Phase field theory of polycrystalline solidification in three dimensions

Abstract

A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the two-dimensional case, where a single orientation field suffices, in three dimensions, minimum three fields are needed. The free energy of grain boundaries is assumed to be proportional to the angular difference between the adjacent crystals expressed here in terms of the differences of the four symmetric Euler parameters. The equations of motion for these fields are obtained from variational principles. Illustrative calculations are performed for polycrystalline solidification with dendritic, needle and spherulitic growth morphologies.

7 pages, 4 figures, submitted to Europhysics Letters on 14th February, 2005

References in corpus (3)

• Phase-Field Model of Dendritic Sidebranching with Thermal Noise
• Nucleation and Bulk Crystallization in Binary Phase Field Theory
• Sharp interface limit of a phase-field model of crystal grains

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• A model for hierarchical patterns under mechanical stresses
• On topological defects in two-dimensional orientation-field models for grain growth
• Efficient and quantitative phase field simulations of polycrystalline solidification using a vector order parameter
• Existence of solutions to a phase-field model of 3D-grain boundary motion governed by a regularized 1-harmonic type flow