E. Fried et Me. Gurtin, A PHASE-FIELD THEORY FOR SOLIDIFICATION BASED ON A GENERAL ANISOTROPIC SHARP-INTERFACE THEORY WITH INTERFACIAL ENERGY AND ENTROPY, Physica. D, 91(1-2), 1996, pp. 143-181
Using balance laws for microforce and energy in conjunction with const
itutive equations consistent with the second law, we develop a general
phase-field theory that allows for a constitutive dependence of the i
nternal 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 s
hear, and dissipative transition kinetics.