A review of continuous modeling of periodic pattern formation with modified phase-field crystal models

The phase-field crystal (PFC) method is known as a relatively new continuum approach for describing the microstructural dynamics of materials during structural and phase transitions. In contrast to molecular dynamics (MD) or density functional theory (DFT) methods, PFC allows description processes on diffusion time scales while maintaining an atomistic spatial resolution which explains its attraction to scientists over the last 20 years. After certain development, PFC serves today as a solution of a wide variety of new and increasingly complex problems. As a result, dozens of various modifications of the original PFC model are already helping to study special features in material science. New possibilities and challenges arise when extended spatio-temporal correlations are introduced in PFC model. The current paper briefly systematizes and characterizes PFC model’s applications mainly focused on spatio-temporal correlations, systems with memory and models suitable for the description of non-equilibrium phase transformations.