A model for the energy of a semicoherent interface between two crystal planes is presented. The interface is decomposed into coherent regions and defect regions, such that the defects compensate for the misfit between the two planes. The relaxed energy of the interface - the energy after separation into coherent and defect regions - is given by a weighted average of the energy of the individual regions. Thus, given any two crystal structures with arbitrary lattice parameters, one can find the planes and relative rotations that yield good-fitting, low energy interfaces. Calculations are performed by varying both the planes comprising the interface and the rotation between them, and computing the associated energy. Results for low energy habit planes in face centered cubic (FCC)/body centered cubic (BCC) systems match well with experimental data. The results also show that in many, but not all, cases, the optimal relative rotation between planes corresponds to an invariant line orientation.
Bibliographical noteFunding Information:
Initial development of the model for noncoherent interfaces was supported by a grant from the National Science Foundation grant CMS–9503393 until June 31, 1999. Application of the model to habit plane selection was supported by the Department of Energy through grant DE–FG02–99ER45770 beginning July 1, 1999. The authors appreciate many interesting and educational conversations with Bill Reynolds at VPI, Jim Howe and Bill Johnson at UVa, Kaushik Bhattacharya at Caltech and the entire Solid Mechanics group at Minnesota. Finally, PHL would like to thank the Max–Planck–Institute for Mathematics in the Natural Sciences in Leipzig, Germany and Caltech for their hospitality during the completion of this work.