University of Pittsburgh
Department of Mathematics
eme11@pitt.edu
Abstract: 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.