Perturbative solution of a propagating interface in the phase field model

TL;DR

This paper derives a perturbative solution for a propagating interface in the phase field model, revealing how interface temperature deviates from equilibrium and demonstrating a square root time dependence during phase transition.

Contribution

It introduces a novel perturbative approach to analyze propagating interfaces in phase field models, explicitly calculating leading-order effects and interface temperature deviations.

Findings

Interface displacement scales with the square root of time under certain conditions.

Interface temperature deviation is proportional to interface velocity.

Explicit leading-order contribution derived for the propagating interface.

Abstract

When a stable ordered phase and a metastable disordered phase are separated by a flat interface, the metastable state changes to the stable state through the propagation of the interface. For cases in which latent heat is generated, the interface displacement during some time interval is proportional to the square root of the time interval when the extent of supercooling is less than a certain value. We demonstrate this behavior by deriving a perturbative solution for a propagating interface in the phase field model. We calculate the leading-order contribution explicitly, and find that the interface temperature deviates from the equilibrium transition temperature in proportion to the interface velocity.