. Measurements of stored energy in particle-containing copper alloys (Baker and Martin, 1983) show an increase in stored energy with strain which is in approximate agreement with Equations (9-1) and (9-2). The effect of particles on the homogeneity of the deformation, for example on the formation of deformation or shear bands is however less clear (see Humphreys, 1985). At particles larger than around 0.1 |im, Figure 9-34 shows that plastic relaxation results in the formation of rotated structures or deformation zones near the particles. Detailed study of the zones in aluminium single crystals deforming by single slip (Humphreys, 1979 b) has shown that for large particles, the maximum misorientation occurs at the particle surface, and is equal to t a n - 1 y , where y is the shear strain. The axis of rotation is perpendicular to the primary Burgers vector and to the slip plane normal. The misorientation falls rapidly with distance from the particle, and the size of the deformation zone is related to the particle size. A simple model of plastic relaxation by lattice rotation, proposed by Humphreys and Kalu (1990a) is shown in Figure 9-35. Figure 9-35 c shows how rotation of the particle and the adjacent matrix, together with the generation of secondary dislocations (not shown), allow the relaxation of elastic
i
ill
1 a)
b)
c)
d)
Figure 9-35. Schematic diagram of plastic relaxation at a large particle, a) Undeformed. b) Unrelaxed plastic deformation, c) Relaxation by rotation and generation of secondary dislocations (not shown), d) Formation of impenetrable zone (dotted) at larger strains (Humphreys and Kalu, 1990 a).
stresses at the particle. On further straining, the relaxation debris forms an impenetrable zone, preventing glide dislocations from approaching close to the particle (Figure 9-35 d), and further relaxation results in both the particle and the impenetrable region rotating. Such a mechanism leads to a maximum rotation angle of y and a decrease in misorientation with increasing distance from the particle which is in accord with that found experimentally (Humphreys, 1979 b). Although the above model is applicable only to crystals deforming by single slip, Humphreys and Kalu (1990 a) have extended it to polycrystals deformed in compression. In this model, based on the Taylor theory of polycrystalline plasticity (see Volume 6, Chapter 3), several deformation zones, resulting from activity on the various slip systems, may be formed at a single particle, although significant rotations are not predicted in more than 3 or 4 such zones. Figure 9-36 shows the maximum misorientations in different zones ( P I PS) predicted for particles in a grain of initial orientation I and final orientation M, for a grain in a polycrystal. Experimental measurements of the orientations of deformation zones in compressed Al-Si polycrystals are consistent with this type of model. Although some relaxation by local lattice rotation does occur at particles as small as 0.1 Jim, other relaxation mechanisms also operate, and in aluminium, lattice rotation does not become the dominant relaxation mechanism until the particles are larger than around 2-3 \im (Humphreys, 1979 b). For particles in this intermediate size range the lattice rotations are a function of both strain and particle size, as may be seen from Figure 9-34. Although most work has been carried out on equiaxed particles, there is evidence
9.8 Recrystailization of Two-Phase Alloys
Figure 9-36. Predicted orientations (P1? P 2 and P3) of the deformation zones near particles in a grain of initial orientation I in a compressed f.c.c. polycrystal (Humphreys and Kalu, 1990 a).
(Herbst and Huber, 1978; Humphreys, 1979 b) that lattice rotations at the ends of elongated particles are particularly large. 9.8.3 Particle-Stimulated Nucleation of Recrystallization (PSN) Nucleation of recrystallization may occur within the deformation zones discussed above, and this is commonly referred to as particle-stimulated nucleation (PSN). 9.8.3.1 Mechanisms of Nucleation Although specimens annealed to produce recrystallization nuclei and which are subsequently examined metallographically, can provide information about the kinetics of recrystallization and the orientation of the new grains, there is little that can be deduced from these specimens about the mechanisms of nucleation, and most direct evidence has come from in-situ observations in the HVEM. From a study of recrystallization at particles in rolled
407
aluminium, Humphreys (1977) concluded that: - Recrystallization originates at a preexisting subgrain within the deformation zone, but not necessarily at the particle surface. - Nucleation occurs by rapid subboundary migration. - The grain may stop growing when the deformation zone is consumed. Later in-situ work (Bay and Hansen, 1979), together with work on bulk annealed specimens (Herbst and Huber, 1978) has supported these general conclusions. A sequence of electron micrographs from an in-situ annealing sequence, Figure 9-37, shows the occurrence of particlestimulated nucleation in aluminium. The kinetics of nucleation, as determined by in-situ HVEM annealing of A l Si are illustrated in Figure 9-38. The rapid annealing of the deformation zone, shown in Figure 9-38 a is due to the high dislocation density and small subgrain size, compared to the matrix. The drop in the maximum misorientation within a deformation zone shown in Figure 9-38 b is consistent with the fact that the nucleus may not originate in the region of highest misorientation at the interface, but elsewhere in the deformation zone. There is no evidence that PSN occurs by a mechanism different from nucleation of recrystallization at heterogeneities in single-phase materials, and the models of PSN are consistent with the earlier model of recrystallization at transition bands proposed by Dillamore et al. (1972). Although the nucleus usually is misoriented by at least 10 ° from the matrix, it has been suggested (Humphreys, 1979 a) that an alternative annealing process might involve the growth of a matrix subgrain into the deformation zone, thus producing a
408
9 Recrystallization and Recovery
Figure 9-37. In-situ HVEM annealing of Al-Si. Recrystallization originated in the deformation zone near the particle (arrowed).
