Elastic properties and lattice dynamics of ruthenium at high pressures

The elastic properties and structural stability in ruthenium under pressure are investigated. The analysis is performed in the framework of Landau theory and nonlinear elasticity. For this purpose the definition of effective elastic constants (EC) of n-th (n= 2) order characterizing elastic properties of loaded crystal and the relations between effective EC and corresponding EC of Bragger type for hcp crystals is given. The conditions of hcp lattice stability to the uniform shear strain under the pressure P are expressed in terms of the second order effective EC. The method of effective EC calculations for hcp crystals under hydrostatic pressure is presented. The equation of state and EC of second and third order and phonon dispersion relations in high-symmetry directions in the pressure range of 0 -600 GPa are calculated in the framework of the density functional theory (DFT) and the density functional perturbation theory (DFPT) respectively. EC are in the good agreement with available experimental data and increase monotonically with pressure, no softening or stability condition violation are observed. Softening of phonon frequencies near the Brillion zone center is also not observed.