Temperature dependence of stacking fault energy in close-packed metals and alloys

Materials Science and Engineering, 36 (1978) 47 - 63 © Elsevier Sequoia S.A., Lausanne -- Printed in the Netherlands

47

Temperature Dependence of Stacking Fault Energy in Close-Packed Metals and Alloys

L. RI~MY and A. PINEAU

Groupe de Mdtallurgie Mdcanique-Equipe de Recherche Associde au CNRS, Centre des Matdriaux-Ecole des Mines de Paris, B.P. 87, 91003 Evry-Cedex (France) B. THOMAS

IRSID B.P. 129, 78104 Saint-Gerrnain en Laye Cedex (France) (Received February 24, 1978)

SUMMARY

1. INTRODUCTION

The experimental data currently available concerning the temperature dependence of the stacking fault energy (SFE, 7) observed in the study of the size variation of stacking fault nodes and ribbons in thin foils on a heating or a cooling stage in an electron microscope are reviewed. It is shown that in spite of the experimental difficulties useful information can be obtained by this technique. In pure cobalt and a number of transition metal alloys (Co-Ni, Co-Fe, Fe-Cr-Ni and Fe-Mn-Cr) a marked increase of the SFE with increasing temperature has been unambiguously demonstrated even though the observed changes in node size are partly irreversible. In the case of silver-base and copper-base alloys the experimental data are often contradictory and, except in the case of Ag-Sn alloys which show a small reversible increase in SFE with temperature, the quantitative estimates of the temperature dependence of SFE are less reliable. The influence of temperature on SFE can be related to the stability of the face-centred cubic phase with respect to the hexagonal close-packed phase at constant composition. Fairly good agreement is observed between the measured value of d7/dT and that estimated from thermodynamic data, at least in the case of transition metal alloys. The possibility of explaining the observed temperature dependence of SFE in terms of recent calculations based on electron theory is discussed.

Because of the importance of the stacking fault energy (SFE), hereafter denoted by 7, in relation to the mechanical behaviour of face-centred cubic (f.c.c.) metals and alloys, a considerable amount of research has been devoted to the measurement of this parameter and to the investigation of the effects of alloying additions and temperature. These aspects have been previously discussed by Christian and Swann [1] and Gallagher [2]. New results published since these earlier papers appeared have stimulated the preparation of the present article, the aim of which is to review the currently available experimental data concerning the temperature dependence of SFE in various pure metals and alloys and where possible to compare these data with theoretical predictions based on thermodynamic considerations and the electron theory of metals. A variety of techniques have been devised to measure SFEs and the advantages and drawbacks of each method have been extensively reviewed [3 - 7]. The most convenient method for the study of the temperature dependence of SFE is that of the direct observation of the size variation of stacking fault configurations (in particular triple nodes and stacking fault ribbons) in thin foils on a heating or a cooling stage in a transmission electron microscope [3]. The work discussed in this paper will be restricted for the most part to experiments of this kind. However, it is worth noting that this technique can be

48 applied only over a limited range of SFE corresponding to values of 7/p b lying between about 5 × 10 -3 and 5 × 10 -4, where p is the shear modulus of the material and b is the magnitude of the Burgers vector of the partial dislocations bounding the stacking fault configuration. Moreover, quantitative determinations of the temperature dependence of SFE from the measurement of size variations of stacking fault configurations may be rather difficult for a variety of reasons which are discussed in some detail in Section 2. In spite of these difficulties experimental results are n o w available for a number of close-packed noble metals and transition metal alloys. These results are summarized in Section 3, where it is shown that the temperature dependence of SFE varies considerably from one system to another. In Section 4 an a t t e m p t is made to rationalize the observed difference in terms of the temperature dependence of the relative stability of the f.c.c, and h.c.p, phases in each alloy using the model of short range interaction which Ericson applied earlier to the C o - N i system [ 8 ] . The limitations of this approach are pointed out, and finally the possibility of explaining the observed temperature dependence of SFE in terms of recent theoretical calculations based on electronic structures is discussed.

2. DIFFICULTIES INVOLVED IN DETERMINING THE VARIATION OF SFE WITH TEMPERATURE FROM IN SITU ELECTRON MICROSCOPE OBSERVATIONS Although the determination of SFE from measurements of the dimensions of stacking fault nodes and ribbons is straightforward in principle, a certain number of theoretical and experimental difficulties are encountered in practice and these are magnified when the temperature is varied during the experiments. 2.1. Experimental difficulties The theoretical calculations relating SFE to the fault configuration dimensions take into account only the forces derived from the energy of the stacking fault and the energy of the partial dislocations bounding the fault. The validity of these calculations within this approximation may be considered to be satis-

factory and for a full discussion of this point the reader is referred to papers by Brown [9] and R u f f [3]. In practice, however, the dimensions of stacking fault nodes and ribbons observed in a given foil at room temperature generally exhibit considerable scatter and standard deviations in the experimental measurements of the order of 10 - 20% of the mean value are quite common. Part of this scatter is u n d o u b t e d l y due to difficulties involved in locating and measuring precisely, on normal bright field micrographs, the position of the partial dislocations at'the edges of the fault. This obviously continues to be one of the sources of error in the determination of the temperature dependence of SFE. Although the recent development of the weak beam imaging technique [10] has led to a remarkable improvement in this respect, most of the work reviewed in the present paper was done without resort to this procedure. Another source of scatter in isothermal measurements of SFE can be attributed to forces due to the proximity of neighbouring dislocations and the foil surfaces. This effect can be reduced to a minimum by a careful choice of the nodes or ribbons used for the measurements. Finally it almost goes without saying that when observations are carried out at various temperatures, the temperature of the specimen must be controlled and measured with reasonable precision. Local electron heating of the foil is generally n o t a problem. The other main problem is to ensure good thermal contact between the thin foil and the specimen holder heating/cooling device. However, errors in temperature measurement are probably always smaller than the errors in the estimation of SFE and they are of minor importance in measuring the temperature variation of SFE. 2.2. Theoretical difficulties In his review of the literature Gallagher [2] pointed o u t that numerous factors besides a true variation of SFE with temperature may give rise to a temperature dependence of the node size. The main factors are changes in elastic constants, changes in lattice friction forces, changes in the local or global chemical composition of the alloy, solute or impurity pinning of dislocations, Suzuki segregation to the stacking fault and changes in short range

49 order and global chemical composition due to changes in the solubility of the alloying element with temperature.

2.2.1. Elastic constants Since the changes in the elastic constants are instantaneous and readily measured independently of in situ experiments, corrections can in fact easily be made for this effect. 2.2.2. Lattice friction forces and solute or imp urity pinning of dislocations As realized early by Christian and Swann [ 1], who introduced the concept of "solute impedance force", lattice friction forces (due for instance to the presence of two kinds of atoms in a random solid solution) and solute or impurity pinning of dislocations lead to similar effects on stacking fault configurations. Both effects impede dislocation movement. In isothermal experiments, however, the assessment of the effects of friction forces is practically impossible except perhaps in cases where serrations, kinks or cusps are clearly visible on the dislocations bounding the fault as has been observed in some highly alloyed silver and copper base alloys of low SFE [2]. Nevertheless nodes and ribbons introduced b y room temperature deformation are expected to have a size smaller than the equilibrium size as discussed previously and borne o u t b y some experiments carried o u t when such friction forces are present [11 - 14]. In most cases an increase in temperature of the specimen above room temperature can lead to a decrease in the effective local friction forces owing to thermal activation of the dislocation movement. However, an increase in specimen temperature can in certain cases lead to an increase in dislocation pinning forces due to the formation of solute or impurity atom atmospheres which subsequently reduce the dislocation mobility. It is therefore difficult to establish a priori general rules for predicting friction forces, although these forces are expected to increase with the size factor of the solute atom, and their influence on the fault configurations during thermal cycling. In the cases where irreversible changes in node size or hysteresis effects are observed the separation of the effects of changes in dislocation mobility from those due to a true SFE temperature dependence is

difficult and each particular case must be treated separately. However, if the stacking fault configurations change size reversibly during thermal cycling it can be concluded that the friction forces are negligible.

