J . Phys. Chem. 1987, 91, 3494-3498
3494
C O , is calculated to be 4.0 kcal/mol if the dissociation energy of the (CO,),+ complex is determined from the C,, structure at the [MP4SDQ/6-31G*] ZPC level (12.0 kcal/mol). The experimental valuesI4 for complete dissociation and dissociation of one C 0 2are 23.0 and 7.4 kcal/mol, respectively. The calculated entropy change of 47.9 cal mol-' K-'is 26.6 cal mol-' K-'greater than the dissociation of one C 0 2 from (C02),+ (Table VII). This value compares favorably with the experimental valueI4 of 42.5 cal mo1-I K-'for the sum of the first two steps and 23.4 cal mo1-I K-' for the entropy change of the second step.
+
ConcIusion A study has been made of the energetics of clustering in C 0 2 . The neutral (cO2), complex is more stable in a c2h symmetry structure and is bound by 1.3 kcal/mol. The (C02)2+ion complex displays two types of binding. In the C2, ion complex the interaction is an ion-induced dipole interaction while the ion complex is bound by a 2-center 3-electron bond. The structure is predicted to be 4.4 kcal/mol more stable but higher levels of correlation could favor the Cz0 structure relative to the cz), structure. The fact that photoionization and thermodynamic
c,,
c,,
determinations of the dissociation energy disagree may indicate a large geometry change upon ionization. From a comparison of the C2h and the C,, symmetry ion complexes, it is clear that both involve large changes in geometry from the C2h symmetry neutral dimer. Therefore differences in the photoionization and thermodynamic dissociation energies cannot be used to determine which complex is more likely. Higher levels of theory will be required before a definitive prediction can be made for the structure of this ion complex. The trimer ion is predicted to be of DZhsymmetry. The first C 0 2 is calculated to be bound by 12.0 kcal/mol while the second C 0 2 is bound by 4.0 kcal/mol, which is in reasonable agreement with experimental values corrected to 0 K (15.6 and 7.4 kcal/mol, respectively). The entropy change for dissociation of C 0 2 from (C02)2+is calculated to be 21.3 entropy units while dissociation of one CO, from (CO2)3+ is 26.6 entropy units.
Acknowledgment. M.L.M thanks the Auburn University Computer Center for a generous allotment of computer time and internal grant 86-71 for financial support. This work was partially support by a grant from the National Science Foundation (CHE83-12505).
An Infrared and Raman Study of the Isotopic Species of a-Quartz Robert K. Sato* and Paul F. McMillan Department of Chemistry, Arizona State University, Tempe, Arizona 85287 (Received: February 9, 1987)
We have obtained Raman and infrared spectra for the 28/30 Si and 16/18 0 isotopic species of a-quartz. The isotopic frequency shifts give valuable information on atomic participation in individual vibrational modes. Comparisons of our isotopic shifts with displacement patterns predicted from a number of dynamical calculationshave been made. Most calculated modes agree well with the observed isotope shifts, but some do not. For example, the strong Raman line at 464 cm-' shows no silicon displacement but a large oxygen shift, consistent with its usual assignment to a motion of the bridging oxygens in the plane bisecting the SiOSi linkage. However, the soft mode at 206 cm-', which is commonly accepted as being due to motion of Si and 0 around a 3-fold screw axis related to the a+ displacive transition in quartz, shows no Si isotope shift and hence no silicon participation in this vibration.
Introduction The dynamics of a-quartz have been the subject of considerble experimental and theoretical study. This phase is of particular interest since it forms the simplest crystalline silicate, and also because it shows a displacive phase transition associated with soft phonon behavior to the (?-form at 575 OC.I In the present study, we have applied the classic technique of isotopic substitution to gain a better understanding of the atomic displacements associated with k = 0 vibrational modes in a-quartz. Quartz is an excellent candidate for an isotopic substitution experiment since there are only two atom types, Si and 0,each of which has a stable substitutable isotope, and all of the vibrational modes at k = 0 are optically active (species AI, A2, and E). In this paper, we report infrared and Raman frequencies for 28Si180,,and 30Si1602 isotopic species of quartz. the zsSi1602, Experimental Section The 28Si1602 sample was prepared by gelling Si(OC,H,), (TEOS) with doubly distilled, deionized H 2 0 . The gel was fired at 1000 O C for 12 h, and then loaded into a platinum capsule with a trace of ultrapure H 2 0 . The mix was crystallized hydrothermally at 500 OC and 1 kbar for 1 week in a cold-seal pressure vessel to obtain a-quartz. This was verified by optical microscopy and (1) Sosman, R. B. The Phases ofSilica; Rutgers University Press: New Brunswick, NJ, 1965.
