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000022906 084__ $$2WoS$$aPhysics, Mathematical
000022906 1001_ $$0P:(DE-Juel1)VDB104034$$aBrener, E.A.$$b0$$uFZJ
000022906 245__ $$aOnsager approach to the one-dimensional solidification problem and its relation to the phase-field description
000022906 260__ $$aCollege Park, Md.$$bAPS$$c2012
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000022906 500__ $$aWe thank M. Plapp for useful discussions. We acknowledge the support of the Deutsche Forschungs-gemeinschaft under Project No. SFB 917.
000022906 520__ $$aWe 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.
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000022906 7001_ $$0P:(DE-HGF)0$$aTemkin, D.E.$$b1
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