2.2.3. Suzuki segregation In order to predict the change in SFE due to the segregation of solute atoms to the faults, a precise definition of SFE in solid solutions is necessary. This matter has been discussed in detail in an excellent paper by Hirth [15]. For the purposes of the present paper, we can summarize as follows. A stacking fault can be considered as either a Gibbs dividing surface [15] or a region of finite width [16]. When treated correctly, these approaches are strictly equivalent as pointed out by Hirth [15]. Quantitative estimations of equilibrium segregation have been obtained by Ericsson [16] with the aid of the finite width model. His results, which were based on a thermodynamic calculation, have been confirmed by the pair-potential calculations of Nourtier [17] which were applied to the case of dilute solutions of normal metals. The principal conclusions which can be drawn from these calculations are as follows: (1) at thermodynamic equilibrium the SFE of a segregated fault is higher than that of an unsegregated alloy with the solute content of the segregated fault [14, 15, 18] ; (2) the SFE of a segregated fault is lower than that of the alloy in the absence of segregation [14, 18]. In the present c o n t e x t the important point is that if Suzuki segregation occurs when the specimen temperature is raised it will lead to an increase in the node size of an initially unsegregated node. It follows that a reversible decrease in fault dimensions with increasing temperature (allowing for the changes in elastic constants) provides convincing evidence of a true SFE increase with temperature even though the magnitude of dT/dT may be incorrectly estimated because of the presence of Suzuki segregation. 2.2.4. Changes in degree of order or in the global composition of solid solutions During thermal cycling, changes in the degree of short range ordering or in the global composition of the alloy (precipitation or

50

re-solution) may occur and contribute to the apparent change in SFE. In principle their effect can be allowed for with the aid of independently determined data concerning the change in SFE with ordering and composition together with a knowledge of the kinetics of the ordering process or the precipitation/ dissolution phenomena. This discussion can then be summarized as follows. In order to obtain reliable information concerning the temperature dependence of SFE from in situ electron microscope observations multicycle experiments are desirable. Such experiments can be classified into three categories according to the observed variations in node size with temperature. 2.2.4.1. Completely reversible changes in node size. In this case the effects of lattice and solute impedance forces, Suzuki segregation and global composition changes can be neglected. The sign of the temperature dependence is unambiguous and the magnitude of d7/dT can be estimated correctly from the variations in the dimensions of stacking fault configurations after correcting for the change in elastic constants with temperature. 2.2.4.2. Reversible changes in node size with hysteresis. In this case lattice and solute

impedance forces are not negligible but remain small compared with the true SFE change with temperature. The sign of dT/dT can be determined unambiguously but the estimation of the magnitude of dT/dT is generally less reliable than in the previous case.

2.2.4.3. Partly or wholly irreversible changes in node size. In this case lattice friction forces, solute or impurity pinning forces and/or composition changes mask the effect of an eventual temperature dependence of SFE. In some cases it is possible to determine the sign of d7/dT. The determination of its magnitude is generally uncertain.

3. SUMMARY OF EXPERIMENTAL DATA

The metals for which experimental data concerning the temperature dependence of SFE are currently available can be classified into two groups: (a) noble metals and alloys; (b) transition metals and alloys. The experimental observations concerning these two groups of alloys are described below and the experimental values of the rate of change of SFE with temperature are summarized in Tables 1 and 2.

TABLE 1 Summary of observed SFE variation with temperature for noble metals and alloys Metal or alloy

dT/dT (mJ m -2 K -1)

(Temperature range

References

--dp_/dT

Comments

(107 N m -2)

~1010 N m -2)

(K)) Practically no size variation Significant and reversible (?)

Ag

--0.013

(293 - 493)

[2]

1.3 a

2.98 a

Ag-Zn

--0.013

( 2 9 3 - 593)

[2]

1.3

2.98

Ag-7.5 at.% In Ag-11.5 at.% In Ag-9 at.% Sn

0.015 0.02 +0.008

(450 - 700) (450 - 700) (543 - 773)

[20 ] [20 ] [13]

1.3

2.08

1.0

2.39

Ag-11.9at.%Sn -0.006 (h.c.p.)

(543 - 773)

[13]

1.0

2.3

( 4 7 3 - 673) (293 - 593)

[12]

1.8 a

4.77 a

Bulk annealed

[2] [2] [2] [2]

1.8 1.8 1.8 1.8

4.77 4.77 4.77 4.77

Irreversible Irreversible Irreversible Irreversible

Cu-1 5 at.% Al C u - 1 6 at.% Al C u - 3 0 at.% Zn Cu-6.8 at.% Ge Cu-8.6 at.% Si

0.02 0.015 Small Small

(293 - 593) (293 - 593) (293 - 593)

aValues when unavailable from the original work were taken from ref. 49.

Irreversible Reversible between 543 and 773 K Irreversible below 543 K

51 TABLE 2 Summary of observed SFE variation with temperature for transition metals and alloys Metal or alloy

d?/dT _ ( m J m - z K -1)

(Temperaturerange

References

( 1 0 7 N m -2)

Comments ~1010 ~ N m -2)

--dpJdT

(K)) Co (h.c.p.) --0.03 C o - 1 5 at.% Ni (h.c.p.) Co- 33 at.% Ni 0.03 Co-32 at.% Ni 0.04 Co-35 at.% Ni 0.05 C o - 6 at.% Fe 0.04 C o - 8 at.% Fe C o - 3 0 wt.% Ni 0.03 15 wt.% Cr

(293 - 643)

[16]

3.1

7.4

Probably reversible

(293 (100 (100 (100

- 823) - 400) - 400) - 600)

[16] [24] [18] [24]

3.4 2.5 2.5 2.3

Probably reversible Probably reversible Reversible Unknown reversibility

(500 - 800)

[18]

Complex a

8.4 7.5 7.25 6.75 6.9 7.25

F e - 1 5 . 9 wt.% C r12.5 wt.% Ni Fe-17.8wt.%Cr14.1 wt.% Ni Fe-18.3 wt.%Cr10.7 wt.% Ni F e - 18 . 7 wt.% C r 15.9 wt.% Ni F e - 1 8 wt.% C r7 wt.% N i 0.18 wt.% C F e - 1 8 wt.% C r14 wt.% Ni 4 wt.% Si F e - 2 0 wt.% M n 4 wt.% C r0.5 wt.% C

0.08

(100 - 400)

[26]

5.1

7.4

Irreversible above 500 K; no variation below Reversible

0.06

(100 - 300)

[26]

0.05

(293 - 600)

[11]

3.6

6.7

Mainly reversible

0.10

(293 - 600)

[11]

0.10

(293 - 600)

[28]

5.2

7.4

0.04

(150 - 400)

[29]

5.2

7.4

0.06

(100 - 400)

[ 14 ]

Complex a

7.6

Irreversible with unpinning effects on cooling " Partly reversible

Mainly irreversible with unpinning effects on cooling

aThe complex variation of the shear modulus arose from a magnetic transition of austenite (see the text).

