Search

Funder: Engineering and Physical Sciences Research Council; doi: https://doi.org/10.13039/501100000266, Recently published density functional theory results using the PBE functional (Whaley-Baldwin and Needs 2020 New J. Phys. 22 023020) suggest that elemental sulfur does not adopt the simple-cubic (SC) P m 3 ̄ m phase at high pressures, in disagreement with previous works (Rudin and Liu 1999 Phys. Rev. Lett. 83 3049--52; Gavryushkin et al 2017 Phys. Status Solidi B 254 1600857). We carry out an extensive set of calculations using a variety of different exchange–correlation functionals (both local and non-local), and show that even though under LDA and PW91 a high-pressure SC phase does indeed become favourable at the static lattice level, when zero-point energies (ZPEs) are included, the transition to the SC phase is suppressed in every case, owing to the larger ZPE of the SC phase; thus confirming the transition sequence as R 3 ̄ m → BCC, with no intervening SC phase. We reproduce these findings with pseudopotentials that explicitly include core electronic states, and show that even at these high pressures, only the n = 3 valence shell contributes to bonding in sulfur. We then compare our findings against the all-electron code ELK, which is in excellent agreement with our pseudopotential results, and examine the roles of the exchange and correlation contributions to the total energy. We further calculate anharmonic vibrational corrections to the ZPEs of the two phases, and find that such corrections are several orders of magnitude smaller than the ZPEs and are thus negligible. The effect of finite temperatures is also considered, and we show that the P m 3 ̄ m phase becomes even more unfavourable with an increase in temperature. Finally, the experimental consequences of our results on the equation of state of sulfur and its superconducting critical temperature are explicitly calculated.

We use first-principles density functional theory to conduct an extensive structure search using the AIRSS package for elemental sulfur in the range 50–550 GPa. We then obtain the low-temperature phase diagram of sulfur in the same pressure range, including vibrational effects through the harmonic approximation. We do not find any structures lower in energy than those already reported in experiment, although the phase diagram below 100 GPa is found to be crowded with structures separated by only a few meV. We report the transition sequence I 4 1 / acd → P 1 ¯ → ICM → C 2 / m → R 3 ¯ m → I m 3 ¯ m and obtain accurate pressures for each transition, although we find the second-order C 2 / m → R 3 ¯ m transition particularly difficult to define. Contrary to previous first-principles works (Pavel et al; Rudin and Liu 1999 Phys. Rev. Lett. 83 3049–52), we do not reproduce a trigonal → simple cubic transition at either the static lattice or harmonic level. We also undertake a detailed analysis of the incommensurately modulated (ICM) phase of sulfur phase using a commensurate approximant found in the structure search. We find that the modulation amplitude is zero above 96 GPa; some 40 GPa below the experimentally reported transition to the unmodulated phase. We find that the body-centred atoms in the relaxed ICM approximant are, in addition to the dominant transverse modulation (which is a frozen-in optical phonon mode), slightly displaced longitudinally in the b-direction. We subsequently discover that this (small) longitudinal modulation is coupled to the transverse mode, and hence report previously unnoticed weak-mode coupling between transverse and longitudinal optical phonons in the ICM phase.