On the creep activation energies of alloys

Materials Science and Engineering, 86 (1987) 211-218

211

Correspondence

On the creep activation energies of alloys

SUN IG HONG Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia, PA 19104 (U.S.A.) (Received March 10, 1986; in revised form April 25, 1986)

predicted activation energies decrease and become smaller than those of diffusion in the high stress region where the stress exponent becomes larger (see ref. 1, Fig. 2). A careful examination, however, shows that this model is not incompatible with the established results. Furthermore, the validity of activation energies which have been reported for solid solution alloys and particle-hardened alloys is called into question as a result of this study.

ABSTRACT

2. ANALYSIS

It is demonstrated that the creep activation energies predicted from the model recently developed by the present author are not incompatible with those reported for alloys. This model tells us that the creep activation energies may be dependent on the temperature intervals used for the measurement o f activation energies; it predicts normal activation energies which are equal to those for selfdiffusion in the so-called class I creep region and predicts very high activation energies in the region o f high stress e x p o n e n t as in particlehardened alloys if temperature changes much larger than 1 OK (20-100 K ) a r e used. However, the predicted activation energies, when temperature changes smaller than 10 K are used, contrast sharply with the established activation energies.

It is at present generally believed that the activation energies for creep are identical with those of diffusion in solid solution alloys [2- 5]. However, in some solid solution alloys, anomalies in creep activation energies have been reported [ 6-12]. The anomalies in activation energies may have caused some discomfort to some experimentalists and these difficulties have generally not been emphasized [13]. Earlier, in 1960, Weertman [2] expressed his concern a b o u t the validity of creep activation energies in some alloys. As he pointed out, in an alloy where order may be changing with temperature, difficulty in determining the activation energies can be expected. If creep is controlled by any one of a number of ordering processes, the temperature dependence of ordering must be considered [2]. Some of the anomalies in activation energies have been related to some form of dynamic strain aging [6, 11, 14]. However, the differences between the observed activation energies and those for diffusion have generally been explained in terms of the temperature dependence of the elastic modulus [ 8, 9] or recrystallization during creep [10]. As stated in Section 1, the recent creep model [ 1 ] predicts anomalies in creep activation energies. However, if the activation energies are determined using the usual formula relating el, e2, T1 and T e (where T1 -- Te ~ 30 K) after the strain rates ~1 and e2 had been calculated at T1 and T2, the activation energies predicted by this model

1. INTRODUCTION Recently an attempt [ 1 ] to explain the creep behavior of solid solution alloys in terms of dynamic strain aging was made by the present author. During the reviewing process of that paper, one of the referees pointed o u t that the predicted activation energies from the model developed by the present author contrast sharply with those established until now. As pointed o u t by the referee, this model predicts large activation energies in the region where the so-called class I creep occurs. The 0025-5416/87/$3.50

© Elsevier Sequoia/Printed in The Netherlands

212

in the temperature range where the so-called class I creep occurs are equal to those for diffusion. This model, therefore, indicates that the experimentally determined activation energies can be a function of temperature interval used for the measurement of activation energies. Temperature changes of the order of 2 0 - 5 0 K have generally been used for the measurement of activation energies. Many experimentalists may have preferred large temperature changes because of concern a b o u t the accuracy of measuring temperature during creep. It is also possible that the anomalies in activation energies, which may be observed when a small temperature interval is used, may lead some experimentalists to use large temperature changes. The following creep equation was suggested f o r A1-Mg alloys at 600 K by the present author [1, 14] : = 3.57 × 10-12(aapp --OD)4"76C-0"96

--

1"09 ×102° ~R-~) TGT3.76 ((~app--aD)4"76C-0"96exp ' Q*

(3) Here, D60o and DT are the diffusivities at 600 K and the test temperature respectively, G600 and G T a r e the shear moduli [15] at 600 K and the test temperature respectively, and Q* (= 143.4 kJ mo1-1) is the activation energy for lattice self-diffusion of pure aluminum [1618]. If aD is negligible, the creep activation energies are equal to those for self-diffusion. However, for alloys, the creep activation energies become significantly different from those representing diffusion as a consequence of the temperature dependence of OD. The creep activation energies can be calculated b y differentiating the creep rate equation with respect to l/T: Qapp = Q* +

(1) 1.97 × I O a n R C T 2 ( T -

Here, Oapp is the applied stress, C is the mole fraction of magnesium and OD is the strengthening term due to dynamic strain aging which can be expressed as follows: OD = O° exp

