A Thermodynamically-Consistent Phase Field Crystal Model of Solidification with Heat Flux

TL;DR

This paper introduces a thermodynamically consistent phase field crystal model for solidification with heat flux, capturing temperature-dependent free energy variations and demonstrating solidification processes.

Contribution

The paper presents a novel, thermodynamically consistent PFC model incorporating heat flux, enabling accurate simulation of solidification with temperature effects.

Findings

Model maintains positive entropy production in bulk and boundaries.

Successfully constructs temperature-atom-density phase diagram.

Demonstrates solidification process using the new model.

Abstract

In this paper we describe a new model for solidification with heat flux using the phase field crystal (PFC) framework. The equations are thermodynamically consistent, in the sense that the time rate of change of the entropy density is positive in the bulk and at the boundaries of the domain of interest. The resulting model consists of two equations, a heat-like equation and a mass-conservation equation that describes how the atom density changes in time and space. The model is simple, yet it can properly capture the variation in the free energy landscape as the temperature is changed. We describe to construct a temperature-atom-density phase diagram using this energy landscape, and we give a simple demonstration of solidification using the model.