J . Phys. Chem. 1990, 94, 540-544
540
is again in accord with the HCIC2H2complex observed in this study when the environment seen by the primary photochemical products is taken into account. No reference to gas-phase Hg(3P) photosensitization of VBr could be found in the literature, possibly due to the added complication of competing direct photolysis.
Conclusion The feasibility of atomic photosensitized chemistry in lowtemperature solids with a range of sensitizers and reactants has clearly been demonstrated. In one case, VCI, the 3P sensitized photochemistry was investigated by using all three group IIB metals. The primary products in all experiments proved to be identical hydrogen-bonded a complexes. The use of Cd and Zn as sensitizers reaffirms the utility of the matrix technique in the investigation of the photochemistry of typically high-temperature atomic species.
Weaker product bands have provided further strong evidence of nearest-neighbor metal atom insertion into C-C1 and C-Br bonds, but not into C-F and C-H bonds. The selectivity of the process, as well as the elimination chemistry, can be explained in terms of new reaction surfaces which become accessible through use of a triplet sensitizer. Metal atom insertion into carbonhalogen bonds is unique to the matrix photochemistry where the cage effect and low temperature probably act to stabilize intermediates leading to the halovinyl metal compounds thus formed.
Acknowledgment. This work was supported by the Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U S . Department of Energy, under contract No. DE-AC03-76SF00098. Registry No. VCI, 75-01-4; Hg, 7439-97-6; Cd, 7440-43-9; Zn, 7440-66-6;Kr, 7439-90-9;VF, 75-02-5; VBr, 593-60-2;HCI, 7647-01-0; C2CI2,74-86-2;HBr, 10035-10-6;(CH2=CH)HgCI, 762-55-0; (CH,= CH)HgBr, 16188-37-7.
Raman Study of Sulfate Orientational Dynamics in cu-Potassium Alum and in the Deuterated and Oxygen-18 Enriched Forms Murray H. Brooker* Chemistry Department, Memorial University of Newfoundland, St. John's, Newfoundland, Canada A1 B 3x7
and Hans Herman Eysel Anorganisch- Chemisches Institut der Universitat Heidelberg, Im Neuenheimer Feld 270, 06900 Heidelberg 1, FRG (Received: March 29, 1989; I n Final Form: July 6 , 1989)
The temperature-dependent,dynamic exchange of the sulfate ion between two lattice sites in potassium alum has been studied by Raman spectroscopy for crystalline forms of pure alum, KAI(S04)2.12H20,KAI(S04)2.12D20,and 8% S18042-in KA1(S04)2.12Hz0. Differences between the peak frequencies and half-widths, and relative intensities for KAI(S04)z-12H20 and KAI(S04).I 2D20indicated hydrogen bonding differencesbetween the two sites. Differences between the relative intensities of bands associated with the two sites for spectra measured at 298 and 77 K for the pure alums confirmed a recent report that the dynamic exchange between the two sites had a nonlinear Arrhenius behavior, Le., at 77 K the second site had a significantly higher occupancy than expected. Similar relative intensity measurements for the bands associated with the two sites for the isotopically dilute S'8042-ion showed that the second site was essentially unoccupied and gave agreement with the prediction of Arrhenius behavior based on the high-temperature data. It was concluded that intermolecular coupling of identical modes of vibration between different S042- ions in the ordered lattice of the pure alums imparted an unexpected stability to the second site and this coupling strength became greater at lower temperature. The isotopically dilute S'8042ions were totally decoupled from the ordered lattice and did not have the added stabilization from the resonance energy-exchange process.
