Thermoelasticity and anomalies in the pressure dependence of phonon velocities in niobium

Compressional and shear wave velocities of polycrystalline niobium have been measured at simultaneously high pressures and temperatures up to 5.8 GPa and 1073 K, respectively, using ultrasonic interferometry in conjunction with synchrotron x-ray techniques. An anomalous pressure-induced softening behavior in the phonon velocities, probably owing to the topological change in the Fermi surface, has been observed at ∼4.8 GPa during cold compression, which is supported by the elasticity data from our first-principles calculations. In contrast, both the bulk (B_S) and shear (G) moduli increase with pressures but decrease with temperatures upon compression at extreme P-T up to 5.8 GPa and 1073 K. Using finite strain equation-of-state approaches, the elasticity of bulk and shear moduli and their pressure and temperature dependences are derived from the directly measured velocities and densities, yielding B_S0 = 174.9(3.2) GPa, G₀ = 37.1(3) GPa, ℓ?B_S/ℓ?P = 3.97(9), ℓ?G/ℓ?P = 0.83(5), ℓ?B_S/ℓ?T = -0.064(7) GPa/K, and ℓ?G/ℓ?T = -0.012(3) GPa/K. On the basis of the current thermoelasticity data, Debye temperature and the high-pressure melting curve of Nb are derived. The origin of the anomalies in shear behavior at high pressure might be attributed to the progressive s-d electron-transfer-induced topological changes of the Fermi surface upon compression.