Downloaded at UNIVERSITY OF VICTORIA on April 4, 2020 ioeD Panfilis De Simone a Zhang Huichao SO in dense forms amorphous polymeric and molecular of existence and amorphization Pressure-induced www.pnas.org/cgi/doi/10.1073/pnas.1917749117 polyamorphism with molecules simple of of consisting bonds. example multiple system an a provides in study This polyamorphism molecules. of intact made with residual atoms, chains few oxygen was polymeric via connected disordered local form atoms of sulfur respective three-coordinated mainly amorphous the consist polymeric of to found analysis high-pressure detailed The to structures. window detected, were a transitions The reverse opening and cell. forward simula- anvil both dynamics where molecular diamond tions, Raman initio a ab both by by in corroborated were observed diffraction results was X-ray transformation regime, and The temperature K. spectroscopy broad 300 a to over K GPa 77 26 at re- found transition and the amorphization SO pressure-induced forms of 2019) amorphous 15, two October the between review transformation for structural here versible (received 2020 5, report March approved and We PA, Philadelphia, University, Temple Klein, L. Michael by Edited Italy Florence, 50125 (CNR-INO), Ricerche Kingdom; United 3JZ, China; EH9 201203, Edinburgh Edinburgh, of University Conditions, Italy; Fiorentino, Sesto Slovakia; Bratislava, China; 48 230026, Hefei China, of Technology atssessc sS 8,SiO (8), Si as such systems tant (7). water of point existence critical to second related a be and to transition suggested liquid–liquid was of ice water forms amor- of two two forms of the phous existence in The density. resulting different former, substantially the having of the shell in differs coordination molecules ices water first LDA non–hydrogen-bonded and of HDA presence low- the the in by as order structural known (HDA) local amorphous identified, The high-density ices. were and (LDA) ice amorphous water density amorphous of different com- forms two specific least Through at state. protocols, amorphous ice pression/decompression/heating an of et to compression Mishima transformation that by a 1984 observing in 6), ice (5, water al. in discovered was behavior phic con- of gradual a absence forms. for the different allowing to very in periodicity, between related transformation lattice transitions is by sharp, This prescribed continuous. and straints more be order are to and first forms likely often isotropic of between are occur principle) systems case transitions amorphous the in structural in least the While, (at temperature. polymorphs, and and crystalline 3 pressure forms refs. of by amorphous see driven different reviews, be these recent can (for between 2) Transformations (1, 4). coor- in density changes and stoichiometry. by accompanied the dination differ- also preserving often liquid, while is phenomenon order or This structural amorphous local either in forms, ing disordered more or P h oymrhs srltdt hnefo erhda to tetrahedral from where examples change Other pressure. a high to at coordination related octahedral is polyamorphism the e aoaoyo aeil hsc,Isiueo oi tt hsc,CieeAaeyo cecs ee 301 China; 230031, Hefei Sciences, of Academy Chinese Physics, State Solid of Institute Physics, Materials of Laboratory Key iia hnmn aeas enosre nohrimpor- other in observed been also have phenomena Similar polyamor- of example celebrated most perhaps and first The ncytliesld.I scaatrzdb h xsec ftwo of existence the by characterized is It observed solids. polymorphism crystalline of in counterpart the is olyamorphism 2 oeua mrhu n oyei mrhu,with amorphous, polymeric and amorphous molecular : i etefrLf aoSine siuoIain iTcooi,011Rm,Iay and Italy; Rome, 00161 Tecnologia, di Italiano Istituto Science, Nano Life for Centre | ufrdioxide sulfur a,b nrjT Ondrej , f d colo hsc n srnm,Uiest fEibrh dnug H J,Uie Kingdom; United 3JZ, EH9 Edinburgh Edinburgh, of University Astronomy, and Physics of School i eateto hmsr,Uiest fFoec,511Foec,Italy; Florence, 50121 Florence, of University Chemistry, of Department 2 ai Santoro Mario , | ihpressure high oth ´ 2 c 91) n GeO and (9–11), ioD Liu Xiao-Di , c eateto xeietlPyis aut fMteais hsc n nomtc,Cmnu nvriy 842 University, Comenius Informatics, and Physics Mathematics, of Faculty Physics, Experimental of Department a,e,j,1 | oyei form polymeric eeioAaeGorelli Aiace Federico , I h a,1 t7 induced K 77 at 2 oet Bini Roberto , 1) where (12), h etrfrHg rsueSineTcnlg dacdRsac,Shanghai, Research, Advanced Technology Science Pressure High for Center d,e doi:10.1073/pnas.1917749117/-/DCSupplemental at online information supporting contains article This 1 the under Published Submission.y Direct PNAS a is article This interest.y competing no P.D.-S., declare E.G., authors R.B., results.y The X.-D.L., of and discussion paper; the to the contributed wrote S.D.P. R.B., R.M. and X.-D.L., O.T., and F.A.G., data; M.S., analyzed S.D.P., R.M. P.D.