Vibrational study of CsH2PO4 and CsD2PO4 single

Vibrational study of CsH2PO4 and CsD2PO4 single crystals B. Marchon and A. Novak Citation: The Journal of Chemical Physics 78, 2105 (1983); doi: 10.1063/1.445073 View online: http://dx.doi.org/10.1063/1.445073 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/78/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in 1 7O NQR study of the pseudoonedimensional ferroelectric phase transition in CsH2PO4 J. Chem. Phys. 81, 3247 (1984); 10.1063/1.448033 Investigation of various ways of forming CsH by irradiating a Cs+H2 mixture with laser light J. Chem. Phys. 79, 2839 (1983); 10.1063/1.446105 Infrared, Raman, and Brillouin spectra of CsH2PO4 J. Chem. Phys. 74, 5923 (1981); 10.1063/1.440911 31P chemical shift and relaxation study of the pseudoonedimensional ferroelectric transition in CsD2PO4 J. Chem. Phys. 72, 3626 (1980); 10.1063/1.439623 The dissociation energy of CsH J. Chem. Phys. 69, 1791 (1978); 10.1063/1.436720

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:42

Vibrational study of CsH 2P04 and CsD2 P04 single crystals B. Marchon and A. Novak Laboratoire de Spectrochimie Infrarouge et Raman. c'N.R.S. 2. Rue Henri Dunant. 94320 Thiais, France (Received 16 July 1981; accepted 25 March 1982) The infrared and Raman spectra of disordered paraelectric and ordered ferroelectric phases of CsH2PO. and CsD2PO. single crystals have been investigated at various temperatures in the 4000-10 and 4000-0 cm- I range, respectively. An assignment of lattice and internal vibrations in terms of symmetry species and approximate type of motion is given. Most of the external vibrations of the paraelectric phase follow the selection rules of the C 2h factor group symmetry, whereas the internal modes do not obey the mutual exclusion rule. The Raman spectra of the ferroelectric phase show TO-LO splitting up to 50 em-I for a number of lattice and internal vibrations which is correlated with infrared intensities. Disordered short and ordered long hydrogen bonds are distinguished spectroscopically and the OH stretching and bending frequencies are correlated with x-ray and neutron diffraction data. A large positive isotope effect on the short hydrogen bond is manifested by a low (1.13)vOHlvOD frequency ratio. The short OH··.O, but not OD...O, bond contracts at higher temperature as shown by the increased hydrogen bond and decreased OH stretching frequency. The Raman intensity of the 74 cm- I mode and 507 cm-1LO band plot vs temperature gives a curve of the order parameter type. The half-width of the OH···O Raman band increases three times more steeply with increasing temperature than that of the OD···O band which is ascribed mainly to a larger activation energy of the proton jumps along the OD···O bond.

I. INTRODUCTION

II. EXPERIMENTAL

Cesium dihydrogen phosphate appears interesting since it exhibits a number of unusual properties which have so far not been found in other ferroelectric systems. 1 This monoclinic crystal undergoes a pseudoone-dimensional paraelectric-ferroelectric phase transition at 153 K while CSDzPO. becomes ferroelectric at 267 K. The large isotope effect on the transition temperature Tc on deuteration shows the role of OH·· . 0 hydrogen bonds on mechanism of the transition. CSHzPO. and CsDzPO. have been investigated by various methods, 1-10 however, very little vibrational data have been published: Orel and HadZi ll recorded the far infrared spectrum of the paraelectric phase of CSHzPO. while Wada et al. 1Z examined Raman spectra in the 0700 cm- 1 range at different temperatures near Tc. The latter authors did not detect any soft mode or any substantial changes in the spectra during the transition.

Single crystals of CSHzPO. and CsD2 PO. were kindly provided by Professor Blinc. They were carefully cut in parallelepipedic forms with sides perpendicular to the axes of the ellipsoid of the indices for Raman work. Small plates containing binary axis parallel to the face developed were cut from single crystals and polished with alumina powder until they were thin enough for infrared transmission measurements.

We have thus investigated single crystals of CsH2 PO. and CSDzPO. by Raman (4000-0 cm- 1) and infrared (4000-10 cm- 1) spectroscopy in the 300-80 K temperture range and, in particular, in the vicinity of Tc. We wanted to characterize the paraelectric and ferroelectric phases spectroscopically, by analyzing both lattice and internal modes, and we inquired about the phase transition by studying the temperature dependence of frequency, intensity, and half -width of a number of infrared and Raman bands. Some preliminary results have already been published 13 and we are reporting here a full account of spectroscopic data. The first three parts of the paper deal with the vibrational analysis of the paraelectric and ferroelectric phase. The fourth chapter discusses some correlations of the spectroscopic and crystallographic data concerning hydrogen bonding and the last one gives the results pertinent to the phase transition. J. Chern. Phys. 78(5),1 March 1983

Raman spectra of single crystals of CSHzPO. and CSDzPO, were recorded on a Coderg T 800 triple monochromator instrument. The 514.5 nm line of about 800 mW power of a Spectra-Physics argon ion laser was used as exciting line. Normal and backscattering geometries were used. A conventional cryostat was employed for low-temperature measurements and the accuracy was about ± 1 K in the 300-80 K region. Infrared spectra were studied with a Perkin-Elmer 180 spectrophotometer and a Polytec FIR 30 instrument in the 4000-50 and 200-10 cm- 1 region, respectively. Infrared dichroism of thin plates was measured with the electric vector of the incident light E parallel and perpendicular to the crystallographic binary axis using Perkin-Elmer polarizers which consist of gold wire grids on AgBr and polyethylene substrate for midinfrared and far-infrared, respectively. The polycrystalline material was examined as an emulsion in Nujol or Fluorolube between CsI and TPX windows. III. RESULTS AND DISCUSSION

A. Crystal structure and symmetry considerations The crystal structures of paraelectric and ferroelectric phases of CsH2 PO, have been studied by x_ ray 3.7 and neutron diffraction. '-8,8.9 The structure of the paraelectric phase of CSDzPO. has also been determined. 9 There are two crystallographically inequiva-

0021·9606/83/052105·16$2.10

© 1983 American Institute of Physics

2105


B. Marchon and A. Novak: Spectra of CsH 2P0 4 and CsD 2 P0 4

2106

paraelectric phase (P2 1 /m;; C~) the results of the factor group analysis are shown in Table I. Nine Raman (5A,. +4B,.) and six infrared (3A,,+3B,,) active lattice modes are expected and can be further subdivided into rotational (6R/) and translational (91") motions. It can easily be shown that all the rotational vibrations are hydrogen bond stretching or bending motions, whereas some translational modes do not necessarily involve hydrogen bonds and may correspond essentially to the motions of the cations against rigid hydrogen bonded phosphate layers. Internal vibrations, 12 Raman (8A,. +4 B,.) and 18 infrared (7 Au + 11 Bu) active, on the other hand, can approximately be divided into eight skeletal stretching, ten skeletal bending, and 12 OH group vibrations (Table I). The symmetry of the ferroelectric phase is reduced to P2 1 ;; C~ and all the lattice (8A +7 B) and internal (15A + 15 B) vibrations become infrared and Raman active, the A and B vibrations being derived from A,., A" and B,., Bu species of the paraelectric phase, respectively.

