Formation and Stability of the Crystalline Structures in Two-Mode Phase-Field Crystal Model

The two-mode phase-field crystal (PFC) model is an extended classical PFC model which allows one to describe hexagonal and other complex lattices. In such model the order parameter is periodic in crystalline state and constant in disordered or liquid phase. The PFC model allows linking mesoscopic and microscopic spatial–temporal scales and to implement in the results of the molecular dynamics method into phase-field models. In present work the regimes of crystallization of two-dimensional structures using the two-mode PFC method was studied. A quasi-crystalline anisotropic striped phase was found, this phase qualitatively corresponds to the obtained ones in colloidal solutions. The stability of structures during phase transitions between crystals with various symmetries was investigated. A structure diagram was constructed, and the melting curve was presented. A numerical approach for the two-mode PFC model was developed and the simulations were carried out using finite-element method in direct space. The dependence of the types of crystalline structures on the control parameters was investigated. It is shown that the scale parameters q₀, q₁ allow one to control the lattice symmetry type, and the shift parameters r₀, r₁ affect on the position of the structures existence regions and the melting curve. Also the shift parameters allow one to control the formation of the quasi-crystalline structures. The stability of structures with hexagonal and quadratic symmetries was investigated. During such transitions the change in near- and far-order symmetry occurs sequentially. The possible existence of a crystal with 5-fold symmetry as an intermediate phase was figured out. The sequence of transitions from triangular through honeycomb and square lattice to the liquid phase is shown. It is shown that the transitions themselves occur through the mixed glassy phase. Proposed model and method is applicable for modeling of the transitions between three-dimensional hexagonal (HCP) and cubic (FCC/BCC) lattices in metals and alloys.