10580
J. Phys. Chem. 1993,97, 10580-10584
The Far-Infrared Spectrum of Crystalline C@t Roberto Bini, Piero Procacci, Pier Remigio Salvi, and Vincenzo Schettino' Laboratorio di Spettroscopia Molecolare, Dipartimento di Chimica, Universith di Firenze, via Gin0 Capponi 9, 501 21 Firenze, Italy, and Laboratorio Europe0 di Spettroscopie non Lineari, Dipartimento di Fisica, Universith di Firenze, Largo Enrico Fermi 2, 501 35 Firenze, Italy Received: March 25, 1993; In Final Form: June 29, 1993"
The infrared spectrum of crystalline C60 has been measured in the frequency range 500-20 cm-l a t various temperatures between 300 and 10 K. Since no dipole-allowed intramolecular vibration is active below 500 cm-I, the infrared absorption is determined by crystal and quadrupolar interactions. Davydov splittings of several intramolecular vibrations have been observed. The infrared activity of H, modes is discussed. In the lattice region the two translational phonons of Tusymmetry a r e observed a t 41 and 58.5 cm-I a t 8 K. Considerations on the orderaisorder phase transition of C60 crystal are advanced on the basis of our experimental results.
2. Experimental Section High-purity c 6 0 (99.99%+) was purchased from Syncom (The The infrared spectrum of C60 has been one of the first evidences Netherlands). Pellets of variable thickness ( N 1-2 mm) were of the icosahedral symmetry for this molecule. In the I h symmetry prepared for the infrared experiment using a pressure of ~3 C a is expected to show four infrared-active fundamentals, of TI, kbar, below the value corresponding to the phase transition of C a species. Four bands, at 527, 577, 1183, and 1428 cm-I, are in at room t e m p e r a t ~ r e . ~The ~ , ~far-infrared ~ spectra in the range fact seen as the strongest in the infrared spectrum of thin c 6 0 500-20 cm-I were measured from room temperature to 10 K and films.'-5 Later on, it was found that the spectrum of thicker vice versa on a FTIR HR120 Bruker interferometer with samples has greater complexity and this was related to crystal bolometric detection at liquid He temperature with results interactions.6 independent, at each temperature, of the sample history. The Solid-state effects were first considered explicitely with sample was mounted on the cold finger of a closed-circuit H e reference to the Raman spectrum of a CW single crystal at low cryostat with an indium gasket around the sample to ensure a It was pointed out that, because of the ordered good thermal contact. The cryostat was linked to the interferpacking, each molecular mode is split into multiplets and several ometer through shock-absorbing bellows. In this way we could examples of Davydov splittings were reported. In most cases, reduce the number of windows along the infrared beam path with however, the number of the observed components resulted to be a consequent signal enhancement which allows a measurement smaller than predicted by group-theoretical arguments. Crystal with high resolution alsoon strongly absorbing or, as in the present interactions are also responsible for the spectral structure in the case, very thick samples. Furthermore the use of shock-absorbing lattice phonon region. In the low-temperature crystal phase, five bellows prevents the transmission of the mechanical vibrations phonons are expected to be active in the Raman and two in the originated by the cryostat, which otherwise could strongly affect infrared spectrum. Librons show weakly in the Raman spectrum on a strong background signal in number less than p r e d i ~ t e d . ~ , ~ the bolometer detection. Over 100 correlated scans were acquired at each temperature for Fourier processing. Well-resolved (Au In the only reported far infrared spectrum,1° on the other hand, N 0.4 cm-l) spectra with a large signal-to-noise ratio were the observed bands are assigned to