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

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. Keywords Nucleation

• Type: Journal
• Year: 2008
• Where: JSCIC
• Authors: Lei Zhang, Long-Qing Chen, Qiang Du
• Keywords: Critical Nucleus Morphology, Energy Functional, JSCIC 2008, Phase-field Model