Elastic constants and thermodynamical quantities for crystal lattices from many-body perturbation theory

TL;DR

This paper derives algebraic expressions for elastic and thermodynamical properties of crystal lattices using many-body Green's functions, extending previous results to higher orders and providing new physical insights.

Contribution

It introduces a third-order perturbation expansion for elastic and thermodynamical quantities, including a novel interpretation of harmonic phonon eigenvectors.

Findings

Derived algebraic expressions for elastic constants and thermodynamical quantities.

Extended existing models to include higher-order terms in interatomic force constants.

Provided a new physical interpretation of harmonic phonon eigenvectors.

Abstract

The method of many body Green's functions is used to derive algebraic expressions for the different elastic and thermodynamical quantities such as the free energy, internal energy, entropy, heat capacity, elastic constants (adiabatic and isothermal) and the coefficient of thermal expansion. The perturbation expansion is developed up to third-order and diagrams corresponding to the equations are represented. The present results extend the existing ones by giving expressions for the elastic constants of arbitrary order and terms which are higher-order in the interatomic force constants that have been obtained earlier. The perturbation expansion in terms of arbitrary macroscopical parameters is considered and the similarity of expansions with respect to different parameters is emphasized. A physical interpretation of the harmonic phonon eigenvectors is considered. To the author's knowledge, no such similar interpretation of the harmonic phonon eigenvectors has been given in the literature before.