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Pressure-induced decomposition of solid hydrogen sulfide

Defang Duan, Xiaoli Huang, Fubo Tian, Da Li, Hongyu, Yu, Yunxian Liu, Yanbin

Ma, Bingbing Liu, Tian Cui a)

State Key Laboratory of Superhard Materials, College of Physics,

Jilin University, Changchun 130012, People’s Republic of Chinaa) Electronic address: cuitian@jlu.edu.cn

Solid hydrogen sulfide is well known as a typical molecular crystal but its

stability under pressure is still under debate. Particularly, Eremets et al. found the high

pressure superconductivity with Tc 190 K in a H2S sample [arXiv: 1412.0460 (2014)]

which is associates with the elemental decomposition into H3S [Sci. Rep. 4, 6968

(2014)]. Therefore, on what pressure H2S can decompose and which kind of the

products of decomposition urgent need to be solved. In this paper, we have performed

an extensive structural study on different stoichiometries HnS with n> 1 under high

pressure using ab initio calculations. Our results show that H2S is stable below 50

GPa and decomposes into H3S and sulfur at high pressure, while H3S is stable at least

up to 300 GPa. The other hydrogen-rich H4S, H5S, and H6S are unstable in the

pressure range from 20 to 300 GPa.

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I. Introduction

Solid hydrogen sulfide is known as a typical molecular crystal which has been

studied extensively at high pressure1-15. Up to now, the exact structures and molecular

dissociation of H2S at high-pressure is still under debate. Experimentally, at room

temperature, hydrogen sulfide transforms to phase IV with monoclinic Pc8 or

tetragonal I41/acd9. Upon compression, further transformation is complicated by the

partial dissociation of H2S and the appearance of elemental sulfur. But there have

been two opinions of the dissociation pressure of H2S derived from optical

experiments. One is 46 GPa6 at room temperature by infrared-absorption spectra

measurement, another is 27 GPa at room temperature and higher pressures around 43

GPa at 150 K by powder x-ray diffraction experiments13. Another Raman and IR

spectra of D2S revealed that it dissociates to sulfur at pressures above 27 GPa at room

temperature. When the pressure is higher, metallization occur near 96 GPa6, which

can be attribute to elemental sulfur that is known to become metallic above 95 GPa16.

Theoretically, Rousseau et al. studied the structure and stability of H2S at room

temperature through ab initio MD simulations. They suggested that phase IV has

partial rotational disorder with P42/ncm10 and the H2S molecules lose their identity in

phase V with forming H3S+ and HS- ionic species and uctuating S–S chains11.

Another ab initio MD simulation predicted an Ibca structure at 15 GPa and 100 K

with the initial con guration of the P42/ncm structure. When temperature increases to

350 K, it transforms to a proton disorder structure which is important to the

decomposition of H2S. Recent theoretical work have revised the phase diagram of

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H2S up to 200 GPa, and suggested that it is stable with respect to decomposition into

hydrogen and sulfur. In addition, a superconducting critical temperature (Tc) of ~80 K

at 160 GPa was predicted.

It is reported experimentally that mixing hydrogen sul de (H2S) and hydrogen

(H2) can form a stoichiometric compound (H2S)2H2 near 3.5 GPa, which is a

rotationally disordered structure with I4/mcm symmetry.17 Upon compression, an

ordering process occurs with structural transformation above 17 GPa. We have

explored the high-pressure ordered crystal structures of (H2S)2H2 by means of ab

initio calculations.18 Four high-pressure phases have been found and the Tc of cubic

phase was predicted to reach 191~204 K at 200 GPa for the first time. Recently,

Eremets et al. found superconductivity in a H2S sample with Tc 190 K above 150

GPa and 220 K which is likely associates with the dissociation of H2S into HnS (n>2)

formation19.

In the present work, we aim to elucidate the high pressure stability of different

stoichiometric HnS (n>1) hydrides using ab initio calculations and investigate whether

H2S can decompose and what the products of decomposition are. The results show

that H2S molecule is only stable below 50 GPa and it will decomposes into H3S and

sulfur element at higher pressures.

II. Methods

Searches for the stable compounds and structures for different stoichiometric

HnS (n>1) hydrides are performed by merging the evolutionary algorithm and ab

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initio total-energy calculations, as implemented in the USPEX code (Universal

Structure Predictor: Evolutionary Xtallography)20-22. The details of the search

algorithms and its several applications have been described elsewhere23,24. In the first

generation, structures (population size: 10-60 structures, increasing with system size)

are produced randomly. All produced structures are relaxed and the appropriate

thermodynamic potential is used as fitness function. The subsequent generation is

created from 60% of the lowest-enthalpy structures of the preceding generation. New

structures are created by heredity (60%), permutation (20%), and lattice mutation

(20%) operations. The best structure of each generation is also carried over to the next

generation. The calculation stops when the best structure does not change for more

than 20 generations.

