Lattice statics Green's function method for calculation of atomistic structure of grain boundary interfaces in solids: Part I. Harmonic theory

Abstract

A lattice statics Green's function method is described for calculating the atomistic structure of a solid near a grain boundary interface. First, a reference state is defined which is ‘near’ the equilibrium state. The Green's function for the reference state is obtained in terms of the perfect lattice Green's function by mapping the lattice sites of the reference state to the perfect lattice sites and solving the Dyson's equation within a supercell. This Green's function gives the response of the reference state which determines the atomic relaxations under the net forces which would be present in the reference state. The specific case of a ∑5 tilt boundary in a fec lattice has been considered, assuming the validity of the harmonic approximation.