10 Minutes
(a) (b) Figure 9-38. Changes in subgrain size and misorientation within the deformation zone of Si particles in Al, as determined by in situ annealing, a) Growth kinetics, b) The maximum misorientation within the deformation zone (Humphreys, 1980).
9.8 Recrystallization of Two-Phase Alloys
nucleus which was not highly misoriented. 0rsund and Nes (1988) have found evidence of such a process. In deformed AlMn alloys, they found that although PSN occurred after annealing at all temperatures, at high annealing temperatures the resultant texture was consistent with nuclei growing from the core of the deformation zone, whereas after low temperature annealing, the texture was consistent with nuclei originating in the outer regions of the deformation zones, which are only slightly misoriented from the matrix. 9.8.3.2 The Efficiency of PSN An important application of PSN is in controlling the grain size of recrystallized alloys, and in particular, the production of fine grained material. If each particle nucleates one grain, then the resultant grain size will be directly related to the number of particles per unit volume. If several grains nucleate at a particle, then an efficiency (grains/particles) of greater than 1 may occur. However, as multiple nucleation generally only occurs for particles larger than 5-10 jam, this is rarely achieved. If the particle size is close to the minimum, then the nucleation efficiency is very low, and the expected fine grain size is not achieved (Wert et al., 1981). As nuclei are essentially in competition with each other, we only obtain a high efficiency if all nucleation events occur simultaneously (site saturation), and if they grow at similar rates. Although this condition may be met for alloys with widely spaced particles (e.g., Humphreys, 1977), if the particles are closely spaced, or if growth of nuclei is affected by for example a fine dispersion of particles, then the nucleation efficiency may decrease markedly. It is possible that particles in different situations, e.g., at grain bound-
409
aries, shear bands, etc., may nucleate at different rates. However, there is as yet little direct evidence of this effect. The main parameters known to affect PSN are discussed in the following section. 9.8.3.3 Factors Affecting PSN Strain and Particle Size The main parameters which determine whether or not PSN occurs are the strain and the particle size. This is clearly seen in Figure 9-39 for rolled aluminium containing Si particles. Two criteria must be fulfilled for growth of a nucleus beyond the deformation zone (Humphreys, 1977). Firstly, a deformation zone with sufficient rnisorientation to create a high angle boundary must be created on deformation. The conditions for this are seen in Figure 9-39, and comparison with Figure 9-34 shows that this is a necessary but not a sufficient criterion for nucleation, because the nucleus must also be able to grow into the surrounding matrix which has a stored energy Es. On an energy balance, Humphreys showed that this condition approximated to: d =4EH/Es = 4EH/p1 100
> o
80
>
0
O
i
I
#
o \
60 > o
#* »# v ••
o
o
(9-18)
Nucleation at Particles
oo
*
20 n u
0
2
U 6 8 Particle Diameter [|im]
10
Figure 9-39. The effect of rolling reduction and particle size on the occurrence of particle-stimulated nucleation (Humphreys, 1977).
