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Recrystallization nucleation mechanism along boundaries in hot deformed Al bicrystals
Materials Science and Engineering A272 (1999) 73 – 82 www.elsevier.com/locate/msea
Recrystallization nucleation mechanism along boundaries in hot deformed Al bicrystals M.C. Theyssier a,1, J.H. Driver b,* b
a IRSID, 57283 Maizie`res-le`s-Metz, France Materials and Processing Department, Ecole des Mines de Saint Etienne, 42023 Saint Etienne, France
Abstract The orientation dependency of strain induced boundary migration (SIBM) has been studied on 99.995% purity aluminium bicrystals deformed in hot plane strain compression. Four bicrystal combinations were chosen to represent some typical grain boundaries in hot rolled aluminium, i.e. boundaries between a grain of S {142} B211\ orientation and adjacent grains with cube, Cu {112} B111\, Bs {011}B112\ or another S variant orientation. The bicrystals were deformed in a channel die to true strains of 1.5 at 300–400°C and then annealed for short periods to allow grain boundary movement, usually by SIBM. The microstructural changes were followed by channelling contrast SEM and EBSD microtexture measurements. The stored energies of the individual grains were estimated from measurements of the average cell size and misorientation using the Read Shockley expression for the sub-boundary energies; typical values range from 10 to 50 kJ m − 3. SIBM occurs extensively in bicrystals containing boundaries with the 40° B 111\ orientation relation. Grain boundaries in other bicrystals either scarcely move or, in the case of the S/Bs combination, become nucleation sites for near-cube germs. The boundary mobilities – as deduced from the local driving forces and the migration distances – are compared with previous data from deformed polycrystals. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Aluminium bicrystals; Hot deformation; SIBM; Recrystallization nucleation; Local orientations
1. Introduction Grain boundary migration is of fundamental importance for understanding and modelling grain coarsening and recrystallization phenomena. However, as attested by several recent reviews [1 – 3], it is very difficult to quantitatively determine boundary migration rates under the driving forces typical of recrystallization of deformed metals, particularly after cold deformation. This is essentially because of the heterogeneous nature of the cold deformed microstructures so that the local driving forces can easily vary by an order of magnitude both within a grain and between grains. Controlled experiments of boundary migration have therefore usu Dedicated to Professor Herbert Herman on the occasion of his 65th birthday. * Corresponding author. Tel.: + 33-477-420196; fax: +33-477420057.. 1 Work carried out as part of a Doctoral thesis at the Ecole des Mines de Saint Etienne
ally been carried out under the relatively low driving forces of individual boundary energies using bicrystals with curved boundaries, e.g. Gottstein et al [4]. Under these conditions the driving pressure arises solely from curvature effects without any contribution from crystal defects; the pressures are also significantly lower, typically of the order of 103 –104 Pa compared with 105 –107 Pa for recrystallization,. Recent observations of hot deformed Al polycrystals reveal a very homogeneous deformation substructure within the grains in which boundaries migrate quite easily. Single crystals deformed in hot plane strain compression have also been shown to develop homogeneous dislocation cell structures whose size and misorientations can be characterized by EBSD [5]. As shown by Samadjar and Doherty [6] and Bardal et al. [7] for hot deformed polycrystals these parameters can then be used to determine the local stored energies. It is therefore possible to characterize boundary mobilities in hot deformed bicrystals by taking advantage of modern
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microdiffraction techniques and the homogeneous deformation substructures of these materials. The present paper describes experimental results on Al bicrystals deformed by high temperature channel die compression to strains of 1.5 and annealed for short periods to allow the boundaries to move. During hot rolling of Al polycrystals a b-fibre texture develops, composed of S {123} B412 \, ‘Brass’ {110}112 and ‘Copper’ {112}111 components. To understand the behaviour of grain boundaries in hot rolled polycrystals we have therefore chosen some representative bicrystal combinations containing these orientations. In particular, since the S component is usually quite strong and is often associated with the formation of the cube recrystallization texture, we have taken bicrystals with a common S oriented grain. The adjacent crystals are the Bs, Cu, cube and another S variant.
2. Experimental procedures
2.1. Bicrystal preparation The bicrystals were prepared by controlled horizontal solidification using two seed crystals and a starting material of 99.993%Al provided by the Pechiney research centre. The major impurities of this aluminium were, in wt ppm: 12 Si, 10 Fe, 7 Mg and 45 Cu. Controlled solidification was carried out in alumina moulds, under a partial pressure of argon, to form bicrystals of typical dimension 15× 2 × 1cm. During directional solidification many of the impurity elements segregated towards the end of the bar which solidified last. Samples for the present experiments were therefore only taken from the other, high purity, end with typical composition: 10– 25 ppm Cu and less than 5 ppm each of Si, Fe and Mg.
Channel die samples of dimension (8× 9 ×5 mm) were carefully sectioned from the bicrystal bars so that the grain boundary was contained in the XY compression plane, Fig. 1. The reference system used here is X= elongation direction (equivalent to RD in rolling), Y= transverse direction along which the strain is zero (TD) and Z = normal compression direction (ND). Final orientations were measured by means of Electron Channeling Patterns in an SEM. A common S orientation, close to (1( 42)[2( 1( 1] was chosen, as explained above, for each of the four bicrystal combinations. The other, adjacent, grains had cube (001) [100], ‘Cu’ (1( 3( 1)[3( 23], Bs (1( 01)[12( 1] and a different S variant, rotated p about the X (RD) axis, denoted SX (1( 4( 2)[2( 11].
2.2. Plane strain compression The bicrystals were deformed by high temperature plane strain compression in a channel die equipped with a retractable side wall which enables the sample to be extracted from the die and then water quenched within 3 s of the end of deformation [8]. The channel die equipment was used in a computer controlled Instron screw-driven machine to give constant strain rates in the range from 10 − 3 to 10 − 1 s − 1 for true, logarithmic, strains up to 1.5. The bicrystals were wrapped in Teflon films and the tool surfaces greased with a graphite spray mixture to reduce friction effects. The temperatures used for the bicrystal experiments varied from 300 to 400°C. Some samples were annealed after deformation in a salt bath.
2.3. Microstructures The microstructures and local orientations of the deformed and annealed samples were characterized by optical microscopy using polarized light on anodized surfaces and also by SEM associated with an EBSD microtexture system as described by Driver et al. [9]. The microstructural observations of the grain boundary regions were carried out on the longitudinal XZ plane on sections taken close to the sample centre. Sub-grain sizes were determined by the line intercept method along directions perpendicular to the principal subgrain blocks. Misorientations are the average value of about 100 2-mm steps across sub-boundaries on the XZ plane.
