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Raman and far infrared spectra of the solid phases of carbon tetrachloride
Volume 61, number 1
RAMAN
CHEMICAL
AND FAR INFRARED
A. ANDERSON,
B.H. TORRIE
SPEaRA
PHYSICS
1 February
LETTERS
OF THE SOLID PHASES OF CARBON
1979
TETRACHLORIDE
and W.S. TSE
Department of PlzFsics. Unir’ersitv of Waterloo.
Waterloo.
Ovtario.
Carzada
Received 1 November 1978
The hdtice vtbmtlons of carbon tetrachloride have been studied by Raman and infrared spectroscoptc techniques oter the temperature range 18 K to the melting point at 2.50 K. Comparisons are made aith previous results on CCli and other tetrahedral molecules, and the observed peaks for the monoclinic phase II are assigned = tnmshtional modes.
1_ Introduction At saturated vapour pressure, carbon tetrachloride is known to e.xist in three solid phases [ l-41 _The liquid freezes to a face-centred cubic solid at 250.3 K (phase Ia). When these crystals are maintained between 250.3 and 223.5 K for several hours, they transform spontaneousIy to a rhombohedra1 phase (nhase lb)_ At temperatures beiow 225.5 K, both the metastable cubic phase and the rhombohedrai phase transform to a monoclinic phase (phase II). The cubic Table 1 Cryst;tllogmphic
data for carbon termchloride ---
Phase
Twnsition poinr
In
T = 250.3 K
I__
--__
-~
Type ____
-_
fwe-centred rhombohedml
Ib 7-=2L?55K or T=3GOK ( p =64kbar
monoclinIc
III
T=3GOK p = 10 kbbar
monoclmic
IV
T>533K p > 2Okbar
cubic?
II
in nature, with the molecules rotating about their centres of mass. In the other two phases, the molecules are expected to be more hig_hly ordered, but the exact structures are not known_ Under high pressures, two new phases (III and IV) of Ccl, have been observed [1,4]. In addition, spectroscopic evidence of a phase change at saturated vapour pressure and Iow temperatures has been reported by Shurvell [5] and wiI1 be discussed later. Crystahographic data for the phases Ia, Ib, II and III are summarized in table I_ phase is plastic
-----
cubic
Space group and number of molecules i=
4
Lattice constants _-_-_a=
8.34 A
==21
a = 14-4 OI= 90.0”
x
c2/c a = 31
a = 20.3 b= 11.6 c = 19.9 p = 111”
X A A
PZ,iC
a= b =
-=
f
4
9 079 A 5.764A C= 9.201 _s 13= 104.29” ?
119
Volume 61. number I
CHEMICAL
1 Febrllltry 1979
PHYSICS LETIERS
The present work was undertaken to clarify the nature of the solid phase transitions occurring at saturated vapour pressure. Previous Raman studies are described in refs. [S--8]. No previous far infrared investigations of the solid have been found in the literature_
2. Experimental
techniques
Raman spectra were recorded using a standard 90“ scattering conliguration. The light source was a Spectra-physics 155 3rgon ion laser opemting 3t OAW on the 5 145 _S line_ Scattered light was snalyzed using 3 Spex 1-N 1 double monochromator, coupIed to a Spex I-?42 third monochrom3tor, 3nd detected with sn RCA 31034 photomultiplier, cooled by a flow of nitrogen g3s. The output pulses were fed to a D2t3 Genenrl Nov3 Z/IO computer rind subsequently displayed on a stor3ge oscilloscope or X-Y plotter_ F3r infrsred spectrs were obtained by interferometric techniques using 3 Fourier spectrophotometer (RIIC-Beckman, model FS-620)_ A high pressure mercury lamp was used as source and a germanium bolometer operating at 4.2 K as detector. Output signals were digitized and fed to the Nova Z/IO computer where they were transformed and ratioed with background intensities_ Interferograms were typicaily of 500 points on each side of centre, corresponding to an instrumental resolution of 2-5 cm-l _ Samples for R3man and infrared studies were prepared by v3por.u deposition on to a substrate at SO K. followed by annealing 3t approximately 150 K. Because ofemporatron, these samples were suitabie only for low tempemture studies of the monoclinic phase II. Samples were also grown by slowly cooling bulk samples of the liquid, and these were used for Ramm studies of311 three norm31 pressure phases.
