Diffusion-Controlled Anisotropic Growth of Stable and Metastable Crystal Polymorphs in the Phase-Field Crystal Model

We use a simple density functional approach on a diffusional time scale, to address freezing to the body-centered cubic (bcc), hexagonal close-packed (hcp), and face-centered cubic (fcc) structures. We observe faceted equilibrium shapes and diffusion-controlled layerwise crystal growth consistent with two-dimensional nucleation. The predicted growth anisotropies are discussed in relation with results from experiment and atomistic simulations. We also demonstrate that varying the lattice constant of a simple cubic substrate, one can tune the epitaxially growing body-centered tetragonal structure between bcc and fcc, and observe a Mullins-Sekerka–Asaro-Tiller-Grinfeld-type instability.

Figure 1

(a) Driving force of crystallization, $\Delta \omega$, and (b) $\Delta \omega /\Delta {\omega }_{bcc}$ vs initial number density for various polymorphs.

Figure 2

bcc crystal growth as predicted by the PFC model. (a) Simulation box with crystal growing into the (100) direction. (b) Local and coarse-grained (filtered) densities across the $\{100\}$ interface. (c) Coarse-grained densities for the $\{100\}$, $\{110\}$, and $\{111\}$ interfaces. (d) Depth of the depletion zone vs dimensionless time ($\tau$) in (b). (e) Peak amplitude vs $\tau$ for (b). (f) Interface position vs $\tau$ and (g) the velocity coefficients vs $n_0$ for the three low index orientations.

Figure 3

Heteroepitaxy in the PFC model: (a) Axial ratio $c/a$ of the bct structure, and (b) the average growth rate ($\overline{v}$) vs the lattice constant ($a_0$) of the substrate. Bars denote the scattering of $\overline{v}$ due to the variation of the front position $Z$.