Two dimensional phase field crystal study of thermo-density coupling: Thermal expansion, recalescence, and plasticity

Abstract

In this article we present a thermal coupling to a recently published two-time scale phase field crystal model (MPFC) to describe latent heat contributions of systems undergoing rapid phase transformations. We call this formulation Temperature Field Crystal (TFC), which permits the study of coupled density, vacancy and temperature field dynamics at the length-scale of atomic ordering. Following a derivation of the new thermo-density coupled MPFC model, several physical properties of the model are demonstrated. We reproduce the thermo-density interface profiles encountered in the steady state solidification growth limit. We further illustrate the existence of a vacancy concentration inherent in the phase field crystal amplitude. It is shown that with a frozen thermal gradient, of the form often used in directional solidification studies, a vacancy gradient is established along with an associated thermal stress. In particular, we show that within the isochoric limit of the model, effects of thermal expansion are incorporated through the change of amplitude with respect to temperature, rather than by increasing the equilibrium lattice length. The TFC model is then applied to the study of select solidification processes. It is shown that the release of latent heat during recalescence is accompanied by a change in the average thermal pressure. Further, we illustrate, to our knowledge for the first time, that modulations of the recalescence curve can be indicative of plastic deformation, dislocation activity, and phonon scattering. Notably, the temperature evolution may be used as a marker for the grain distribution attained from nucleation following a system quench.