Development of Angle-Dependent Phase Field Crystal Model for Vapor-Liquid-Solid Transitions

As an efficient and fast-developing continuum modeling approach, the phase field crystal (PFC) method is able to resolve systems on atomic length and diffusive timescales. It can well describe system elasticity, plasticity and other important properties by introducing a free energy functional of a conserved atomic density field. However, what is lacking in majority of PFC models is the interaction or coexistence between vapor and condensed phases, an important factor for many physicochemical processes. Here we present a new PFC model based on the angle-adjustable density field formulation we developed before, which incorporates bond-angle dependence of anisotropic interparticle interactions. The relative stability of vapor, liquid and solid phases, the coexistence and transitions between them, and the corresponding interfacial dynamics can be well described by the model. The pressure-temperature phase diagram for pure substance has been obtained, with results consistent with those of some real material systems. Our new PFC model could serve as an effective tool to model realistic experimental processes such as chemical vapor deposition and vapor-liquid-solid growth.