The underlying structure relaxations are performed using density functional

theory as implemented in the Vienna ab initio simulation package VASP code25. The

generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof (PBE)26 is

adopted to describe the exchange-correlation potential. The all-electron projector

augmented wave (PAW) method27 is adopted with the core radii are 0.8 a.u. for H (1s2)

and 1.5 a.u. for S (3s23p4). For the initial search over structures, Brillouin zone (BZ)

sampling using a grid of spacing 2 × 0.05 Å-1 and a plane-wave basis set cutoff of

500 eV are found to be sufficient. But we recalculate the enthalpy curves with higher

accuracy using the energy cutoff 800 eV and k-mesh of 2 ×0.03 Å-1 within the

Monkhorst-Pack (MP) scheme are chosen to ensure that the total energy are well

converged to better than 1 meV/atom.

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III Results and discussion

The structure predictions are performed considering simulation sizes ranging

from 1 to 4, 6, and 8 formula units per cell (f. u./cell) for H2S and H3S at pressures

between 20 and 300 GPa. For the case of H4S, H5S and H6S, the structure predictions

are performed within 2 and 4 f. u. at pressures of 50, 100, 200 and 300 GPa. The

stability of HnS (n>1) can be quantified by constructing the thermodynamic convex

hull at the given pressure, which is defined as the formation enthalpy per atom of the

most stable phases at each stoichiometry:

hf (HnS) = [h(HnS) h(S) nh(H2)/2]/(n+1).

where hf is the enthalpy of formation per atom and h is the calculated enthalpy

per chemical unit for each compound. The enthalpies h for HnS are obtained for the

most stable structures as searched by the USPEX method at the desired pressures. The

known structures of P63m, C2/c, and Cmca 28 for H2, I41/acd 29 and -Po 30 for S in

their corresponding stable pressure are adopted. Any structure with the enthalpy lies

on the convex hull is considered to be thermodynamically stable and synthesizable

experimentally31. The convex hulls at selected pressure of HnS are depicted in Fig. 1.

If a tie-line is drawn connecting hf (A) and hf (B), while hf (C) falls beneath it,

then compounds A and B will react to form compound C, provided the kinetic barrier

is not too high. If another compound D with hf (D) falls above the tie-line connecting

hf (A) and hf (B), it is expected to decompose into these two compounds A and B. The

solid line in Fig. 1 traces out the estimated convex hull of stoichiometries HnS (n>1)

at 20, 40 50, 100, 200 and 300 GPa. At 20 GPa (Fig. 1a), the enthalpy of formation

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for H2S and H3S stoichiometries fall on the convex hull, indicating that both

compounds are thermodynamically stable at this pressure. In addition, H2S has the

most negative enthalpy of formation, which is consistent with the knowledge that H2S

exists at low pressure range. For H3S, it can be synthesized using S and H2 as

precursors or using H2S and H2 as precursors, which has been confirmed by T.A.

Strobel et al..17 They reported that mixtures of H2S and H2 were loaded into diamond

anvil cells and compression up to 3.5 GPa, a compound (H2S)2H2 (H3S with

hydrogen-sulfur stoichiometric ratio 3:1) was formed. With increasing pressure, H3S

become the most stable stoichiometry and H2S starts to deviation the tie-line at 50

GPa (Fig. 1c). This clearly suggests that H2S is unstable and will decompose to H3S

and sulfur: 3H2S 2H3S+S. Moreover, H3S remains the most stable stoichiometry up

to 300 GPa, the highest pressure examined in this work. In contrast, the calculations

show that H4S, H5S, and H6S stoichiometries are unstable in our study pressure range.

Therefore, the dissociation 2H2S H4S+S, 5H2S 2H5S+3S, and 3H2S H6S+2S are

energetically unfavorable.

Form the Fig. 1d it is clearly seen that the H2S deviates far away the tie-line and

the H3S has the most negative enthalpy of formation at 200 GPa. Therefore, Eremets

et al. reported H2S sample19 with high Tc of 190 K might decompose to mixture H3S

and S under high pressure. The stable pressure ranges for H2S and H3S are predicted

in Fig. 2.

