R. W. De Blois, Appl. Phys. 36, 1647 (1965). 29. F. Ogburn, B. Paretzkin and H. Peiser, Acta crystallogr. 17, 774 (1964). 30. H. Herring, Phys. Rev. 112, 87 (1951) ...
Acta metall, mater. Vol. 39, No. 7, pp. 1603-1615, 1991 Printed in Great Britain
0956-7151/91 $3.00 + 0.00 Pergamon Press pie
MULTIPLE TWINNING AND SPECIFIC PROPERTIES Z = 3n B O U N D A R I E S I N F . C . C . C R Y S T A L S
OF
CH. V. K O P E Z K Y I, A. V. A N D R E E V A 1 and G. D. S U K H O M L I N 2 qnstitute of Microelectronics Technology and High Purity Materials, U.S.S.R. Academy of Sciences, 142432 Chernogolovka, Moscow District, U.S.S.R. 2All-Union Scientific-Research Tube Institute, Dnepropetrovsk, The Ukraine, U.S.S.R. (Received 20 April 1990; in revised form 26 November 1990)
Abstract--The dominant role of multiple twinning (appearance of the spectrum of _r = 3n boundaries) in the formation of recrystallization texture of materials with a low stacking fault energy (stainless steel, high purity copper, silicon) has been determined. The importance of the formation, development and disappearance of twins as "channels" of the decrease of the system energy during annealing of deformed high purity aluminium is shown. The processes of structure self-organization during annealing, namely, the formation of stable groups of_r = 3n boundaries, new types of metastable defects of polycrystals, such as multiple junctions (M J), multiple nodes (MN), unequiaxial stable grain forms are considered. The crystallography classification, symmetry properties, topology and energetic estimation of the stability of (M J) and (MN) have been performed. Rrsumr---On a drtermin6 le r61e prrpondrrant du maclage multiple (apparition du spectre des joints Z = 3n) dans la formation de la texture de recristallisation des matrriaux ~i faible 6nergie de drfaut d'empilement (acier inoxydable, cuivre de haute puretr, silicium). On a montr6 l'importance de la formation, du drveloppement et de la disparition des macles comme moyens de diminuer l'rnergie du systrme, pendant le recuit d'un aluminium de haute puretr, drformr. On considrre les mrcanismes d'auto-organisation de la structure au cours du recuit, c'est-fi-dire la formation de groupes stables de joints S = 3n, de nouveaux types de drfauts mrtastables des polycristaux (tels que les jonctions multiples, les noeuds multiples) ainsi que des formes stables non 6quiaxes de grains. On donne une classification cristallographique, les proprirtrs de symrtrie, la topologie ainsi qu'une estimation 6nergrtique de la stabilit6 des jonctions et des noeuds multiples. Zusmnmenfassung--Die iiberrangende Rolle der Vielfachzwillingswillingsbildung (Auftreten eines Spektrums von _r = 3n.Korngrenzen) bie der Bildung der Rekristallisationstextur in Werkstoffen mit niedriger Stapelfehlerenergie (rostfreier Stahl, hochreines Kupfer, Silizium) wird dargelegt. Es wird gezeigt, dab Bildung, Entwicklung und Verschwinden der Zwillinge wichtige "Kanfile" f/Jr die Abnahme der Energie des Systems w/ihrend des Ausheilens von verformten, hochreinem Aluminium sind. Die Prozesse der Selbstorganisation der Struktur ffahrend des Ausheilens werden bretrachtet, n/imlich die Bildung stabiler Gruppen von _r = 3~.Korngrenzen, neur Typen metastabiler Defekte von Polykristallen, wie Mehrfachverbindungen (M J), Mehrfachknoten (MN), nichtgleichachsige stabile Kornformen. Kristallographische Klassifikation, Symmetrieeigenschaften, Topologie und energetische Absch/itzungen der Stabilit/it von MJ und MN werden bestimmt.
INTRODUCTION The work brings into concord the developed concepts of the interface crystallography theory as applied to the twinning processes and experimental study of the formation of stable polycrystal structure during recrystallization [1-6]. The processes of formation and development of stacking faults (SF), which give rise to annealing and deformation twins, are typical of a number of materials. The tendency o f the material to twinning increases with decreasing YSF, i.e. with increasing probability of lattice dislocation splitting. Recrystallization twins follow the spienel law of twinning and are described by the geometrical theory as 27 = 3 boundaries for almost all substances with f.c.c, structure, Since for f.c.c, crystals the crystallography of the
coherent twin boundary coincides with that of (SF), the internal (SF) can be considered as two coherent E = 3 boundaries with an atom layer (0 layer twin) between them (Fig. 1). Boundaries of higher twin orders (~ = 3 n) [1-3, 7-9] may appear due to the interaction of 27 = 3 boundaries during migration. 27 = 3 n boundaries may also appear as a result of grain boundary dissociation [3,4, 10, 11]. Materials, characterized by the formation of annealing twins, show unusual spectrum distributions of Z = 3n boundaries and the fraction of these boundaries is high in the recrystallization texture [1-3, 1 1-14]. The objective of the work is to investigate the role of 27 = 3n boundaries obtained by multiple twinning in the formation of polycrystal structure during annealing.
