Mathematical and Numerical Aspects of a Phase-field Approach to Critical Nuclei Morphology in Solids

Authors:
Lei Zhang;Long-Qing Chen;Qiang Du
Affiliations:
Department of Mathematics, Penn State University, Centre County, USA 16802;Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802;Department of Mathematics and Department of Materials Science and Engineering, Penn State University, Centre County, USA 16802
Venue:
Journal of Scientific Computing
Year:
2008

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Diffuse-interface approach to predicting morphologies of critical nucleus and equilibrium structure for cubic to tetragonal transformations

Journal of Computational Physics

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Abstract

We investigate a phase-field model for homogeneous nucleation and critical nucleus morphology in solids. We analyze the mathematical properties of a free energy functional that includes the long-range, anisotropic elastic interactions. We describe the numerical algorithms used to search for the saddle points of such a free energy functional based on a minimax technique and the Fourier spectral implementation. It is demonstrated that the phase-field model is mathematically well defined and is able to efficiently predict the critical nucleus morphology in elastically anisotropic solids without making a priori assumptions.