B

T)exp{--(T-

T)2/B}

B (a~p -- aD) (4) where n (= 4.76) is the stress exponent. Reference 1, eqn. (11), is substituted into eqn. (3) to give qapp = q * +

where o ° is the maximum value of OD, T is the temperature at which this maximum occurs and B measures the width of the distribution about T. As explained in the previous paper [ 1], the frictional stress due to dynamic strain aging has its maximum p o t e n c y at some intermediate temperature. Since OD dies o u t at high and low temperatures, the frictional stress due to dynamic strain aging can be approximately represented by eqn. (2) irrespective of the detailed mechanisms of dynamic strain aging. However, discussion on the responsible dynamic-strain-aging mechanisms of AI-Mg alloys is given in Appendix A. Also the validity of the dynamic-strain-aging model of this study is examined in Appendix A. If the change in elastic modulus (G (MPa) -3.022 × 104 -- 16T) and the diffusivity with temperature are incorporated in eqn. (1), we can obtain the following equation: 2.14 × IO-9DTGsoo 3"7s e =

TDsooGT3.76

(aapp-- gO)4"76C-0'96

7 . 7 8 n R C °'s T 2 ( T -- T ) exp {-- (T -- I')2/B}

BdO.21

(5)

The activation energies predicted when the parameters given above were inserted in eqn. (5) are plotted in Fig. 1 against strain rate. Equation (5) cannot be applied to A1-Mg alloys with a high magnesium concentration (greater than 3-4 mol.% Mg at 600 K) because the effective magnesium concentration in the matrix decreases as the magnesium concentration increases above 3-4 mol.%. It should be noted that eqn. (5) predicts the activation energies determined with almost no change in temperatures. Practically, it is impossible to measure the activation energies without a temperature change. The maximum creep activation energy is predicted to be at a strain rate of 10 -4 s-1 and the minimum at 5 X 10 -3 s-1 at 600 K. Unfortunately, there are no data available to support these predictions. These values are offered here in the hope that some investigators have unpublished data which

213 STRESS,

;

2,14 300

,o

MPa

7,

, 7

10-I

',

,5°, 10- 2 Q

200 E

10-:

C

10"4

i I i

oi

10-8

I

lO-S i 10-7

i 10 - 6

l 10 "5 STRAIN

i 1(5 4 RATE,

I 10-3

i 1 0-2

S-~ 10- 6

Fig. 1. The strain rate dependence of creep activation energies predicted from eqn. (5) for Al-l.09mol.%Mg alloy.

10-7

may support this prediction. It is the present author's belief that Borch e t al. [6] could observe the anomaly in activation energies because they used temperature changes as small as 3 K below 450 K. Many investigators have measured activation energies using temperature changes of a b o u t 50 K or more than 50 K [15, 19, 20], and they could not observe the anomaly in activation energies. If the anomaly in activation energies observed at 325 K in A1-Mg alloys is due to dynamic strain aging as claimed by the present author [ 14], the temperature range in which this anomaly is observed increases if the strain rate is increased. The calculation of activation energies* using the creep data of Dushman e t al. [21] shows that large activation energies are observed at a b o u t 650 K when the strain rate is 2 X 10 .5 s-1 and at 550 K when the strain rate is a b o u t 4.5 X 10 .7 s-1. (Dushman e t al. used a temperature change of 10 K.) In spite of their relatively crude experimental equipment, the trend of their data is in good agreement with the present model. If we use temperature changes much larger than 10 K, the temperature interval where the anomaly occurs will decrease because the change in activation energies will be smoothed out. Furthermore, the deviation of activation energies from the normal values may be smoothed o u t or the temperature range where the anomaly occurs may be skipped over. *These calculations can be obtained from the present author on request.

~o~

10"8

1.5

1.6

1.7 1,"T x

1.8

1 0 ~ ( K -~)

Fig. 2. Temperature dependence of the steady state creep rates predicted from eqn. (3) for A11.09mol.%Mg alloy.

