Raman investigation of the structure of solid sulfur dioxide

Journal of MoZecuIar Structure, 112 (1984) 221-232 Elsevier Science Publishers B-V., Amsterdam -Printed

RAMAN INVESTIGATION DIOXIDE

in The Netherlands

OF THE STRUCTURE

OF SOLID SULFUR

M. H. BROOKER Chemistry Department, MemoTial University Newfoundland AIB 3X7 (Canada)

of Newfoundland,

St. John’s,

(Received 9 June 1983)

ABSTRACT Raman spectra of solid SO, provide strong evidence to corrolxxate the orthorhombic structure with acentric C:: space group. The assignment of correlation components is based on qualitative depolarization studies of single crystals. Longitudinal optical modes are observed at frequencies which depend on crystal orientation. Numerous peaks due to isotopically different molecules have been assigned. An interesting example is presented of an invisible band due to an isotopically different molecule that does not shift enough to decouple from the normal lattice mode. INTRODUCTION

Sulfur dioxide is an important molecule in a large number of industrial processes_ The present study results from an interest in the role of SO2 as a component of a solvent or as a by-product in various lithium-sulfur batteries_ Raman spectroscopic methods are being developed to follow the electrode processes and it is important to characterize the possible components as completely as possible. Raman spectra of liquid SOP indicate that resonance energy exchange occurs between neighboring molecules [l--4]. Apparently the alignment of dipole moments imparts local ordering in the liquid. A detailed assignment of the effects of intermolecular coupling on the Raman spectrum of solid SO, became necessary to form the basis of a comparison to the Raman spectrum of the liquid. Previous infrared and Raman studies of solid SO, by Anderson and Savoie [l] and Anderson and Campbell 153 were in excellent agreement with predictions based on the Cl: space group determined by Post et al. [S] . These authors correctly attributed extra bands in the spectra to various naturally abundant isotopic forms of SO2 and to longitudinal optical modes. A recent study by Swanson et al. [7] of solid SO2 identified two high pressure phases, but in their analysis of the normal solid they did not take into account the presence of isotopically different ions or longitudinal optical modes and concluded that the structure proposed by Post et al. [S] was incorrect_ Results of the present study confirm most of the assign0022-2860/84/$03.00

o 1984 Elsevier Science Publishers B.V.

222

ments of And&on ad Savoie [l] and Andefion and Campbell [ 53 and are supported by depolarization measurements of oriented single crystals not previously avaiIable. Raman measurements, together with recent ir&ared measurements [S]. of solid 32S’602 and 37SxsOi, provide strong evidence to support the .acentric C:z structure. The correlation-field components and longitudinal optical modes have been well characterized for solid SO2 and it has been shown that although the correlation-field coupling effects influence the ZQand v2 modes of liquid SO2 the TO/TL mode splittings have no counterpart in the liquid [ 41. EXFERIMENTAL

AND RESULTS

Raman specka were measured with a Coderg PHO Raman spectrometer after sample excitation with the 488.0 or 514.5 nm line of a Control Laser, model 553A argon ion laser. Plasma lines from the laser were removed with a narrow-band-pass interference filter. Power levels at the sample were about 500 mW. Peak positions were calibrated against argon ion plasma lines and the Rayleigh line itself. Polarization of the incident beam was controlled with a half-wave plate, and the 90” scattered light was analyzed with Polaroid film placed before the slit. A quarter-wave plate just before the slit was used to scramble the polarization of the scattered light to offset the effect of grating preference. High purity SO2 gas was condensed and frozen into a 4 mm id. Pyrex tube and sealed under vacuum. When thawed this gave about 0.5 ml of SO2 liquid under its own vapor pressure. The sample was mounted on the cold tip of an evaporating liquid nitrogen cryostat with conducting grease. Rapid cooling of the sample inevitably led to non-oriented polycrystalline material. However, ‘on several occasions the spectra exhibited anomalous peaks which were later identified as discrete longitudinal optic peaks of small single crystals. It was later concluded that on different occasions crystals had been grown accidently with the C axis both parallel and perpendicular to the tube axis. Attempts to grow oriented single crystals by slow cooling resulted in one preferred orientation with the c axis parallel to the tube axis. Post et al. [S] observed a similar growth orientation_ It was necessary to select the best part of the crystal by trial and error. Spectra were then obtained for a(cc)b, a(ca)b, a(bc)b, a(ba)b orientations. Although spill-over and contributions from polycrystalline material also contributed to the spectra the depolarization measurements were sufficient to make positive assignments. The crystal structure of sulfur dioxide has been determined by Post et al. [S] for a single crystal at 143 K. These authors deduced that the acentric space. group Aba (C::)was most probable and determined that the orthorhombic unit cell contained four molecules (two per primitive cell). Cell dimensions were a = 6.07, b = 6.94 and c = 6.14. The molecules sit on C2 sites with .the C2 axis of the molecule (z axis) coincident with the crystallographic c axis. The molecular plane (yz) and the molecular cV plane