~CS

b

B. Paraelectric phase

,~,

1. Lattice vibrations

FIG.!. Structure of CsH 2P0 4 crystal (after Frazer et ai., Ref. 6).

lent hydrogen bonds in the unit cell (Fig. 1). The shorter bond (2.48 A) links the phosphate groups into chains running along the b axis and the longer one (2.54 A) which is always ordered, crosslinks the chains to form the (100) layers. The shorter hydrogen bond is disordered in the paraelectric phase and becomes ordered at the transition to the ferroelectric phase. The crystallographic center of inversion is thus lost and the P21/ m space group symmetry is reduced to P21 whereas the number of molecules per unit cell (Z =2' does not change. There are thus 16 atoms in the unit cell, and in the wave-vector-equal-to-zero approximation 45 optically active vibrations are expected. The intramolecular forces within HzPO'4 ions being much stronger than intermolecular ones, 30 internal and 15 external or lattice modes can be distinguished. In the case of the

All the Raman (Fig. 2) and infrared (Fig. 3) bands of CsHZP04 crystal observed in the region below 300 cm- 1 must be due to lattice vibrations, since the lowest internal mode frequency is found at 352 cm- 1• The expected nine Raman bands are observed and can be assigned to 5 A,. and 4 B,. modes from their polarization (Fig. 2, Table II). Six absorption bands are identified using polarized infrared radiation: three of them, at 220, 100, and 74 cm-t, appear when the electric vector E is parallel to the b axis and are assigned to Au speCies, whereas the other three at 146, 106, and 76 cm- 1 are strong with E perpendicular to this direction and correspond to Bu species (Fig. 3, Table II). The interpretation of the lattice modes in terms of translational and rotational vibrations is less straightforward since the crystal symmetry does not require a separation of these motions. Nevertheless, the isotopic shifts can help to some extent: for the isotopiC pair DzPO'4/HzPO'4 the square root of the mass ratio is equal to 1. 01 and those of the three moments of inertia (IV Ik)l/ Z (k =x, y, z) have been estimated to vary between 1.02 and 1. 05. In the Raman spectra, three bands at

TABLE I. The symmetry species and the character table of the paraelectric phase of Csll 2P0 4 (P2 I1m ;; C~h' Z=2). a

C~h

E

C2

A,.

1 1 1 1

1 -1 1 -1

B,.

Au B"

1 1 -1 -1

(J

NI

TI

T'/

R'/

n/

1 -1 -1 1

13 8 12 15

0 0 2 1

4 2 1 2

1 2 2 1

8 4 7 11

°3

1

2 2 3

"I

"OH

0011

yOIl

3 1 1 3

1 0 1 2

1 0 1 2

0 1 2 1

Re

IRb

f f Mb

Mac

O!xrQyyQ zzCi xz

uxyu ya

f f

aNI: Number of degrees of freedom belonging to i species; T/: Number of overall translations; Tj: Number of translational vibrations; Rj: Number of rotational vibrations; nl: Number of intramolecular vibrations;

0/: Number of skeletal bending vibrations; "/: Number of skeletal stretching vibrations; "Oil, OOH, and yOH: OH stretching, in-plane, and out-of-plane bending vibrations; IR: Infrared; R: Raman; f: Forbidden. ba, b, c: Crystallographic axes; b: twofold axis. ex, y, z: Principal axes of the polarizability derivative tensor. y;; b. J. Chern. Phys., Vol. 78, No.5, 1 March 1983


B. Marchon and A. Novak: Spectra of CsH 2P0 4 and CsD 2P0 4

234, 219, and 110 cm- 1, show significant isotopic frequency ratio of 1. 05, 1. 04, and 1. 02, respectively, and may be attributed to rotational motions, the A, species corresponding to a libration about the binary axis R~ (Table II). The infrared lattice bands, on the other hand, are much broader and their frequencies cannot be measured with the same accuracy as those of Raman bands. Nevertheless, the deuteration shifts of the 220 (Au) and 106 (Bu) cm- 1 bands are considerably higher (12 and 9 cm- 1) than the experimental error (±3 cm- 1) and are doubtless due to rotational motions, the Bu species being a R~ vibration. The third libration belongs to Au species (Table 1) and can thus correspond to either of the infrared bands at 100 and 74 cm- 1 • The former is preferred because it has a higher frequency.

Z(XXIV

Ag

Z (VVIX

Ag

> I-

Y(ZZIX

III

Ag

z

...

x4

I-

As far as translational vibrations are concerned those which correspond to the motions of cesium ions against rigid phosphate layers are expected to have the lowest frequencies as they do not involve hydrogen bonds. Two Raman AI bands at 49 and 42 cm- 1 and a B, band at 46 cm- 1 can thus be assigned to predominantly Cs· motions. The remaining six translational motions, three infrared and three Raman active, on the other hand, may correspond to hydrogen bond vibrations. The BI components of all translations can be considered as T~ motions along the b axis.

z

H

Y(XZ)X

...

Ag

>

le(

...

oJ

iii:

Y(XY)X 8g

Hydrogen bond vibrations are usually divided into stretching v (OR) 0 and bending Ii (OH)· o. 0, modes. The librations at 234 (B , ), 220 (Au), and 219 (AI) cm- 1 can be assigned to the former since they have the highest frequencies and a considerable half-width. The 220 cm- 1 infrared absorption is the strongest of all the lattice bands whereas the Raman active (OH)· .. 0 stretching bands are quite weak. The other infrared and Raman frequenCies, which appear in the 150-60 cm- 1 range, are believed to be predom inantly (OH)··· 0 bending modes derived from rotational and/or translational motions. 0

Y(ZYIX 8g x4

200

100

~cm-1

FIG. 2. Low-frequency Raman spectra of CsH2PO, single crystal at 300 K.

CsH2PO,

••

Thus, lattice vibrations of the paraelectric phase of

TABLE II. Raman and infrared frequencies (cm-I ) assigned to lattice vibrations of the paraelectric phase of CsH2PO, and CsD 2PO, at 300 K.

