Scalar and fully relativistic pressure and temperature-dependent ab-initio thermodynamics study of simple cubic polonium

Abstract

The ab-initio thermodynamic properties of simple cubic polonium (α-Po) were studied within the quasi-harmonic approximation (QHA), where both lattice vibrations (phonons) and electronic excitations contributions are included in the Helmholtz free energy. We investigate the influence of spin-orbit coupling (SOC) by comparing the scalar relativistic (SR) and fully relativistic (FR) pseudopotentials on the thermodynamic properties of polonium and evaluate the performance of three popular exchange-correlation functionals, GGA (PBE and PBEsol), and LDA (PZ). Temperature and pressure-dependent thermodynamic properties were compared with the available experimental and theoretical studies. We found that the effect of electronic excitations is negligible for all the thermodynamic properties. LDA+SOC provides a better agreement with the experimental volume, while the thermal expansion coefficients from LDA+SOC and PBEsol + SOC closely match experimental values. SOC effects appear insignificant for the isobaric heat capacity but substantially contribute to the adiabatic bulk modulus. The phonon dispersions and mode-Grüneisen parameters (γqη) were interpolated at the lattice constant corresponding to 301 K. The SR dispersions exhibit several anomalies in all directions, which were suppressed significantly by the inclusion of SOC. The role of SOC on the elastic constant-coefficient (Cij) and elastic anisotropy factor at 0 K is also studied. The Pugh ratio confirmed that simple cubic polonium is ductile, and we observed that the elastic anisotropy factor and Pugh ratio decreased with increasing pressure. The effect of SOC on the Cauchy pressure is also determined.