Crystal Structure of the Superconducting Phase of Sulfur Hydride

Abstract

A superconducting critical temperature above 200 K has recently been discovered in H₂S (or D₂S) under high hydrostatic pressure^{1, 2}. These measurements were interpreted in terms of a decomposition of these materials into elemental sulfur and a hydrogen-rich hydride that is responsible for the superconductivity, although direct experimental evidence for this mechanism has so far been lacking. Here we report the crystal structure of the superconducting phase of hydrogen sulfide (and deuterium sulfide) in the normal and superconducting states obtained by means of synchrotron X-ray diffraction measurements, combined with electrical resistance measurements at both room and low temperatures. We find that the superconducting phase is mostly in good agreement with theoretically predicted body-centered cubic (bcc) structure for H₃S (Ref.³). The presence of elemental sulfur is also manifest in the X-ray diffraction patterns, thus proving the decomposition mechanism of H₂S to H₃S + S under pressure^4–6.

Recently, a very high T_c of 200 K has been discovered in hydrogen sulfide system^{1, 2}. This work was initiated by prediction of a substantial superconductivity H₂S⁷, which in turn arises from the idea that hydrogen dominant metallic alloys might be superconductors with high critical temperature similar to pure metallic hydrogen.⁸

The superconducting transition was proved by the sharp drop of the resistance to zero, a strong isotope effect in study of D₂S, a shift of the superconducting transition with magnetic field, and finally by measuring the magnetic susceptibility and magnetization. As a likely explanation, the authors^{1, 2} suggested that H₂S decomposes under pressure (with the assistance of temperature) to pure sulfur and some sulfur hydride with a higher content of hydrogen (such as SH₄ or similar). At the same time, a theoretical work appeared which considered a different starting material (H₂S)₂H₂ (stoichiometry H₃S) and found R3m and Im-3m structures under pressure above 111 GPa and 180 GPa, respectively.³ These structures and other stoichiometric compounds were further carefully studied theoretically by different groups in numerous works^{4, 6, 9–25} and T_c ∼ 200 K was consistently obtained for the Im-3m structure. The calculated T_c as well as its pressure dependence⁹ are close to the experimental data^{1, 2}. This suggests that the high T_c observed in the experiments relates not to H₂S, but to the H₃S in the Im-3m structure. Later calculations supported this idea: H₂S is indeed unstable at high pressures and should decompose to sulfur and higher hydrides, most likely to H₃S^{4, 6, 12}. The goal of the present work is to check experimentally the structure of the superconducting hydrogen sulfide and compare with the theoretically predicted structure.

Samples were prepared in the same way as described in Ref.1, 2– H₂S was loaded at temperatures of ∼ 200 K, then pressure was increased to ∼ 150 - 170 GPa and sample was annealed at room temperature. Typical X-ray diffraction (XRD) images of sulfur hydride and sulfur deuteride pressurized to 150 - 173 GPa are shown in Fig. 1. The XRD patterns of sulfur hydride and sulfur deuteride samples do not differ from each other. The diffraction patterns appear to be produced by two major phases. This clearly follows from the different pressure dependence of the peaks (Fig. 2 and Fig. SI3) and different variation of intensities while scanning the sample over its diameter (Fig. SI1): One group is fitted by elemental sulfur of β-Po structure²⁶ and another group is described by the bcc-structure of H₃S from the theoretical work³. We can conclude that H₂S (D₂S) solid most likely decomposes under pressure with route: 3H₂S → 2H₃S + S.

Figure 1. XRD of the sulfur hydride and sulfur deuteride samples.

a, Unrolled powder diffraction image of sulfur hydride at 150 GPa at room temperature recorded on the imaging plate. b, c, The integrated XRD patterns obtained with extraction of the background. The patterns of bcc H₃S and β-Po elemental sulfur at 150 GPa and 170 GPa calculated according to Ref.5, 26 lie below the obtained patterns. The marks of star indicate the peaks which do not belong to the sample as follows from the scan over the sample (Fig. SI1): these peaks remain unchanged while the sample peaks change with radius of the sample both in position and intensity. Open circle indicates a reflection from high-pressure phase IV of elemental sulfur (incommensurately modulated body centered monoclinic structure). d, XRD patterns of sulfur deuteride at 173 GPa at 300 K and 13 K. The peaks marked by star (⋆) which do not the reflection from sample. The results of analyses are shown in table SI1 in supplementary information.

