Phase-field crystal modeling of crystal growth patterns with competition of undercooling and atomic density.

Crystal growth with various patterns, hexagonal, circular, square, rectangular, star-like, and faceted, was investigated using the one-mode approximation of phase-field crystal (PFC) modeling. The simulations were carried out at different temperatures and average densities of the diverse patterns. The pattern selection of crystal growth is caused by the competition between undercooling temperature ε and average density ψ. When the undercooling temperature reaches ε = -0.75, the crystal evolves into a stable striped phase. Further increasing from ε = -0.75 to -0.25, a combination of a triangular-striped coexistence pattern, a triangular-liquid coexistence phase and a stable triangular pattern forms with average densities ψ = -0.130, -0.185 and -0.285, respectively. In particular, when the time, undercooling temperature and average density increase, the crystal grows to a secondary pattern. The introduction of noise terms breaks the symmetry in the growth morphology. For a hexagonal lattice, a large undercooling temperature ε leads to faster crystallization. Finally, a morphological phase diagram under the effect of ε and ψ with star-like dendrite and compact spherical shape (CSS) is constructed as a function of the phase-field crystal parameters.