Hybrid Functional Study Rationalizes the Simple Cubic Phase of Calcium at High Pressures

TL;DR

This study uses advanced hybrid density functional calculations to confirm the stability of the simple cubic phase of calcium at high pressures, resolving previous debates and aligning with recent experimental data.

Contribution

It demonstrates the importance of hybrid functionals in accurately predicting phase stability and clarifies the structure of calcium's high-pressure phases.

Findings

SC phase is energetically stable above 33 GPa.

No imaginary phonons found in SC phase across studied pressures.

Experimental Ca-III' matches the simulated X-ray diffraction of I41/amd structure.

Abstract

Simple cubic (SC) phase has been long experimentally determined as the high-pressure phase III of elemental calcium (Ca) since 1984. However, recent density functional calculations within semi-local approximation showed that this SC phase is structurally unstable by exhibiting severely imaginary phonons, and is energetically unstable with respect to a theoretical body-centered tetragonal I41/amd structure over the pressure range of phase III. These calculations generated extensive debates on the validity of SC phase. Here we have re-examined the SC structure by performing more precise density functional calculations within hybrid functionals of Heyd-Scuseria-Erhzerhof (HSE) and PBE0. Our calculations were able to rationalize fundamentally the phase stability of SC structure over all other known phases by evidence of its actual energetic stability above 33 GPa and its intrinsically dynamical stability without showing any imaginary phonons in the entire pressure range studied. We further established that the long-thought theoretical I41/amd structure remains stable in a narrow pressure range before entering SC phase and is actually the structure of experimental Ca-III' synthesized recently at low temperature 14 K as supported by the excellent agreement between our simulated X-ray diffraction patterns and the experimental data. Our results shed strong light on the crucial role played by the precise electron exchange energy in a proper description of the potential energy of Ca.