Phase field crystal based prediction of temperature and density dependence of elastic constants through a structural phase transition

Abstract

Explicit, analytical forms are obtained for the elastic constants arising from the phase field crystal (PFC) model in which the dependence of the constants on proxies for the temperature and density in the PFC model is clearly exhibited. The expressions indicate that the elastic constants are multivalued in certain temperature ranges corresponding to regions where two or more phases coexist, in agreement with experimental observations. The analytical formulas for the variation of the elastic constants with density agree with those obtained using a computational approach in [Wang, Huang, and Liu, Phys. Rev. B 97, 144112 (2018)] but only in certain regimes. Specifically, if it is assumed that only the bcc state is present, then our formulas agree with the numerical results presented in [Wang, Huang, and Liu, Phys. Rev. B 97, 144112 (2018)]. In general, the bcc state is not the only phase present and, if other phases are taken into account, then the results differ in those regions where alternative states are favored energetically. Similar conclusions hold if one looks at temperature dependence instead of density variation.