Pressure-induced amorphization and existence of molecular and polymeric amorphous forms in dense SO₂

Significance

Some substances are known to exist in several different structurally disordered solid states and transform between them similarly to structural phase transitions between crystalline polymorphs. This interesting and yet not fully understood phenomenon is called polyamorphism, and notable examples include water, SiO₂, Si, etc. Here we present an example of such behavior in a simple molecular substance, SO₂. By using experimental high-pressure techniques, we observe a reversible transition between different amorphous states around 26 GPa. Experimental results are well supported by ab initio simulations, which identify the high-pressure amorphous form as a nonmolecular, polymeric one consisting of intertwined chains. Our findings contribute to the fundamental understanding of structure of disordered matter as well as high-pressure behavior of simple archetypal molecules.

Abstract

We report here the pressure-induced amorphization and reversible structural transformation between two amorphous forms of SO₂: molecular amorphous and polymeric amorphous, with the transition found at 26 GPa over a broad temperature regime, 77 K to 300 K. The transformation was observed by both Raman spectroscopy and X-ray diffraction in a diamond anvil cell. The results were corroborated by ab initio molecular dynamics simulations, where both forward and reverse transitions were detected, opening a window to detailed analysis of the respective local structures. The high-pressure polymeric amorphous form was found to consist mainly of disordered polymeric chains made of three-coordinated sulfur atoms connected via oxygen atoms, with few residual intact molecules. This study provides an example of polyamorphism in a system consisting of simple molecules with multiple bonds.

Polyamorphism is the counterpart of polymorphism observed in crystalline solids. It is characterized by the existence of two or more disordered forms, either amorphous or liquid, differing in local structural order while preserving the stoichiometry. This phenomenon is often also accompanied by changes in coordination and density (1, 2) (for recent reviews, see refs. 3 and 4). Transformations between these different amorphous forms can be driven by pressure and temperature. While, in the case of crystalline polymorphs, the structural transitions are often (at least in principle) of first order and sharp, transitions in amorphous systems occur between isotropic forms and are more likely to be continuous. This is related to the absence of constraints prescribed by lattice periodicity, allowing for a gradual transformation between very different forms.

The first and perhaps most celebrated example of polyamorphic behavior was discovered in water ice in 1984 by Mishima et al. (5, 6), observing that compression of ice ${\mathrm{I}}_h$ at 77 K induced a transformation to an amorphous state. Through specific compression/decompression/heating protocols, at least two different forms of amorphous water ice were identified, known as low-density amorphous (LDA) and high-density amorphous (HDA) ices. The local structural order in the HDA and LDA ices differs by the presence of non–hydrogen-bonded water molecules in the first coordination shell of the former, resulting in the two forms having substantially different density. The existence of two amorphous forms of water ice was suggested to be related to existence of liquid–liquid transition and a second critical point of water (7).

Similar phenomena have also been observed in other important systems such as Si (8), SiO₂ (9–11), and GeO₂ (12), where the polyamorphism is related to a change from tetrahedral to octahedral coordination at high pressure. Other examples where pressure induces changes in simple molecular systems include amorphous S (13) and liquid S (14) (for more examples and review, see refs. 3 and 4). Dramatic structural changes leading to amorphization have been observed upon compression of molecular crystals where multiple bonds are present. It is well known that pressure can destabilize multiple bonds in molecules in favor of extended polymeric networks with a higher coordination. Due to the associated strong kinetic effects, creation of amorphous forms is often observed, especially when compression is performed at low temperatures. Amorphization of molecular crystals at high pressure has been observed in the famous examples of nitrogen (15, 16), carbon dioxide (17, 18), and benzene (19–21). In nitrogen, the strong triple bond of the molecule breaks under high pressures, giving rise to a single-bonded network. In carbon dioxide, the double bond becomes unstable, and carbon coordination increases to three and four. In the case of benzene, the aromatic ring opens, and a network of hydrogenated carbons with single bonds is formed. The parent crystalline states of these amorphous materials have been discovered both in nitrogen (22, 23) and in carbon dioxide (24, 25) after high-temperature annealing obtained by means of laser heating.

