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The effect of volume fraction on the coarsening behavior of γ′ in Co-Ni-Cr-Ti Alloys
METALLOGRAPHY 8, 329-336 (1975)
329
The Effect of Volume Fraction on the Coarsening Behavior of ~' in Co-Ni-Cr-Ti Alloys
D. W.
CHUNG
AND
M.
C. CHATURVEDI
Metallurgical Science Laboratory, Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Three alloys from the Co-Ni-Cr-Ti System, with different Ti Contents, were investigated. The main precipitating phase was observed to be ~' with an ordered fcc Structure. The growth of ~', with different volume fractions, in the three alloys, followed the Lifshitz-Wagner theory of diffusion controlled coarsening and not the Modified Lifshitz-Wagner theory, which takes into consideration the volume fraction of the growing phase.
Introduction The growth of precipitate particles in m a n y two phase systems has been observed to follow the Lifshitz-Wagner (LSW) theory of diffusion controlled coarsening. According to this theory the kinetic equation for growth is: ~3_
~o3 = K t
(1)
where, ~ is the average particle radius at time t and ~0 is the average particle radius at the onset of coarsening. The rate constant K is given by: K -
2,yDCeVm2 pc2RT
(2)
In this expression ~, is the interfacial free energy of the particle/matrix interface, D is the diffusion coeff of the solute in the matrix, Ce is the concentration of solute in equilibrium with a particle of infinite size, Vm is the M volume of the precipitate, pe is the numerical cons (pc = ~) related to the particle size distribution and R T has its usual meaning. This relationship applies to the growth of spherical particles. For cubic particles it has been modified [-11 b y substituting half the mean edge © American Elsevier Publishing Company, Inc., 1975
330
D . W . C h u n g and M . C. Chaturvedi
length (d/2) for the radius term, f. Therefore, the growth expression becomes: d3 -
do 8 -
6 4.y D C eV 2 t
- K~t
9RT
(3)
In the LSW theory it is assumed that the particles are spherical and the volume fraction is very small, so that the mean distance between the particles is large as compared to their diam. In spite of this assumption the LSW theory has been successfully applied to the coarsening behavior of Cu in Fe-Cu 2, Mn in Mg-Mn 3, ~' in Ni-A11, Ni-Si 4, Ni-Ti 5, and in Ni-CoCr-Ti 6 and Fe3Si in Fe-Si-TF systems. The basic expression of the LSW theory does not contain a volume fraction term. Ardell [-8] has modified this theory to incorporate the volume fraction term, ~, in the above expression. According to the modified Lifshitz-Wagner (MLSW) theory the rate constant K is given by: K where,
6~/D C eV ~ U 3 ~RT
(4)
U = r/r*
=
3 Um2
1 ÷2~um-~
(5)
6~1/3
--
e 8~ r (4)
(6)
The additional symbols in the above equations are: r*-critical particle radius U~-maximum reduced particle size of the theoretical distribution function F(¢)-
x-2/ae - z d x 4,
The MLSW theory predicts that the basic t1/3 kinetics remain the same as the LSW theory, but, the coarsening rates should increase with the increasing volume fraction of the precipitate. The growth of Co precipitate in the Cu-Co system obeys the MLSW theory very well, however, the growth of 7 ~ in Ni-A1 and Ni-Cr-A1 alloys is entirely in contradiction to the MLSW theory [-9].
V' Growth Studies
331
In a 40Co-38Ni-17Cr-5Ti alloy, which has an fcc structure the v' phase was observed to precipitate coherently along the (100) matrix directions in cubic shape and its lattice mismatch was 1.3% [10]. The growth kinetics of the V' phase in that alloy followed the LSW theory very well. However, the particle size distribution was significantly broader than the distribution predicted by the LSW theory [6]. This paper reports the results of the investigations carried out to study the effect of volume fraction on the growth kinetics of V' in the Co-Ni-Cr-Ti system.
