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We report first-principles phonon frequencies and anharmonic thermodynamic properties of h.c.p. Os and Ru calculated within the quasi-harmonic approximation, including Gruneisen 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.

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