High temperature non-harmonic evaluation and bonding in CaO

Abstract

Previous theoretical and experimental investigations on high temperature anharmonic quantities such as thermal expansion, thermal Grüneisen parameter, phonon softening, and various caloric properties for calcium oxide show a large scatter. They were limited to temperatures well below the melting point. However, these rigorous studies are illustrative and suggest that the amount of anharmonicity in an interaction potential depends on the choice of exchange-correlation (XC) functionals and pseudopotentials. One thus requires to understand a counter mechanism to compensate for the extravagant quasiharmonic thermal properties. In the present study, we employ PAW (Projector Augmented Wave) pseudopotentials within the density functional theory (DFT) using two XC-functionals: the local density approximation (LDA) and generalized gradient approximation (GGA). We test their role and accuracy for evaluating the non-harmonic properties of CaO at finite temperatures. We use the lowest-order thermodynamic perturbation theory by treating CaO as a weak-anharmonic oscillator for supplementing the anharmonic phonon contribution to DFT-based quasiharmonic lattice dynamical properties up to 3000 K. A systematic study of anharmonic properties at high-T reveals the importance of anharmonic interaction, where the effect of LDA and GGA on the non-quadratic part of the interaction potential is also determined. T-dependent contribution to various physical properties shows the presence of strong anharmonicity in the interaction potential for the PAW+GGA scheme. It offers a much stiffer effective spring constant and contributes large vibrational energy. To stabilize such a system at finite temperatures requires a significant positive anharmonic contribution. Instead, the PAW pseudopotential at the LDA level gives reasonable thermodynamic properties even within the quasiharmonic approximation (QHA); the role of anharmonicity is modest at the highest temperature. As a major outcome of the study, we could identify the contribution from the interaction potential referenced to the used XC-functionals in determining the degree and nature of anharmonicity operative at finite temperatures. The corollary is assessed and confirmed by accurately evaluating several thermophysical properties up to the melting temperature, including the anharmonicity. Furthermore, we investigate the bonding scenario in expanded CaO by examining the electron band structure. We find that the interaction between the ions is ionic, but the cations strongly influence the interactions. As a result, the charges are more locally deformed at the metal-ions site, and the infiltration of charge in the ionic sphere of Ca+2 from O−2 is more. This fact is manifested as a profound sensitivity of the Ca 3d-band, particularly at the Γ-point. For expansion, the electron-cloud deformation reduces, and one expects more isotropic electron distribution. Thus, the PAW+LDA-based QHA gives a reasonable description for high-T assessment for CaO, but an anharmonic contribution is necessary for an accurate evaluation of thermal properties.