Generalization of the Fourier-spectral Eyre scheme for the phase-field equations: Application to self-assembly dynamics in materials

Self-assembly is one of the most promising ways to develop novel materials with high performance. Thanks to the flexibility in treating of the topological changes in systems, the phase-field approach has emerged as a method of choice to study this phenomenon at mesoscale. In recent years, the phase-field equations have also been upgraded to incorporate the atomic scale effects. In this work, we propose an efficient numerical method based on the generalization of the Fourier-spectral Eyre's scheme, to simulate the dynamics of self-assembly, using the phase-field model at different time and length scales. To show its versatility, the method is explicitly implemented, and numerically tested, for three phase-field models describing patterned structure in systems: the modified Cahn-Hilliard equation for irradiation induced patterned microstructures at mesoscale, and the Phase-field Crystal and Continuous Atomic Density Functional methods, to study the formation of complex crystal structures at atomic scale. (authors)