Polymorphism, crystal nucleation and growth in the phase-field crystal model in 2d and 3d

Abstract

We apply a simple dynamical density functional theory, the phase-field crystal (PFC) model of overdamped conservative dynamics, to address polymorphism, crystal nucleation, and crystal growth in the diffusion-controlled limit. We refine the phase diagram for 3d, and determine the line free energy in 2d, the height of the nucleation barrier in 2d and 3d for homogeneous and heterogeneous nucleation by solving the respective Euler-Lagrange (EL) equations. We demonstrate that in the PFC model, the body-centered cubic (bcc), the face-centered cubic (fcc), and the hexagonal close packed structures (hcp) compete, while the simple cubic structure is unstable, and that phase preference can be tuned by changing the model parameters: close to the critical point the bcc structure is stable, while far from the critical point the fcc prevails, with an hcp stability domain in between. We note that with increasing distance from the critical point the equilibrium shapes vary from sphere to the specific faceted shapes: rhombic-dodecahedron (bcc), truncated-octahedron (fcc), and hexagonal prism (hcp). Solving the equation of motion of the PFC model supplied with conserved noise, solidification starts with the nucleation of an amorphous precursor phase, into which the stable crystalline phase nucleates. The growth rate is found to be time dependent and anisotropic, which anisotropy depends on the driving force. We show that due to the diffusion-controlled growth mechanism, which is especially relevant for crystal aggrega-tion in colloidal systems, dendritic growth structures evolve in large-scale isothermal single-component PFC simula-tions. Finally, we present results for eutectic solidification in a binary PFC model.