Grain-boundary structures in hexagonal materials: Coincident and near coincident grain boundaries
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I.
INTRODUCTION
THE present work is to address the question of grainboundary structure in materials crystallizing in the hexagonal structure. Despite the technological importance of these materials, very few atomistic studies of interfaces in hexagonal materials have been performed. Furthermore, new interest has arisen in intermetallic compounds with hexagonal structures, and grain boundaries are expected to play an important role in the mechanical behavior of these alloys. Computer simulation of grain-boundary structure in pure cubic metals has been carried out for a number of years, and our present understanding of the atomic structure of grain boundaries relies to a great extent on the results of these simulations. Most of the present understanding of the atomic structure of grain boundaries is derived from studies on cubic materials. This understanding requires the analysis of calculations and experimental observations. So far such an analysis has been carried out only for cubic materials. [~] For hexagonal structures, only pair potential simulations have been performed for twin interfaces. 12.37In the present work, we computed structures for various symmetrical tilt boundaries with the [li00] tilt axis, using the embedded atom method (EAM). Accurate interatomic potentials developed recently by Pasianot et a/. 141 were used, as described subsequently. On the basis of atomistic simulations for cubic materials, some general models have been developed, such as the structural unit model, [s,6't] which applies to both tilt and twist boundaries and has been generalized even to nonperiodic boundaries, tT's] In the analysis of our results, we study the applicability of these models to hexagonal metals. Geometrical understanding of the DIANA FARKAS, Professor, is with the Department of Materials Science and Engineering, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0237. Manuscript submitted October 1, 1993. METALLURGICAL AND MATERIALS TRANSACTIONS A
symmetry principles of grain boundaries in cubic alloys has also been developed, 19] including the group theoretical formulation of the geometry of grain boundaries. This formulation can be applied to materials with any type of symmetry. Therefore, coincidence lattice theory, developed from the study of grain-boundary structure in cubic metals, has also been used to model grain boundaries in hexagonal close-packed (hcp) metals, tl~ The original concept of coincidence was extended to "near coincidence." Exact and near coincident site lattices (CSLs) for hcp metals have been tabulated for rotations, about [0001], [li00], and [1 lff.0],ill,12] It can be shown that exact CSLs can be obtained in hcp crystals only when (c/a) 2 is rational, except for rotations about the [0001] axis. lt~ An important objective of the present work is studying the relation between exact coincidence and near coincidence boundaries in hexagonal materials, as revealed by computer simulation studies. It has been proposed t6,~3,8] that an important parameter to the grain-bo
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