-S., per- and F.A.G. E.G., F.A.G., and M.S., O.T., S.D.P., O.T., H.Z., H.Z., research; research; designed formed R.M. and F.A.G., M.S., contributions: Author n rsaln ttso hs mrhu aeil aebeen have materials amorphous par- these The of formed. network is a states and bonds crystalline opens, single ent ring with aromatic carbons four. the hydrogenated and benzene, of three of becomes to case single- bond increases the a In double coordination to the carbon dioxide, and rise unstable, carbon giving the In of pressures, network. bond high triple bonded 18), under the strong (17, the breaks in dioxide nitrogen, molecule observed carbon In 16), (19–21). been benzene (15, has and nitrogen pressure of of com- examples Amorphization high famous when temperatures. at especially low crystals at observed, molecular coor- performed creation often is higher effects, is kinetic pression a forms strong with amorphous associated networks the of polymeric to Due extended well dination. of molecules is in favor It bonds multiple present. in destabilize lead- are can pressure changes of bonds that compression multiple and known structural upon where examples Dramatic observed crystals more been 4). molecular have (for and amorphization (14) to 3 ing S refs. liquid include see systems and review, molecular (13) simple S in amorphous changes induces pressure owo orsodnemyb drse.Eal [email protected] xiaodi@issp. 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CHEMISTRY discovered both in nitrogen (22, 23) and in carbon dioxide (24, C 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 Intensity (a.u.) 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 B of 60 GPa and over a broad temperature regime. Observa- tions via Raman spectroscopy and X-ray diffraction (XRD), well supported by ab initio simulations, provide a detailed descrip- tion, on the atomistic level, of the transformations under com- pression/decompression cycles. These findings give evidence of a hitherto unobserved example of polyamorphism related to a reversible transformation between molecular and polymeric Intensity (a.u.) amorphous forms of SO2.

Raman Spectroscopy In Fig. 1, we present a selection of Raman spectra measured A 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 compres- sions 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 pres- sure and those reported previously (28). However, the dramatic

spectral changes at low temperatures were not observed previ- Intensity (a.u.) ously, as pressures were limited to only 22 GPa (28). From these datasets, what is readily evident is the progression from sharp −1 −1 molecular peaks of SO2, that is, ν1 1,050 cm to 1,220 cm , −1 −1 −1 −1 ν3 1,240 cm to 1,320 cm , and ν2 520 cm to 600 cm , to much broader, weaker peaks upon compression. In addition, new broad and weak bands appear at different frequencies, char- acteristics which are compatible with pressure-induced amor- Fig. 1. Vibrational spectra of solid SO2.(A and B) Selected Raman spec- phization together with major changes in the local structure. tra of an SO2 sample measured upon (A) increasing pressure at 77 K and (B) decreasing pressure at room temperature. During compression, the ini- Further, the well-defined molecular peaks of SO2 are recovered tially sharp molecular peaks of SO2, ν1, ν2, and ν3, broaden and become upon decreasing pressure, while the new broad bands result- very weak, while new broad and weak bands appear at different frequen- ing from symmetry loss disappear, demonstrating that these cies, indicating pressure-induced amorphization together with changes in changes are, indeed, reversible and are therefore incompatible the local structure. Upon decompression, the sharp molecular peaks of SO2, with any irreversible processes, such as chemical decomposition ν1, ν2, and ν3, are recovered, while the new broad bands disappear at the (SO2 → S + O2). same time, showing that amorphization and overall changes in the local Taking a detailed analysis of the spectra, we can shed light structure are reversible. (C) Evolution of VDOS from ab initio MD simula- on a number of remarkable features. We find that the numer- tions along compression (solid lines) and decompression (dashed lines) at ous sharp lattice peaks, observed below 300 cm−1 to 400 cm−1, T = 300 K. Color represents structural state of the system: black, molecu- lar crystal; red, molecular amorphous; blue, polymeric amorphous. Star in B weaken above 16 GPa (or above 10 GPa at 210 K; SI Appendix, marks ruby peaks. 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 icant modifications to the Raman signature are observed; the region. However, at higher frequencies, under the same condi- ν2 and ν3 peaks progressively diminish and are barely observ- tions, we do not observe any additional peaks other than the able above 30 GPa to 34 GPa. Conversely, the strongest Raman −1 −1 molecular peaks, ν1, ν2, and ν3, of SO2 up to 25 GPa. The excitation of SO2, ν1 (1,170 cm to 1,200 cm [Fig. 1A]), is vis- linewidth of the crystal peaks severely increases upon growing ible to the maximum pressures of 50 GPa to 60 GPa (see also pressure, while the intensity decreases substantially. These spec- Fig. 1B), albeit comparatively weaker. The ν1 band peak is found tral changes are highly indicative that, upon cold compression to merge with an altogether new weak and broad peak centered −1 −1 above 10 GPa to 15 GPa, crystalline molecular SO2 undergoes at 1,220 cm to 1,230 cm , denoted as α in Fig. 1A. In addi- a structural transformation into an amorphous form while pre- tion to emergence of the α-peak, another new and broad band −1 −1 serving its molecularity, that is, consisting of SO2 molecular appears at 600 cm to 1,000 cm with a high-frequency edge units. Amorphization could have been enhanced by the shear at around 900 cm−1, which we call β. Both bands α and β appear stress, which is, in turn, related to the deformation of the gas- to be of nonmolecular origin, which suggests that the emer- ket hole. This is supported also by our density functional theory gence of these excitations signals that amorphous-molecular (DFT) calculations (Ab Initio MD Simulations). Upon further SO2 undergoes a transformation into a nonmolecular/extended compression, above 22 GPa to 25 GPa, additional and signif- amorphous form.