Experiments

Sulfur dioxide is an important molecule in chemistry, serves a significant role in industrial applications, and has been attributed to atmospheric and geological processes. Unlike CO₂, the SO₂ molecule is bent, described by two resonant structures with one single and one double bond (26, 27). The crystalline forms of SO₂ have been previously experimentally studied at pressures up to 32 GPa, by Song et al. (28). Here, we present a combined experimental and computational study of SO₂ up to pressures of 60 GPa and over a broad temperature regime. Observations via Raman spectroscopy and X-ray diffraction (XRD), well supported by ab initio simulations, provide a detailed description, on the atomistic level, of the transformations under compression/decompression cycles. These findings give evidence of a hitherto unobserved example of polyamorphism related to a reversible transformation between molecular and polymeric amorphous forms of SO₂.

Raman Spectroscopy

In Fig. 1, we present a selection of Raman spectra measured upon increasing pressure up to 60 GPa, at 77 K (Fig. 1A), as well as subsequent decompression back to ambient pressure at room temperature (Fig. 1B). Similar experiments for compressions at 210 K were also conducted and are reported in SI Appendix, Fig. S1. We find, in general, an agreement between our Raman measurements of solid molecular SO₂ under pressure and those reported previously (28). However, the dramatic spectral changes at low temperatures were not observed previously, as pressures were limited to only 22 GPa (28). From these datasets, what is readily evident is the progression from sharp molecular peaks of SO₂, that is, ${\nu }_1$ 1,050 cm⁻¹ to 1,220 cm⁻¹, ${\nu }_3$ 1,240 cm⁻¹ to 1,320 cm⁻¹, and ${\nu }_2$ 520 cm⁻¹ to 600 cm⁻¹, to much broader, weaker peaks upon compression. In addition, new broad and weak bands appear at different frequencies, characteristics which are compatible with pressure-induced amorphization together with major changes in the local structure. Further, the well-defined molecular peaks of SO₂ are recovered upon decreasing pressure, while the new broad bands resulting from symmetry loss disappear, demonstrating that these changes are, indeed, reversible and are therefore incompatible with any irreversible processes, such as chemical decomposition (SO₂ $\to$ S + O₂).

Fig. 1.

Vibrational spectra of solid SO₂. (A and B) Selected Raman spectra of an SO₂ sample measured upon (A) increasing pressure at 77 K and (B) decreasing pressure at room temperature. During compression, the initially sharp molecular peaks of SO₂, ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$, broaden and become very weak, while new broad and weak bands appear at different frequencies, indicating pressure-induced amorphization together with changes in the local structure. Upon decompression, the sharp molecular peaks of SO₂, ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$, are recovered, while the new broad bands disappear at the same time, showing that amorphization and overall changes in the local structure are reversible. (C) Evolution of VDOS from ab initio MD simulations along compression (solid lines) and decompression (dashed lines) at $T=300$ K. Color represents structural state of the system: black, molecular crystal; red, molecular amorphous; blue, polymeric amorphous. Star in B marks ruby peaks.

Taking a detailed analysis of the spectra, we can shed light on a number of remarkable features. We find that the numerous sharp lattice peaks, observed below 300 ${\text{cm}}^{-1}$ to 400 ${\text{cm}}^{-1}$, weaken above 16 GPa (or above 10 GPa at 210 K; SI Appendix, Fig. S1) until they become undetectable above 21 GPa at 77 K (Fig. 1A) (or above 22 GPa at 210 K; SI Appendix, Fig. S1), and instead are replaced by a new broad band in the same spectral region. However, at higher frequencies, under the same conditions, we do not observe any additional peaks other than the molecular peaks, ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$, of SO₂ up to 25 GPa. The linewidth of the crystal peaks severely increases upon growing pressure, while the intensity decreases substantially. These spectral changes are highly indicative that, upon cold compression above 10 GPa to 15 GPa, crystalline molecular SO₂ undergoes a structural transformation into an amorphous form while preserving its molecularity, that is, consisting of SO₂ molecular units. Amorphization could have been enhanced by the shear stress, which is, in turn, related to the deformation of the gasket hole. This is supported also by our density functional theory (DFT) calculations (Ab Initio MD Simulations). Upon further compression, above 22 GPa to 25 GPa, additional and significant modifications to the Raman signature are observed; the ${\nu }_2$ and ${\nu }_3$ peaks progressively diminish and are barely observable above 30 GPa to 34 GPa. Conversely, the strongest Raman excitation of SO₂, ${\nu }_1$ (1,170 cm⁻¹ to 1,200 cm⁻¹ [Fig. 1A]), is visible to the maximum pressures of 50 GPa to 60 GPa (see also Fig. 1B), albeit comparatively weaker. The ${\nu }_1$ band peak is found to merge with an altogether new weak and broad peak centered at 1,220 cm⁻¹ to 1,230 cm⁻¹, denoted as $\alpha$ in Fig. 1A. In addition to emergence of the $\alpha$-peak, another new and broad band appears at 600 cm⁻¹ to 1,000 cm⁻¹ with a high-frequency edge at around 900 cm⁻¹, which we call $\beta$. Both bands $\alpha$ and $\beta$ appear to be of nonmolecular origin, which suggests that the emergence of these excitations signals that amorphous-molecular SO₂ undergoes a transformation into a nonmolecular/extended amorphous form.