0022-3654/87/2091-3494$01.50/0
by Raman spectroscopy. The well-formed, terminated crystals were 20-50 pm in dimension. The "Si and I60 were present in their natural abundances (92.18 atom % and 99.757 atom %, respectively). Powdered 30Si02(95.2 atom % 3?3) was purchased from MSD Isotopes. The amorphous material was crystallized hydrothermally at 500 OC and 1 kbar for 1 week to give a-quartz. The Si1802 starting material was prepared by hydrolyzing SiCI4 with H2I80(99 atom % I 8 0 ) , obtained from MSD Isotopes. This was carried out in a drybox under an atmosphere of dry N, to powder avoid contamination with atmospheric oxygen. The Si1802 was then loaded into a platinum capsule with H2Is0. This sample did not crystallize quartz under the same hydrothermal conditions as the samples above, but consistently gave cristobalite.2 a-Quartz was obtained by hydrothermal treatment at 400 OC and 4 kbar for 48 h in an internally heated argon gas pressure vessel. Raman spectra were obtained with an Instruments S.A. U- 1000 Raman system, using the 5145-A line of a Coherent Innova 90-4 argon laser for sample excitation. The microassembly (using 50X and lOOX Olympus objectives) was used due to the small sizes of the samples. Laser power at the sample ranged from 5 to 50 mW, and the instrumental slit width was 200 wm, corresponding to a spectral band-pass of near 1.8 cm-I. The absolute wavelength scale of the spectrometer was calibrated against the emission lines of atomic Hg and Ne. Individual spectra in the present study (2) Carr, R. M.; Fyfe, W . S. A m . Mineral. 1958, 43, 908.
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3495
Isotopic Species of a-Quartz
s102
L ,
1200
,
,
1050
do0
d
d
' 150 ' URVENUMBERS
600
450
400
Figure 2. Infrared powder transmission spectra for a-quartz, Si02, )OSiO,, and SiI8O2.
N
provided by a He-Ne laser. The KBr disks were dried overnight in a vacuum oven at 115 "C to remove traces of adsorbed surface water.
Results and Discussion
250
500 RAMAN
750
SHIFT
io00
1250
( ~ n - ~ )
Figure 1. Raman spectra for isotopic species of a-quartz, S O z ,30Si02, and Sit802.(Note: the frequencies listed in Table I were not taken from the spectra in this figure, but from high-resolution scans over individual peaks as described in text.)
used plasma lines from the Ar laser and Hg lines from the laboratory fluorescent lights as internal standards. Each Raman peak was scanned 20-30 times wifh 0.2-cm-' steps. Reported Raman shifts are given as the mean of these measurements, and errors are reported as 2 standard deviations of the mean (Table I). Fourier-transform infrared spectra were run on pressed KBr disks on a Nicolet MX-I interferometer, with internal calibration
Observed infrared and Raman spectra for the three isotopic species of quartz studied are shown in Figures 1 and 2 , and peak positions are summarized in Tables I and T I . Factor group analysis3 gives the k = 0 species as
r
= 4A1(R)
+ 4A2(TR) + 8E(R+IR)
where R and IR denote Raman and infrared activity respectively. All of the E modes are split at the zone center into transverse and longitudinal components. Since a-quartz is not centrosymmetric, this TO-LO splitting is also observed in the Raman spectrum. In the present study, we observed all Raman-active modes for all isotopic species, except for the weak E ( l ) component near 1200 (3) Fateley, W. G.; Dollish, F. R.; McDevitt, N. T.; Bentley, F. F. Infrared and Raman Selection Rules f o r Molecular and Lattice Vibrations: The Correlation Method Wiley-Interscience: New York, 1972.