3_ Results and discussion When the bulk samples of CCI, were carefully cooled, they formed a transparent solid, which was 3ssumed to be in the cubic phase (la)_ The low frequency Raman spectrum from such 3 s.rmpIe is shown in fig. la_ When these samples were cooled to 250 K and kept at this temperature for approximately 3 h, they suddenly developed cracks, indicating that 3 first or120
I
20
a0 40 FREQUENE I CM-‘)
loo
Fig. I _The low frequenc?i Rnm3n spectrum as a function rempmture.
of
der transition to the rhombohedral phsse (lb) h3d occurred. The lattice spectrum of this new ph3s.e is shown in figs. lb and Ic_ When samples in either the cubic or rhombohedral phases were cooled below 3-25 K, further crscking xxas observed, 3s the first order transition to the monoclinic phase II took place. Raman spectra of bulk samples in this phase are shown in figs_ Id-1 f. Raman and infrared spectra of the vapour deposited samples in the monoclinic phase are shown in rigs_ 1 and 3 respectively_ Raman spectra of the intern31 modes of Ccl, in the monoclinic phase were also recorded at temperatures between IS K and SO K, but these were not subst-3ntially different to those of Shurvell [S] at liqurd nitrogen temperatures, and details will not be repeated here_ It is important to note, however, that there was no evidence of a further phase transition 3t low temperatures, 3s reported by Shurveli 151, from any of our spectra: infrared or Raman, internal or Iattice regions, bulk or annealed powder samples_ Previous experiences with HI [9] and HBr [lo] have shown that a disordered state may be produced in thin film samples deposited at very low temperatures, presumably as the result of strains in the films, but this effect is not seen with bulk samples
CHEMICAL PHYSICS LEl-TEiZS
Volume 61, number 1
1 February 1979
An attempt was made to obtain re-orientatlonal relaxation times by fitting a Debye function to the Rayleigh wings shown in fig_ 1 [ 11] _ The spectra at 240 K for the face-centred cubic and rhombohedral phases and that at 223 K for the monoclinic phase were used for this analysis_ Relaxation times of the order of 1O-12 s gave reasonable fits, but the problem of separating out a background spectrum made it impossible to obtain times which were accurate enough tc; clearly distinguish one phase from another. The fact, however, that no clearly defined lattice modes are observed in either the cbbic or rhombohedral phases strongly suggests that these structures are both orientationally disordered_
4.
20
40
60 FXQUENCY
80 (CM-’
IOC
I
Pig.. 2. The low frequency Ram~n spectrum of the monoclinic phase at 18 KS indwates z plasma line.
