Assessment of phase-field-crystal concepts using long-time molecular dynamics

The ability of the phase-field-crystal (PFC) model to quantitatively predict atomistic defect structures in crystalline solids is addressed. First, general aspects of the PFC model are discussed within the context of obtaining quantitative results in solid materials. Then a specific example is used to illustrate major points. Specifically, accelerated molecular dynamics is used to compute the one-particle probability density rho((1))(r) in a complex atomistic defect consisting of a Lomer dislocation with an equilibrium distribution of vacancies in the core, and the results are considered within the general framework of the PFC model. As expected,.(1)(r) shows numerous spatially localized peaks with integrated densities smaller than unity, as would arise in a PFC computation. However, the rho((1))(r) actually corresponds to a time-averaged superposition of a few well-defined atomic configurations each having a well-defined energy. The deconvolution of rho((1))(r) to obtain the actual distinct atomic configurations is not feasible. Using a potential energy functional that accurately computes the energies of distinct configurations, the potential energy computed using rho((1))(r) differs from the actual average atomistic energy by similar to 50 eV divided among approximately 46 atoms in the core of the defect. Attempts to rectify this deviation by introducing correlations cannot significantly reduce this error. The simulations show energy barriers between distinct configurations varying by up to 0.5 eV, indicating that the simple kinetic evolution law used in PFC cannot accurately capture the true time evolution in this problem. Overall, these results demonstrate, in one nontrivial case, that the PFC model is probably unable to predict atomistic defect structures, energies, or kinetic barriers at the quantitative levels needed for application to problems in materials science.