Introduction Potassium alum is an example of an unusual type of crystal because it has two occupied nonequivalent crystallographic sites for the sulfate ion with a temperature-dependent occupancy rate.'-3 The a-alum crystal type belongs to the cubic class with space group Pa3(Th6)and 4 formula units per unit ~ e l l . l * ~However, >~ X-ray diffraction studies of potassium alum by Larson and Cromer' indicated the unusual situation of two possible orientations of the sulfate ion with oxygens directed toward aluminum (site 1) with probability p l or potassium (site 2) with probability p2. There was evidence for dynamic disorder with the value of the roomtemperature probability ratio p l / p 2 = 2.33. The results of the X-ray study have been verified by Raman ~pectroscopy.~.~ Eysel and Eckert5 have demonstrated that the Raman spectra from oriented single alum crystals were consistent with the unit-cell group analysis based on the Pa3 structure with the exception of an extra band about 20 cm-I lower in frequency than the sym-
* Author to whom correspondence should be addressed. 0022-3654/90/2094-0540$02.50/0
metric stretching band of sulfate. It is interesting to note that although there was partial disorder of the sulfate and the sulfates were well spaced by the presence of water molecules, there was evidence for intermolecular coupling between identical modes of neighboring sulfate ions. In subsequent studies by Eysel and Schuhmacher2 and Sood et ale3the two bands in the symmetric stretching region of sulfate at about 990 and 970 cm-' have been assigned to sulfates on site 1 and site 2 and the intensity ratio has been studied as a function of temperature in order to follow the probability ratio. The room-temperature probability ratio from the Raman measurement was in good agreement with the X-ray results. Eysel and Schuhmacher2 found Arrhenius behavior for (1) Larson, A. C.; Cromer, D.T . Acta Crystallogr. 1967, 22, 793. (2) Eysel, H. H.; Schuhmacher, G. Chem. Phys. Lett. 1977, 47, 168. (3) Sood, A. K.; Arora, A. K.; Dattagupta, S.; Venkataraman, G. J . Phys. C: Solid State Phys. 1981, 14, 5215. (4) Best, S . P.; Beattie, J. K.; Armstrong, R. S . J. Chem. SOC.,Dalton Trans. 1984, 26 1 1. ( 5 ) Eysel, H. H.; Eckert, J. Z . Anorg. Allg. Chem. 1976, 424, 68.
0 1990 American Chemical Society
Raman Study of Sulfate Orientational Dynamics the probability ratio over a small temperature interval (268-293 K) and reported an activation energy of 2.0 kJ mol-l K-I for the dynamic exchange of sulfate between the two sites. Sood et aL3 have studied the dynamics of the reorientation over a much wider range of temperature (90-298 K) and found serious departure from linear Arrhenius behavior at low temperatures. Sood et al. proposed a model that included a temperature-independent contribution to the reorientation rate, the physical origin of which was associated with coupling between sulfate ions. In the present study the coupling model was tested and verified by studies of the bands due to decoupled S18042-ions on sites 1 and 2. The present study and that of Eysel and EckertS were primarily directed toward studies of the modes due to sulfate. Best et aL4 have reported on the Raman studies of the modes primarily associated with the water molecules. Crystals with molecules or molecular ions on crystallographically different sites are not too common although there are a few well documented cases. For instance R b N 0 , and CsNO, have nitrate ions on three different sites.6 Crystals such as the a-alums with dynamic disorder between different crystallographic sites are even more unusual, although it appears that several ionic nitrate crystals have nitrate groups on ordered and disordered sites in dynamic eq~ilibrium.’,~Raman studies of sodium nitrite have also been interpreted on a two-site model in dynamic equilibrium?