Figure 2. Pressure dependence of XRD in sulfur hydride and sulfur deuteride samples.

a, b, XRD patterns taken at room temperature and different pressures. Upper (red) and lower (green) ticks indicates the peak position of the predicted bcc structure of H₃S and β-Po elemental sulfur, respectively. The peaks marked with star do not belong to the sample as follows from Fig. SI1. On decreasing pressure in sulfur hydride, it is considerable that the phase transition of elemental sulfur is observed - the peak from β-Po sulfur gradually disappears and that from phase IV (open circle) is enhanced. c, Pressure dependence of the atomic volume of sulfur hydride and deuteride. The experimental data were obtained with increasing of pressure and are fitted with first-order Birch EoS (the black solid line). The volumes of hexagonal (R3m) and bcc (Im-3m) phases obtained from the theoretical work³ are shown with solid squares (■) and triangle (▲), respectively, and the broken line. The estimated standard deviations are smaller than the size of the symbols.

The pressure dependence of the atomic volume, V_atm, of sulfur hydride and sulfur deuteride are shown in Fig. 2c. It is fitted by a first-order Birch equation of state²⁷ with the bulk modulus B₀ = 506 (30) GPa, and its pressure derivative B₀’ = 6 (fixed). The value of experimentally observed V_atm is slightly larger but the compressibility is in good agreement with the Duan’s calculation³. The pressure dependence of the normalized atomic volume V/V₀ of elemental sulfur in the β-Po structure is shown in Fig. SI3. It is in a good agreement with the experimental data of Ref.26 at high pressures P > 170 GPa, and with our DFT calculations (see Methods).

Our powder X-ray diffraction measurements do not allow us to distinguish between the predicted bcc-structures: Im-3m and R3m. In these structures the positions of sulfur atoms are the same and the only difference is position of hydrogen atoms: hydrogen atoms are situated symmetrically between the neighbor sulfur atoms in the Im-3m structure and slightly asymmetrical in the R3m structure (Fig. SI2). However, the position of the hydrogen atoms cannot be determined from the powder measurements as hydrogen atoms are extremely weak scatterers.

The low temperature data help with further analysis. We measured simultaneously the XRD and electrical resistance at the same setup²⁸ (Fig. 3). The transition to the superconducting state was determined from the sharp drop of the resistance (Fig. 3a and 3b). We found that the normal and the superconducting state have the same structure as the XRD patterns are the same at room and low temperatures (Fig. 1d). Moreover, the structure of the sample visibly does not change over the pressure range 92 - 173 GPa. This is in a contrast with the dependence of the critical temperature on pressure which has a pronounced kink at 150 GPa for H₃S and 160 GPa for D₃S (Fig. 3c). This kink finds a natural explanation in the theoretical predictions^{9, 23}: the pressure dependence of the critical superconducting temperature is different in the R3m phase at lower pressures and in the Im-3m phase at higher pressures. Our X-ray diffraction measurements support this interpretation as R3m and Im-3m phases differ only in ordering of hydrogen atoms and the same XRD patterns should be the same in the both pressure domains. Thus one can conclude that the highest critical temperature of 203 K² corresponds to the Im-3m phase.

Figure 3. Pressure dependence of SC transition in sulfur hydride and sulfur deuteride.

a, b, Temperature dependence of resistance in sulfur hydride (on decease of pressure) and sulfur deuteride (on increase of pressure). c, Pressure dependence of critical temperature of superconductivity T_c of sulfur hydride (black points) and sulfur deuteride (red points). Open circles and squares are taken from Ref.2. The points marked with solid symbols are from the present work: the circles represent data on decreasing of pressure, the squares and triangles – at increasing of pressure. Broken lines (black for sulfur hydride and red for sulfur deuteride) indicate the phase boundary between R3m and Im-3m structural phase. The error bars indicate the difference between T_c onset and the zero-resistance temperature at each pressures (Fig. 3a and 3b).

Methods

The sample and electrical probes were prepared similar to Ref.2. Angle-dispersive powder x-ray diffraction measurements were carried out at SPring-8 (beamline BL10XU) with monochromatic beam of the energy of ∼ 30.0 keV (λ ∼ 0.412 0.414 Å). XRD and electrical resistance were measured simultaneously with the aid of a cryostat²⁸. The diffraction patterns were recorded by using an imaging plate with an exposure time between 120 and 300 seconds. Four probe electrical measurements were performed with a AC-resistance bridge (Linear Research Inc., LR-700). We determined the pressure-volume dependence of β-Po sulfur by using first-principles calculations based on the density functional theory. The Quantum ESPRESSO code²⁹ was used for the calculations, in which the Perdew-Burke-Ernzerhof generalized gradient approximation³⁰ and the Vanderbilt ultrasoft pseudopotential³¹ were employed. The k-space integration over the Brillouin zone was performed on a 24 × 24 × 24 grid, and the energy cut-off of the plane wave basis was set at 80 Ry.