active and inactive translational obtained. phonons, suggesting a breaking of the symmetry rules. Inelastic neutron scattering on powderedl1-l3 and ~ i n g l e - c r y s t a l ~c ~6 0J ~ 3. Symmetry Considerations give additional information on the phonon modes. Molecular and lattice Dynamics c a l c ~ l a t i o npredict s ~ ~ ~ phonon ~ frequencies The low-temperature crystal structure of C a has been found in general good agreement with experimental data. to be cubic,20Jl space group Th6, with four molecules on sites of The present paper reports on the infrared absorption of S6symmetry in the primitive unit cell, Le., along the main diagonals crystalline c 6 0 in the range 500-20 cm-I between room temperof the cube. The site and factor group analysis based on these ature and 8 K. The purpose of the paper is 2-fold. On one hand, structural data are shown in Figure 1. Each vibration is split into since no intramolecular vibration in the isolated molecule can be several components and, in particular, thoseof G and H symmetry active below 500 cm-l, infrared absorption is a good measure of in seven (G 2A + E + 4T) and eight ( H A 2E 5T) the crystal interactions. As high-resolution spectra are easily components. In the infrared only Tucrystal modes are active and obtained with FTIR techniques, we haveobserved the full multiplet accordingly we expect three, four, and five peaks for each T1,2,, structure of forbidden molecular modes. On the other hand, we G,, and H, vibration, respectively. As to the phonon modes, the have also observed phonons a t 41 and 58.5 cm-l at 8 K. Our total number of branches with nonvanishing k = 0 frequencies data, therefore, complement previous results10 under highare 2 1, whose 9 of u, A, + E, 2T,, and 12 of g symmetry, A, resolution conditions and provide a vibrational assignment of + E, + 3T,. The phonon modes at k = 0 have pure rotational translational phonons without ambiguity. (g) or pure translational (u) character. Only two lattice phonons Finally, it was found that the order-disorder phase transitions22 may be observed in the far infrared spectrum, both of Tusymmetry. strongly affects the crystal spectrum. Our data indicate that a At 255 K the CSOcrystal undergoes a first-order transition to an partial order is present in the high-temperature phase at room orientationally disordered phase.20J5*26According to X-ray temperature. scattering on powdered c60, the room temperature structure has been found to be fcc,20Th3,with four molecules in the conventional f This work was supported by the Italian Minister0 Universiti e Ricerca unit cell on sites of Th symmetry. In the disordered Th3 phase Scientifica e Tecnologica (MURST) and Consiglio Nazionale delle Ricerche all molecular modes (except A,) become active at least as singlets (CNR). either in infrared or in Raman spectroscopy. In addition, G, and *Abstract published in Aduance ACS Abstracts. August 15, 1993, 1. Introduction
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0022-3654/93/2097-10580$04.00/0 0 1993 American Chemical Society
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The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
Far-IR Spectrum of Crystalline c 6 0 Molecular symmetry
Site
Factor group
symmetry
ty"W
Ih
s 6
Th
lO!W
200 K
8C m
2
120
Figure 1. Correlation diagram for the low-temperaturecrystal phase of Ca. Infrared active modes are of TI, symmetry in the molecule and of Tusymmetry in the crystal.
460 ' 420 ' 4 0 460 Wavenumbers (cm-1) Figure 2. Infrared spectrum of crystalline Cm as a function of the temperature(300,200,100,and 10K, from top tobottom)in the frequency range 370-470 cm-I. '
380
'
'
'
300 K
4
310
330 350 Wavenumbers (cm-1)
370
I
Figure 3. Infrared spectrum of crystalline Cm as a function of the temperature(300,200,100,and10K, from toptobottom)inthefrequency range 300-380 cm-I.
