An approach to local band average for the temperature dependence of lattice thermal expansion

TL;DR

This paper presents an analytical local bond average approach that explains the nonlinear temperature dependence of lattice thermal expansion, aligning well with experimental data without relying on traditional mode Gruneisen constants.

Contribution

The paper introduces a novel analytical method based on local bond averaging to model lattice thermal expansion's temperature dependence, simplifying previous complex models.

Findings

Thermal expansion coefficient closely follows Debye specific heat.

Model matches experimental data using Debye temperature and atomic cohesive energy.

Approach suggests a fundamental understanding of lattice expansion mechanisms.

Abstract

It has long been puzzling regarding the mechanism behind the nonlinearity of lattice thermal expansion at low temperatures despite modeling considerations from various perspectives in classical or quantum approximations. An analytical solution in terms of local bond average is presented herewith showing that the thermal expansion coefficient follows closely the specific heat of Debye approximation without the involvement of mode Gruneisen constant or the bulk modulus. Matching predictions to experimental observations using the Debye temperature and the atomic cohesive energy as input evidences that the current approach may represent the true situation of temperature induced lattice expansion though the exact form of phonon density of states need to be considered for further refinement.