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On the origin of cube texture in copper
Acta metall, mater. Vol. 41, No. 6, pp. 1921-1927, 1993 Printed in Great Britain. All rights reserved
0956-7151/93 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
ON THE ORIGIN OF CUBE TEXTURE IN COPPER B. J. D U G G A N , t K. L ~ C K E , 2 G. K ( ~ H L H O F F 2 and C. S. LEE 3
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 21nstitut ftir Metallkunde und Metallphysik, RWTH, Aachen, Kopernikusstr. 14, D-5100, Aachen, Germany and 3School of Metallurgy and Materials, University of Birmingham, B15 2TT, England (Received 13 July 1992)
A~traet--A crystallographic etch in which 111 planes are exposed in copper has been used to determine the orientation of the neighbouring substructures surrounding cube oriented microbands in heavily cold rolled copper. These, after characterisation into orientation groups, were compared with the neighbourhoods of undeveloped cube oriented microbands in lightly annealed material in which almost all well developed recrystallised grains were of cube orientation. By inspection of the two sets of orientation neighbourhoods it is demonstrated that only cube microbands surrounded by material with a 0 ° (111 ) orientation relationship provide cube nuclei. Thus the cube texture arises from competition between nuclei in a variety of orientation environments, the successfulnuclei having environments into which they initially grow characterised by a 0 ° (111) relationship. The process is best described as micro-growth selection, in which the local texture determines the viability and competitive advantage of nuclei, while the global deformation texture (i.e. that determined by traditional diffraction methods) is that which is consumed by those nuclei, with the possibility of further growth selection as recrystallisation proceeds.
1. INTRODUCTION It is a remarkable fact that after almost six decades of research in textures, the sharpest of all textures, the cube texture in copper, is still lacking an explanation which commands general support. Theories of oriented growth (OG), of oriented nucleation (ON-) or a combination of both were proposed long ago by Barrett [1] and Beck [2]. Presently, the strongest advocates of the OG theory are associated with the Aachen school [3-5], while the majority of modern workers could be said to follow the ON theory, of which the most recent substantial example is due to Hjelen et al. [6]. These authors demonstrated the power of the electron backscatter pattern (EBSP) technique [6-8] which allows local orientations to be measured point by point in their modified SEM with an orientation resolution within a degree and a spatial resolution claimed to be < 1/~m. Patterns are degraded if the crystals are heavily dislocated. Fundamentally the information given by this technique is identical to that derived from methods available in TEM, STEM or HVEM, but the large contiguous areas available using surface scanning techniques makes EBSP undoubtedly superior for point to point texture measurement. Exploiting this advantage, Hjelen et al. [6] investigated in great detail the microstructure of cold rolled and partially annealed chili-cast aluminium. They measured the orientation of the material in which cube grains were growing and concluded that cube oriented grains in aluminium are nucleated from transition bands preferentially located in [112] (111 ) (i.e. C) oriented grains or ND rotated C. Of the two theories of cube texture formation, ON or OG, only OG specified a particular
relationship between cube and its deformed neighbourhood, and it claims that for maximum growth rate in fairly pure f.c.c, metals the grain consumed needs to be misoriented to cube by a 300-40 ° rotation about a common (111) axis. As C and cube do not share a common (111 ) direction, these authors ruled out OG as a dominent mechanism for cube texture origin. On reflection it is startling that the EBSP technique is claimed to have resolved all the major problems to do with cube texture formation, because the experimental design is similar to that adopted by many other workers (e.g. [9-11]) and so the information gained can only be of similar nature. While conceding that the EBSP data in [6] is the best available for this kind of experiment, the authors of the present work consider that this and all similar experiments, in principle, cannot resolve the arguments between the ON and OG theories. The weakness lies in the fact that successful nucleation destroys both the evidence of the nucleus state as well as its neighbourhood, since the nucleus in question has already consumed its original neighbours. Therefore, processes like "micro-growth selection", introduced many years ago by Liicke et al. [3], cannot be checked, and much of the literature in which nucleus-matrix orientation relationships have apparently been measured, might be wrong. On the other hand, if only the deformed state is examined, then it is not possible to conclude anything other than whether cube is contained in such things as transition bands, but such volumes might not act as nuclei. What is needed to advance discussion on the relative merits of ON or OG are different kinds of experiments, namely those in which the evidence of
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the nucleus and its surroundings is not destroyed. One direct approach to the general problem of nucleation is to continuously follow the transformation from the deformed state to the recrystallised condition in a hot stage of a high voltage electron microscope as recently reported by Berger et al. [12] in tensile deformed aluminium single crystals. However, the validity of this kind of experiment is still subject to debate because it is unclear as to how the relatively large foil surface energies compared to the intercrystalline energies involved in nucleation and growth affects the recrystallisation process. The present work attempts to solve the philosophical problem of the "destroyed evidence" implicit in all experiments similar to those performed by Hjelen et al. [6], by using a crystallographic etch introduced by Krhlhoff et al. [13] and Liicke [14], which for copper gives the same kind of extensive local texture data as EBSP. The experimental plan requires a knowledge of the orientation of the environment of the cube subgrains in the as-rolled structures. In principle this is peculiarly simple in the case of cube cells, for they are extensive in the microstructure, often greater than 50/tm in length, and consist of between one and six cells in thickness, i.e. the bands are 1-4 # m in width [15, 16]. Secondly the plan requires light annealing to such an extent that "successful" cube nuclei develop into well established recrystallised grains, but not to such a size that impingement with other grains occurs. Then the microstructure is searched for "unsuccessful" cube oriented cells, which are also analysed in terms of local orientation relationships. Finally comparison of both sets of data yields information on the orientation neighbourhoods of the successful cube nuclei. From this it is possible to discuss ON and OG rather different terms to those which have been possible previously. 2. EXPERIMENTAL
In order to exclude the possibility that the results might be specific to a certain type of copper, three different types labelled as A (originating in Australia), B (originating in Germany) and C (originating in the U.S.A.) were used. Type A was O F H C copper supplied in the form of hot rolled plate of a thickness of 9 mm and of an initial grain size of 50/tm. This was cold rolled to 92% reduction on a 2 High mill using paraffin lubricant, with care being taken to ensure plane strain deformation over most of the rolling procedure. Annealing was carried out for A at either 300°C for complete recrystallisation or in boiling water for various periods to obtain partial recrystallisation of cube grains, yet without impingement of these grains. Types B and C were high purity copper supplied as cold rolled 90% sheet of between 1 and 2 mm in thickness and these were annealed at various temperatures in an oil bath. The experimental details regarding preparation and