Experimental Section Single crystals of alum were grown from a saturated solution of the salt in double-distilled water. The solution was treated with activated carbon to remove fluorescent impurities and filtered through a fine glass frit. The 0-18 enriched alum was prepared by adding about 10% of 98% 0-18 enriched K 3 0 4 to normal alum in H 2 0 and allowing the liquid to evaporate to dryness. Small clear crystals of 0-18 enriched alum were obtained. The Raman analysis indicated that the alum sample was 8% S1*02-, less than 0.7% S16018032-, and 91.3% S16042-.There was no exchange of 0-18 between the water and or the sulfate of normal enrichment from the alum. The K2S04was prepared with a vacuum line procedure. A solution of 0-18 enriched KOH was prepared by reaction of potassium metal with 99% enriched 0-18 water (Isomet) at 0 OC under nitrogen. An appropriate quantity of 98% enriched 0 - 1 8 SO2 (Fluka) was condensed into the hydroxide solution, and then pure C12 gas was dissolved into the solution to assure oxidation of the sulfite to sulfate. The sample was e v a p orated to dryness. The 0 - 1 8 enrichment of the K2S04solid was determined by Raman intensity measurements to be 98%. Alum-d2 was prepared by dissolving appropriate quantities of K2S04 and A12(S04), dried at 130 OC into 99.8% D 2 0 , evaporating to dryness, and recrystallizing from D20. Raman measurements of the OH and O D stretching regions revealed a very intense band at 2495 cm-l due to D 2 0 and a very weak band at 3350 cm-’ due to H 2 0 . From the ratio of intensities it was estimated that the KAI(S04)2-12Dz0was 99% enriched with DzO. Relatively clear crystals with natural faces were used in the study. Raman spectra were measured with a Coderg P H O Raman spectrophotometer. The 488.0-nm line of a Control Laser Model 52 argon ion laser was used to excite the sample. Plasma lines were removed with a narrow band-pass interference filter. Peak positions were calibrated against laser plasma lines. The slit widths were set at 1 .O cm-l. The power level at the sample was about 300 mW. There was some evidence of local heating and sample degradation at the beam focus. This was most serious for the 0 enriched sample, which had a slight fluorescence, but could be avoided with the use of laser power levels at 300 mW or less. In an effort to find bands due to the Fg modes in the symmetric stretching region of sulfate, Raman spectra for an oriented single crystal of the normal alum were obtained at 77 and 298 K on the copper cold tip of an evaporating liquid nitrogen cryostat. The (6) Brooker, M. H. J. Chem. Phys. 1973, 59, 5828. (7) Brooker. M. H. J. Solid State Chem. 1979, 28, 29. (8) Brooker, M. H. J. Phys. Chem. Solids 1978, 39, 657. (9) von der Leith, C. W.; Eysel, H.H.J . RamanSpecrrosc. 1982, 13, 120.
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 541 crystal was oriented for the incident and scattered light to be perpendicular to principal planes to give the x ( z z ) y and x(yx)y scattering geometries. Polarization of the incident beam was controlled by a half-wave plate, and the 90° scattered light was analyzed with Polaroid films which accepted parallel or perpendicular polarized light. A quarter wave-plate before the entrance slit served to compensate for grating polarization preference. The Raman scattered light was detected with a photomultiplier tube (PMT) cooled to 250 K connected to the Coderg photon counter. Analog spectra were output on a strip-chart recorder. Digital data files were created by integrating the photon counts with a homebuilt box-car averager interfaced to the Memorial University VAX 8800 computer. In the present case four points were collected per wavenumber. At least two sets of data were collected for each spectrum. Spectra were signal averaged and smoothed once with a three-point Savitsky-Golay smoothing function. A base-line program was applied that corrected the measured intensity for the fourth power frequency factor and then set the lowest data point to zero and the highest data point to 999 on a relative intensity scale. This form of the data is defined as our I ( w ) spectrum, which should be independent of excitation frequency. The same base-line program was applied with the option to correct for the fourth power scattering factor, the Bose-Einstein temperature factor, E = [ 1 - exp(-hcw/kT)], and the frequency factor, w, to give the reduced or RQ(w)spectrum, which is directly proportional to a point by point relative scattering activity in terms of mass-weighted normal coordinates S Q ( w ) in the double harmonic approximation. RQ(w)is the form of the Raman spectrum that most closely approaches the vibrational density of states.I0 The relationship between the I ( @ ) and RQ(w) forms of the spectra is given by eq 1. It is our preference to plot Sq(0)
Rq(w) = I ( 0 ) w B
(1)
the spectrum in the RQ(w)form because the Bose-Einstein factor removes the vibrational state dependent temperature factor of the excited-state transitions and leaves the effect that is due to concentration changes. Only in the low-frequency region are the I(w) and RQ(w)significantly different. One consequence of the use of the RQ(o)spectra is the symmetrization of the Raman bands in accordance with the principle of detailed balance. It is the symmetrized band that should be used in most curve resolution routines. Raman spectra from the computer files were plotted with an interactive Tektronix 4662 plotter. Analog recorder plots of all the measured spectra were also available. Curve resolution of the two bands in the symmetric stretching region of sulfate was achieved with a nonlinear least-squares program. Good fits were achieved with a Lorentzian-Gaussian product function (equal weights) with three adjustable parameters per band (frequency, half-width, and intensity). Since the spectral slit widths were at least 5 times smaller than the natural bandwidths, no slit function correction was included in the curve resolution procedure. Curve resolution was also achieved by hand with the assumption of symmetric band shapes. Excellent agreement between the two methods was achieved. Frequency differences between the two components were estimated to be accurate to 0.1 cm-I. Relative intensities and half-widths are estimated to be accurate to about 5%.
