The crystallography and atomic structure of line defects in twin boundaries in hexagonal-close-packed metals
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INTRODUCTION
INTERFACIAL processes can make very important contributions to the mechanical and electrical behavior of polycrystalline materials. This has been recognized for many years and has stimulated intensive research into the atomic configurations and mechanisms at interfaces. Experimental observations have repeatedly demonstrated that linear features frequently arise superimposed on interfaces and that these play significant roles in a variety of processes. Careful analysis of such linear features has shown that they are discontinuities in the underlying interracial structure and can exhibit defectlike attributes, for example, dislocation character, and may also incorporate steps in the interface. Some workers refer to these discontinuities as "ledges," but the present authors prefer a nomenclature which reflects the fact that a diverse range of topological linear discontinuities, including-interracial dislocations, disclinations, and defect-free steps, can actually arise in various types of interfaces. The objective of the present paper is to discuss the crystallography of line discontinuities from a general point of view and to illustrate the atomic structure of some examples in twin boundaries in hexagonal-close-packed (hcp) metals, obtained by computer-generated atomistic simulations. The crystallographic analysis presented brings together two distinct approaches. First, a method is described whereby all the conceivable structural configurations for a given interface (excluding the possibility of local atomic relaxation) can be represented by points in an appropriately def'med two-dimensional (2-D) space. This idea was described in the literature previously for the case of materials with a monoatomic basis. [t.21 In the R.C. POND, Reader, and D.J. BACON, Professor, are with the Department of Materials Science and Engineering, The University of Liverpool, Liverpool L69 3BX, United Kingdom. A. SERRA, Lecturer, is with the Department de Matematica Aplicada, 3, Universitat Politecnica de Catalunya, Barcelona 08034, Spain. A.P. SUTTON, Royal Society Research Fellow, is with the Department of Metallurgy and Science of Materials, University of Oxford, Oxford OX1 3PH, United Kingdom. This paper is based on a presentation made in the symposium "The Role of Ledges in Phase Transformations" presented as part of the 1989 Fall Meeting of TMS-MSD, October 1-5, 1989, in Indianapolis, IN, under the auspices of the Phase Transformations Committee of the Materials Science Division, ASM INTERNATIONAL. METALLURGICAL TRANSACTIONS A
present work, we extend the method to the general case of interphase interfaces between crystals with multiatomic bases and apply it to the case of twin boundaries in hcp metals which, of course, exhibit double-atom bases. With the aid of such "structure maps," the nature of a discontinuity separating any two specified interfacial structures can be established. Thus, for example, the dislocation character and step height associated with the necessary discontinuity can be obtained provided the tw
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