3.1. Noble metals and alloys Silver is the only pure f.c.c, metal which can be studied b y the node m e t h o d at room temperature. Of the noble metal alloys both silver-base and copper-base alloys have been widely investigated. 3.1.1. Silver A slight increase in node size has been observed in this metal b y means of hot-stage studies [2] in the temperature range 300 493 K. These changes were perfectly reversible on recooling to room temperature, and when the effect of the decrease in shear modulus is taken into account a value of dT/dT = --0.013 mJ m -2 K -1 is obtained. In view of the small size of the nodes at and above r o o m temperature, further experiments at subzero temperatures would be useful to confirm the sign and magnitude of dT/dT in silver.

Since the preparation of this paper Saka et al. [19] have published work concerning the temperature dependence of the SFE of silver.

3.1.2. Silver-base alloys Experimental results are available for three silver-base systems: Ag-Zn, A g - I n and Ag-Sn. The A g - Z n alloys were studied by Gallagher [2] who observed the same nodes at 300, 493 and 593 K. The results are similar to those obtained on pure silver, i.e. a small reversible increase in node size with temperature. Hot-stage experiments were performed on Ag-7.5 at.% In and A g - l l . 5 at.% In alloys by Gallagher and Washburn [ 2 0 ] . A strong b u t irreversible shrinkage of stacking fault nodes was observed at room temperature after annealing at various temperatures above

52

A 9 - 9 Sn A~

4

E •"~ 3 E tlJ U. 2 (I)

7 E• b-j

10

*3

O~

~SSS

E

~F,A

LL

"100

• Cu- 16At • Cu-3OZn • Cu-8.6Si o Cu-6.SGe

SSS S SS

AO

i

2

Ss

iaA

t

j~

tess** 5--

I

i I 500 Temperoture,

I 700

J

K

Fig. 1. Variation of SFE with temperature for Ag9 at.% Sn alloy (after Ruff and Ives [13]). Room temperature measurements were made in four different conditions: A.D., as-deformed foil; Q, foil heated to 770 K and cooled to room temperature at about 480 K m i n - 1 ; F.A., foil annealed at 720 K and cooled to room temperature at about 7 K r a i n - l ; B.A., foil prepared from bulk specimen annealed at 720 K for I h.

300 K. The apparent increase of the SFE is of the order of 0.015 mJ m - 2 K -z for Ag-7.5 at.% In and 0.02 mJ m -2 K -z for A g - l l . 5 at.% In. Because of the irreversibility of the changes in node size it is difficult, however, to assess the true variation of SFE with temperature. A thorough study of a A g - 9 at.% Sn alloy (f.c.c.) and a A g - l l . 9 at.% Sn alloy (h.c.p.) was more recently carried o u t by R u f f and Ives [ 1 3 ] . Their results obtained on the f.c.c. alloy are illustrated in Fig. 1. These authors observed that the node size decreased with increasing temperature and that this decrease was reversible in the temperature range 543 773 K. The size variation of the nodes corresponds to a true SFE increase dT/dT = 8 × 10 -3 mJ m -2 K -z. However, below 543 K the change in node size was no longer reversible. R o o m temperature node measurements in this alloy after various annealing treatments suggest that the irreversibility is due to solute pinning which prevents the dislocations from returning to their equilibrium positions. Similar behaviour was observed in the h.c.p. alloy, b u t in this case the SFE decreases at a rate dT/dT = --6 × 10 -3 mJ m -2 K -z in the temperature range 543 - 773 K.

-i1._

i 300

2

! 400

[ 500

13

j 600

Temperoture, K

Fig. 2. Variation of apparent SFE with temperature for copper-base alloys (after Gallagher [2] )*.

temperature dependence of the SFE of copper-base alloys have appeared in the literature. Figure 2 shows the variation of the apparent SFE observed over a single thermal cycle (300 - 600 K) for four copper-base alloys given b y Gallagher: C u - 1 6 at.% A1, C u - 3 0 at.% Zn, Cu-6.8 at.% Ge and Cu-8.6 at.% Si. In the Cu-A1 and C u - Z n alloys it was observed that the node size decreases markedly with temperature but the size changes are largely irreversible on cooling. The nodes observed in the C u - G e and Cu-Si alloys also decrease irreversibly b u t in these alloys the size changes are quite small. It was argued that the decrease in node size in the first two alloys was n o t due to an increase in SFE b u t merely an indication that the nodes observed at room temperature were above equilibrium size as a result of solute pinning of the partial dislocations. We have already discussed the invalidity of this explanation in Section 2. The size factors of the germanium and silicon atoms are rather similar to those of aluminium and zinc [ 2 1 ] , and one would expect the solute atom-dislocation interaction to be strong in all alloys. Even when allowance is made for the differences in atom concentration it is difficult to see w h y the nodes should be initially pinned above their equilibrium size in the aluminium and zinc alloys and n o t in the other t w o alloys. An alternative viewpoint is that the SFEs of the C u - 1 6 at.% A1 and C u - 3 0 at.% Zn alloys in fact increase quite strongly with

3.1.3. Copper-base alloy Since Gallagher's earlier review [2] practically no new reliable data concerning the

*All the numbers in this figure and others refer to the chronological order of in situ measurements.

53

temperature and that the dislocations are prevented from returning to their equilibrium positions on recooling to room temperature as a result of the development of short range order at high tenzperature which is known to occur in both these alloys [22]. This argument was developed specifically for the Cu15 at.% A1 alloy by Tisone et al. [12] in the light of results obtained in a series of measurements at room temperature after bulk annealing. In a first series of experiments Tisone et al. showed that room temperature SFE decreases with the degree of short range order. They then carried out two further series of bulk annealing experiments to study the effect of temperature on the SFE. Specimens were annealed for 10 min at 873 K (treatment A), deformed at room temperature and then aged at a temperature Te of 473, 573, 673, 773 or 873 K for 35 400, 1650, 200, 75 or 10 min respectively in order to produce approximately the same degree of short range order at each temperature. In view of the solute impedance forces resulting from short range order the nodes subsequently observed at room temperature are expected to conserve the size developed at the annealing temperature Te. The results shown in Fig. 3 (experimental points A, D, Te) indicate an increase in SFE up to 700 K followed by an apparent decrease above this temperature. A second set of experiments was then carried out on specimens which were first deformed at room temperature and then annealed at 873 K before aging at the short range order temperature Te. The values of SFE obtained from these specimens (experimental points D, A, Te in Fig. 3) are in good agreement with those of the first set of

Cu- 15AI

7 F

12

E 10 IJJ U. u~

8

• D , A , Te

6

,

J

500

700

i

J

900

Temperoture, K Fig. 3. Variation of SFE with temperature for Cu15 at.% A] ahoy (after Tisone et al. [12]). The symbols are explained in the text.

