First-principles study of thermoelasticity and structural phase diagram of CaO

We present pressure $\left(P\right)$ and temperature $\left(T\right)$ 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 $>140\mathrm{GPa}$ 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 $\sim 200\mathrm{GPa}$. 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.

Figure 1

Phonon dispersion curve of B1 phase.

Figure 2

Phonon dispersion curve of B2 phase.

Figure 3

Volume thermal expansion of B2 phase as a function of temperature.

Figure 4

Equation of state for CaO.

Figure 5

B1-B2 enthalpy crossing at different temperatures.

Figure 6

Mode Grüneisen parameter of B1 phase.

Figure 7

Mode Grüneisen parameter of B2 phase.

Figure 8

$C_{11}$ and $C_{11}^{{}^{\prime }}$ as a function of pressure.

Figure 9

$C_{12}$ and $C_{12}^{{}^{\prime }}$ as a function of pressure.

Figure 10

$C_{44}$ and $C_{44}^{{}^{\prime }}$ as a function of pressure.

Figure 11

Elastic moduli of B1 phase as a function of pressure.

Figure 12

Elastic moduli of B2 phase as a function of pressure.

Figure 13

Poisson ratio and anisotropy factor as a function of pressure.

Figure 14

Thermal pressure as a function of temperature.

Figure 15

Grüneisen parameter as a function of volume ratio.

Figure 16

Structural phase diagram of CaO. Red and purple lines represent the melting curves of B1 and B2 phase, respectively. Dashed line shows the unstable part of the melting curve, and solid lines show the stable part of the phase. Inset shows the comparison of B1-B2 phase diagram with the available data due to Karki and Wentzcovitch [10].

Figure 17

Electronic band structure (left panel) and electron density of states (e-DOS; right panel) in B2 phase of CaO at 0 GPa (blue), 140 GPa (green), and 200 GPa (red).