Comparison with the pressure-induced molecular to amorphous-nonmolecular transformation in CO₂ (17, 18, 25) can help to interpret the transformation observed here in SO₂, as it bears similarities. Carbonia, the nonmolecular amorphous CO₂, has been shown to be made of a mixture of C in a threefold and fourfold oxygen coordination in similar proportions. The threefold coordinated C sites are uniquely identified by C=O stretching peaks in the Raman and the infrared (IR) spectrum, 1,900 cm⁻¹ to 2,000 cm⁻¹ at 50 GPa to 60 GPa, which roughly corresponds to the average value, $\nu$(stretch CO₂), between the symmetric and the antisymmetric stretching modes of molecular CO₂. However, when considering the full Raman and IR spectra, the single C–O bond stretching and deformation modes ascribed to both threefold and fourfold coordinated C sites form a broad spectral distribution extending over 500 cm⁻¹ to 1,500 cm⁻¹, ∼0.26 to 0.77 of the average $\nu$(stretch CO₂). Consequently, in the case of SO₂, the aforementioned peak, $\alpha$, is roughly the average frequency of the two molecular stretching modes, and can therefore be attributed to the S=O stretching modes for nonmolecular/extended SO₂ with S in threefold coordination by O. In addition, in the frequency range given by 0.26 to 0.77 of $\alpha$, 320 cm⁻¹ to 940 cm⁻¹, we observe the previously described band $\beta$. Therefore, again in accordance with the CO₂ analogue, the $\beta$ band can be attributed to single S–O bond stretching and deformation modes in the nonmolecular/extended SO₂. A discrepancy of using carbonia as an analogue, however, is that the fourfold oxygen coordination is absent in SO₂, in accordance with our DFT simulations (discussed later). We do, however, also have a two-component system, considering that the ${\nu }_1$ peak for molecular SO₂ is still present at the highest pressures, although weak. Therefore, we infer that the overall nonmolecular/extended SO₂ consists of a mixture of trace twofold S sites, still molecular in nature, in a bulk of nonmolecular threefold coordinated S sites. An alternative possibility compatible with experimental data would be that molecular parts of the sample with twofold coordinated S and nonmolecular parts with S in higher coordination are phase-separated on a macroscopic/mesoscopic scale.

On decompression, the spectral changes and transformations identified previously on compression are reverted, as shown in Fig. 1B. However, a minor hysteresis is observed, attributed to the kinetically limited structural changes. We observe that, when the sample is decompressed below 30 GPa to 25 GPa, both the $\alpha$ peak and $\beta$ band disappear, while the well-defined molecular peaks ${\nu }_1$, ${\nu }_2$, and ${\nu }_3$ emerge suddenly. Further, in the low-frequency/lattice region below 350 cm⁻¹, a diffuse, liquid-like band clearly develops, with no additional substantial changes down to about 5 GPa. These changes demonstrate again a change in the amorphous structure, recovering molecular SO₂ units at 25 GPa to 5 GPa on decompression. This molecular amorphous form is then found to further transform into a crystalline molecular SO₂ structure below 5 GPa, indicated by the sharp lattice mode peaks observed below this pressure and crystalline XRD (discussed later). Interestingly, an additional peak is found below 20 GPa at around 600 cm⁻¹ which was also observed in a previous study, where it was attributed to the formation of molecular clusters (28). The reversible transformations of SO₂ to molecular and nonmolecular amorphous forms again parallel the similar case of CO₂ (17, 18, 25), and are at odds with the cases of aromatic molecules, where, instead, amorphous nonmolecular forms obtained at high pressures are recoverable to ambient conditions (19–21, 29, 30).

