A simple anisotropic surface free energy function for three-dimensional phase field modeling of multi-crystalline crystal growth

• Published in: Journal of crystal growth Vol. 362; pp. 62 - 65
• Main Authors: Lin, H.K., Chen, C.C., Lan, C.W.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Amsterdam Elsevier B.V 01-01-2013; Elsevier
• Subjects: A1. Crystal morphology; A1. Dendrites; A1. Solidification; Anisotropy; Condensed matter: structure, mechanical and thermal properties; Cross-disciplinary physics: materials science; rheology; Crystal growth; Exact sciences and technology; Free energy; Growth from melts; zone melting and refining; Materials science; Mathematical analysis; Mathematical models; Melts; Methods of crystal growth; physics of crystal growth; Phase diagrams and microstructures developed by solidification and solid-solid phase transformations; Physics; Solidification; Theory and models of crystal growth; physics of crystal growth, crystal morphology and orientation; Thermal properties of condensed matter; Thermal properties of crystalline solids; Thermodynamic properties; Three dimensional; Three dimensional models; A1. Solidification; A1. Crystal morphology; A1. Dendrites; Crystal growth; Interface energy; Digital simulation; Equilibrium shape; Phase field method; Free energy function; Free energy; Solidification; Anisotropy; Growth mechanism; Dendrites; Crystal morphology; Thermodynamic properties; Surface energy
• ISSN: 0022-0248; 1873-5002
• DOI: 10.1016/j.jcrysgro.2012.01.004

Phase field modeling has emerged as a powerful tool in crystal growth simulation, but the description of the anisotropic function for three-dimensional (3D) interfacial free energy without miss-orientation remains quite difficult, especially for the multi-crystalline cases. In this paper, a simple function for keeping the convexity in the reciprocal surface free energy is proposed, and the simulated equilibrium shapes are in good agreement with the analytical ones. Some examples on the dendritic growth in a supercooled melt for mono- and multi-crystalline crystals are also illustrated.
► A new function with a single parameter n for the highly anisotropic interfacial energy without missing orientation. ► The value n varies with the anisotropic strength ε4 in two- and three-dimensions. ► Good agreement with the traditional model in the equilibrium shapes and dendritric growth. ► This new function makes the phase field simulation of multicrystalline growth with high anisotropy much easier.