Thermoelastic equation of state of molybdenum

We report some high P-T diffraction experimental results on molybdenum using synchrotron x-ray and time-of-flight neutron-diffraction techniques. Unit-cell dimensions, measured up to P=10 GPa and T=1475 K, were derived from the refinement results and fitted to a high-temperature third-order Birch-Murnaghan equation of state. The derived thermoelastic parameters for molybdenum are: isothermal bulk modulus KT0=266(9) GPa with a pressure derivative of bulk modulus ∂K/∂P=4.1(9), temperature derivative of bulk modulus ∂K/∂T=-3.4(9)x10-2 GPa/K, volumetric thermal expansivity α=a+bT having a=1.32(14)x10-5 K-1 and b=1.26(15)x10-8 K-2. Further, all of the previous experimental data involving shock wave, ultrasonic, thermal-expansion measurements were also analyzed and fitted to a high-temperature Birch/Vinet equation of state (EOS) and the thermal pressure approach of Mie-Grueneisen EOS, respectively. With the greatly extended P-V-T data coverage, we refined the thermoelastic parameter set for molybdenum as isothermal bulk modulus KT0=268(1) GPa with pressure derivatives of bulk modulus ∂K/∂P=3.81(6), ∂K2/∂P2=-1.41(13)x10-2, temperature derivative of bulk modulus ∂K/∂T=-2.13(31)x10-2 GPa/K, volumetric thermal expansivity α=a+bT having a=1.31(10)x10-5 K-1 and b=1.12(11)x10-8 K-2, and an invariant of αKT=5.43(5)x10-3 GPa/K over a wide P-T range. We have conducted a neutron-diffraction study at simultaneous high pressures and high temperatures. Thermal vibrations of atoms (Debye-Waller factors) of molybdenum were derived as a function of pressure and temperature. The experimental results of thermoelastic equation of state parameters are compared with previous experimental data derived from shock wave and ultrasonic elasticity measurements