Raman

2107

CsD 2PO,

Infrared

234

Raman

Infrared

223 220

219

208 211

146

146

B,. R' (OH) ···0 Au. R' stretch AI' Rt

61

61

T' T' R' Rt (OH) ···0 Au. R' bend T' Bu. A,. T' Au. T& B,. Tt

49 46 42

49 45 42

AI' T' B I • Tt Cs' A" T'

118 110

118 108 106 100 76

75

97 102 76 75

74

74

,.-

\

Assignmenta

Bu. AI' BI • Bu.

ab; Binary axis; (OH) ···0; Hydrogen bond vibrations; Cs'; Motions involving cations.

0.5

I

I ,, I

L&.I

U Z

,/

c(

CD 0

iii:

o

----- ------

",

,-

I

\

, ,, ,,\ , , ,, ,,

, \

\

\ \

I

'.

\ \

I I

,-"'..._,

\

,

' ... ....

r-----------~-------------L----------__4

I/)

IQ c(

o.

OL-__________

~

200

__________

~

____

~----~

1 0 0 " em-1

FIG. 3. Polarized far-infrared spectra of CsH2PO, and CsD 2PO, platelets. Solid and broken lines represent the absorption with the electric vector parallel and perpendicular to the crystallographic b axis. respectively.

J. Chern. Phys., Vol. 78, No.5, 1 March 1983


2108

B. Marchon and A. Novak: Spectra of CsH 2 P0 4 and CsD 2P0 4

Z(XX)V

Ag

Z(VV)X

Ag

V(ZZ)X

FIG. 4. High-frequency Raman spectra of CsH 2PO, single crystal at 300 K.

2500

2000

1000

CsHzPO, and CSDzPO, seem to follow the selection rules derived from the CZh factor group symmetry and Z = 2 (Table I) and see the crystal symmetry much in the same way as x-ray and neutron diffraction.

There are 30 optically active internal vibrations of CSHzPO, crystal and they can be described in terms of group vibrations as 10 skeletal bending, 8 skeletal stretching, and 12 OH group motions (Table I). Their frequencies are expected, by analogy with the spectra of similar dihydrogen phosphates such as KHzPO., 14-18 NH,H zPO,,18 and NaHzPO,' 2 HzO,17 between 300 and 600 cm- 1 for skeletal bending, 800 and 1200 cm- 1 for skeletal stretching, and 1200 and 3600 cm"1 for OH group vibrations, except for out-of-plane OH modes which fall in the skeletal stretching region. We shall examine successively these regions of CsHaPO, and CsDaPO, Raman and infrared spectra of which are shown in Figs. 4-6.

ysis of CsHzPO, crystal predicts five Raman (3 A .. +2 B .. ) and five infrared (2Ay +3 By) active skeletal bending modes (Table I). The Raman spectra of CsHzPO, (Fig. 4), however, show seven 4A.. and 3 B.. and the infrared spectra six (Fig. 6) 3Ay and 3 B" skeletal bending bands. The same Raman results are obtained for CsDaPO, single crystal (Fig. 5) while the corresponding infrared spectra (Fig. 6) exhibit seven (3A" and 4B,,) skeletal bending bands (Table III). The comparison of the band frequencies due to g and u species also indicates that the selection rules involving the center of symmetry (mutual exclusion rule) are not obeyed: three Ramaninfrared pairs are observed for CsHaPO, (515-509, 471-476, 389-390 cm- 1) and four for CSDzPO, (535-539, 505-502, 481-485, 384-385 cm"1). The A-B splitting involving the twofold axis, on the other hand, appears to follow the predictions of the Cz factor group symmetry. From the above observationI'! it can be concluded that the skeletal bending vibrations, unlike the lattice modes, do not see the average C2h symmetry of the crystal. .

a. Skeletal bending region. These motions can approximately be considered as derived from the triply degenerate Fa mode near 567 cm- 1 and doubly degenerate E mode near 420 cm"1 of the free phosphate ion of Td point group symmetry. 18 The C2h factor group anal-

The skeletal bending frequencies decrease more or less on deuteration and the maximum shift amounts to 23 cm"1 (Table III). These low-frequency shifts are due mainly to the mass effect and to some coupling with yOD vibrations which appear in the 600-700 cm"1 range

2. Internal vibrations

J. Chern. Phys., Vol. 78, No.5, 1 March 1983 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:42

B. Marchon and A. Novak: Spectra of CsH ZP0 4 and CsD zP0 4

2109

V(XX)Z

Ag

X(VV)Z

Ag

> lI/)

Z

V(ZZ)X

w

I-

z H

w

FIG. 5. High-frequency Raman spectra of CsD 2PO. single crystal at 300 K.

V(ZX)Z

>

Ag

le(

..... w

Z(XV)X

a::

8g

X (VZ)V

8g

2500

2000

1500

1000

(Fig. 6). There is, however, a notable exception: the Raman band at 471 and its infrared counterpart at 476 cm-! increase in frequency by about 10 cm-! when going from hydrogenated to deuterated compound. A high frequency shift in this region is unusual and may be related to different geometries of HzPO' and DzPO, ions observed by neutron diffraction. 9

b. Skeletal stretching region. Eight skeletal stretching, four Raman (3A I +BI ) and four infrared (A"+3B") active, and four OH out-of-plane, one Raman (BI ), and three infrared active (2 A .. +BII ) modes, are expected in the 1200-800 cm- 1 region. The observed Raman spectra show three AI bands at 1128, 991, and 921 cm-! and a BI band at 1086 cm-! which can all be assigned to the skeletal stretching vibrations. The 921 cm-! band is very strong and similar to the totally symmetric motion of the free PO~- ion. The}{)H bands are usually very weak in Raman and thus overlapped by stronger 1/ P-O bands. The polarized infrared spectra, on the other hand, allow to distinguish four bands belonging to A" species at 1123, 1016, 948, and 872 cm- 1 and four B" bands at 1154, 1072, 966, and 897 cm-! all the absorption bands being very strong. There is, thus, a surplus of A" bands and we believe that only the 948 cm-! band

can be assigned to the expected P-O stretching vibration of A" species whereas the 1124 and 1016 cm-! absorption correspond to the forbidden modes the ~ counterparts of which are observed in Raman data at 1128 and 991 cm- t • The lowest 872 cm-! infrared band of A" species must be ascribed to a }{)H mode on the ground of its isotopic shift. All the B" bands, except the 966 cm-1 yOH absorption, are identified as the expected skeletal stretching modes (Table III). The deuteration shifts the yOH frequencies out of the investigated region but instead it brings liOD vibrations which couple more or less with the skeletal stretching motions as shown by frequency shifts and intensity variations (Figs. 5 and 6). Raman skeletal stretching frequencies at 1128, 1086, and 991 cm-! increase to 1155, 1096, and 1014 cm-!, respectively, while the 921 cm-! frequency decreases. Much the same is true of the infrared bands at 1154, 1124, 1072, and 1016 cm- 1 which shift towards higher wave numbers on deuteration (Table III). The OOD bands can thus be identified at 949 and 883 cm- 1 in Raman and at 956, 931, and 865 cm-! in infrared spectra. There are again more liOD bands observed than predicted from Table I showing-like skeletal stretching and bending modes-that the eM factor



2110


300 K

Cs H2 PO..