H,modes are split into doublets. Only one lattice phonon occurs, of T, symmetry. 4. The Infrared Spectrum IntramolecularVibrations. The FTIR spectrum of crystalline Cm in the range 500-100 cm-1 is shown in Figure 2-4 at various temperatures between 300 and 10 K. As the lowest allowed molecular fundamental occurs at 527 cm-1, the spectrum takes
160 200 240 280 Wavenumbers (cm-1) Figure 4. Infrared spectrum of crystalline Cm as a function of the temperature(300,200,100,and 10 K, from top to bottom) in the frequency range 100-300 cm-I. strength from crystal interactions. Two sets of close lying bands are found around 350 cm-I with strong enhancement lowering the temperature. The average frequency of each set agrees quite well with those observed by inelastic neutron scatteringl1J2 a t 345 and 355 cm-I. These bands were already assigned to G, and Tzusymmetry." In fact, all theoretical calculations on the isolated m0lecule2~-31predict two almost degenerate G, and Tzu modes in this frequency range. From the appearance of our spectrum it is plausible that themultiplet above 35Ocm-1should becorrelated to the same molecular mode. In this case, noting from Figure 1 that G, molecular modes are split into infrared quartets, the 35 1,353,354, and 359 cm-1 peaks are assigned to the G,vibration. Thelower multiplet has a morecomplex structure (347.4-, 345.3-, 341-cm-1 bands with shoulders at 340 and 339 cm-I) and the factor group splitting into three active crystal components of a Tzumode cannot be solely responsible of the observed pattern. Isotopic impurities may be important. The monosubstitution of l3C into the c 6 0 cage (WC59) lowers the symmetry of the cluster to C,. Therefore, a degenerate intramolecular vibration in isotopically pure c 6 0 splits, in the monosubstituted WC59, into as many components as the degeneracy index, presumably very close each to the other on the low-frequency side of the main peak. In addition, since there are 60 equivalent positions for the isotopic substitution, the corresponding transition intensity with respect to the parent band is -0.6. Doubling the isotopic substitution, clusters I3C2C58 of different symmetry, Le., Cl,C,, and Ci, may be obtained, according to the sites of substitution. The (many) closely spaced 13C2C5~ peaks shift to frequencies lower than thoseof 13CC59and havea totalintensity -0.17 I(Cm), due to the 1770 (almost) equivalent combinations resulting from inclusion of two 13C masses into the Cm cluster. Hence, given that the intensities of isotopic peaks are comparable to that of the main peak, the asymmetry of the 341-cm-I band may be related to isotopic effects. As a further check of our hypothesis we have calculated the intramolecular frequencies introducing one and two 13C into the icosahedral cluster and using the force field for c60 reported in ref 3 1. For the Tzumode, the computed shifts for mono- and bisubstitution are 1.O and = 1.5 cm-I, respectively. This fairly agrees with the two shoulders on the low-frequency side observed at N 1 and -2 cm-I from the main peak a t 341 cm-1. The calculated isotopic shifts for the G, mode are -0.8 cm-1 (monosubstitution) and 1.8 cm-I (bisubstitution). In this case, however, the isotopic bands are not seen. It is probable that, being the G, crystal splitting much larger than that of Tzu origin, in the former case the isotopic peaks must be considered as resonant states embedded into the vibron continuum and, as a consequence, not resolvable as in the Tzu case. The Gu;T2, pair provides the first example of completely resolved multiplet structure in the c.50crystal. As a first estimate
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Bini et al.
10582 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
of the crystal splittings, using the atomic coordinates of c 6 0 in the solid state obtained by X-ray scattering,j2 we have also calculated the normal frequencies of the distorted molecule with symmetry S,. In fact, for highly degenerate molecular modes the site symmetry is the first source of crystal field splitting. As shown in Figure 1 each Tzumode is split in two components, A, + E,, and each G, mode in three, 2A, E,, by site symmetry. In our case, using for the molecule in the s.5site the same force field as for the isolated c 6 0 system,31 we find splittings A(T2,,) and A(G,) =2 and 7 cm-I, respectively. Although this is not a very accurate calculation of the crystal interactions, it may serve as a rough indication and agrees qualitatively with our experimental results. At higher frequency a band with two components, 403 and 404 cm-1, and a shoulder at 402 cm-1 is observed, in close correspondence with the neutron-scattering band at 404 cm-I. According to ours31 and several others cal~ulations,2~-~~ a H, vibration is expected here. The multiplet structure must be considered as due to Davydov splitting, although only three of the five expected components (see Figure 2) can be resolved in the spectrum. The other two components are probably too weak to be observed and well separated from the former set of three as indicated by the calculated splitting of the H, mode in the distorted configuration ( N 8 cm-1). The two lowest Raman active modes, of H, symmetry, have been r e p ~ r t e d ~around -~ 265 and 430 cm-I. The first shows strongly as a triplet in the crystal (262, 266, and 272 cm-1) and the second more weakly as a doublet (428 and 433 cm-I). In our IR spectrum two multiplets are found within the same limits with intensity in reverse order. The lowest multiplet should be interpreted as due to H, symmetry, in absence of nearby u modes. This means that either (i) our sample, due to crystal defects, can be locally less symmetrical than expected with loss of the inversion center on the molecules or (ii) the absorption strength of these bands are related to the interaction of even transition multipole moments with the radiation field. As to the first hypothesis, the loss of the inversion center would make all the g modes active, without any symmetry restraint. On the contrary, there is no evidence of occurrence in the infrared spectrum of the Raman active A, mode at 496 cm-I, for instance. Let us now discuss the second possibility. In the I h symmetry each element of the permanent quadrupole tensor is zero while nonvanishing transition quadrupole moments are in principle of H, symmetry. The form of the 5-fold degenerate H, tensor is
+
with b = c = 31J2a. Given a chargedistribution for the icosahedral molecule and the eigenvectors, qi, i = 1, ...,5, of an H, mode, the transition quadrupole moment can be calculated by numerical derivation of the permanent quadrupole moment with respect to the normal coordinates qi, i.e.