Materials and Experimental Techniques Three alloys, whose compositions are given in Table 1, were investigated. 500 g melts of these alloys were made in a vacuum induction furnace using 99.99% pure alloying elements, except for Ti which was 99.9% pure. The ingots were homogenized at 1523°K and cold rolled, with frequent intermediate anneals at the same temperature, to produce about 125 ~m thick strips. These strips were solution treated at 1523°K and quenched in iced brine. The quenched specimens were aged at 1073 and 1173°K for various lengths of time. All heat-treatments were carried out with specimens sealed in argon filled Vycor capsules. Thin foils for electron microscopy were prepared by an electrolytic jet-polishing technique using a 5% perchloric acid-95% methanol bath at 233-223°K. As stated earlier, the v' particles are cubic in shape and align themselves in (100) matrix directions. Therefore, whenever possible, the particle size was measured in the {100} thin foil orientation, otherwise in the {110} orientation along (100} directions. The particle size was averaged for 200 measurements. The volume fraction of v' was calculated by determining the thickness of thin foils by the slip trace width measurements. A few of these calculations were confirmed by extracting the precipitate by the anodic dissolution of the matrix, using a 10% sulpheric acid-90% methanol bath at 4V. TABLE 1 CompositionofAlloysInvestigated(Wt %) No.
Cobalt
Nickel
Chromium
Titanium
1 2 3
39.58 40.00 40.42
37.60 38.00 38.40
16.82 17.00 17.18
6.00 5.00 4.00
332
D. W. Chung and M. C. Chaturvedi
Results and Discussion
The main precipitate in all three alloys at both temperatures of aging, within the grains, was 7'. Some hexagonal Ni3Ti precipitate formed at the grain boundaries. Figures 1 and 2 show typical structures of 4% Ti alloy aged at 1073°K and 6% Ti alloy aged at 1173°K, respectively. These are the darkfield structures, taken with the help of [-1003 superlattice spots of 7', and show the cubic shape of 7' particles. In both the alloys, the 7' particles are also seen to align themselves along (100) matrix directions. To evaluate the growth kinetics of 7' in these alloys, a 3 was plotted as a function of aging time, at both the temperatures. Figures 3 and 4 show these plots for all the three alloys at 1073 and 1173°K, respectively. It is seen that at both the aging temperatures, for all three alloys, (particle size) a varies linearly with aging time. This suggests that the growth of 7' particles in these alloys, at both the temperatures of aging, follows a diffusion controlled mechanism. It is also observed that at t = 0 the extrapolated lines pass through a point close to the origin thereby suggesting that the value of do ~ 0. The applicability of LSW or MLSW theory was further confirmed by the log (d/2) vs log t plot. As shown in Fig. 5, for all the three alloys, at both the temperatures, these plots are straight lines with a slope of ½. The rate constants, K', were calculated from the plots shown in Figs. 3 and 4 and are given in Table 2. This table also indicates the volume fraction
FIG. 1. Dark field micrograph of a 4% Ti alloy aged for 120 h at 1073°K.
"y' Growth Studies
FIG. 2.
333
Dark field micrograph of a 6 % Ti alloy aged for 6 h at 1173°K.
of 7' in all the three alloys at various temperatures. It is observed that although the volume fraction of ~' at 1173°K varies from 7% to 16%, the value of K' is constant within the experimental limits. Similarly, at 1073°K the value of ~ varies from 10% in 4% Ti alloy to 20% in 6% Ti alloy, the value of K' is constant.
30, TEMPERATURE - 1073=K °'~--° 6% T;
=
I
~,o /
5% Ti
20
"Eo Icj
5
I0
15
20
Time, t, xlO s, sec
FIG. 3. alloys.
The variation in -y' (particle size) 3 with time at 1073°K for 4, 5 and 6 % Ti
D. W. Chung and M. C. Chaturvedi
334
I
i
i
TEMPERATURE- 1175°K o--'-o 6 % Ti 5 % T, o,----,o 4 % Ti
/a
x ~o
I 5
I IO
I 15
Time, t, x 104, s e c
FIG. 4.
The variation in ~' (particle size) 3 with time at 1173°K for 4, 5 and 6% Ti
alloys. The diffusion coefficient D in Eq. (4) is defined as D = Do exp ( - Q/RT), where, Do is the frequency factor, Q is the activation energy and RT have their usual meaning. Therefore, for cubic particle, the constant K ' can be written as: 9
T exp
(7)
It is usual to determine the activation energy, Q, by the slope of In (K'T/Ce) vs 1/T plot. The values of various parameters for this plot are given in Table 3. Unfortunately, at 973°K data for only the 5% Ti alloy are available. Therefore, the activation energy can not be determined accurately. However, it is observed that for a common temperature of aging the values of (K'T/Ce) for all three alloys are the same. This suggests that the activation energy for the growth process of ~', in all three alloys is the same, despite a significant difference in the volume fraction of ~'.