7
1
50 FREQUENCY
(CM-‘,
80
Fig. 3. The far infrared spectrum of the monoclinic
-l Ill 3
phase_
Lattice
modes for the monoclinic
phase
The observed lattice mode frequencies are listed in table 2, and compared w?th the Raman frequencies reported by Nevzorov and Sechkarev [6] and Ebisuzaki [S], the latter for samples at elevated pressures_ There are obvious similarities between the results of the Raman studies, both in frequency listings and spectral band shapes, indicating that both high pressure phases and the low temperatures monoclinic phase are closely related. The complete phase diagram for Ccl, is not yet avadable. and it is not definitely known, for example, which of the high pressure phases are stable at low temperatures and saturated vapour pressure, although it seems probable that only phase II fits this category_ The rather drastic ch%nges observed in the lattice spectrum of phase II as the temperature is lowered suggest that an ordering process is taking place, probably a decrease in the rotational amplitudes of the molecules_ It is also possible that in phase II, molecules on certain sites continue to rotate freely, whereas others switch to hbrational motion, as in the case of methane [I21 _Another point of interest is that the Raman spectrum of the vapour-deposited sample at 1 S K, although obviously similar to that of the bulk sample at 28 K, has much sharper peaks, with frequencies a few cm-t lower. Normally one would expect slightly higher lattice frequencies at lower temperatures, as the lattice contracts and intermolecular forces strengthen. The method of crystal growth and its thermal treatment are clearly very sensitive factors influencing the spectra, an extreme example of which is the disorder-
121
Vo!ume 61, number 1
CHEMICAL
1 February1979
PHYSICS LE-ITERS
Table 2 Infrared and R~‘IZUI Lpectra of monoclinic carbon tetrachioride lattice region (in cm-‘) l-his
wxk
(phasez11) I
Previous u ork (Raman)
Raman
infrared
f8Ka~ 28K 8@K3 (otttrated wpour pressure)
i8Ii
a)
8OKi3
242
28 343 423 415 53.6 65.7
26 295 38 45 54 59 -
T= 300K p = 10 kbar [8] III
T=80K p=o 11
161
--
-
245 29 36 43 50.5 555 665
T= 300K p = 6.4 kbar [8] II
40 44
39 42 5
58 b)
56
27
24 30 39 48
43 46
36 44
60 97
59 74 97
56 68 98
a) Porbder nmples: other data from bulk crystals. b, An additional infrared peak at 65 cm-’ IS _ of doubtful origin since it sbo\\ed no temperature dependence.
ed state observed at Iow temperatures by Shurvell IS] _ The space group of Ccl, II is reported to be Cc or C& with a large unit cell containing 32 molecules on general (C,) sites [Z?,S]_?hsse III on the other hand has only 4 molecules in the unit cell, with space group @t/c [4!_The Raman spectra of phases II and iI at elevated pressures, recorded by Ebisuzaki [Sl) are very similar, indicating that any differences between the two structures are small. These spectra and our present results are all more consistent with a smal:er unit cell. However, many of the individual peaks predicted in the richer spectrum for the large unit cell would probably be unobservable because of overlap effects_ The group theoretical analysis for the smaller unit cell, PZr/c, based on the well-known correlation method [ 131 predicts 9 infrared lattice modes (3 of translational and 6 of hhrational origin) and 12 noncoincident Raman modes (6 of each type)- Because of the low symmetry. mixing between fransIational and librational modes of the same species is possible, so that the above labeliing is not exact_ For these near-spherical moIecules, it is expected that librational modes will involve only small changes in the electricaY dipole and polarizability derivatives,
points: served modes, to the
for crystalline CH* and CD, (phase II) the obfar infrared spectra derive from translational since their frequencies ratios are proportional ratios of the square roots of molecular masses