1603
1604
KOPEZKY
et al.:
MULTIPLE
TWINNING
g A
O-A
AfiOA O A B O
ll
O-C
Fig. 1. Sequence of atomic layers in the (SF) of f.c.c. structure ["0-layer twin", arrows show (TB)]. The following problems are suggested: 1. Determination of the crystallography parameters of 27 = 3" boundaries and comparison of these parameters with those of the special boundaries in the geometrical CSL-model. 2. Investigation of the twinning processes in f.c.c. crystals, which includes: (a) experimental study of the crystal geometry of 27 = 3" boundaries and comparison of the experimental data with the theoretical ones; (b) revealing of topological distinctions of 2; = 3" boundaries; (c) statistical estimations. For simplicity, we have accepted the following abbreviations: special boundaries (SB); general or "trivial" boundaries (GB or Tr); twin boundaries fiB); triple junction of boundaries (TJ); multiple junction of boundaries (M J); multiple node of boundaries and junctions (MN); stacking-fault (SF); twin interlayer (TI); stacking fault energy (FsF); specific surface energy of the boundary (y); resultant of boundary tension forces in the junction (AF); coincident site lattice (CSL). CRYSTALLOGRAPHY OF MULTIPLE AND THE CSL MODEL
TWINNING
In accordance with the coincidence models (CSL and 0-lattice), a high-angle boundary structure depends on the orientation relation between the crystals and does not depend on the type and positions of atoms forming the crystal structure. On the basis of the geometrical models it is impossible to understand the transition from low- to high-angle boundaries, the existence of (SB) and (GB), and distribution of different spectra of low energy boundaries in materials with various values of (?SF) [2, 12, 15--17]. The geometrical models available cannot explain the physics of structure formation, while multiple twinning makes a sub-
IN F.C.C. CRYSTALS
stantial contribution to the formation of polycrystal structure. The calculation experiment was carried out in an effort to check, within the experimental error, the crystallographic parameters of CSL boundaries (270~< 51) with respect to parameters of multiple twin boundaries (27i = 3"). The algorithms and programmes developed for this purpose are presented in more detail in [6, 18]. The numerical experiment has shown that the crystallographic parameters of the (SB) in the CSL-model within the experimental error can be determined as 27 = 3" boundary parameters. For instance, Z 0 = 7 ([111], 0 = 38.213 °) (SB) may be expressed as Z i = 36 ([877], 0 = 38.942 °) boundary, Z 0 = 11 ([110], 00 = 50.479 °) as 27i= 36 ([17 15 1], Oi = 49.701°), 270= 21 ([211], 00=44.415 °) as Zi=35 ([955], 43.076°); 270=33 ([110], 00=58.992 ° ) as Zi=35 ([11111], 0t = 60°), etc. The detailed tables of comparison between the crystallographic parameters of (27o~ 70 is required (Fig. 10, where 7o is the specific energy of (GB) to which the twin adjoins). From this it follows that the boundary torque has a dominant role in this process, because ?T ~ ~Nr < ?0 is true for most materials in the quazi-equilibrium state. The process of (TI) separation is expected to proceed in materials with a higher value of (p). This takes place in aluminium compared to steel, in which (TI) pass through the whole grain or intercross. From the experimental data it follows that the quantity of 27 = 3" (SB) increases with increasing duration of annealing in materials with a low value of ?SF- (SB) interact more frequently with each other.
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KOPEZKY et al.: MULTIPLE TWINNING IN F.C.C. CRYSTALS
The number of (SB), (M J), (MN) increases. They inhibit the grain growth in pure metals in the absence of dispersed inclusions, which play the role of stabilizers of fine grains in special alloys. On the whole, the formation of stable groups of 27 = 34 boundaries, of new metastable defects of polycrystals, such as multiple junctions and nodes during recrystallization of materials with a low value of YSF may be considered as the process of structure self-organization [41].
CONCLUSIONS The dominant role of multiple twinning in the formation of the recrystallization texture of materials with a low value of ~sF is shown. From the computer program comparison of the crystallographic parameters of Z = 3n twin boundaries and special boundaries in the CSL-model it was found that: 1. Multiple twinning gives rise to a great number of new orientations with respect to the initial ones. 2. Misorientations characteristic of (SB) in the CSLmodel (boundaries with a high density of coincident sites and a low value of 27) are realized by mulitiple twinning within the experimental error. The higher the twin order, the greater the number of the oriented relationships close to the special ones within the scope of the CSL-model. 3. Misorientations characteristic of low- and middle-angle boundaries may also appear as a result of multiple twinning. The effect of localized lattice defects (dislocations, SF) on the formulation of the complex defects (grain boundaries) is discussed. The experimental studies, made it possible to distinguish special topological and energetic properties of 27 = 3n boundaries in materials with a low value of 7SF'
4. It is shown that for 27 = 3n grain boundaries there is a good agreement between the experimental rotation angles and theoretical ones. 27 = 3~ boundaries may be used as standards for further investigation of the structure and properties of grain boundaries in polycrystalline materials. 5. It has been found that 27 = 3~ boundaries are characterized by faceting and opposite angles in junctions exceeding 120°, which testify the reduced specific energy of the boundaries. The facets of 27 = 3~ boundaries are usually parallel to closely packed planes in CSL and contain a (110) rotation axis along which the density of the coincident sites is maximal. 6. The experimental data prove that the low-angle (0 = 7.4 ° (110)) boundary is a 27 = 243 boundary of the 5th twinning order and exhibits all the properties of special boundaries. 7. The formation of new metastable defects of polycrystals, such as multiple junctions and nodes, is observed during recrystallization. The experimental and theoretical analysis on the topology of (M J),
(MN) and noneequiaxial stable forms of grains are presented. 8. The experimental data on the significance of twinning as "dissipation channels" of energy during recrystallization of high purity aluminium are given. 9. The number of 27 --- 3n (SB), (M J) and (MN) was found to increase during annealing. The low mobility of coherent 27 = 3 (TB), (M J) and (MN) may be responsible for the formation of "rigid" grain boundary groups, which encourage stabilization of bulk polycrystal structure. The formation of new metastable defects of polycrystals, such as (M J), (MN) may be considered as the processes of structure self organization.
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