"y' Growth Studies
335
mOO0
i
o~o
i
6 % Ti 5% Ti
IO0
I
I
I0
I00
10(:30
Time (Hours)
FIG. 5. Log-log plots of half mean edge length of ~' vs aging time for 4, 5 and 6% Ti alloys at 1073 and 1173°K. T h e L S W as well as M L S W theories of diffusion controlled g r o w t h assume a s t e a d y state diffusion, b u t with a different g e o m e t r y of diffusion. I n the L S W t h e o r y the v o l u m e fraction of the growing phase is assumed to be nearly zero which implies t h a t the interparticle spacing is m u c h greater t h a n the particle size. I n the M L S W theory, on the other hand, a s t e a d y state diffusion is assumed to occur t h o u g h concentric spheres [-81. Now, according to B r o w n and H a m ~ l l J , the interparticle spacing 'L', for spherical precipitates of radii r, is given b y L = [-(Tr/0)1/~ _ 2"] (9)I/2r, where, 0 is TABLE 2 Rate constant, K', and Volume Fraction of ~' of Different Alloys at various Aging Temperatures Temperature (°K)
%Ti
1073 1073 1073 1173 1173 1173
4 5 6 4 5 6
Volume Fraction of ~' (~)
(~Vsec)
0.103 0.140 0.196 0.075 0.100 0.167
(1.4106 ± 0.0587) X l0 s (1.410 -4- 0.0416) X 102 (1.458 ± 0.108) X 102 (2.726 i 0.118) X 103 (2.590 ± 0.054) X 103 (2.737 ± 0.051) X 108
K'
336
D. W. Chung and M. C. Chaturvedi
TABLE 3 Data for the Determination of thn Activation Energy Q Temperature (°K)
Ti (Wt %)
C, (At %)
973 1073 1073 1073 1173 1173 1173
5 4 5 6 4 5 6
1.78 2.70 2.70 2.70 3.73 3.73 3.73
K 'T / Co (.~K/sec)
1.505 5.606 5.603 5.794 8.573 8.145 8.607
>< 106 >( 106 )< 10e >< 106 )< 107 >< 107 >< 107
the volume fraction of the precipitate. I n the present alloys the particles are cubic and, as stated earlier, it is assumed t h a t r = a/2. Therefore, in a 6 % Ti specimen aged for one hour at 1073°K, where a/2 = 82A, L is calculated to be 133 A. This is less t h a n the particle size, i.e., 164 A. Similarly, at higher volume fractions, the ~/particle size is always greater t h a n the interparticle spacing. This is contrary to the assumptions of the LSW theory, yet the growth of ~/particles follows the LSW theory and not the M L S W theory. Therefore, the assumption and approach of the M L S W theory, attractive as they m a y be, do not seem to a p p l y to the growth of ~,' particles in the present alloy system. A similar conclusion was reached b y Chellman and Ardell [91 while working on Ni-A1 and Ni-Cr-A1 alloys. o
This work was financially supported by the National Research of Canada, Ottawa.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. J. Ardell and R. B. Nicholson, J. Phys. Chem. Solids 27, 1793 (1966). G. R. Speich and R. A. Oriani, Trans. AIME 233, 623 (1965). A. F. Smith, Acta Met. 15, 1867 (1967). P. K. Rastogi and A. J. Ardell, Acta Met. 19, 321 (1971). A. J. Ardell, Met. Trans. L 525 (1970). M. Chaturvedi and D. W. Chung, J. Inst. Metals 101, 253 (1973). E. N. Bower and J. A. Whiteman, The Mechanism of Phase Trans. in Cryst. Solids, Inst. Metals Monograph No. 33, 119 (1969). A. J. Ardell, Acta Met. 20, 61 (1972). D. J. Chellman and A. J. Ardell, Aeta Met. 22, 577 (1974). D. W. Chung and M. Chaturvedi, Metal Sc. J. 6, 134 (1972). L. M. Brown and R. K. Ham, in Strengthening Mechanisms in Crystals (A. Kelly and R. B. Nicholson, Eds.), Elsevier, 1971, p. 9.
