  We present a derivation of the recently proposed eighth order phase field
crystal model [Jaatinen et al., Phys. Rev. E 80, 031602 (2009)] for the
crystallization of a solid from an undercooled melt. The model is used to study
the planar growth of a two dimensional hexagonal crystal, and the results are
compared against similar results from dynamical density functional theory of
Marconi and Tarazona, as well as other phase field crystal models. We find that
among the phase field crystal models studied, the eighth order fitting scheme
gives results in good agreement with the density functional theory for both
static and dynamic properties, suggesting it is an accurate and computationally
efficient approximation to the density functional theory.

Materials Science