High-pressure behavior and thermoelastic properties of niobium studied by in situ x-ray diffraction

Abstract

In situ synchrotron energy dispersive x-ray diffraction (XRD) experiments on Nb have been conducted at pressures up to 6.4 GPa and temperatures up to 1073 K. From the pressure-volume-temperature measurements, thermoelastic parameters were derived for the first time for Nb based on the thermal pressure (ΔPth) equation of state (EOS), modified high-T Birch-Murnaghan EOS, and Mie-Grüneisen-Debye EOS. With the pressure derivative of the bulk modulus KT′ fixed at 4.0, we obtained the ambient isothermal bulk modulus KT0 = 174(5) GPa, the temperature derivative of bulk modulus at constant pressure (∂KT/∂T)P=−0.060(8) GPa K−1 and at constant volume (∂KT/∂T)V=−0.046(8) GPa K−1, the volumetric thermal expansivity αT(T)=2.3(3)×10−5+0.3(2)×10−8T (K−1), as well as the pressure dependence of thermal expansion (∂α/∂P)T=(−2.0±0.4)×10−6 K−1 GPa−1. Fitting the present data to the Mie-Grüneisen-Debye EOS with Debye temperature Θ0 = 276.6 K gives γ0 = 1.27(8) and KT0 = 171(3) GPa at a fixed value of q = 3.0. The ambient isothermal bulk modulus and Grüneisen parameter derived from this work are comparable to previously reported values from both experimental and theoretical studies. An in situ high-resolution, angle dispersive XRD study on Nb did not indicate any anomalous behavior related to pressure-induced electronic topological transitions at ∼5 GPa as has been reported previously.