~

0.5

I" ,,

\

I I

\ \

,,

\

,,

\ \ \

t,)

\

\

\

....

, ,,

" ___ O~-~~~~____~__~__~~____~______~______~ --_-_-_-~______~'_'-~-

...

_, CsHzPO.. \

*

zO.5

'" ~

\

O~

\""

I

,I'"~

\

~

~

____

300K ,,

CSD2 PO..

~

~

,

0.5

* .... ~ ,

O~ ..

I

...

,

-,,' .. -'

I

'

I

'\

\

I

\

,

' .... ' \

\

"--

,i· ,, \

I

I

"

,

"''''''

""

\

'

,

"

'-,/

/

:,

,, "

,

~.......

'\ \

,,_,/'\ ....

' I

-L~______~________~________~________~________~____ ~

\

\

It

".

.

,..'

\

I'

I,'

10K

0.5

____

:~~ ,

,,

~\,'" / \..

///

lID

'"

\ /\

, * --~ ____ ____

II::

o

10K

\

u

,

,/

'

\

\

\.~,/ r./\

\

,~

"

:\,'\

""""', "

f\\,

~

V.../ "-:*--..__~ ~____~~~__~~______~________~__________~______~-L________~~~~ 3000 2000 1000 't em- 1

O~~~_~~~~~_

FIG. 6. Mid-infrared spectra of CsH2P0 4 and CsD 2P04 at 300 and 80 K. Solid and broken lines represent the absorption with the electric vector parallel and perpendicular to the crystallographic b axis, respectively. The asterisks represent the absorption of the paraffine.

group selection rules are no longer obeyed.

c. OH group vibrations. The infrared spectra of CsH2 PO, (Fig. 6) show tqree broad absorptions near 2700, 2300, and 1700 cm- 1 of the ABC type which are usually interpreted as OH stretching modes in Fermi resonance with combinations involving OH bending vibrations. 19 Similar bands appear for both parallel and perpendicular polarization. The spectra of CsD 2 PO,. on the other hand, exhibit only two broad vOD bands of B" and A" species near 2100, 1750 and 2000, 1725 cm-l, respectively. ABC bands appear in Raman only for XX and ZZ geometries corresponding to A, species with, however, very different intensity distribution (Fig. 4). The vOD vibrations give rise to a doublet near 19801755 cm-1 in the case of XX geometry whereas only one strong band is observed at 2090 cm-1 in the ZZ spectrum. All the expected OH in-plane-bending vibrations (Table I) are identified at 1303 (Bu), 1244 (Au), and 1227 (Bu) cm- 1 in infrared and at 1223 (A,) cm- 1 in Raman spectra. Their OD analogs are more or less mixed with the skeletal stretching vibrations as already discussed above, nevertheless, the 976 (B,,), 956 (A,,), and 865 (Au) cm- 1 infrared bands are believed to, correspond to mostly roD motions yielding isotopic frequency ratio of 1. 34, 1. 30, and 1. 42, respectively. The same applies to the Raman bands at 949 and 883 cm- 1 • It should be pointed out that 60H Raman band is

very weak while 60D bands appear much stronger because of the coupling with v p-o motions. Finally, the aSSignment of the infrared bands at 707 (Bu ), 690 (A,,), and 627 (A,,) cm- 1 to yOD vibration;; is straightforward since they appear in the region free of other absorptions (Fig. 6). The yOH bands, on the other hand, are found in the p-o stretching region and are more difficult to locate, the 966 (B,,) and 872 (A,,) bands of CsH2PO, being likely candidates. No out-ofplane OH and OD bands have been observed in Raman. C. Ferroelectric phase

1. Lattice vibrations All the 15 lattice vibrations (8A + 7 B) become infrared and Raman active in the ferroelectric phase of CsH2PO, belonging to P21 space group. New bands, which are forbidden in the paraelectric phase are thus expected to appear. This is observed in the far infrared spectra (Fig. 7) for instance, where two such modes at 125 and 110 cm- 1 corresponding to the Raman frequencies of the paraelectric phase at 118 and 108 cm- 1 , can be identified (Table IV). The Raman spectra of the ferroelectric phase, however, are more complicated. In the case of normal (90°) scattering there is a surplus of Raman bands. In particular, in the 260-200 cm- 1 region where at most three librations are expected, six different bands of A and B species are observed (Fig. 8).




2111

TABLE III. Raman and infrared frequencies (em-I) assigned to internal vibrations of the paraelectric phase of CSHzPO, and CsD 2PO, at 300 K.

Raman

Infrared

Assignmenta

Raman

Infrared

Assignmenta

2100

2750 2090 1755

2740 2350

1750

2300 1420

1700 1700

2000

2660 1980

2660

1725

/iOH+'YOH

2250 1750 1740

vOHshort

and 2 «SOD

1710

2 'YOD

1345 1303 1244 1227 1223 1154 1128 1124 1086 1072 1016 991 966 948 921 897 872

vPO vPO vPO vPO vPO vPO vPO

1180 1160 1155 1096 1080 1034 1014 976 956

'YOH vPO,'YOH vPO vPO

931 b 917

bending

531 505

707 690

Au

627

Au 'YODloDll

A,

509

B,

476

/iOPO

485

Au /iOPO

381 385

Bu

Au

352

Au

417

428 389 390

B,

384

389 352

Bu modes

A,

481

471

Bu B, Skeletal Bu

A, bending

502

modes

Bu 'YO Bahort

A, 532

544 541 515

_

Au

539 535

I

865

538 Skeletal

/iOD

888 883

550

Bu

Au /iOD.hort

Au vPO A, vPO Bu vPO

911

561

A, vPO B, vPO Bu vPO Au vPO A, vPO

A,

949

'YOH

Bu vPO

Au vPO

A,

aLong; long hydrogen bond; short; short hydrogen bond. ~ands seen in polycrystalline spectrum only.

These observations can be interpreted in terms of TO-W splitting of Raman modes and of a modification of selection rules of the polar ferroelectric phase; backward (180 scattering geometry must thus be used for a correct assignment. Theoretical considerations20 show that, near Brillouin zone center, the frequency of a polar vibration varies as a function of the mutual or0

)

ientation of its wave vector k and the transition moment. When k and IJ. are not perpendicular, long range electrostatic forces due to oscillating dipole moment give rise to longitudinal optical vibrations. Their frequencies are higher than those of transverse optical vibrations which appear when the two vectors are perpendicular. For intermediate orientations coupling be-



2112

, Z(XX)Z 300K

>

... Z

...

../'...