223

(zx) are approximately parallel to the planes which bisect the a and b crystallographic axes. Discrete pairs of molecules cannot be identified and the not bidentate (Fig. 1). neighboring S---O interactions a.rz monodentate, The proposed unit cell has a net dipole moment which results in piezoelectric properties as well as Reman active longitudinal optic (LO) modes. Transverse optical-longitudinal optical (TO/LO) splittings are not predicted in the usual unit-cell group analysis but will occur for normal modes which are infrared active (i.e. polar modes). For acentric crystals TO/LO splitting may be observed in the Raman spectrum if the mode is simultaneously infrared active [9-121. The correlation diagram (Fig. 2) for the factor-group analysis based on the above structure is easily constructed by standard methods [l, 91. The choice of B1 And B2 designations is arbitrary. Fifteeen optical modes are predicted and these may be separated into 6 internal modes of SO2 molecules and 9 external modes involving rotatory and translatory modes of whole SO1 groups:

Fig. 1. Structural arrangementof solid SO, in the acentric Cl<. space group.

Point Grocp

yI .v2

*Tz

.Tr .Ry %, Ty .R, 8~~~

Group

GV

“y/A,

RZ A,-/

v3

Space

Site Grap 6

=2v

(T0.L0)

&.

‘&CT01

,‘%

Tc,o,,,q,p,,

(m,Lo)

Q,b

T,.Rb.

&UO. Lo) Tb.

ucc

R,I

R.ia

Qta

R, . Qbc

R.X

R.1

Fig. 2. Correlation diagram.of solid SO, to illustrate the relationship of the point group normal modes to the unit cell group normal modes.

224 = !&I I(TO I?internal

+ LO) + ?& (TO only) + Bi (TO + LO) + B2 (TO + LO)

= A,(TO + LQ) + ti,(TO

r .,,,&

only) + 3Bl(T0

f LO) + 3B2(T0

+ LO)

The Raman spectrum of solid SO2 will be complication by the fact that for the infrared active modes of AI, B1 and B2 character the TO and LO components will occur at different frequencies and essentially double the number- of predicted peaks for these modes. Further complications can result for single crystals-with low symmetry since the LO mode frequency may vary with sample orientation. The results of the present Raman study (Table 1) of polycrystalline SO1 and partly oriented single crystals together with published infrared results [ 81’ are in er;cellent agreement with predictions based on the acentric A ba structure. Raman spectra of the v2 and u3 regions (Fig. 3) and vI tid TABLE

1

Vibrational frequencies(un-')forsolid SO, assignmentsbased on the Ci:spacegroupa Infrared Ref. 5 20K

Ref.8 77K

67

80 86(sh) 102.5 138 159&l) 517 525= ia 546(t) 1136 1140.5 1147= ia 1160(t) 1304 1313 1327 1358(t)

516.0b 522.0 ia 1120.6 1134.9 1140.4 1144.8= ia 1302.8 1306 1315.2= 1323.2

Ref. 5 20K 67.5 70.5 76 81 85 93.5 102.5 140.5 163.5(sh) 516.5" 520 522 543 1121 1135b 1140.5 1144 1148 1152(sh) 1304 1309.5 1324 1340.5(sh) 1348.5(ab)

Thiswork 77K

-4ssignmentsbasedon depolarizationstudies

66 69 73

99 140 517.2 521.9 524.3 543 1120.5 1134.6 1140.5 1143.6 1148.2 1153.8(sh) 1304(w,sh) 1305.0 1310.6 1323.6 1337 1353

4 (R,) &U-,1 LO? 9ZS'601~0 A,(TO) A, -4,(LO) atS'601'0 3*SMQ110 34SM.O AAm\ _4= A,(LO)

vz

"1

37S'60 2

'XS'60

I

32s16f-y30 3W60,

"sh = shoulder,ia = infrared ina&ve,~=weak,t=tail.~The presentassignmentismore consistent with quantitativeisohapic abundance measurements_ ?The contributionofthe LO componentwii shift the 'Lnfrared peak maximum to ahigher value than the Raman frequency.

