Analytic elastic constants in molecular calculations: Finite strain, non-affine displacements, and many-body interatomic potentials

TL;DR

This paper develops a comprehensive theoretical framework for calculating elastic constants in molecular simulations, explicitly including finite strains and non-affine displacements, and applies it to various materials under different stress states.

Contribution

It extends existing elastic constant theory to incorporate non-affine displacements and many-body potentials, providing analytical expressions and applying them to real materials.

Findings

Analytical expressions for second derivatives of potential energy for many-body potentials.

Revised elastic constants for silicon, silicon carbide, and silicon dioxide under various conditions.

Insights into stability limits of crystalline lattices under multiaxial stress.

Abstract

Elastic constants 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 constants is complicated by two factors not yet having been concurrently discussed: finite-strain and non-affine, internal displacements. Here, we revisit the theory behind zero-temperature, finite-strain elastic constants and extend it to explicitly consider non-affine 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 new results, we outline the effect of multiaxial stress states as opposed to volumetric deformation on the limits of stability of their crystalline lattices.