Rhenium is a rare transition element which, owing to its high melting point and strength increase under plastic deformation, is well suited to be used as a metal gasket in high-pressure experiments with the diamond-anvil cell. In these experiments, particularly at very high pressures, the gasket itself can be used to estimate the pressure by x-ray diffraction at the point of contact with the sample. The pressure is then obtained from the equation of state (EOS) of the gasket's material [1].
The EOS of hexagonal close-packed rhenium has been previously determined up to 1.5 TPa (V/V0 ~ 0.46) using all-electron (AE) density functional theory (DFT) including core relativistic effects [2]. This work focuses on exploring the influence of core electrons on the EOS of rhenium above 1 terapascal (TPa), by comparing results obtained using plane-wave/pseudopotentials (PW/PPs) with previous AE calculations. DFT calculations were performed using fully relativistic PPs with Quantum Espresso [3]. We tested two norm-conserving PPs generated with the optimized Vanderbilt approach, one using the PBE exchange-correlation functional [4] and the other, more recently developed, using PBEsol [5]. Calculations were performed using the PBEsol exchange-correlation functional and the same conditions of the previous all-electron study, where applicable.
Both pseudopotentials yield results in good agreement with all-electron calculations. In particular, we observe a nonmonotonic variation of the c/a ratio with pressure. The fitted parameters of the Rose-Vinet EOS, the bulk modulus, B0 (380(2) GPa and 379(3) GPa for the PBE and PBEsol PPs, versus 377(5) GPa for AE), and its pressure derivative, B0’ (4.58(2) and 4.59(2) for the PBE and PBEsol PPs, versus 4.62(3) for AE), are identical (considering the uncertainties). The results differ mostly for the equilibrium volume at zero pressure, V0 (199.9(2) Bohr³ and 199.2(2) Bohr³ for PBE and PBEsol PPs, versus 195.2(3) Bohr³ for AE). For a given V/V0 ratio, the pressures estimated using the EOS derived from the PPs and AE calculations are in very good agreement, thus suggesting that the PPs used in this study are valid even at such high compression regime.
The support from the Brazilian agencies CNPq - grants 304831/2014-0 (CAP) and 304675/2015-6 (JEZ), PRONEX/FAPERGS, and CAPES - Finance Code 001 is gratefully acknowledged. This research was made possible also thanks to resources supplied by NCC/GridUNESP, CESUP/UFRGS, and NACAD/COPPE.
[1] Anzellini, S., Dewaele, A., Occelli, F., Loubeyre, P., & Mezouar, M. (2014). J. Appl. Phys, 115(4), 043511.
[2] Rech, G. L., Zorzi, J. E. & Perottoni, C. A. (2019). Manuscript in preparation.
[3] Giannozzi, P., Andreussi, O., Brumme, T., Bunau, O., Nardelli, M. B., Calandra, M., ... & Colonna, N. (2017). J. Phys. Condens. Matter, 29(46), 465901.
[4] Scherpelz, P., Govoni, M., Hamada, I., & Galli, G. (2016). J. Chem. Theory Comput., 12(8), 3523-3544.
[5] Van Setten, M. J., Giantomassi, M., Bousquet, E., Verstraete, M. J., Hamann, D. R., Gonze, X., & Rignanese, G. M. (2018). Comput. Phys. Commun., 226, 39-54.