225

!,,I.,,... 1350

II,

.1,.1.1111.1..1~1

1340

A0

1320

1310

IMO

540

.I,

‘ZQ’

I,,

520’

.

cm-1 Fig. 3. Raman spectra of the v, and v3 regions of poiycrystalline solid SO, at 77K.

external mode region (Fig. 4) for the polycrystalline material are shown to illustrate the relative intensities of the different features. The need to assign “extra” peaks to isotopically different molecules and LO modes was recognized by Anderson and Savoie [1] and Anderson and Campbell (51, but not considered by Swanson et al. [7] . Relative intensity studies of the peaks assigned to isotopically different molecules (Table 1) were in excellent agreement with natural isotopic abundance ratios and followed the expected enhancement when isotopically enriched samples were studied [S, 131. Peak frequencies observed for the isotopically different molecules were in excellent agreement with normal coordinate calculations. In the v1 region of 32S160, two factor group components are predicted and these are observed at 1143.8 (Al,TO) and 1148.2 (A,).As predicted, the non-polar A2 mode is only observed in the Raman spectrum and is most intense in the a(ba)b scattering geometry (Fig. 5). The A i component is observed in both the infrared and Raman spectra. Infrared and Raman

AZ

1 A,(TOl

L I

Fig. 4. Raman spectra of the v, and external mode regions of polycrystalline solid SO, at 77 K.

I 1050

Id40

A v5k0

I 540

5’jo

1 520

cm-l Fig. 5. Raman spectra crystalat 77 K.

for the v1 and Y, regions

of solid

SO,

for a partly

oriented

singIe

peak frequencies of the AI (TO) component are predicted to be coincident, but the influence of the LO component can shift the measured infrared maximum to higher frequencies [14, 15]_ Theoretically, the infrared radiation should not interact with the LO mode for normal incidence but ideal experimental conditions are seldom achieved except for very thin samples. The shapes of strongly act;;;e infrared peaks are often distorted by this anomalous dispersion [14, 153 . In this regard the infrared frequencies reported by Anderson and Campbell (Table 1) appear to be most shifted and probably resulted in these authors reversing the correct A, and A2 assignments of a previous publication [l] . The LO component of A I is allowed in certain orientations of the Raman scattering experiment and the frequency will be strongly dependent on the scattering geometry of the crystal because of the low crystallographic symmetry_ In the present study we have detected the Al (LO) mode as a discrete maximum on two occasions for poorly oriented crystals, once at 1146 cm-’ and once at 1150 cm-l, but the angular dependence of the peak could not be studied as a function of scattering angle with respect to the crystallo@phic axis, because of lack of knowledge of the crystal orientation and intensity contributions from

polycrystalline

material.

