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Carnegie Mellon Center for Nonlinear Analysis
A Discrete Phase Field Model with Microscopic Potential


Emre Esenturk
University of Pittsburgh
Department of Mathematics

: It has been known that the interfacial free energy has a significant effect on the kinetics and morphology of the growing crystal. Building on the approach of [Xinfu Chen, Gunduz Caginalp, Emre Esenturk, to appear in Arch. Rat. Mech. Anal], we present a discrete version of phase field model with non-local interaction to calculate the interfacial free energy. The model naturally suits the discrete geometry of a lattice and provides a methodology to understand the process of transfer of microscopic scale. As an example, we consider a system with Lennard-Jones type potential, calculate the interfacial free energy in [100] and [110] directions and find the anisotropy solid-liquid interface.