First-Principles Calculation of the Thermodynamic Properties of Pb10(PO4)6O

Abstract

Since the discovery of the room-temperature superconductor Pb_10–xCu_x(PO₄)₆O (0.9 < x < 1.1) (LK-99) as reported by Lee et al. (http://arxiv.org/abs/2307.12008), the material have attracted wide attention from researchers, however subsequent studies by Chang Liu, Kaizhen Guo et al. have refuted LK-99 superconductivity claims (Phys. Rev. Mater. 7, 084804 (2023); Sci. China: Phys. Mech. Astron. 66, 107411 (2023)). The thermodynamic properties of material are one of the important factors for its practical applications, so it is necessary to conduct in-depth research on the parent compound Pb₁₀(PO₄)₆O. In this paper, we employed the first-principles method combined with the quasi-harmonic Debye model approximation calculations to study Pb₁₀(PO₄)₆O. Key thermodynamic quantities of Pb₁₀(PO₄)₆O are presented. For example, at 300 K, the bulk modulus value is 155.4 GPa, the coefficient of thermal expansion is 3.04 × 10^–5 K^–1, the entropy is 24.05 J/mol K, the vibration free energy is 1.12 KJ/mol and the specific heat capacity at constant volume is 22.25 J/mol K for the system at 10 GPa. Comparing with the results at 900 K, it is found that bulk modulus, bulk expansion coefficient and fixed volume heat capacity are more weakly affected by temperature, while the entropy and vibration free energy are strongly affected by temperature. These findings provide valuable theoretical insights and expand the research for related materials, such as Pb_10–xCu_x(PO₄)₆O.