We present a systematic ab initio study of the thermoelastic properties of hcp osmium as functions of temperature and pressure within the quasiharmonic approximation (QHA). The precision of the zero static internal stress approximation (ZSISA) and of the volume-constrained ZSISA (V-ZSISA) is rigorously assessed. For osmium, we find negligible deviations between ZSISA and a full free energy minimization approach. Also, the V-ZSISA approximation influences the results very little, as we found already in beryllium, despite the markedly different behavior of the $c/a$ ratio with temperature in the two metals. Our QHA-derived elastic constants (ECs) show excellent agreement with available experimental data in the temperature range of 5–301 K, outperforming the results obtained from the quasistatic approximation (QSA). Additionally, we report the pressure-dependent QHA ECs at 5, 301, and 1000 K, spanning pressures from 0 to 150 kbar.

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• Thermal properties
• Thermoelasticity
• 3-dimensional systems
• Metals
• Density functional theory
• First-principles calculations