High-temperature creep and grain-boundary behaviour in a Cu—10% Zn alloy

49 Materials Science and Engineering, 21 (1975) 49--56

© Elsevier Sequoia S.A., Lausanne -- Printed in The Netherlands

High-Temperature Creep and Grain-Boundary Behaviour in a Cu--10% Zn Alloy

I. SAXL, V. SKLENI~KA and J. CADEK Czechoslovak Academy of Sciences, Institute of Physical Metallurgy, 616 62 Brno (Czechoslovakia)

(Received in revised form June 2, 1975)

SUMMARY High-temperature creep and grain-boundary behaviour in a Cu - 10% Zn alloy was investigated in a temperature interval of 773 to 973 K. It was found that grain-boundary sliding (GBS) and grain-interior deformation (GID) are two independent mechanisms of the creep deformation. The ratio of the activation energies of these processes is close to about 0.6 and, consequently, GID controlled by volume diffusion dominates at higher while GBS controlled by grain-boundary diffusion dominates at lower temperatures. The differences of creep behaviour as to GIC, GBS and intercrystalline void formation (IVF) are discussed. It is shown that grain-boundary migration (GBM) in creep is more frequent in a Cu - 10% Zn alloy than in a Cu - 30% Zn alloy and that the migration distance is proportional to the total GBS vector. The main part of GBM can be explained as a structurally necessary process accompanying GBS.

1. INTRODUCTION Recently, considerable attdntion has been devoted to the deformation processes operating during high-temperature creep. The nature and significance of grain-boundary sliding (GBS) has been extensively studied especially in relation to diffusional (i.e. Nabarro - Herring [1] or Coble [2]) creep. If no volume changes are associated with the deformation, i.e. if perfect compatibility of material is conserved t h r o u g h o u t it, GBS must be accompanied by diffusional flow [3 - 6] if the applied stresses are relatively low.

In this case the contribution of GBS to the total strain should not significantly exceed 50% [3]. In some metals and alloys the properly adjusted conditions then lead to superplastic behaviour [7]. If the applied stresses are high plastic deformation involving motion of lattice dislocations (grain interior deformation -- GID) can instead accommodate the incompatibility due to GBS [4], though also another opinion has been advanced, namely, that GBS accommodates GID being caused by a combination of glide and climb movement of lattice dislocations along grain boundaries [8]. However, there is a large group of materials in which GBS is accompanied by the relative volume changes of the order of 10 -5 to 10 -3 caused by in tercrystalline void formation (IVF). The accommodation of GBS by IVF is then possible. This accommodation can lead to higher rates of GBS than diffusional one or the accommodation due to GID. At the same time it, naturally, leads to the fracture at relatively low strains, especially when the contribution of GID is negligible. Also, the decrease of the stress exponent m' = (~ lnes/~ lnO)T (where es is the steady state creep rate, o the applied stress and T the absolute temperature) Corresponding to the passage from dominating GID to dominating GBS is then less pronounced. In the previous papers [9 - 11] concerning surface analysis of grain boundary behaviour in a Cu - 30% Zn alloy (mean grain diameter 500 pm) it has been shown that two independent processes, namely GID and GBS, simultaneously contribute to the total creep strain and that the necessary a c c o m m o d a t i o n is provided by IVT. As the apparent activation

50 energies of GID, Qg, and GBS, Q~, differ substantially (Qgb ~-- 0.6 Qg) and also as the stress exponent m for GID is higher than the corresponding stress exponent n for GBS, GID dominates at higher temperatures and stresses, whereas GBS controls the creep deformation at lower temperatures and stresses. The above work has been continued to obtain further results supporting the conclusion on the mutual independence of GBD and GID. At the same time, greater attention has been paid to the quantitative evaluation of grain boundary migration (GBM) and to its relation to both deformation processes, i.e. GID and GBS.

