title: Onsager approach to the one-dimensional solidification problem and its relation to the phase-field description.
abstract: We give a general phenomenological description of the steady-state 1D front propagation problem in two cases: the solidification of a pure material and the isothermal solidification of two-component dilute alloys. The solidification of a pure material is controlled by the heat transport in the bulk and the interface kinetics. The isothermal solidification of two-component alloys is controlled by the diffusion in the bulk and the interface kinetics. We find that the condition of positive-definiteness of the symmetric Onsager matrix of interface kinetic coefficients still allows an arbitrary sign of the slope of the velocity-concentration line near the solidus in the alloy problem or of the velocity-temperature line in the case of solidification of a pure material. This result offers a very simple and elegant way to describe the interesting phenomenon of a possible non-single-value behavior of velocity versus concentration that has previously been discussed by different approaches. We also discuss the relation of this Onsager approach to the thin-interface limit of the phase-field description.
authors.affiliation: Peter Grünberg Institut, Forschungszentrum Jülich, Jülich, Germany.
authors.forename: Efim A
authors.initials: EA
authors.lastname: Brener
authors.forename: D E
authors.initials: DE
authors.lastname: Temkin
mesh_terms: D000497:Alloys / Q000737:chemistry*; D003198:Computer Simulation; D008670:Metals / Q000737:chemistry*; D008956:Models, Chemical; D008958:Models, Molecular; D044367:Phase Transition; D013696:Temperature
chemical_list: D000497:Alloys; D008670:Metals