410
9 Recrystallization and Recovery
where dc is the critical particle diameter and En is the grain boundary energy. It is difficult to accurately predict values of Es in deformed alloys. However, if reasonable values are taken (Humphreys, 1977) or if experimental subgrain data are used, then this equation gives agreement with the results shown in Figure 9-39, showing that the growth criterion is the critical one. The Effect of Particle Distribution There is evidence that nucleation occurs preferentially at pairs or groups of particles, even if the individual particles are below the critical size for nucleation. This has been detected statistically (Gawne and Higgins, 1971), from metallographic observations (Herbst and Huber, 1978) and from in-situ annealing (Bay and Hansen, 1979). A recent detailed study of the distribution of recrystallization nuclei in Al-Si specimens containing particles of diameters close to the critical size of Figure 9-39 (Koken etal., 1988) has also shown that under these conditions, nucleation is favored in sites of particle clustering. If the spacing of the large particles becomes small, which will happen with large volume fractions, then the recrystallization may be inhibited by particle pinning effects. As this effect is of importance in the recrystallization of metal-matrix composites, we will discuss this aspect of PSN later. The Effect of Deformation Temperature If the temperature of deformation is raised, then PSN may become less viable. We need to consider the effect of deformation temperature on the two criteria for PSN - the formation of deformation zones and growth of the nucleus beyond the particle.
At high temperatures, dislocations may be able to bypass particles without forming deformation zones. Humphreys and Kalu (1987) have shown that critical strain rate for the formation of a deformation zone is given by: + K2exp(-QB/kBT)/Td3
(9-19)
where K± and K2 are derived constants and Qy and QB are the activation energies for volume and boundary diffusion. For large particles the second term will generally be negligible. For a constant strain rate, the critical particle size for zone formation thus increases with temperature. The growth criterion (Equation (9-18)) is also affected by temperature, because the stored energy (E) is reduced at elevated temperatures, although this effect is more difficult to assess (Kalu and Humphreys, 1986). An investigation of aluminium alloy AA3004 by Oscarsson et al. (1987), in which E was calculated from measurements of subgrains suggests that in the temperature range at which the alloy is hot-rolled, the growth criterion is the critical condition for PSN. 9.8.4 Pinning Effects of Particles (Zener Drag) A dispersion of particles will exert a retarding force, on a grain boundary. The effect is known as Zener drag after the original analysis by Zener which was published by Smith (1948). When a grain boundary, of specific energy EH, migrates onto a spherical incoherent particle, when it can be assumed that the interfacial energy of the particle is unchanged by the passage of the grain boundary, then the particle, of radius r, effectively removes an area of the bound-
9.8 Recrystallization of Two-Phase Alloys
ary equal to 71 r2, and the energy is reduced
by AE: AE=nr2
(9-20)
To move the boundary past the particle a force p must be applied and the maximum value of p is: p = nrEH
(9-21)
If the boundary is planar, and randomly intersects particles, then the number of particles (TV) per unit area of boundary is:
N=3FJ2nr2
(9-22)
The pinning force exerted on the boundary is then given by: = 3FvEH/2r
(9-23)
The Zener drag force has been examined by several authors, and the reader is referred to the reviews by Nes et al. (1985), Hillert (1988) and Doherty et al. (1989) for further details. These authors conclude that the more sophisticated calculations do not lead to relationships which differ significantly from Equation (9-23). If the particles are initially coherent, then they will lose choherence during the passage of a grain boundary, and therefore the energy will be significantly higher than beforehand. It is therefore clear that coherent particles will be more effective in pinning boundaries than will incoherent particles. The increase in energy may be sufficiently great to induce the particle either to rotate into a coherent orientation in the new grain, or to dissolve in the boundary and to re-precipitate in a coherent orientation (Grant etal., 1984; Randle etal., 1986; Ringer etal., 1989). The particle shape, if not spherical, will have some effect on the pinning force, and non-uniform particle distributions, particularly planar arrays of inclusions will make grain boundary mobility anisotropic
411
in the material (Nes et al, 1985; Ringer etal., 1989). In certain circumstances, the force of the boundary on the particle may actually drag the particle with the boundary (see Ashby, 1980). However, this effect, which may be controlled by diffusion within the matrix, particle or interface, is unusual, and is only likely to occcur for low volume fractions of small particles at high temperatures. Although Equation (9-23) has been applied extensively to grain growth in fully recrystallized material, because of the difficulty of determining the driving force accurately, it has not been properly verified for primary recrystallization. Nevertheless, particle pinning is undoubtedly the cause of retarded recrystallization in alloys containing closely spaced small particles, and plays a dominant role in grain growth after recrystallization (Section 9.8.8). 9.8.5 Bimodal Alloys and the Prediction of Grain Size Many commercial alloys contain distributions of both large (> 1 jim) particles which will act as nucleation sites and small particles which will pin the migrating boundaries. In such a situation, the driving force is offset by the Zener pinning force and the critical particle size for nucleation (Equation (9-18)) now becomes: Pl-3FvEH/2r
Thus, as the Zener pinning force increases, the critical particle diameter for PSN increases. As there will be a distribution of particle sizes in a real alloy, this means that less particles are able to act as nuclei, and that the recrystallized grain size will increase.