3. Results
3.1. Microstructures Fig. 1. Schematic of bicrystal configuration used for the high temperature plane strain compression tests.
Fig. 2 shows the microstructure along the grain boundary of the Cube/S bicrystal deformed to a (loga-
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Fig. 2. Optical micrograph (polarized light on anodized XZ section) showing extensive SIBM along the boundary interface region in the cube/S bicrystal deformed to o = 1.37 at 400°C. The {111} pole figures are measured by EBSD from the indicated areas and displayed, by appropriate rotation, in the standard XY compression plane.
rithmic) strain of 1.37 at 400°C. The orientations of the adjacent grains are indicated by the corresponding {111} pole figures obtained by EBSD. It is clear that large segments of the upper cube oriented grain have grown into the lower S oriented grain by strain-induced boundary migration (SIBM). Close examination reveals that, with the exception of some small areas near the original boundary, the growing cube grains have no deformation substructure, i.e. no significant dynamic recrystallization has taken place during the 14 s period of the deformation. It is therefore considered that this growth essentially occurs by static SIBM during the 2 –3 s quench time. The deformation structures of the grains are quite typical of hot deformed single crystals [5]. The S oriented grain deformed at 10 − 1 s − 1 develops a very homogeneous and regular mosaic pattern of sub-grains of average size, d 17 mm and a relatively high average misorientation, u 6.3°. In contrast the cube grain is characterised by even larger subgrains of lower average misorientation, typically 4°. Similar microstructural observations have been made on the hot channel-die compressed single crystals of the same orientations [5,10]. It should be noted that the orientation relation between the cube and S grains is characterized by a
rotation of 37° about their common 111 axis, close to the classic 40°111 S7 high mobility boundary. In fact, given the orientation spread of about 96° in the deformed S grain, the preferred cube/S growth relation can be described as 40°111 9 6°. In the bicrystals the cube grains systematically grow along a direction at 30° to the elongation or x-axis. This major growth direction is perpendicular to the common 111 rotation axis, i.e. the growing interface at the extremities of the long segments has a 379 6° tilt axis and the slower sideways growth in their thickness is associated with a twist boundary. As shown by Fig. 3 the SX/S bicrystal exhibits similar behaviour to the cube/S combination, i.e. after deformation at 400°C some segments of the SX grain have migrated into the reference S crystal over distances up to 400 mm during the quench. In this case the reference S has developed, as expected, the same substructure as in the cube/S bicrystal but the other S, of initial orientation (1( 4( 2)[2( 11], develops dislocation sub-grains with walls principally aligned at a relatively low angle of about 10°, to the long axis and the boundary plane. Note that the two S variants used here are symmetrical with respect to the x-axis and are relatively stable. (This contrasts with the room temperature channel-die experiments of Blicharski et al. [11] on an Al bicrystal
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composed of 2 S variants only one of which was stable). Note also that the two crystals are disoriented by 40° about 111. The sense of the boundary migration can be understood on the basis of the Bailey-Hirsch [12] model of boundary bulging which requires a critical value of the energy balance DE ]2g/R where R is the radius of the bulge between the pinning points; this radius is clearly greater for the substructure composed of walls inclined at a glancing angle to the boundary plane so the critical energy difference for nucleation, DE, is significantly lower for this configuration. The other two bicrystals, S/¦Cu¦ and S/Bs did not exhibit any significant evidence of boundary movement after quenching from the deformation temperature of 400°C. Some of these samples were then annealed for periods of 5–10 min. at 400°C at which stage new grains developed from the free surface (not the boundary regions) before consuming the deformed bicrystals by grain growth. To induce recrystallization by SIBM a second series of PSC deformation experiments was carried out by deformation at 300°C with the aim of increasing the stored energies. This, together with a subsequent anneal, was sufficient to generate boundary migration in the sample centre. The boundary region of the S/Cu bicrystal deformed at 300°C and annealed 10 s at 400°C is shown in Fig. 4. In both grains a regular sub-grain structure is visible with sub-grain dimensions significantly smaller than after deformation at 400°C (5 – 7 mm according to the grain orientation). As seen in the same figure, strain-induced boundary migration may occur in both direc-
tions, mainly from S to Cu but sometimes from Cu to S. The migration distances of about 50 mm are much smaller than those observed in the S/cube and S/SX bicrystals, indicating a much greater difficulty for boundary movement despite the higher stored energies. The disorientation angle/axis pair for this boundary is 46°/ B 7 4 10\ . The very particular behaviour of the S/Bs bicrystal is shown in Fig. 5 after deformation at 300°C and a 10 s anneal at the same temperature. The dislocation substructures are very homogeneous in both grains (which are perfectly stable up to large strains). However, in this case there is no apparent SIBM but nucleation of dislocation-free small grains along the interface. EBSD measurements show that the new grains possess orientations which are close to cube, usually somewhat rotated about RD, i.e. they are not, in principle, part of the deformation substructure, neither in the grains nor along the interface. Orientation scans along the deformed boundary regions adjacent to the nucleated grains did not reveal major orientation gradients; all the local orientations were within 10° of Bs or S. We have also checked the possibility that the new grains could have grown in from the sample surfaces; throughpolishing did not indicate grains coming into the boundary regions from the free surfaces. This is therefore quite a remarkable form of nucleation which appears to be related to the specific behaviour of this boundary. In fact the boundary appears to split up from a 23°/ B 325\ relation to two boundaries, a 39°B213\ for the Bs/near cube and a 31°B212\ relation for the near cube /S (Fig. 6). This splitting then
Fig. 3. Polarized light optical micrograph showing SIBM along the boundary in the S/SX bicrystal deformed at 400°C, o =1.5.
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Fig. 4. Boundary regions of S/Cu bicrystal deformed at 300°C, o =1.37and annealed 400°C 10 s; (a) polarized light optical micrograph showing interpenetrating SIBM; (b) orientation contrast SEM image of sub-grain structure and a growing sub-grain.
brings the boundaries closer to the mobile 40°B 111\ relation.
