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

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.

arXiv comment17 pages, 4 figures

References in corpus (20)

• Modeling Elasticity in Crystal Growth
• Modeling Elastic and Plastic Deformations in Non-Equilibrium Processing Using Phase Field Crystals
• Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview
• Free energy functionals for efficient phase field crystal modeling of structural phase transformations
• Renormalization group approach to multiscale simulation of polycrystalline materials using the phase field crystal model
• An Efficient Algorithm for Solving the Phase Field Crystal Model
• Phase-field modeling of crystal nucleation in undercooled liquids -- A review
• Renormalization group theory for the phase field crystal equation
• Exploring the complex world of two-dimensional ordering with three modes
• Consistent Hydrodynamics for Phase Field Crystals
• Dislocation dynamics and crystal plasticity in the phase field crystal model
• Mesoscale model of dislocation motion and crystal plasticity
• Phase-field-crystal models and mechanical equilibrium
• Closing the gap between atomic-scale lattice deformations and continuum elasticity
• Free energy of the bcc-liquid interface and the Wulff shape as predicted by the Phase-Field Crystal model
• Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization
• Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks
• Self-consistent modeling of anisotropic interfaces and missing orientations: Derivation from phase-field crystal
• The elastic inclusion problem in the (amplitude) phase field crystal model
• Improved time integration for phase-field crystal models of solidification