First Principles Derivation of Effective Ginzburg-Landau Free Energy models for Crystalline Systems

TL;DR

This paper derives a fundamental expression for the free energy density of crystalline systems using classical density functional theory, extending previous work and discussing its limitations for modeling elastic relaxation and boundary conditions.

Contribution

It provides a first-principles derivation of Ginzburg-Landau free energy models for crystals, improving theoretical understanding and application scope.

Findings

Derived gradient expansion of free energy density

Extended previous derivation by L{"o}wen et al.

Discussed limitations related to elastic relaxation and boundary conditions

Abstract

The expression of the free energy density of a classical crystalline system as a gradient expansion in terms of a set of order parameters is developed using classical density functional theory. The goal here is to extend and complete an earlier derivation by L{\"o}wen et al (Europhys. Lett.9, 791, 1989). The limitations of the resulting expressions are also discussed including the boundary conditions needed for finite systems and the fact that the results cannot, at present, be used to take into account elastic relaxation.