412
9 Recrystallization and Recovery
The number of particles capable of acting as nuclei (TV) is the number of particles of diameter greater than dc. The grain size, D N , will be given approximately by: DN = N-''3
Nucleation limit
(9-25)
In an alloy containing large particles, then, if other nucleation sites are neglected, TV is the number of particles larger than Fv/r
There is considerable interest in being able to predict the grain size of particlecontaining alloys as a function of the particle parameters and the thermomechanical processing route, and Nes (1976,1986) and Wert (Wert and Austin, 1988) have developed models, based on the mechanisms discussed above for recrystallization in commercially important aluminium alloys. There are two important situations which may be considered, site-saturated nucleation in which all nucleation events occur at the start of the anneal, and JohnsonMehl kinetics, in which the nucleation rate is low, and constant with time. 9.8.5.1 Site-Saturated Nucleation
If all nuclei are formed at the same time, and grow at the same rate, then the final grain size depends only on the number of viable nuclei (TV), as given by Equation (9-25), assuming that the nuclei are evenly distributed. This is likely to be the situation when the alloy contains a large fraction of particles of diameter greater than dc.
Figure 9-40. Schematic diagram showing the effect of the particle dispersion (FJr) on the recrystallized grain size. As FJr increases, both the limiting grain size and the number of viable nucleation sites are reduced.
At high temperatures, as discussed in Section 9.6, grain growth may occur after recrystallization is complete, and the limiting grain size, DG, is then given by Equation (9-27). The recrystallized grain size as a function of the volume fraction and size of the small particles is then as shown schematically in Figure 9-40. At small values of Fv/r the grain size is determined by growth (Equation (9-27)), but at large values of Fy/r, it is determined by nucleation (Equation (9-26)). In reality, the situation is more complicated than this. Nevertheless, from a combination of fundamental theory and semi-empirical parameters, useful models, capable of predicting grain sizes in commercial alloys undergoing realistic thermomechanical processing schedules have been developed.
9.8.5.2 Johnson-Mehl Kinetics If there a limited number (TV) of viable nucleation sites in the material, and if the nucleation rate is TV, then the average grain size is given (Johnson and Mehl, 1939) as: (9-26) where G is the growth rate.
9.8.6 Particulate Composites
Particulate metal matrix composites, such as aluminium alloys containing around 20 vol. % of SiC particles are of increasing interest in applications such as automotive and aerospace ones, where a high strength and stiffness combined with
9.8 Recrystallization of Two-Phase Alloys
413
dicted conditions for this are shown in Figure 9-41. Experimental work has broadly confirmed these predictions (Humphreys et al., 1990) although other factors such as grain growth after recrystallization (Section 9.8.8) and small particles introduced during the manufacture of the composite, may also affect the annealing behavior.