measurements and support the hypothesis of a reversible change of SFE with temperature at a constant degree of short range order. The corresponding value of dT/dT is 2 × 10 -2 mJ m-2 K-1 which is in good agreement with the value estimated from Gallagher's in situ measurements on a similar alloy. The apparent decrease in SFE after annealing at temperatures above 700 K is probably due to the fact that the short range order developed in the annealing treatments was in fact insufficient to pin the dislocations at the high temperature positions when the specimens were cooled to room temperature [12]. Summarizing, then, it seems likely that both Cu-16 at.% A1 and Cu-30 at.% Zn alloys exhibit a fairly strong increase in SFE with temperature whereas in the Cu-6.8 at.% Ge and the Cu-8.6 at.% Si alloys d ~ / d T is small or negligible. Since the preparation of this paper Saka et al. [23] have published work concerning the temperature dependence of the SFE of Cu-A1 alloys. 3.2. Transition metals and alloys The only pure transition metal which can be studied by the node method is cobalt. The temperature dependence of SFE in this metal can be investigated in both the h.c.p, and f.c.c, phases since the phase transition temperature is readily obtainable in the electron microscope. In the case of transition metal alloys a number of cobalt-base and iron-base systems have been recently examined. 3.2.1. Cobalt This metal which has a h.c.p, structure at room temperature was first studied by Ericsson [8]. In both annealed and lightly deformed specimens the node size was found to increase with increasing temperature. To study the nodes in the f.c.c, phase, deformed h.c.p, specimens were heated in the microscope to temperatures above the phase transition temperature. Because of the rudimentary nature of the specimen stage used in these experiments it was not possible to observe the same node at different temperatures and only the mean node size could thus be determined. The temperature dependence obtained by Ericsson is shown in Fig. 4. When the temperature is increased, the SFE of the h.c.p, phase decreases whereas the SFE of the f.c.c, phase

54

.T

30 ~ . "r I "~.,~J E

HCP

FCC

3O 7 E

20 w h U~ 10

~ ~ o -

33N~.

Co

300

500

700

900

0

Temperature, K

Fig. 4. Variation of SFE with temperature for pure cobalt (after Ericsson [8 ] ). increases. The magnitude of the change is, however, approximately the same in both cases, i.e. IdT/dTI = 3 × 10 -2 mJ m -2 K -1. In these experiments the reversibility of the variations in node size could n o t be checked. It should be noted that the SFE does n o t appear to extrapolate to zero at the h.c.p.f.c.c, equilibrium temperature To*. At this temperature the SFE is about 15 mJ m -2 in both phases.

400

600 800 Temperature, K

Fig. 5. Variation of SFE with temperature for Co33 at.% Ni alloy (after Ericsson [8] ).

15 E

F: 10 UJ IJ. Ul 5 o le

IT° o

J 100

L 200

l 300

I 400

Temperature, K

3.2.2. Cobalt-base alloys 3.2.2.1. Co-Ni alloys. Among the cobaltbase alloys the Co-Ni system has been the most widely investigated. The structure of these alloys is either f.c.c, or h.c.p, depending on composition and temperature. Ericsson [8] examined a h.c.p. Co-15 at.% Ni alloy in the temperature range 293 - 693 K and found the same temperature dependence as t h a t observed in pure h.c.p, cobalt. F.c.c. Co-Ni alloys were studied by Ericsson (Co33 at.% Ni) [8], Tisone (Co-32 at.% Ni) [24] and R~my (Co-35 at.% Ni) [18]. The measurements made by these different authors are in quite good agreement and give a value of 0.03 - 0.05 mJ m -2 K -1 for the temperature dependence of the intrinsic SFE (cf. Figs. 5- 7). As shown in Fig. 7, R6my's experiments demonstrate unambiguously the reversibility of the variations in node size in the C o - 3 5 at.% Ni alloy. As in the case of pure cobalt the intrinsic SFE has a non-zero value of approximately 12 - 16 mJ m -2 at the *The temperature TO at which the free energy change associated with the f.c.c. -~ h.c.p, martensitic transformation is zero, is not very well known in these alloys. Estimates of To can, however, be made from measurements of the temperature E d below which the f.c.c. -~ h.c.p, transformation can be strain induced during tensile testing [ 18 ].

Fig. 6. Variation of SFE with temperature for Co32 at.% Ni alloy: 7i, intrinsic SFE; 7e, extrinsic SFE

(after Tisone [24]).

Co-35Hi 25

7

#a ~m

E

/'

,4 E 20 I,,U U. If)

2

Iv0 L

100

,

L

~

'zOO Temperature,

K

F i g . 7. V a r i a t i o n o f S F E w i t h t e m p e r a t u r e

for Co-

315 at.% Ni alloy (after R~my [18] ). phase equilibrium temperature To in these alloys. Tisone [24] also measured the variation of the extrinsic SFE in the C o - 3 2 at.% Ni alloy, as shown in Fig. 6. His results indicate that the extrinsic SFE increases more rapidly with temperature than the intrinsic SFE. Moreover, as illustrated in Fig. 6, the

55 extrinsic SFE becomes smaller than the intrinsic SFE at temperatures below about 200 K, i.e. below the martensitic phase transformation temperature Es*.

Co - 3 0 N i -

t.

25

E

3.2.2.2. Co-Fe alloys. The intrinsic and extrinsic SFE of a series of Co-Fe alloys were also measured by Tisone [24]. The results obtained on two of these alloys, Co-6 at.% Fe and Co-8 at.% Fe, are reproduced in Fig. 8. In both alloys the temperature dependences of the intrinsic and extrinsic SFE are very similar, i.e. dT/dT -~ 5 × 1 0 - 2 mJ m-2 K-1, at temperatures above 300 K. The ratio 7e/7i remains less than unity even at temperatures which are definitely above To and Es. For these alloys, the author made no mention of the reversibility of the stacking fault configurations.

30

E 20 E hi U. tr~

10

~S~,S S

0

I 100

,

•

'1 300

Co-6Fe Col8 Fe

J 500

700

Ternperoture, K

Fig. 8. Variation of S F E with t e m p e r a t u r e for C o Fe alloys: 7i, intrinsic S F E ; 7e, extrinsic S F E (after Tisone [24] ).

3.2.2.3. C o - N i - C r alloys. Ternary Co-Ni15 wt.% Cr alloys were recently studied in the temperature range 100 - 800 K [18]. In these alloys the ferromagnetic-paramagnetic transition occurs in this temperature range and the shear modulus passes through a maximum at the Curie temperature 0c [18]. The apparent variation of the SFE with temperature in the Co-35 wt.% Ni-15 wt.% Cr alloy (0c = 463 K) is illustrated in Fig. 9. The node size was observed to be practically constant from liquid *E s is the t e m p e r a t u r e corresponding to the spontaneous f.c.c. -~ h.c.p, martensitic phase transformation.

