Abstract
The anisotropy of solid-liquid interfacial energy dominates the morphology of micro-structures in the solidification process, and material properties deeply depend on the morphology of microstructures. Therefore, the anisotropy of solid-liquid interfacial energy is an important physical parameter that controls properties of materials. On the other hand, because the phase field crystal model can describe the density wave of structure and dynamics at the atomic scale, it reasonably can describe the solid-liquid interfacial energy, elastic properties, etc. Thus, we use the phase field crystal (PFC) model to study the anisotropy of solid-liquid interfacial energy. We derive the amplitude equations and corresponding free energy functional from the PFC model under different assumptions. There are two factors that distinguish various amplitude equations, namely, the rotational invariance and the mean density difference between solid and liquid phases. We study how these two factors affect the anisotropy of solid-liquid interfacial energy. We show that the anisotropy of solid-liquid interfacial energy is weaker while the rotational invariance is present and it is stronger while the mean density difference between solid and liquid is considered. In addition, we analyse the amplitude profiles across the interface and we find that the physical origin of the anisotropy of solid-liquid interfacial energy is due to different amplitude profiles at the different orientation. Furthermore, we find that the rotational invariance gives rise to variation of the atomic spacing which genuinely captures fundamental properties across the solid-liquid interface. Finally, we show that the coupling between the amplitude profiles and the mean density is not negligible, and the mean density difference results in sharp amplitude profiles across the interface, hence a larger anisotropy of solid-liquid interfacial energy.