The thermodynamics of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>CaSiO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math> perovskite in Earth's lower mantle

The lower mantle of Earth, characterized by pressures of 24-127 GPa and temperatures of 1900-2600 K, is still inaccessible to direct observations. In this work, we investigate by first principles the stability, phase diagram, elastic properties, and thermal conductivity of Davemaoite (CaSiO3 perovskite), which constitutes a significant component of Earth's lower mantle. Notably, our simulations fully capture the anharmonic ionic fluctuations arising from the extreme temperatures and pressures of the lower mantle, thanks to stochastic self-consistent harmonic approximation. We show that the cubic phase of CaSiO3 is the ground state at the lower mantle's thermodynamic conditions. The phase boundary between the cubic and tetragonal phases increases linearly from 300 K to 1000 K between 12 and 100 GPa. Accounting for temperature-renormalized phonon dispersions, we evaluate the speed of sound as a function of depth. Our results downplay the role of octahedral rotations on the transverse sound velocity of cubic CaSiO3, advocated in the past to explain discrepancies between theory and experiments. The lattice thermal conductivity, assessed thanks to the recently introduced Wigner formalism, shows a predominance of particle-like transport, thus justifying the standard Boltzmann transport approach even in a system with such strong ionic anharmonicity.