Phase-Field Crystal Models and Elastic Excitations

Phase Field Crystal (PFC) models and their amplitude expansions are a novel attempt to bridge the gap between atomistic and continuum models in materials modeling. The studied quantity is the atomic density field that varies in time and space. Not only do these new models allow longer length scales but also longer time scales: many interesting phenomena happen over diffusive time scales that are beyond the reach of classical molecular dynamics or Monte Carlo methods. As with Dynamic Density Field theory a local equilibrium in the system is assumed leading into diffusive dynamics. This implies that the time scale under study is lot slower than time scale of elastic excitations in the system. In other words, we are assuming that phonon modes die out instantaneously. However, it turns out that the system exhibits elastic excitations that have to be relaxed separately. We propose a physical constraint to the time evolution of the density field, which ensures elastic equilibrium at all times.