Review of high pressure phases of calcium by first-principles calculations

Abstract

We review high pressure phases of calcium which have obtained by recent experimental and first-principles studies. In this study, we investigated the face-centered cubic (fcc) structure, the body-centered cubic (bcc) structure, the simple cubic (sc) structure, a tetragonal P43212 [Ishikawa T et al. 2008 Phys. Rev. B 77 020101(R)], an orthorhombic Cmca [Ishikawa T et al. 2008 Phys. Rev. B 77 020101(R)], an orthorhombic Cmcm [Teweldeberhan A M and Bonev S A 2008 Phys. Rev. B 78 140101(R)], an orthorhombic Pnma [Yao Y et al. 2008 Phys. Rev. B 78 054506] and a tetragonal I4/mcm(00) [Arapan S et al. 2008 Proc. Natl. Acad. Sci. USA 105 20627]. We compared the enthalpies among the structures up to 200 GPa and theoretically determined the phase diagram of calcium. The sequence of the structural transitions is fcc (0- 3.5 GPa) → bcc (3.5 – 35.7 GPa) → Cmcm (35.7- 52GPa) → P43212 (52-109 GPa) → Cmca (109-117.4GPa) → Pnma (117.4-134.6GPa) → I4/mcm(00) (134.6 GPa -). The sc phase is experimentally observed in the pressure range from 32 to 113 GPa but, in our calculation, there is no pressure region where the sc phase is the most stable. In addition, we found that the enthalpy of the hexagonal close-packed (hcp) structure is lower than that of I4/mcm(00) above 495 GPa.