To describe the homogeneous nucleation process, an interfacial free energy adjustable phase-field crystal model (IPFC) was proposed by reconstructing the energy functional of the original phase field crystal (PFC) methodology. Compared with the original PFC model, the additional interface term in the IPFC model effectively can adjust the magnitude of the interfacial free energy, but does not affect the equilibrium phase diagram and the interfacial energy anisotropy. The IPFC model overcame the limitation that the interfacial free energy of the original PFC model is much less than the theoretical results. Using the IPFC model, we investigated some basic issues in homogeneous nucleation. From the viewpoint of simulation, we proceeded with an in situ observation of the process of cluster fluctuation and obtained quite similar snapshots to colloidal crystallization experiments. We also counted the size distribution of crystal-like clusters and the nucleation rate. Our simulations show that the size distribution is independent of the evolution time, and the nucleation rate remains constant after a period of relaxation, which are consistent with experimental observations. The linear relation between logarithmic nucleation rate and reciprocal driving force also conforms to the steady state nucleation theory.

A modified phase-field-crystal (PFC) model is proposed to describe solid-liquid phase transitions by reconstructing the correlation function. The effects of fitting parameters of our modified PFC model on the bcc-liquid phase diagram, numerical stability, and solid-liquid interface properties during planar interface growth are examined carefully. The results indicate that the increase of the correlation function peak width at $k=k_m$ will enhance the stability of the ordered phase, while the increase of peak height at $k=0$ will narrow the two-phase coexistence region. The third-order term in the free-energy function and the short wave-length of the correlation function have significant influences on the numerical stability of the PFC model. During planar interface growth, the increase of peak width at $k=k_m$ will decrease the interface width and the velocity coefficient $C$, but increase the anisotropy of $C$ and the interface free energy. Finally, the feasibility of the modified phase-field-crystal model is demonstrated with a numerical example of three-dimensional dendritic growth of a body-centered-cubic structure.