XRD

The noncrystalline nature of SO₂ at high pressure has also been assessed by XRD, and the evolution of the static structure factor upon room-temperature decompression of sample compressed at low temperature is shown in Fig. 2A. The static structure factor has been obtained by the empty cell subtraction, taking into account the form factors of oxygen and sulfur as well as the Compton contribution from the sample, following a procedure described elsewhere (31). In general, it is found that, at the highest pressures, the two peaks at about 2.2 and 3 Å⁻¹ are of similar intensity, while, on decompression, the first peak significantly increases with respect to the second one, which, at the same time, moves to lower $Q$. The comparison between the patterns measured at 35.5 GPa and 23.5 GPa shows a clear change of the static structure factor. The first contribution, centered at 2.2 Å⁻¹, becomes more prominent and sharpens markedly, while the second has a more subtle loss of intensity. These changes, corresponding to the transformation from an extended amorphous to a molecular amorphous form, are in strong agreement with the Raman results outlined previously.

Fig. 2.

Static structure factor of solid SO₂ under pressure. (A) Experimental $S\left(Q\right)$ measured along a room-temperature decompression run. (B) $S\left(Q\right)$ computed from simulations at 300 K during decompression (the graph computed from simulation of compression is in SI Appendix, Fig. S2). Region of $S\left(Q\right)$ beyond 4.5 Å⁻¹ in A is inaccessible because of limited angle in experiment, while the region below 1.5 Å⁻¹ in B is not reliable because of limited RDF range, resulting from the simulation supercell size of 14 Å. The Bragg peaks at 6.5 GPa in A have been partially indexed on the basis of an Aea2 space group with a = 5.5430 Å, b = 5.4011 Å, and c = 5.5356 Å as obtained from simulations (see also SI Appendix, Fig. S11).

Furthermore, similarly to what was observed in the Raman experiments, at the lowest pressures, the molecular amorphous form is found to start transforming into a crystalline molecular SO₂ structure at about 6.5 GPa. The observed Bragg peaks can be partially assigned on the basis of the Aea2 structure (experimentally found at ambient pressure) compressed to 6.5 GPa (see also SI Appendix, Fig. S11 and Evolutionary Crystal Structure Prediction).

Summary of Experimental Observations

In summary, we have observed two distinct structural transformations: at lower pressures, the transformation from a molecular crystal to a molecular, van der Waals-type, amorphous solid, with no changes in the molecular unit, and to a nonmolecular/extended state on further compression. Interestingly, a substantial effect of temperature is observed for the former transformation, despite expecting the energy barrier to be comparatively small. For example, instead of an expected isobaric phase line, the transformation occurs at 5-GPa-lower pressures at 210 K compared with 77 K isotherm. Conversely, the second transformation, to a nonmolecular/extended amorphous state, is a chemically reconstructive one, and therefore would logically have a higher associated energy barrier and consequently a stronger temperature dependence. Instead, this transformation is observed at roughly the same pressures for both isotherms studied, 77 K and 210 K, at around 25 GPa to 30 GPa, counterintuitively suggesting that the barrier for polymerization is small in relation to the one for the initial molecular amorphization. We note that this is quite different from the case of CO₂ and N₂, where a much stronger hysteresis is reported (23–25).

Ab Initio Molecular Dynamics Simulations

In order to obtain a better understanding of the processes on an atomistic level, we performed ab initio molecular dynamics (MD) simulations following a pressure path akin to the experiment. We first performed a test in order to check whether applying shear stress to a perfect Aea2 molecular crystal at low pressure might result in amorphous molecular structure as observed in experiments. We gradually induced shear strain by deforming the $\gamma$-angle of the supercell by up to ${\mathrm{30}}^{○}$ and observed transformation into a disordered molecular form, confirming the experimentally observed amorphization.

The full simulation protocol is shown in SI Appendix, Fig. S3. In order to start the compression from a well-defined amorphous molecular structure, we melted a perfect Aea2 molecular crystal (32) in a $3\times 3\times 3$ supercell (108 SO₂ molecules, equivalent to a 324-atom unit cell) by heating at $P=0$ GPa to 600 K. Through subsequent cooling to 0 K, we prepared the amorphous structure, which served as an initial configuration for further simulations. Following the experimental pathway, we performed a gradual compression to 60 GPa and subsequent decompression to 10 GPa (in 10-GPa steps) at 300 K in order to accelerate the structural transformations (both on compression and decompression). Interestingly, at this temperature, we observed some diffusion of molecules in the molecular phase, suggesting that the sample might possibly be in metastable liquid state.

