Analytic elastic coefficients in molecular calculations: Finite strain, nonaffine displacements, and many-body interatomic potentials

Abstract

Elastic moduli are among the most fundamental and important properties of solid materials, which is why they are routinely characterized in both experiments and simulations. While conceptually simple, the treatment of elastic coefficients is complicated by two factors not yet having been concurrently discussed: finite-strain and nonaffine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic moduli and extend it to explicitly consider nonaffine displacements. We further present analytical expressions for second-order derivatives of the potential energy for two-body and generic many-body interatomic potentials, such as cluster and empirical bond-order potentials. Specifically, we revisit the elastic constants of silicon, silicon carbide, and silicon dioxide under hydrostatic compression and dilatation. Based on existing and recent results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.