where xo represents the equilibrium structure (icosahedral simmetry, zero quadrupole moment) and hq,, the distortion along the ith eigenvector for the 5-fold degenerate H, mode. A charge distribution has been recently p r ~ p o s e dwith ' ~ 60 positive centers +6 on the C atoms and 30 negative centers -26 midway on the short interpentagonal bonds. We assume that, during a normal vibration, the extra center midway the short bond moves such that its instantaneous position vector is given by r = 0.5(rl + r2), where rI and r2 are the instantaneous position vectors of the carbon
TABLE I: Calculated a Elements (Units of Electrons amu-1'2 A) of the Quadrupole Transition Tensors for the Modes and Corresponding IR Intensities I (Arbitrary Units
Hf
P
U
I
P
a
I
284 422 622 761
0.1183 0.2375 0.1533 0.1266
0.0140 0.0564 0.0235 0.0160
1144 1244 1438 1619
0.3454 0.3592 0.0372 0.0830
0.1193 0.1290 0.0014 0.0069
a
Calculated frequencies (cm-I) using the force field of ref 3 1.
atoms involved in the short bond. The 6 parameter enters the calculation simply as a scale factor and does not affect the relative magnitude of the elements of the transition tensors. The tensor components of eq 1 may be easily computed by evaluating the anisotropic invariant33
6(8$
+ 0; + 031 = 9a2 = 3b2 = 3c2
V i = 1,
,.., 5 (3)
with Ohs given by eq 2. The results for the a constants of all the eight H, modes of C60 are shown in Table I. The absolute squares of these values are proportional to the intensities of the H, bands in the IR spectrum and are in good qualitative agreement with experiment (see Table I). As already pointed out, the intensity of the 265- and 430-cm-l bands in the infrared and in the Raman spectra follows opposite trends. Therefore our calculations strongly suggest that the observed multiplet a t 430 and 270 cm-l, of H, type, are due to quadrupole-induced transitions, rather than to local simmetry loss. Furthermore, according to Table I, the 1100- and 1250-cm-I H,vibrationsshould be the most intense in the infrared. This is confirmed by our measurements on thick c 6 0 pellets in the midinfrared region. Also, considering our spectrum it may be noted that the strongest quadrupole-induced IR absorption bands are comparable or smaller than the weakest dipole-induced u bands. Comparing with infrared allowed TI, modes, an intensity ratio between quadrupole-induced and allowed transitions may be estimated roughly in the range lO-'-lO-4, as expected for quadrupolar transition^.^^ A third point of interest is the temperature dependence of the very weak but reproducible bands occurring a t 257, 291, 41 1, and 450 cm-1. As their intensity decreases lowering the temperature, up to complete disappearance at 10 K, they must be interpreted as hot bands involving most probably the lowest H, modes 265 and 430 cm-I, appreciably populated at high temperature. The 257-cm-l band may be confidently assigned as 527(Tl,)-270(H,) cm-I. The other weak bands may be more tentatively correlated to the 7 11-cm-I mode which, although not of TI, symmetry, shows strongly in the infrared spectrum of thick films, as results from our own measurements. As a final comment on the low-frequency internal vibrations, we note that the 203-cm-l peak intensifies with decreasing temperature and therefore cannot be assigned as a hot band. No calculation on intramolecular c60 vibrations predicts normal modes with frequency below 250 ~m-I.2~-31On the other hand, there is no evidence of C70 impurities in our mid- and far-infrared spectra. As an example, attention must be drawn to the total absence of the 458 cm-1 c70 band294 in our spectrum of Figure 2. A band at 203 cm-I is observed also in current experiments on the far infrared spectrum of crystalline c 7 0with ~ ~ similar intensity behavior with temperature (being the 458-cm-1 peak orders of magnitude more intense). Therefore this band is due to impurities, not related to C70, probably C600.36 Translational Lattice Phonons. The infrared spectrum of crystalline c 6 0 in the range 20-100 cm-l is shown in Figure 5 at two different temperatures, 8 and 80 K (lower and upper trace, respectively). At 8 K two weak bands are observed at 41 and 58.5 cm-1. They shift to lower frequencies and broaden appreciably as the temperature increases to 80 K. Four translational