2. EXPERIMENTAL TECHNIQUE The Cu - 10% Zn alloy investigated was melted in an induction furnace from component metals of purities not lower than 99.99%. The ingot was rolled to a strip 11 m m in thickness from which creep specimens 50.0 mm in gauge length and 7.0 × 3.2 mm 2 in cross section were machined in such a way t h a t the tensile stress axis was parallel to the rolling direction. Creep specimens were annealed for 1 h at 1123 K in a vacuum of 10 - 6 Torr. The annealing resulted in a mean grain diameter d = 320 pm. The specimens were carefully electropolished before creep tests, the electropolishing being performed in a 60% aqueous solution of phosphoric acid at a potential of about 2 V and a temperature of about 310 K. Constant load creep tests were carried out in purified dried hydrogen at temperatures of 773, 8 4 3 , 9 1 3 and 973 K at the initial stress of 20 MN/m 2. Several specimens were tested at each temperature; various tests were stopped after gradually.increasing time intervals covering the primary and tertiary stages of creep separated from each other by an inflection point only. The creep strain e and its components were evaluated metallographically from the measurements made on the surface of specimens; e from the displacement of gauge markers, egb due to GBS from the longitudinal offset Uw of the transverse scratch markers (eg b = - U T X s L / d , where XSL is the fraction boundaries with observable sliding as measured along the longitudinal traverse [12]), the c o m p o n e n t ec due to IVF from the measurement of the total crack width in the tensile stress axis direc-

tion (for details of the measurement and the necessary corrections see reference 9). The strain eg due to GID was obtained by means of the equation eg = e --(egb + ec).

(1)

Further details concerning the experimental procedure are given elsewhere [9]. Grain boundary migration is characterized by the mean migration distance ~ and by the ratio R = ~/~, where p is the total sliding vector Also the true mean value R = (g/p), where g and p are measured simultaneously at the same boundary, has been evaluated with the conclusion that the difference between R and R is not significant. The mean total sliding vector was estimated from the mean vertical component V of GBS measured interferometrically using the relation [13] p = 2.25Vx/1 + e. The detailed formula for ~is dependent on the assumed angular distribution of migrating planes. Assuming that all the angles 0 of the boundaries normal with respect to the measured surface are equally probable, then [14] ~ = 0.64(h -- V),

(2)

where h is the distance between boundary traces on the surface and V is the height of the corresponding step (measured interferometrically). If only the boundaries with the angles 0 in the interval (Ir/4, ~/2)are taken into account, then = 0.9h -- OAF.

(3)

All our calculations have been carried out using eqn. (2), which is probably more appropriate for "as c u t " surfaces.

3. RESULTS

3.1. Grain-boundary sliding and grain-interior deformation The time dependences of the total creep strain e and its components egb, eg at lower and higher temperatures in the temperature range investigated are shown in Fig. la, b. Whereas at 913 and 973 K the explanation of the tertiary stage put forward in the previous paper [9] conserves its validity (i.e. the explanation involving the propagation of a limited number of cracks of critical dimensions) at lower temperatures another mechanism should be expected. In fact, the minimum creep rate

