Edge-to-edge interfaces in Ti-Al modeled with the embedded atom method
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NTRODUCTION
THE manner in which two crystals meet at the boundary that separates them has been the subject of fundamental research for decades. Although the idea that planes of atoms from adjacent phases meet in an “edge-to-edge” fashion dates back as far as 1953,[1] the importance of this atomic arrangement in producing low-energy boundaries was not recognized until much later by Shiflet and van der Merwe.[2] These workers noted that an interphase boundary has a low energy when the atoms in the boundary region are arranged along parallel rows, each row being formed by the intersection of one atomic plane from each of the adjoining phases. The edge-to-edge concept was subsequently incorporated into a geometrical model capable of explaining crystal orientation relationships and boundary orientations by Kelly and Zhang.[3] The same geometric boundary configuration was discovered independently using two different approaches: a “g” reciprocal lattice construction that identifies principal primary O-lattice planes,[4,5] and a method based on identifying moiré planes in electron diffraction patterns.[6,7] An edge-toedge boundary, a principal primary O-lattice plane (normal to a particular g vector), and a moiré plane are thus different ways of describing the same boundary geometry. In the Kelly and Zhang view, matching considerations suggest that directions in the two crystals with similar interatomic spacings are good candidates for the row direction in the boundary. Once the row direction is set, the boundary plane is selected to make the boundary commensurate in the direction perpendicular to the row direction. W.T. REYNOLDS, Jr. and D. FARKAS, Professors, are with the Materials Science and Engineering Department, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061-0237. Contact e-mail: reynolds@ vt.edu This article is based on a presentation made in the “Hume-Rothery Symposium on Structure and Diffusional Growth Mechanisms of Irrational Interphase Boundaries,” which occurred during the TMS Winter meeting, March 15–17, 2004, in Charlotte, NC, under the auspices of the TMS Alloy Phases Committee and the co-sponsorship of the TMS-ASM Phase Transformations Committee. METALLURGICAL AND MATERIALS TRANSACTIONS A
One might assume edge-to-edge boundaries have a low energy because the phases match well along the atom rows lying in the interphase boundary plane. From a qualitative perspective, such matching could be expected to yield bonding close to that in the bulk phases. Faceted, edge-to-edge boundaries formed during a massive transformation in Ti-Al make clear, however, that good atomic matching along the rows is not required for such boundaries to appear.[8,9] The boundaries in this system exhibit edge-to-edge matching, yet the matching along the atom rows in a boundary is poor and varies from one boundary to the next. The absence of row matching differentiates the boundaries in Ti-Al from the edge-to-edge boundaries considered by Zhang and Kelly,[10] and it suggests that the presence of atom rows in
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