Study of compressed sulfur based on reliable first-principles calculations

We investigated the high-pressure phases of sulfur using first-principles calculations with high precision. In a previous study, Rudin et al. [Phys. Rev. Lett. 83, 3049 (1999)] predicted that the β-Po type rhombohedral structure is followed by a simple cubic (sc) structure. Strictly limiting the comparison to the work of Rudin et al. and four atoms per unit cell, our high-precision calculations that couple an originally developed structure search method demonstrate that the proposed sc structure is not the ground state at any pressure value, and that compressed S undergoes a first-order phase transition to a body-centered-cubic phase above 500 GPa. The potential energy surface constructed by the pseudopotential employed by Rudin et al. does not conform with that constructed by an all-electron calculation. Our findings extensively contribute to the ongoing effort in forming an accurate picture of the structural phase transitions of compressed S, and also brings to light the importance of careful treatments necessary when calculating high-pressure states using the pseudopotential method.

Figure 1

The calculated enthalpy H for sc, hcp, β-Po, and Fdd2 structures of S relative to the bcc one as a function of pressure. The solid circle, open triangle, solid triangle, solid square, and open circle represent the enthalpies of the bcc, sc, hcp, β-Po, and Fdd2 structures, respectively. We note that the bcc, sc, hcp, and β-Po structures have four atoms per unit cell, whereas the Fdd2 one has 16 atoms per unit cell in reproducing the results of Whaley-Baldwin et al. [11]. The solid lines are guides to the eye.

Figure 2

The variation of the total energy as a function of the rhombohedral angle at constant unit cell volumes V of $55.63\mathrm{a}.\mathrm{u}{.}^3$ (200 GPa) (open square), $48.48\mathrm{a}.\mathrm{u}{.}^3$ (300 GPa) (solid square), $44.51\mathrm{a}.\mathrm{u}{.}^3$ (400 GPa) (open circle), $41.26\mathrm{a}.\mathrm{u}{.}^3$ (500 GPa) (solid circle), and $38.79\mathrm{a}.\mathrm{u}{.}^3$ (600 GPa) (open triangle). The calculations are based on the ultrasoft pseudopotential method of quantum espresso. The angle around 104° corresponds to the local β-Po minimum.

Figure 3

The variation of the total energy as a function of the rhombohedral angle at constant unit cell volumes V. (a) The calculations based on the FLAPW method of wien2k at $55.63\mathrm{a}.\mathrm{u}{.}^3$ (200 GPa) (open square), $48.48\mathrm{a}.\mathrm{u}{.}^3$ (300 GPa) (solid square), $44.51\mathrm{a}.\mathrm{u}{.}^3$ (400 GPa) (open circle), $41.26\mathrm{a}.\mathrm{u}{.}^3$ (500 GPa) (solid circle), and $38.79\mathrm{a}.\mathrm{u}{.}^3$ (600 GPa) (open triangle). (b) The comparison between the results obtained by the ultrasoft pseudopotential (PP) [9] method (solid triangle) and the FLAPW method (open circle) at the unit cell volume of $44.51\mathrm{a}.\mathrm{u}{.}^3$ (400 GPa). The solid lines are guides to the eye. The angle around 104° corresponds to the local β-Po minimum.

Figure 4

The phonon dispersion curves of bcc S (a) at 300, 500, 800, and 1000 GPa, and (b) at 1000, 1200, 1400, and 1600 GPa. The solid lines are guides to the eyes.