Thermoelastic properties of tungsten at simultaneous high pressure and temperature

The compressional (P) and shear wave velocities (S) and unit cell volumes (densities) of polycrystalline tungsten (W) have been measured simultaneously up to 10.5 GPa and 1073 K using ultrasonic interferometry in conjunction with X-ray diffraction and x-radiography techniques. Thermoelastic properties of W were derived using different methods. We obtained the isothermal bulk modulus KT0 = 310.3(1.5) GPa, its pressure derivative K′T0 = 4.4(3), its temperature derivative at constant pressure (â K T/â T) P =-0.0138 (1) GPa K-1 and at constant volume (â K T/â T) V =-0.0050 GPa K-1, the thermal expansion α(0, T) = 1.02(27) × 10-5 + 7.39(3.2) × 10-9 T (K-1), as well as the pressure derivative of thermal expansion (â α/â P) T =-1.44 (1) × 10-7 K-1 GP a-1 based on the high-temperature Birch-Murnaghan equation of state (EOS), the Vinet EOS, and thermal pressure approach. Finite strain analysis allowed us to derive the elastic properties and their pressure/temperature derivatives independent of the choice of pressure scale. A least-squares fitting yielded KS0 = 314.5(2.5) GPa, KS0′ = 4.45(9), (â KS/â T)P =-0.0076(6) GPa K-1, G0 = 162.4(9) GPa, G0′ = 1.8(1), (â G/â T)P =-0.0175(9) GPa K-1, and α 298 K = 1.23 × 10-5 K-1. Fitting current data to the Mie-Grüneisen-Debye EOS with derived θ 0 = 383.4 K yielded γ 0 = 1.81 (6) and q = 0.3. The thermoelastic parameters obtained from various approaches are consistent with one another and comparable with previous results within uncertainties. Our current study provides a complete and self-consistent dataset for the thermoelastic properties of tungsten at high P-T conditions, which is important to improve the theoretical modeling of these materials under dynamic conditions.