2 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1917749117 Zhang et al. Downloaded at UNIVERSITY OF VICTORIA on April 4, 2020 Downloaded at UNIVERSITY OF VICTORIA on April 4, 2020 o07 fteaverage the of spec- broad 0.77 cm a 500 to form over extending sites both distribution C to tral coordinated ascribed fourfold modes and deformation single threefold and the stretching spectra, IR bond and Raman C–O full the considering CO when molecular ever, of modes stretching antisymmetric value, the and average the cm to 1,900 spectrum, cm (IR) stretching 2,000 infrared C=O the to and by Raman identified the in uniquely threefold peaks are The four- sites proportions. and threefold C similar a coordinated in in C coordination of mixture oxygen a fold of CO made be amorphous to shown nonmolecular been the SO in Carbonia, here similarities. observed transformation the interpret to CO in transformation phous-nonmolecular hn tal. et Zhang compressed sample factor of structure static decompression the room-temperature of evolution upon the and XRD, by assessed SO of nature noncrystalline The ambient to XRD recoverable are pressures 30). 29, high (19–21, conditions nonmolecular at amorphous obtained instead, forms where, molecules, aromatic CO similar of the parallel case again forms SO amorphous molecular of nonmolecular of and transformations lar formation reversible the The to (28). attributed clusters was it where cm study, 600 ous around at below XRD GPa found crystalline 20 is peak and additional an pressure Interestingly, this later). (discussed below observed molec- peaks crystalline mode a into transform SO further amorphous ular to molecular found This then decompression. is on form GPa SO 5 molecular to recovering GPa 25 structure, change amorphous a again the demonstrate changes in These GPa. 5 changes about substantial to additional down no with develops, clearly cm band 350 like GPa, below 25 region to low-frequency/lattice GPa 30 peaks below molecular that, decompressed attributed observe the is We observed, both changes. sample is structural the hysteresis limited when minor kinetically in the a shown to as However, reverted, 1B. are Fig. compression on previously identified macroscopic/ a S on with sam- phase-separated parts scale. the are mesoscopic nonmolecular of coordination and higher parts S in coordinated molecular twofold that with threefold with compatible be nonmolecular ple possibility would of alternative data bulk An experimental a sites. in S nature, coordinated in molecular nonmolecu- still overall the the SO that infer lar/extended that we Therefore, considering weak. however, although system, SO do, molecular two-component We for peak a later). (discussed have SO simulations also in the DFT absent that our is is with however, coordination analogue, an oxygen as fourfold carbonia SO using nonmolecular/extended of the crepancy in modes deformation of 0.77 β to 0.26 by given range cm frequency 320 non- the for in modes addition, stretching In can S=O and the modes, SO to molecular/extended stretching attributed molecular be two therefore the of frequency age SO of case β hrfr,aani codnewt h CO the with accordance in again Therefore, . oprsnwt h rsueidcdmlclrt amor- to molecular pressure-induced the with Comparison ndcmrsin h pcrlcagsadtransformations and changes spectral the decompression, On adcnb trbtdt igeSObn tecigand stretching bond S–O single to attributed be can band −1 2 α tutr eo P,idctdb h hr lattice sharp the by indicated GPa, 5 below structure o90cm 940 to 2 − ekand peak 2 h frmnindpeak, aforementioned the , 1 1,1,2) n r tod ihtecssof cases the with odds at are and 25), 18, (17, t5 P o6 P,wihruhycorresponds roughly which GPa, 60 to GPa 50 at 2 ν ossso itr ftaetoodSsites, S twofold trace of mixture a of consists 1 , − ν 1 2 eosretepeiul ecie band described previously the observe we , β and , ν 2 2 srthCO (stretch addsper hl h well-defined the while disappear, band ssilpeeta h ihs pressures, highest the at present still is ν ihSi hefl oriainb O. by coordination threefold in S with − srthCO (stretch 1 ν hc a loosre naprevi- a in observed also was which 3 mresdel.Frhr nthe in Further, suddenly. emerge 2 thg rsuehsas been also has pressure high at 2 ,btentesymmetric the between ), 2 −1 .Cneunl,i the in Consequently, ). sruhyteaver- the roughly is α, o150cm 1,500 to 2 − 1,1,2)cnhelp can 25) 18, (17, 1 ifs,liquid- diffuse, a , 2 naccordance in , 2 nlge the analogue, 2 2 si bears it as , omolecu- to − 2 2 1 dis- A . nt at units 2 , How- . ∼0.26 2 has , −1 ν α, 1 i.2. Fig. xeiet,a h oetpesrs h oeua amorphous molecular the pressures, lowest the at experiments, agreement previously. strong outlined in results amor- are Raman changes, form, extended the amorphous with These an molecular intensity. from a of to transformation phous loss the subtle to more corresponding a has at second centered the contribution, change first