Lattice dynamics and thermophysical properties of h.c.p. Os and Ru from the quasi-harmonic approximation

We report first-principles phonon frequencies and anharmonic thermodynamic properties of h.c.p. Re and Tc calculated within the quasi-harmonic approximation, including Gr\"uneisen parameters, temperature-dependent lattice parameters, thermal expansion, and isobaric heat capacity. We discuss the differences between a full treatment of anisotropy and a simplified approach with a constant $c/a$ ratio. The results are systematically compared with the available experimental data and an overall satisfactory agreement is obtained.