Onsager approach to 1D solidification problem and its relation to 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 which 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.

5 pages, 1 figure, submitted to Physical Review E

References in corpus (2)

• Capillary-Wave Model for the Solidification of Dilute Binary Alloys
• Diffusion-Induced Oscillations of Extended Defects

Cited by in corpus (6)

• Kinetic cross coupling between non-conserved and conserved fields in phase field models
• Interface kinetics in phase field models: isothermal transformations in binary alloys and steps dynamics in molecular-beam-epitaxy
• Achieving realistic interface kinetics in phase field models with a diffusional contrast
• Variational quantitative phase-field modeling of nonisothermal sintering process
• Elimination of surface diffusion in the non-diagonal phase field model
• Relation Between Bulk and Interface Descriptions of Alloy Solidification