performance are to be found in Ref. [16] for B and [17] for C. Macro textures were measured by X-rays using the back reflection technique. For local texture measurement a crystallographic etching technique developed by Krhlhoff et al. [13] and LiJcke [14] ( K - L etching technique) suitable for Cu and Cu-base alloys was used. It consists of etching in concentrated nitric acid by which 111 planes are most slowly attacked and hence revealed. A schematic diagram, Fig. 1, shows how a 110 oriented grain appears after etching, together with a more general diagram indicating the principles of orientation determination. The etched samples were examined using secondary electron contrast in SEM. Since the spatial resolution of the etch is about 1/~m, bands of this thickness can be analysed with reasonable accuracy using a SEM. The orientation resolution depends on the orientation, being ~ 5 ° over most of the unit triangle, but if a known texture component is analysed by sectioning techniques, the accuracy increases to ~ 2 °. Thus this technique is not as precise as EBSP, but it does have the advantage of not requiring a low dislocation density for providing orientation information, as does EBSP, so that recovery annealing was not necessary in this experiment. Furthermore, this etch allows the orientations of a large area of the microstructure to be analysed and so to distinguish the selectivities of nucleation and of growth. Cube oriented crystals in longitudinal sections ("LS") have { 100} faces which etch as densely packed pyramids yielding a very poor angular resolution. To solve this problem, specimens were cut and polished at 45 ° to the rolling plane and the longitudinal surface (i.e. LS 45 ° surface), and in this face {100} planes belonging to the cube component were revealed as parallel lines on that surface perpendicular to the projected rolling plane surface similar to those shown in Fig. l(b), but rotated 90 ° about the viewing axis. Montages of micrographs taken at 3000X were prepared from four different specimens, the montages reaching from surface to surface. These were scanned, cube areas located and cube neighbourhoods characterized. In a few cases the results were ambiguous and these were discarded. 3. RESULTS Pole figures revealed that all the rolling textures of the three coppers were practically identical and similar to those published elsewhere and after annealing all three materials gave strong cube texture in excess of 20X random, the actual value depending on the rolling strain. Figure 2 shows the cold rolled microstructure after K - L etching the longitudinal section (LS) of copper B after cold rolling 95%. Some common orientations are labelled according to the scheme outlined by Hirsch and L/icke [18], for example the volume labelled B/G is close to Brass
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R~
°
(a)
(b)
(c)
(d) Fig. 1. (a) Stereographic projection showing {110} (001), (b) SEM micrograph of crystallographically etched copper {110} (001) as seen in the rolling plane, (c) schematic diagram of ideal, (d) actual surface relief of 110 crystal face after etching to expose 111 planes.
{110}(112) but rotated towards Goss {110}(001), and the G,B volume is close to Goss but rotated towards Brass and C is the Copper orientation, { 112} ( 111 ). A cube oriented layer is located between the B/G and C volumes. Since in the longitudinal section (LS 0 °) a cube grain exhibits {100} faces and thus cannot be precisely analysed, Fig. 2, the LS 45 ° faces were examined. Figure 3 shows an example of such sectioning of B copper after 100 s annealing at 140°C, and the cube grain is clearly seen in an unrecrystallised
Fig. 2. Copper B, cold rolled 95% and crystallographically etched longitudinal section (LS 0°) showing a cube oriented layer sandwiched between C and B/G volumes.
matrix. Here the large cube grain has grown in the N D direction to a thickness of ~ 2 0 ÷ ~/2 ~ 14/tm, and as can be seen from the scale of the microstructure revealed in Fig. 2, this is equivalent to a growth range of several original grain thicknesses. The A and C coppers showed very similar behaviour after light annealing. For quantitative evaluations, the misorientations between the non-developed cube layers and the neighbouring layers were measured for the partially annealed state and compared to such measurements for the cold worked state. For this investigation copper A was used for it had the advantages of good etching characteristics coupled with being available in relatively large amounts. Figure 4 shows a typical cold rolled microstructure after crystallographic etching of the LS/45 ° section. A well developed cube layer towards the top of the micrograph is ~4/~m thick and greater than 60 #m in length contained between two differently oriented layers, the orientations of which are shown and are close to a +30 ° (110). These adjacent layers and about another 50 pairs existing either side of the cube bands were sorted into about 25 types of etch pattern, and further analysed into sets characterised by a common direction and an angular range. The results are shown in Table 1. The most frequent common directions were (111) and (110) occurring for 60% of the cube layers. The remaining
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Common axis (15°-60°) (I 10) (25°-40°) (111) Others Total
Table I Cold rolled (No. of layers) 34 36 48 118
Partiallyannealed (No. of layers) 35 1 22 48
maximum variation from the measured "cube" position to the common (111) pole of the neighbouring material is frequently found, a result which is further considered in Section 4. 4. DISCUSSION
40% could not be classified in either of these ways and they also had little in common with each other. Copper A was annealed at 100°C for 60 min in order to produce a microstructure similar to that of the lightly annealed Copper B, shown in Fig. 3. The unrecrystallised, i.e. non-developed cube areas were then searched for and their misorientation were measured in the same way as for the cube in the as-rolled material. The results are also shown in Table 1 and it is clear that partial annealing has removed all of the non-developed subgrains which shared at least one neighbour related by a (25°-40 °) (111) rotation, and as a proportion, the group characterised as "others" is relatively unchanged. Finally, it must be stated that the accuracy of the orientation descriptions given in Table 1 vary with the rotation axis. In particular the description of the orientation relationship as a (110) rotation is very good, of the order of the resolution of the K - L etch. This is not so for the (111) rotation, where 8°-!0 °
The K - L crystallographic etch of the L/S plane revealed the orientation topography of cold rolled copper as highly organised interleaving layers distinguishable from each other by sharp changes in orientation along the ND direction, Fig. 2. Parallel to RD in this plane, orientation changes more slowly along what are presumably the original grains. There is evidence of severe lattice curvature within some layers, a good example is the near-cube layer sharing a common boundary with the developed cube grain in Fig. 3. This rotated cube layer appears to have effectively stopped the migration of the cube grain boundary. The essentially new data in Table 1 has profound significance for the ON and OG theories but before discussing the new results it is necessary to briefly review these theories. Both have been exhaustively examined in the past 7 years and so much historical work considered in the earlier articles [6,12,19,20] is not recounted here.
Fig. 3. S.E. micrograph of copper B, cold rolled 95% and annealed for 100 s at 140°C;section 45° to rolling plane and micron member parallel to RD (LS 45°) crystallographicallyetched. The montage of the cube recrystallised grain joins at the arrows, and rotated cube material is located at the lower right half of the recrystallised grain.
