Stabilization of S3O4 at High Pressure-Implications for the Sulfur Excess Paradox

The geological conundrum of sulfur excess refers to the finding that predicted amounts of sulfur, in the form of SO2, discharged in volcanic eruptions much exceeds the sulfur available for degassing from the erupted magma. Exploring the source of the excess sulfur has been the subject of considerable interest. Here, from a systematic computational investigation of sulfur-oxygen compounds under pressure, a hitherto unknown S3O4 compound containing a mixture of sulfur oxidation states +II and +IV emerges and is predicted to be stabilized above a pressure of 79 GPa. We predict that S3O4 can be produced via multiple redox reactions involving subducted S-bearing minerals (e.g., sulfates and sulfides) at high pressure conditions relevant to the deep lower mantle, and conversely be decomposed into SO2 and S at shallow depths of Earth. Therefore, S3O4 can be considered as a key intermediate compound to promote the decomposition of sulfates to release SO2, which offers an alternative source of the excess sulfur released during explosive eruptions. These findings provide a possible resolution to the geological paradox of excess sulfur degassing and a viable mechanism for the understanding of S exchange between surface and the lower mantle for the deep sulfur cycle.


INTRODUCTION
Sulfur (S) is one of the major multi-valent volatile elements, broadly distributed throughout the Earth, and participating in a variety of fundamental geochemical processes (e.g., the global biochemical circulation [1], metal transport [2], atmospheric S loading during the volcanic eruption, and core-mantle segregation [3]). Generally, the chemical speciation of S is strongly influenced by a wide range of oxidation states available. Under highly reducing environments, S dominantly exhibits an oxidation state of -II as sulfide, whereas under strongly oxidizing conditions it shows an oxidation state of +VI in sulfate. Other chemical species where S takes up intermediate oxidation states such as polysulfides, elemental S, sulfite, or thiosulfate sulfite may exist as well in different geochemical settings [2,4,5]. It happens often that the behavior of S in natural processes associated with complex oxidation-reduction reactions is unpredictable due to changes in the oxidation state of S across the range -II to +VI. Therefore, the geochemical behavior of S in the Earth is replete with paradoxes, and there are many open questions in geochemical processes related to S-bearing minerals.
A well-known geological paradox called "sulfur excess degassing" has been evidenced at numerous subduction zone volcanoes [6,7], where the amount of S (principally in the form of SO2) released during explosive eruptions can be orders of magnitude larger than that estimated to degassing from the erupted melt [5]. A variety of sources for the excess S released by magmas in volcanic emission [8,9] have been proposed: dissolution in the silicate liquid [10,11] or a coexisting gas phase at depth before eruption [7,12], gas expulsion from magma mixing [13,14], crystallization-induced exsolution (second boiling) [15], or the breakdown of S-bearing minerals [16]. These mechanisms were proposed based on the magmatic systems, which are related to volcanic eruptions in a shallow crust. It should be noted, however, that the ultimate source of the S found near the Earth's surface is derived from the Earth's mantle [17]. Oxygen is one of the most abundant elements in Earth and has provided critical control on the nature of Earth S reservoirs. The compounds formed by S and O have important implications for the geochemical processes and the nature of Earth S reservoirs. Thus, a key question that needs to be resolved regards the formation and properties of S-O compounds under mantle conditions. Various S-O compounds such as SO [18], SO2 [19], SO3 [20], S7O [21], and S8O [22] have been proposed at ambient pressure. High pressure as a characteristic for the mantle can drastically modify chemical properties of elements and promote the formation of unexpected minerals [23][24][25][26]. Currently, several high-pressure SO3 phase have been proposed in theory [27], and only SO2 has been experimentally studied up to 60 GPa [28]. The other S-O compounds have been insufficiently understood at high pressures till now. A pressing task is to investigate the S-O compounds viable under pressure conditions relevant to Earth's mantle.
Here, we report an extensive exploration of the high-pressure phase diagrams of S-O compounds. Besides the known SO2 and SO3 compounds, an unexpected stoichiometry of S3O4 with an intriguing crystal structure, which contains a mixture of +II and +IV oxidation states of S, is predicted to appear at high pressure. We show that S3O4 is able to be produced in reactions of sulfates and sulfides with iron and goethite under high pressure conditions in the deep mantle, and decomposes into SO2 and S at low P-T conditions relevant to shallow depths of Earth, thus offering insightful implications for S cycles, and the origin of excess S degassing observed in volcanic eruptions.

