Journal of Statistical Physics, Vol. 95, Nos. 56, 1999. p. 1141-1164.
A discussion is given of recent advances in phase-field modeling of materials which change phase. On one hand, general models incorporating elasticity properties of the material, nonconserved and conserved order parameters, and nonlocal effects are now available. On the other hand, gradient theories for binary alloys have been developed which reflect such effects as the dependence of capillarity on the concentration of impurities, solute trapping in its dependence on velocity of solidification fronts, and other nonequilibrium phenomena.