The effect of misfit on heterophase interface energies

Most previous atomistic simulations of heterophase interfaces have neglected misfit, the discrepancy between the interatomic length scales parallel to the interface of the two phases. The obstacles to quantitative calculations of interface energies in the presence of misfit are assessed. The most straightforward approach is to perform simulations for a supercell whose size is of the order of the cube of the smallest common periodic length scale (essentially the coincidence-site-lattice periodicity), which varies inversely with the misfit parameter. Such supercells typically contain at least thousands of atoms. First-principles simulations are highly accurate, but are feasible only for a few selected heterophase interfaces with large misfit. Classical interatomic potentials, on the other hand, are efficient numerically, but their accuracy has not been demonstrated in the context of heterophase interface calculations. An approximate formulation of the interface energy is presented here which can be evaluated numerically by first-principle calculations for supercells of only moderate size. This formulation explores the relationship between the interface energies for coherent and semi-coherent interfaces. A numerical application to an interface between tetragonal TiAl and perovskite Ti₃AlC is presented.