Results and Discussion Raman spectra for the symmetric stretching region of the sulfate ion in KAI(SO4),-12H20, KA1(S04)2-12D20,and the 8% S8O2enriched KAI(S04)2m1 2 H 2 0crystals are presented in Figures 1-3. Frequency, half-width, and relative intensity data for the samples studied at 77 and 295 K are collected in Table I. Where comparisons are possible, the present results were in good agreement with the results of Eysel and c o - w o r k e r ~and ~ ~ Sood ~ et aL3 The unit-cell group analysis for a-alum predicts two bands in the symmetric stretching region of sulfate, one with A, character and one with F, ~ h a r a c t e r .However ~ the two bands at about 970 (IO) Brooker, M. H.; Faurskov Nielsen, 0.;Praestgaard, E. J. Raman Spectrosc. 1988, 19, 11.
542
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
Brooker and Eysel
TABLE I: Raman Data for the Symmetric Stretching Region of Sod2-in Alum 8% S1804in KA1(S04)2.12H20 KAI(SOJ2.I 2H20 295 K 77 K 295 K 77 K 918.0" (15.5)b 918.0 (-7) R = 2.5 f 0.lc R = 36 5 A = 15.8 cm-l A = 15.3 cm-' 933.3 (7.7) 933.8 (5.6) 947.0 (-8) 949.0 (-6) 972.8 ( I 0.8) 970.0 (4.8) 972.8 (10.7) 970.0 (4.8) R=2.3*0.1 R=4.2*0.1 Rz2.3f0.1 R=4.2*0.1 A = 16.2 cm-' A = 20.0 cm-' A = 16.2 cm-l A = 20 cm-' 989.0 (5.9) 990.0 (5.3) 989.0 (5.9) 990.0 (5.3)
KAI(SO4)2*12D20 295 K 77 K
site 2
*
SI80 2-
site 1 S180l60
970.5 (8.2) R=2.2f0.1 A = 18.0 cm-l 988.5 (4.6)
site 2
966.5 (2.8) R=3.8f0.1 A = 22.5 cm-l 989.0 (4.3)
-
SI60 2-
site 1
a Frequency of peak maximum given in cm-I. bHalf-width(full width at half-height) given in cm-I. C Rdenotes intensity ratio or probability ratio, p l / p 2 = R . d A denotes separation of peak maximum of site 1 from that of site 2.
X I
& x5 X I
I
I
1000
950 cm-'
Figure 1. Raman spectra for the vI region of sulfate in normal KAI(S04)2-12 H 2 0 single crystals for the x(zz)y and x @ x ) y orientations.
and 990 cm-' with unequal intensity in the Raman spectra for an oriented single crystal have the same A, symmetry (Figure l ) , and there is no indication of a band with F, symmetry. A correlation field coupling model cannot account for the two bands. et aL3 have assigned the band Eysel and c o - w o r k e r ~and ~ ~Sood ~ at 990 cm-l to the A, unit-cell group component (site 1) and the band at 970 cm-' to the symmetric stretching mode of a sulfate on site 2 in accordance with the two-site model of Larson and Cromer.' There should be an F, component associated with the band of A, character at 990 cm-I, but there is some question as to whether or not an F, component should be associated with the band at 970 cm-' because the concentration of molecules on site 2 is sufficiently small and the band is sufficiently shifted from the site 1 band for the 970-cm-' band to be treated as due to an Eysel and EckertS reported F, components impurity 1 cm-' higher in frequency than the A, components for each of the site 1 and site 2 bands of potassium alum. The present study with an oriented crystal at 77 K for the x ( z z ) y and x(vx)y orientations failed to reveal any evidence for the F, component in either region (Figure I ) . The weak intensity in the x(vx)y orientation was attributed to spillover of the A, intensity because the peak positions were identical in both orientations. The presence of only one strong symmetric component and the absence of other correlation field components is not unusual in other ionic sulf a t e ~ . ' * - 'Since ~ the F, components were absent and the bands
1
,
,
1
,
1
1
1
1
950
1
1
1000
cm-'
1
30A, 2179.