clear The a factor. shows 2.2 structure GPa static 23.5 the and the GPa at of 35.5 which, at one, measured second terns lower to the moves to signif- time, peak respect same first with 3 the and increases decompression, 2.2 icantly on about while, at the intensity, peaks at similar as two that, found the well is pressures, proce- it as highest a general, sulfur In following (31). and sample, elsewhere described oxygen the structure taking dure from of static subtraction, contribution factors cell The Compton form empty the 2A. the the Fig. account by in obtained into shown been has is factor temperature low at also (see 5.5430 simulations from = a with 14 group of in space size GPa supercell 6.5 simulation at the peaks from resulting range, 1.5 RDF below region the while ment, in is com- S compression graph of (the simulation decompression from during K puted 300 at simulations from computed tal B A eod4.5 beyond (Q) utemr,smlryt htwsosre nteRaman the in observed was what to similarly Furthermore, S A ˚ esrdaogaro-eprtr eopeso u.( run. decompression room-temperature a along measured (Q) − 1 ttcsrcuefco fsldSO solid of factor structure Static eoe oepoietadsapn akdy while markedly, sharpens and prominent more becomes , A ˚ − 1 A in aebe atal nee ntebsso an of basis the on indexed partially been have A siacsil eas flmtdagei experi- in angle limited of because inaccessible is ). 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CHEMISTRY form is found to start transforming into a crystalline molecular A SO2 structure at about 6.5 GPa. The observed Bragg peaks can be partially assigned on the basis of the Aea2 structure (exper- imentally 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 transfor- mations: at lower pressures, the transformation from a molec- ular crystal to a molecular, van der Waals-type, amorphous solid, with no changes in the molecular unit, and to a non- molecular/extended state on further compression. Interestingly, a substantial effect of temperature is observed for the former transformation, despite expecting the energy barrier to be com- paratively small. For example, instead of an expected isobaric phase line, the transformation occurs at 5-GPa-lower pressures B 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 logi- cally have a higher associated energy barrier and consequently a stronger temperature dependence. Instead, this transforma- tion is observed at roughly the same pressures for both isotherms studied, 77 K and 210 K, at around 25 GPa to 30 GPa, counterin- tuitively 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 exper- iment. We first performed a test in order to check whether applying shear stress to a perfect Aea2 molecular crystal at C low pressure might result in amorphous molecular structure as observed in experiments. We gradually induced shear strain by deforming the γ-angle of the supercell by up to 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 amor- phous molecular structure, we melted a perfect Aea2 molecular crystal (32) in a 3 × 3 × 3 supercell (108 SO2 molecules, equiv- alent 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 subse- quent 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 temper- ature, we observed some diffusion of molecules in the molecular Fig. 3. Partial S–O RDF [gSO(R)] and concentration of sulfur coordination phase, suggesting that the sample might possibly be in metastable states at different pressures from MD simulations at 300 K. (A) RDF during liquid state. compression, (B) RDF during decompression, and (C) fraction of two- and Analysis of the partial radial distribution functions (RDFs) three-coordinated S atoms during compression (solid line) and decompres- (Fig. 3), obtained from simulations, can provide a more detailed sion (dashed line). Coordination number was determined within the cutoff description of the observed transformations on an atomistic of 1.92 A.˚ 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 atoms with respect to O atoms is 2. Upon compression to 20 GPa, for the experimentally observed forms and their associated modifications in the RDF are observed, and, at 30 GPa, there reversibility. Upon compression of the initial molecular amor- is a substantial change: The first peak becomes weaker while phous sample to 10 GPa at 300 K, SO2 retains its molecular a new peak at slightly longer distance, 1.6 A,˚ appears. These units. Evidenced in Fig. 3A, the peak at 1.44 A,˚ corresponding changes indicate that some of the S=O double bonds are bro- to the double bond, is sharp and well separated from the next ken and replaced by single ones. In the same pressure regime, neighbor at 2.5 A˚ to 3.0 A˚ and the coordination number of S three-coordinated S atoms appear with two single S–O bonds