3.2. Stored energies As already pointed out, the homogeneous deformation substructures developed in the bicrystals by channel-die compression at 300 – 400°C are very similar to those of the oriented single crystals [5,9]. They are characterised by well-defined subgrain sizes d and mis-
orientations u which can be used to estimate the orientation dependency of the stored energies of the grains through the well-known Read-Schockley equation. This is conveniently written in terms of the maximum largeangle boundary energy per unit surface gm: g= gm
u u 1− ln um um
n
(1)
where um is the angle at which g takes the value gm. We shall approximate g by the simple linear relation
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g:
gm u um
and take gm = 0.45 J m − 2 at um =15°. The stored energy per unit volume is then given by 2 Ev = g d where the factor 2 comes from the number of cells/ unit vol for cells highly elongated along TD. The effect of the boundary type, i.e. tilt, twist or mixed, is neglected in this estimation. Analysis of the rotation axes associated with the misorientations [10] shows that the subgrains in the Bs and Cu oriented crystals are predominantly of tilt character but that the S and cube grains have rather ill-defined mixed boundaries. Table 1 gives the values of u, d and Ev for the hot deformed crystals (at strains of 1 – 1.5).
The higher temperature significantly increases the sub-grain size and also tends to slightly increase the average misorientation (with the exception of the Bs orientation whose sub-grain misorientation is virtually independent of temperature and strain over these ranges). The very low stored energy in the cube grain deformed at 400°C should also be noted. No measurements of the cube grain deformed at 300°C were carried out because of the unstable nature of the cube orientation at this temperature. On average the stored energies decrease with increasing temperature from about 30 kJ m − 3 at 300°C to 10–20 kJ m − 3 at 400°C. Obviously these are only approximate values but they fit reasonably well with the measured flow stresses s of the single crystals [5,10]. At a strain of 1 these are 30–35 MPa at 300°C and 14–18 MPa at 400°C. If we take the flow stress as
Fig. 5. S/Bs bicrystal deformed at 300°C to o = 1.55 and annealed 10 s at 300°C. Polarized light optical micrographs: (a) and (b) of XZ section.
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on octahedral and non-octahedral systems [13] and given that m=25 GPa then one evaluates the average stored energies as about 43 and 21 kJ m − 3 at 300°C and 400°C, respectively. These values lie on the upper end of the values estimated from the Read-Schockley equation as can be expected since the latter do not include the dislocation densities within the cell interiors.
3.3. Mobilities
Fig. 6. S/Bs bicrystal deformed and annealed as in Fig. 5. Orientation contrast SEM image of cube grain nucleus and local misorientation EBSD scan along the Z direction.
s = 0.3mbM r and the stored energy as EV $ 0.5r m.b 2 then the stored energy can be determined from the average flow stress, the Taylor factor M and the shear modulus m. Assuming a Taylor factor M 2.3 for slip
Grain boundary mobility M is usually defined by the relation M= 6/P where 6 is the boundary velocity and P the driving pressure. It is generally accepted that the temperature dependency of M follows the Arrhenius law. In the present case we shall evaluate the mobilities of the different boundary types from the stored energy P of the adjacent grains and the maximum boundary displacements over the times estimated at temperature. During the first stages of SIBM both grains are deformed so the stored energy differences are relatively small (in some cases virtually zero but maximal for the S/cube bicrystal). The boundaries are considered to move over small distances of a few microns due to local boundary tension effects creating small dislocation free ‘grains’, possibly during deformation. When this has occurred the stored energy difference between the dislocation free area and the deformed matrix is equal to the stored energy in the latter – this is the value taken here. Table 2 summarises the mobilities at 400°C estimated in this way from the set of results described above. Clearly these results confirm a strong orientation dependency; the two boundaries close to the 40°111 relationship possess mobilities 2 orders of magnitude greater than the S/Cu boundary. The absolute values given above should be treated with some precaution given the errors involved in determining P and 6 (over times of a few seconds). Nevertheless they are not very far off the classical mobility measurements in high purity Al due to Gordon and Vandermeer [14]. These authors determined the mobilities of grain boundaries during recrystallization of cold rolled high purity Al containing trace additions of Cu by measuring the
Table 1 The average cell sizes d, misorientations u and estimated stored energies of high purity Al crystals deformed in hot channel-die compression (strain rate 0.1 s−1). Orientation
Def temp. (°C)
Def (ol)
u°
d (mm)
Ev (kJ m−3)
Bs
300 400
1.55 1.21
3.1 3.1
5.6 12
33.2 15.5
S
300 400
1.46 1.37
3.6 6.3
7.5 17
28.8 22.2
Cu
300 400
1.46 1.12
2.8 4.3
5.2 14
32.3 18.4
Cube
400
1.37
4.0
23
10.4
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Table 2 Estimated boundary mobilities at 400°C from the bicrystal boundary displacements Bicrystal
Driving pressure (P) 103 Pa
Velocity (v ms−1)
Mobility (m4 J−1 per s)
S/cube S/SX S/Cu
22.2 22.2 30
4.10−4 2.10−4 5.10−6
18.10−9 9.10−9 0.14.10−9
growth rates G of the fastest growing grains. They published plots of G(1/T) over temperatures up to 200°C as shown in Fig. 7. The mobilities of the fastest growing grains can be estimated from the growth rates and the stored energy of cold deformation. At the time Gordon and Vandermeer gave a stored energy value of 400 kJ m − 3. This is probably a little high since the room temperature flow stress of high purity Al deformed 40% in plane strain compression is about 80 MPa [15] which, using the above equations, can be translated into a stored energy of 200 kJ m − 3. Taking the latter value the mobilities of Gordon and Vandermeer are scaled as shown in Fig. 7. Extrapolating their values for the 17ppm Cu alloy to 400°C gives a value of 10 − 7 m4 J − 1 per s, within a factor of about five of the value given in Table 2 for the fastest growing (S/cube) boundary.
of 15%. The same tendency is nevertheless observed on both studies; S grains tend to possess the highest values, cube grains the lowest and Bs or Cu components have intermediate values. As shown in Fig. 8, the microstructures of the grains in hot compressed Al polycrystals are very similar to those of the bicrystals.