15 C r

~; 2o E

m 15 ! I

100

,

J

300

,

~[

500

J

700

Temperature, K Fig. 9. Variation of apparent SFE with temperature for Co-30 wt.% Ni-15 wt.% Cr alloy (after R6my

[181). nitrogen temperature up to about 500 K. The corresponding small increase in the apparent SFE shown in Fig. 9 arises from the change in shear modulus below the Curie temperature. It is believed that this small variation in node size is due to strong friction forces arising from solute pinning. At higher temperature the observed decrease in node size corresponds to an apparent increase in SFE of the order of 3 × 1 0 - 2 mJ m -2 K-1. However, on cooling the thin foil from the highest temperature obtained (800 K) the node size remained practically unchanged. The large decrease in node size observed at temperatures above 500 K is indicative of an important increase in SFE with temperature, but in this case the magnitude of the SFE temperature dependence cannot be accurately estimated. This behaviour was interpreted in terms of Suzuki segregation at elevated temperatures which tends to offset the decrease in node size during heating and to prevent the nodes from returning to their equilibrium size on cooling. In fact a detailed estimation from Ericsson's model [16] and available thermodynamic data [25] predicts that chromium atoms segregate to the stacking fault nodes [18]; for example at 800 K, assuming thermodynamic equilibrium is obtained, the calculated excess chromium concentration at the fault is 3.7 at.% and the corresponding decrease in SFE is about 3.3 mJ m -2.

3.2.3. Iron-base alloys Because of their practical importance f.c.c. stainless steels have been studied by several authors. Apart from Fe-Cr-Ni alloys, iron-

56 base alloys are rather poorly documented; only F e - M n - C r alloys have been examined recently.

3.2.3.1. F e - C r - N i alloys. Low carbon F e 18 wt.% Cr-12 wt.% Ni alloys were examined by Lecroisey and coworkers [26, 27] in the temperature range 150 - 400 K. The large linear increase in SFE observed in these alloys (d~/dT = 7 X 10 -2 mJ m -2 K -1) is illustrated in Fig. 10. In these experiments the temperature cycles were repeated several times on the same node and the variations in node size were found to be perfectly reversible over the whole temperature range. Figure 10 also shows an example of the results obtained on a F e - 1 5 . 9 wt.% Cr-12.5 wt.% Ni alloy. Latanision and R u f f [11] examined two similar stainless steels: Fe-18.3 wt.% Cr10.7 wt.% Ni and Fe-18.7 wt.% Cr-15.9 wt.% Ni in the temperature range 300 - 600 K (Fig. 11). Most of the increase in SFE observed above room temperature was reversible, the difference in SFE measured on the same nodes before and after the thermal cycling being less than 2 mJ m -2. Between 300 and 400 K the increase in SFE with temperature is large and of the same order as that determined by Lecroisey and Thomas, i.e. dT/dT = 5 X 10 -2 mJ m -2 K -1 and 0.10 mJ m -2 K -1 for the F e - 1 8 . 7 wt.% Cr15.9 wt.% Ni and Fe-18.3 wt.% Cr-10.7 wt.% Ni alloys respectively. However, above 400 K the temperature dependence appears to be less marked. This can be partly attributed to the decreasing accuracy of node measure-

2 •

30

?

E 25

E

d 2o U.

J 300

I

I

~oo soo Temperature~ K

I soo

Fig. 11. Variation of SFE with temperature for FeCr-Ni alloys (after Latanision and Ruff [11]). ments as the SFE increases. Moreover, Latanision and R u f f suggested that solute segregation to the partial dislocations may also contribute to the less marked increase in SFE with temperature at higher temperatures and also explain the small irreversibility on recooling at room temperature. The behaviour of high carbon stainless steels appears to be more complex than that of the "interstitial-free" alloys. This is illustrated by Abrassart's measurements [28] on an F e - 1 8 wt.% Cr-7 wt.% Ni-0.18 wt.% C steel in the temperature range 300 - 600 K. Although in these experiments the changes occurring in each individual node were n o t carefully checked, the mean size was found to change discontinuously on heating. Figure 12 shows that the average SFE increases linearly up to 500 K at a r a t e of 0.1 mJ m -2 K -1

5O

fO

25

'i

7 E 20

E u..

10

Fe - t6 Cr - 13Ni

'E 30 tJ. t~

20

Fe- 18Cr- 7 Ni-O,18C

10

• Fe-tT, SCr~IgNi

I

I

J

100

200

300

[ ~00

Temperoture, K

Fig. 10. Variation of SFE with temperature for F e Cr-Ni alloys (after Lecroisey and Thomas [ 2 6 ] ) .

[

J

[

I

300

400

500

600

Temperoture, K

Fig. 12. Variation of apparent SFE with temperature for Fe-Cr-Ni-C alloy (after Abrassart [28 ] ).

57

b u t above this temperature the rate of increase appears to drop off markedly. On recooling to room temperature the nodes in this alloy did n o t recover their original size and, moreover, a large scatter in node dimensions was observed. The decrease in node size on heating is presumably due, for the most part, to a true SFE change with temperature since the magnitude of d~//dT is very similar to that observed in the low carbon stainless steels. The irreversibility on cooling was attributed to the formation of Cottrell atmospheres of carbon atoms around the partial dislocations at high temperature. The large scatter in node size on recooling can be explained by differences in carbon segregation from one node to another or by the statistical nature of the thermally activated unpinning process. The levelling of the variation of node size above 500 K may also be explained by the formation of Cottrell atmospheres which would inhibit the movem e n t of the partial dislocations. However, here again the imprecision in measurements of node size at small node sizes prevents definite conclusions from being drawn. In the case of the quaternary F e - 1 8 wt.% C r - 1 4 wt.% N i - 4 wt.% Si alloy studied by Lecroisey and Thomas [29] the way in which the nodes expanded and contracted during thermal cycling provided convincing visual evidence of the presence of strong local lattice friction forces. As the temperature was varied from one measuring temperature to another the partial dislocations were observed to move in discrete jumps. The combined effects of strong friction forces and a strong temperature dependence of SFE could explain the large hysteresis in plots of apparent SFE against temperature. An example of the behaviour of one node examined during two successive temperature cycles is shown in Fig. 13.

3.2.3.2. Fe-Mn-Cr alloys. SFEs were recently studied by R6my [14] in a F e 20 wt.% M n - 4 wt.% Cr-0.5 wt.% C alloy in the temperature range 100 - 400 K. It should be noted that this alloy exhibits an antiferromagnetic-paramagnetic transition at 283 K [18]. The results of SFE measurements are shown in Fig. 14. On cooling from 300 to 100 K a small reversible increase in node size is observed which suggests a true SFE varia-

Fe

-

18 C r - IJ; N i

-/,

Si

12,5

E ~4 E lO U. U3

7, 5

I s t cycle 2 nd cycle

5

I

[

[

200

300

400

Temperature, K

Fig. 13. Variation of apparent SFE with temperature for Fe-Cr-Ni Si alloy (after Thomas and Lecroisey [29]).

Fe - 2O Mn - z Cr - O,S C

T T

/'°

it1

T

'7,

E E LU LL 10 U~

100

20O

300

4OO

Temperature, K

Fig. 14. Variation of apparent SFE with temperature for Fe-Mn-Cr-C alloy (after R6my [14]).

tion. The rate of change of SFE with temperature may in fact be greater than the indicated value since the dislocation mobility m a y be reduced by lattice friction forces due to carbon atoms in solid solution and to ferromagnetic interactions produced between nearest neighbours by the displacement of the partial dislocations [30]. Calculations for F e - M n binary alloys suggest, however, that the lattice friction forces arising from this ferromagnetic interaction effect are fairly small [ 3 0 ] . On heating above room temperature, the node size decreases more rapidly than in the low temperature range b u t this variation is mainly irreversible. The rate of change of node size above 300 K is equivalent to an apparent SFE temperature dependence of a b o u t 6 X 1 0 - 2 m J m - 2 K - 1 . This value is of the same order of magnitude as those measured in stainless steels. Assuming that the

58

decrease in node size is a consequence of a true change in SFE the irreversibility can be explained, as in the case of the high carbon stainless steel studied by Abrassart [28], by the formation of CottreU atmospheres which prevent the nodes from recovering their equilibrium size on recooling to room temperature. This interpretation is supported by two complementary experiments. Firstly the variations in node size were found to be reproducible during a second thermal cycling. Secondly, nodes annealed in bulk at 400 K for 20 min (equal to the holding time in the hot-stage electron microscope observations) exhibit a very important size increase which occurs abruptly when the foil is subsequently cooled down to 100 K in the electron microscope.