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Fig. · The · S· ) S5 2.2 Fig. around Appendix, peak, total (SI the first pairs decompose atomic reversible to experimental from us contributions the be allow into with Simulations to well 2). cal- found very (Fig. the one agrees are and factor hysteresis, changes small structure All a culated with 2A. height above albeit decompression, Fig. the patterns upon XRD GPa, in reflecting 60 GPa about similar, At 35.5 becomes at peaks pressure. peak both increasing diffraction of with , Appendix first grows the which (SI of compression intensity 2.2 The upon S2). changes Fig. upon important pressure sug- shows higher GPa, to 30 shifted at start is to transition at temperature. increasing polymerization also the the simulation that found compression gesting and not similar K does a transforma- 500 and performed structural hysteresis the We small across tion. very features particular in a any shown shows exhibit decompression, S4, dependence and 3C) Fig. pressure compression Appendix, (Fig. The upon character. pressure density first-order of on weakly might transition atoms a the that have S suggests which of hysteresis, some SO exhibits number of coordination forms the molecular amorphous between obser- polymeric transitions experimental backward and the and identify forward insights as can that vations calculations means MD agree- simulations the strong and from The experiment state. reverts between amorphous system molecular ment the initial its and to 4), back (Fig. entirely on Additionally, observed disappear chains 3C. polymeric compression Fig. identified previously in the GPa, atoms 10 S at three-coordinated number and the two- of of dependence pressure akin the evolution, by 3B), oxy- reverse demonstrated (Fig. the further threefold observed decompression in we On observations, being experimental GPa. to atoms 60 is S at second of coordination the gen 82% is while in peak intensity resulting first in the enhanced, diminish compression, progressively further to On snap- 4). found (see Fig. chains in polymeric shown forming shots bond, double S=O one and bv 0Ga h acltdsai tutr factor, structure static calculated the GPa, 20 Above ar,wietewae eodpa,a 3 at peak, second weaker the while pairs, S A ˚ ,ad nly h ra ek rud5 around peak, broad the finally, and, O, − (A–C 1 S rp,wieanwpa per,aon 3 around appears, peak new a while drops, (Q h einn fcmrsina 0Gaweethe where GPa 10 at compression of beginning The (A) pressures. different at simulations MD from sample amorphous the of Snapshots ) ) sacneuneo hne nteSOcontri- S–O the in changes of consequence a is 2 2 A ˚ rmM iuaina 0Ga h oo fSaosrpeet oriain w-oriae tm mlcl)aeylo,and yellow, are (molecule) atoms two-coordinated coordination: represents atoms S of color The GPa. 30 at simulation MD from tutr uigcmrsina 0Gaweetesml otisbt oeue n oyei his ( C chains. polymeric and molecules both contains sample the where GPa 40 at compression during Structure (B) molecules. − 1 rgntsmil rmnonbonded from mainly originates , 2 h eedneof dependence The . A ˚ − A ˚ 1 − oe from comes , 1 smainly is , S S S A ˚ (Q (Q (Q − SI ), 1 2 ) ) , hisi crystalline in Chains (D) . tutrlsac fcytliepae fSO of performed phases we crystalline pressure, of high search at structural existence a to possible order In their experimentally. check determined knowledge, our to been, lower at group same pres- the at pressures. from behave well-known elements elements heavier the like light pressure that applying high stating by (36–38) rule understood homology be sure be can to This found 35). was SeO forms for molecular differ- kcal/mol −19.7 and energy could the polymeric polymer Quantitatively, between the pressure. ence that high proposed at was stabilized it be and form, atoms. molecular S SO its by polymeric Downeyite that concluded in was atoms It Se stud- substituting was chains by in polymeric obtained infinite Additionally, ied, with structure calculated. crystal a were 35, oligomers ref. various of energies of existence possible SO The (33)]. polymeric Downeyite [mineral chains of K, ing a 201 pressure, below ambient at temperature forms, low and pressure an SO ambient counterparts. at crystalline it forms, underlying forms amorphous their two discuss the to of useful origin is the understand to order In Prediction Structure Crystal Evolutionary with agreement in decom- observed, upon 1B). is Again, (Fig. evolution experiment chains. reverse polymeric the conver- into gradual pression, molecules the The reflects of or (S=O). clearly atoms VDOS (S–O–S) sion S total atoms to the S bonded of in doubly two evolution are or position, between chains terminal molecules position the polymeric in bridging at either in a be atoms at can O either atoms Moreover, O chains. and Appendix, polymeric S (SI Both atoms con- O S6). into and Fig. VDOS S states distinct total structurally of the from density tributions of vibrational decomposition projected allowing can the (VDOS), peaks cm the from of 1,200 understood evolution The be around 