A Non-Isothermal Phase-Field Crystal Model with Lattice Expansion: Analysis and Benchmarks

TL;DR

This paper develops a comprehensive non-isothermal phase-field crystal model that incorporates heat flux and lattice expansion, validated through analytical derivations and numerical benchmarks, advancing mesoscale solidification modeling.

Contribution

It introduces a novel non-isothermal phase-field crystal model with thermal expansion and heat flux, including analytical derivations and extensive numerical benchmarks.

Findings

Derived thermal compatibility and entropy-production conditions

Validated model through numerical benchmark simulations

Explored parameter effects on density and temperature during solidification

Abstract

We introduce a non-isothermal phase-field crystal model including heat flux and thermal expansion of the crystal lattice. The thermal compatibility condition, as well as a positive entropy-production property, is derived analytically and further verified by numerical benchmark simulations. Furthermore, we examine how the different model parameters control density and temperature evolution during dendritic solidification through extensive parameter studies. Finally, we extend our framework to the modeling of open systems considering external mass and heat fluxes. This work sets the ground for a comprehensive mesoscale model of non-isothermal solidification including thermal expansion within a positive entropy-producing framework, and provides a benchmark for further meso- to macroscopic modeling of solidification.