25
9.8.7 Interaction of Precipitation and Recrystallization
0.1
0.2 0.3 Volume Fraction
T1 There is no precipitation possible, and so the recrystallization behavior is that of a solute containing alloy. II) T1>T>T2 Recrystallization occurs before precipitation, therefore the recrystallization is similar to I. III) T< T2 Precipitation occurs before recrystallization. The particles control the recovery rate (see extended recovery in Section 9.3.4). Eventually recrystallization may occur. In some cases discontinuous precipitation may occur on migrating high-angle grain boundaries. 9.8.8 Grain Growth in Two-Phase Alloys
During grain growth of a fully recrystallized alloy, the driving force is much smaller than during primary recrystallization. Therefore the pinning effects of particles on grain boundaries discussed in Section 9.8.4 are relatively more important. The pinning force (pz) exerted on a boundary by an array of particles is given by Equation (9-23). During grain growth, the driving force arises solely from the curvature of the boundaries as discussed in Section 9.4.1, and the magnitude of this driving force is given by Equation (9-13). On average, we expect the grains to stop
growing at a diameter D (the limiting grain size or Zener limit) when pz = p2, that is: Dz=4r/3FY
(9-27)
More sophisticated treatments of the pinning of grain boundaries by particles (Gladman, 1966; Nes etal., 1985; Hillert, 1988; Doherty etal., 1989) yield rather similar results. The pinning effect of very low volume fractions of small particles is sufficient to limit the grain size significantly. For example, a volume fraction of 5 x 10 ~3 of particles of diameter 50 nm gives Dz = 67 jim. This analysis averages the particle pinning force over the boundary, which may be valid if the average number of particles per grain (NPG) is very large. However, if NPG is small, then we might expect the particles to lie predominantly on the grain boundaries (Hellman and Hillert, 1975; Hutchinson and Duggan, 1978). In this case, Pz is given approximately by: Pz = 3FyD/8nr2
(9-28)
From Equations (9-13) and (9-28) we find: (9-29) with k ~ 6. For the particle dispersion above, this gives Dc ~ 4 |im. The number of particles per grain is now small and it is doubtful whether Equation (9-29) which neglects the correlation of particles and boundaries is valid. A more extreme case arises if the particles are at the grain corners (Hellman and Hillert, 1975). We see that the derivation of an accurate value of limiting grain size is not straightforward in circumstances where there is strong correlation between particles and boundaries. However, it is reasonable to assume that there will be a small limiting grain size Z>c, given by a more accurate
9.9 Recrystallization Textures
form of Equation (9-29), when the number of particles per grain is small. We should perhaps think in terms of two limiting grain sizes. If the material crystallises to a grain size less than Dc then we expect the grains to stop growing at about this size. However, if primary recrystallisation produces a grain size larger than Dc then we might expect the grains to be able to grow to the larger limiting size Dz. The experimental evidence necessary to test Equations (9-27) and (9-29) is not particularly clear, as has been discussed by Cahn (1983) and Doherty et al. (1989). Computer simulations of grain growth have been used extensively to study this problem (see Anderson (1986) and Doherty et al. (1989) for reviews). Two-dimensional simulations give results in agreement with Equation (9-29), and three-dimensional simulations suggest a dependence on iC 0 " 3 3 .
9.9 Recrystallization Textures When a metal is recrystallized, the crystallographic orientations of the new grains may be quite different from those of the old ones. If this is the case, then the recrystallization texture will be different from the deformation texture. As textures have a significant effect on the mechanical and physical properties of a material, the understanding of the origin of textures is of great importance. The control of textures during the mechanical processing of metals is discussed in more detail in Chapter 10 of this volume. The published literature on the subject of textures is extensive, and there are several contentious issues which continue to arouse much debate. For further general information the reader is referred to reviews by Hatherly and Dillamore (1975),
415
Grewen and Huber (1978), Nes and Hutchinson (1989) and Hatherly (1990). The series of trienniel international conferences on texture of which the most recent was in Avignon in 1990 also provide much reference material. A texture can be described in terms of the ideal orientation or group of orientations to which it approximates. We will confine ourselves to textures produced on rolling and on subsequent annealing, and to materials of cubic symmetry. In this case the ideal orientation is given as (hkl) [uvw], where (hkl) is the plane parallel to the rolling plane and [uvw] is the lattice vector parallel to the direction of rolling. In some cases the texture has a single component, for example (113 [2lT]). However, more commonly the texture of the material corresponds to several ideal orientations. Thus the texture of deformed aluminium may contain the components (112) [111], (Oil) [211] and (427) [232] (see also Chap. 10, Sec. 10.2.2). Although such descriptions are convenient and concise, they give no indication of how closely the material approximates to these orientations, and if the material has only a weak preferred orientation then these descriptions are of little use. A graphical representation of the texture spread is provided by a pole figure, which is obtained directly from X-ray diffraction data. A pole figure is essentially a stereographic projection in the rolling plane of the specimen in which the orientations from all the grains in the material, of a particular type of crystallographic pole, e.g. 2 then the microstructure develops as shown in Figures 9-50 a-c, the material is always partly recrystallized and a smooth curve with a single peak if found. However, if D0/DR) r
rm (or R) R t
t,t0 u
(uvw} w o ,w
crystal axes Fourier transform final and initial grain diameters lattice plane spacing Young's modulus