Symbol

Stress (MPa)

Q (kJ mo1-1)

o L

3 6 10 25 40

149 155 157 146 172

• •

To check the validity of the explanation given above, the creep rates at various temperatures are calculated from eqn. (3) and, using these creep rates, the activation energies are calculated. In Fig. 2, the creep rates of Al-l.09mol.%Mg alloy at a stress of 3, 6, 10, 25 and 40 MPa predicted from eqn. (2) are plotted against temperature ( 5 7 0 , 6 0 0 and 640 K). The predicted creep rate is in reasonably good agreement with the data of Oikawa e t al. [22]. As shown in Fig. 1, the predicted activation energies (150 kJ mo1-1) when the temperature change is much larger than 10 K are in good agreement with those reported for A1-Mg alloys [3, 4, 17-20, 23]. The activation energies for A1-3mol.%Mg alloy predicted by the same method as above are also in good

214 agreement with those for self-diffusion [24]. The reason why Oikawa e t al. [22] obtained large activation energies (170 kJ mo1-1) in region L (where the applied stress is smaller than 5; for the definition of region L, see ref. 22) is not clear. This model tells us that the magnitude of measured activation energies is dependent on the temperature intervals used for the measurement of activation energies. In the region where the stress exponent is about 3 (so-called class I creep occurs), the creep stress Oc consists of two separable parts: the stress aB due to dislocation motion in the lattice in the absence of dynamic strain aging and the stress OD due to dynamic strain aging (see ref. 1, Fig. 2). If the temperature change is small, the effect of OD on the creep rate is significant because dynamic strain aging changes rapidly with temperature; this results in a high activation energy. However, if the temperature change is large in this region, the effect of aD on the activation energies is masked by the large change in aB; this results in normal activation energies (which are equal to those for diffusion). Another point to be noted is the magnitude of the activation energies predicted in the high stress region where the high stress exponent is observed. Actually, Hong attempted to explain the anomalously high stress exponent observed in particle-hardened alloys in terms of dynamic strain aging (for details see ref. 1). The present model predicts the high stress exponents in the high stress region as shown in ref. 1, Fig. 2. Depending on the diffusivity of solutes responsible for dynamic strain aging, the strain rate region where the high stress exponent is observed would shift to lower or higher values. Therefore, the stress region of high stress exponent varies with the alloy. As shown in Fig. 2, this model predicts very low activation energies in the region of high stress exponent (where the applied stress is about 40 MPa). As aD increases with solute concentration, the activation energies predicted from eqn. (5) in this region become even smaller than these. However, interestingly enough, the activation energies calculated using the creep rate predicted at 570,600 and 640 K from eqn. (3) for Al-l.09mol.%Mg (172 kJ mo1-1) are larger than those of diffusion (143.4 kJ mol-1). The activation energies calculated by the same method for A1-3.2mol.%Mg (310 kJ mo1-1) are

much larger than those for diffusion whereas the activation energies predicted from eqn. (5) in this region are as low as Q = 0 [24]. To the knowledge of the present author, no data on the creep activation energies have been reported in this region for solid solution alloys. If aD is larger for some particle-hardened alloys, the activation energies calculated using the creep rates predicted from eqn. (3) become larger if the temperature difference is much larger than 10 K. This model predicts very high activation energies in this region if the temperature change is much larger than 10 K and predicts very low activation energies if the temperature change is smaller than 10 K. The reason for the singularity of activation energies in this region is given schematically in Fig. 3. As explained, the creep stress a c consists of two separable parts. The stress aD due to dynamic strain aging moves towards a higher strain rate with increasing temperature because solute diffusivity increases with temperature [1]. In Fig. 3, if the temperature change is relatively small, the change in creep rate with temperature change is smaller than that expected in the absence of dynamic strain aging; this results in lower activation energies than those for diffusion. If the temperature change is much larger than 10 K, the change in creep rates with temperature change is much larger than that expected in the absence of dynamic strain aging; this results in large activation energies. Because, in most cases, the activation energies for creep of particlehardened alloys (which is much larger than those for diffusion) were measured using a temperature change larger than 30 K [25-28], the predictions of this model are not incompatible with the reported activation energies.

3. CONCLUSIONS The main purpose of this study is to demonstrate that the activation energies predicted from the model developed in the previous paper [ 1 ] are not incompatible with those reported for solid solution alloys and particlehardened alloys. However, the validity of creep activation energies which have been reported for alloys are called into question as a result of this study. The measured activation energies may be dependent on the temperature interval used for the measurement. Although some

215 ACKNOWLEDGMENTS

The author would like to express his gratitude to all three referees of his previous paper [1] whose remarks inspired him to clarify a number of statements and to undertake this study.

