  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.
