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

Crystal growth with various patterns, a hexagonal, circular, square, rectangular, star-like, and facet were 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 e and average density ψ. When the undercooling temperature reaches to e = – 0.75, the crystal is evolved into a stable striped phase. Further increasing from e = – 0.75 to – 0.25, a combination of triangular-striped coexistence pattern, triangular-liquid coexistence phase, and 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 growth morphology. For hexagonal lattice, large undercooling temperature e leads to a faster crystallization. Finally, a morphological phase diagram under the effect of e and ψ on star-like dendrite and compact spherical shape (CSS) is constructed as a function of phase-field crystal parameters.