°t S

'

o~,3"

/~. ~.+ o~•

/

o~ (o)

lnO"

',

i

_c

(h)

InC~

Fig. 3. Schematic plot of the stress dependence of the steady state creep rates: (a) the change in creep rates at a a is smaller than that expected in the absence of dynamic strain aging for a small temperature change, which results in smaller activation energies than those for diffusion, (b) the change in creep rates at o a is larger than that expected in the absence of dynamic strain aging for a large temperature change, which results in larger activation energies than those for diffusion.

investigators have reported anomalies in activation energies in some alloys, the predictions of this study could not be verified because no proper data are available. If the claim made here is true, the current creep theories on alloys must undergo modification. In either case, more systematic experimental work is required.

REFERENCES 1 S. I. Hong, Mater. Sci. Eng., (1986). 2 J. Weertman, Trans. AIME, 218 (1960) 207. 3 F. A. Mohamed and T. G. Langdon, Acta Metall., 22 (1974) 779. 4 K. L. Murty, Scr. Metall., 7 (1973) 899. 5 O. D. Sherby and P. M. Burke, Prog. Mater. Sci., 13 (1967) 324. 6 N. R. Borch, L. A. Shepard and J. E. Dorn, Trans. Am. Soc. Met., 52 (1960) 494. 7 A. Lawley, J. A. Coll and R. W. Cahn, Trans. AIME, 218 (1960) 266. 8 W. R. Johnson, C. R. Barrett and W. D. Nix, Metall. Trans., 3 (1972) 963. 9 S. I. Hong, I. S. Choi and S. W. Nam, J. Mater. Sci., 19 (1984) 1672. 10 R. G. Stang, W. D. Nix and C. R. Barrett, Metall. Trans., 4 (1973) 1695. 11 R. D. Warda, V. Fidleris and E. Teghtsoonian, Metall. Trans., 4 (1973) 1201. 12 V. A. Pavlov, M. G. Gaidukov and V. V. Mel'nikova, Fiz. Met. Metalloved., 12 (1961) 748. 13 J. P. Poirier, Acta Metall., 26 (1978) 629. 14 S. I. Hong, Scr. Metall., 18 (1984) 1351. 15 P. Yavari and T. G. Langdon, Acta Metall., 30 (1982) 2181. 16 T. S. Lundy and J. F. Murdock, J. Appl. Phys., 33 (1962) 1671. 17 M. Beyeler and Y. Adda, J. Phys. (Paris), 29 (1968) 345. 18 F. A. Mohamed and T. G. Langdon, Metall. Trans. 5 (1974) 2339. 19 R. Horiuchi and M. Otsuku, Trans. Jpn. Inst. Met., 13 (1972) 284. 20 K. L. Murty, F. A. Mohamed and J. E. Dorn, Acta MetaU., 20 (1972) 1009. 21 S. Dushman, L. W. Dunbar and H. Huthsteiner, J. Appl. Phys., 15 (1944) 108. 22 H. Oikawa, H. Sato and K. Maruyama, Mater. Sci. Eng., 75 (1985) 21. 23 H. Oikawa, J. Kariya and S. Karashima, Met. Sc£ J., 8 (1974) 106. 24 S. I. Hong, University of Pennsylvania, unpublished research, 1985. 25 J. H. Hausselt and W. D. Nix, Acta Metall., 25 (1977) 1491. 26 R. W. Lund and W. D. Nix, Metall. Trans. A, 6 (1975) 1329. 27 B. A. Wilcox and A. H. Clauer, Trans. AIME, 236 (1966) 570. 28 R. W. Cahn, Physical Metallurgy, North-Holland, Amsterdam, 1971.

