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

摘要

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-Gruneisen-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 A~3, K_T=260±1 GPa, and K_T~1 = 4.21±0.05. The derived thermoelastic parameters for the HTBM include (σK_T/σT)_P = -0.019±0.001 GPa/K and thermal expansion α = a_0 + a_1T with a_0= 1.55 (±0.05) x 10~(-5) K~(-1) and a_1 =0.68 (±0.07) × 10~(-8)K~(-2). Fitting to the MGD relation yields γ_0 = 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 (O)_(E10) = 366K and Θ_(E20) = 208 K; Grueneisen 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.