Thermodynamically consistent models of phase-field type for the kinetic of phase transitions

doi:10.1016/0167-2789(90)90015-H

Physica D: Nonlinear Phenomena

Volume 43, Issue 1, May 1990, Pages 44-62

https://doi.org/10.1016/0167-2789(90)90015-H Get rights and content

Abstract

A general framework is given for the phenomenological kinetics of phase transitions in which not only the order parameter but also the temperature may vary in time and space. Instead of a Ginzburg-Landau free energy functional, as used in formulating the Cahn-Hilliard equation, we use the analogous entropy functional. Model entropy functionals, and the kinetic equations resulting from them, are constructed for various cases: phase transitions with and without a critical point, and (in the former case) with or without a latent heat. The class considered is general enough to include the entropy functionals for the Ising model in mean-field approximation, the van der Waals fluid, and a simplified version of the density-functional theory of freezing. A case without critical point, for which the energy is conserved but the order parameter is not, provides a thermodynamically consistent derivation of the phase-field equations studied by Caginalp, Fix and others, and also leads in a natural way to the Lyapunov functional given by Langer for these equations; but the treatment also suggests that a modified version of the phase-field equations might provide a more realistic model of freezing.

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Thermodynamically consistent models of phase-field type for the kinetic of phase transitions

Abstract

Acta Metall.

Acta Metall.

Physica D

Spectral comparison principles for the Cahn-Hilliard and phase-field equations, and the coarsening effect

Physica D

Surface tension and supercooling in solidification theory

An analysis of a phase field model of a free boundary

Arch. Rat. Mech. Anal.

Higher-order phase field models and detailed anisotropy

Phys. Rev. B

Dynamics of layered interfaces arising from phase boundaries

SIAM J. Appl. Math.

Free energy of a nonuniform system I. Interfacial free energy

J. Chem. Phys.

Diffuse interface model of diffusion-limited crystal growth

Phys. Rev. B

Mathematical aspects of reacting and diffusing systems

Phase field methods for free boundary problems

The gradient theory of phase transitions for systems with two potential wells

Renormalization group methods for critical dynamics I. Recursion relations and effects of energy conservation

Phys. Rev. B