METHODS
The crystal structure searches on SxOy (x=1-3, y=1-4) at the selected pressures of 50, 70, and 100 GPa have been performed using the swarm intelligence based-CALYPSO method [29][30][31], which has been successful in resolving crystal structures of a large number of materials at high pressure [32]. The maximum simulation cell of structure searches contains 40 atoms for each composition. Structural optimization, electronic structure, and phonon calculations were performed in the framework of density functional theory within the generalized gradient approximation [33] as implemented in the VASP code [34]. The electron-ion interaction was described by the projector augmented-wave potentials [35], with 3s 2 3p 4 and 2s 2 2p 4 configurations treated as the valence electrons of S and O, respectively. A kinetic cutoff energy of 900 eV and a spacing of 2π × 0.03 Å -1 for Monkhorst-Pack k-mesh sampling [36] were adopted to give well converged total energies (~1 meV/atom). The ionic positions were fully relaxed until the residual force acting on each ion was less than 1 meV/Å. Due to the layered structure of S3O4, influence of van der Waals interactions was considered using the optB88-vdW functional [37]. The dynamic stability of the predicted new phases was verified by phonon calculations using the direct supercell method as implemented in the PHONOPY code [38].

RESULTS
Our main structure searching results are depicted in the convex hull diagrams of Fig. 1(a). The energetic stabilities of a variety of S-O structures are evaluated from their formation enthalpies relative to the dissociation products of the relevant elemental S [39,40] and O solids [41]. At 50 and 70 GPa, the known stoichiometries SO2 and SO3 are readily identified as stable in our structure searching simulations. At 100 GPa, an unexpected composition of S3O4 becomes stable with respect to the dissociation products of the elemental S and SO3. The predicted stable pressure ranges for the considered structures are listed in Fig. 1(b). SO3 is found to be the most stable phase against decomposition throughout the studied pressure range (50-100 GPa). S3O4 is energetically favorable relative to decomposition into element S and SO2 or SO3 in the pressure range of 79-102 GPa (Fig. 1c). The emergence of S3O4 leads to the instability of SO2 above 81.5 GPa. We calculated phonon dispersions and observed no imaginary frequencies for the S3O4 structures ( Fig. S1), indicating that these predicted structures are dynamically stable.
. The known S-III [39], S-IV [40] and ε-O2 phase [41] selected as the reference structures in the corresponding stable pressure ranges. The stable structures locate on the solid lines, while the metastable structures sit on the dashed lines. (b) Predicted pressure-composition phase diagram of S-O phases. (c) Calculated pressureenthalpy diagram for the reactions 3S3O4→4SO3+5S and S3O4→2SO2+S using optB88-vdw functional. The zero-point energy was included in the above energy calculations. (d) Crystal structure of C2/m-S3O4 contains mixed four-fold (S1) and six-fold (S2) coordination of S.
The structure of S3O4 ( Fig. 1d) is inherently layered and contains mixed four-fold and six-fold coordination of S. Specifically, S1 is linearly coordinated to two O atoms, while S2 is square-coordinated to four O atoms. All S atoms are bonded to two adjacent S atoms, thus forming zigzag polymeric all-S chains. The S1-S1 and S1-S2 bond lengths are 2.22 and 2.13 Å at 80 GPa, respectively, slightly longer than the S-S bond lengths (2.01 Å) in the S-III phase, therefore indicating relatively weaker covalent S-S bonding. To further decipher the nature of the bonding, we have examined the electron localization function (ELF) [42] of S3O4 in the (100) and (010) planes (Fig.  2a). Two inequivalent S atoms are clearly seen, while a less localized charge distribution is seen on the S-O bonds, indicating a significant degree of ionicity between the O anions and S cations. Clear covalent S-S bonding is evidenced by the strong charge localization between the nearest-neighbor S-S.  [43,44].
The oxidation states of S in geological environments play pivotal roles in deciding planetary chemical and physical dynamics [45]. Generally, the oxidation state of element is closely related to the local coordination and charge transfer. The S oxidation states in SO2 and SO3 can be assigned unambiguously as +IV and +VI, respectively. In contrast, the two-and four-fold coordination of S atoms with O atoms in S3O4 reveals its mixedvalence state. A bader charge analysis [46], summarized in Table 1, corroborates this interpretation. Note that the bader charges systematically underestimate the formal charge state (O 2here has a charge -1.28e in the SO2). In SO3, S has a formal charge state of +VI, and there is a charge transfer of 3.90 e from S to O, very close to that in SF6 (~3.73 e). In SO2, S has a formal charge state of +IV, the charge transfer is 