Pressure–temperature phase diagram of calcium up to 50 GPa pressure

Abstract

Theoretically, we have determined pressure–temperature (P–T) phase diagram of calcium up to 50 GPa pressure and 1500 K temperature employing density functional theory and quasi-harmonic approximations (QHA). We have considered four different phases of calcium, namely, face centered cubic (fcc), body centered cubic (bcc), body centered tetragonal (bct) and simple cubic (sc). Firstly, we have calculated the 0 K equation of state (EOS) and phonon properties of Ca for these phases which show good agreement with earlier calculations. Also from band structure analysis we have predicted an electronic topological transition at L-, K-, W-, and U-point of the Brillouin zone (BZ) near 8 GPa i.e. close to fcc–bcc structural transition. Then we have incorporated temperature effect in pressure–volume equation of state using accurate phonon density of states, obtained from first principles calculations. Furthermore, we have calculated fcc–bcc transition temperature at ambient and high pressure within QHA. Our calculated fcc transition temperature (1355.2 K) at ambient pressure is comparatively much higher than experimental value (740 K) indicating possible anharmonic effects in Ca.