,
Figure 2. Raman spectra for the v I region of sulfate for the I80enriched KA1(S04)2.12H20at 295 K.
900 ( 1 1 ) Belousov, M. V.; Pogarev, D. E.; Shultin, A. A. Phys. Srafus Solidi 1977, B80,417. ( I 2) Meserole, F.; Decius, J. C.; Carlson, R. E. Specrrochim. Acra 1974,
1
900
,
,
,
,
1
950
,
1
~
1
1
~
lo00
cm-' Figure 3. Raman spectra for the v I region of the sulfate for the '*O enriched KAI(S0,)2.12H20 at 77 K.
Raman Study of Sulfate Orientational Dynamics at about 990 and 970 cm-l had the same depolarization ratios, the relative intensity measurements from partly oriented single crystals were uncomplicated by misorientation problems. This was important because the relatively clear single crystals of alums gave better spectra with better signal to noise ratios than was possible from polycrystalline samples. Further support for the two-site model was obtained in the present study from the region of the 8% SI80:- ion in the 0 - 1 8 enriched alum. Again, two bands were observed in the S18042region at about 933 (site 1) and 918 (site 2) cm-' with relative intensity similar to that of the two bands in the S16042-region at 990 and 970 cm-l (Figure 2). A weak band at 947 cm-' was The presence of the assigned to a small amount of S16018032-. two bands in the SI8O:- region is consistent with a two-site model and inconsistent with a correlation field coupling model because at the 8% concentration level the S18042-will be decoupled from the ordered lattice mode of the coupled S16042-ions. At least in the symmetric stretching region the 8% S1804"ions give rise to impurity modes, one for each lattice It was also noted that the 8% Sl802-impurity had no effect on the SI6O:- regions of the Raman spectrum. The 8% S18042-impurity was not sufficient to disrupt the coupling between the S'6042- ions on the ordered lattice. The half-widths of the impurity bands of Si80:at 933 and 91 8 cm-' were considerably larger than those of the SI60?- counterparts at 990 and 970 cm-' for the ordered lattice (Table I). These results were similar to those for dilute N180,in Sr(N03)2.6 Consistent values were obtained for the probability ratios (pl/p2) for the samples at 295 K. For pure KAI(S04).12H20 at room temperature the intensity ratio of the bands due to the two sites gave pl / p 2 = 2.3 f 0.1, which was identical with the value from X-ray studies of Larson and Cromer' and only a little smaller than the previous Raman measurement^.^^^ For KAl(S04).12D20 the ratiopllp2 = 2.2 f 0.1 was just slightly smaller, but the difference was not outside experimental error. The probability ratio measured from the two bands of S'8042-in the KA1(S04).12H20 was p l / p 2 = 2.46 f 0.2, which was within experimental error of the ratio for the S16042-region. The most significant part of this study concerns the effect of temperature on the relative intensities of the bands due to the two sites. When the crystals were cooled to 77 K, the intensity ratio for the S16042-ions of the ordered lattice increased but reached a constant value (e.g.,pl/p2 = 4.2 f 0.1 for the KAl(S04).12H20 at 77 K) because of appreciable occupancy of site 2 even at 77 K. However the intensity ratio for bands due to the impurity SI8Od2-ion gave a much higher value (e.g., p l / p 2 = 36 f 5 at 77 K ) because the intensity of the band at 918 cm-' due to site 2 went to a very small value as the band essentially disappeared (Figure 3). These measurements were repeated on several crystals and the integrations measured by different methods, all with the same results. The 15% error for the SI8O:- region for the crystal a t 77 K was due to the difficult area measurement for the very weak residual band at 918 cm-I. These new data points were plotted (Figure 4) as In (pl/p2) versus 1 / T together with the literature values of Eysel and Schuhmacher2 and by Sood et aL3 The present results for the bands due to SI602- in KAI(S04). 1 2 H 2 0 and KAI(SO4)-12 D 2 0 were in good agreement with the room-temperature results of Eysel and Schuhmacher and of Sood et al. and confirmed the non-Arrhenius behavior of the ratio at low temperature as reported by Sood et aIs3 However the value of In @l/p2) does not fall off for the S18042-ions as it does for the S'6042-ions, and the value of In (pl/p2) = 3.6 f 0.15 at 77 K actually falls on the line which corresponds to an activation energy of 2.0 kJ mol-' K-' for the reorientational exchange process for the high-temperature data for SI6O:-. Although the exchange process for the S16042-ions between the two sites of the ordered lattice does not follow an Arrhenius behavior at low temperature and the site 2 occupancy freezes into a constant value, it appears that the populations of the two sites for the disordered S'8042( I 3) Dawson, P.; Hargreave, M. M.; Wilkinson, G. R. Specrrochim. Acta 1977, 33A, 83.
