Ab initio quasi-harmonic thermoelasticity, piezoelectricity, and thermoelectricity of polar solids at finite temperature and pressure: Application to wurtzite ZnO

Abstract: We generalize a previously established ab initio approach-originally developed for hexagonal close-packed (hcp) metals-to accommodate solids with both internal and external degrees of freedom. This extension enables the thermodynamic and thermoelastic characterization of insulators, including those with non-vanishing piezoelectric and pyroelectric tensors. Utilizing Density Functional Theory (DFT) and Density Functional Perturbation Theory (DFPT) within the quasi-harmonic approximation, we derive the pressure and temperature dependence of these properties. Specifically, we investigate internal degrees of freedom using two distinct frameworks: the Zero Static Internal Stress Approximation (ZSISA) and Full Free Energy Minimization (FFEM). We then compare these approximations by computing internal and external thermal expansions, as well as temperature-dependent piezoelectric and pyroelectric tensors. Finally, we demonstrate the generalized formalism by calculating the thermodynamic properties of wurtzite ZnO across a broad range of pressures and temperatures.