For

polycrystalline

samples

the

weighted

227 average for all orientations will be observed as a tail which starts close to the TO mode and extends to the LO mode cut-off frequency of 1153 cm-’ and then drops quickly to zero (Fig. 4). Similar results have been reported for the v3 mode of polycrystalline NaNO, which also has an acentric orthorhombic space group, C,t [lO-121. Oriented single crystal studies have been performed for NaNOz to measure the dependence of the LO mode frequency on scattering geometry [lo, 111 _ In addition to the peaks due to 3’S02 v, correlation field components, single peaks were also observed for the 32S’60180, 32S’601i0 and 3%‘60, molecules at 1120.5, 1134.6 and 1140.5 cm-’ respectively (Table 1). These isotopically different molecules can be treated as ‘ideep-well” impurity centers because their frequency shifts are sufficiently large to place the peaks outside of the span of the density of states of the coupled 32S’602 system, and their concentrations are much too low to allow coupling between pairs of like molecules [16] . Vibrational frequencies of these dilute isotopic molecules provide a means of obtaining “static” field frequencies, 05, for 32S1602, uncomplicated by the correlation field effects. Barbe et al. [S] have measured w, at 1148.4 cm-’ for dilute 3’S’602 in solid “SLs02. For 3%‘602 the o, value is 1140.5 cm-’ which corresponds to an isotope shift A = 7.9 cm-l, compared to a A value of 7.3 cm-’ from gas-phase Raman measurements [13] _ Similarly, for 32S’60180 the value of w, is 1120.5 cm-’ which corresponds to A = 27.9 cm-‘, in excellent agreement with the value for the gas phase A = 28.3 [13]. It should be pointed out t.hat the gas phase values of 32S*602, 3’S’60180 and 3rS’S02 are 1151.3, 1123.0 and 1100.8 cm-’ respectively, which means that 32S’601s0 is not symmetrically shifted from 32S’602 and 3’-S’s0,, because 4 values are 28.3 and 22.2 cm-‘. Finally the coupling scheme for the v1 region can be deduced (Fig. 6). From this diagram it is clear that an anomalous isotope shift could be inferred unless static field frequencies are considered. Methods are being developed for calculating w s from correlation field components [ 91. The results for the. v2 region of solid SO2 are similar to those of the Y 1 region because both regions are derived from k 1 of free SO,. The A, mode occurs at 524.3 cm-’ and is only Raman active. The A, (TO) mode occurs at 521.9 cm-’ and is both Raman and Infrared active (and coincident): Table 1. Depolarization measurements confirmed these assignments (Fig. 5). For polycrystalline samples the A i (LO) mode starts from the TO mode and tails out to the cut-off frequency 543 cm-’ (Fig. 3). Again a discrete LO peak may occur anywhere between the TO component and the LO cutoff frequency for selected orientations of single crystals. Similarly to our results for v1 above, a discrete LO peak was observed at 528 cm-’ for a SO, crystal of unknown orientation. In the v2 region only the 3zS’60180 vibration at 517.2 cm -’ falls outside the span of the density of states (Figs. 3 and 5). The assignment of this peak is based on relative intensity calculations and normal coordinate calculations. Barbe et al. [S] have measured o, = 527.3 cm-’ for dilute 32S’602 in solid

Fig. 6. The cou$ing scheme for the normal modes of solid SO, at ‘i7 K as derived from the~static field value.

32S1802. The value of A = 10.1 cm-’ is in good agreement with the value for gas phase 32S’602 and 3*S160180 where A = 10.9 cm-’ [13]. For v2 of gas phase 32S’602 and 34S*cj02A = 5.3 cm-’ which, when considered for naturally abundant 34S1602 in 32S1602, means that Y, of 34S’602 will not shift outside of the span of the density of states of the coupled 32S’602 system. This means that 3W60 2 will couple to the 32S’602 system as a shallow-well impurity and cannot exhibit a separate peak in the V, region. This is not a resolution problem but a consequence of resonance energy exchange between 34S’602 and 32S’602 molecules. The coupling scheme for the z+ region (Fig. 6) really develops from a w, value, which is a weighted average of the naturally abundant 32S and 34S isotopes. The v3 region of solid SO2 is more complicated than the V, and v2 regions because’ the Bz and B2 modes are both Raman and infrared active and both will have TO and LO components. The polycrystalline sample (Fig. 3) showed peaks at 1310.6,1323.6,1337 and 1353 cm-’ which were assigned as B1 {TO), B2 (TO), B1 (LO) and B2 (LO), respectively. The peaks at 1337 and 1353 cm-’ appear to be due to the LO cutoff effects. The choice of B1 (LO) and B2 (LO) was made to keep the TO/LO splittings about equal for both the B1 and B2 modes s:Gxe both modes have similar infrared intensity and non-crossing rules are not applicable. Again for selected single cry&J orientations, the LO modes may occur at any frequency between the TO mode and the LO cut-off. Raman spectra of a partly oriented single crystal under different scattering conditions illustrate the changes in relative intensity with polarization selection and changes of frequency and relative intensity with rotation of the sample around the c axis (Figs. 7 and 8). These spectra show a discrete B1 (LO) at about 1316 cm-’ for one crystal orientation, but it has been also observed at 1321 cm-’ in another orientation. The B1 (LO) mode has-been seen as a discrete peak at 1334 cm-’ and 1353 cm-‘. The BI (TO) and B2 (TO) modes do not shift in frequency with change of crystal orientation. Although the B, {TO) mode appears more intense than the B2 (TO) mode for the different sample geometries shown (Fig. 7), this is believed to be an orientation effect because the two peaks have equal intensity for a polycrystalhne sample (Fig. 3). The 34S’602 and ‘2S160180 peaks for v3 of .solid SO2 are both shifted outside the span of the-density of states for the v3 of the coupled 3%?602