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990 543 K
I / T x loo0 K "
Figure 4. Plot of In pl/p2 versus 1/T for the potassium alums: 0 , data of Sood et al. (ref 3); 0 , ratio based on the 934-, 918-cm-' bands of S1*02-; A,ratio based on bands of S'6042in KAI(S04),~12D,00, ratio based on bands of SI60:- in normal alum KAI(S0,)2.12H20and the I8O enriched form; a, data of Eysel and Schuhmacher (ref 2).
impurity do follow Arrhenius behavior to 77 K, at which temperature the second site is almost depopulated. Sood et aL3have proposed a model that contains an additional relaxation term to account for the non-Arrhenius behavior of the reorientation process. It was inferred that weak coupling between the sulfate ions became important below 150 K. The present results for the S I 8 0 t - enriched alum are consistent with the model of Sood et aL3 and can provide an insight into the intermolecular coupling factor. On first consideration it appeared as if intermolecular coupling between vibrational modes of neighboring sulfate ions could not be the source of the additional stabilization energy that slows down the reorientation process and results in the freezing-in of a high occupancy population for site 2. However, Eysel and E c k e d have measured the Raman spectra for oriented single crystals of potassium and other alums and found evidence for intermolecular coupling in the other regions of sulfate while finding no evidence for separate modes due to site 2 sulfates in the other regions. It appears that frequency shifts associated with the site 2 sulfates are not sufficient to decouple the two forms of sulfate in the v2, vj, and v4 regions of sulfate. On the other hand the vibrational frequencies of the dilute S'80:- ion in alum should be sufficiently shifted to decouple the v2 and v4 modes, where the isotope shifts are greater than the intermolecular coupling splitting, but perhaps not v3, where the isotope shift is smaller than the reported intermolecular coupling splitting. In a separate study the frequency differences between the SI6O:- and SI80:- forms of sulfate were found to be 56,26, 27, and 33 cm-l for the vlr v2, v3, and v4 modes of ~u1fate.l~ Raman spectra of the 400-700-cm-' region of the natural and S'8042-enriched alum revealed a new band at 429 cm-I, which has been assigned to the v2 ( E ) mode of the S'80?- impurity ion decoupled from the correlation field components of the SI6Od2ions of the ordered lattice at 441 ( F ) 458 (Fg), and 475 cm-' (E,) (Figure 5 ) . The assignment was G aSed on three observations: (a) The relative intensity was found to be about 10%; (b) the frequency shift from the mean of the three correlation field (14) Brooker, M. H., unpublished.