Z

,J

H

(J ~

_2

\OJ

w

z
i=

JV\.

ft

ALO

o

..J \OJ

I/)

80K

CD

A

V

'-

~

TABLE IV. Raman frequencies (cm-1) of A modes, and infrared frequencies observed in a polycrystalline sample assigned to lattice vibrations of the ferroelectric phase of CsHaPO, and CsD 2PO, at 80 K.

Y (XY)X

B

\

~

Z(YZ)Y

Raman

Infrared

Raman

249 205 130 122

219 148 125

238 215 122 122

110

104 98

B ~

200

100

~ "fcm-

85 1

FIG. 8. Low-frequency Raman spectra of CsH2 PO, single crystal at 80 K.

79 74

79

54 46

79 74

54 45

Infrared

217 124 110 104 95 85

77

Assignment A LO R' A TO R' A LO T' A TO

R' R'

A A A A

T' T{, T' Cs· T'



2113

Y(XX)Y ALO x~

x2

.2

z(yy) Z >-

ATO

x 1-'4

ICIl

...z~~~==~==~========~~~~~===c====~~==C=~ X(ZZ) X

I-

FIG. 10. High-frequency backward Raman scattering of CsH2P04 single crystal at 80 K, showing A TO and ALO modes.

Z H

... > I-

C~_ _~~=C==4=~~~L-~~~==========~~==db=9 ~

Y (ZX)

...

2500

Y

2000

3000-300 cm- l region are shown in Figs. 6, 10, and 11. The frequencies of the corresponding bands are given in Table V. In order to check the assignment of infrared and Raman bands of A speCies, the theoretical infrared oscillator strength has been calculated from TO-LO splitting of the Raman spectra of CSH2PO~.

The integrated infrared intensity Ija of a polar mode Ell a (a =x, y, z) is proportional to Sja w~a, Sja being the strength of the oscillator and w ja its frequency, 22 and can be related to the WLO and Wro frequencies by the following relationship23-25: J observed with

In the case of a monoclinic crystal this relationship is valid only for the vibrations of A species; i. e., for the bands of CSH2PO~ observed with Ellb. The results are shown in Table VI. Only the intensities of the bands above 300 cm- 1 could be measured with a sufficient accuracy. The intensities of the bands were measured and calculated with respect to that of the 470-505 cm- 1 reference band. The agreement between the TO-LO

splitting observed in Raman and the corresponding infrared intenSity appears satisfactory. As far as Raman bands for which TO-LO splitting is within the experimental error, it should be pointed out that this error is about 1 cm -1 for narrow bands but amounts to 20 cm- 1 for broad OH stretching and combination bands in the 3000-1500 cm-1 region. Similar errors in the TO and LO frequencies have been reported from infrared reflection spectra by Orel. 26 The infrared intensities calculated for such bands taking into account these errors are lower than or equal to the experimental values except for the 1800-1820 cm-l band (C-band), thecalculated intenSity of which is lower than the observed one. Finally, in the 800-1100 cm- 1 region, only the sum of the four infrared absorption could be measured (5.47) and compared to the calculated sum (4.65). The latter value is only a rough estimation because there are some missing TO and LO Raman lines in this region (Fig. 10). D. Hydrogen bonding There are two types of hydrogen bonds in CSH2PO~: the shorter one (2.48 A) is disordered in the high-temperature but ordered in the low-temperature phase

J. Chem. Phys., Vol. 78, No.5, 1 March 1983 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:42

2114


x8

X(YY)X

>-

A TO

~

f/)

z

FIG. 11. High-frequency backward Raman scattering of CsD 2PO( single crystal at 80 K, showing A TO and A LO modes.

LU

X(ZZ)X

~

z

ATO

~

LU

Y(ZZ)Y

> ~

Cl

....

...

Y(ZX)

Q:

Y

ALO

2500

1500

500

while the longer one (2.54 A) remains ordered in both phases. Thus, it appears interesting to characterize these two hydrogen bonds spectroscopically and to correlate the vibrational and crystallographic data. The vibrational distinction of short and long hydrogen bond is based on the usual relationship between distances and frequencies; a shortening of the O· .. 0 distance decreases the OH stretching and increases the OH bending frequencies. 27

1. OH bending vibrations In the case of OH in-plane-bending vibrations the distinction is clearcut: the low-temperature infrared spectra of CsH2PO, (Fig. 6) show two pairs of oOH bands with opposite dichroism, the high-frequency pair at 1301-1258 cm"1 being assigned to the short hydrogen bond and the low-frequency pair at 1232-1220 cm"1 to the long one. In Raman, only A species of oOH bands, one due to the short and one to the long bond, appear and show TO-LO splitting (Table V, Fig. 11). The correlation field as well as TO-LO splitting is considerably larger for the oOH modes belonging to the short

"em-1

hydrogen bond than those of the long one. In the infrared spectra of CsD2PO, (Fig. 6, Table V), the high frequency doublet at 726-702 cm"1 corresponds to the 00 out-of-plane bending due to the short hydrogen bond, the two components being due to Davydov splitting; they have different polarization and the spectrum of an isotopically diluted crystal, containing about 5% of D and 95% of H, shows only one component at 717 cm"1. The low-frequency band at 628 cm"1, on the other hand, is single and due to long hydrogen bond. The oOD and yOH modes have already been discussed and show to be more or less mixed with P-O stretching vibrations.

2. OH stretching vibrations The infrared stretching region (Fig. 6) is difficult to interpret since the ABC bands are very strong and broad and result from a superposition of the OH stretching fundamentals and Fermi resonance combinations of both short and long hydrogen bonds. Moreover, each of these bands of CsH2PO. shows parallel and perpendicular dichroism. Thus, it appears preferable to discuss the Raman spectra where we can distinguish the

J. Chem. Phys., Vol. 78, No.5, 1 March 1983



2115

TABLE V. Raman and infrared frequencies (cm"!) assigned to internal vibrations of A symmetry of the ferroelectric phase of CsH 2PO( and CsD 2PO( at 80 K. CsD 2PO(

CsH2PO( Raman 2680 2400 2340 1680 2660 2250 1800 1264 1256 1221 1219 1142 1134 1051 993 981

Infrared 2730

Assignmen~

vOH lona 2.s0H

2330 1740 1660

1220 1138 1006 963

2.s0H .sOH+yOH vOHshort

LO TO "PO LO vPO TO LO

TO

563 543 505 470 392 388 365

yOH. hort vPO vPO

910 872

LO

TO

jlOHloog

564 544 470 389 362

1970

2030 1860 1690 1270 1220

Assignment" vOD lona 2.s0H

1720 1360

vODsbort and 2 .sOD 2 yOD

LO .sOH.hort TO LO OOHloog TO

921 880 869

Infrared 2170

2 yOH

2660 2260 2180 1840

1258

Raman 2090 1760

LO TO .sOPO LO TO

1165 1155 1061 1011 970 955 933 918 881

542 533 505 480 388 385 362 360

1160 1020 961 923

LO TO LO TO LO TO LO TO

vPO vPO

.sODsbort vPO

874

vPO

702 628

yODshort yOD loDII

531 482 386 358

LO TO LO .sOPO TO LO TO

aLong =long hydrogen bond; short =short hydrogen bond.

