## Abstract

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 V_{0} = 31.71 ± 0.02 Å^{3}, 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 = a_{0} + a_{1}T with a_{0} = 1.35 (±0.04) × 10^{-5} K^{-1} and a_{1} = 0.21 (±0.05) × 10^{-8} K^{-2}. Fitting to the MGD relation yielded γ_{0} = 1.81 ± 0.02 and q = 0.71 ± 0.02 with the Debye temperature (θ_{0},) 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 γ_{0} = 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, a_{0} = 6.2 × 10^{-5} K^{-1}, and electronic contribution, e_{0} = 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.

Original language | English |
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Article number | 133505 |

Journal | Journal of Applied Physics |

Volume | 113 |

Issue number | 13 |

DOIs | |

Publication status | Published - 2013 Apr 7 |

## ASJC Scopus subject areas

- Physics and Astronomy(all)