Phase field model of interfaces in single-component systems derived from classical density functional theory

TL;DR

This paper derives a phase field model for interfaces in single-component systems from classical density functional theory, providing physical insights and suggesting improvements.

Contribution

It offers a first-principles derivation of the phase field model from density functional theory, clarifying its physical meaning and limitations.

Findings

Derivation of phase field model from density functional theory for crystal-liquid interfaces.

Physical interpretation of the phase field and its parameters.

Suggestions for improving phase field models.

Abstract

Phase field models have been applied in recent years to grain boundaries in single-component systems. The models are based on the minimization of a free energy functional, which is constructed phenomenologically rather than being derived from first principles. In single-component systems the free energy is a functional of a ``phase field'', which is an order parameter often referred to as the crystallinity in the context of grain boundaries, but with no precise definition as to what that term means physically. We present a derivation of the phase field model by Allen and Cahn from classical density functional theory first for crystal-liquid interfaces and then for grain boundaries. The derivation provides a clear physical interpretation of the phase field, and it sheds light on the parameters and the underlying approximations and limitations of the theory. We suggest how phase field models may be improved.