Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard phase fie
ld models for binary alloy solidification with elasticity are derived, providing an explicit connection between phase field crystal and phase field models. Sample simulations of solute migration at grain boundaries, eutectic solidification and quantum dot formation on nano-membranes are also presented.
