Phase diagram, shock equation of states, and elasticity of metal ruthenium under high pressure

In this paper, we searched the high-pressure structure of metal Ru with the advanced crystal structure prediction algorithm combined with the density functional theory (DFT). We discovered two experimentally unknown structures, the face-centered-cubic (fcc) and the structure with the R (3) over barm symmetry, except for the known hexagonal-closely-packaged (hcp) structure. We constructed a wide-range high-pressure and temperature phase diagram of Ru from ambient conditions up to 500 GPa and 10,000 K based on the quasi-harmonic approximation (QHA). The dynamic Hugoniot equation of states of Ru was investigated for the first time, which shows a slight mismatch between hcp and fcc on their phase boundary. Finally, using the stress-strain method we verified the previous high-pressure elastic constants calculated by the energy-strain method. Furthermore, we analyzed the variations of the elastic moduli, elastic anisotropy, sound velocities, and Debye temperature with pressure.