Phase-field model of solidification of a binary alloy

We develop a rather general thermodynamically consistent phase-field model for solidification of a binary alloy, based on an entropy functional that contains squared gradient terms in the energy density, the composition and the phase-field variable. By assuming positive local entropy production, we derive generalized phase-field equations for an alloy, including cross terms that connect thermal and compositional driving forces to energy and solute fluxes. We explore this model in detail for a regular solution and show that four existing models can be recovered as special cases. We also use it to develop a new phase-field model for an alloy in which an explicit phase-field variable is absent.