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The d i f f e r e n t t e m p e r a t u r e d e p e n d e n c e s o f emm and o f the creep strain c o m p o n e n t rates • min ' m i n egb , eg are s h o w n in Fig. 2, which clearly d e m o n s t r a t e s the m u t u a l i n d e p e n d e n c e o f the c o r r e s p o n d i n g d e f o r m a t i o n mechanisms. T h e observed creep rates are c o n s i d e r a b l y lower t h a n in a Cu - 30% Zn alloy. In Fig. 2 are also p l o t t e d the e x p e c t e d d e p e n d e n c e s ~nm (T), .min eg~ (T) for the Cu - 30% Zn alloy at the initial stress o f 20 M N / m 2 ( o b t a i n e d graphically f r o m the results o f the previous p a p e r [10] using the m e t h o d p r o p o s e d in r e f e r e n c e 11), egb'm~is "ram a p p r o x i m a t e l y fifty r o u g h l y t h i r t y times, eg times lower in a Cu - 10% Zn t h a n in a Cu 30% Zn alloy. The latter d i f f e r e n c e is o f the same o r d e r o f m a g n i t u d e as the ratio o f the values of a p p r o p r i a t e lattice diffusion coefficients in a Cu - 30% Zn and a Cu - 10% Zn, n a m e l y 20 t o 30 in the t e m p e r a t u r e range studied [ 15 ]. T h e a p p a r e n t activation energies Qg and Qgb for Cu - 10% Zn are 2 2 9 . 4 k J / m o l and 129.1 k J / m o l ; t h e y are slightly higher t h a n those for a Cu - 30% Zn alloy [ 1 0 ] . Assuming t h a t eg = eg(p) + e ~ ( t -- tp)g and t h a t a similar relation holds for Qb, w h e r e eg(p), egb(P) are the strains at the end o f the p r i m a r y stage o f the creep c o m p o n e n t s versus time curves (in general n o t c o r r e s p o n d i n g to the end o f the p r i m a r y stage o f creep [10] ), we o b t a i n for sufficiently long times t h a t • min • t "m~n 6g a g + 6g 6g

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is a t t a i n e d at the very beginning o f t h e test. C o n s e q u e n t l y , the n o n l i n e a r t i m e d e p e n d e n c e s o f egb and eventually o f eg also c o u l d be ex-min .min p e c t e d (with m i n i m u m values o f egb , eg at the time t n o t m u c h d i f f e r e n t f r o m zero). In the present case the relation b e t w e e n eg and t i m e is linear w i t h i n the e x p e r i m e n t a l error, Fig. 1.

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w h e r e a g = e g ( p ) - - e g-mE. tp(g) with tp(g) being the t i m e at eg = egb(P); a similar relation is obt a i n e d for ag b. Thus, the eg/egb ratio a p p r o a c h e s eg/egb at high strains or times. B o t h the ratios are c o m p a r e d in Fig. 3. The a g r e e m e n t is fairly good, o n l y at high t e m p e r a t u r e s (973 K) is 6 g / e g b < egmin /6gmin b as a c o n s e q u e n c e of a relatively long p r i m a r y stage, Fig. l b . 3.2. I n t e r c r y s t a l l i n e void f o r m a t i o n

The intercrystalline void f o r m a t i o n is n o t so p r o n o u n c e d in a Cu - 10% Zn as in a Cu - 30% Zn alloy, Fig. 4. Whereas in a Cu - 30% Zn alloy the ratio/3 o f ec t o the t o t a l v o l u m e conserving strain eve = eg + egb is n e a r l y c o n s t a n t and equals 0.5 t o 0.7, in the present case/3 is ternp e r a t u r e d e p e n d e n t and attains a value in this interval o n l y at 773 K. It should be n o t e d t h a t the ratio/3 (in b o t h the alloys) is a p p r o x i m a t e l y c o n s t a n t during the p r i m a r y and also during the

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major part of tertiary creep stage, b u t it increases considerably when approaching fracture as a consequence of the spontaneous growth of the cracks of critical dimensions. Thus, the values of/3 for nearly fractured specimens are not included in Fig. 4; they are, e.g., 0.32 at 913 K and 0.15 at 973 K. The relation between GBS and IVF throughout the major part of the test can be estimated. from the ratio ~ = ec/eg b. ~ is again strain independent with the exception of the strains fQOF~

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The grain-boundary migration (GBM) does not contribute to the creep strain; however,

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IT x 104 Ef/K.7 Fig. 4. Comparison of temperature dependences of ec/evc and ec/egb ratio for Cu - 10% Zn and Cu - 30% Zn alloys•