3496
The Journal of Physical Chemistry, Vol. 91 No. 13, 1987
Sato and McMillan
TABLE I: Raman Frequencies (cm-I) for SiO,, %io,, and Si'80zand Corresponding Isotopic Shift Values E(t) A1
+ E(1)
E(t) + E(1) AI
E(t) E(]) AI
E(t) + VI) E(t) E(1)
E(t) AI
E(t) + E(1) E(1)
Si02
'OsiOz
128.0 f 0.2 205.6 f 1.2 263.1 f 0.4 354.3 f 0.1 393.8 f 0.1 401.8 f 0.2 463.6 f 0.3 697.4 f 0.9 796.7 f 0.5 808.6 f 0.6 1066.1 f 1.1 1083.0 f 0.3 1160.6 f 0.9 1231.9 f 1.4
127.5 f 0.2 205.5 f 0.7 262.3 f 0.3 348.8 f 0.4 390.1 f 0.6 397.8 f 2.5 463.4 f 0.3 681.1 f 0.8 778.8 f 0.6 790.1 f 1.6 1058.1 f 1.0 1075.3 f 1.0 1 156.4 f 0.3 1220.8 f 1 . 1
A0 -0.5 -0. I -0.8 -5.5 -3.7 -4.0 -0.2 -16.3 -17.9 -18.5 -8.0 -7.7 -4.2
si'*o2 120.1 f 0.2 192.6 f 0.4 250.4 f 0.3 346.8 f 0.2 379.9 f 0.4 384.7 f 0.3 442.8 f 1.0 684.7 f 0.6 787.1 f 0.9 795.8 f 0.6 1027.7 f 2.2 1046.2 f 1.5 1109.7 f 0.8
A0 -7.9 -13.0 -1 2.7 -7.5 -13.9 -17.1 -20.8 -12.7 -9.6 -1 2.8 -38.4 -36.8 -50.9
-.ll.l
"Shift from 28Si'602 TABLE 11: Infrared Data for SiO,, %io2, and Si'802from Spectra (Figure 2) and Corresponding Isotopic Shift Values Ac Si''0, SO2" S i 0 2 b '"SiOZ Ac E 797.0 797 776 -21 789 -8 A,
E E A2
777.0 695.0 393.5 363.5
778 694 397 370
753 682 394 363
-25 -12 -3 -7
712 686 380 354
-6 -8 -17 -16
"Reference 6; TO frequencies from reflectance study. *This study (powder transmission minima). CShiftfrom 28Si1602. cm-I for SiIg02,and the E(t)-E(l) pair at 450/509 cm-1,4which is hidden by the strong A , mode (Figure 1). The infrared data (Figure 2) are complicated by the fact that they were obtained for powdered samples. This scrambles mode symmetries and gives an unknown mix of absorption and reflectance components in the spectra, resulting in distortion of the peak shapes and generally shifting peak positions to higher wavenumber, especially for strong infrared modes5 T o evaluate the extent of this problem, we have compared our powder results for normal isotopic quartz (2gSi1602) with the TO mode frequencies obtained from the reflectance study of Gervais and Piriou6 (Table I). The A, mode near 778 cm-' and the E modes near 397,694, and 797 cm-l (positions for the normal isotopic species) correspond to fairly weak oscillators6 which are generally well separated from other modes in the spectrum; hence their positions may be reliably estimated from the powder spectra, while the A2 mode at 370 cm-' also appears as a sharp distinct peak in the transmission spectra (Figure 2). The transmission minima measured for these peaks in the present study compare well with the TO mode frequencies obtained in the reflectance study of Cervais and Pirioq6 while there is good agreement between the infrared and Raman determinations of the E(t) mode frequencies in the present study (Table I). The magnitudes of the silicon isotopic shifts range up to 26 cm-I, while the observed oxygen shifts range up to near 50 cm-I (Table I ) . The dominant A , Raman line at 464 cm-' and the A , soft mode at 206 cm-l show no measurable silicon participation within experimental error (the error limits on the soft mode frequency are larger than for the other A , Raman lines, since this peak is so broad at room temperature), while the E modes at 128 and 263 cm-l show only minor silicon shifts. These modes must be associated with little or no silicon displacement. The E modes near 697-809 cm-' show the largest silicon shifts and are associated with considerable silicon displacement. The above observations are generally consistent with simple dynamical models for crystalline and amorphous S O 2 ,which suggest that the 464-cm-' peak is associated with predominantly oxygen motion in the plane bisecting the SiOSi linkage and the modes near 800 cm-' with (4) Scott, J. F.; Porto, S . P. S. Phys. Rec. 1967, 161, 903. (5) Sherwood, P. M. A. Vibrational Spectroscopy of Solids: Cambridge University Press: Cambridge, U.K., 1972. ( 6 ) Gervais, F.; Piriou, B. Phys. Rec. B 1975. 1 1 , 3944.