The Journal of Physical Chemistry, Vol. 97, No. 41, 1993 10583
Far-IR Spectrum of Crystalline c 6 0
TABLE 111: Experimental and Calculated Frequencies of the Lattice Phonons at l'(O,O,O) and R(O.S,O.S,O.S) Points of tbe Brillouin Zone Using the Potential Model of Table 11' r R sYm
Tu Eu T" A"
TE
T* E, Tg A,
20
60 80 Frequency (cm-1)
40
100
Figure 5. Infrared spectrum of crystalline Ca as a function of the temperature (80 and 8 K, from top to bottom) in the frequency range 100-20 cm-1. The two spectra have been measured on pellets of different thickness.
TABLE 11: Potential Parameters for the Low-Temperature Pa3 Phase of C d ~
c-c C-*
*-*
e
r0
a
0.028 345 0.008 405 0.090 9 15
4.102 71 4.21 1 92 4.128 89
12.352 9.625 21.816
Following the potential model of ref 17, the asterisk denotes the interaction center midway on the short interpentagon bond. Thequantities e, ro, and a are the well depth (kcal/mol), the distance (A), and the curvature at minimum, respectively, of the Buckingham potential in the reduced form. (I
+
phonons with nonvanishing k = 0 frequencies, A, E, + 2T,, are expected for crystalline Cm, according to the conclusions of section 3. Among them, only those of Tusymmetry are infrared active. Therefore the observed bands are assigned to Tuphonons, in perfect agreement with symmetry predictions. Our bands compare satisfactorily with two of the four bands of the earlier spectrum at 2 K.10 We have not observed the additional bands reported a t 37 and 26.6 cm-I. The former has been assigned to inactive-infrared phonons appearing in the spectrum due to crystal imperfections.I0 We suggest that the 37-cm-I peak is spurious and probably due to absorption of the sapphire window present in the optical arrangement of the experiment.lo In fact a prominent sapphire peak at 386 cm-1 has been observed1" and in our own measurements we have found that below 25 K the far-infrared spectrum of a blank sapphire window shows an absorption band at 37 cm-I, in addition to that at 386 cm-1. As to the 26.6-cm-1 band, this has, according to ref 10, roughly the same intensity as that a t 58.5 cm-I and therefore should be easily seen also in our experiment. In our opinion, the discrepancy is related to the occurrence of interference fringes in the reported spectrum, as seems evident considering the band progression starting at 8.5 cm-l,10 This is a well-known effect of the far-infrared spectrum when the linear dimensions of optical elements along the beam path match the radiation ~ a v e l e n g t h . ~ ~ Lattice dynamics calculations are in good agreement with conclusions drawn from experiment. We have performed the calculation on the basis of our and n e u t r ~ n - s c a t t e r i n g data, ~~J~ using a slightly modified version of the Klein potential (see Table II).16 The results of calculation are summarized in Table 111for the most interesting points of the Brillouin zone. The equilibrium conditions with respect to the crystal structure and molecular rotations32 are satisfied with great accuracy. The sublimation energy has been estimated to be -45.0 kcal/mol at 100 K, considering the sublimation value a t 707 K, -40.1 k c a l / m ~ l e , ~ ~ and heat capacity data.26 As may be seen from Table 111, the agreement with experimental data is excellent. At k = 0 librons
calc 58.44 44.74 41.99 41.67 30.07 22.95 20.10 17.12 15.25
exP 58Sb)
sYm
calc 57.94 31.32 31.28 27.37 22.08 17.76
U U
41(b)
U
27@) 2 1(c)
g g g
expC 55 30 29 22 18
18@)
(I The potential derivatives at the experimental structure at 5 K32 with respect to the lattice constant and to the rotation angle about the [ 11 11 direction are, respectively, 0.5 kcal mol-' A-l and 0.04 kcal mo1-I rad-I. The calculated lattice constant and [ 11 11 rotation angle at equilibrium are 14.059 A and 98O, to be compared with the experimental values32 of 14.0408 A and 98O. Data from our spectrum at 8 K. Data taken from refs 14 and 15.
