First-principles anharmonic vibrational study of the structure of calcium silicate perovskite under lower mantle conditions

Calcium silicate perovskite (${\mathrm{CaSiO}}_3$) is one of the major mineral components of the lower mantle, but has been the subject of relatively little work compared to the more abundant Mg-based materials. One of the major problems related to ${\mathrm{CaSiO}}_3$ that is still the subject of research is its crystal structure under lower mantle conditions—a cubic $Pm\overline{3}m$ structure is accepted in general, but some have suggested that lower-symmetry structures may be relevant. In this paper, we use a fully first-principles vibrational self-consistent field method to perform high accuracy anharmonic vibrational calculations on several candidate structures at a variety of points along the geotherm near the base of the lower mantle to investigate the stability of the cubic structure and related distorted structures. Our results show that the cubic structure is the most stable throughout the lower mantle, and that this result is robust against the effects of thermal expansion.

Figure 1

The currently accepted form of the geotherm in the lower mantle and outer core, showing the conditions that can be found in this region of the Earth's interior. Note the significant discontinuity in the gradient of the geotherm near the core-mantle boundary (CMB), marked by the line at around 136 GPa, and the steeper section at pressures just below the CMB corresponding to the ${\mathrm{D}}^{″}$ layer. Figure adapted from Ref. [33].

Figure 2

The crystal structures of calcium silicate considered in this paper. (a) shows the basic cubic perovskite $Pm\overline{3}m$ structure, viewed along any of the Cartesian axes. (b) shows the distorted I4/mcm structure, viewed along the $y$ axis (the cubic structure's $b$ axis). (c) shows the distorted C2/m structure, viewed along the $z$ axis (the cubic structure's $c$ axis). In all figures, Ca is green, O is red, and Si is brown.

Figure 3

The main data from Table 2 presented visually—the Gibbs free energy per formula unit of the distorted structures relative to the cubic perovskite structure at each pressure, and at the upper and lower bounds of the temperature range associated with that pressure on the geotherm.

Figure 4

The same soft mode mapped twice, using different reference structures. (a) shows the soft mode that was followed to obtain the I4/mcm structure at 100 GPa, with the cubic structure at 0 amplitude. (b) shows the same mode but mapped with the I4/mcm structure as the reference structure at 0 amplitude. In both cases, the amplitude is measured in units of $\frac{1}{\sqrt{2\left|\omega \right|}}$, where $\omega$ is the frequency of the soft mode in the cubic structure.