On pointed minima in the interfacial energy of bicrystal systems

Abstract

A parabolic Frenkel-Kontorova model was used to investigate the misfit dependence of the interfacial energy of a bicrystal system. An exact solution was obtained substantiating the conclusions drawn by other authors from approximate solutions of more complicated models. The main conclusion is that pointed minima of various orders of strength exist in the graph where the lattice constants are in the ratio of small integers and where previous less accurate calculations predicted a smooth variation. A correlation between the complexity of the misfit and the order of strength of the minima is also obtained.