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Fig. 6. Relation between mean migration distance and mean total sliding vector ~. 5c), Whereas a boundary frequently migrates along the whole facet, local migration is also often observed, namely at higher temperatures. Such a migration occurred preferentially at the triple point junctions. The time dependence of GBM is also included in Fig. l b and the temperature dependence of minimum migration rate gm~ is shown in Fig. 2. The migration distance g was linearly related to the corresponding local values of the vertical component V of GBS, hence on the average also to the total sliding vector fi, Fig. 6. The ratio R is strain and temperature independent. The scatter of values is relatively small and R is equal to 1.93 + 0.06. The temperature dependence of the migration rate follows closely that of the GBS; thus the apparent activation energy of GBM, Qm, is close to the apparent activation energy Qgb of GBS (Fig. 2).

4. DISCUSSION Fig. 5. Micrographs of surface grain boundary migration at 773 K (a), 843 K (b) and 773 K (c). Tensile stress axis horizontal.

it could influence the deformation behaviour as it can reduce the local stress concentrations. The characteristic features of GBM can be seen from Fig. 5a. The intercrystalline cracks are less developed along migrating parts of the boundary facets (Fig. 5b) and in certain cases GBM suppresses cracking considerably (Fig.

4.1. Activation energies for GID and GBS The value of the initial applied stress of 20 MN/m 2 ensures that the diffusional or "linear" creep does not control the rate of deformation. Burton and Greenwood [16] found that the transition stress ot between the diffusional and dislocation creep is 5 to 10 MN/m 2 for copper and alpha brasses and Hostinsk~ and Cadek [17] found for the same alloy as studied in the present work that the stress exponent m' = (a In es/a In O)T approximately equals 5 in

54 the range of experimental conditions chosen. The present results fully confirm the conclusions drawn from the investigation of a Cu 30% Zn alloy. The GBS and GID are independent mechanisms of deformation in a Cu - 10% Zn as well as in a Cu - 30% Zn alloy. It is only the choice of experimental conditions, namely of the stress and temperature, together with the magnitude of grain diameter, t h a t determines which of simultaneously operating mechanisms is dominating. The apparent activation energies Qgb and Qg differ considerably (their ratio is 0.56) and are only slightly higher than in the Cu - 30% Zn alloy [2]. To determine the true activation energy of creep, it is necessary to correct the obtained values with respect to temperature dependence of the preexponential term, i.e. with respect to the temperature dependence of the elastic modulus. Using K6ster's data [18] on temperature dependence of Young's modulus and the values of 5 for the stress exponent m = 5 In ~ m / ~ In a and 3 for the stress exponent n = 5 In Qb "m~/ 5 1 n a f o r the Cu - 30% Zn and the Cu - 10% Zn alloy (only m has been measured [17] but n ~ m - - 2 ) we obtain the corrections 12.1 k J / m o l and 8.4 k J / m o l for Qg and Qgb, respectively. Thus, our value of Qg after the correction is 217.3 kJ/mol, which is slightly higher than the value of the activation enthalphy AH~ for diffusion in which the self-diffusion of both the components of the solid solution contribute. The value AH~ = 195.9 kJ/mol follows from the results deduced by Oikawa and Karashima [15], namely D (895 K) = 1.4 × 10 - s cm2/s, (823 K) = 1.4 × 10 - 9 cm2/s. The ratio Qg/Qgb 0.6 is within the range of values expected for the ratio of activation enthalpies of diffusion along the grain boundaries and inside the grains. On the other hand, it should be noted that the accuracy of the determination of activation energies Qg and Qgb is rather low as the evaluation of eg is not straightforward and the results of ec determination are dependent on the specific model [9]. Consequently, only the value of Qg -- Qgb confirmed also by the temperature variation of the eg/egb ratio is sufficiently reliable. In spite of this, the agreement between Qg and AH~ is relatively good, at least much better than in the Cu - 30% Zn alloy, where AH5 evaluated from the values of D in reference 15 equals 170.4 kJ/mol, whereas Qg equal to 219.0 kJ/mol was found [10].

