A phase-field theory for solidification based on a general anisotropic sharp-interface theory with interfacial energy and entropy

Using balance laws for microforce and energy in conjunction with constitutive equations consistent with the second law, we develop a general phase-field theory that allows for a constitutive dependence of the internal energy and entropy on the order-parameter gradient. A matched asymptotic analysis - appropriate to the limit of decreasing interface thickness - demonstrates the consonance of our theory with a general, thermodynamically consistent sharp-interface theory that accounts for anisotropic interfacial energy and entropy, interfacial tension and shear, and dissipative transition kinetics.