229

B, (TO1 \

Fig. ‘7. Ftaman spectra of the V, region of solid SO, for a partly oriented sample at 77 K. The extent of misalignment and contribution from polycrystalline material can be deduced by the intensity of the EiI (TO) and B2 (TO) modes in the a(cc)b and a(bo)b orientations which should not have any Raman activity. Fig. 9. Raman spectra of the vj region of solid SO, from a partly oriented sample at 77 K. The changes in the relative intensities are due to rotation of the sample about the probable c axis. The change in location of the discrete LO peaks is apparent.

system and hence appear as single decoupled peaks. The isotope shifts for 34S’602 and 32S’60180 are similar (17.6 and 20 cm-‘, respectively) and the 32S’60180 peak appears as a weak shoulder on the 34S02 peak (Table 1) (Fig. 3). Barbe et al. [S] have measured w, = 1325.5 cm-’ for dilute 32S’“Oa in 3’S’802. The value of A = 20.5 cm-’ between o, values of 3rS’602 and 34S1602 is in good agreement with the gas phase value 4 = 17.6 cm-‘. The correlation diagram for v3 is shown (Fig. 6). The low frequency region of SO,,,, is difficult to assign even with qualitative depolarization data (Fig. 9). Assignments of character designations are reasonably certain (Table 1) for more intense bands, but several bands ob

233

a(bc)b -

--w

1

I

cm-’ Fig. 9_ Ftaman spectra of the estemal single crystal at 77 K.

mode region of solid SO= for a partly oriented

served at 20 K by Anderson and Campbell f5] were not resolved at 77 K in’the present study. The most intense low-frequency Raman modes are expected to. be derived from rotatory motions of the plane of the SOt molecule’ iu,,) about the molecular z and y axes since the ratio of moments of inertia are I,:I,:I, = 6.79:5,86:1.00. Rotation about these axes is primary responsible for the pure rotational spectra for gaseous SO2 1171 and is believed to be the origin of thelkayleigh wing intensity in liquid SO* [ 18,191. Rotatory motion about ‘the~1:axis will not contribute significantly. Rotatory modes of pIanar molecules are usually of greater intensity and lower. frequency than translatory modes and the assignments (Table 1) reflect this generality. Detailed assignments of the low-frequency region will probably

231

require single measurements at low temperatures of both ‘*S’601_ and 3%‘s02 in order to distin_guish between translatory and rotatory modes. Lattice dynamics calculations 1201 of solid SO1 are in general agreement with the present assignments, and these calculations indicate that for modes above 80 cm-’ there is considerable mixing between roftatory and translatory motions. The external modes (except for _42) should also eshibit TO/LO splitting, but there were no peaks which exhibited the correct characteristics. cm-’ should have the most intense LO The strong infrared peak at -140 peak with greatest separation from the TO peak, and possibly the shoulder at 163.5 cm-’ reported by Anderson and Campbell [5] is the LO mode of the 140 cm-’ B, (TO). The magnitudes of correlation field and TO/LO splittings increase in the order vI < v2 < vj. In fact the TO/LO splittings are 10.0, 21.1, 26.4 and 29.4 cm-’ for the v1 (A,), v2(A1), v3(B1) and v3(B2) modes respectively, while the correlation field splittings are 4.4, 2.4, and 13.0 cm-’ for the components of vl, vt and v3. Correlation field splittings, TO/LO splittings and gas phase infrared absolute intensities are all proportional to (au/a Q)‘, and the present results are consistent with this relationship_ The TO/LO components can be used to calculate the value of (au/a Q)i for comparison to values obtained from infrared intensity measurements. An approximate formula proposed by Hass and Homig [21] appears to work reasonably well. 37&c’ = N(n’,

