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/content/aip/journal/jap/113/9/10.1063/1.4794127
2013-03-05
2016-05-31

Abstract

A comprehensive P-V-T dataset for bcc-Mo was obtained at pressures up to 31 GPa and temperatures from 300 to 1673 K using MgO and Au pressure calibrants. The thermodynamic analysis of these data was performed using high-temperature Birch-Murnaghan (HTBM) equations of state (EOS), Mie-Grüneisen-Debye (MGD) relation combined with the room-temperature Vinet EOS, and newly proposed Kunc-Einstein (KE) approach. The analysis of room-temperature compression data with the Vinet EOS yields V 0 = 31.14 ± 0.02 Å3, KT  = 260 ± 1 GPa, and KT ′ = 4.21 ± 0.05. The derived thermoelastic parameters for the HTBM include (∂KT /∂T) P  = −0.019 ± 0.001 GPa/K and thermal expansion α = a 0 + a 1 T with a 0 = 1.55 ( ± 0.05) × 10−5 K−1 and a 1 = 0.68 ( ± 0.07) × 10−8 K−2. Fitting to the MGD relation yields γ0 = 2.03 ± 0.02 and q = 0.24 ± 0.02 with the Debye temperature (θ 0) fixed at 455-470 K. Two models are proposed for the KE EOS. The model 1 (Mo-1) is the best fit to our P-V-T data, whereas the second model (Mo-2) is derived by including the shock compression and other experimental measurements. Nevertheless, both models provide similar thermoelastic parameters. Parameters used on Mo-1 include two Einstein temperatures ΘE10 = 366 K and ΘE20 = 208 K; Grüneisen parameter at ambient condition γ 0 = 1.64 and infinite compression γ = 0.358 with β  = 0.323; and additional fitting parameters m = 0.195, e 0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, m E1 = m E2 = 1.5 in expression for Einstein temperature, and a 0 = 0 (an intrinsic anharmonicity parameter). These parameters are the best representation of the experimental data for Mo and can be used for variety of thermodynamic calculations for Mo and Mo-containing systems including phase diagrams, chemical reactions, and electronic structure.

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