Local Elastic Constants in Thin Films of an FCC Crystal

TL;DR

This paper introduces a new formalism for calculating local elastic constants in inhomogeneous systems like thin films, avoiding the need for volume partitioning, and validates it through simulations of Lennard-Jones crystals and surface melting.

Contribution

It presents a novel formalism for local elastic constants calculation that does not require system partitioning, applicable to inhomogeneous systems such as thin films.

Findings

Local elastic constants match average bulk values.

Stress profiles agree with predictions from local elastic constants.

Surface melting behavior aligns with experimental data.

Abstract

In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of finite volumes over which average elastic constants are calculated. Results for the calculation of the local elastic constants of a nearest neighbor Lennard-Jones fcc crystal in the bulk and in a thin film are presented. The local constants are calculated at exact planes of the (001) face of the crystal. The average elastic constants of the bulk system are also computed and are consistent with the local constants. Additionally we present the local stress profiles in the thin film when a small uniaxial strain is applied. The resulting stress profile compares favorably with the stress profile predicted via the local elastic constants. The surface melting of a model for argon for which experimental and simulation data are available is also studied within the framework of this formalism.