PHYSICAL REVIEW B 107, 014107 (2023) First-principles study of thermoelasticity and structural phase diagram of CaO Pooja Vyas , 1 , * A. B. Patel, 2 and N. K. Bhatt 1 , † 1 Department of Physics, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar 364001, Gujarat, India 2 Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218, USA (Received 26 September 2022; revised 9 January 2023; accepted 10 January 2023; published 23 January 2023) We present pressure (P) and temperature (T ) variations of elastic and anisotropic properties, solid-solid (rocksalt, B1 to cesium chloride, B2) and solid-liquid structural phase transitions of CaO. We employed first- principles density functional theory supplemented with an anharmonic contribution to phonon dynamics. Good agreement is obtained for all properties up to the pressure and temperature range relevant to the Earth’s mantle and outer core. Born elastic criteria are generalized for arbitrary stress to elaborate the structural phase diagram from a thermoelastic viewpoint. We propose a self-consistent computational scheme to incorporate the effect of thermal hysteresis into Lindemann’s melting law. This improvised melting law exhibits quantitative agreement with reported findings for the high-P melting curve. We find the triple point (i.e., the coexistence of B1, B2, and liquid phases) at 23 GPa and 4600 K. By examining the pressure-term included elastic properties, we can show that the solid-solid transition is mechanical in a pressure range of 0–200 GPa and temperature up to 3000 K. The softening of shear elastic constant C 44 drives the B1-B2 phase transition. This assertion is corroborated by examining the phonon dispersion curve and mode Grüneisen parameter at different pressures for both B1 and B2 phases. The solid-liquid phase boundary can be treated accurately through the temperature-dependent thermodynamic Grüneisen parameter. Furthermore, in this paper, we predict a negative melting slope >140 GPa with a peak temperature of 7800 K, suggesting a smaller molar volume on the liquid side than that of the solid phase. This finding is supported by electronic band structure calculation. It is proposed that the hybridization of the empty 3d band of the cation with s orbitals lowers the conduction band to cross the Fermi energy at the Brillouin zone center and leads the insulator-to-metal/semimetal phase transition ∼200 GPa. Different electronic states on solid and liquid sides make the liquid phase more compressible than the solid phase, eventually reducing the melting temperature with pressure. DOI: 10.1103/PhysRevB.107.014107 I. INTRODUCTION Lime (CaO) is one of the important components in the Earth’s lower mantle (LM) and upper mantle (UL), and it is believed that the region D ′′ at the bottom of the mantle is enriched in CaO [1]. The study of high-pressure structural phase transition (SPT) and elastic properties of lime and its usage in deriving calcium silicate perovskite CaSiO 3 (CaPv) from a geophysical viewpoint is vital for understanding the Earth’s LM and outer core. For instance, thermal conductivity and mass transport mechanisms depend sensitively on the thermoelasticity and the structure [2]. The pressure (P ) and temperature (T ) across the LM and outer core span over 23 to >200 GPa at 2000 to >4000 K. As computed in this paper, this is the (P , T ) region where the rocksalt (B1) structure with face-centered-cubic (fcc) space lattice, the cesium chlo- ride (B2) structure with simple cubic space lattice, and the liquid phase have competing free energies. Transport across the rocky LM and the molten metallic core thus requires the knowledge of P , T variation of SPT and elasticity for these phases separately as well as at the onset of the phase * poojavyas1251995@gmail.com † bhattnisarg@hotmail.com, nkb@mkbhavuni.edu.in transition. It is also essential to unveil the role played by the thermal stress at finite P , T conditions on elastic moduli and their connection in determining the high-P melting curve. It is noted that, in closely related compounds of the mantle, the anharmonic effect is also important. For instance, anhar- monicity is detected in (i) the Raman spectrum of MgSiO 3 at ambient pressure [3], (ii) at the boundary across the olivine to wadsleyite transition [4], (iii) high-T stabilization of the cubic phase of CaPv [5], and (iv) in Mg orthoenstatite [6], to mention a few. Also, recent first-principles density func- tional theory (DFT)-based studies [7–16] on high-T thermal assessment of CaO have clearly shown the inadequacy of quasiharmonic approximation (QHA) above room tempera- ture (RT). We [17] have thoroughly investigated the role of anharmonicity in reference to the projector augmented-wave (PAW) pseudopotential and the effect of exchange correlation (XC) on high-T thermodynamic properties for the B1 phase of CaO extending up to 3000 K. In this paper, we also discuss the bonding scenario in CaO at expanded volumes. In this conclusive paper, we suggest a non-negligible contribution due to phonon anharmonicity for CaO beyond RT, lesser for the local density approximation (LDA)+PAW scheme. There- fore, these studies advocate the need to calculate anharmonic phonon dynamics while deriving free energy for geophysical and geochemical exploration from a thermoelastic viewpoint. 2469-9950/2023/107(1)/014107(14) 014107-1 ©2023 American Physical Society