4. Discussion The present experimental study of the behaviour of Al bicrystals deformed in hot plane strain compression has amply demonstrated and confirmed the importance of boundary misorientation and relative stored energies in controlling SIBM. Application to the more general case of hot deformed polycrystals in industrial processing of metallic alloys requires that the deformation modes of the bicrystals can be considered representative of grains in hot rolled polycrystals. Discounting the surface layers of hot rolled aluminium alloys [16], the principal deformation in the centre layers is PSC and the temperature range varies typically from 300 to 500°C as practised here. The major difference relates to the strain rates which in industrial schedules are 5–50 s − 1 as opposed to the present values of 10 − 1 s − 1. The stored energies developed at these relatively low strain rates are therefore much lower. For example, using the same techniques Petterson et al. [17] measured values of 500 kJ m − 3 in a 3104 alloy deformed at 100 s − 1 and 350°C. The present study does, however, have the advantage of measuring the orientation dependency of the stored energies with much greater accuracy since in crystals deformed at fixed temperature and strain rate they can easily vary by a factor of two. In the recent study of Petterson on a 3104 alloy maximum energy variations due to grain orientation are only of the order
Fig. 7. Estimated boundary mobilities of bicrystals and comparison with the polycrystal data of Gordon and Vandermeer [14].
Fig. 8. Polarized light optical micrograph of longitudinal XZ section of polycrystalline high purity Al deformed in PSC at 400°C to o = 1.3 and annealed 20 s at 400°C.
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These stored energies have been used to evaluate boundary mobilities after hot deformation. It is shown that the absolute mobility values estimated for short annealing times are in reasonable agreement with the data of Gordon and Vandermeer. One could therefore be tempted to extend the use of bicrystals to other measurements of boundary mobilities in deformed metals. We feel, however, that since the advent of automatic EBSD techniques local misorientations and stored energies can now be evaluated with much less effort in the individual grains of large-grained polycrystal samples. Bicrystals should rather serve as a reference for some of the polycrystal studies. The real advantage of studying bicrystals lies in the possibilities of characterising the details of nucleation mechanisms along boundaries knowing that only one boundary is present. In the present case the cube/S and SX/S boundaries exhibit high mobilities and lead to rapid recrystallization nucleation by SIBM. Both these boundaries are characterised by 40°111 9 6° misorientations and both possess similar mobilities in the adjacent deformed grains. The strong effect of the near S7 boundaries tends to support the oriented growth-or microgrowth-theory of recrystallization texture formation, at least at the scale of individual grains. Although there is a significant stored energy difference between cube and S grains favouring subsequent cube growth, the boundary mobility must play a major role since the SX/S boundary migrates over almost the same distance despite the handicap of starting off with an initial stored energy difference which is practically negligible. Clearly an accurate knowledge of the general orientation dependency of boundary mobilities is required in order to successfully model recrystallization kinetics and texture formation in polycrystals. The S/Cu bicrystal reveals classical SIBM with growth occurring, virtually at random, from one side to the other. This behaviour is frequently observed along the boundaries of deformed polycrystals and indicates similar stored energies and ‘near-average’ boundary mobilities (at least compared with the 40°/111 boundaries). It should also be noted that, although rather slow, SIBM does occur extensively in this bicrystal after hot deformation, in contrast to the behaviour of the same type of bicrystal deformed in channel-die at room temperature. Liu et al [18] have deformed an aluminium bicrystal of S/Cu orientations to a thickness reduction of 90% (o 2.3) and annealed it at 300°C for various times. Recrystallization nucleation occurred essentially along the micro-shear bands which form in the Cu-oriented grain as characterised by Driver et al. [19]. Although some examples of SIBM were found the authors concluded that ‘the bicrystal boundary does not seem to be a strong nucleation site’. This tends to confirm the real difference in the operative recrystallization mechanisms between hot and cold deformed sam-
81
ples as a consequence of the homogeneous deformation substructures developed at high temperature. The behaviour of the S/Bs bicrystal is significantly different from the other cases examined here in that the boundary scarcely moves and some isolated new grains are nucleated along the boundary, apparently in the S grain. These new grains possess orientations within 10 or 20° of cube (usually rotated about RD) and which were not obviously present after deformation. EBSD scans along the boundary areas in the S grain did not reveal major orientation gradients which could have formed the rotated cube nuclei; only random misorientations of 9 5–10° were measured, (Fig. 6). However, some recent Finite Element calculations [20] of the room temperature behaviour of S oriented crystals in a S/Bs bicrystal combination indicate the creation of large orientation gradients by the formation of localized shear bands which can include near-cube orientations of the type {001}uv0, i.e. ND rotated cube zones. As mentioned above, cold deformation microstructures are not necessarily reproduced at high temperatures so the relevance of the FE calculations to the present results needs to be examined in further detail. Further work using EBSD generated orientation maps along the boundary areas of hot deformed bicrystals should provide further information on this important point. Finally, it should be noted that the mechanisms of boundary movement and recrystallization nucleation along grain boundaries in bicrystals tend to favour the cube and S orientations; these are in fact the recrystallization texture components which often dominate in annealed aluminium alloys after hot plane strain deformation.
5. Conclusions (1) It is shown that hot channel-die compression of aluminium bicrystals is a reasonable method for estimating boundary mobilities from the local stored energies and it is proposed that the method can probably be extended to deformed polycrystals by using automatic EBSD. (2) There is a clear orientation dependency of the boundary mobilities with a strong advantage for 40111 boundaries; the energy difference is not the only factor controlling SIBM kinetics since SX/S boundaries migrate at relatively high rates. (3) The Bs/S boundary appears to be immobile so that internal energy reduction takes place by near-cube grain nucleation; this could also occur in polycrystals. (4) Rapid growth of cube and S grains is favoured by the SIBM nucleation mechanisms observed in the bicrystals so that these orientations usually become the strongest texture components of recrystallized Al.
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Acknowledgements The authors wish to thank the Pechiney research centre at Voreppe for financial support and many useful discussions. They are also particularly grateful to G. Triboulet of the Ecole des Mines for help in growing the bicrystals.