Analysis of the partial radial distribution functions (RDFs) (Fig. 3), obtained from simulations, can provide a more detailed description of the observed transformations on an atomistic level. The RDFs clearly indicate the reversible amorphous to amorphous transformation, corresponding to the S in twofold to threefold O coordination change, providing further evidence for the experimentally observed forms and their associated reversibility. Upon compression of the initial molecular amorphous sample to 10 GPa at 300 K, SO₂ retains its molecular units. Evidenced in Fig. 3A, the peak at 1.44 Å, corresponding to the double bond, is sharp and well separated from the next neighbor at 2.5 Å to 3.0 Å and the coordination number of S atoms with respect to O atoms is 2. Upon compression to 20 GPa, modifications in the RDF are observed, and, at 30 GPa, there is a substantial change: The first peak becomes weaker while a new peak at slightly longer distance, 1.6 Å, appears. These changes indicate that some of the S=O double bonds are broken and replaced by single ones. In the same pressure regime, three-coordinated S atoms appear with two single S–O bonds and one S=O double bond, forming polymeric chains (see snapshots shown in Fig. 4). On further compression, the first peak is found to progressively diminish in intensity while the second is enhanced, resulting in 82% of S atoms being in threefold oxygen coordination at 60 GPa. On decompression (Fig. 3B), akin to experimental observations, we observed the reverse evolution, further demonstrated by the pressure dependence of the number of two- and three-coordinated S atoms in Fig. 3C. Additionally, at 10 GPa, the previously identified polymeric chains observed on compression disappear entirely (Fig. 4), and the system reverts back to its initial molecular amorphous state. The strong agreement between experiment and simulations means that insights from the MD calculations can identify the experimental observations as forward and backward transitions between molecular and polymeric amorphous forms of SO₂. The dependence of the coordination number of S atoms on pressure (Fig. 3C) exhibits some hysteresis, which suggests that the transition might have a weakly first-order character. The pressure dependence of density upon compression and decompression, shown in SI Appendix, Fig. S4, shows a very small hysteresis and does not exhibit any particular features across the structural transformation. We performed a similar compression simulation also at 500 K and found the polymerization to start at 30 GPa, suggesting that the transition is shifted to higher pressure upon increasing temperature.

Fig. 3.

Partial S–O RDF [$g_{SO}$(R)] and concentration of sulfur coordination states at different pressures from MD simulations at 300 K. (A) RDF during compression, (B) RDF during decompression, and (C) fraction of two- and three-coordinated S atoms during compression (solid line) and decompression (dashed line). Coordination number was determined within the cutoff of 1.92 Å.

Fig. 4.

(A–C) Snapshots of the amorphous sample from MD simulations at different pressures. (A) The beginning of compression at 10 GPa where the sample consists only of SO₂ molecules. (B) Structure during compression at 40 GPa where the sample contains both molecules and polymeric chains. (C) Structure after decompression to 10 GPa where the sample reverted from polymeric back to molecular. Simulation supercells are not to scale. (D and E) Comparison of polymeric chains in crystalline and amorphous forms of SO₂. (D) Chains in crystalline Ama2 and ${Pmc2}_{\mathit{\text{1}}}$ phases. (E) Selected disordered chain in a configuration of a-SO₂ from MD simulation at 30 GPa. The color of S atoms represents coordination: two-coordinated atoms (molecule) are yellow, and three-coordinated ones (polymeric chains) are blue-gray.

Above 20 GPa, the calculated static structure factor, $S\left(Q\right)$, shows important changes upon compression (SI Appendix, Fig. S2). The intensity of the first diffraction peak at about 2.2 Å⁻¹ drops, while a new peak appears, around 3 Å⁻¹, which grows with increasing pressure. At 60 GPa, the height of both peaks becomes similar, reflecting XRD patterns above 35.5 GPa in Fig. 2A. All changes are found to be reversible upon decompression, albeit with a small hysteresis, and the calculated structure factor agrees very well with the experimental one (Fig. 2). Simulations allow us to decompose the total $S\left(Q\right)$ into contributions from atomic pairs (SI Appendix, Fig. S5) The first peak, around 2.2 Å⁻¹, originates mainly from nonbonded S$\cdot \cdot \cdot$S pairs, while the weaker second peak, at 3 Å⁻¹, comes from O$\cdot \cdot \cdot$O, and, finally, the broad peak, around 5 Å⁻¹, is mainly due to the S–O pairs. It is clear that the loss of the first peak of total $S\left(Q\right)$ is a consequence of changes in the S–O contribution, which exhibits a pronounced drop above 20 GPa (SI Appendix, Fig. S5). Therefore, the observed evolution of $S\left(Q\right)$ directly reflects changes of the distance of S–O neighbors upon polymerization.