The stable structures calculated for each stoichiometry are shown in Fig. 3 and

Fig. 4 H2S is stable in the P2c (20~30 GPa) and Pc (30~50 GPa) structures up to 50

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GPa, which are agreement with the recently theoretical reported by Li et al.15, as

shown in Fig. 3a and b. At higher pressures, H2S decomposes into H3S and sulfur

above 50 GPa, which is consistent with experimental observation that H2S molecular

dissociation near 43 GPa at 150 K13. Moreover, in the recently experiment19, there is a

abrupt change in the Raman spectra and H2S sample starts to conduct at ~50 GPa

indicating a structural transition at this pressure.

The high pressure structures, metallization, and superconductivity of H3S

stoichiometry have been elucidated in our previously work.18 At 20 GPa, H3S adopts

P1 structure, which consists of an ordered H-bonded H2S network and H2 molecular

units occupying the interstitial sites, as shown in Fig. 3c. Above 37 GPa, the Cccm

structure is energetically favored with partial hydrogen bond symmetrization. (Fig.3d).

On further compression, H2 units disappear and two intriguing metallic structures with

R3m and Im-3m symmetries (Fig. 3e and 3f) are reconstructive above 111 GPa and

180 GPa, respectively. The Im-3m structure is characterized by S atoms located at a

simple body centered cubic lattice and H atom located symmetrically between the S

atoms and coordination number of the S atom is six.

Although H4S, H5S, and H6S stoichiometries are only metastable, it is instructive

to examine the evolution of the crystal structure comparing with H3S. Selected

structures of H4S, H5S, and H6S at 200 GPa and 300 GPa are shown in Fig. 4. For H4S,

it forms orthorhombic structure with Fmmm symmetry (16 f.u./cell) at 200 GPa. In

this structure, the coordination number of the S atom is six which is the same as

Im-3m phase of H3S. In addition, there are H2 molecular units between H3S Im-3m

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blocks. For the case of H5S at 200 GPa, it forms orthorhombic structure with Fmmm

symmetry (8 f.u./cell). H6S adopts orthorhombic structure with Cmma symmetry (4

f.u./cell) at 200 GPa. For the structure of H4S, H5S, and H6S at 200 GPa, there is a

common feature that they all consist of H3S Im-3m blocks interbedded H2 molecular

units forming sandwich type structure. This suggests the possibility of decomposition

to mixture H3S and H2. In contrast, H2 molecular units disappear in H6S-Pbcn

structure characteristic as six H-S bonds in the H6S molecular unit at 300 GPa, as

shown in Fig. 4d. It suggests that H6S may become stable at higher pressures.

V. Conclusions

In summary, we explore the phase stabilities and the structures of different

stoichiometries HnS (n>1) between 20 and 300 GPa through ab initio calculations.

The results demonstrate that H2S decompose to H3S and sulfur above 50 GPa and H3S

is stable up to 300 GPa. By contrast, the other hydrogen-rich H4S, H5S, and H6S are

unstable in the pressure range we studied. Therefore, H2S sample with Tc 190 K at

high pressure might decompose to mixture H3S and S. Our finding resolve the debate

about the pressure-induced decomposition of H2S for a long time. Further

experimental studies of H2S and pure H3S at high pressure are still greatly demanded.

Acknowledgements

This work was supported by the National Basic Research Program of China (No.

2011CB808200), Program for Changjiang Scholars and Innovative Research Team in

University (No. IRT1132), National Natural Science Foundation of China (Nos.

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51032001, 11204100, 11074090, 10979001, 51025206, and 11104102), National

Found for Fostering Talents of basic Science (No. J1103202), Specialized Research

Fund for the Doctoral Program of Higher Education (20120061120008 and

20110061120007), and China Postdoctoral Science Foundation (2012M511326 and

2013T60314). Parts of calculations were performed in the High Performance

Computing Center (HPCC) of Jilin University.

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Fig. 1 | Chemical stabilities of stoichiometric HnS (n> 1) hydrides under pressure.

Predicted formation enthalpy of HnS with respect to decomposition into S and H2

under pressure. Dashed lines connect data points, and solid lines denote the convex

hull.

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Fig. 2 | Predicted pressure-composition phase diagram of stoichiometric HnS

(n>1) hydrides.

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Fig. 3 | Stable structures of H2S and H3S stoichiometries. a, H2S at 20 GPa in a P2c

structure. b, H2S at 40 GPa in a Pc structure. c, H3S at 20 GPa in a P1 structure. d,

H3S at 60 GPa in a Cccm structure. e, H3S at 130 GPa in a R-3m structure. f, H3S at

200 GPa in a Im-3m structure.

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Fig. 4 | Selected metastable structures of H4S, H5S and H6S stoichiometries. a,

H4S at 200 GPa in a Fmmm structure. b, H4S at 200 GPa in a Fmmm structure. c, H6S

at 200 GPa in a Cmma structure. d, H6S at 300 GPa in a Pbcn structure.