[8] [9] [10] [11] [12] [13] [14]
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Symp. Materials Science, Microstructures and Crystallographic Aspects of Recrystallization. Roskilde, Denmark, 1995. C. Maurice, J.H. Driver, Acta Metall. Mater. 41 (1993) 1653– 1664. J.H. Driver, M.C. Theyssier, C. Maurice, Mater. Sci. Techn. 12 (1996) 851 – 858. M.C. Theyssier, Doctoral thesis, Ecole des Mines de Saint Etienne-INP Grenoble, 1996. M. Blicharski, R. Becker, H. Hu, Acta Metall. Mater. 41 (1993) 2007 – 2016. J.E. Bailey, Phil. Mag. 5 (1960) 833 – 842. C. Maurice, J.H. Driver, Acta Mater. 45 (1997) 4727–4738. P. Gordon, R.A. Vandermeer, Trans. AIME 224 (1962) 917– 928. R. Fortunier, B. Orlans-Joliet, F. Montheillet, J.H. Driver Large strain multiple slip work hardening behaviour of fcc and bcc crystals, Proc. 8th Riso Symp. Materials Science, Constitutive relations and their Physical Basis, Roskilde, Denmark, 1987, pp. 317 – 324. F. Perocheau, J.H. Driver. Int. J. Plasticity (submitted). T. Petterson, A. Bardal, I. Lindeseth, E. Nes, Characterization of deformation microstructure in hot plane strain compressed Al-1Mg-1Mn, Recrystallization and Related Phenomena, in: T.R. McNelley (Ed.), Proc. ReX’ 96, Monterey 1997, pp. 495– 501. Y.L. Liu, H Hu, N. Hansen, Acta Metall. Mater. 43 (1995) 2395 – 2405. J.H. Driver, D. Juul Jensen, N. Hansen, Acta Metall. Mater. 42 (1994) 3105 – 3114. A.J. Beaudoin Jr., H. Mecking, U.F. Kocks. Phil. Mag. A 73 (1996) 1503 – 1517.
Recrystallization nucleation mechanism along boundaries in hot deformed Al bicrystals M.C. Theyssier a,1, J.H. Driver b,* b
a IRSID, 57283 Maizie`res-le`s-Metz, France Materials and Processing Department, Ecole des Mines de Saint Etienne, 42023 Saint Etienne, France
Abstract The orientation dependency of strain induced boundary migration (SIBM) has been studied on 99.995% purity aluminium bicrystals deformed in hot plane strain compression. Four bicrystal combinations were chosen to represent some typical grain boundaries in hot rolled aluminium, i.e. boundaries between a grain of S {142} B211\ orientation and adjacent grains with cube, Cu {112} B111\, Bs {011}B112\ or another S variant orientation. The bicrystals were deformed in a channel die to true strains of 1.5 at 300–400°C and then annealed for short periods to allow grain boundary movement, usually by SIBM. The microstructural changes were followed by channelling contrast SEM and EBSD microtexture measurements. The stored energies of the individual grains were estimated from measurements of the average cell size and misorientation using the Read Shockley expression for the sub-boundary energies; typical values range from 10 to 50 kJ m − 3. SIBM occurs extensively in bicrystals containing boundaries with the 40° B 111\ orientation relation. Grain boundaries in other bicrystals either scarcely move or, in the case of the S/Bs combination, become nucleation sites for near-cube germs. The boundary mobilities – as deduced from the local driving forces and the migration distances – are compared with previous data from deformed polycrystals. © 1999 Elsevier Science S.A. All rights reserved. Keywords: Aluminium bicrystals; Hot deformation; SIBM; Recrystallization nucleation; Local orientations
1. Introduction Grain boundary migration is of fundamental importance for understanding and modelling grain coarsening and recrystallization phenomena. However, as attested by several recent reviews [1 – 3], it is very difficult to quantitatively determine boundary migration rates under the driving forces typical of recrystallization of deformed metals, particularly after cold deformation. This is essentially because of the heterogeneous nature of the cold deformed microstructures so that the local driving forces can easily vary by an order of magnitude both within a grain and between grains. Controlled experiments of boundary migration have therefore usu Dedicated to Professor Herbert Herman on the occasion of his 65th birthday. * Corresponding author. Tel.: + 33-477-420196; fax: +33-477420057.. 1 Work carried out as part of a Doctoral thesis at the Ecole des Mines de Saint Etienne
ally been carried out under the relatively low driving forces of individual boundary energies using bicrystals with curved boundaries, e.g. Gottstein et al [4]. Under these conditions the driving pressure arises solely from curvature effects without any contribution from crystal defects; the pressures are also significantly lower, typically of the order of 103 –104 Pa compared with 105 –107 Pa for recrystallization,. Recent observations of hot deformed Al polycrystals reveal a very homogeneous deformation substructure within the grains in which boundaries migrate quite easily. Single crystals deformed in hot plane strain compression have also been shown to develop homogeneous dislocation cell structures whose size and misorientations can be characterized by EBSD [5]. As shown by Samadjar and Doherty [6] and Bardal et al. [7] for hot deformed polycrystals these parameters can then be used to determine the local stored energies. It is therefore possible to characterize boundary mobilities in hot deformed bicrystals by taking advantage of modern
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microdiffraction techniques and the homogeneous deformation substructures of these materials. The present paper describes experimental results on Al bicrystals deformed by high temperature channel die compression to strains of 1.5 and annealed for short periods to allow the boundaries to move. During hot rolling of Al polycrystals a b-fibre texture develops, composed of S {123} B412 \, ‘Brass’ {110}112 and ‘Copper’ {112}111 components. To understand the behaviour of grain boundaries in hot rolled polycrystals we have therefore chosen some representative bicrystal combinations containing these orientations. In particular, since the S component is usually quite strong and is often associated with the formation of the cube recrystallization texture, we have taken bicrystals with a common S oriented grain. The adjacent crystals are the Bs, Cu, cube and another S variant.
2. Experimental procedures
2.1. Bicrystal preparation The bicrystals were prepared by controlled horizontal solidification using two seed crystals and a starting material of 99.993%Al provided by the Pechiney research centre. The major impurities of this aluminium were, in wt ppm: 12 Si, 10 Fe, 7 Mg and 45 Cu. Controlled solidification was carried out in alumina moulds, under a partial pressure of argon, to form bicrystals of typical dimension 15× 2 × 1cm. During directional solidification many of the impurity elements segregated towards the end of the bar which solidified last. Samples for the present experiments were therefore only taken from the other, high purity, end with typical composition: 10– 25 ppm Cu and less than 5 ppm each of Si, Fe and Mg.
Channel die samples of dimension (8× 9 ×5 mm) were carefully sectioned from the bicrystal bars so that the grain boundary was contained in the XY compression plane, Fig. 1. The reference system used here is X= elongation direction (equivalent to RD in rolling), Y= transverse direction along which the strain is zero (TD) and Z = normal compression direction (ND). Final orientations were measured by means of Electron Channeling Patterns in an SEM. A common S orientation, close to (1( 42)[2( 1( 1] was chosen, as explained above, for each of the four bicrystal combinations. The other, adjacent, grains had cube (001) [100], ‘Cu’ (1( 3( 1)[3( 23], Bs (1( 01)[12( 1] and a different S variant, rotated p about the X (RD) axis, denoted SX (1( 4( 2)[2( 11].
