Calculations of isothermal elastic constants in the phase-field crystal model

The phase-field crystal (PFC) method is an emerging coarse-grained atomistic model that can be used to predict material properties. In this work, we describe procedures for calculating isothermal elastic constants using the PFC method. We find that the conventional procedures used in the PFC method for calculating the elastic constants are inconsistent with those defined from a theory of thermoelasticity of stressed materials. Therefore we present an alternative procedure for calculating the elastic constants that are consistent with the definitions from the thermoelasticity theory, and show that the two procedures result in different predictions. Furthermore, we employ a thermodynamic formulation of stressed solids to quantify the differences between the elastic constants obtained from the two procedures in terms of thermodynamic quantities such as the pressure evaluated at the undeformed state.