41) + 41) 128 cm-1
4 1
-0.5
60 -7.9
Figure 3. Selected eigenvectors from a valence force field calculation of k = 0 modes of a-quartz, from work by Mirgorodskii et al.9 Filled circles, Si; open circles, 0. Values at bottom of each figure are the observed isotopic shifts (in cm-') from normal Si02.
asymmetric stretching vibrations of silicon against its tetrahedral oxygen cage.' The present work shows, however, that the 800cm-' modes also have quite large oxygen displacements. The high-frequency modes above 1060 cm-I show large oxygen displacements and moderately large silicon shifts. Again this is consistent with simple vibrational models for SiO, polymorphs, which suggest that these modes are due to asymmetric Si-0 stretching motions within the SiOSi linkages.' There have been a large number of dynamical calculations for a-quartz and related S i 0 2 I n a few of these ( 7 ) McMillan, P. Am. Mineral. 1984, 69, 622. (8) Boysen, H.: Darner. B.; Frey, F.; Grimm, H. J . Phys. C 1980, 13,6127. Elcombe, M. Proc. Phys. Soc. 1967, 91, 947. Kleinman, D. A,; Spitzer, W. G. Phys. Rec. 1961, 125, 16. Saksena, B. D. Proc. Indian Acad. Sci. 1944, ,419. 357.
The Journal of Physical Chemistry, Vol. 91, No. 13, 1987 3497
Isotopic Species of a-Quartz
A2 794 cm'' (778)
A1 modes 464 cm.1
206 c m.1
a
&Si A1
A1
464 cm-1 206 cm-l
-0.2 -0.1
A 0 -20.8 -13.0
Figure 4. Calculated displacement patterns for two modes of a-quartz by Etchepare et a1.I0 Values at bottom of each figure are the observed isotopic shifts (in cm-I) from normal SO2. Filled circles, 0 open circles, Si.
studies, the authors have presented calculated atomic displacement patterns for individual vibrational modes, permitting a qualitative comparison with the present isotopic data. Mirgorodskii and co-workersg carried out a valence force field calculation for the k = 0 modes of quartz, and published a complete set of calculated eigenvectors. In general, these agree well with the present isotopic substitution data, except for the A2 mode at 778 cm-l and the A I soft mode at 206 cm-l (Figure 3). For the A2 mode, Mirgorodskii and co-workers indicate moderate and similar amounts of both silicon and oxygen motion in their displacement patterns, while we find essentially no oxygen motion but a large silicon displacement (Table 11; Figure 2). For the A, soft mode, the opposite is true: Mirgorodskii et al. predict both oxygen and silicon displacements, while we find no silicon participation in this mode. Etchepare and co-workers10 have published displacement patterns from a valence force field calculation for two A , modes occurring at 464 and 207 cm-I (Figure 4). The results of our isotopic substitution study agree with the displacement patterns of the 464-cm-I m o d e s m a l l silicon participation and large oxygen displacement-but again we disagree with the calculated atomic displacements for the A, soft mode (Figure 4). In a related publication, Etchepare" has further presented eigenvectors for the A2 mode at 777 cm-l and finds that this mode is associated with large silicon displacement but small to moderate oxygen displacement. This is in good agreement with our measurement (Figure 5). Finally, Bates12has published atomic displacement patterns for the related phase @-quartz (Figure 6). The three 6-quartz modes, A, (465 cm-I), E, (1063 cm-I), and E2 (407 cm-') correlate with the three a-quartz modes A, (464 cm-I), E (1066 cm-I), and E (394 cm-I), respectively. For each of these three modes, Bates indicates very small to no silicon participation but moderate oxygen participation. Our isotopic study agrees quite well with the calculations performed by Bates. All of the vibrational calculations considered above seem to reproduce at least qualitatively most of the observed isotopic shifts, (9) Mirgorodskii, A . P.: Lazarev, A. N.; Makarenko, 1. P. Opt. Spectrosc. 1970, 29, 289. (10) Etchepare, J.; Merian, M.; Smetankine, L. J. J . Chem. Phys. 1974, 60, 1873. (1 1) Etchepare, J. These d'Etat, UniversitC de Paris VI, 1975. (12) Bates, J. B. J . Chem. Phys. 1972, 56, 1910.