rather than moments of inertia [14]. Secondly, the far infrared spectrum and structure of crystalline CF4 phase II !lS] are very similar to those of Ccl, II, with corresponding frequencies also scaling according to the square roots of the molecular masses. Preliminary results from this laboratory on other solid tetrahalides of similar structure (GeCI,. Tic?, and SiC14) also fit this pattern [ 16]_ Finally, excluding the weak peak at 66 cm-l, the observation of 3 infrared and 6 Raman non-coincidental peaks is precisely that predicted for translations based on the smaller unit cell. It is clear from the above discussion that further research on solid Ccl, is needed, before a fuller understanding of its various crystalline phases is obtained_ In particular, completion of the phase diagram at low temperatures using X-ray and calorimetric techniques, and NMR studies of the molecular motions in all phases would be useful_
and hence the infrared and Raman intensities will be
Acknowledgement
low. The obsemed lattice spectra are therefore postulated to involve primarily translation;rI motions- This assignment is supported by the following additional
Financial support from the National Research Council of Canada is gratefully acknowledged_
122
Volume 61. rsmber 1
CHEMICAL
References [l] P-W. Bridgman, Phys. Rev. 3 (1914) 153. [2] R_ Rudman and B. Post. Science I54 (1966) 1009. [3 ] C-E_ Weir, G.J. fiermarini and S. Block, f_ Chem. Phj s. SO (1969) 2089. [4] G-J. Piennarini and A.B. Braun, J. Chem. Phys 58 (1973) 1974. (51 H-F. Shurvell, Spectrochim. Acta 27A (1971) 2375. [6] B-P- Nenorov and A-V. Sechkarev, Soviet Phys. 3.14 (1971) 199. [7] 1.1. Kondilenko. P-A_ Korotkov and GC_ Litvinov, opt. spectry. 30 (1971) 51. [S J Y. Ebisuzrtki, Proceedings of the International Conference on Lattice Dynamics, Paris (1977) p_ 505,
PHYSICS LE’ITERS
1.February 1979
[9] A. Anderson, B.W. Torrie and W.S. Tse, to be published_ [lo] R. Savoie and A. Anderson, J. Chem. Phys_ 44 (19 66) 548_ [ll] 1-L. Fabelinskii, hfofecular scatterm of tight {Plenum Press, New York, 1968) p_ 110. [12] W. Press, J. Chem. Phys. 56 (1972) 2597; Acta Cryst. A29 (1973) 257, [ 131 W-G. Fate&. F-R_ Dolhsh. N-T_ McDevitt and F-f_ Bentley. Infrared and Raman selection rules for molecular and lattice viixations (Wley-Interscience. New York, 1972). [ 141 R. Savoie and R.P. rournier, Chem. Phys. Letters 7 (1970) I_ [ 151 Y-A. Sataty. A. Ron and F-H. Herbstein. J. Chem. Ph)r 62 (1975) 1094. [ 16 ] A. Anderson, J-IV. Leech and B.H. Torrie, Indian J. Pure Appl. Phys. 16 (1978) 243.
RAMAN
CHEMICAL
AND FAR INFRARED
A. ANDERSON,
B.H. TORRIE
SPEaRA
PHYSICS
1 February
LETTERS
OF THE SOLID PHASES OF CARBON
1979
TETRACHLORIDE
and W.S. TSE
Department of PlzFsics. Unir’ersitv of Waterloo.
Waterloo.
Ovtario.
Carzada
Received 1 November 1978
The hdtice vtbmtlons of carbon tetrachloride have been studied by Raman and infrared spectroscoptc techniques oter the temperature range 18 K to the melting point at 2.50 K. Comparisons are made aith previous results on CCli and other tetrahedral molecules, and the observed peaks for the monoclinic phase II are assigned = tnmshtional modes.
1_ Introduction At saturated vapour pressure, carbon tetrachloride is known to e.xist in three solid phases [ l-41 _The liquid freezes to a face-centred cubic solid at 250.3 K (phase Ia). When these crystals are maintained between 250.3 and 223.5 K for several hours, they transform spontaneousIy to a rhombohedra1 phase (nhase lb)_ At temperatures beiow 225.5 K, both the metastable cubic phase and the rhombohedrai phase transform to a monoclinic phase (phase II). The cubic Table 1 Cryst;tllogmphic
data for carbon termchloride ---
Phase
Twnsition poinr
In
T = 250.3 K
I__
--__
-~
Type ____
-_
fwe-centred rhombohedml
Ib 7-=2L?55K or T=3GOK ( p =64kbar
monoclinIc
III
T=3GOK p = 10 kbbar
monoclmic
IV
T>533K p > 2Okbar
cubic?
