Controlling crystal symmetries in phase-field crystal models

We investigate the possibility to control the symmetry of ordered states in phase-field crystal models by tuning nonlinear resonances. In two dimensions, we find that a state of square symmetry as well as coexistence between squares and hexagons can be easily obtained. In contrast, it is delicate to obtain coexistence of squares and liquid. We develop a general method for constructing free energy functionals that exhibit solid-liquid coexistence with desired crystal symmetries. As an example, we develop a free energy functional for square-liquid coexistence in two dimensions. A systematic analysis for determining the parameters of the necessary nonlinear terms is provided. The implications of our findings for simulations of materials with simple cubic symmetry are discussed.