2.2. Plane strain compression The bicrystals were deformed by high temperature plane strain compression in a channel die equipped with a retractable side wall which enables the sample to be extracted from the die and then water quenched within 3 s of the end of deformation [8]. The channel die equipment was used in a computer controlled Instron screw-driven machine to give constant strain rates in the range from 10 − 3 to 10 − 1 s − 1 for true, logarithmic, strains up to 1.5. The bicrystals were wrapped in Teflon films and the tool surfaces greased with a graphite spray mixture to reduce friction effects. The temperatures used for the bicrystal experiments varied from 300 to 400°C. Some samples were annealed after deformation in a salt bath.
2.3. Microstructures The microstructures and local orientations of the deformed and annealed samples were characterized by optical microscopy using polarized light on anodized surfaces and also by SEM associated with an EBSD microtexture system as described by Driver et al. [9]. The microstructural observations of the grain boundary regions were carried out on the longitudinal XZ plane on sections taken close to the sample centre. Sub-grain sizes were determined by the line intercept method along directions perpendicular to the principal subgrain blocks. Misorientations are the average value of about 100 2-mm steps across sub-boundaries on the XZ plane.
3. Results
3.1. Microstructures Fig. 1. Schematic of bicrystal configuration used for the high temperature plane strain compression tests.
Fig. 2 shows the microstructure along the grain boundary of the Cube/S bicrystal deformed to a (loga-
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Fig. 2. Optical micrograph (polarized light on anodized XZ section) showing extensive SIBM along the boundary interface region in the cube/S bicrystal deformed to o = 1.37 at 400°C. The {111} pole figures are measured by EBSD from the indicated areas and displayed, by appropriate rotation, in the standard XY compression plane.
rithmic) strain of 1.37 at 400°C. The orientations of the adjacent grains are indicated by the corresponding {111} pole figures obtained by EBSD. It is clear that large segments of the upper cube oriented grain have grown into the lower S oriented grain by strain-induced boundary migration (SIBM). Close examination reveals that, with the exception of some small areas near the original boundary, the growing cube grains have no deformation substructure, i.e. no significant dynamic recrystallization has taken place during the 14 s period of the deformation. It is therefore considered that this growth essentially occurs by static SIBM during the 2 –3 s quench time. The deformation structures of the grains are quite typical of hot deformed single crystals [5]. The S oriented grain deformed at 10 − 1 s − 1 develops a very homogeneous and regular mosaic pattern of sub-grains of average size, d 17 mm and a relatively high average misorientation, u 6.3°. In contrast the cube grain is characterised by even larger subgrains of lower average misorientation, typically 4°. Similar microstructural observations have been made on the hot channel-die compressed single crystals of the same orientations [5,10]. It should be noted that the orientation relation between the cube and S grains is characterized by a
rotation of 37° about their common 111 axis, close to the classic 40°111 S7 high mobility boundary. In fact, given the orientation spread of about 96° in the deformed S grain, the preferred cube/S growth relation can be described as 40°111 9 6°. In the bicrystals the cube grains systematically grow along a direction at 30° to the elongation or x-axis. This major growth direction is perpendicular to the common 111 rotation axis, i.e. the growing interface at the extremities of the long segments has a 379 6° tilt axis and the slower sideways growth in their thickness is associated with a twist boundary. As shown by Fig. 3 the SX/S bicrystal exhibits similar behaviour to the cube/S combination, i.e. after deformation at 400°C some segments of the SX grain have migrated into the reference S crystal over distances up to 400 mm during the quench. In this case the reference S has developed, as expected, the same substructure as in the cube/S bicrystal but the other S, of initial orientation (1( 4( 2)[2( 11], develops dislocation sub-grains with walls principally aligned at a relatively low angle of about 10°, to the long axis and the boundary plane. Note that the two S variants used here are symmetrical with respect to the x-axis and are relatively stable. (This contrasts with the room temperature channel-die experiments of Blicharski et al. [11] on an Al bicrystal
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composed of 2 S variants only one of which was stable). Note also that the two crystals are disoriented by 40° about 111. The sense of the boundary migration can be understood on the basis of the Bailey-Hirsch [12] model of boundary bulging which requires a critical value of the energy balance DE ]2g/R where R is the radius of the bulge between the pinning points; this radius is clearly greater for the substructure composed of walls inclined at a glancing angle to the boundary plane so the critical energy difference for nucleation, DE, is significantly lower for this configuration. The other two bicrystals, S/¦Cu¦ and S/Bs did not exhibit any significant evidence of boundary movement after quenching from the deformation temperature of 400°C. Some of these samples were then annealed for periods of 5–10 min. at 400°C at which stage new grains developed from the free surface (not the boundary regions) before consuming the deformed bicrystals by grain growth. To induce recrystallization by SIBM a second series of PSC deformation experiments was carried out by deformation at 300°C with the aim of increasing the stored energies. This, together with a subsequent anneal, was sufficient to generate boundary migration in the sample centre. The boundary region of the S/Cu bicrystal deformed at 300°C and annealed 10 s at 400°C is shown in Fig. 4. In both grains a regular sub-grain structure is visible with sub-grain dimensions significantly smaller than after deformation at 400°C (5 – 7 mm according to the grain orientation). As seen in the same figure, strain-induced boundary migration may occur in both direc-
tions, mainly from S to Cu but sometimes from Cu to S. The migration distances of about 50 mm are much smaller than those observed in the S/cube and S/SX bicrystals, indicating a much greater difficulty for boundary movement despite the higher stored energies. The disorientation angle/axis pair for this boundary is 46°/ B 7 4 10\ . The very particular behaviour of the S/Bs bicrystal is shown in Fig. 5 after deformation at 300°C and a 10 s anneal at the same temperature. The dislocation substructures are very homogeneous in both grains (which are perfectly stable up to large strains). However, in this case there is no apparent SIBM but nucleation of dislocation-free small grains along the interface. EBSD measurements show that the new grains possess orientations which are close to cube, usually somewhat rotated about RD, i.e. they are not, in principle, part of the deformation substructure, neither in the grains nor along the interface. Orientation scans along the deformed boundary regions adjacent to the nucleated grains did not reveal major orientation gradients; all the local orientations were within 10° of Bs or S. We have also checked the possibility that the new grains could have grown in from the sample surfaces; throughpolishing did not indicate grains coming into the boundary regions from the free surfaces. This is therefore quite a remarkable form of nucleation which appears to be related to the specific behaviour of this boundary. In fact the boundary appears to split up from a 23°/ B 325\ relation to two boundaries, a 39°B213\ for the Bs/near cube and a 31°B212\ relation for the near cube /S (Fig. 6). This splitting then
Fig. 3. Polarized light optical micrograph showing SIBM along the boundary in the S/SX bicrystal deformed at 400°C, o =1.5.