II
in nature, with the molecules rotating about their centres of mass. In the other two phases, the molecules are expected to be more hig_hly ordered, but the exact structures are not known_ Under high pressures, two new phases (III and IV) of Ccl, have been observed [1,4]. In addition, spectroscopic evidence of a phase change at saturated vapour pressure and Iow temperatures has been reported by Shurvell [5] and wiI1 be discussed later. Crystahographic data for the phases Ia, Ib, II and III are summarized in table I_ phase is plastic
-----
cubic
Space group and number of molecules i=
4
Lattice constants _-_-_a=
8.34 A
==21
a = 14-4 OI= 90.0”
x
c2/c a = 31
a = 20.3 b= 11.6 c = 19.9 p = 111”
X A A
PZ,iC
a= b =
-=
f
4
9 079 A 5.764A C= 9.201 _s 13= 104.29” ?
119
Volume 61. number I
CHEMICAL
1 Febrllltry 1979
PHYSICS LETIERS
The present work was undertaken to clarify the nature of the solid phase transitions occurring at saturated vapour pressure. Previous Raman studies are described in refs. [S--8]. No previous far infrared investigations of the solid have been found in the literature_
2. Experimental
techniques
Raman spectra were recorded using a standard 90“ scattering conliguration. The light source was a Spectra-physics 155 3rgon ion laser opemting 3t OAW on the 5 145 _S line_ Scattered light was snalyzed using 3 Spex 1-N 1 double monochromator, coupIed to a Spex I-?42 third monochrom3tor, 3nd detected with sn RCA 31034 photomultiplier, cooled by a flow of nitrogen g3s. The output pulses were fed to a D2t3 Genenrl Nov3 Z/IO computer rind subsequently displayed on a stor3ge oscilloscope or X-Y plotter_ F3r infrsred spectrs were obtained by interferometric techniques using 3 Fourier spectrophotometer (RIIC-Beckman, model FS-620)_ A high pressure mercury lamp was used as source and a germanium bolometer operating at 4.2 K as detector. Output signals were digitized and fed to the Nova Z/IO computer where they were transformed and ratioed with background intensities_ Interferograms were typicaily of 500 points on each side of centre, corresponding to an instrumental resolution of 2-5 cm-l _ Samples for R3man and infrared studies were prepared by v3por.u deposition on to a substrate at SO K. followed by annealing 3t approximately 150 K. Because ofemporatron, these samples were suitabie only for low tempemture studies of the monoclinic phase II. Samples were also grown by slowly cooling bulk samples of the liquid, and these were used for Ramm studies of311 three norm31 pressure phases.
3_ Results and discussion When the bulk samples of CCI, were carefully cooled, they formed a transparent solid, which was 3ssumed to be in the cubic phase (la)_ The low frequency Raman spectrum from such 3 s.rmpIe is shown in fig. la_ When these samples were cooled to 250 K and kept at this temperature for approximately 3 h, they suddenly developed cracks, indicating that 3 first or120
I
20
a0 40 FREQUENE I CM-‘)
loo
Fig. I _The low frequenc?i Rnm3n spectrum as a function rempmture.
of
der transition to the rhombohedral phsse (lb) h3d occurred. The lattice spectrum of this new ph3s.e is shown in figs. lb and Ic_ When samples in either the cubic or rhombohedral phases were cooled below 3-25 K, further crscking xxas observed, 3s the first order transition to the monoclinic phase II took place. Raman spectra of bulk samples in this phase are shown in figs_ Id-1 f. Raman and infrared spectra of the vapour deposited samples in the monoclinic phase are shown in rigs_ 1 and 3 respectively_ Raman spectra of the intern31 modes of Ccl, in the monoclinic phase were also recorded at temperatures between IS K and SO K, but these were not subst-3ntially different to those of Shurvell [S] at liqurd nitrogen temperatures, and details will not be repeated here_ It is important to note, however, that there was no evidence of a further phase transition 3t low temperatures, 3s reported by Shurveli 151, from any of our spectra: infrared or Raman, internal or Iattice regions, bulk or annealed powder samples_ Previous experiences with HI [9] and HBr [lo] have shown that a disordered state may be produced in thin film samples deposited at very low temperatures, presumably as the result of strains in the films, but this effect is not seen with bulk samples
CHEMICAL PHYSICS LEl-TEiZS
Volume 61, number 1
1 February 1979
An attempt was made to obtain re-orientatlonal relaxation times by fitting a Debye function to the Rayleigh wings shown in fig_ 1 [ 11] _ The spectra at 240 K for the face-centred cubic and rhombohedral phases and that at 223 K for the monoclinic phase were used for this analysis_ Relaxation times of the order of 1O-12 s gave reasonable fits, but the problem of separating out a background spectrum made it impossible to obtain times which were accurate enough tc; clearly distinguish one phase from another. The fact, however, that no clearly defined lattice modes are observed in either the cbbic or rhombohedral phases strongly suggests that these structures are both orientationally disordered_
4.