Received August 197~
329
The Effect of Volume Fraction on the Coarsening Behavior of ~' in Co-Ni-Cr-Ti Alloys
D. W.
CHUNG
AND
M.
C. CHATURVEDI
Metallurgical Science Laboratory, Department of Mechanical Engineering, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
Three alloys from the Co-Ni-Cr-Ti System, with different Ti Contents, were investigated. The main precipitating phase was observed to be ~' with an ordered fcc Structure. The growth of ~', with different volume fractions, in the three alloys, followed the Lifshitz-Wagner theory of diffusion controlled coarsening and not the Modified Lifshitz-Wagner theory, which takes into consideration the volume fraction of the growing phase.
Introduction The growth of precipitate particles in m a n y two phase systems has been observed to follow the Lifshitz-Wagner (LSW) theory of diffusion controlled coarsening. According to this theory the kinetic equation for growth is: ~3_
~o3 = K t
(1)
where, ~ is the average particle radius at time t and ~0 is the average particle radius at the onset of coarsening. The rate constant K is given by: K -
2,yDCeVm2 pc2RT
(2)
In this expression ~, is the interfacial free energy of the particle/matrix interface, D is the diffusion coeff of the solute in the matrix, Ce is the concentration of solute in equilibrium with a particle of infinite size, Vm is the M volume of the precipitate, pe is the numerical cons (pc = ~) related to the particle size distribution and R T has its usual meaning. This relationship applies to the growth of spherical particles. For cubic particles it has been modified [-11 b y substituting half the mean edge © American Elsevier Publishing Company, Inc., 1975
330
D . W . C h u n g and M . C. Chaturvedi
length (d/2) for the radius term, f. Therefore, the growth expression becomes: d3 -
do 8 -
6 4.y D C eV 2 t
- K~t
9RT
(3)
In the LSW theory it is assumed that the particles are spherical and the volume fraction is very small, so that the mean distance between the particles is large as compared to their diam. In spite of this assumption the LSW theory has been successfully applied to the coarsening behavior of Cu in Fe-Cu 2, Mn in Mg-Mn 3, ~' in Ni-A11, Ni-Si 4, Ni-Ti 5, and in Ni-CoCr-Ti 6 and Fe3Si in Fe-Si-TF systems. The basic expression of the LSW theory does not contain a volume fraction term. Ardell [-8] has modified this theory to incorporate the volume fraction term, ~, in the above expression. According to the modified Lifshitz-Wagner (MLSW) theory the rate constant K is given by: K where,
6~/D C eV ~ U 3 ~RT
(4)
U = r/r*
=
3 Um2
1 ÷2~um-~
(5)
6~1/3
--
e 8~ r (4)
(6)
The additional symbols in the above equations are: r*-critical particle radius U~-maximum reduced particle size of the theoretical distribution function F(¢)-
x-2/ae - z d x 4,
The MLSW theory predicts that the basic t1/3 kinetics remain the same as the LSW theory, but, the coarsening rates should increase with the increasing volume fraction of the precipitate. The growth of Co precipitate in the Cu-Co system obeys the MLSW theory very well, however, the growth of 7 ~ in Ni-A1 and Ni-Cr-A1 alloys is entirely in contradiction to the MLSW theory [-9].
V' Growth Studies
331
In a 40Co-38Ni-17Cr-5Ti alloy, which has an fcc structure the v' phase was observed to precipitate coherently along the (100) matrix directions in cubic shape and its lattice mismatch was 1.3% [10]. The growth kinetics of the V' phase in that alloy followed the LSW theory very well. However, the particle size distribution was significantly broader than the distribution predicted by the LSW theory [6]. This paper reports the results of the investigations carried out to study the effect of volume fraction on the growth kinetics of V' in the Co-Ni-Cr-Ti system.
