Dissociation products and structures of solid ${\mathrm{H}}_2\mathrm{S}$ at strong compression

Hydrogen sulfides have recently received a great deal of interest due to the record high superconducting temperatures of up to 203 K observed on strong compression of dihydrogen sulfide (${\mathrm{H}}_2\mathrm{S}$). A joint theoretical and experimental study is presented in which decomposition products and structures of compressed ${\mathrm{H}}_2\mathrm{S}$ are characterized, and their superconducting properties are calculated. In addition to the experimentally known ${\mathrm{H}}_2\mathrm{S}$ and ${\mathrm{H}}_3\mathrm{S}$ phases, our first-principles structure searches have identified several energetically competitive stoichiometries that have not been reported previously: ${\mathrm{H}}_2{\mathrm{S}}_3, {\mathrm{H}}_3{\mathrm{S}}_2, {\mathrm{HS}}_2$, and ${\mathrm{H}}_4{\mathrm{S}}_3$. In particular, ${\mathrm{H}}_4{\mathrm{S}}_3$ is predicted to be thermodynamically stable within a large pressure range of 25–113 GPa. High-pressure x-ray diffraction measurements confirm the presence of ${\mathrm{H}}_3\mathrm{S}$ and ${\mathrm{H}}_4{\mathrm{S}}_3$ through decomposition of ${\mathrm{H}}_2\mathrm{S}$ that emerges at 27 GPa and coexists with residual ${\mathrm{H}}_2\mathrm{S}$, at least up to the highest pressure of 140 GPa studied in our experiments. Electron-phonon coupling calculations show that ${\mathrm{H}}_4{\mathrm{S}}_3$ has a small $T{}_c$ of below 2 K, and that ${\mathrm{H}}_2\mathrm{S}$ is mainly responsible for the observed superconductivity of samples prepared at low temperature ($<100$ K).

Figure 1

Results from structure searching at 25 (a), 50 (b), 100 (c), and 150 GPa (d). Convex hulls are shown as continuous lines, with (red) and without (black) the inclusion of zero point vibrational enthalpy (ZPE).

Figure 2

Energetically favorable structures of ${\mathrm{H}}_4{\mathrm{S}}_3$ with space groups $\mathrm{P}{2}_1{2}_1{2}_1$ (a) and Pnma (b). Small and large spheres represent H and S atoms, respectively. (c) Calculated enthalpy curves of the $\mathrm{P}{2}_1{2}_1{2}_1$ structure with respect to the Pnma structure for ${\mathrm{H}}_4{\mathrm{S}}_3$ as a function of pressure. (d) Decomposition enthalpy curves of ${\mathrm{H}}_4{\mathrm{S}}_3$ into (${\mathrm{H}}_3\mathrm{S}+\text{S}$) as a function of pressure.

Figure 3

(a) XRD patterns of ${\mathrm{H}}_2\mathrm{S}$ collected at various pressures at room temperature with an incident wavelength of 0.6199 Å. (b) and (c) Rietveld refinements of XRD profiles at 45.6 GPa based on the compositions Pc-${\mathrm{H}}_2\mathrm{S}$, $\mathrm{I}{4}_1$/acd-S, C2/c-${\mathrm{H}}_3\mathrm{S}$, and $\mathrm{P}{2}_1{2}_1{2}_1-{\mathrm{H}}_4{\mathrm{S}}_3$ with phase fractions of 1147:85:31:1 and at 65.7 GPa based on compositions of Pnma-${\mathrm{H}}_4{\mathrm{S}}_3$, C2/c-${\mathrm{H}}_3\mathrm{S}$, and Pc-${\mathrm{H}}_2\mathrm{S}$ with phase fractions of 5:3.4:1, respectively. The cross symbols and red solid lines represent observed and fitted patterns, respectively. The solid lines at the bottom are the difference between the observed and fitted patterns. Vertical bars under the pattern represent the calculated positions of reflections arising from the compositions.

Figure 4

Rietveld refinements of XRD profiles at 81.3 GPa based on Pnma-${\mathrm{H}}_4{\mathrm{S}}_3$ + C2/c-${\mathrm{H}}_3\mathrm{S}+\mathrm{Pmc}{2}_1-{\mathrm{H}}_2\mathrm{S}$ with phase fractions of 43:6:1 (a) and at 139.5 GPa based on Pnma-${\mathrm{H}}_4{\mathrm{S}}_3$ + R3m-${\mathrm{H}}_3\mathrm{S}$ + P-1-${\mathrm{H}}_2\mathrm{S}$ with phase fractions of 56:7:1 (c).

Figure 5

Superconducting transition temperatures ($T_c$) calculated for various H-S compounds and experimental values for compressed ${\mathrm{H}}_2\mathrm{S}$ [1]. Solid squares and circles show experimental data from Fig. 1 and Fig. 2 of Ref. [1], respectively, where different runs are represented by the same symbols. The open stars, squares, and circles show calculated data from Ref. [30], Ref. [36], and Ref. [55], respectively. Open triangles denote calculated $T_c$ for Pnma-${\mathrm{H}}_4{\mathrm{S}}_3$ in the present study. Note that the $T_c$ values (open squares) for $\mathrm{Im}\overline{3}\mathrm{m}-{\mathrm{H}}_3\mathrm{S}$ taken from Ref. [36] include anharmonic effects, while all other estimated $T_c\mathrm{s}$ are calculated within the harmonic approximation.