Journal of Scientific Computing

, Volume 37, Issue 1, pp 89–102

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


  • Lei Zhang
    • Department of MathematicsPenn State University
  • Long-Qing Chen
    • Department of Materials Science and EngineeringPenn State University
    • Department of Mathematics and Department of Materials Science and EngineeringPenn State University

DOI: 10.1007/s10915-008-9207-7

Cite this article as:
Zhang, L., Chen, L. & Du, Q. J Sci Comput (2008) 37: 89. doi:10.1007/s10915-008-9207-7


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.


NucleationCritical nucleiPhase field simulationAnisotropic elasticitySolid state phase transformation
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© Springer Science+Business Media, LLC 2008