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Fig. 4. Boundary regions of S/Cu bicrystal deformed at 300°C, o =1.37and annealed 400°C 10 s; (a) polarized light optical micrograph showing interpenetrating SIBM; (b) orientation contrast SEM image of sub-grain structure and a growing sub-grain.
brings the boundaries closer to the mobile 40°B 111\ relation.
3.2. Stored energies As already pointed out, the homogeneous deformation substructures developed in the bicrystals by channel-die compression at 300 – 400°C are very similar to those of the oriented single crystals [5,9]. They are characterised by well-defined subgrain sizes d and mis-
orientations u which can be used to estimate the orientation dependency of the stored energies of the grains through the well-known Read-Schockley equation. This is conveniently written in terms of the maximum largeangle boundary energy per unit surface gm: g= gm
u u 1− ln um um
n
(1)
where um is the angle at which g takes the value gm. We shall approximate g by the simple linear relation
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g:
gm u um
and take gm = 0.45 J m − 2 at um =15°. The stored energy per unit volume is then given by 2 Ev = g d where the factor 2 comes from the number of cells/ unit vol for cells highly elongated along TD. The effect of the boundary type, i.e. tilt, twist or mixed, is neglected in this estimation. Analysis of the rotation axes associated with the misorientations [10] shows that the subgrains in the Bs and Cu oriented crystals are predominantly of tilt character but that the S and cube grains have rather ill-defined mixed boundaries. Table 1 gives the values of u, d and Ev for the hot deformed crystals (at strains of 1 – 1.5).
The higher temperature significantly increases the sub-grain size and also tends to slightly increase the average misorientation (with the exception of the Bs orientation whose sub-grain misorientation is virtually independent of temperature and strain over these ranges). The very low stored energy in the cube grain deformed at 400°C should also be noted. No measurements of the cube grain deformed at 300°C were carried out because of the unstable nature of the cube orientation at this temperature. On average the stored energies decrease with increasing temperature from about 30 kJ m − 3 at 300°C to 10–20 kJ m − 3 at 400°C. Obviously these are only approximate values but they fit reasonably well with the measured flow stresses s of the single crystals [5,10]. At a strain of 1 these are 30–35 MPa at 300°C and 14–18 MPa at 400°C. If we take the flow stress as
Fig. 5. S/Bs bicrystal deformed at 300°C to o = 1.55 and annealed 10 s at 300°C. Polarized light optical micrographs: (a) and (b) of XZ section.
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on octahedral and non-octahedral systems [13] and given that m=25 GPa then one evaluates the average stored energies as about 43 and 21 kJ m − 3 at 300°C and 400°C, respectively. These values lie on the upper end of the values estimated from the Read-Schockley equation as can be expected since the latter do not include the dislocation densities within the cell interiors.
3.3. Mobilities
Fig. 6. S/Bs bicrystal deformed and annealed as in Fig. 5. Orientation contrast SEM image of cube grain nucleus and local misorientation EBSD scan along the Z direction.
s = 0.3mbM r and the stored energy as EV $ 0.5r m.b 2 then the stored energy can be determined from the average flow stress, the Taylor factor M and the shear modulus m. Assuming a Taylor factor M 2.3 for slip
Grain boundary mobility M is usually defined by the relation M= 6/P where 6 is the boundary velocity and P the driving pressure. It is generally accepted that the temperature dependency of M follows the Arrhenius law. In the present case we shall evaluate the mobilities of the different boundary types from the stored energy P of the adjacent grains and the maximum boundary displacements over the times estimated at temperature. During the first stages of SIBM both grains are deformed so the stored energy differences are relatively small (in some cases virtually zero but maximal for the S/cube bicrystal). The boundaries are considered to move over small distances of a few microns due to local boundary tension effects creating small dislocation free ‘grains’, possibly during deformation. When this has occurred the stored energy difference between the dislocation free area and the deformed matrix is equal to the stored energy in the latter – this is the value taken here. Table 2 summarises the mobilities at 400°C estimated in this way from the set of results described above. Clearly these results confirm a strong orientation dependency; the two boundaries close to the 40°111 relationship possess mobilities 2 orders of magnitude greater than the S/Cu boundary. The absolute values given above should be treated with some precaution given the errors involved in determining P and 6 (over times of a few seconds). Nevertheless they are not very far off the classical mobility measurements in high purity Al due to Gordon and Vandermeer [14]. These authors determined the mobilities of grain boundaries during recrystallization of cold rolled high purity Al containing trace additions of Cu by measuring the
Table 1 The average cell sizes d, misorientations u and estimated stored energies of high purity Al crystals deformed in hot channel-die compression (strain rate 0.1 s−1). Orientation
Def temp. (°C)
Def (ol)
u°
d (mm)
Ev (kJ m−3)
Bs
300 400
1.55 1.21
3.1 3.1
5.6 12
33.2 15.5
S
300 400
1.46 1.37
3.6 6.3
7.5 17
28.8 22.2
Cu
300 400
1.46 1.12
2.8 4.3
5.2 14
32.3 18.4
Cube
400
1.37
4.0
23
10.4
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Table 2 Estimated boundary mobilities at 400°C from the bicrystal boundary displacements Bicrystal
Driving pressure (P) 103 Pa
Velocity (v ms−1)
Mobility (m4 J−1 per s)
S/cube S/SX S/Cu
22.2 22.2 30
4.10−4 2.10−4 5.10−6
18.10−9 9.10−9 0.14.10−9
growth rates G of the fastest growing grains. They published plots of G(1/T) over temperatures up to 200°C as shown in Fig. 7. The mobilities of the fastest growing grains can be estimated from the growth rates and the stored energy of cold deformation. At the time Gordon and Vandermeer gave a stored energy value of 400 kJ m − 3. This is probably a little high since the room temperature flow stress of high purity Al deformed 40% in plane strain compression is about 80 MPa [15] which, using the above equations, can be translated into a stored energy of 200 kJ m − 3. Taking the latter value the mobilities of Gordon and Vandermeer are scaled as shown in Fig. 7. Extrapolating their values for the 17ppm Cu alloy to 400°C gives a value of 10 − 7 m4 J − 1 per s, within a factor of about five of the value given in Table 2 for the fastest growing (S/cube) boundary.
of 15%. The same tendency is nevertheless observed on both studies; S grains tend to possess the highest values, cube grains the lowest and Bs or Cu components have intermediate values. As shown in Fig. 8, the microstructures of the grains in hot compressed Al polycrystals are very similar to those of the bicrystals.