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Fig. 4. LS 45 ~ of copper A. after cold rolling 92%, crystallographically etched. The cube volume is sandwiched between layers of material rotated +__30° about a common (110) axis. This and similar data are summarised in Table 1. Oriented nucleation is loosely defined as the idea that recrystallisation textures develop by preferential nucleation of new grains that have a narrow range of orientation. To metallographers or texture workers the significant event is the development of a nucleus possessing the orientation of a grain or of a main texture component present in the final microstructure, while to an electron microscopist it is the development of a low energy block of material in a high energy matrix. They are not necessarily the same thing [5]. The most successful attempt to put ON on a firm theoretical basis is the Dillamore and Katoh (DK) theory [21]. It identifies certain divergent orientations which by further deformation, rotate in two different ways towards alternative end orientations. These two orientations are then linked by a transition band which is a nucleation site. This theory successfully predicted some b.c.c, recrystallisation textures and also explains the presence of significant amounts of cube in the rolling texture of high SFE f.c.c, metals. Nucleus orientations (i.e. orientations which form transition bands) are predicted to lie in the zone between cube and Goss positions which corresponds with the observed scattering of the cube in recrystallisation textures [5, 22] and which has been confirmed in plane strain single crystal work by Akef and Driver [23]. Also the unexpectedly high cube grain density found in partially recrystallised polycrystalline aluminium is explained by the suggestion [6] that any grain belonging before deformation to the (001) ND fibre, will split and rotate around the normal and transverse directions in such a way that the cube orientation will be stabilised at the centre of the orientation spread. The remaining question as to why cube, rather than any other transition band subgrains, are nuclei is related to size and relative stored energy. In general, if a subgrain is surrounded by a higher than average misorientation, then it must be larger than average [24]. Therefore although subgrain boundaries are here made up of geometrically necessary dislocations
[25], a transition band nucleus is still distinguished from its neighbouring subgrain by its relative size, which, in turn is a matter of chance, depending on the details of the initial local conditions. Ridha and Hutchinson [15] supported these ideas by detecting elongated cube oriented volumes of low dislocation density in transition bands and by realising that cube volumes have a lower hardening rate since the Burgers vectors of the four active slip systems are orthogonal to each other, which ensures that no interactions between the corresponding dislocations of the four active slip systems occur. These cube volumes are thus inherently low energy blocks. Their plate-like shape has the additional advantage of providing ideal geometry for nucleation by bulge formation [26]. It is thus clea~: that on this view of what comprises the nucleus and ON should satisfy both the texture worker and microscopist interested in the origin of cube texture. OG theory states that grains with a special orientation relationship with the deformed matrix will have a growth rate that is larger than the growth rate of randomly oriented grains, and that the recrystallisation texture is the result of competition between many nuclei having a variety of growth rates into the main deformation texture components. For this theory the evidence, largely supplied by the Aachen school [3, 4, 27], is very strong in lightly deformed single crystals which have been abraded at one end to give many randomly oriented nuclei [3, 28] and in many other single crystal recrystallisation experiments. The main result is that for f.c.c, metals maximum mobility is found for both primary and secondary recrystallisation, when the migrating boundary has a misorientation of 30°-40 ° (111 ). For polycrystals the situation is less clear although also here in many cases a 30°-40 ° (111) relationship indicates OG. Specifically, it must be recognised that a cube grain has a 40 ° (111) orientation relationship to the S orientation which is often the main component of the rolling texture. In other circumstances
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as observed in A1, when the matrix consists not of an S- but a C-orientation, the resulting component is shifted towards an orientation having a 40 ° (111) relationship with respect to C [29]. But there still exists the problem of variant selection. Generally not all of the 8 possible 0 (111) rotations are found in the recrystallisation texture. This has led the Aachen group to ascribe recrystallisation texture as arising from the availability of nuclei, which is a combined theory of O G / O N [4]. Such a combination was proposed in early work by Beck to explain cube texture development [2] and was later applied by other authors. More recently, Duggan et al. [ 16] discussed their HVEM results from heavily deformed large grain sized copper also in terms of a combined O N / O G frame work using the term micro-growth selection introduced by Liicke et al. in early b.c.c, work [3]. Liicke and Engler [30] used this concept in order to successfully interpret their results on particle containing A1 alloys, and also Akef e t al. [29] needed both O G and ON to explain their single crystal experiments. This combined O N / O G approach removes the variant selection problem and weakens the 0 (111) requirement with the general texture by distinguishing between global orientation distributions (i.e. those comprising the sample) and local orientation distributions (i.e. those of the crystallites immediately surrounding a particular nucleus). However these combined theories were merely other attempts to explain cube texture formation and, for the reasons given in the Introduction, clearly remained incapable of disproof of OG if the experimental approach was not radically altered. Turning now to Table 1, it is clear that, upon partial annealing, those cube subgrains of the deformed state which possess a 300-40 ° (111) relationship to one of their neighbours do not stay in the non-developed state, but develop, i.e. they form a cube nucleus, whereas the cube bands without such neighbours, i.e. without a high mobility 0 (111) boundary, are not able to grow. This is prima facie evidence that micro-growth selection is occurring. The question arises as to whether the ON theory can also be used to explain the results in Table 1. In a directionally solidified material consisting of mm scale grains Hjelen et al. [6] found relatively few growing grains which possessed a 40 ° (111 ) relationship to the matrix. These grains were all separated from each other. From this they reasoned that because only grains with a 400 (111) relationship were growing, and no others, their success could not be the result of growth competition so that OG could be ruled out. Instead they found heterogeneities and shear bands with a core substructure having a 40 ° (111) orientation relationship to the surrounding matrix. Assuming that these heterogeneities are nucleation sites they concluded that a 40 ° (111) orientation relationship confirms an ON mechanism rather than OG.
