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 R3̄m 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. •We discovered two experimentally unknown structures of Ru.•We constructed its wide-range high-pressure and temperature phase diagram.•The dynamic Hugoniot equation of states of Ru are investigated for the first time.•We addressed the elastic anisotropy of Ru using our proposed stress–strain method.