+ 2y

6% -

S$)

where n, is the index of refraction at (X = -), c is the velocity of light, of the LO ard TO components and N the FL and fir the wavenumbers number of vibrating groups per cm3. This equation is strictly applicable to cubic crystals and can give at best only approximate arc/a8 values for an orthorhombic crystal. The calculations were performed for N = 9.04 X 10” unit-cells cmm3 and no = 1.41. Calculated values for the (&r/aQ) from rp,(A ,) and vI(Al) TO/LO pairs were 5’1.8 and 51.3 cm3’2 s-‘, in reasonable agreement with values obtained from gas phase infrared Intensity measurements 58.1, 63.3 cm3’” s-l. Similar calculations for the 4 B1 and Bz TO/LO components lead to au/aQ values of 90.4 and 95.9 cm3’2 s-’ which are much smaller than the au/aQ value of 165.1 cm3’2 s-* obtained from the gas phase infrared intensity measurement of v,, but this is due to the distribution of energy over the two correlation field components in solid SOz. A reassignment of the LO modes would give a TO/LO pair at 1310.6 and 1353 cm-’ which corresponds to a value of au/aQ of 115 cm3’2 s-l. It is clear that transition dipole-transition dipole interactions can adequately account for the magnitude of the TO/LO and correlation field effects observed in solid SO?, since the magnitudes of the effects follow the infrared intensities, i.e. v3 > v1 = y2.

232 ACKNOWLEDGMENT

The author gmtefully acknowledges thb support of the Natural Sciences and Engineering Research Council of Canada in the form of an operating grant and a strategic grant for the sulfur battery project. REFERENCES 1 A. Anderson and Ra. Savoie, Can. J. Chem., 43 (1965) 2271. 2 M. Kamoun, J. Raman Spectrosc., 8 (1979) 225. 3 M. H. Brooker and H. H. Eysel, In W. F. Murphy (Ed.), Proceedings VII International Ccnferenee on Raman Spectroscopy, North-Holland, Amsterdam, 1980, p. 266. 4 M. H. Brooker and H. H. Eysel, in preparation. 5 A. Anderson and M. C. W. Campbell, J. Chem. Phgs., ti7 (1977) 4300. 6 B. Post, R. S. Schwartz and I. Fankuchen, Acta Cryszallogr., 5 (1952) 372. 7 B. 1; Swanson, L. M. Babcock, D. Schiferl, D. C. Moody, R. L. Mills and R. R. Ryan, Chem. Phys. L&t., 9i (1982) 393. 8 A. Barbe, A. Delahaigue and P. Jouve, Spectrochim. Acta, Part A, 27 (1971) 1439. 9 3. C. Decius azd R. M. Hext-er, Molecular Vibrations in Crystals, McGraw-Hill, New York, 1977. 10 C. K. Asawa and M. K. Barnoski, Phys. Rev. B, 2 (1970) 205. 11 C. M. Hart-wig, E. Wiener-Avnear and S. P. S. Porto, Phys. Rev. B, 5 (1972) 79. 12 M. H. Brooker and D. E. Irish, Can. J. Chem., 49 (1971) 1289. 13 M. H. Brooker and H. I-I. Eysel, J. Raman Spectrosc., ll(l981) 322. 14 M. H. Brooker and J. B. Bates, J. Chem. Phys., 54 (1971) 4788. 15 D. WV.Berreman, Phys. Rev., 130 (1963) 2193. 16 M. V. Belousov, D. E. Pogarev and A. A. Shultin, Phys. Status Solidi B, 80 (1977) 417. 17 W. F. Murphy, J. Raman Spectrosc., 11 (1981) 339. 18 A. Rousset, J. Phys. Radium, 12 (1935) 507. 19 M. H. Brooker, D. J. Gardiner and J. G. Shapter, to be published. 20 A. Rostogi, A. Anderson and J. W. Leech, Can. J. Phys., 57 (1979) 2120. 21 C. h'as and D. F. Hornig, J. Chem. Phys.; 26 (1957) 707.