It is difficult to compare the aluminium results of Hjelen et al. [6] with the copper results presented here for in the copper only cube and near cube oriented material nucleates. To establish that no general nucleation had occurred, it was necessary to use TEM on edge sections, and these showed that the microstructure of the cold rolled material was almost indistinguishable from that after annealing in boiling water. Hence the results in Table 1 cannot be treated as confirming ON, for cube is associated with many different orientation environments, but only certain of them provide nuclei. Hence the micro-growth selection process postulated in [16] is a valid description of cube texture formation in copper, however else the same process may be described. It is necessary to note that elongated cube subgrains which are incapable of nucleation due to the orientations of their neighbours, provide barriers to the migration of growing cube grains. This appears to be the case in Fig. 3, in which a rotated cube deformed lattice growing cube grain meets and migration is effectively stopped, a result which is expected since low angle boundaries are of low mobility. Concerning the accuracy of the description of the orientation relationships between cube and its surroundings by (110) or (111) rotations (see Section 3), deviations from ideality have been commonly observed. But these mostly concern relationships between the initial and final texture. These are discussed by Hatherly [20] who considers impurities to be responsible, arising from the well-known influence on grain boundary mobility. The evidence presented here is that the departures from ideality are a feature of cube oriented grains with respect to the material into which they grow. But the observed difference, large scattering of (111) poles and precise correspondence for (110) poles, is not yet understood. It must have to do with the formation mechanism of cube oriented material. For example, if it is accepted that cube precursor orientations lie in the (110) ND fibre then orientation splitting of the various orientations of this fibre during deformation leads to cube orientations differently oriented with respect to their surroundings as proposed in detail in [23] and [6]. Even if this model is correct it is clear from Table 1 that this does not form cube nuclei in copper by the time cube grains have grown extensively. 5. CONCLUSIONS A crystallographic etch in which 111 planes are exposed in copper has been used to determine the orientations of the neighbouring substructures surrounding cube oriented microbands in heavily cold rolled copper. From these measurements it is shown that: (i) cube oriented microbands have a variety of orientation neighbourhoods;
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(ii) there remains, after nucleation and growth of cube grains without impingement, a set of cube oriented microbands showing no development; (iii) the undeveloped cube volumes have a variety of orientation environments but not those characterised by a 0 (111) orientation relationship, by growth these have declined from ~ 30% of the total to almost zero. F r o m these observations it is concluded that the oriented growth theory of cube texture formation is the most appropriate explanation for the origin of cube nuclei in heavily rolled copper. Because the process is seen to operate at the earliest stages of recrystallisation, the term micro-growth selection is a better description of what has been observed. Furthermore, the distinction between local and global orientation distributions is of vital importance in understanding the cube recrystallisation process, and explains some of the problems found in earlier work where there was no obvious 0 ° (111 ) relationship between the deformation texture and the cube recrystallisation texture. authors thank the Croucher Foundation for the provision of electron microscope facilities, and for a Studentship and Fellowship for Dr Lee. Also the authors are grateful to Dr O. Engler and Mr M. Sindel for valuable discussions. Finally they acknowledge financial support given by the Deutsche Forshungsgemeinschaft. Acknowledgements--The
REFERENCES
I. C. S. Barrett, Trans. Am. Inst. Min. Engrs 137, 128 (1940). 2. P. A. Beck, Adv. Phys. 3, 245 (1953). 3. G. Ibe and K. L6cke, in Recrystallisation, Grain Growth and Textures (edited by H. Margolin), p. 434. Am. Soc. Metals, Metals Park, Ohio (1966). 4. U. Schmidt, K. Liicke and J. Pospiech, 4th Int. Conf. on Textures o f Materials (edited by G. J. Davies), p. 147. The Metals Society, London (1976). 5. K. Liicke, 7th Int. Conf. on Textures o f Materials, Zwizndrecht (edited by C. M. Brakman, P. Jongenberger and E. J. Mittemeijer), p. 195. Netherlands Soc. Materials Sci. (1984).
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6. J. Hjelen, R. Orsund and E. Nes, Acta metall, mater. 39, 1377 (1991). 7. J. A. Venables and C. J. Harland, Phil. Mag. 27, 1193 (1973). 8. D. J. Dingley, 8th Int. Conf. on Textures o f Materials, Santa Fe (edited by J. S. Kallend and G. Gottstein), p. 189. The Metallurgical Society of AIME (1988). 9. H. Hu, Textures in Research and Practice, Clausthal (edited by J. Grewen and G. Wassermann), p. 200. Springer, Berlin (1969). 10. R. K. Ray, W. B. Hutchinson and B. J. Duggan, Acta metall. 23, 831 (1975). 11. C. J. E. Smith and I. L. Dillamore, Metall. Sci. J. r, 161 (1970). 12. A. Berger, P. J. Wilbrandt, F. Ernst, U. Klement and P. Haasen, Prog. Mater. Sci. 32, 1 (1988). 13. G. D. Krhlhoff, X. Sun and K. Liicke, in Ref. [8], p. 183. 14. K. Lficke, in Electron Microscopy in Plasticity and Fracture Research o f Materials (edited by U. Messerschidt et al.), p. 33. Akademie, Berlin (1990). 15. A. A. Ridha and W. B. Hutchinson, Acta metall. 30, 1929 (1982). 16. B. J. Duggan, M. Sindel, G. D. K6hlhoffand K. L/icke, Acta metall, mater. 38, 103 (1990). 17. C. Necker, R. D. Doherty and A. D. Rollett, Text. Microstruc. 14--18, 635 (1992). 18. J. Hirsch and K. Liicke, Acta metall. 36, 2863 (1988). 19. R. D. Doherty, G. Gottstein, J. Hirsch, W. B. Hutchinson, K. Liicke, E. Nes and P. J. Wilbrandt, in Ref. [8], p. 563. 20. M. Hatherly, in Ref. [7], p. 59. 21. I. L. Dillamore and H. Kato, Metal Sci. 8, 73 (1974). 22. J. Hirsch and K. Liicke, Acta metall. 33, 1927 (1985). 23. A. Akef and J. H. Driver, Mater. Sci. Engng, in press. 24. R. D. Doherty, in 1st Ris~ Int. Syrup. on Metals and Materials Science (edited by N. Hansen, A. R. Jones and T. Leffers), p. 57 (1980). 25. I. L. Dillamore, P. L. Morris, C. J. E. Smith and W. B. Hutchinson, Proc. R. Soc. A 329, 405 (1972). 26. J. E. Bailey and P. B. Hirsch, Proc. R. Soc. A 267, I1 (1962). 27. J. Hirsch, in 7th Ris~ Int. Symp. on Metals and Materials Science (edited by N. Hansen et al.), pp. 349-361 (1986). 28. G. Ibe, W. Dietz, A.-C. Fraker and K. Liicke, Z. Metallk. 61, 498 (1970). 29. A. Akef, R. Fortunier, J. H. Driver and T. Watanabe, Text. Microstruct. 14-18, 617 (1992). 30. K. Liicke and O. Engler, Mater. Sci. Technol. 6, 1113 (1990).