/lOH and /100 bands belonging to two kinds of hydrogen bonding. The room-temperature Raman spectrum of CsD2 P04 (Fig. 5) shows two types of 00 stretching bands; a high frequency singlet at 2090 cm"1 observed only in a(ZZ)/3 scattering geometry and a low frequency doublet at 1970-1710 cm"1 followed by a weaker 1345 cm"1 band which appear in a(XX)/3 scattering. When the temperature is lowered to 80 K the frequencies of these bands do not change much the behavior of their bandwidths, however, being rather different (Fig. 11). The high-frequency band half-width narrows from 220 to 70 cm"1 while the bands of the doublet remain broad with .6./1112 =260 cm"l. Thus, we can aSSign the high-frequency singlet to the long and the low-frequency doublet to the short hydrogen bond, respectively. The doublet is interpreted as an 00 stretching fundamental in Fermi resonance with 2 000 overtones. The analogous OH stretching bands are less straightforward being more perturbed by various combination levels. Nevertheless, the 2750 cm"1 band observed in a(ZZ)/3 geometry can easily be identified as vOH fundamental in Fermi resonance with 2 OOH or oOH + yOH combination near 2330 cm"1 and 2 yOH level near 1700 cm"1 all of A,

speCies. All these bands narrow spectacularly (Fig. 10) when CsH2 PO, crystal is cooled to 80 K, the 2750 cm"1 band half-width being reduced from 470 to 85 cm"l. The short hydrogen bond, on the other hand, gives rise to a triplet at 2660-2250-1750 cm"l, in a(XX)/3 geometry, the band shape of which is much less temperature sensitive. It may appear surprising that the OH stretching band of the long and ordered hydrogen bond narrows so much on cooling while that of the short bond which goes from disordered to an ordered state below Tc does not. However, it should be born in mind that the most important band shaping mechanism in the case of strong hydrogen bonds is anharmonic coupling of the OH stretching and low-frequency hydrogen bond modes 28 and this may hide the effect of ordering. The vOH band broadening due to structural disorder, on the other hand, can be detected easily in the case of weaker hydrogen bonds such as found in ices 29 or some protonic conductors. 30 The OH stretching frequencies of the paraelectric phase corrected for Fermi resonance interactions are estimated to be near 2600 (vOD =2050) and 2100 (vOD =1860) cm"1 for the long and short hydrogen bond, re-


2116


TABLE VI. Calculated and observed infrared intensities for CsH2P0 4 A modes at 80 K. a

Spectroscopic studies of structural phase tranSitions, in particular of the order-disorder type, show frequently a strong temperature dependence of the Raman bandwidths in the vicinity of the transition temperature. 32033 A considerable line broadening caused by proton jumps along the OH' .. 0 bonds has been observed for an internal P-O stretching mode of KHZPO. 3Z and for three internal and a lattice mode of squaric acid. 34 A search for similar effects was undertaken for CSHzPO. and CsD zP04 and the temperature dependence of frequency, intensity, and half-width of a number of infrared and Raman bands was investigated.

a

TO

LO

1caJ.c

1."1}

122 205 365 b 388 470 543b 563b 869 900c 970c

129 249 366 392 505 544 564 880 910c 931 1051 1142 1221 1264 1820 2270 2680

0.12 0.75 0.03 0.12 1. 00 0.02 0.02

0.03 0.10 1. 00 0.01 0.03

4.65

5.47

0.26 0.10 0.34 1.69 2.09 2.35

0.36 0.10 0.41 2.45 1.04 0.96

993 1134 1219 1256 1800b 2250b 2660b

E. Phase transition

~he 470-505 cm"! band intensity is

taken as reference. ~he TO-LO splitting is supposed to be

within the experimental error. cThese values were estimated from the infrared intensities (see the text).

spectively. The values obtained for the ferroelectric phase at 80 K are close to 2630 ("OD =2080) cm"l for the long and near 2200 (vOD = 1870) cm"l for the short hydrogen bond. The OH stretching frequencies appear somewhat high for the reported 0 ... 0 distances. 27 3. Isotope effect

The above OH and OD stretching frequencies of the paraelectric phase yield vOH/vOD isotopiC frequency ratios of 1. 27 and 1. 13 for the long and short hydrogen bond, respectively, i. e., considerably lower than 1. 37, the harmonic oscillator value. This lowering of the isotopic frequency ratio is a spectroscopic manifestation of a positive isotope effect of assymetric hydrogen bonds z7 and can be correlated with neutron diffraction data given by Semmingsen and Thomas. 9 They found that the short hydrogen bond lengthens for 0.022 A on deuteration with Ro 3D... O. =2. 498 A and Ro 3 H... O. =2.476 A, while the longer hydrogen bond varies much less, RolJ)o ••oz =2. 540 A and RolH... Oz =2. 537 A, under the same conditions. Thus, stronger isotope effect and lower isotopiC frequency ratio is observed for shorter hydrogen bond as expected from the relation: vOH/vOD =p/[(pl/2 -1)("OOH/vOH + 1)],

with p = J.LD/ J.LH

established by Savelev and Sokolov3l where "oOH corresponds to the frequency of a free OH group. Assuming "oOH =3600 cm"l the calculated "OH/vOD ratios are equal to 1.28 and 1. 17 in fair agreement with the observed values. Similar isotopic frequency ratios (1. 27 and 1.13) have been observed and (1. 28 and 1.19) calculated for the ferroelectric phase.