The dominating role of the GBS at low temperatures and of the GID at high temperatures manifest themselves by the change in slope of versus 1/T plot. Even when not reported for alpha Cu - Zn solid solutions [17,19] this phenomenon was found for copper [20,21] and was ascribed [21] to the diffusion along the dislocations inside the grains. Our results clearly show that the change in the value of apparent activation energy is connected with the passage from the GBS to the GID in alpha Cu - Zn solid solutions as well as in pure copper [22]. 4.2. Intercrystalline void formation Probably the most notable difference between the creep behaviour of the Cu - 30% Zn and the Cu - 10% Zn alloys is the significantly less pronounced IVF in the latter alloy. In a Cu 30% Zn alloy the IVF is connected to the same extent with the GBS as with the GID, which may be documented either by the temperature and strain independence of the ratio fl or by the linear relation between the total crack width E~-and the total creep strain, Fig. 7. On the other hand, in a Cu - 10% Zn alloy the ratio fl decreases with increasing temperature in the same way as the a m o u n t of GBS decreases, Fig. 4, and the plots of E~ versus e are distinctly different at different temperatures. One of the possible explanations of this behaviour could follow from the difference in the values of the stacking fault energy 3'. The dislocations climbing along the boundaries are more widely split. Thus the stress concentrations at the boundaries promote the formation of voids. The strain dependence of void formation reveals that the differences in the IVF are qualitative rather than quantitative only. The total width of cracks in the tensile stress axis direction ~ can be represented as the product of the mean number of cracks Nc and the mean w i d t h ~ of crack, i.e. Z~ =SNc (Fig. 8). The versus E~ and Nc versus E~ relations are temperature independent in both the alloys. However, in the Cu - 30% Zn alloy both quantities increase as a square root of E~ up to the saturation of N c (50 - 60% of boundaries cracked) and then ~ is linearly related to E~. In a Cu 10% Zn alloy N¢ saturates first, and then only sidewise growth of cracks starts, Fig. 8. Thus it seems that the sidewise growth of crack is more difficult than its formation and propaga-

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tion along one grain facet. From the model proposed in reference 9 it follows t h a t the sidewise growth of primary cracks* is closely connected with the formation of secondary cracks* [9]. In agreement with this reasoning the frequency of secondary crack occurrence is considerably lower in a Cu - 10% Zn alloy and limited only to the highest strains. These and related problems will be discussed in detail in a forthcoming paper.

4.3. Grain-boundary migration The grain-boundary migration is closely connected with the GBS and not with the GID as is clearly revealed by its temperature dependence and by the constancy of ~/~ ratio. Hence, the observed GBM is not driven by deformation energy stored inside the grains as a consequence of the GID. Ashby [23] proposed t h a t GBM accompanies GBS as a natural consequence of mutual interlocking of neighbouring crystals along the boundary; although this idea is based mainly on the observation made on bubble models, it is in good agreement with the results of atomic calculations. On the basis of this * Primary cracks develop by coalescence of cavities, whereas secondary cracks result from an edgewise growth of primary cracks along the boundary facet terminating in the same triple point.

model the ratio R does not exceed one for high angle (tilt) boundaries. Generalizing this result for general boundaries we can conclude, since in our case R ~- 2, that probably another migration-inducing mechanism interferes. Assuming that the GBS is realised by the movement of secondary grain-boundary dislocations (SGBD's) present in the boundaries having a misorientation near a coincidence lattice misorientation [24], a further GBS induced contribution to the boundary migration can be expected. The Burgers vector of SGBD's forms, in general, a non-zero angle with the boundary and their non-conservative movement causes not only the GBS but also the GBM. The ratio R is then proportional to bjbsll, for one system of moving SGBD's (b=~ and bsLiare the components of the Burgers vector bs of SGBD's perpendicular to and parallel with the boundary, respectively). Hence the mean value of R obtained by averaging over all partial twist boundaries with the same Ib~l is R(mean) = 0.64. Besides these "structural" sources of migration, the accommodation effect manifested by reduced cracking at least in some cases must also be admitted. Then the GBM could be locally influenced also by the GID, but a relatively small or local contribution due to GID to the total value of ~ cannot substantially alter the statistical relation g ~ p.