1A). (Fig. peak experiments with broad ment single peaks, a molecular into two cm the 1,100 around Meanwhile, enhanced. become cm 400 the eosreqaiaieysmlreouin bv 0Ga the GPa, 20 Above 1A), evolution. (Fig. distinct similar spectra qualitatively Raman observe experimental we with 1C) (Fig. ulations h tutr fcytlieplmrcpae fSO of phases polymeric crystalline of structure The ncmrsin oprn h irtoa pcr rmsim- from spectra vibrational the comparing compression, On Aea2 ν oeua rsa 3) ovrey t nlgeSeO analogue its Conversely, (32). crystal molecular 2 −1 eka 5 cm 550 at peak 2 o50cm 500 to plslt)wssuidi es 4ad3,where 35, and 34 refs. in studied was (polysulfite) − Ama2 1 and and 2 −1 ν n . clmlfrSO for kcal/mol 5.5 and 3 Pmc2 bv ,0 cm 1,200 above n 0 cm 600 and − P4 1 1 rgesvl iapas while disappears, progressively 2 hss (E phases. /mbc 2 seegtclyhge than higher energetically is oyei rsa consist- crystal polymeric −1 NSLts Articles Latest PNAS eetddsree chain disordered Selected ) o90cm 900 to − − 1 1 rdal merge gradually , gi nagree- in again , 2 2 mlyn an employing , tbe1i ref. in 1 (table − 2 1 D a not has regions | and f7 of 5 ν E 1 2 2 ) )

CHEMISTRY evolutionary approach (details are described in Materials and forms have well-defined values (e.g., Oterminal–S–Obridge–S angle Methods). We show here the main results of our search. The around 136◦), in the amorphous form, one can find nearly all enthalpy vs. pressure graph for low-enthalpy phases is shown values of the dihedral angles. We note that, in an early study in SI Appendix, Fig. S7. At zero pressure, we found the lowest (35), the effect of conformational changes on the energy of SO2 enthalpy for the molecular crystal structure with space group oligomers was studied, and it was found that, in this respect, the Aea2, in agreement with experiment (32). Upon increasing pres- potential energy surface is very soft. This rationalizes our obser- sure, we found another molecular crystal structure P21/c which vation of the variety of dihedral angles found in chains in the becomes stable above 1 GPa. Besides this structure, there are amorphous form. two low-lying metastable molecular structures, Pc and Cc, which, To assess quantitatively the effects of structural disorder, we upon further compression, transform into polymeric structures. calculated the enthalpy of the amorphous form (relaxed to T = The molecular Cc structure spontaneously transforms to poly- 0) and found it, at 10 GPa, to be about 0.26 eV per formula meric Ama2 phase beyond 13 GPa (reaching limit of dynamical unit above the crystalline phases (it is shown in SI Appendix, stability), and, in the same manner, molecular Pc phase trans- Fig. S7). Above 20 GPa, where the transition starts, the curve forms beyond 17 GPa into polymeric Pmc21 phase (all structures changes slope, and goes down, but much slower than the crys- are shown in SI Appendix, Fig. S8, and cif files of the Pc, Cc, talline polymeric phases, because of incomplete polymerization Pmc21, and Ama2 structures are included in SI Appendix). Both in the amorphous form. We note that, because of the short time polymeric structures have very similar enthalpy and become scale available in the ab initio MD simulations (of the order thermodynamically stable with respect to the molecular phases of 10 ps), the amorphous structure might not be fully relaxed already at 11 GPa. They also have the same conformation of structurally. We also determined, with our DFT simulations, chains and differ only in chain stacking. The mechanism of poly- the electronic properties of the a-SO2 phase and found that merization is illustrated in SI Appendix, Fig. S9, showing the the system does not metalize up to 60 GPa, having a band gap pressure evolution of bond lengths upon compression. A similar (in the Perdew–Burke–Ernzerhof [PBE] approximation) of at polymerization mechanism is likely to apply also in the amor- least 0.6 eV. phous form when molecules of suitable orientation approach Conclusions each other (see also Connection between Crystalline and Amor- phous Forms). Both polymeric structures have the same confor- We observed a pressure-induced amorphization and a reversible structural transition between molecular and polymeric amor- mation of chains as SeO2 Downeyite, but the stacking of chains is different. The stable polymeric structure has, at 20 GPa, a bond phous forms of SO2 at pressures around 26 GPa. The transition ˚ has small hysteresis, pointing to the fact that the associated length of 1.46 A between S atom and terminal oxygen (S=O) kinetic barriers are low. The lower pressure of the transition and 1.65 A˚ between S atom and bridging oxygen (S–O), simi- between molecular and polymeric amorphous forms, as well as lar to the peak positions of S–O RDF (Fig. 3). The sulfur atom the back-transformation, is qualitatively facilitated by the molec- in the chain is surrounded by three oxygen atoms