The paraferroelectric phase transition of CSHzPO. implies ordering of protons of the short hydrogen bonds while the long bonds remain ordered. The most suitable bands for studying the corresponding OH or OD groups are the infrared yOD bands since they appear in a region free from interference of other bands, they are associated with relatively pure out-of-plane OD motions and are not perturbed by various combinations like OH or OD stretching modes. The frequencies vary surprisingly little for both short and long hydrogen bond while the corresponding half -widths appear more temperature sensitive (Fig. 12). However, there is no sudden change frequency 0 r half -width change near Te the relationship being linear in the 200-320 K region. Much the same is true of the OD stretching and of a number of other Raman and infrared bands, except that the vOD bandwidth of the long hydrogen bond is much more temperature sensitive than that of the short one. This absence of any drastic bandwidth variation in the vicinity of Tc contrasts sharply with the behavior of other ferroelectric crystals such as KH2P0 432 or H2C404.34 1. New lattice modes

There are two lattice modes at 148 and 74 cm"t, which are Raman inactive in the paraelectric phase, and appear in the spectra of the ferroelectric phase. The intenSity of the Raman bands in the 30-95 cm"l region was carefully measured between 80 and 170 K using X(Y :)Z scattering geometry. The result concerning the band at 74 cm"l is given in Fig. 13 where the relative intenSity of this bands is plotted as a function of temperature. The intenSity of this mode decreases with increaSing temperature and vanishes at T e , giving a curve of the order parameter type. However, the intensity measurements are not sufficiently accurate for the extraction of a critical exponent. 2. TO·LO splitting

Unlike the appearance of new modes which occurs only for lattice vibrations, TO-LO splitting occurs for lattice as well as internal vibrations of the polar lowtemperature phase. Some skeletal bending bands were examined in more detail and Fig. 14 shows the Raman spectra in the 430-580 cm"l region recorded at different temperatures in the Y(Xf)Y geometry corresponding to ALO bands. Two Raman skeletal bending bands at 563 and 543 cm"l appear temperature and transition



2117

B. Marchon and A. Novak: Spectra of CsH 2P0 4 and CsD 1P0 4 6.J}S

cm-1 40

30

20

1

,

,1TC

-Jcm-' 720

- SHORT-B . 1

b

0

II A

SHORT-A o

T(K)

300

260

220

0

0 0 10 0

o

6

450 640 LONG-A

•

•

. ..

.'... I I I I

FIG. 14. Backward Raman scattering of CsH2PO. single crystal using Y(X~) Y geometry at different temperatures in the 430-580 em-1 range.

.. ..

..

, Tc

600

220

260

550 cm-1

500

"T

300

(K)

FIG. 12. Half-width (~V1/2) and frequency (v) vs temperature plot for three out-of-plane OD infrared bands of CsD 2PO.; x-'YOD band of B species due to the short hydrogen bond, o-'YOD band of A species due to the short hydrogen bond, ~-'YOD band of A species due to the long hydrogen bond.

insensitive and they were taken as reference for the relative intensity measurements. The 470 cm- 1 band of the paraelectric phase, on the other hand, splits into a TO component at the same frequency and a LO component at 505 cm- 1 (a weak band at 500 cm- 1 is a leak of an oblique mode). The intensity of the LO band at 505 cm- 1 increases from zero at Tc with the decreasing temperature while the intensity of the 470 cm- 1 band decreases at the same time (Fig. 15). It should be pointed out that the intensity of the 470 cm- 1 band ought

> ~

III

Z

w ~

Z lot

cu >

..

w

->

os

~

II

C ....0 W

II::

'" Tc

10

110

130

T (K)

FIG. 13. Intensity of the 74 em-1 Raman line [X(Y§)Z geometry) vs temperature plot.

10

110

130

T

(K)

FIG. 15. Temperature dependence of the intensity of the 470 (0) and 505 (x) cm-1 Raman lines of CsH2PO. using Y(X~Y geometry.

J. Chem. PhY5., Vol. 78, No.5, 1 March 1983 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:42


2118

>

eter type and is very similar to that of the new mode at 74 cm- 1 (Fig. 13).

Z

The intensity of the mode at 470 cm- 1 studied in Z(x:rZ geometry leading to A-TO modes in the ferro-

.... iii zIII ....

....

electric phase, on the other hand, varies but little with temperature and the intensity vs temperature plot yields a smooth curve, even when crossing the transition point (Fig. 16). The same is true of the temperature dependence of its frequency and half-width showing that the "forbidden" modes of the paraelectric phase are the TO components of the polar modes. The fact that the LO counterparts were not observed in this phase remains unexplained for the present. Finally, the 470 and 505 cm- 1 bands show a rather different behavior as far as their bandwidth is concerned (Fig. 16); the half -width of the LO component of about 5 cm -1 almost does not change in the 80-150 K range while that of the TO band increases from 8-16 cm- 1 under the same conditions and reaches 28 cm- 1 at 220 K. This cannot be generalized for other TO-LO pairs as some bands, such as the 1051 cm- 1 LO band, are broader than the corresponding TO components (Fig. 11).

III

....~

e...

III

iii:

I

1Tc I

AIIYz cm-1

20

I

10

I

3. Hydrogen bond vibrations

I LO 501cm-1

+

J

I t

j

~

I I

Tc

0 120

80

160

200

T (K)

FIG. 16. Upper curve: Temperature dependence of the 470 cm -I Raman line intensity of C sHaPO, using Y(x~ Y geometry. Lower curves: Temperature dependence of the half-widths of the 470 and 505 cm-I Raman lines, using Z(x~)Z and Y(Xi)Y geometries, respectively.

to drop to zero below Tc since the TO component is forbidden in the Y(Xf)Y geometry the nonzero value being due to a TO leak. The intensity of the LO component vs temperature curve is also of the order param-

V cm- 1 LO-CsH2 P04

250

~

t

An interesting feature is found for the hydrogen bond stretching vibration corresponding to a R' lib ration of A species of CsH2PO.. This mode shows the largest relative LO-TO splitting 249-205 cm- 1 at 80 K. The LO frequency is almost temperature insensitive while the TO frequency remains constant up to Tc but increases strongly from 205-220 cm- 1 above Tc which is a rather unusual behavior for a lattice mode. The analogous TO frequency of CsD 2 PO., on the other hand, does not vary under the same conditions (Fig. 17). A possible explanation of such temperature dependence of this hydrogen bond stretching vibration is that the hydrogen bond becomes stronger at higher temperature. In fact, the Os' .. O. distance of the short hydrogen bond shortens from 2.488-2.476 Awhen going from the lowto the high-temperature phase 9 and the corresponding

I I I I

t~1

I I

I

LO-Cs D2P04

I

I

I

23

I

+~

FIG. 17. Temperature dependence of the hydrogen bond stretching frequencies (R'y libration of A species) of CsHaPO, and CsDaPO,.