2.56 e. In S3O4, the partial charge of 2.68 e in square coordinated S2 is almost equal to that in the SO2 case, so that S2 can be considered as having an oxidation state of +IV. On the other hand, S1 is significantly less positively charged (1.04 e) than the S +4 anion in SO2. This result highlights a crucial distinction of the S1 compared to S in SO2, indicating that the linearly coordinated S1 in S3O4 adopts the rare +II S oxidation state. The S-O compounds tend to be insulating, as satisfying the octet rule usually leads to the opening of a band gap. This rule is applicable to the predicted polymeric phases of SO2 and SO3. However, in S3O4 two bands are found to cross the Fermi level, forming an electron pocket around the Z point and a hole pocket spanning the X and Y points (Fig. 2b), giving rise to a clear metallic character of S3O4. The projected density of states (Fig.  2b) shows that both O and the linearly coordinated S1 contribute to the density of electronic states at the Fermi level, and the latter contribution is dominant. The metallic character originates from an overlap of the S1 electron lone pairs, which depends on interlayer distance (Fig. S2).
Since both the S and O are typical light elements, the stability of S-O compounds may be quite sensitive to temperature. To assess the viability at high temperature, we further examine their energetic and structural stability at relevant simultaneous high P-T conditions. The free energies including the vibrational contributions and entropic effects are evaluated for each phase using the quasi-harmonic approximation. Formation enthalpy calculations further reveal that S3O4 is energetically favorable relative to decomposition into SO3 and S above 70 GPa, and temperature has a minor impact on the threshold pressure (Fig.  3a). Against decomposition into SO2 and S, the stability region of S3O4 is shifted to higher pressure with rising temperature, increasing from 79 GPa at 0 K to 100 GPa at 2,300 K (Fig. 3b). Ab-initio molecular dynamics calculations show that S3O4 remains firmly solid at 2,000 K in the pressure range 80-100 GPa corresponding to deep mantle conditions (see Fig. S3), revealing that S3O4 may exist in solid form in the deep mantle. Overall, the predicted S3O4 is stable at P-T conditions relevant to Earth's lower mantle [47], but decomposes into SO2 and S at low pressure. Figure 3. The P-T phase diagrams for the reactions of (a) 4SO3+5S→3S3O4 and (b) 2SO2+S→S3O4. The geotherm curve is adapted from Ref. [47] It is well-known that the exchange of S between Earth's surface and the mantle, i.e., transporting S to the mantle via subduction and returning it to the surface by volcanic degassing, results in a global S cycle [48]. The global S cycle involves the transformations of S species via redox-driven chemical processes (e.g., sulfate reduction and sulfide oxidation). Previous studies have indicated that sulfates (e.g., CaSO4 and MgSO4) [48,49] and sulfides (e.g., FeS and FeS2) [50,51] may exist in Earth's mantle. It is estimated that ~1 weight % metallic Fe is present due to self-reduction reactions in lower mantle [52]. Also, the pyritetype FeOOH could still survive at the P-T conditions of the lower mantle within the deeply subducted slabs [53]. Thus, we explore the possibility to produce S3O4 by decomposition of sulfates using Fe as a reducing agent or oxidation reactions of sulfides with the FeOOH as an oxidizing agent. We have explored 39 possible reaction routes, in which the iron oxides and hydrogen-bearing minerals that possibly exist in the interior of Earth were chosen as products. The calculated negative reaction enthalpies of seven routes support the formation of S3O4 via redox reactions at 100 GPa (Fig. 4a), which is relevant to the deep mantle pressure.
According to our results, three possible processes can occur for the S cycle in the Earth (Fig. 4b). Firstly, the S-carrying sulfates or sulfides (e.g., CaSO4, FeS2 [54], and FeS [55]) are transported to the deep mantle within subduction slabs. Then they can react with Fe or FeOOH (minerals present in Earth's mantle) to produce S3O4 at reducing or oxidizing conditions. If S3O4 formed in the deep mantle ascends, by mantle dynamic processes, to shallow depths of Earth and low pressure conditions, it would decompose into S and SO2, which is the principal form of S released during explosive eruptions (Fig. 3c). While the mechanism of direct decomposition of S-bearing minerals (e.g., CaSO4, FeS2, and FeS) to release SO2 as an explanation of the "sulfur excess" paradox is not supported even at high pressure [11] (see Fig. S4 for enthalpy calculations), the present compound S3O4, which was not previously considered, provides an alternative S reservoir in the deep mantle, completes the deep S cycle and helps to explain the paradox of "sulfur excess" in volcanic eruptions.  Table S2. (b) The proposed processes for exchange of S between Earth's surface and mantle.