20
40
60 FXQUENCY
80 (CM-’
IOC
I
Pig.. 2. The low frequency Ram~n spectrum of the monoclinic phase at 18 KS indwates z plasma line.
7
1
50 FREQUENCY
(CM-‘,
80
Fig. 3. The far infrared spectrum of the monoclinic
-l Ill 3
phase_
Lattice
modes for the monoclinic
phase
The observed lattice mode frequencies are listed in table 2, and compared w?th the Raman frequencies reported by Nevzorov and Sechkarev [6] and Ebisuzaki [S], the latter for samples at elevated pressures_ There are obvious similarities between the results of the Raman studies, both in frequency listings and spectral band shapes, indicating that both high pressure phases and the low temperatures monoclinic phase are closely related. The complete phase diagram for Ccl, is not yet avadable. and it is not definitely known, for example, which of the high pressure phases are stable at low temperatures and saturated vapour pressure, although it seems probable that only phase II fits this category_ The rather drastic ch%nges observed in the lattice spectrum of phase II as the temperature is lowered suggest that an ordering process is taking place, probably a decrease in the rotational amplitudes of the molecules_ It is also possible that in phase II, molecules on certain sites continue to rotate freely, whereas others switch to hbrational motion, as in the case of methane [I21 _Another point of interest is that the Raman spectrum of the vapour-deposited sample at 1 S K, although obviously similar to that of the bulk sample at 28 K, has much sharper peaks, with frequencies a few cm-t lower. Normally one would expect slightly higher lattice frequencies at lower temperatures, as the lattice contracts and intermolecular forces strengthen. The method of crystal growth and its thermal treatment are clearly very sensitive factors influencing the spectra, an extreme example of which is the disorder-
121
Vo!ume 61, number 1
CHEMICAL
1 February1979
PHYSICS LE-ITERS
Table 2 Infrared and R~‘IZUI Lpectra of monoclinic carbon tetrachioride lattice region (in cm-‘) l-his
wxk
(phasez11) I
Previous u ork (Raman)
Raman
infrared
f8Ka~ 28K 8@K3 (otttrated wpour pressure)
i8Ii
a)
8OKi3
242
28 343 423 415 53.6 65.7
26 295 38 45 54 59 -
T= 300K p = 10 kbar [8] III
T=80K p=o 11
161
--
-
245 29 36 43 50.5 555 665
T= 300K p = 6.4 kbar [8] II
40 44
39 42 5
58 b)
56
27
24 30 39 48
43 46
36 44
60 97
59 74 97
56 68 98
a) Porbder nmples: other data from bulk crystals. b, An additional infrared peak at 65 cm-’ IS _ of doubtful origin since it sbo\\ed no temperature dependence.