4. DISCUSSION The above review of the available experimental results on the temperature dependence of SFE shows that in practically all of the f.c.c, systems that have been studied the SFE increases with temperature. The notable exceptions are pure silver and a Ag-Zn alloy for which the experimental results indicate negative but small values of dT/dT. In spite of the various factors which make a precise determination of the magnitude of dT/dT unrealistic, there do appear to be quite large differences in the temperature dependence of SFE from one system to another. The theoretical justification for this behaviour can be sought from considerations based on thermodynamics or electronic structure. 4.1. C o m p a r i s o n w i t h t h e r m o d y n a m i c

data

The simplest way to account for a temperature dependence of SFE is to consider a model of short range interactions of atomic structure according to which an infinite intrinsic stacking fault can be viewed as an h.c.p, platelet with a thickness of two closepacked planes. This procedure, which was applied by Ericsson [8] in his study of cobalt and Co-Ni alloys, leads to the following relation between the intrinsic SFE and the bulk free energy difference between h.c.p. and f.c.c, phases with the same composition:

~fce

_+ hcp

~/-3

8

1

a Z N 7i

(1)

where AF ecc -~ hop is the free energy change between the h.c.p, and the f.c.c, phases at constant composition, i.e. for the case of a martensitic transformation, a is the f.c.c. lattice parameter and N is Avogadro's number. From eqn. (1) it follows immediately that the temperature dependence of intrinsic SFE (i.e. the derivative dT/dT) is related to the entropy difference between both phases at constant composition by _d7 _ _

dT

8 a2N ~ f c c --~ hcp

(2)

V~-

This reasoning introduces a simple physical explanation of the existence of a temperature dependence of SFE and the model is qualitatively consistent with the fact that relatively high values of d7/dT have been unambiguously determined only in those alloy systems in which a f.c.c. -~ h.c.p, transformation occurs at a temperature in the range over which dT/dT was studied. The model is, however, clearly simplified in particular because it implies that the SFE is zero at the temperature To at which the phases are in thermodynamic equilibrium and this is definitely not the case for example in Co-Ni alloys or in certain iron-base alloys. Although in general To cannot be accurately determined experimentally in these alloys because the f.c.c. -~ h.c.p, transformation is martensitic and undercooling or plastic deformation are required to induce the phase change, a lower limit to the value of To can be obtained from a determination of the temperature E d below which the transformation can be induced by plastic deformation. In Co-Ni alloys To -~ E d [31] and ~/o -~ 15 mJ m - 2 [ 8 , 18] whilst in Fe-Cr-Ni alloys To > Ed and ~/o > 7d -~ 20 mJ m -2 [26 - 28]. However, Ruff and Ives [13] estimated the value of ~/o to be 1 mJ m -2 in a Ag-Sn alloy. Unfortunately no satisfactory improvement of this simple model has so far been proposed. Ericsson suggested that an additional term may arise from the interaction between neighbouring faults [8]. Recently Olson [32] tried to circumvent this difficulty using the phenomenological theory of martensite nucleation but this approach raises the question of

59 TABLE 3 Comparison between experimental and calculated values of d v / d T for transition metals and alloys Metals and alloys

Co C o - 3 2 at.% Ni C o - 3 5 at.% Ni C o - 6 at.% Fe C o - 8 at.% Fe F e - 1 7 at.% Cr14 at.% Ni F e - 1 9 at.% Cr13 at.% Ni F e - 1 9 at.% Cr12 at.% Ni F e - 2 0 at.% C r 15 at.% Ni F e - 2 0 at.% M n 4 at.% Cr (2 at.% C)

Calculated ~ksfCC --* hcp a (cal mo1-1

Measured ~ f c c --* hcp (cal mo1-1

K -1)

K -1)

--0.15 -0.20

--0.16

References

[33]

Calculated dT/dT (mJ m - 2

Measured dT/dT (mJ m - 2

References

K -1)

K -1)

0.04 0.05

[8] [24] [18]

-0.20 -0.22

0.05 0.05

0.03 0.04 0.05 0.04 0.04

--0.71 a

0.18

0.08

[26]

--0.69 a

0.17

0.06

[26]

--0.70 a

0.175

0.10

[11]

--0.66 a

0.165

0.05

[11]

--0.64 b

0.16

0.06 b

[14]

[24 ]

aThese values were calculated with AS = 0.15 cal mo1-1 K- 1 for pure chromium, --1 cal mo1-1 K -1 for pure iron (at 300 K) and --0.3 cal mo1-1 K -1 for pure nickel. bThe quoted values are valid for T ~- 300 K. TABLE 4 Comparison between experimental and calculated values of d'~/dT for noble metals and alloys

Metals and alloys

Ag Ag-7.5 at.% In A g - l 1 . 5 at.% In A g - 9 at.% Sn Cu- 15 at.% A1 C u - 3 0 at.% Zn

Calculated a

Measured

Calculated

Measured

~tsfcc "-*hcp (cal mo1-1

~ksfcc -* hcp (cal mo1-1

d'y/dT (mJ m - 2

dT/dT (mJ m - 2

K -1)

K -1)

K -1)

K -1)

--0.3 ---0.25 --0.22 --0.19 --0.33

References

0.057 0.045 --0.03

[34]

0.006 0.045 0.08

--0.013 (?) 0.015 0.008 0.02 0.015

References

[2] [20] [13] [12, 2] [2]

aThese values were calculated with AS = +0.43 cal mo1-1 K -1 for aluminium and indium, --0.3 cal mo1-1 K -1 for copper and --0.4 cal tool -1 K -1 for zinc.

the validity of the concept of surface energy for a defect of one atomic layer in thickness. Nevertheless eqn. (2) should give a first order estimate of the temperature derivative of SFE from the entropy difference associated with a f.c.c. -~ h.c.p, transformation. Unfortunately experimental data for ~ c c -: hop are available only for pure cobalt [33] and A g - 1 0 at.% Sn alloy [ 3 4 ] . In both cases the estimated derivative o f the intrinsic SFE is in good agreement with the SFE measurements as shown in Tables 3 and 4.

We.have estimated ~ c c -* hop for the other alloys mentioned in this review b y using thermodynamic solid solution models. In the regular solution approximation [34, 35] the entropy difference associated with the f.c.c. -~ h.c.p, transformation for an alloy at constant composition can be related to that for pure components (A Si ) by ~ f c c -0 hcp = ~,Xi ~k~ifcc ~ hcp

(3)

where xi is the atomic fraction of element i.