On compression, comparing the vibrational spectra from simulations (Fig. 1C) with experimental Raman spectra (Fig. 1A), we observe qualitatively similar evolution. Above 20 GPa, the distinct ${\nu }_2$ peak at 550 cm⁻¹ progressively disappears, while the 400 cm⁻¹ to 500 cm⁻¹ and 600 cm⁻¹ to 900 cm⁻¹ regions become enhanced. Meanwhile, the two molecular peaks, ${\nu }_1$ around 1,100 cm⁻¹ and ${\nu }_3$ above 1,200 cm⁻¹, gradually merge into a single broad peak around 1,200 cm⁻¹, again in agreement with experiments (Fig. 1A). The evolution of the peaks can be understood from the projected vibrational density of states (VDOS), allowing decomposition of the total VDOS into contributions from structurally distinct S and O atoms (SI Appendix, Fig. S6). Both S and O atoms can be either in molecules or in polymeric chains. Moreover, O atoms in polymeric chains are either at a bridging position between two S atoms (S–O–S) or at the terminal position, doubly bonded to S atoms (S=O). The evolution of the total VDOS clearly reflects the gradual conversion of molecules into polymeric chains. Again, upon decompression, the reverse evolution is observed, in agreement with experiment (Fig. 1B).

Evolutionary Crystal Structure Prediction

In order to understand the origin of the two amorphous forms, it is useful to discuss their underlying crystalline counterparts. SO₂ forms at ambient pressure and low temperature below 201 K, an Aea2 molecular crystal (32). Conversely, its analogue SeO₂ forms, at ambient pressure, a ${P4}_2$/mbc polymeric crystal consisting of chains [mineral Downeyite (33)]. The possible existence of polymeric SO₂ (polysulfite) was studied in refs. 34 and 35, where energies of various oligomers were calculated. Additionally, in ref. 35, a crystal structure with infinite polymeric chains was studied, obtained by substituting Se atoms in Downeyite by S atoms. It was concluded that polymeric SO₂ is energetically higher than its molecular form, and it was proposed that the polymer could be stabilized at high pressure. Quantitatively, the energy difference between polymeric and molecular forms was found to be −19.7 kcal/mol for SeO₂ and 5.5 kcal/mol for SO₂ (table 1 in ref. 35). This can be understood by applying the well-known pressure homology rule (36–38) stating that light elements behave at high pressure like heavier elements from the same group at lower pressures.

The structure of crystalline polymeric phases of SO₂ has not been, to our knowledge, determined experimentally. In order to check their possible existence at high pressure, we performed a structural search of crystalline phases of SO₂, employing an evolutionary approach (details are described in Materials and Methods). We show here the main results of our search. The enthalpy vs. pressure graph for low-enthalpy phases is shown in SI Appendix, Fig. S7. At zero pressure, we found the lowest enthalpy for the molecular crystal structure with space group Aea2, in agreement with experiment (32). Upon increasing pressure, we found another molecular crystal structure ${P2}_1$/c which becomes stable above 1 GPa. Besides this structure, there are two low-lying metastable molecular structures, Pc and Cc, which, upon further compression, transform into polymeric structures. The molecular Cc structure spontaneously transforms to polymeric Ama2 phase beyond 13 GPa (reaching limit of dynamical stability), and, in the same manner, molecular Pc phase transforms beyond 17 GPa into polymeric ${Pmc2}_1$ phase (all structures are shown in SI Appendix, Fig. S8, and cif files of the Pc, Cc, ${Pmc2}_1$, and Ama2 structures are included in SI Appendix). Both polymeric structures have very similar enthalpy and become thermodynamically stable with respect to the molecular phases already at 11 GPa. They also have the same conformation of chains and differ only in chain stacking. The mechanism of polymerization is illustrated in SI Appendix, Fig. S9, showing the pressure evolution of bond lengths upon compression. A similar polymerization mechanism is likely to apply also in the amorphous form when molecules of suitable orientation approach each other (see also Connection between Crystalline and Amorphous Forms). Both polymeric structures have the same conformation of chains as SeO₂ Downeyite, but the stacking of chains is different. The stable polymeric structure has, at 20 GPa, a bond length of 1.46 Å between S atom and terminal oxygen (S=O) and 1.65 Å between S atom and bridging oxygen (S–O), similar to the peak positions of S–O RDF (Fig. 3). The sulfur atom in the chain is surrounded by three oxygen atoms in roughly trigonal pyramid coordination (at 20 GPa, bond angle O–S–O is ${\mathrm{90}}^{○}$ and O=S–O is ${\mathrm{100}}^{○}$), suggesting the presence of ${\mathrm{s}\mathrm{p}}^3$ hybridization (see also ref. 35, where it was suggested that the dimerization of SO₂ is related to sp²→ sp³ rehybridization). In order to quantitatively assess the bond order of S–O bonds in molecular and polymeric SO₂, we employed the density driven electrostatic and chemical (DDEC6) atomic population analysis method (39). We found a bond order of 2.12 in molecule and 2.14 and 1.15 for S=O and S–O bonds in the polymeric phase. In SI Appendix, Fig. S10, we show the electronic density of states including projections on s and p orbitals for the crystalline molecular Cc and polymeric Ama2 phase (no d-orbital participation was found). We also note that the diffraction pattern of the recrystallized phase upon decompression to 6.5 GPa (Fig. 2A) shows a strong similarity to the diffraction pattern of the molecular phase Aea2 at the same pressure (for comparison, see SI Appendix, Fig. S11). This provides additional evidence that the system after the compression/decompression cycle returns to its parent state.

