First-principles investigation of elastic anomalies in niobium at high pressure and temperature

Abstract

Niobium does not show any structure transition up to very high pressures. Nonetheless, by using density functional theory, we demonstrate in this work that it exhibits striking softening in elastic moduli C44 and C' at a pressure from 20 to 150 GPa. A novel anomaly softening in C44 from 275 to 400 GPa is also predicted. The physics behind these two anomalies is elaborated by electronic structure calculations, which revealed that they are actually different, with the first one directly relates to an underlying rhombohedral distortion whereas the latter originates in an electronic topological transition. The large magnitude of the softening leads to a remarkable elastic anisotropy in both the shear and the Young's moduli of Nb. Further investigation shows that thermo-electrons have an important role on these anomalies. This effect has not been noticed before. With increased electronic temperature, it is found that all anomalies (both the elastic softening and anisotropy) in Nb are gradually diminished, effectively giving rise to a temperature-induce hardening phenomenon.

Kohn Anomaly and Phase Stability in Group VB Transition Metals

“…Wang et al [92] have concluded that this anomalous behavior of the Nb shear modulus C 44 in the pressure range 0-600 kbar mainly comes from the underlying Rh1 and Rh2 distortion and has the same softening mechanism which is observed in vanadium. According to Jing et al [88], a similar hypothesis can be also applied to the softening of the shear modulus in tantalum.…”

“…As was mentioned above, Struzhkin et al [40] have observed anomalies in the superconducting transition temperature T c in Nb at 50-60 kbar and suggested that this anomaly arises from the ETT. Wang et al [92] have also suggested that the ETT could be responsible for the unusual behavior of the compressive strength around 50-60 kbar.…”

“…Wang et al [92] have recently predicted a novel anomaly softening in C 44 of niobium between 2.75 Mbar and 4.0 Mbar. However, this softening is not related to the FS nesting in Nb, which terminated at 750 kbar [59,76], but originates purely from the ETT.…”

“…However, this softening is not related to the FS nesting in Nb, which terminated at 750 kbar [59,76], but originates purely from the ETT. Wang et al [92] have emphasized that the significant magnitude of the softening leads to an impressive elastic anisotropy in both the shear and Young's moduli of Nb. At 600 kbar, the anisotropy on the shear elastic constant approaches a maximum.…”

Temperature dependence of the Kohn anomaly in bcc Nb from first-principles self-consistent phonon calculations

“…Landa et al [5,6] and Koči et al [7] predicted a shear elastic softening of Nb from 20 to 150 GPa based on 0 K density functional theory (DFT) calculations. Based on the assumption that the thermal excitation of the electrons is the most significant temperature effect, Wang et al [8] performed static DFT calculations, varying the electronic temperature and including the thermoelectronic entropy to predict the temperature dependence of the C 44 shear elastic constant. The occurrence of the shear elastic softening has been suggested up to 2000 K. However, an absence of any phonon contribution which is expected to be significant at high temperatures calls for a reconsideration of this conclusion.…”