ed state observed at Iow temperatures by Shurvell IS] _ The space group of Ccl, II is reported to be Cc or C& with a large unit cell containing 32 molecules on general (C,) sites [Z?,S]_?hsse III on the other hand has only 4 molecules in the unit cell, with space group @t/c [4!_The Raman spectra of phases II and iI at elevated pressures, recorded by Ebisuzaki [Sl) are very similar, indicating that any differences between the two structures are small. These spectra and our present results are all more consistent with a smal:er unit cell. However, many of the individual peaks predicted in the richer spectrum for the large unit cell would probably be unobservable because of overlap effects_ The group theoretical analysis for the smaller unit cell, PZr/c, based on the well-known correlation method [ 131 predicts 9 infrared lattice modes (3 of translational and 6 of hhrational origin) and 12 noncoincident Raman modes (6 of each type)- Because of the low symmetry. mixing between fransIational and librational modes of the same species is possible, so that the above labeliing is not exact_ For these near-spherical moIecules, it is expected that librational modes will involve only small changes in the electricaY dipole and polarizability derivatives,
points: served modes, to the
for crystalline CH* and CD, (phase II) the obfar infrared spectra derive from translational since their frequencies ratios are proportional ratios of the square roots of molecular masses
rather than moments of inertia [14]. Secondly, the far infrared spectrum and structure of crystalline CF4 phase II !lS] are very similar to those of Ccl, II, with corresponding frequencies also scaling according to the square roots of the molecular masses. Preliminary results from this laboratory on other solid tetrahalides of similar structure (GeCI,. Tic?, and SiC14) also fit this pattern [ 16]_ Finally, excluding the weak peak at 66 cm-l, the observation of 3 infrared and 6 Raman non-coincidental peaks is precisely that predicted for translations based on the smaller unit cell. It is clear from the above discussion that further research on solid Ccl, is needed, before a fuller understanding of its various crystalline phases is obtained_ In particular, completion of the phase diagram at low temperatures using X-ray and calorimetric techniques, and NMR studies of the molecular motions in all phases would be useful_
and hence the infrared and Raman intensities will be
Acknowledgement
low. The obsemed lattice spectra are therefore postulated to involve primarily translation;rI motions- This assignment is supported by the following additional
Financial support from the National Research Council of Canada is gratefully acknowledged_
122
Volume 61. rsmber 1
CHEMICAL
References [l] P-W. Bridgman, Phys. Rev. 3 (1914) 153. [2] R_ Rudman and B. Post. Science I54 (1966) 1009. [3 ] C-E_ Weir, G.J. fiermarini and S. Block, f_ Chem. Phj s. SO (1969) 2089. [4] G-J. Piennarini and A.B. Braun, J. Chem. Phys 58 (1973) 1974. (51 H-F. Shurvell, Spectrochim. Acta 27A (1971) 2375. [6] B-P- Nenorov and A-V. Sechkarev, Soviet Phys. 3.14 (1971) 199. [7] 1.1. Kondilenko. P-A_ Korotkov and GC_ Litvinov, opt. spectry. 30 (1971) 51. [S J Y. Ebisuzrtki, Proceedings of the International Conference on Lattice Dynamics, Paris (1977) p_ 505,
PHYSICS LE’ITERS
1.February 1979
[9] A. Anderson, B.W. Torrie and W.S. Tse, to be published_ [lo] R. Savoie and A. Anderson, J. Chem. Phys_ 44 (19 66) 548_ [ll] 1-L. Fabelinskii, hfofecular scatterm of tight {Plenum Press, New York, 1968) p_ 110. [12] W. Press, J. Chem. Phys. 56 (1972) 2597; Acta Cryst. A29 (1973) 257, [ 131 W-G. Fate&. F-R_ Dolhsh. N-T_ McDevitt and F-f_ Bentley. Infrared and Raman selection rules for molecular and lattice viixations (Wley-Interscience. New York, 1972). [ 141 R. Savoie and R.P. rournier, Chem. Phys. Letters 7 (1970) I_ [ 151 Y-A. Sataty. A. Ron and F-H. Herbstein. J. Chem. Ph)r 62 (1975) 1094. [ 16 ] A. Anderson, J-IV. Leech and B.H. Torrie, Indian J. Pure Appl. Phys. 16 (1978) 243.