DOE OSTI2020
In this work, 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 K T 0 = 310.3(1.5) GPa, its pressure derivative K ' T 0 = 4.4(3), its temperature derivative at constant pressure ( ∂ K T / ∂ T ) P = – 0.0138 ( 1 ) GPa K – 1 and at constant volume ( ∂ K T / ∂ 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 ( ∂ α / ∂ 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 K S 0 = 314.5(2.5) GPa, K S 0 ' = 4.45(9), (∂ K S /∂ T ) P = – 0.0076(6) GPa K –1 , G 0 = 162.4(9) GPa, G 0 ' = 1.8(1), (∂ G /∂ 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.