Thermo-Density Coupling in PFC Type Models for the Study of Rapid Crystallization

We self-consistently derive a formalism that couples a Phase Field Crystal (PFC) density field to thermal transport. It yields a theory for non-uniform transient temperature and density evolution, and includes local latent heat release during atomic rearrangements of the PFC density field. The basic formalism is applied to the basic PFC model, demonstrating the approach's capacity to capture solidification and recalescence. With an aim towards linking physical temperature to PFC temperature, a new classical density field theory for solid/liquid/vapor systems is then derived. It presents a different approach to those traditionally used in the PFC literature while still retaining the major advantages that have become the hallmark of PFC modelling. The new model is based entirely on physical density and temperature scales. We end the paper by applying the thermal-density coupling formalism to this new multi-phase density functional theory/PFC model.