Thermodynamic properties of fcc lead: A scalar and fully relativistic first principle study

TL;DR

This study uses ab-initio methods to analyze the thermodynamic properties of face-centered cubic lead, examining the effects of spin-orbit coupling and exchange-correlation functionals on various physical properties.

Contribution

It provides a comprehensive first-principles analysis of fcc lead's thermodynamic properties, including the influence of SOC and different exchange-correlation functionals, which was not extensively studied before.

Findings

Electronic excitations have negligible impact on thermodynamic properties.

Spin-orbit coupling effects decrease with increasing pressure but remain significant.

Results show SOC effects lead to differences from scalar relativistic calculations, with no consistent improvement in experimental agreement.

Abstract

This study investigates the thermodynamic properties of face-centered cubic lead (fcc-Pb) using ab-initio methods within the quasi-harmonic approximation (QHA), examining the influence of spin-orbit coupling (SOC) and the exchange-correlation functionals. Two types of ultrasoft pseudopotential (US-PP) are considered: one that excludes (scalar relativistic PP) and one that includes the SOC effects (fully relativistic PP). Further, for each PP, we test the performance of three popular exchange-correlation functionals: Perdew-Burke-Ernzerhof generalized gradient approximation (PBE) (Perdew et al. Phys. Rev. Lett. 77, 3865 (1996)), PBE modified for dense solids (PBEsol) (Perdew et al. Phys. Rev. Lett. 100, 136406 (2008)), and local density approximation (LDA) (Perdew et al. Phys. Rev. B 23, 5048 (1981)). We calculate the Helmholtz free energy, incorporating lattice vibrations (phonons) and electronic excitation contributions. The estimated equation of state (at 4 K and 301 K), phonon dispersions (at 100 K and 300 K), mode-Gr\"uneisen parameters ({\gamma}q{\eta}) (at 100 K), volume thermal expansion coefficient (\b{eta}), isobaric heat capacity (CP), bulk modulus (BS), and thermodynamic average Gr\"uneisen parameter ({\gamma}) are compared with the available experimental and theoretical studies. Moreover, the 0 K pressure-dependent elastic constant-coefficient (Cij) of fcc lead and Pugh ratio, Debye temperature, and longitudinal and transverse sound velocities for polycrystalline lead are presented. The contributions of electronic excitations in all the thermodynamic properties are found to be negligible. With increasing pressure, the role of spin-orbit effects decreases but does not vanish. Our findings demonstrate that SOC leads to results distinct from the SR approach, but agreement with the experiment is not consistently improved by including SOC.