60 Estimates of the e n t r o p y difference /~Si were made b y Kaufman and Bernstein [36] for elements of groups IVA - VIII using the lattice stability concept. In this model the entropy difference is unique for a group number and independent of temperature above 300 K. The model cannot be applied to iron and manganese since magnetic contributions are n o t taken into account. For these elements the free energy change associated with the f.c.c. -~ h.c.p, transformation was estimated using the classical decomposition of specific heat into lattice, electronic and magnetic contributions proposed by Weiss and Tauer [ 3 7 ] . The free energy change was determined for iron in the temperature range 0 - 1800 K from data on F e - R u alloys [38, 3 9 ] . For manganese this free energy change was calculated b y Breedis and Kaufman using Weiss and Tauer's data from 300 to 1600 K [40] ; the data were extended to lower temperatures by R~my [14, 18]. The entropy differences calculated for various cobalt-base and iron-base alloys are given in Table 3. The corresponding derivatives dT/dT calculated from eqn. (3) are compared with the values measured at room temperature in this table. For cobalt-base alloys both sets of values are in good agreement. For iron-base alloys the agreement is n o t very satisfactory, the experimental values being only from one-third to one-half of the calculated ones. Nevertheless for all these alloys the observed values of dT/dT are in the same order as that of the calculated values. The AS i values given by Kaufman and Bernstein for elements of groups IB - IIIB (i.e. for noble and some normal elements) are less reliable since the lattice stability concept is less justified [ 4 1 ] . Therefore the calculated values of dT/dT given in Table 4 must only be considered as giving an order of magnitude. According to these estimates a positive temperature dependence should exist in pure silver and in various copper and silver alloys. Although the magnitude of the calculated values is considerably higher than that of the experimental values, an experimental verification of the reported decrease in SFE with increasing temperature in the case of silver appears to be necessary. The good agreementbetween the calculated value of dT/dT (based on an experimental determination of AS~CC-* hcp [34] ) and the careful experimental

determinations of dT/dT b y R u f f and Ives [ 13] is, however, encouraging.

4.2. Comparison with computations from electron theory Theoretical derivations of SFE based on the electronic structure have been obtained for pure normal metals b y Blandin et al. [42] and Nourtier [17] and for transition metals b y Ducastelle and Cyrot-Lackman [43]. Blandin's theory was recently extended to account for the case of noble metals [44, 4 5 ] . These computations of SFE are very attractive b u t a major difficulty with the electron theory is to account for alloying and temperature effects (see e.g. ref. 46). However, it is interesting to consider the conclusions of this theory in the case of transition metals for which the experimental measurements of dT/dT seem to be fairly well established. Using a tight-binding scheme Ducastelle and Cyrot-Lackman [43] have approximated the density of states to its four first moments. Accordingly the extrinsic and intrinsic SFE are identical and both are proportional to the energy difference 8Ec between the f.c.c, and h.c.p, phases: 5Ec = E ( f . c . c . ) - E(h.c.p.). This energy difference SEe is positive but small near the edges of the d band and it has a negative minimum in the middle of this band. This energy difference has two zeros near Z ~ 3 and Z ~ 7 and is symmetrical with respect to the middle of the band. This behaviour is in qualitative agreement with enthalpy and free energy differences between the f.c.c, and h.c.p, phases estimated at 300 K by Kaufman and Bernstein [36] for 4d and 5d elements. However, the energy minimum seems in fact to be shifted towards the b o t t o m of the d band. Further improvement of this theory is to be expected from the consideration of higher order moments of the density of states. In particular Ducastelle and Cyrot-Lackman [43] showed that the difference between the extrinsic SFE 7e and the intrinsic SFE 7i is in fact an oscillating function of the number of d electrons with at least four zeros. This prediction is borne o u t b y Tisone's experiments on C o - F e and C o - 3 2 at.% Ni alloys [ 2 4 ] . In the latter case the 7J7i ratio decreased below unity near 100 K while in the former case it is smaller than unity (about 0.5 - 0.7) over the whole temperature range

61

studied. It is worth connecting this result with the recent identification of a double h.c.p. phase in low alloyed C o - F e crystals [47] since in models of short range interactions an extrinsic fault can be viewed as a double h.c.p, phase nucleus. In the same way if higher order moments were taken into account, the SFE should be no longer simply proportional to the energy difference between the h.c.p, and the f.c.c. phases. This might provide a physical interpretation of the non-zero value ~/0 of SFE at the phase equilibrium temperature To. This is of interest since this quantity is fairly high, in the range 10 - 25 mJ m -2 in transition alloys [8, 18, 26] while it seems to be negligible in noble alloys, namely a few millijoules per square metre [ 13]. This model predicts an influence of ferromagnetism upon SFE due to the splitting of the d band into t w o spin ~ and spin ~ subbands. It was shown that the SFE of pure cobalt must increase drastically as it changes from ferromagnetic to paramagnetic. Therefore a high positive temperature dependence of SFE is expected in the vicinity of the Curie temperature. The only measurements of SFE near this temperature are those made by R~my [18] on C o - N i - C r alloys but it was n o t possible to test the validity of the theoretical prediction because of the effects of solute pinning of the dislocations. On the other hand a strong increase of the temperature dependence of SFE was recently observed near the antiferromagnetic-paramagnetic transition of a high manganese steel [ 1 4 ] , b u t the influence of antiferromagnetism on SFE is unfortunately still b e y o n d the present possibilities of the electron theory [ 4 8 ] . Nevertheless using the classical decomposition of specific heat due to Weiss and Tauer [37] and eqn. (2), the increase in d~//dT was shown to arise for the most part from the magnetic contribution [ 1 4 ] . In the case of noble and normal metals Tisone t o o k into account the influence of temperature in a phenomenological way through the relaxation time of conduction electrons [42] and a significant negative value of d'~/dT was predicted for pure normal metals. Comparison with Kaufman and Bernstein's data shows good agreement in the case of pure aluminium but this prediction is at variance for pure zinc (see the f o o t n o t e to

Table 4). For pure noble metals and their dilute alloys, the contribution of free electrons is much smaller than that of d electrons and the SFE is hence expected to be quite temperature insensitive. This is at variance with Kaufman's data b u t is supported by Gallagher's SFE measurements on pure silver and low alloyed A g - Z n alloys [2]. In contrast, in concentrated noble metal alloys (Z > 1.14) a significant increase of SFE with temperature should be observed. A large effect is expected for trivalent solutes such as indium or aluminium while a smaller one is predicted for two-valence and four-valence solutes such as tin, germanium, silicon and zinc. As a matter of fact Ag-In alloys and C u - 1 5 at.% A1 alloys seem to exhibit a temperature dependence of SFE. However, a smaller temperature dependence was clearly observed in Ag-Sn alloys in agreement with Tisone's prediction [13]. Further observations on C u - G e and Cu-Si alloys seem to indicate a small variation of SFE with temperature [2].

