# [023] Formalism for the calculation of local elastic constants at grain boundaries by means of atomistic simulation

M. D. Kluge, D. Wolf, J. F. Lutsko, and S. R. Phillpot., "Formalism for the calculation of local elastic constants at grain boundaries by means of atomistic simulation", *J. App. Phys.*, **67**, 2370 (1990)

## 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 Cuand 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.