Distortions and stabilization of simple-cubic calcium at high pressure and low temperature

Ca-III, the first superconducting calcium phase under pressure, was identified as simple-cubic (sc) by previous X-ray diffraction (XRD) experiments. In contrast, all previous theoretical calculations showed that sc had a higher enthalpy than many proposed structures and had an imaginary (unstable) phonon branch. By using our newly developed submicrometer high-pressure single-crystal XRD, cryogenic high-pressure XRD, and theoretical calculations, we demonstrate that Ca-III is neither exactly sc nor any of the lower-enthalpy phases, but sustains the sc-like, primitive unit by a rhombohedral distortion at 300 K and a monoclinic distortion below 30 K. This surprising discovery reveals a scenario that the high-pressure structure of calcium does not go to the zero-temperature global enthalpy minimum but is dictated by high-temperature anharmonicity and low-temperature metastability fine-tuned with phonon stability at the local minimum.