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

Konstantin D. Litasov, Pavel N. Gavryushkin, Peter I. Dorogokupets, Igor S. Sharygin, Anton Shatskiy, Yingwei Fei, Sergey V. Rashchenko, Yury V. Seryotkin, Yiji Higo, Kenichi Funakoshi, Eiji Ohtani

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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 Å3, KT = 308 ± 1 GPa, and KT′ = 4.20 ± 0.05. Estimated thermoelastic parameters for HT include (∂KT/∂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, ΘE1o = 314 K and ΘE2o = 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 mE1 = mE 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.

Original languageEnglish
Article number133505
JournalJournal of Applied Physics
Issue number13
Publication statusPublished - 2013 Apr 7

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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