Amplitude Expansion Phase Field Crystal (APFC) Modeling based Efficient Dislocation Simulations using Fourier Pseudospectral Method

Crystalline defects critically influence material properties, necessitating accurate simulation methods. Existing approaches, from atomic-scale configurations to continuum elasticity, face inherent limitations in modeling dislocation-induced lattice deformation. The amplitude expansion of the phase field crystal (APFC) model bridges this gap with a mesoscopic description. This paper introduces a computationally efficient Fourier pseudospectral method for solving the APFC equations. The method exploits system periodicity and solution analyticity--the latter's rigorous proof remaining an open question, as discussed herein--to enable precise implementation of periodic boundary conditions. Numerical experiments on 2D triangular and 3D body-centered cubic lattices demonstrate that the method accurately reproduces the strain fields of edge dislocations, matching continuum theory predictions. These results confirm the APFC model's potential for capturing complex defect structures at the mesoscale, paving the way for simulating more intricate defect dynamics.