0956-7151/93 $6.00 + 0.00 Copyright © 1993 Pergamon Press Ltd
ON THE ORIGIN OF CUBE TEXTURE IN COPPER B. J. D U G G A N , t K. L ~ C K E , 2 G. K ( ~ H L H O F F 2 and C. S. LEE 3
Department of Mechanical Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, 21nstitut ftir Metallkunde und Metallphysik, RWTH, Aachen, Kopernikusstr. 14, D-5100, Aachen, Germany and 3School of Metallurgy and Materials, University of Birmingham, B15 2TT, England (Received 13 July 1992)
A~traet--A crystallographic etch in which 111 planes are exposed in copper has been used to determine the orientation of the neighbouring substructures surrounding cube oriented microbands in heavily cold rolled copper. These, after characterisation into orientation groups, were compared with the neighbourhoods of undeveloped cube oriented microbands in lightly annealed material in which almost all well developed recrystallised grains were of cube orientation. By inspection of the two sets of orientation neighbourhoods it is demonstrated that only cube microbands surrounded by material with a 0 ° (111 ) orientation relationship provide cube nuclei. Thus the cube texture arises from competition between nuclei in a variety of orientation environments, the successfulnuclei having environments into which they initially grow characterised by a 0 ° (111) relationship. The process is best described as micro-growth selection, in which the local texture determines the viability and competitive advantage of nuclei, while the global deformation texture (i.e. that determined by traditional diffraction methods) is that which is consumed by those nuclei, with the possibility of further growth selection as recrystallisation proceeds.
1. INTRODUCTION It is a remarkable fact that after almost six decades of research in textures, the sharpest of all textures, the cube texture in copper, is still lacking an explanation which commands general support. Theories of oriented growth (OG), of oriented nucleation (ON-) or a combination of both were proposed long ago by Barrett [1] and Beck [2]. Presently, the strongest advocates of the OG theory are associated with the Aachen school [3-5], while the majority of modern workers could be said to follow the ON theory, of which the most recent substantial example is due to Hjelen et al. [6]. These authors demonstrated the power of the electron backscatter pattern (EBSP) technique [6-8] which allows local orientations to be measured point by point in their modified SEM with an orientation resolution within a degree and a spatial resolution claimed to be < 1/~m. Patterns are degraded if the crystals are heavily dislocated. Fundamentally the information given by this technique is identical to that derived from methods available in TEM, STEM or HVEM, but the large contiguous areas available using surface scanning techniques makes EBSP undoubtedly superior for point to point texture measurement. Exploiting this advantage, Hjelen et al. [6] investigated in great detail the microstructure of cold rolled and partially annealed chili-cast aluminium. They measured the orientation of the material in which cube grains were growing and concluded that cube oriented grains in aluminium are nucleated from transition bands preferentially located in [112] (111 ) (i.e. C) oriented grains or ND rotated C. Of the two theories of cube texture formation, ON or OG, only OG specified a particular
relationship between cube and its deformed neighbourhood, and it claims that for maximum growth rate in fairly pure f.c.c, metals the grain consumed needs to be misoriented to cube by a 300-40 ° rotation about a common (111) axis. As C and cube do not share a common (111 ) direction, these authors ruled out OG as a dominent mechanism for cube texture origin. On reflection it is startling that the EBSP technique is claimed to have resolved all the major problems to do with cube texture formation, because the experimental design is similar to that adopted by many other workers (e.g. [9-11]) and so the information gained can only be of similar nature. While conceding that the EBSP data in [6] is the best available for this kind of experiment, the authors of the present work consider that this and all similar experiments, in principle, cannot resolve the arguments between the ON and OG theories. The weakness lies in the fact that successful nucleation destroys both the evidence of the nucleus state as well as its neighbourhood, since the nucleus in question has already consumed its original neighbours. Therefore, processes like "micro-growth selection", introduced many years ago by Liicke et al. [3], cannot be checked, and much of the literature in which nucleus-matrix orientation relationships have apparently been measured, might be wrong. On the other hand, if only the deformed state is examined, then it is not possible to conclude anything other than whether cube is contained in such things as transition bands, but such volumes might not act as nuclei. What is needed to advance discussion on the relative merits of ON or OG are different kinds of experiments, namely those in which the evidence of
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the nucleus and its surroundings is not destroyed. One direct approach to the general problem of nucleation is to continuously follow the transformation from the deformed state to the recrystallised condition in a hot stage of a high voltage electron microscope as recently reported by Berger et al. [12] in tensile deformed aluminium single crystals. However, the validity of this kind of experiment is still subject to debate because it is unclear as to how the relatively large foil surface energies compared to the intercrystalline energies involved in nucleation and growth affects the recrystallisation process. The present work attempts to solve the philosophical problem of the "destroyed evidence" implicit in all experiments similar to those performed by Hjelen et al. [6], by using a crystallographic etch introduced by Krhlhoff et al. [13] and Liicke [14], which for copper gives the same kind of extensive local texture data as EBSP. The experimental plan requires a knowledge of the orientation of the environment of the cube subgrains in the as-rolled structures. In principle this is peculiarly simple in the case of cube cells, for they are extensive in the microstructure, often greater than 50/tm in length, and consist of between one and six cells in thickness, i.e. the bands are 1-4 # m in width [15, 16]. Secondly the plan requires light annealing to such an extent that "successful" cube nuclei develop into well established recrystallised grains, but not to such a size that impingement with other grains occurs. Then the microstructure is searched for "unsuccessful" cube oriented cells, which are also analysed in terms of local orientation relationships. Finally comparison of both sets of data yields information on the orientation neighbourhoods of the successful cube nuclei. From this it is possible to discuss ON and OG rather different terms to those which have been possible previously. 2. EXPERIMENTAL
In order to exclude the possibility that the results might be specific to a certain type of copper, three different types labelled as A (originating in Australia), B (originating in Germany) and C (originating in the U.S.A.) were used. Type A was O F H C copper supplied in the form of hot rolled plate of a thickness of 9 mm and of an initial grain size of 50/tm. This was cold rolled to 92% reduction on a 2 High mill using paraffin lubricant, with care being taken to ensure plane strain deformation over most of the rolling procedure. Annealing was carried out for A at either 300°C for complete recrystallisation or in boiling water for various periods to obtain partial recrystallisation of cube grains, yet without impingement of these grains. Types B and C were high purity copper supplied as cold rolled 90% sheet of between 1 and 2 mm in thickness and these were annealed at various temperatures in an oil bath. The experimental details regarding preparation and