in roughly ular polarity. This, supported by the high density attainable trigonal pyramid coordination (at 20 GPa, bond angle O–S– under pressure, drives the intermolecular interaction and lowers O is 90◦ and O=S–O is 100◦), suggesting the presence of sp3 the activation energy of the transformation. To our knowledge hybridization (see also ref. 35, where it was suggested that the this kind of transition was not previously observed and provides 2 3 dimerization of SO2 is related to sp → sp rehybridization). In an example of reversible structural transition between disordered order to quantitatively assess the bond order of S–O bonds in nonequilibrium states of solid matter. Unlike in a-CO2, where molecular and polymeric SO2, we employed the density driven polymeric a-carbonia contains three- as well as four-coordinated electrostatic and chemical (DDEC6) atomic population analy- C atoms, here the molecular form converts into polymeric form sis method (39). We found a bond order of 2.12 in molecule with only three-coordinated S atoms. It will be of interest to and 2.14 and 1.15 for S=O and S–O bonds in the polymeric study whether the two structurally distinct forms continue to exist phase. In SI Appendix, Fig. S10, we show the electronic density of also in liquid state, either in stable or metastable (supercooled) states including projections on s and p orbitals for the crystalline regions. For example, a transition between molecular and poly- molecular Cc and polymeric Ama2 phase (no d-orbital participa- meric liquid has been proposed in nitrogen (40), and a cross-over tion was found). We also note that the diffraction pattern of the between such forms was observed in recent computational study recrystallized phase upon decompression to 6.5 GPa (Fig. 2A) of amorphous nitrogen (41). Further experimental and theoret- shows a strong similarity to the diffraction pattern of the molec- ical work is necessary to accurately map the solid and liquid ular phase Aea2 at the same pressure (for comparison, see SI regions and uncover further details of the phase diagram of SO2. Appendix, Fig. S11). This provides additional evidence that the system after the compression/decompression cycle returns to its Materials and Methods parent state. Experimental Methodology. The SO2 gas was loaded into the diamond anvil cell (DAC) by means of cryogenic loading: The gas was condensed Connection between Crystalline and Amorphous Forms between one diamond anvil and the gasket placed on the other dia- mond of a DAC, which was opened by a few millimeters and cooled to To make a connection to the polymeric amorphous form, we note liquid nitrogen temperature inside a sealed glove box purged with nitro- that different molecular crystalline phases shown in SI Appendix, gen to avoid moisture condensation. We performed Raman spectroscopy Fig. S7 have different limits of dynamical stability with respect to using a state-of-the-art confocal Raman microscope with 15 and 2 µm of polymerization. While the P21/c phase remains molecular even axial and transverse resolution, respectively. The spectrometer consisted at 30 GPa, the phases Cc and Pc polymerize beyond 13 and of a Spectra Pro 750-mm monochromator, equipped with a Pixis Prince- 17 GPa, respectively (SI Appendix, Fig. S9). This points to the ton Instrument charge-coupled device detector. Bragg grate filters were fact that the pressure threshold for polymerization depends on used to attenuate the laser light and spatial filtering of the collected −1 the relative orientation of molecules. In the amorphous form, light to obtain high-quality spectra down to 7 cm with minimal back- where random relative orientations are present, polymerization ground 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 needs a higher pressure beyond 20 GPa to start. In Fig. 4 D and Laser Torus at 660 nm with 10 mW of power and Laser Ventus at 532 nm E, we show a comparison of chains from crystalline polymeric with 0.5 mW of power to check for the presence of eventual fluores- phases Pmc21 and Ama2 and selected disordered chain from the cence bands in the spectrum. We generally used a 300-grooves-per-mm amorphous sample. It can be seen that the local environment grating, as the spectral features were getting very broad and weak with is similar, except for the dihedral angles. While the crystalline pressure. The pressure was determined by the fluorescence of a small

