Journal of Scientific Computing

, Volume 37, Issue 1, pp 89–102 | Cite as

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



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.


Nucleation Critical nuclei Phase field simulation Anisotropic elasticity Solid state phase transformation 


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© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  1. 1.Department of MathematicsPenn State UniversityCentre CountyUSA
  2. 2.Department of Materials Science and EngineeringPenn State UniversityCentre CountyUSA
  3. 3.Department of Mathematics and Department of Materials Science and EngineeringPenn State UniversityCentre CountyUSA

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