, Volume 37, Issue 1, pp 89-102
Date: 20 Jun 2008

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

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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.