5. C O N C L U S I O N S

In spite of the experimental difficulties useful information concerning the temperature dependence of the SFEs can be obtained by careful measurements of the size variation of stacking fault configurations in thin foils on a heating or a cooling stage in the electron microscope. In order to assess the perturbing effects of lattice friction forces, partial dislocation pinning or Suzuki segregation it is desirable to cycle the specimen several times over the experimental temperature range. (1) In pure cobalt and a number of transition metal alloys (Co-Ni, C o - F e , F e - C r - N i , F e - M n - C r ) a strong increase in SFE with temperature has been unambiguously demonstrated even though in some cases the observed changes in node size are partly or wholly irreversible. In the case of silver-base and copper-base alloys the experimental data are often contradictory and, except in the case of a A g - 9 at.% Sn alloy which shows a small reversible increase in SFE with temperature, the quantitative estimation of d 7 / d T is less reliable. In pure silver and A g - Z n alloys the SFE appears to decrease slightly with increasing temperature whilst in the copper-base

62 alloys dT/dT is positive, the magnitude of the temperature dependence decreasing in the order Cu-16 at.% AI, C u - 3 0 at.% Zn, Cu-6.8 at.% Ge and Cu-8.6 at.% Si. (2) The temperature dependence of intrinsic SFE can be related to the stability of the f.c.c, phase with respect to the f.c.c. -~ h.c.p, martensitic transformation. In this approximation the temperature derivative of intrinsic SFE is proportional to the entropy difference associated with this transformation. Good agreement was found for Ag10 at.% Sn alloy and pure cobalt for which entropy measurements were available. Fairly good agreement (within a factor of 2 or 3) was found for transition alloys using estimated data based on the lattice stability concept. For alloys of noble metals with normal solute elements no reliable lattice stability data are available. In this case qualitative agreement is found with theoretical computations based on electron theory. Tisone's phenomenological treatment of the influence of temperature predicts no significant temperature dependence in pure noble metals and in dilute alloys (Z < 1.14). A larger positive temperature dependence of SFE is predicted in concentrated alloys with three-valence solutes (e.g. Cu-A1 and Ag-In alloys) than with two-valence or four-valence solutes, all features which are in agreement with experimental results. It would seem worthwhile to carry out further experiments on silver and certain silver-base and copperbase alloys is order to put the experimental data on a firmer basis for comparison with theoretical calculations (in particular to verify the small decrease in SFE with temperature in silver and A g - Z n alloys). (3) The need is felt for (a) new experimental studies on alloy systems in which solute impedance forces are expected to be low (i.e. systems in which the size o f the solute atoms is close to that of the solvent) and (b) further development of electron theory calculations to account for alloying and temperature effects at least in transition metal alloys where numerous and rather well established experimental data are now available. ACKNOWLEDGMENTS T h e authors express their thanks to Professor F. Gauthier a n d Dr. F. DucasteUe

for helpful discussions and to Professors J. Friedel, J. Phflibert and G. Saada for their comments on the manuscript. REFERENCES 1 J. W. Christian and P. R. Swann, in Massalsky (ed.), Alloying Behavior and Effects in Concentrated Solid Solutions, Gordon and Breach, N e w York, 1965, p. 105. 2 P. C. J. Gallagher, Metall. Trans., 1 (1970) 2429. 3 A. W. Ruff, Jr., Metall. Trans., 1 (1970) 2391. 4 R. P. I. Adler, H. M. Otte and C. N. J. Wagner, Metall. Trans., 1 (1970) 2375. 5 R. Smallman and P. Dobson, Metall. Trans., 1 (1970) 2383. 6 M. Ahlers, Metall. Trans., 1 (1970) 2415. 7 Syrup. on the Dissociation of Dislocations, Beaune (France), J. Phys. (Paris),35 (1974) C7. 8 T. Ericsson, Acta Metall., 14 (1966) 853. 9 L. M. Brown, Philos. Mag., 10 (1964) 441. 10 D. H. J. Cockayne, I. L. F. Ray and M. J. Whelan, Philos. Mag., 20 (1969) 1265. 11 R. M. Latanision and A. W. Ruff, Metall. Trans.,

2 (1971) 505. 12 T. C. Tisone, J. O. Brittain and M. Meshii, Phys. Status Solidi, 27 (1968) 185. 13 A. W. Ruff and L. K. Ives, Phys. Status Solidi A, 16 (1973) 133. 14 L. R~my, Acta Metall., 25 (1977) 173. 15 J. P. Hirth, Metall. Trans., 1 (1970) 2367. 16 T. Ericsson, Acta Metall., 14 (1966) 1073. 17 C. Nourtier, Acta Metall., 20 (1972) 415. 18 L. R~my, Thesis, Orsay, 1975. 19 H. Saka, T. Iwata and T. Imura, Philos. Mag., 37 (1978) 291. 20 P. C. J. Gallagher and J. Washburn, Philos. Mag., 14 (1966) 971. 21 M. De and S. P. Sen Gupta, Scr. Metall., 8 (1974) 1373. 22 S. Matsuo and L. M. Clarebrough, Acta Metall.,

11 (1963) 1195. 23 H. Saka, Y. Sueki and T. Imura, Philos Mag., 37 (1978) 273. 24 T. C. Tisone, Acta Metall., 21 (1973) 229. 25 L. Kaufman and H. Nesor, Z. Metallkd., 64 (1973) 249. 26 F. Lecroisey and B. Thomas, Phys. Status Solidi A, 2 (1970) K217. 27 F. Lecroisey and A. Pineau, Metall. Trans., 3 (1972) 387. 28 F. Abrassart, Metall. Trans., 4 (1973) 2205. 29 B. Thomas and F. Lecroisey, unpublished results, 1971. 30 J. Echigoya, Phys. Status Solidi A, 17 (1973)677 31 J. B. Hess and C. J. Barrett, Trans. Am. Inst. Mech. Eng., 194 (1952) 645. 32 G. B. Olson and M. Cohen, Metall. Trans., 7A (1976) 1897. 33 R. L. Hultgren, R. L. Orr, P. D. Anderson and K. K. Kelley, Selected Values of Thermodynamic Properties of Metals and Alloys, Wiley, New York, 1963. 34 G. H. Laurie, A. W. H. Morris and J. N. Pratt, Trans. Am. Inst. Mech. Eng., 236 (1966) 1390.

63 35 L. Kaufman and M. Cohen, Prog. Met. Phys., 7 (1958) 165. 36 L. Kaufman and H. Bernstein, Computer Calculation of Phase Diagrams, Academic Press, New York, 1970. 37 R. J. Weiss and K. J. Tauer, J. Phys. Chem. Solids, 4 (1958) 135. 38 L. D. Blackburn, L. Kaufman and M. Cohen, Acta Metall., 13 (1965) 533. 39 G. Stepakoff and L. Kaufman, Acta Metall., 16 (1968) 13. 40 J. F. Breedis and L. Kaufman, Metall. Trans., 2 (1971) 2359. 41 K. F. Michaels, W. F. Lange, J. R. Bradley and H. I. Aaronson, Metall. Trans., A6 (1975) 1843.

42 A. Blandin, J. Friedel and G. Saada, J. Phys. (Paris), 27 (1966) 128. 43 F. DucasteUe and F. Cyrot-Lackman, J. Phys. Chem. Solids, 32 (1971) 285. 44 T. C. Tisone, R. C. Sundahl and G. Y. Chin, Metall. Trans., 1 (1970) 1561. 45 T. C. Tisone, Metall. Trans., 3 (1972) 427. 46 F. Gautier, Propridt~s Electroniques des M~taux et AUiages, Masson, Paris, 1973, p. 365. 47 T. Onozuka, S. Yamaguchi, M. Hirabayashi and T. Wakiyama, J. Phys. Soc. Jpn, 33 (1972) 857; 37 (1974) 687. 48 F. Ducastelle, personal communication, 1976. 49 M. W. Guinan and D. J. Steinberg, J. Phys. Chem. Solids, 35 (1974) 1501.