4. Discussion The present experimental study of the behaviour of Al bicrystals deformed in hot plane strain compression has amply demonstrated and confirmed the importance of boundary misorientation and relative stored energies in controlling SIBM. Application to the more general case of hot deformed polycrystals in industrial processing of metallic alloys requires that the deformation modes of the bicrystals can be considered representative of grains in hot rolled polycrystals. Discounting the surface layers of hot rolled aluminium alloys [16], the principal deformation in the centre layers is PSC and the temperature range varies typically from 300 to 500°C as practised here. The major difference relates to the strain rates which in industrial schedules are 5–50 s − 1 as opposed to the present values of 10 − 1 s − 1. The stored energies developed at these relatively low strain rates are therefore much lower. For example, using the same techniques Petterson et al. [17] measured values of 500 kJ m − 3 in a 3104 alloy deformed at 100 s − 1 and 350°C. The present study does, however, have the advantage of measuring the orientation dependency of the stored energies with much greater accuracy since in crystals deformed at fixed temperature and strain rate they can easily vary by a factor of two. In the recent study of Petterson on a 3104 alloy maximum energy variations due to grain orientation are only of the order
Fig. 7. Estimated boundary mobilities of bicrystals and comparison with the polycrystal data of Gordon and Vandermeer [14].
Fig. 8. Polarized light optical micrograph of longitudinal XZ section of polycrystalline high purity Al deformed in PSC at 400°C to o = 1.3 and annealed 20 s at 400°C.
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These stored energies have been used to evaluate boundary mobilities after hot deformation. It is shown that the absolute mobility values estimated for short annealing times are in reasonable agreement with the data of Gordon and Vandermeer. One could therefore be tempted to extend the use of bicrystals to other measurements of boundary mobilities in deformed metals. We feel, however, that since the advent of automatic EBSD techniques local misorientations and stored energies can now be evaluated with much less effort in the individual grains of large-grained polycrystal samples. Bicrystals should rather serve as a reference for some of the polycrystal studies. The real advantage of studying bicrystals lies in the possibilities of characterising the details of nucleation mechanisms along boundaries knowing that only one boundary is present. In the present case the cube/S and SX/S boundaries exhibit high mobilities and lead to rapid recrystallization nucleation by SIBM. Both these boundaries are characterised by 40°111 9 6° misorientations and both possess similar mobilities in the adjacent deformed grains. The strong effect of the near S7 boundaries tends to support the oriented growth-or microgrowth-theory of recrystallization texture formation, at least at the scale of individual grains. Although there is a significant stored energy difference between cube and S grains favouring subsequent cube growth, the boundary mobility must play a major role since the SX/S boundary migrates over almost the same distance despite the handicap of starting off with an initial stored energy difference which is practically negligible. Clearly an accurate knowledge of the general orientation dependency of boundary mobilities is required in order to successfully model recrystallization kinetics and texture formation in polycrystals. The S/Cu bicrystal reveals classical SIBM with growth occurring, virtually at random, from one side to the other. This behaviour is frequently observed along the boundaries of deformed polycrystals and indicates similar stored energies and ‘near-average’ boundary mobilities (at least compared with the 40°/111 boundaries). It should also be noted that, although rather slow, SIBM does occur extensively in this bicrystal after hot deformation, in contrast to the behaviour of the same type of bicrystal deformed in channel-die at room temperature. Liu et al [18] have deformed an aluminium bicrystal of S/Cu orientations to a thickness reduction of 90% (o 2.3) and annealed it at 300°C for various times. Recrystallization nucleation occurred essentially along the micro-shear bands which form in the Cu-oriented grain as characterised by Driver et al. [19]. Although some examples of SIBM were found the authors concluded that ‘the bicrystal boundary does not seem to be a strong nucleation site’. This tends to confirm the real difference in the operative recrystallization mechanisms between hot and cold deformed sam-
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ples as a consequence of the homogeneous deformation substructures developed at high temperature. The behaviour of the S/Bs bicrystal is significantly different from the other cases examined here in that the boundary scarcely moves and some isolated new grains are nucleated along the boundary, apparently in the S grain. These new grains possess orientations within 10 or 20° of cube (usually rotated about RD) and which were not obviously present after deformation. EBSD scans along the boundary areas in the S grain did not reveal major orientation gradients which could have formed the rotated cube nuclei; only random misorientations of 9 5–10° were measured, (Fig. 6). However, some recent Finite Element calculations [20] of the room temperature behaviour of S oriented crystals in a S/Bs bicrystal combination indicate the creation of large orientation gradients by the formation of localized shear bands which can include near-cube orientations of the type {001}uv0, i.e. ND rotated cube zones. As mentioned above, cold deformation microstructures are not necessarily reproduced at high temperatures so the relevance of the FE calculations to the present results needs to be examined in further detail. Further work using EBSD generated orientation maps along the boundary areas of hot deformed bicrystals should provide further information on this important point. Finally, it should be noted that the mechanisms of boundary movement and recrystallization nucleation along grain boundaries in bicrystals tend to favour the cube and S orientations; these are in fact the recrystallization texture components which often dominate in annealed aluminium alloys after hot plane strain deformation.
5. Conclusions (1) It is shown that hot channel-die compression of aluminium bicrystals is a reasonable method for estimating boundary mobilities from the local stored energies and it is proposed that the method can probably be extended to deformed polycrystals by using automatic EBSD. (2) There is a clear orientation dependency of the boundary mobilities with a strong advantage for 40111 boundaries; the energy difference is not the only factor controlling SIBM kinetics since SX/S boundaries migrate at relatively high rates. (3) The Bs/S boundary appears to be immobile so that internal energy reduction takes place by near-cube grain nucleation; this could also occur in polycrystals. (4) Rapid growth of cube and S grains is favoured by the SIBM nucleation mechanisms observed in the bicrystals so that these orientations usually become the strongest texture components of recrystallized Al.
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Acknowledgements The authors wish to thank the Pechiney research centre at Voreppe for financial support and many useful discussions. They are also particularly grateful to G. Triboulet of the Ecole des Mines for help in growing the bicrystals.
[8] [9] [10] [11] [12] [13] [14]
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