Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2D and3D

Abstract

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) modelof overdamped conservative dynamics, to address polymorphism, crystal nucleation, andcrystal growth in the diffusion-controlled limit. We refine the phase diagram for 3D, anddetermine the line free energy in 2D and the height of the nucleation barrier in 2Dand 3D for homogeneous and heterogeneous nucleation by solving the respectiveEuler–Lagrange (EL) equations. We demonstrate that, in the PFC model, thebody-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close-packedstructures (hcp) compete, while the simple cubic structure is unstable, and that phasepreference can be tuned by changing the model parameters: close to the critical point thebcc structure is stable, while far from the critical point the fcc prevails, with anhcp stability domain in between. We note that with increasing distance fromthe critical point the equilibrium shapes vary from the sphere to specific facetedshapes: rhombic dodecahedron (bcc), truncated octahedron (fcc), and hexagonalprism (hcp). Solving the equation of motion of the PFC model supplied withconserved noise, solidification starts with the nucleation of an amorphous precursorphase, into which the stable crystalline phase nucleates. The growth rate is foundto be time dependent and anisotropic; this anisotropy depends on the drivingforce. We show that due to the diffusion-controlled growth mechanism, which isespecially relevant for crystal aggregation in colloidal systems, dendritic growthstructures evolve in large-scale isothermal single-component PFC simulations. Anoscillatory effective pair potential resembling those for model glass formers has beenevaluated from structural data of the amorphous phase obtained by instantaneousquenching. Finally, we present results for eutectic solidification in a binary PFC model.