6 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.1917749117 Zhang et al. Downloaded at UNIVERSITY OF VICTORIA on April 4, 2020 Downloaded at UNIVERSITY OF VICTORIA on April 4, 2020 8 .A oty,RRusa,M atr,F oel,S cnoo ie hefl and threefold Mixed Scandolo, S. Gorelli, F. Santoro, amorphous M. Rousseau, High-pressure R Mao, Montoya, A. H. J. 18. Hemley, a Santoro R. for M. evidence Goncharov, 17. Optical F. Hemley, A. R. Gregoryanz, Liu, Z. E. Mao, 16. H. Gregoryanz, E. Goncharov, F. A. 15. Pressure- Manghnani, H. M. Ming, C. L. Mao, K. H. Jephcoat, P. A. Hemley, J. R. 10. 9 .Caii .Snoo .Bn,V cetn,Hg rsueratvt fsldbenzene solid of reactivity pressure High Schettino, V. Bini, R. Santoro, M. Ciabini, L. 19. in transition Structural pressure-induced Hanfland, the Henry M. of Degtyareva, L. study O. 14. Gregoryanz, spectroscopic E. Raman Sanloup, Wolf, C. 13. H. G. coordination Durben, pressure-induced J. for D. evidence 12. Spectroscopic Jeanloz, R. Williams, Q. 11. 1 .Ciabini opening ring L. photoinduced pressure 21. High Schettino, V. Bini, R. Santoro, M. Ciabini, L. 20. 3 .I rmt,A .Gviik .A rjn .A zvno .Belr Single-bonded Boehler, R. Dzivenko, A. D. Trojan, A. I. Gavriliuk, G. A. Eremets, I. nitrogen. M. Polymeric McMahan, 23. K. A. Yang, H. L. Mailhiot, C. 22. 4 .Dth,B alc,A aaa,S ie,Srcueo oyei abndioxide carbon polymeric of Structure Ninet, S. Salamat, A. Mallick, B. Datchi, F. 24. hl,i Dcluain,w sdterglroe n ihacutoff a with O and S ones regular the used we calculations, MD in while, S we calculations, harder enthalpy the and employed of relaxations, parametrization structural functional. search, (46) exchange–correlation evolutionary PBE In approximation and atoms) gradient O generalized and six the S (with codes both pseudopotentials sim- 5.4 for and initio electrons wave 5.3 Ab valence augmented VASP cell. in projector unit implemented employing a as within (43–45), DFT atoms) by (12 performed units were formula ulations four with GPa 50 SO of phases Methodology. Simulations obtained the when easily run chamber. case, decompression sample this the of in end been, amor- the at has SO an cell DAC, empty from the the scattering importance measuring in by diffuse fundamental sample metallic the liquid of the of or is from phous measurements which reliable lines subtraction, obtain diffraction cell to spurious empty sam- of the The presence of gasket. patterns the diffraction clean without obtain ple to transverse us excellent allows The resolution spectroscopy. while spatial Raman temperature with an low changes at of the compression decompression monitoring a along from only obtained sample measured amorphous been have patterns diffraction eouino h eu.TeXDmaueet eemd tPetra at 42.7- with made beam (2,048 diamond were XRD1621 X-ray the PerkinElmer measurements monochromatic (λ of spatial a XRD energy excellent part using keV The the I-20181128) stressed to setup. ID: thanks the (proposal the accuracy from high of or with resolution detect sample we the which anvil, in placed ruby hn tal. et Zhang .M rmdth oyopimi mrhu SiO amorphous in Polymorphism Grimsditch, M. 9. transi- phase metastable density-driven A of Machon, D. behaviour Daisenberger, Phase D. Wilson, Stanley, M. E. McMillan, F. H. P. Essmann, new 8. U. A between Sciortino, kbar: transition F. 10 first-order Poole, and apparently H. P. An k Whalley, 77 7. E. at Calvert, I D. L. ice’ Mishima, ‘Melting O. Whalley, E. 6. Calvert, D. L. Mishima, O. 5. Anisimov A. M. 4. amor- Pressure-induced McMillan, P. Wilson, M. Wilding, M. Meersman, F. Machon, D. glasses. and 3. liquids in transformations in Polyamorphic transitions McMillan, phase F. Polymorphic P. McMillan, F. P. 2. Angell, A. C. Grande, T. T. Poole, H. P. 1. 2 orodcro oriaini opesdCO compressed in coordination carbon fourfold nitrogen. GPa. 150 above nitrogen of phase nonmolecular 2017). 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Director’s with Hefei discussions Sciences stimulating the acknowledges of and Academy Chal- (TZ2016001), Chinese Science (CXJJ-19-B08), Project Grant Innovation lenge 51727806), Sciences and of 11774354, Science Academy 51672279, Natural Chinese Ini- (11874361, National Grant Fellowship China 2019VMA0027), of International and Foundation President’s (2018VMA0053 Sciences Fund of tiative Academy Chinese the in ACKNOWLEDGMENTS. available are manuscript the and in in compression and to article along the referred pressures Static data several All GPa. at runs. 60 trajectories decompression to MD from GPa RDFs 10 the from autocorrelation pressures stan- velocity factors at the structure mass-weighted trajectories in of MD computed from transform were function Fourier VDOS as microcanonical projected way constant-volume dard and 20-ps running Total sam- then simulation. and a NpT (NVE) equilibrating in ps by 6 generated for ple were function autocorrelation velocity 10,000 ps and 2.0 respectively, and freedom, 10.0 of coefficients friction by ther- Langevin performed with were and simulations mostat heating (NpT) and isothermal-isobaric variable-cell decompression, 6-ps Compression, eV. 520 of nitrogen. methodology. and theory partitioning (1998). h und hoher Bereich im Materie one-dimensional Pressure and oligomeric Se). covalent S, = of (X compounds investigation xo2-based quantum periodic and study. functional density Mater. 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