Formalism for the calculation of local elastic constants at grain boundaries by means of atomistic simulation

Abstract

A new formalism for use in atomistic simulations to calculate the full local elastic-constant tensor in terms of local stresses and strains is presented. Results of simulations on a high-angle (001) twist grain boundary are illustrated, using both a Lennard–Jones potential for Cu and an embedded-atom potential for Au. The two conceptionally rather different potentials show similar anomalies in all elastic constants, confined to within a few lattice planes of the grain boundary, with an especially dramatic reduction in the resistance to shear parallel to the grain-boundary plane. It is found that the primary cause of the anomalies is the atomic disorder near the grain boundary, as evidenced by the slice-by-slice radial distribution functions for the inhomogeneous interface system.