Growth of two-dimensional hexagonal lattices in the phase-field crystal model

The crystallization of a supercooled metastable homogeneous phase into a hexagonal periodic lattice has been studied within the phase-field crystal model. The numerically determined velocities of the crystallization front of the hexagonal lattice are compared to the analytical traveling wave solution. The growth of the hexagonal lattice during the crystallization of the undercooled liquid phase has been described within a second-order (two-mode) model, where the amplitudes of the first and second sublattices are taken into account separately. The hexagonal lattice is formed after the formation of the metastable triangular phase; the kinetics of the crystallization front is determined by the symmetry of the growing phase and by the driving force mag-nitude.