I I

TO-CsD2P04

i 2

I I I I

~ ~14 I I

-80

-40

0

4

40

T -Tc

(K)



OH stretching frequencies decrease more on heating the crystal (from 2200 to 2100 cm- 1) than the OD stretching frequencies (1870 to 1860 cm- 1). The temperature dependence of the half -width of these hydrogen bond stretching Raman bands is also different; the slope of the t1111/ z vs temperature curve is much steeper for CSHzPO. with a maximum value of 45 cm- 1 than for CSDzPO. with t1111/ z '" 15 cm- 1 • This difference may be related to proton jumps along the OH· . ·0 and OD· .. 0 hydrogen bonds and to different anharmonicity of II (OH) •.. 0 and II(OD)' •• 0 vibrations. It may be argued qualitatively that the activation energy which is roughly the height of the potential barrier of the double well potential, must be considerably higher for OD ... 0 than for OH· .. 0 hydrogen bond, the former being longer. The corresponding correlation time, or tunneling probability, and half-width thus, are expected to be smaller for OD' .. 0 than for OH' .. 0 stretching vibration. A striking difference in bandwidth of the infrared bands near 220 and 208 cm- 1 due to 1I0H· •• 0 and vOD· •• 0 vibration, respectively (Fig. 3), is likely to be associated with the same phenomenon. IV. CONCLUSION

The external vibrations of the disordered paraelectric phase of CSHzPO. and CSDzPO. crystals follow generally the selection rules of the C2/I factor group and thus, see the statistical symmetry of the crystal in the same way as the x-ray and the neutron diffraction. The internal vibrations, on the other hand, do not obey these selection rules and do not see centers of inverSion, but only the TO modes are observed in Raman. The internal and external vibrations of the ordered ferroelectric phase are consistent with the selection rules derived from the C~ space group. Two new features are observed in Raman spectra; appearance of antisymmetric (u) modes of the paraelectric phase and TO-LO splitting. The former appear only for lattice modes while the latter is observed for a number of both lattice and internal Vibrations. The observed infrared intensities of the A bands agree reasonably well with the values calculated from the TO-LO splitting of the corresponding Raman bands. The Raman intensity of the LO component of a skeletal bending mode vs temperature plot gives a curve of the order parameter type and the same is true of the intensity of a new external mode. A systematic study of the temperature dependence of a number of Raman and infrared bands shows that no sudden frequency or half -width change occurs near Tc which contrasts with the behavior of other ferroelectric crystals such as KHaPO. 3a and HaC.O•. 34 No soft mode behavior has been observed. The fact that a hydrogen bond stretching frequency near 205 cm- 1 increases strongly with increasing temperature above Tc is probably due to a strengthening of the hydrogen bond at higher temperature which is corroborated by the behavior of the corresponding OH stretching frequencies and OH ..• O distances. 9 The half-width of the vOH'" 0 Raman band increases

2119

much faster with increasing temperature than that of the corresponding vOD· •• 0 band which may be ascribed mainly to the activation energy of the proton jumps expected to be larger for the OH' .. 0 than for the OD· .. 0 hydrogen bonds. ACKNOWLEDGMENTS

We are greatly indebted to Professor R. Blinc for single crystals and for having suggested this study, as well as to Professor R. Pick and to Dr. R. Krauzman for helpful discussions and for critical reading of the manuscript. Our thanks are also due to Dr. D. Semmingsen for having communicated his unpublished results, to Dr. F. Fillaux who developed a computer program for treatment of Raman bands, and to Mrs. J. Belloc for technical assistance.

lR. Blinc, B. :leks, A. Levstik, C. Filipic, J. Slak, M. Burgar, and I. ZupanciC, Phys. Rev. Lett. 43, 231 (1979). 2A. Levstik, R. Blinc, P. Kadaba, S. Cizikov, I. Levstik, and C. Filipic, Solid State Commun. 16, 1339 (1975). Sy. Uesu and J. Kobayashi, Phys. Status Solidi A 34, 475 (1976). 'D. Semmingsen, W. D. Ellenson, B. C. Frazer, and G. Shirane, Phys. Rev. Lett. 38, 1299 (1977). ~. J. Nelmes and R. N. P. Choudhary, Solid State Commun. 26, 823 (1978). Ga. C. Frazer, D. Semmingsen, W. D. Ellenson, and G. Shirane, Phys. Rev. B 20, 2745 (1979). 7M. Matsunaga, K. !toh, and E. Nakamura, J. Phys. Soc. Jpn. 48, 2011 (1980). By. Iwata, N. Koyano, and I. Shibuya, J. Phys. Soc. Jpn. 49, 304 (1980). 90. Semmingsen and R. Thomas (unpublished). lIR. Blinc, I. Zupancic, G. Lahajnar, J. Slak, V. Rutar, M. Verbec, and S. Zumer, J. Chern. Phys. 72, 3626 (1980). UB. Orel and D. Hadzi, J. Mol. Struct. 18, 495 (1973). 12M. Wada, A. Sawada, and Y. Ishibashi, J. Phys. Soc. Jpn. 47, 1571 (1979). lJa. Marchon, B. Pasquier, N. Le Calve, A. Novak, M. Copic, M. Zgonik, D. L. FOX, and B. B. Lavrencic, J. Chern. Phys. 74, 5923 (1981). 14J. P. Coignac and H. Poulet, J. Phys. 32, 679 (1971). 15y. Sato, J. Chern. Phys. 53, 887 (1970). 16H. Ratajczak, J. Mol. Struct. 3, 27 (1969). UN. Toupry-Krauzman, H. Poulet, and M. Le Postollec, J. Raman Spectrosc. 8, 115 (1979). 18K. Nakamoto, Infrared Spectra of Inorganic and Coordination Compounds, 3rd ed. (Wiley, New York, 1978), p. 142. 190. Hadzi and S. Bratos, in The Hydrogen Bond, edited by P. Schuster, G. Zundel, and C. Sandorfy (North-Holland, Amsterdam, 1976). 2oH. Poulet and J. P. Mathieu, SPectres de Vibration et Symetrie des Cristaux (Gordon and Breach, Paris, 1970), p. 160. 21R • P. Canterford and F. Ninio, J. Phys. C 8, 1750 (1975). 22C. Pigenet, N. Le Calve, and B. Pasquier, J. Raman Spectrosc. 9, 393 (1980). 23A. S. Barker, Phys. Rev. A 136, 1290 (1964). 2'R. Kurosawa, J. Phys. Soc. Jpn. 16, 1298 (1961). 2~. Claus, Proceedings of the International School of Physics Enrico Fermi, edited by S. Califano (Academic, New York, 1975), p. 470. 2Ga. Orel (private communication). 27A. Novak, Struct. Bonding 18, 177 (1974). 28s. Bratos, J. Lascombe, and A. Novak, in Molecular Interactions, edited by H. Ratajczak and W. J. Orville-Thomas

J. Chem. Phys., Vol. 78, No.5, 1 March 1983 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 147.143.2.5 On: Sat, 20 Dec 2014 18:09:42

2120


(Wiley, Chichester, 1980), Vol. I, p. 30l. 29J. E. Bertie and E. Whalley, J. Chern. Phys. 40, 637 (1964). 30p. Colomban and A. Novak, Solid State Commun. 32, 467 (1979). 31N. D. Sokolov and V. A. Savel'ev, Chern. Phys. 22, 383

(1977). 32 1.

Laulicht, J. Phys. Chern. Solids 39, 901 (1978). 3Jc. Sourisseau and G. Lucazeau, J. Raman Spectrosc. 8, 311 (1979).

MD. Bougeard and A. Novak, Solid State Commun. 27, 453 (1978).