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TOTAL CRACK WIDTH Z'~ x fO-~[~um/m3 Fig. 8. Dependence of mean crack width ~ and mean number of cracks Nc on total crack width ~ per unit length for Cu - 10% Zn and Cu - 30% Zn alloys at the same temperatures in the interval of 883 to 1023. 5. CONCLUSIONS

1. GBS and GID are two independent mechanisms of the creep deformation in Cu - 10% Zn alpha solid solution and their temperature dependences are characterized by different activation energies. The ratio of these activation energies is close to 0.6. Consequently, the GID controlled by volume diffusion dominates at higher temperatures (above 850 K at a stress of 20 MN/m2), whereas the GBS controlled by grain boundary diffhsion is preponderant at lower temperatures. 2. The main differences between Cu - 10% Zn and Cu - 30% Zn alloys may be summarized as follows: (a) in the Cu - 10% Zn alloy the void formation is initiated mainly by GBS, and is less pronounced; (b) the development of cracks is governed by different laws in b o t h alloys; (c) the GBM is more frequent in the Cu - 10% Zn alloy and the migration distance is proportional to the total sliding vector. The main part of the GBM can be explained as structurally necessary migration accompanying the GBS. REFERENCES 1 C. Herring, J. Appl. Phys., 21 (1950) 437. 2 R.L. Coble, J. Appl. Phys., 34 (1963) 1679. 3 D. McLean, Metal Sci. J., 4 (1970) 144.

4 R. Raj and M.F. Ashby, Met. Trans., 2 (1971) 1113. 5 R.N. Stevens, Surface Sci., 31 (1972) 543. 6 R.C. Gifkins, T.G. Langdon and D. McLean, Metal Sci. J. 9 (1975) 141. 7 M.F. Ashby and R.A. Verrall, Acta Met., 21 (1973) 149. 8 H. Gleiter and B. Chalmers, in B. Chalmers, J.W. Christian and T.B. Maszalski (eds.), Progr. Mater. Sci., 16 (1972) 179. 9 V. Skleni~ka, I. Saxl, J. Popule and J. Cadek, Mater. Sci. Eng., 18 (1975) 271. 10 V. Skleni(~ka, I. Saxl, J. Popule and J. (Jadek, Phys. Status Solidi (a), 29 (1975) 315. 11 I. Saxl, V. Skleni(~ka and J. (Jadek, Phil. Mag., 31 (1975) 233. 12 V. Skleni~ka, K. Proch~zka and J. Cadek, Z. Metallk., 64 (1973) 65. 13 M. McLean, J. Inst. Metals, 81 (1952 - 53) 133. 14 D. McLean, Rev. MEt., 53 (1956) 139. 15 H. Oikawa and S. Karashima, Scripta Met., 5 (1971) 909. 16 B. Burton and G.W. Greenwood, Acta Met., 18 (1970) 1237. 17 T. Hostinsk:~ and J. (Jadek, Met. Mater., 12 (1974) 396. 18 W. K~ster, Z. Metallk., 32 (1940) 160. 19 R.M. Bonesteel and O.D. Sherby, Acta Met., 14 (1966) 385. 20 P. Feltham and J.D. Meakin, Acta Met., 7 (1959) 614. 21 C.R. Barrett and O.D. Sherby, Trans. AIME, 230 (1964) 1322. 22 V. Skleni~ka, I. Saxl and J. (~adek, Trans. Japan Inst. Metals, to be published. 23 M.F. Ashby, Surface Sci., 31 (1972) 498. 24 W. Bollmann, Crystal Defects and Crystalline Interfaces, Springer, Berlin, 1970, p. 215.