A nonlocal phase-field crystal (NPFC) model is presented as a nonlocal counterpart of the local phase-field crystal (LPFC) model and a special case of the structural PFC (XPFC) derived from classical field theory for crystal growth and phase transition. The NPFC incorporates a finite range of spatial nonlocal interactions that can account for both repulsive and attractive effects. The specific form is data-driven and determined by a fitting to the materials structure factor, which can be much more accurate than the LPFC and previously proposed fractional variant. In particular, it is able to match the experimental data of the structure factor up to the second peak, an achievement not possible with other PFC variants studied in the literature. Both LPFC and fractional PFC (FPFC) are also shown to be distinct scaling limits of the NPFC, which reflects the generality. The advantage of NPFC in retaining material properties suggests that it may be more suitable for characterizing liquid-solid transition systems. Moreover, we study numerical discretizations using Fourier spectral methods, which are shown to be convergent and asymptotically compatible, making them robust numerical discretizations across different parameter ranges. Numerical experiments are given in the two-dimensional case to demonstrate the effectiveness of the NPFC in simulating crystal structures and grain boundaries.

翻译：本文提出了一种非局部相场晶体（NPFC）模型，该模型作为局部相场晶体（LPFC）模型的非局部对应物，同时也是从晶体生长与相变的经典场论导出的结构相场晶体（XPFC）模型的一个特例。NPFC模型引入了有限空间范围内的非局部相互作用，能够同时考虑排斥与吸引效应。其具体形式由数据驱动，通过对材料结构因子的拟合确定，其精度可显著高于LPFC模型及先前提出的分数阶变体模型。特别地，该模型能够匹配实验结构因子数据直至第二峰值，这是现有文献中其他PFC变体模型无法实现的。研究同时表明，LPFC模型与分数阶相场晶体（FPFC）模型均可视为NPFC模型的不同尺度极限，这体现了NPFC模型的普适性。NPFC模型在保持材料物性方面的优势表明，其可能更适用于表征液-固相变体系。此外，我们研究了基于傅里叶谱方法的数值离散格式，该格式被证明具有收敛性与渐近相容性，从而成为适用于不同参数范围的鲁棒性数值离散方法。文中通过二维算例展示了NPFC模型在模拟晶体结构及晶界方面的有效性。