extend approximately from 15 up to 30 cm-I and translational phonons from 41 to 59 cm-l, with an intermediate energy gap of 11 cm-l. Thephonon bandsat 41 and58.5cm-Ihaveaverylow intensity, comparable to that of the lowest H, mode. This is not difficult to understand considering the mechanisms of infrared absorption in molecular crystals.39 The intensity of the infrared-active phonons is proportional to the squared derivative of the crystal dipole moment with respect to the translational phonons, being the dipole induced by multipole moments through the polarizability. However, considering c 6 0 as isolated system, all oddorder permanent moments are zero due to the inversion center while the first nonvanishing even-order multipole is the 64th pole. As the interaction field of the 64th pole depends on r7, the induced molecular dipole in the crystal may be reasonably neglected for any instantaneous configuration. On the other hand, we must consider that the c 6 0 molecule in the cubic lattice lies on Ss site symmetry and, as a result, may acquire a permanent small quadrupole moment with elements Qxx = QU, = -Qzz/2 (being z along the main cube diagonal). Since the molecular distortion is quite small, also the elements of the quadrupole moment (and hence the corresponding induced dipole components) are close to zero. However, the field strength decreases in this case with r3 and may induce an appreciable change of the induced dipole moment during a crystal vibration. It follows from these considerations that, being the phonon transitions quadrupoleinduced, their intensity should be comparable to that of the intramolecular H, modes. The relative intensity of the two Tuphonons may be estimated on the basis of the previous theory. The crystal dipole induced by site quadrupoles Q depends only on the molecular polarizability a and on Q as follows:39
P = 'I3aS3Q
(4)
where S3 is the third-order crystal propagation tensor .for quadrupolar interactions. The two translational phonons of Tu symmetry may be expressed as a linear combination of molecular rigid displacements tia as 4
T~=
3
7,y,ctjarja
i = 1,2
j = la- 1
where the j index runs over all molecules in the unit cell and a = x, y , z . Therefore the crystal transition moment is
Due to crystal symmetry, the (aP/arj.) quantities are not
Bini et al.
10584 The Journal of Physical Chemistry, Vol. 97, No. 41, 1993
force field.3’ Three important points have been considered by the present study: (1) H,molecular modes are observed in the infrared spectrum as a result of quadrupolar interactions. The intensity, comparable to that of weakest u modes, has been estimated from quadrupole transition moments and was found in good agreement with experimental data. (2) The two infrared active phonons of Tu symmetry are observed at 41 and 58.5 cm-I with weak intensity in good agreement with expectations. (3) The infrared spectrum of the high-temperature phase shows structured bands.
al
0
i
g J
References and Notes
320
360
400
440
Wavenumbers (cm-1) Figure 6. Infrared spectrum of crystalline Ca as a function of the temperature (265 and 245 K, from top to bottom) in the frequency range 300-470 cm-I.