216 APPENDIX A

The possible dislocation-solute interaction mechanisms which can affect the glide motion of dislocations are [A1] as follows: (1) the elastic interaction between solute atoms and dislocations (the Cottrell mechanism); (2) the chemical interaction between solute atoms and partial dislocations connected by stacking faults (the Suzuki mechanism); (3) the stressinduced order of solute atoms around dislocations (the Schoeck-Snoek mechanism); (4) the destruction of short-range order or clustering (the Fisher mechanism); (5) the creation of an antiphase boundary in the long-range ordered structure. The Suzuki mechanism can be eliminated as the dislocation-solute interaction mechanism responsible since the stacking fault energy of A1-Mg alloy is very high and no dissociated dislocations are observed in this alloy. Long-range order and stress-induced order have not been observed in this alloy. Also the frictional stress due to the Fisher mechanism does not seem to be strain rate dependent. Therefore the Cottrell mechanism appears to be the most likely mechanism for dislocation-solute interaction in A1-Mg alloys. The conclusion drawn here is consistent with previous results [A2-A5]. Cottrell and Jaswon [A6] showed that the stress increase due to dragging of solute atoms increases almost proportionally to the dislocation velocity when the velocity is sufficiently low relative to the diffusivity of solute atoms. However, in the temperature and strain rate ranges where the diffusion rate of solute atoms is comparable with the dislocation velocity, the atmosphere which can follow the dislocation motion will be reduced in size and concentration with increasing velocity of dislocations, and then the dragging stress will decrease also [A7-A9]. Recently, Takeuchi and Argon [A9] simulated the steady viscous motion of a straight edge dislocation surrounded by a Cottrell atmosphere and calculated the drag force using a computer. They found that the critical velocity vc at which the Cottrell atmosphere produces a maximum drag force F (= a ° b ) is approximately D k T/A with F being of the order o f A C / Y L Here, D (= 1.24 × 10 -4 e x p ( - - 1 3 0 / R T ) ) [A10] is the diffusion coefficient of the solute atom in the solvent, k is the Boltzmann constant, T is the absolute temperature, C is

the solute concentration, ~2 is the atomic volume, A is the interaction parameter between the dislocation and the solute atoms due to a size misfit which is expressed by l+v A -

~(1 - v )

(A1)

Vb~e

where v is Poisson's ratio, G the shear modulus, b the Burgers vector and e the size misfit parameter. The drag force versus dislocation velocity relations predicted by the computer simulation are shown in Fig. A1. In this figure, a is the lattice constant, l is the length unit which is defined as A / k T and v is the dislocation velocity. As shown in Fig. A1, then the edge dislocations move relatively slowly in comparison with the solute diffusion (v ~ vc ), aD increases with increase in velocity and, at high velocities where solute diffusion cannot follow the dislocation motion effectively, aD decreases with increase in velocity. As I/a is about 2.7 for A1-Mg alloys (see ref. A9, Table I), aD versus v relations are approximately symmetrical a b o u t the critical velocity vc and, therefore, can be conveniently modelled by a symmetrical distribution function [ A l l ] . According to the results of Takeuchi and Argon [A9], a ° can be calculated from the following equation: F = o°b

l+v

- eL

(A2)

GbeC

~'(1 - - v)

10 2

101 .1

1 0"4

1 0.2

1 v,

10 2

10 4

D/9.

Fig. A1. Relation between the drag force and the glide velocity (results o f Takeuchi and A r g o n [ A 9 ] ) : curve a, I/a = 0.5; curve b, I/a = 1; curve c, l/a = 2.

217 For A1-3.25mol.%Mg alloys, v = 0.34 [ 1 1 2 ] , b = 2.863 X 10-1° m, e = 0.12 [A13], C = 0.0325, G = 20 620 MPa at 600 K and ~ is a correlation factor which is between 0.1 and 1 depending on the size misfit parameter. To make o°u -- 32 MPa as suggested by Hong [111], ~ is determined to be 0.62 for A1-Mg alloys. According to eqn. (A2), O0D increases with decrease in temperature because the shear modulus increases with decrease in temperature. This prediction is unreasonable because dynamic strain aging does not occur at sufficiently low temperatures to immobilize the solute atoms. Therefore, eqn. (A2) may not hold in the low temperature regions where o ° may decrease with temperature. The deviation of the drag force predicted by Takeuchi and Argon [A9] from the drag force for a real crystal may arise from [18, A9] (1) the nonlinear elastic interaction of the solute atoms with a dislocation near the dislocation core, (2) a concentration-dependent diffusion coefficient, (3) the variance in the atomistic structure of the dislocation core and (4) the anisotropic local arrangement of solute atoms. In this study, OOD was assumed to be independent of temperature because the variation in a ° in the temperature range of this study seems to be very small (O0D predicted from eqn. (A2) is 32.7 MPa at 570 K, 32 MPa at 600 K and 31MPa at 640 K). The critical dislocation velocity vc at which the atmosphere produces a m a x i m u m drag force is given approximately by the following equation [19] : ~(1 -- v) kTD Vc

(1 + v) Gb~te = ~ exp(--~)