Materials and Experimental Techniques Three alloys, whose compositions are given in Table 1, were investigated. 500 g melts of these alloys were made in a vacuum induction furnace using 99.99% pure alloying elements, except for Ti which was 99.9% pure. The ingots were homogenized at 1523°K and cold rolled, with frequent intermediate anneals at the same temperature, to produce about 125 ~m thick strips. These strips were solution treated at 1523°K and quenched in iced brine. The quenched specimens were aged at 1073 and 1173°K for various lengths of time. All heat-treatments were carried out with specimens sealed in argon filled Vycor capsules. Thin foils for electron microscopy were prepared by an electrolytic jet-polishing technique using a 5% perchloric acid-95% methanol bath at 233-223°K. As stated earlier, the v' particles are cubic in shape and align themselves in (100) matrix directions. Therefore, whenever possible, the particle size was measured in the {100} thin foil orientation, otherwise in the {110} orientation along (100} directions. The particle size was averaged for 200 measurements. The volume fraction of v' was calculated by determining the thickness of thin foils by the slip trace width measurements. A few of these calculations were confirmed by extracting the precipitate by the anodic dissolution of the matrix, using a 10% sulpheric acid-90% methanol bath at 4V. TABLE 1 CompositionofAlloysInvestigated(Wt %) No.
Cobalt
Nickel
Chromium
Titanium
1 2 3
39.58 40.00 40.42
37.60 38.00 38.40
16.82 17.00 17.18
6.00 5.00 4.00
332
D. W. Chung and M. C. Chaturvedi
Results and Discussion
The main precipitate in all three alloys at both temperatures of aging, within the grains, was 7'. Some hexagonal Ni3Ti precipitate formed at the grain boundaries. Figures 1 and 2 show typical structures of 4% Ti alloy aged at 1073°K and 6% Ti alloy aged at 1173°K, respectively. These are the darkfield structures, taken with the help of [-1003 superlattice spots of 7', and show the cubic shape of 7' particles. In both the alloys, the 7' particles are also seen to align themselves along (100) matrix directions. To evaluate the growth kinetics of 7' in these alloys, a 3 was plotted as a function of aging time, at both the temperatures. Figures 3 and 4 show these plots for all the three alloys at 1073 and 1173°K, respectively. It is seen that at both the aging temperatures, for all three alloys, (particle size) a varies linearly with aging time. This suggests that the growth of 7' particles in these alloys, at both the temperatures of aging, follows a diffusion controlled mechanism. It is also observed that at t = 0 the extrapolated lines pass through a point close to the origin thereby suggesting that the value of do ~ 0. The applicability of LSW or MLSW theory was further confirmed by the log (d/2) vs log t plot. As shown in Fig. 5, for all the three alloys, at both the temperatures, these plots are straight lines with a slope of ½. The rate constants, K', were calculated from the plots shown in Figs. 3 and 4 and are given in Table 2. This table also indicates the volume fraction
FIG. 1. Dark field micrograph of a 4% Ti alloy aged for 120 h at 1073°K.
"y' Growth Studies
FIG. 2.
333
Dark field micrograph of a 6 % Ti alloy aged for 6 h at 1173°K.
of 7' in all the three alloys at various temperatures. It is observed that although the volume fraction of ~' at 1173°K varies from 7% to 16%, the value of K' is constant within the experimental limits. Similarly, at 1073°K the value of ~ varies from 10% in 4% Ti alloy to 20% in 6% Ti alloy, the value of K' is constant.
30, TEMPERATURE - 1073=K °'~--° 6% T;
=
I
~,o /
5% Ti
20
"Eo Icj
5
I0
15
20
Time, t, xlO s, sec
FIG. 3. alloys.
The variation in -y' (particle size) 3 with time at 1073°K for 4, 5 and 6 % Ti
D. W. Chung and M. C. Chaturvedi
334
I
i
i
TEMPERATURE- 1175°K o--'-o 6 % Ti 5 % T, o,----,o 4 % Ti
/a
x ~o
I 5
I IO
I 15
Time, t, x 104, s e c
FIG. 4.
The variation in ~' (particle size) 3 with time at 1173°K for 4, 5 and 6% Ti
alloys. The diffusion coefficient D in Eq. (4) is defined as D = Do exp ( - Q/RT), where, Do is the frequency factor, Q is the activation energy and RT have their usual meaning. Therefore, for cubic particle, the constant K ' can be written as: 9
T exp
(7)
It is usual to determine the activation energy, Q, by the slope of In (K'T/Ce) vs 1/T plot. The values of various parameters for this plot are given in Table 3. Unfortunately, at 973°K data for only the 5% Ti alloy are available. Therefore, the activation energy can not be determined accurately. However, it is observed that for a common temperature of aging the values of (K'T/Ce) for all three alloys are the same. This suggests that the activation energy for the growth process of ~', in all three alloys is the same, despite a significant difference in the volume fraction of ~'.