Connection between Crystalline and Amorphous Forms

To make a connection to the polymeric amorphous form, we note that different molecular crystalline phases shown in SI Appendix, Fig. S7 have different limits of dynamical stability with respect to polymerization. While the ${P2}_1$/c phase remains molecular even at 30 GPa, the phases Cc and Pc polymerize beyond 13 and 17 GPa, respectively (SI Appendix, Fig. S9). This points to the fact that the pressure threshold for polymerization depends on the relative orientation of molecules. In the amorphous form, where random relative orientations are present, polymerization needs a higher pressure beyond 20 GPa to start. In Fig. 4 D and E, we show a comparison of chains from crystalline polymeric phases ${Pmc2}_1$ and Ama2 and selected disordered chain from the amorphous sample. It can be seen that the local environment is similar, except for the dihedral angles. While the crystalline forms have well-defined values (e.g., ${\mathrm{O}}_{terminal}$–S–${\mathrm{O}}_{bridge}$–S angle around ${\mathrm{136}}^{○}$), in the amorphous form, one can find nearly all values of the dihedral angles. We note that, in an early study (35), the effect of conformational changes on the energy of SO₂ oligomers was studied, and it was found that, in this respect, the potential energy surface is very soft. This rationalizes our observation of the variety of dihedral angles found in chains in the amorphous form.

To assess quantitatively the effects of structural disorder, we calculated the enthalpy of the amorphous form (relaxed to $T=0$) and found it, at 10 GPa, to be about 0.26 eV per formula unit above the crystalline phases (it is shown in SI Appendix, Fig. S7). Above 20 GPa, where the transition starts, the curve changes slope, and goes down, but much slower than the crystalline polymeric phases, because of incomplete polymerization in the amorphous form. We note that, because of the short time scale available in the ab initio MD simulations (of the order of 10 ps), the amorphous structure might not be fully relaxed structurally. We also determined, with our DFT simulations, the electronic properties of the a-SO₂ phase and found that the system does not metalize up to 60 GPa, having a band gap (in the Perdew–Burke–Ernzerhof [PBE] approximation) of at least 0.6 eV.

Conclusions

We observed a pressure-induced amorphization and a reversible structural transition between molecular and polymeric amorphous forms of SO₂ at pressures around 26 GPa. The transition has small hysteresis, pointing to the fact that the associated kinetic barriers are low. The lower pressure of the transition between molecular and polymeric amorphous forms, as well as the back-transformation, is qualitatively facilitated by the molecular polarity. This, supported by the high density attainable under pressure, drives the intermolecular interaction and lowers the activation energy of the transformation. To our knowledge this kind of transition was not previously observed and provides an example of reversible structural transition between disordered nonequilibrium states of solid matter. Unlike in a-CO₂, where polymeric a-carbonia contains three- as well as four-coordinated C atoms, here the molecular form converts into polymeric form with only three-coordinated S atoms. It will be of interest to study whether the two structurally distinct forms continue to exist also in liquid state, either in stable or metastable (supercooled) regions. For example, a transition between molecular and polymeric liquid has been proposed in nitrogen (40), and a cross-over between such forms was observed in recent computational study of amorphous nitrogen (41). Further experimental and theoretical work is necessary to accurately map the solid and liquid regions and uncover further details of the phase diagram of SO₂.