performance are to be found in Ref. [16] for B and [17] for C. Macro textures were measured by X-rays using the back reflection technique. For local texture measurement a crystallographic etching technique developed by Krhlhoff et al. [13] and LiJcke [14] ( K - L etching technique) suitable for Cu and Cu-base alloys was used. It consists of etching in concentrated nitric acid by which 111 planes are most slowly attacked and hence revealed. A schematic diagram, Fig. 1, shows how a 110 oriented grain appears after etching, together with a more general diagram indicating the principles of orientation determination. The etched samples were examined using secondary electron contrast in SEM. Since the spatial resolution of the etch is about 1/~m, bands of this thickness can be analysed with reasonable accuracy using a SEM. The orientation resolution depends on the orientation, being ~ 5 ° over most of the unit triangle, but if a known texture component is analysed by sectioning techniques, the accuracy increases to ~ 2 °. Thus this technique is not as precise as EBSP, but it does have the advantage of not requiring a low dislocation density for providing orientation information, as does EBSP, so that recovery annealing was not necessary in this experiment. Furthermore, this etch allows the orientations of a large area of the microstructure to be analysed and so to distinguish the selectivities of nucleation and of growth. Cube oriented crystals in longitudinal sections ("LS") have { 100} faces which etch as densely packed pyramids yielding a very poor angular resolution. To solve this problem, specimens were cut and polished at 45 ° to the rolling plane and the longitudinal surface (i.e. LS 45 ° surface), and in this face {100} planes belonging to the cube component were revealed as parallel lines on that surface perpendicular to the projected rolling plane surface similar to those shown in Fig. l(b), but rotated 90 ° about the viewing axis. Montages of micrographs taken at 3000X were prepared from four different specimens, the montages reaching from surface to surface. These were scanned, cube areas located and cube neighbourhoods characterized. In a few cases the results were ambiguous and these were discarded. 3. RESULTS Pole figures revealed that all the rolling textures of the three coppers were practically identical and similar to those published elsewhere and after annealing all three materials gave strong cube texture in excess of 20X random, the actual value depending on the rolling strain. Figure 2 shows the cold rolled microstructure after K - L etching the longitudinal section (LS) of copper B after cold rolling 95%. Some common orientations are labelled according to the scheme outlined by Hirsch and L/icke [18], for example the volume labelled B/G is close to Brass
DUGGAN et al.: CUBE TEXTURE IN COPPER
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R~
°
(a)
(b)
(c)
(d) Fig. 1. (a) Stereographic projection showing {110} (001), (b) SEM micrograph of crystallographically etched copper {110} (001) as seen in the rolling plane, (c) schematic diagram of ideal, (d) actual surface relief of 110 crystal face after etching to expose 111 planes.
{110}(112) but rotated towards Goss {110}(001), and the G,B volume is close to Goss but rotated towards Brass and C is the Copper orientation, { 112} ( 111 ). A cube oriented layer is located between the B/G and C volumes. Since in the longitudinal section (LS 0 °) a cube grain exhibits {100} faces and thus cannot be precisely analysed, Fig. 2, the LS 45 ° faces were examined. Figure 3 shows an example of such sectioning of B copper after 100 s annealing at 140°C, and the cube grain is clearly seen in an unrecrystallised
Fig. 2. Copper B, cold rolled 95% and crystallographically etched longitudinal section (LS 0°) showing a cube oriented layer sandwiched between C and B/G volumes.
matrix. Here the large cube grain has grown in the N D direction to a thickness of ~ 2 0 ÷ ~/2 ~ 14/tm, and as can be seen from the scale of the microstructure revealed in Fig. 2, this is equivalent to a growth range of several original grain thicknesses. The A and C coppers showed very similar behaviour after light annealing. For quantitative evaluations, the misorientations between the non-developed cube layers and the neighbouring layers were measured for the partially annealed state and compared to such measurements for the cold worked state. For this investigation copper A was used for it had the advantages of good etching characteristics coupled with being available in relatively large amounts. Figure 4 shows a typical cold rolled microstructure after crystallographic etching of the LS/45 ° section. A well developed cube layer towards the top of the micrograph is ~4/~m thick and greater than 60 #m in length contained between two differently oriented layers, the orientations of which are shown and are close to a +30 ° (110). These adjacent layers and about another 50 pairs existing either side of the cube bands were sorted into about 25 types of etch pattern, and further analysed into sets characterised by a common direction and an angular range. The results are shown in Table 1. The most frequent common directions were (111) and (110) occurring for 60% of the cube layers. The remaining
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DUGGAN et aL: CUBE TEXTURE IN COPPER
Common axis (15°-60°) (I 10) (25°-40°) (111) Others Total
Table I Cold rolled (No. of layers) 34 36 48 118
Partiallyannealed (No. of layers) 35 1 22 48
maximum variation from the measured "cube" position to the common (111) pole of the neighbouring material is frequently found, a result which is further considered in Section 4. 4. DISCUSSION
40% could not be classified in either of these ways and they also had little in common with each other. Copper A was annealed at 100°C for 60 min in order to produce a microstructure similar to that of the lightly annealed Copper B, shown in Fig. 3. The unrecrystallised, i.e. non-developed cube areas were then searched for and their misorientation were measured in the same way as for the cube in the as-rolled material. The results are also shown in Table 1 and it is clear that partial annealing has removed all of the non-developed subgrains which shared at least one neighbour related by a (25°-40 °) (111) rotation, and as a proportion, the group characterised as "others" is relatively unchanged. Finally, it must be stated that the accuracy of the orientation descriptions given in Table 1 vary with the rotation axis. In particular the description of the orientation relationship as a (110) rotation is very good, of the order of the resolution of the K - L etch. This is not so for the (111) rotation, where 8°-!0 °
The K - L crystallographic etch of the L/S plane revealed the orientation topography of cold rolled copper as highly organised interleaving layers distinguishable from each other by sharp changes in orientation along the ND direction, Fig. 2. Parallel to RD in this plane, orientation changes more slowly along what are presumably the original grains. There is evidence of severe lattice curvature within some layers, a good example is the near-cube layer sharing a common boundary with the developed cube grain in Fig. 3. This rotated cube layer appears to have effectively stopped the migration of the cube grain boundary. The essentially new data in Table 1 has profound significance for the ON and OG theories but before discussing the new results it is necessary to briefly review these theories. Both have been exhaustively examined in the past 7 years and so much historical work considered in the earlier articles [6,12,19,20] is not recounted here.
Fig. 3. S.E. micrograph of copper B, cold rolled 95% and annealed for 100 s at 140°C;section 45° to rolling plane and micron member parallel to RD (LS 45°) crystallographicallyetched. The montage of the cube recrystallised grain joins at the arrows, and rotated cube material is located at the lower right half of the recrystallised grain.