(13)

where Q (= 130 kJ mo1-1) [A12] is the activation energy for diffusion of magnesium atoms in aluminum and ~ = n(1 -- v) k T D o / (1 + v) Gb~te (= 1.824 X l 0 s m s-1 at 600 K). From the above equation, we can calculate the critical strain rate at which the maximum drag force aOD occurs as follows: ~c = pbvc

= pb~ e x p ( - - R ~ )

(A4)

where p is the dislocation density. From eqn. (A4) and ref. 1, eqn. (3), we can obtain the following equation: A = pb(J

(A5)

A was determined to be 2.25 X l 0 s for the best fit between the calculation of Hong [ A l l ] and the data of Oikawa et al. [ 1 1 4 ] . From eqn. (A5), the dislocation density is calculated to be 4.31 X 1 0 1 2 m -2, a value which is in good agreement with the experimental result of Horiuchi and Otsuku [A15]. Here, is a function of temperature as shown in eqn. (13) whereas A was considered to be independent of temperature. The constancy of A has been confirmed experimentally by some investigators [A16-A18]. This discrepancy may be due to the temperature dependence of dislocation density. The increase in with temperature may be compensated for by the decrease in dislocation density. Finally the strain rate dependence of the drag force o-D predicted using the computer simulation results of Takeuchi and Argon and eqn. (A4) is in good agreement with that predicted by eqn. (2). The dynamic-strain-aging model of the previous study [ A l l ] and this study is generally in good agreement with the computer simulation results of Takeuchi and Argon [A9]. As suggested by Hong [ A l l ] , the temperature and strain rate dependences of drag stress OD can be obtained by the subtraction m e t h o d (see ref. A17, Fig. 1). o ° and B obtained by the subtraction m e t h o d from the flow stress versus temperature plot (ref. A3, Fig. 4) were 36 MPa and 1.8 X 104 K 2 respectively for A13.23mol.%Mg alloy. These values are a little larger than those (o ° = 32 MPa; B = 4 X 103 K 2) used in this study. These differences may be due to the difference in grain size. The deformation structure in the vicinity of grain boundaries is different from that within the grains because of the geometrically necessary dislocations [A19]. The dislocation velocities are apparently affected by the presence of grain boundaries and the drag force will be changed. The dislocation density affected by the grain boundaries may be inversely proportional to the grain size and this may explain the effect of grain size on the drag force due to dynamic strain aging. No detailed mechanisms for this are available at the moment.

218

References for A p p e n d i x A A1 J. Weetman and J. R. Weertman, Elementary Dislocation Theory, Macmillan, New York, 1967. A2 F. A. Mohamed and T. G. Langdon, Acta Metall., 22 (1974) 779. A3 N. R. Borch, L. A. Shepard and J. E. Dirn, Trans. Am. Soc. Met., 52 (1966) 494. A4 A. H. Cottrell, Philos. Mag., 44 (1953) 829. A5 F. A. Mohamed, Mater. Sci. Eng., 38 (1979) 73. A6 A. H. Cottrell and M. A. Jaswon, Proc. R. Soc. London, Ser. A, 109 (1949) 104. A7 A. H. Cottrell, Dislocation and Plastic Flow in Crystals, Oxford University Press, Oxford, 1953. A8 J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968. A9 S. Takeuchi and A. S. Argon, Philos. Mag., 40 (1979) 65. A10 S. J. Rothman, N. L. Peterson, L. J. Nowicki

All A12

A13 A14 A15 A16 A17 A18 A19

and L. C. Robinson, Phys. Status Solidi B, 63 (1974) K29. S. I. Hong, Mater. Sci. Eng. (1986). ASM Committee on Aluminum and Aluminum Alloys, Metals Handbook, Vol. 2, Nonferrous Alloys and Pure Metals, American Society for Metals, Metals Park, OH, 1979. F. A. Mohamed, Metall. Trans. A, 9 (1978) 1342. H. Oikawa, K. Honda and S. Ito, Mater. Sci. Eng., 64 (1984) 237. R. Horiuchi and M. Otsuku, Trans. Jpn. Inst. Met., 13 (1972) 284. M. Doner and H. Conrad, Metall. Trans., 4 (1973) 2809. S. I. Hong, Mater. Sci. Eng., 76 (1985) 77. S. I. Hong, W. S. Ryu and C. S. Rim, J. Nucl. Mater., 116 (1983) 314. N. Hansen, Metall. Trans. A, 16 (1985) 2167.