Materials and Methods

Experimental Methodology.

The SO₂ gas was loaded into the diamond anvil cell (DAC) by means of cryogenic loading: The gas was condensed between one diamond anvil and the gasket placed on the other diamond of a DAC, which was opened by a few millimeters and cooled to liquid nitrogen temperature inside a sealed glove box purged with nitrogen to avoid moisture condensation. We performed Raman spectroscopy using a state-of-the-art confocal Raman microscope with 15 and 2 μm of axial and transverse resolution, respectively. The spectrometer consisted of a Spectra Pro 750-mm monochromator, equipped with a Pixis Princeton Instrument charge-coupled device detector. Bragg grate filters were used to attenuate the laser light and spatial filtering of the collected light to obtain high-quality spectra down to 7 cm⁻¹ with minimal background from the diamond anvils and strong signal from the sample. The laser beam was expanded and cleaned by a band-pass filter. We used a Laser Torus at 660 nm with 10 mW of power and Laser Ventus at 532 nm with 0.5 mW of power to check for the presence of eventual fluorescence bands in the spectrum. We generally used a 300-grooves-per-mm grating, as the spectral features were getting very broad and weak with pressure. The pressure was determined by the fluorescence of a small ruby placed in the sample or from the stressed part of the diamond anvil, which we detect with high accuracy thanks to the excellent spatial resolution of the setup. The XRD measurements were made at Petra (proposal ID: I-20181128) using a monochromatic X-ray beam with 42.7-keV energy ($\lambda =0.2922$ Å), and the scattered X-rays were detected by a PerkinElmer XRD1621 (2,048 × 2,048 pixels, 200 × 200 $\mathrm{\mu }{\text{m}}^2$) detector. The diffraction patterns have been measured only along decompression of an amorphous sample obtained from a compression at low temperature while monitoring the changes with Raman spectroscopy. The excellent transverse spatial resolution allows us to obtain clean diffraction patterns of the sample without the presence of spurious diffraction lines from the metallic gasket. The empty cell subtraction, which is of fundamental importance to obtain reliable measurements of the diffuse scattering from an amorphous or liquid sample in the DAC, has been, in this case, easily obtained by measuring the empty cell at the end of the decompression run when the SO₂ has completely back-transformed to the gas state and escaped from the sample chamber.

Simulations Methodology.

We performed a structural search for crystalline phases of SO₂ employing the USPEX (42) package at pressures of 10, 20, and 50 GPa with four formula units (12 atoms) within a unit cell. Ab initio simulations were performed by DFT as implemented in VASP 5.3 and 5.4 codes (43–45), employing projector augmented wave pseudopotentials (with six valence electrons for both S and O atoms) and PBE (46) parametrization of the generalized gradient approximation exchange–correlation functional. In evolutionary search, structural relaxations, and enthalpy calculations, we employed the harder S_h and O_h pseudopotentials with a cutoff of 910 eV, while, in MD calculations, we used the regular ones S and O with a cutoff of 520 eV. Compression, decompression, and heating were performed by 6-ps variable-cell isothermal-isobaric (NpT) simulations with Langevin thermostat and $\mathrm{\Gamma }$-point Brillouin zone sampling. We used a time step of 2 fs and friction coefficients of 10.0 and 2.0 ps⁻¹ for atomic and lattice degrees of freedom, respectively, and 10,000 $m_u$ as barostat fictitious mass. Data for velocity autocorrelation function were generated by equilibrating a sample for 6 ps in NpT and then running 20-ps constant-volume microcanonical (NVE) simulation. Total and projected VDOS were computed in the standard way as Fourier transform of mass-weighted velocity autocorrelation function from MD trajectories at pressures from 10 GPa to 60 GPa. Static structure factors $S\left(Q\right)$ were calculated by performing Fourier transform of the RDFs from MD trajectories at several pressures along compression and decompression runs. All data referred to in the manuscript are available in the article and in SI Appendix.