- -
independent each from the other. When j j’, because of the interchange symmetry, (aP/arj,) (aP/arf,) = *(aP/atj,). For a given moleculej, it results (aP,/a,jJ = (aP,/at,,,) (aP,/ arj,) considering the small site distortion, and, in addition, all crossed derivatives, (aP,/dt,p), a # 8, are equal, within the same approximation. Defining (aP,/at,J = A and (aP,/arjp)= B (a # 8), the transition moment (aP/8Ti)depends on the sum of all the components of the phonon eigenvector weighted by A and B. Since the eigenvectors of the two Tuphonons are known from our lattice dynamics calculation, their infrared intensity, proportional to I(BP/dT)IZ,may be calculated as a function of A / B . Making the reasonable assumption A >> B, the intensity ratio for the two phonons 41 and 58.5 cm-I is found 0.57,to becompared with the experimental value 0.44. Temperature Dependence of the Far-Infrared Spectrum. Our spectrum depends strongly on temperature going through the temperature of the phase transition, 255 K.253 This can be best appreciated by inspection of Figure 6,where the infrared spectrum between 300 and 470 cm-I is shown at 245 and 265 K. The broad-band structure around 350 cm-1 observed at 265 K is split lowering the temperature in several components, fully resolved, as already noted in the last section, at 10 K. More dramatically, the H, band at 403 cm-l is found only in the low-temperature phase. Further cooling results in an improved resolution of all multiplets. On the other hand, the two spectra at 265 and 300 Karevery similar each to theother. From this it may beconcluded that the crystal has a discontinuous behavior with temperature between 245 and 265 K, in agreement with previous indications on the Occurrence of a phase transition at 255 K.25326 As it can be seen from Figure 6,the G, mode has a structured band above 255 K with a main peak at 355 cm-I and a shoulder at 360 cm-l, Le., a band profile reminiscent of the multiplet structure below the transition temperature. On the basis of the correlation diagram of the Th3 space group, only one single infrared band, Gaussian-shaped and broad, is expected for each molecular mode (except Au). This suggests that a partial order is present in the crystal phase at room temperature, due to a high percentage of symmetry related molecules. 5. Conclusions In this paper we have discussed the far-infrared spectrum of solid c 6 0 measured by FTIR spectroscopy under high-resolution conditions at several temperatures from 8 to 300 K. All the infrared bands in the frequency range 20-450 cm-l have been assigned. For most of them, a multiplet structure was observed and related to factor group splitting according to Th6space group. This assignment is substantiated by model calculations of site group splittings and of isotopic shifts using a previously reported
(1) Kratschmer, W.; Fostiropoulos, K.; Huffman, D. R. Chem. Phys. Lett. 1990, 170, 167. (2) Taylor, R.; Hare, J. P.; Abdul-Sada, A. K.; Kroto, H. W. J . Chem. Soc., Chem. Commun. 1990, 20, 1423. (3) Meijer, G.; Bethune, D. S. Chem. Phys. Lett. 1990, 175, 1. (4) Bethune, D. S.; Meijer, G.; Tang, W. C.; Rosen, H. J.; Golden, W. G.;Seki, H.; Brown, C. A.;deVries, M.S. Chem.Phys. Lett. 1991,179,181. (5) Cox, D. M.; Behal, S.;Disko, M.; Gorun, S.;Greaney, M.; Hsu, C. S.; Kollin, E.; Millar, J.; Robbins, J.; Robbins, W.; Sherwood, R.; Tindal, P. J . Am. Chem. SOC.1991, 113, 2940. (6) Chase, B.; Herran, H.; Holler, E. J . Phys. Chem. 1992, 96, 4262. (7) van Loosdrecht, P. H.; van Bentum, P. J. M.; Meijer, G. Phys. Rev. Letters 1992, 69, 1176. (8) van Loosdrecht, P. H.;van Bentum,P. J. M.; Verheyen, M. A.; Meijer, G. Chem Phys. Lett. 1992. 