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Fig. 4. LS 45 ~ of copper A. after cold rolling 92%, crystallographically etched. The cube volume is sandwiched between layers of material rotated +__30° about a common (110) axis. This and similar data are summarised in Table 1. Oriented nucleation is loosely defined as the idea that recrystallisation textures develop by preferential nucleation of new grains that have a narrow range of orientation. To metallographers or texture workers the significant event is the development of a nucleus possessing the orientation of a grain or of a main texture component present in the final microstructure, while to an electron microscopist it is the development of a low energy block of material in a high energy matrix. They are not necessarily the same thing [5]. The most successful attempt to put ON on a firm theoretical basis is the Dillamore and Katoh (DK) theory [21]. It identifies certain divergent orientations which by further deformation, rotate in two different ways towards alternative end orientations. These two orientations are then linked by a transition band which is a nucleation site. This theory successfully predicted some b.c.c, recrystallisation textures and also explains the presence of significant amounts of cube in the rolling texture of high SFE f.c.c, metals. Nucleus orientations (i.e. orientations which form transition bands) are predicted to lie in the zone between cube and Goss positions which corresponds with the observed scattering of the cube in recrystallisation textures [5, 22] and which has been confirmed in plane strain single crystal work by Akef and Driver [23]. Also the unexpectedly high cube grain density found in partially recrystallised polycrystalline aluminium is explained by the suggestion [6] that any grain belonging before deformation to the (001) ND fibre, will split and rotate around the normal and transverse directions in such a way that the cube orientation will be stabilised at the centre of the orientation spread. The remaining question as to why cube, rather than any other transition band subgrains, are nuclei is related to size and relative stored energy. In general, if a subgrain is surrounded by a higher than average misorientation, then it must be larger than average [24]. Therefore although subgrain boundaries are here made up of geometrically necessary dislocations
[25], a transition band nucleus is still distinguished from its neighbouring subgrain by its relative size, which, in turn is a matter of chance, depending on the details of the initial local conditions. Ridha and Hutchinson [15] supported these ideas by detecting elongated cube oriented volumes of low dislocation density in transition bands and by realising that cube volumes have a lower hardening rate since the Burgers vectors of the four active slip systems are orthogonal to each other, which ensures that no interactions between the corresponding dislocations of the four active slip systems occur. These cube volumes are thus inherently low energy blocks. Their plate-like shape has the additional advantage of providing ideal geometry for nucleation by bulge formation [26]. It is thus clea~: that on this view of what comprises the nucleus and ON should satisfy both the texture worker and microscopist interested in the origin of cube texture. OG theory states that grains with a special orientation relationship with the deformed matrix will have a growth rate that is larger than the growth rate of randomly oriented grains, and that the recrystallisation texture is the result of competition between many nuclei having a variety of growth rates into the main deformation texture components. For this theory the evidence, largely supplied by the Aachen school [3, 4, 27], is very strong in lightly deformed single crystals which have been abraded at one end to give many randomly oriented nuclei [3, 28] and in many other single crystal recrystallisation experiments. The main result is that for f.c.c, metals maximum mobility is found for both primary and secondary recrystallisation, when the migrating boundary has a misorientation of 30°-40 ° (111 ). For polycrystals the situation is less clear although also here in many cases a 30°-40 ° (111) relationship indicates OG. Specifically, it must be recognised that a cube grain has a 40 ° (111) orientation relationship to the S orientation which is often the main component of the rolling texture. In other circumstances
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DUGGAN et al.: CUBE TEXTURE IN COPPER
as observed in A1, when the matrix consists not of an S- but a C-orientation, the resulting component is shifted towards an orientation having a 40 ° (111) relationship with respect to C [29]. But there still exists the problem of variant selection. Generally not all of the 8 possible 0 (111) rotations are found in the recrystallisation texture. This has led the Aachen group to ascribe recrystallisation texture as arising from the availability of nuclei, which is a combined theory of O G / O N [4]. Such a combination was proposed in early work by Beck to explain cube texture development [2] and was later applied by other authors. More recently, Duggan et al. [ 16] discussed their HVEM results from heavily deformed large grain sized copper also in terms of a combined O N / O G frame work using the term micro-growth selection introduced by Liicke et al. in early b.c.c, work [3]. Liicke and Engler [30] used this concept in order to successfully interpret their results on particle containing A1 alloys, and also Akef e t al. [29] needed both O G and ON to explain their single crystal experiments. This combined O N / O G approach removes the variant selection problem and weakens the 0 (111) requirement with the general texture by distinguishing between global orientation distributions (i.e. those comprising the sample) and local orientation distributions (i.e. those of the crystallites immediately surrounding a particular nucleus). However these combined theories were merely other attempts to explain cube texture formation and, for the reasons given in the Introduction, clearly remained incapable of disproof of OG if the experimental approach was not radically altered. Turning now to Table 1, it is clear that, upon partial annealing, those cube subgrains of the deformed state which possess a 300-40 ° (111) relationship to one of their neighbours do not stay in the non-developed state, but develop, i.e. they form a cube nucleus, whereas the cube bands without such neighbours, i.e. without a high mobility 0 (111) boundary, are not able to grow. This is prima facie evidence that micro-growth selection is occurring. The question arises as to whether the ON theory can also be used to explain the results in Table 1. In a directionally solidified material consisting of mm scale grains Hjelen et al. [6] found relatively few growing grains which possessed a 40 ° (111 ) relationship to the matrix. These grains were all separated from each other. From this they reasoned that because only grains with a 400 (111) relationship were growing, and no others, their success could not be the result of growth competition so that OG could be ruled out. Instead they found heterogeneities and shear bands with a core substructure having a 40 ° (111) orientation relationship to the surrounding matrix. Assuming that these heterogeneities are nucleation sites they concluded that a 40 ° (111) orientation relationship confirms an ON mechanism rather than OG.
