Stability of rhombohedral phases in vanadium at high-pressure and high-temperature: first-principles investigations

Abstract

The pressure-induced transition of vanadium from BCC to rhombohedral structures is unique and intriguing among transition metals. In this work, the stability of these phases is revisited by using density functional theory. At finite temperatures, a novel transition of rhombohedral phases back to BCC phase induced by thermal electrons is discovered. This reentrant transition is found not driven by phonons, instead it is the electronic entropy that stabilizes the latter phase, which is totally out of expectation. Parallel to this transition, we find a peculiar and strong increase of the shear modulus C44 with increasing temperature. It is counter-intuitive in the sense that it suggests an unusual harding mechanism of vanadium by temperature. With these stability analyses, the high-pressure and finite-temperature phase diagram of vanadium is proposed. Furthermore, the dependence of the stability of RH phases on the Fermi energy and chemical environment is investigated. The results demonstrate that the position of the Fermi level has a significant impact on the phase stability, and follows the band-filling argument. Besides the Fermi surface nesting, we find that the localization/delocalization of the d orbitals also contributes to the instability of rhombohedral distortions in vanadium.

Kohn Anomaly and Phase Stability in Group VB Transition Metals

“…One should mention that all calculations, including those by Qiu and Marcus [68], have been performed under hydrostatic conditions and, thus, are inappropriate for Jenei et al's [77] argument (nonhydrostaticity). To verify the reason for the discrepancy between calculations by Lee et al [64] and Qiu and Marcus [68], Wang et al [90] have performed identical calculations to that of Lee et al [64] but additionally optimized the structures. Wang et al [90] have selected Rh1 and Rh2 as the starting structures and optimized them at different pressures.…”

“…To verify the reason for the discrepancy between calculations by Lee et al [64] and Qiu and Marcus [68], Wang et al [90] have performed identical calculations to that of Lee et al [64] but additionally optimized the structures. Wang et al [90] have selected Rh1 and Rh2 as the starting structures and optimized them at different pressures. The calculated enthalpy difference with respect to the BCC phase together with the variation of the structural parameter (the residual angle α) in the Rh1 and Rh2 structures as a function of pressure are shown in Figure 1 (taken from [90]).…”

“…The calculated enthalpy difference with respect to the BCC phase together with the variation of the structural parameter (the residual angle α) in the Rh1 and Rh2 structures as a function of pressure are shown in Figure 1 (taken from [90]). According to Wang et al [90], the results of fully relaxed calculations reveal that the BCC → Rh1 transition does not occur at 300 kbar as was suggested by Jenei et al [77]. The metastable region of the Rh1 phase exists up to 500 kbar, but at lower pressures the Rh1 phase remains highly unstable.…”

“…The metastable region of the Rh1 phase exists up to 500 kbar, but at lower pressures the Rh1 phase remains highly unstable. Wang et al [90] Calculations [59,60,64,65,67,90] assume that the unit cell volume is conserved. As was shown by Le et al [64] and Wang et al [90], the total energy along the deformation path can be corrected from an internal energy, E, to an enthalpy, H, to study phase equilibrium at constant pressure.…”

“…Wang et al [90] have selected Rh1 and Rh2 as the starting structures and optimized them at different pressures. The calculated enthalpy difference with respect to the BCC phase together with the variation of the structural parameter (the residual angle α) in the Rh1 and Rh2 structures as a function of pressure are shown in Figure 1 (taken from [90]). According to Wang et al [90], the results of fully relaxed calculations reveal that the BCC → Rh1 transition does not occur at 300 kbar as was suggested by Jenei et al [77].…”