198. 587. (9) Ma& M.; Kuzmany, H. Appl. Phys. A 1993,56, 241. (10) Huant, S.;Robert, J. B.; Chouteau, G.; Bernier, P.; Fabre, C.; Rassat, A. Phys. Rev. Letters 1992, 69, 2666. (1 1) Coulombeau,C.; Jobic, H.;Bermer,P.; Fabre,C.;Schultz, D.;Rassat, A. J . Phys. Chem. 1992, 96, 22. (12) Prassides, K.; Dennis, T. J. S.;Hare, J. P.; Tomkinson, J.; Kroto, H. W.; Taylor, R.; Walton, D. R. M. Chem. Phys. Lett. 1991, 187, 455. (13) Neumann, D. A.; Copley, J. R. D.; Kamitakahara, W. A.; Rush, J. J.; Cappelletti, R. L.; Coustel, N.; Fischer, J. E.; McCauley, J. P., Jr.; Smith, A. B., 111; Creegan, K. M.; Cox, D. M. J. Chem. Phys. 1992, 96, 8631. (14) Pintschovius, L.; Renker, B.; Gompf, F.;Heid, R.; Chaplot, S.L.; Haluska, M.; Kuzmany, H. Phys. Rev. Lett. 1992, 69, 2662. (15) Pintschovius, L.; Chaplot, S.L.; Heid, R.; Haluska, M.; Kuzmany, H. Proc. Int. Winterschool on Electronic Properties of Novel Materials; Springer Series of Solid State Sciences, Springer, Berlin, in press. (16) Cheng, A.; Klein, M. L. J . Phys. Chem. 1991, 95, 6750. (17) Sprik, M.; Cheng, A.; Klein, M. L. J . Phys. Chem. 1992,96, 2007. (18) Lu, J. P.; Li, X.P.; Martin, R. M. Phys. Rev. Letters 1992,68,1551. (19) Yildirim, T.; Harris, A. B. Phys. Rev. E 1992, 46, 7878. (20) Heiney, P. A.; Fischer, J. E.; McGhie, A. R.; Romanow, W. J.; Denenstein, A. M.; McCauley, J. P.; Smith, A. B.; Cox, D. E. Phys. Rev. Lett. 1991, 66, 2911. (21) Sachindanandam, R.; Harris, A. B. Phys. Rev. Lett. 1991,67, 1467. (22) Tycho, R.; Dabbagh, G.; Fleming, R. M.; Haddon, R. C.; Makhija, A. V.; Zahurak, S.M. Phys. Rev. Lett. 1991, 67, 1886. (23) Samara, G. A.; Schirber, J. E.; Moronu, B.; Hanson, L. V.; Loy, D.; Sylwester, A. P. Phys. Rev. Lett. 1991, 67, 3136. (24) Chandrabas, N.; Shashikala, M. N.; Muthu, D. V. S.;Sood,A. K.; Rao, C. N. R. Chem. Phys. Lett. 1992, 197, 319. J.S.;Hare,J.P.;Prauides. (25) David,;W.I.F.;Ibberson,R.M.;Dennis,T. K. Europhys. Lett. 1992, 18, 219. (26) Jin, Y.; Cheng, J.; Varma-Nair, M.; Liang, G.; Fu, Y.; Wunderlich, B.; Xiang, X.D.; Mostovoy, R.; Zetti, A. K. J. Phys. Chem. 1992, 96, 5151. (27) Stanton, R. E.; Newton, M. D. J . Phys. Chem. 1988, 92, 2141. (28) Negri, F.;Orlandi,G.; Zerbetto, F. Chem. Phys. Lett. 1988,144,31. (29) Wu, Z. C.; Jelski, D. A.; George, T. F. Chem. Phys. Lett. 1987,137, 291. (30) Cyvin, S.J.; Brendsdal, E.; Cyvin, B. N.; Brunvoll, J. Chem. Phys. Letr. 1988, 143, 377. (3 1) Procacci, P.; Cardini, G.; Salvi, P. R.; Marconi, G. Mol. Cryst. Liq. Cryst. 1993, 229, 75. (32) David, W. I. F.; Ibberson, R. M.; Matthewman, J. C.; Prassides, K.; Dennis, T. J. S.;Hare, J. P.; Kroto, H. W.; Taylor, R.; Walton, D. R. M. Nature 1991, 353, 147. (33) Califano, S. Vibrational States, John Wiley: London, 1976. (34) Loudon, R. The Quantum Theory of Light; Oxford University Press: Oxford, 1983. (35) Bini, R.; et al., to be published. (36) Thecomment from the refereeon this point isgratefully acknowledged. (37) Bini, R.; Jodl, H. J.; Califano. S. Phys. Rev. E 1991, 45, 5244. (38) Pan, C.; Sampson, M. P.; Chai, Y.; Hauge, R. H.; Margrave, J. L. J . Phys. Chem. 1991, 95, 2944. (39) Califano, S.; Schettino, V.; Neto, N. Loitice Dynamics of Molecular Crystals; Springer-Verlag: Berlin, 1981.
