  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.
