Thermal equation of state to 33.5 GPa and 1673 K and thermodynamic properties of tungsten

A comprehensive P-V-T dataset for bcc-tungsten was obtained for pressures up to 33.5 GPa and temperatures 300-1673 K using MgO and Au pressure scales. The thermodynamic analysis of these data was performed using high-temperature (HT) and Mie-Grüneisen-Debye (MGD) relations combined with the Vinet equations of state (EOS) for room-temperature isotherm and the newly proposed Kunc-Einstein (KE) EOS. The KE EOS allowed calibration of W thermodynamic parameters to the pressures of at least 300 GPa and temperatures up to 4000 K with minor uncertainties (<1% in calculated volume of W). A detailed analysis of room-temperature compression data with Vinet EOS yields V₀ = 31.71 ± 0.02 ų, K_T = 308 ± 1 GPa, and K_T′ = 4.20 ± 0.05. Estimated thermoelastic parameters for HT include (∂K_T/∂T)_P = -0.018 ± 0.001 GPa/K and thermal expansion α = a₀ + a₁T with a₀ = 1.35 (±0.04) × 10^-5 K^-1 and a₁ = 0.21 (±0.05) × 10^-8 K^-2. Fitting to the MGD relation yielded γ₀ = 1.81 ± 0.02 and q = 0.71 ± 0.02 with the Debye temperature (θ₀,) fixed at 370-405 K. The parameters for KE EOS include two Einstein temperatures, Θ_E1o = 314 K and Θ_E2o = 168 K, Grüneisen parameter at ambient condition γ₀ = 1.67 and infinite compression γ_∞ = 0.66, with β = 1.16 (which is a power-mode parameter in the Grüneisen equation), anharmonicity (m = 3.57) and electronic (g = 0.11) equivalents of the Grüneisen parameter, and additional parameters for intrinsic anharmonicity, a₀ = 6.2 × 10^-5 K^-1, and electronic contribution, e₀ = 4.04 × 10^-5 K^-1 to the free energy. Fixed parameters include k = 2 in KE EOS and m_E1 = m_{E 2} = 1.5 in expression for Einstein temperature. Present analysis should represent the best fit of the experimental data for W and can be used for a variety of thermodynamic calculations for W and W-containing systems including phase diagrams, chemical reactions, and electronic structure.