CONCLUSION
In summary, a hitherto unknown compound S3O4 has been identified to become stable at high P-T conditions relevant to the deep mantle. It contains a mixture of S(II) and S(IV) oxidation states and exhibits a peculiar metallic nature. A systematic examination of relevant formation and decomposition reactions reveals that S3O4 might be considered as a key ingredient to promote redox reactions of sulfate or sulfide in the deep mantle and to release SO2 at shallow depths of Earth, thereby offering insightful implication on the origin of excess S degassing observed in volcanic eruptions. The present results have fundamental significance and implications for practical processes in chemistry and geoscience, and further experimental exploration is highly expected.

ASSOCIATED CONTENT
The supporting information is available free of charge.
Phonon dispersion relations, band gap analysis, mean-square-deviation, calculated enthalpies and Gibbs free energy with different exchange-correlation functionals at high P-T, and pseudopotential measurement of the S3O4; crystallographic information of S-O compounds and other reactants. AUTHOR INFORMATION † These authors contributed equally to this work.

Notes
The authors declare no competing financial interest.      Figure S5. Relative enthalpies and Gibbs free energy of proposed reactions for 4SO3+5S→3S3O4 and 2SO2+S→S3O4 with various van der Waals (vdW) methods at high pressure and temperature (P-T). Both negative energy values of the two reactions reveal that S3O4 is stable. Due to the typical layer structure of S3O4, the vdW interactions were considered to inclusion of the dispersion interactions. All the calculated vdW methods give the conclusion that S3O4 is stable at high P-T. Figure S6. The calculated Gibbs free energy of proposed reactions for 4SO3+5S→3S3O4 and 2SO2+S→S3O4 with three different exchange-correlation functionals at high P-T. Even without the consideration of vdW, the calculations within local density approximation and Perdew-Wang-91 indicate that the S3O4 is stable at high temperature.