'Si
*O
m 25
-6
Figure 5. Calculated displacement patterns for one A2 mode of a-quartz predicted by Etchepare to exist at 794 cm-'.'I Value in parentheses is from this study. Values at bottom of figure are the observed isotopic shifts (in cm-I) from normal SiO,. Filled circles, 0; open circles, Si.
suggesting that the major terms in the force fields used may be realistic, although it is possible that modes for which calculated eigenvectors were not published show large deviations from our experimental data. We also note that none of the calculations reproduce all of our observed isotopic shifts, showing that some features of each force field cannot be realistic. One discrepancy common to all dynamical models for quartz which we have examined lies in the calculated atomic displacements for the soft A, mode with frequency near 206 cm-' at room temperature. This mode is regularly calculated to involve both silicon and oxygen displacements around the 3-fold screw axis (c axis) in quartz, while we find no silicon participation in this mode. This point is discussed further below. We suggest that the force fields used in future dynamical calculations on quartz and related silica polymorphs may be further refined by use of the present isotopic data. The Teller-Redlich product rule is commonly used to formulate and describe isotopic ratios for the vibrational modes of plyatomic molecule^.'^ This rule states that the isotopic ratio for each symmetry species i is given by the ratio of the product of all mode frequencies within that species rI(U'/U),
= II(m/"),'/2
where w'/w is the frequency ratio (0' refers to the heavy isotope) ( 1 3) Herzberg, G.Molecular Spectra and Molecular Structure. [I. Infrared and Raman Spectra; Van Nostrand Reinhold: New York, 1945.
Sat0 and McMillan
3498 The Journal of Physical Chemistry, Vol. 91, No. 13, 1987
LXb
2
e, mode
1063cm.2
e mode
2
398cm.1 I
Y L
X
Y -X
I
Figure 6. Calculated atomic displacement patterns for three modes of @-quartz by Bates.12 Filled circles, 0; open circles, Si.