It is difficult to compare the aluminium results of Hjelen et al. [6] with the copper results presented here for in the copper only cube and near cube oriented material nucleates. To establish that no general nucleation had occurred, it was necessary to use TEM on edge sections, and these showed that the microstructure of the cold rolled material was almost indistinguishable from that after annealing in boiling water. Hence the results in Table 1 cannot be treated as confirming ON, for cube is associated with many different orientation environments, but only certain of them provide nuclei. Hence the micro-growth selection process postulated in [16] is a valid description of cube texture formation in copper, however else the same process may be described. It is necessary to note that elongated cube subgrains which are incapable of nucleation due to the orientations of their neighbours, provide barriers to the migration of growing cube grains. This appears to be the case in Fig. 3, in which a rotated cube deformed lattice growing cube grain meets and migration is effectively stopped, a result which is expected since low angle boundaries are of low mobility. Concerning the accuracy of the description of the orientation relationships between cube and its surroundings by (110) or (111) rotations (see Section 3), deviations from ideality have been commonly observed. But these mostly concern relationships between the initial and final texture. These are discussed by Hatherly [20] who considers impurities to be responsible, arising from the well-known influence on grain boundary mobility. The evidence presented here is that the departures from ideality are a feature of cube oriented grains with respect to the material into which they grow. But the observed difference, large scattering of (111) poles and precise correspondence for (110) poles, is not yet understood. It must have to do with the formation mechanism of cube oriented material. For example, if it is accepted that cube precursor orientations lie in the (110) ND fibre then orientation splitting of the various orientations of this fibre during deformation leads to cube orientations differently oriented with respect to their surroundings as proposed in detail in [23] and [6]. Even if this model is correct it is clear from Table 1 that this does not form cube nuclei in copper by the time cube grains have grown extensively. 5. CONCLUSIONS A crystallographic etch in which 111 planes are exposed in copper has been used to determine the orientations of the neighbouring substructures surrounding cube oriented microbands in heavily cold rolled copper. From these measurements it is shown that: (i) cube oriented microbands have a variety of orientation neighbourhoods;
DUGGAN et al.:
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(ii) there remains, after nucleation and growth of cube grains without impingement, a set of cube oriented microbands showing no development; (iii) the undeveloped cube volumes have a variety of orientation environments but not those characterised by a 0 (111) orientation relationship, by growth these have declined from ~ 30% of the total to almost zero. F r o m these observations it is concluded that the oriented growth theory of cube texture formation is the most appropriate explanation for the origin of cube nuclei in heavily rolled copper. Because the process is seen to operate at the earliest stages of recrystallisation, the term micro-growth selection is a better description of what has been observed. Furthermore, the distinction between local and global orientation distributions is of vital importance in understanding the cube recrystallisation process, and explains some of the problems found in earlier work where there was no obvious 0 ° (111 ) relationship between the deformation texture and the cube recrystallisation texture. authors thank the Croucher Foundation for the provision of electron microscope facilities, and for a Studentship and Fellowship for Dr Lee. Also the authors are grateful to Dr O. Engler and Mr M. Sindel for valuable discussions. Finally they acknowledge financial support given by the Deutsche Forshungsgemeinschaft. Acknowledgements--The
REFERENCES
I. C. S. Barrett, Trans. Am. Inst. Min. Engrs 137, 128 (1940). 2. P. A. Beck, Adv. Phys. 3, 245 (1953). 3. G. Ibe and K. L6cke, in Recrystallisation, Grain Growth and Textures (edited by H. Margolin), p. 434. Am. Soc. Metals, Metals Park, Ohio (1966). 4. U. Schmidt, K. Liicke and J. Pospiech, 4th Int. Conf. on Textures o f Materials (edited by G. J. Davies), p. 147. The Metals Society, London (1976). 5. K. Liicke, 7th Int. Conf. on Textures o f Materials, Zwizndrecht (edited by C. M. Brakman, P. Jongenberger and E. J. Mittemeijer), p. 195. Netherlands Soc. Materials Sci. (1984).
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6. J. Hjelen, R. Orsund and E. Nes, Acta metall, mater. 39, 1377 (1991). 7. J. A. Venables and C. J. Harland, Phil. Mag. 27, 1193 (1973). 8. D. J. Dingley, 8th Int. Conf. on Textures o f Materials, Santa Fe (edited by J. S. Kallend and G. Gottstein), p. 189. The Metallurgical Society of AIME (1988). 9. H. Hu, Textures in Research and Practice, Clausthal (edited by J. Grewen and G. Wassermann), p. 200. Springer, Berlin (1969). 10. R. K. Ray, W. B. Hutchinson and B. J. Duggan, Acta metall. 23, 831 (1975). 11. C. J. E. Smith and I. L. Dillamore, Metall. Sci. J. r, 161 (1970). 12. A. Berger, P. J. Wilbrandt, F. Ernst, U. Klement and P. Haasen, Prog. Mater. Sci. 32, 1 (1988). 13. G. D. Krhlhoff, X. Sun and K. Liicke, in Ref. [8], p. 183. 14. K. Lficke, in Electron Microscopy in Plasticity and Fracture Research o f Materials (edited by U. Messerschidt et al.), p. 33. Akademie, Berlin (1990). 15. A. A. Ridha and W. B. Hutchinson, Acta metall. 30, 1929 (1982). 16. B. J. Duggan, M. Sindel, G. D. K6hlhoffand K. L/icke, Acta metall, mater. 38, 103 (1990). 17. C. Necker, R. D. Doherty and A. D. Rollett, Text. Microstruc. 14--18, 635 (1992). 18. J. Hirsch and K. Liicke, Acta metall. 36, 2863 (1988). 19. R. D. Doherty, G. Gottstein, J. Hirsch, W. B. Hutchinson, K. Liicke, E. Nes and P. J. Wilbrandt, in Ref. [8], p. 563. 20. M. Hatherly, in Ref. [7], p. 59. 21. I. L. Dillamore and H. Kato, Metal Sci. 8, 73 (1974). 22. J. Hirsch and K. Liicke, Acta metall. 33, 1927 (1985). 23. A. Akef and J. H. Driver, Mater. Sci. Engng, in press. 24. R. D. Doherty, in 1st Ris~ Int. Syrup. on Metals and Materials Science (edited by N. Hansen, A. R. Jones and T. Leffers), p. 57 (1980). 25. I. L. Dillamore, P. L. Morris, C. J. E. Smith and W. B. Hutchinson, Proc. R. Soc. A 329, 405 (1972). 26. J. E. Bailey and P. B. Hirsch, Proc. R. Soc. A 267, I1 (1962). 27. J. Hirsch, in 7th Ris~ Int. Symp. on Metals and Materials Science (edited by N. Hansen et al.), pp. 349-361 (1986). 28. G. Ibe, W. Dietz, A.-C. Fraker and K. Liicke, Z. Metallk. 61, 498 (1970). 29. A. Akef, R. Fortunier, J. H. Driver and T. Watanabe, Text. Microstruct. 14-18, 617 (1992). 30. K. Liicke and O. Engler, Mater. Sci. Technol. 6, 1113 (1990).