Thermal equation of state and thermodynamic properties of molybdenum at high pressures

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 V0 = 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 = a0 + a1T with a0 = 1.55 ( ± 0.05) × 10−5 K−1 and a1 = 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 (θ0) 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 γ0 = 1.64 and infinite compression γ∞ = 0.358 with β = 0.323; and additional fitting parameters m = 0.195, e0 = 0.9 × 10−6 K−1, and g = 5.6. Fixed parameters include k = 2 in Kunc EOS, mE1 = mE2 = 1.5 in expression for Einstein temperature, and a0 = 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.

Pressure Dependency Grüneisen Parameter r for bcc Mo

“…It's found that (Litasov, 2013)the values of γ derived from the model Mo-1 seem too high, whereas the model Mo-2 yielded consistent results with shock-wave (SW) data (Asimow, 2009) and theoretical calculations (Zeng, 2011).…”

“…Litasov et al (Litasov, 2013) had discussed two other forms of γ for Mo. One is from Mie−Gruneisen−Debye (MGD) EOS, γ has the following form…”

“…The other form of γ is from Kunc−Einstein (KE) EOS (Litasov, 2013), and γ has the following form by Al'tshuler et al (Al'tshuler, 1987): have different values for different models Mo-1 and Mo-2. It's found that (Litasov, 2013)the values of γ derived from the model Mo-1 seem too high, whereas the model Mo-2 yielded consistent results with shock-wave (SW) data (Asimow, 2009) and theoretical calculations (Zeng, 2011).…”

“…At low temperatures, Mo is stable in the body-centered-cubic (bcc) phase up to a pressure (P) of about 700GPa, where it transforms to fcc phase (Belonoshko, 2008). Considerable experimental and theoretical methods had been developed for Mo to study its thermodynamic properties such as melting temperature T m , thermal equation of state (EOS), Grüneisen parameter γ and Debye temperature Θ D , et al (Hixson, 1992;Zhang, 2008;Errandonea, 2005;Burakovsky, 2004;Kushwah, 2013;Zeng, 2011;Litasov, 2013;Al'tshuler, 1987;Asimow, 2009;Cazorla, 2007;Vinet, 1989). It's found that there exist great discrepancies in the melting curves between laser-heated diamond anvil cell (DAC) (Santamaría-Pérez, 2009) and shock-wave (SW) measurements (Hixson, 1992;Zhang, 2008).…”

Thermoelectric transport properties of molybdenum fromabinitiosimulations

“…Whenever we process or make comparisons to experimental data in the solid phase, we employ the above expressions with a reference density of ̺ 0 = 10.228 g/cm 3 at T 0 = 298 K. 73 At the melting point (2900 K) 74 the density has reduced by about 7%.…”