"y' Growth Studies
335
mOO0
i
o~o
i
6 % Ti 5% Ti
IO0
I
I
I0
I00
10(:30
Time (Hours)
FIG. 5. Log-log plots of half mean edge length of ~' vs aging time for 4, 5 and 6% Ti alloys at 1073 and 1173°K. T h e L S W as well as M L S W theories of diffusion controlled g r o w t h assume a s t e a d y state diffusion, b u t with a different g e o m e t r y of diffusion. I n the L S W t h e o r y the v o l u m e fraction of the growing phase is assumed to be nearly zero which implies t h a t the interparticle spacing is m u c h greater t h a n the particle size. I n the M L S W theory, on the other hand, a s t e a d y state diffusion is assumed to occur t h o u g h concentric spheres [-81. Now, according to B r o w n and H a m ~ l l J , the interparticle spacing 'L', for spherical precipitates of radii r, is given b y L = [-(Tr/0)1/~ _ 2"] (9)I/2r, where, 0 is TABLE 2 Rate constant, K', and Volume Fraction of ~' of Different Alloys at various Aging Temperatures Temperature (°K)
%Ti
1073 1073 1073 1173 1173 1173
4 5 6 4 5 6
Volume Fraction of ~' (~)
(~Vsec)
0.103 0.140 0.196 0.075 0.100 0.167
(1.4106 ± 0.0587) X l0 s (1.410 -4- 0.0416) X 102 (1.458 ± 0.108) X 102 (2.726 i 0.118) X 103 (2.590 ± 0.054) X 103 (2.737 ± 0.051) X 108
K'
336
D. W. Chung and M. C. Chaturvedi
TABLE 3 Data for the Determination of thn Activation Energy Q Temperature (°K)
Ti (Wt %)
C, (At %)
973 1073 1073 1073 1173 1173 1173
5 4 5 6 4 5 6
1.78 2.70 2.70 2.70 3.73 3.73 3.73
K 'T / Co (.~K/sec)
1.505 5.606 5.603 5.794 8.573 8.145 8.607
>< 106 >( 106 )< 10e >< 106 )< 107 >< 107 >< 107
the volume fraction of the precipitate. I n the present alloys the particles are cubic and, as stated earlier, it is assumed t h a t r = a/2. Therefore, in a 6 % Ti specimen aged for one hour at 1073°K, where a/2 = 82A, L is calculated to be 133 A. This is less t h a n the particle size, i.e., 164 A. Similarly, at higher volume fractions, the ~/particle size is always greater t h a n the interparticle spacing. This is contrary to the assumptions of the LSW theory, yet the growth of ~/particles follows the LSW theory and not the M L S W theory. Therefore, the assumption and approach of the M L S W theory, attractive as they m a y be, do not seem to a p p l y to the growth of ~,' particles in the present alloy system. A similar conclusion was reached b y Chellman and Ardell [91 while working on Ni-A1 and Ni-Cr-A1 alloys. o
This work was financially supported by the National Research of Canada, Ottawa.
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
A. J. Ardell and R. B. Nicholson, J. Phys. Chem. Solids 27, 1793 (1966). G. R. Speich and R. A. Oriani, Trans. AIME 233, 623 (1965). A. F. Smith, Acta Met. 15, 1867 (1967). P. K. Rastogi and A. J. Ardell, Acta Met. 19, 321 (1971). A. J. Ardell, Met. Trans. L 525 (1970). M. Chaturvedi and D. W. Chung, J. Inst. Metals 101, 253 (1973). E. N. Bower and J. A. Whiteman, The Mechanism of Phase Trans. in Cryst. Solids, Inst. Metals Monograph No. 33, 119 (1969). A. J. Ardell, Acta Met. 20, 61 (1972). D. J. Chellman and A. J. Ardell, Aeta Met. 22, 577 (1974). D. W. Chung and M. Chaturvedi, Metal Sc. J. 6, 134 (1972). L. M. Brown and R. K. Ham, in Strengthening Mechanisms in Crystals (A. Kelly and R. B. Nicholson, Eds.), Elsevier, 1971, p. 9.
Received August 197~