New calculational method for epitaxial energy: Application to an axial commensurate interface

A new ``mapping technique'' is introduced which allows the study of epitaxy in systems that are commensurate or incommensurate. This method is applied to the epitaxy of fcc(111)/bcc(110) which is commensurate in one direction and incommensurate in the other. The mapping technique predicts a new epitaxial orientation, in good agreement with recent experimental results. The use of second-order perturbation theory in conjunction with the mapping technique predicts a change in epitaxial orientations as a function of island size and stiffness of overlayer lattice.