544
The Journal of Physical Chemistry, Vol. 94, No. 2, 1990
rool
Brooker and Eysel
h
X(ZZ1Y
J
200
0
i
0
"400
sbo
cm-'
Sbo
,
940
A
X(YX)Y
u, Id, 960
980
,
,
IO00
cm-'
Figure 6. Raman spectra for the v I region of sulfate in (a) KAI(S04)2.12H20at 295 K and (b) KA1(S04)2-12D20at 295 K.
io0
Figure 5. Raman spectra for the 400-700-cm-' region of (a) normal KAI(S04)2.12H20and (b) '*Oenriched KA1(S04)2.12H20for oriented crystals at 77 K . The asterisks indicate the u2 ( E ) mode of the S18042impurity type band.
components was found to be very close to the expected value of 26 cm-I; (c) the band appeared to be depolarized. A search of the 600-cm-' region failed to reveal evidence for a separate band due to the v4 (F)mode of decoupled S18042-,but this region was complicated by overlap with bands due to wagging modes of H,O (Figure 5). The 27-cm-I isotope shift would be sufficient to decouple the v4 mode of S1*0?- ions. There was also no evidence for a separate band in the v3 region of sulfate, but in this case a separate band would not be expected because the isotope shift would not shift the band due to vj of S1802-outside the v3 density of states region for the Sl60?- ions of the ordered crystal. Eysel and EckertS have reported that the correlation field components of v3 ranged from 1096 to 1194 cm-I in potassium alum whereas the isotope shift is only 33 cm-l. It appears that the difference in the temperature dependence of the probability ratio between the S16042-ions on the ordered lattice and that for the impurity S18042-ions can be associated with differences in intermolecular coupling of the internal modes of sulfate. Intermolecular coupling of identical vibrational motions of neighboring molecules involves resonance energy exchange or delocalization of a quantum of energy over several molecular ions. The energy-exchange process provides the mechanism for a weak intermolecular interaction; Le., the energy of two coupled molecules will be lower than that of the two separated molecules. In the sulfate reorientational process in alums the S16042-ions on site 2 are only decoupled in the v I region and the intermolecular coupling for the other modes provides an additional stabilization energy that becomes more important at lower temperature and freezes the site 2 population at about 30%. Lower temperature enhances intermolecular coupling because the vibrational thermal
amplitudes are smaller and the number of excited vibrational states are fewer. The same stabilization energy is not a factor for the dilute S18042-ions, which are essentially decoupled, and the exchange process for the reorientation can continue at low temperature until site 2 is depopulated. Differences between vibrational spectra of the KAI(S04).12H20 and KAI(S04).12D20gave evidence for relatively strong hydrogen bonding between water and sulfate and revealed some differences between the two sites. The vibrational frequencies and half-widths are not the same in the normal and deuterated alums (Table I). The differences appear small, but they are well outside experimental error and larger than often observed on deuteration of hydrates. For instance the values for the peak positions for the site 1 and site 2 bands and the difference between the two bands are 990.0,970.0,and 20.0 cm-I for normal alum at 77 K but 980.0, 966.5, and 22.5 cm-' for the deuterated crystal. The half-widths for bands of the deuterated sample were about 20%less than the half-widths of bands of the normal alum. The half-width of the site 2 component in the deuterated alum was especially narrow with a value of 2.8 cm-' compared to the value of 4.8 cm-' for the normal alum at 77 K. The smaller values of the half-widths indicate a smaller distribution of environmental states for the deuterated crystal. The results for the probability ratio indicated that the site 2 population was frozen-in at a higher occupancy level (36%) in the deuterated sample at 77 K. These measurement suggest that the site 2 sulfates are more stabilized by strong hydrogen bonding from D20. This conclusion is consistent with the X-ray study because the sulfates on site 2 are directed toward the potassium rather than the aluminum and therefore will be more available for hydrogen bonding. The differences in the frequency and half-widths between the hydrogen and deuterium forms of alum can be attributed to the decreased thermal amplitudes of the vibrational modes of D,O compared to those of H 2 0 . A consequence of the decreased thermal amplitude of the bending mode of D,O is a stronger, more linear hydrogen bond.
Acknowledgment. This work was supported in part by the Natural Sciences and Engineering Council of Canada and by the Deutsche Forschungsgemeinschaft. The authors thank Margaret Miller for the preparation of the deuterated alum. Registry NO. KAI(S04)2*12H20, 7784-24-9; KAI(SO4)2.12D~O, 103244-71-9; KAI(SO4),-12H20 (I80-enriched (SO,)), 123724-20-9.