and m/m’ is the mass ratio for the isotopic substitution. For quartz, although other points and directions within the Brillouin zone have high symmetry, only the zone center (r point) has symmetry D,,so that zone center vibrational species do not mix with other points in the Brillouin zone. We can compare the calculated Teller-Redlich products with our observed shifts for the zone center A, and E species, for 160/’80 and 28Si/30Si isotopic substitutions. The 30/28 Si and 18/16 0 isotope ratios observed for the A, modes are 0.9766 and 0.8460, respectively, higher than the expected values of 0.871 1 and 0.7901. This is due to the large effect of anharmonicity on the lattice vibration^,'^ which is expected in view of the observed mode softening and the occurrence of displacive phase transitions in quartz. Our data for the E modes are not complete since we did not observe the T-L pair at 450 and 509 cm-’ or the E, component near 1200 cm-’ for the Si1802 sample. Using our observed frequency data, we find 30/28 Si and 18/16 0 isotope shifts of 0.9287 and 0.7705 for the transverse, and 0.9264 and 0.7900 for the longitudinal E components, respectively. The theoretical (harmonic) isotope ratios for these modes are 0.7588 (Si) and 0.6243 (0). We noted above that previous dynamical calculations for aquartz consistently predict atomic displacements for the A, soft mode involving large oxygen and silicon motions around the triad axis,8-12in contradiction with our isotopic results. This mode was
first noted to soften with increasing temperature by Raman and Nedungadi,I4 who suggested that the atomic displacements of this vibrational mode might drive the a-/3 phase transition in quartz at 585 OC. This suggestion was a precursor of Cochran’s soft mode theory15 for displacive phase transformations, and considerable theoretical and experimental work has since been carried out on the dynamics of the transition in quartz. Most of the dynamical calculationss-’2J6suggest that the atomic displacements associated with this mode do in fact correspond to the silicon and oxygen displacements necessary to transform a into p quartz. The most recent experiments show that the transition is not a simple one between the a and p phases but involves a suite of incommensurate phases in the transition region.” The appearance of these incommensurate phases is associated with interactions between the soft optic phonon and acoustic branches close to but not exactly at the Brillouin zone center. Although the mode softening in quartz and its relation to the phase transition is more complex than originally t h o ~ g h t , ” ~it ’remains ~ important to understand the atomic displacements associated with the soft mode near k = 0, and the reasons for its large anharmonicity. As noted above, we find no silicon displacement associated with the soft mode. In discussions of the dynamics of quartz and the displacive phase transformation, it is common to assume that the Si04tetrahedra in the quartz remain rigid throughout the transition and that low-frequency modes involve some relative rotation or torsion of the tetrahedra about the SiOSi linkages.lg In a recent ab initio molecular orbital study, Hess and co-workersZ0have found that low-energy HOSi torsional motions in the prototype silicate molecule H4Si04were sufficient to cause large distortions in the OSiO angles (between 103 and 116 “C). If intertetrahedral torsional motions in quartz are similar, these torsions might also drive OSiO angle bending in the crystal and may be related to the A, mode softening. This possibility will be pursued in a future study of the lattice dynamics of quartz.
Acknowledgment. The present work was supported by N S F Grant EAR-8407105 and a Cottrell Research Grant from the Research Corp. We thank J. R. Holloway and J. Webster of Arizona State University for their assistance with hydrothermal syntheses, and M. O’Keefe for useful discussions. (14) (15) (16) (1 7)
Raman, C. V.; Nedungadi, T. M. K. Nature 1940, 145, 147. Cochran, W. Adu. Phys. 1961, 9, 387. Axe, J. D.; Shirane, G. Phys. Reu. B 1970, I , 342. Dolino, G.; Bachheimer, J. P.; Zeyen, C. M. E. Solid State Commun. 1983, 45, 295. Dolino, G.; Bachheimer, J. P.; Berge, B.; Zeyen, C. M. E. J . Phys. 1984, 45, 361. Dolino, G.; Bachheimer, J. P.; Berge, 8.; Zeyen, C. M. E.; Van Tendeloo, G.; Van Landuyt, J.; Amelinckx, S. J . Phys. 1984, 45,901. Dolino, G. Jpn. J . Appl. Phys. ,1985, 24, 1 5 3 . Berge. B.: Bachheimer. J. P.: Dolino., G.:, Vallade. - ,M. - - Ferroelectrics 1985. 66. 73. (18) Scott, J. F. Phys. Reo. Lett. 1968y21, 9071 (19) Boysen, H.; Dorner, B.; Frey, F.; Grimm, H. J . Phys. C 1980, 13, 6127. Buchenau, U.;Prager, M.; Nucker, N.; Dianoux, A. J.; Ahmad, N.; Phillips, W. A. Phys. Reu. B 1986, 34, 5665. (201 Hess. A. C.: McMillan. P. F.: O’Keefe. M. J . Phvs. Chem. 1986. 90. 5661. Hess, A. C.; McMillan, P. F.; OKeeffe, M. EOS, Trans. Am. Geophys: Union 1986, 67, 1275. ~
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