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Polarized infrared and raman spectra of monoclinic CsH2PO4 single crystal and its deuterated homologue CsD2PO4
Journal of Molecular Structure, 156 (1987) 15-27 Elsevier Science Publishers B.V., Amsterdam -Printed
in The Netherlands
POLARIZED INFRARED AND RAMAN SPECTRA OF MONOCLINIC CsH2P04 SINGLE CRYSTAL AND ITS DEUTERATED HOMOLOGUE CsD2P04 Part II. Internal vibrations of the PO, ion
V. VIDENOVA-ADRABINSKA
and W. WOJCIECHOWSKI
Institute of Inorganic Chemistry and Metallurgy of Rare Elements, of Wrocraw, Smoluchowskiego 23, 50-372 WrocZaw (Poland)
Technical University
J. BARAN Laboratory of Theoretical Chemistry and Chemical Physics, Institute of Chemistry, Wroctaw University, F. Joliot-Curie 14, 50-383 Wrociaw (Poland) (Received 28 May 1986)
ABSTRACT A correlation between the experimentally observed and the theoretically predicted bands of the internal orthophosphate ion vibrations was made. By measuring the infrared spectra in different orientations in the planes of the crystal axes, the problem of coupling effects was elucidated using the polarization properties and the isotopic effect for both internal PO, modes and the hydrogen bond modes. Intra-ion coupling for the PO, stretching modes, as well as interion couplings between the neighbouring PO, groups inside the primitive cell, are inferred from the infrared spectra. The observed anomalies of the paraelectric phase with respect to the selection rules are explained by the disorder character of the short hydrogen bond. The band parameters for the PO, Raman stretching modes vs. temperature were measured and the problem of the abrupt changes observed in some of these characteristics in the vicinity of the ferroelectric change temperature, T,, is discussed. INTRODUCTION
In a previous paper [l] we paid considerable attention to the vibrational properties of the strong hydrogen bonds occurring in the CsH2P04 crystal. However, there was no discussion on the internal modes of the orthophosphate ions linked in the crystal net through these hydrogen bonds. Since none of the workers who have studied the spectra of this crystal [2--41 was concerned with detailed analysis of the PO4 ion internal vibrations we decided to study this with regard to the ion symmetry in the crystal lattice. From our previous experience of investigating KDP-type crystals [5, 61 and from reported data [7-121 we have noticed considerable discrepancy between the number of bands and/or their symmetry predicted by the selection rules and the number of bands observed in the spectra measured. Attempts to explain 0022-2860/87/$03.50
0 1987 Elsevier Science Publishers B.V.
16
these anomalies have been made in different ways [8]. It is essential to consider that the PO4 ions vibrate in the crystal field perturbed by very strong hydrogen bonds. Changes in the PO4 stretching region due to the lowering of the ion symmetry from Td to CsV (or less) and to CzV (or less) in different orthophosphates in H,O and DzO solutions and correlations with some crystal spectra were reported in ref. 13. Since the CsH2P04 single crystal has a relatively low symmetry P2Jm in the paraelectric phase and P21 in the ferroelectric phase, it appears to be appropriate for studying the problem of the phosphate group skeletal vibrations. Our main intentions were: (i) to correlate the experimentally-observed bands with the theoretically-predicted values and to explain any discrepancy; (ii) to ascertain or to reject the possible resonance coupling between the skeletal modes and the hydrogen bond modes. Significant changes in the intensity and the frequency, mainly for the skeletal stretching bands, by different orientations of the electric vector were observed and inspired the present study. Using the polarization properties and the isotopic effect for both the internal modes of PO4 ions and the hydrogen bonds and measuring spectra in different orientations in the planes of the crystal axes we were able to obtain useful information which explained the interference effects and clarified the influence of the surrounding neighbourhood. The experimental conditions used have been reported [l] . CRYSTAL STRUCTURE AND SELECTION VIBRATIONS OF THE ORTHOPHOSPHATE
RULES ION
FOR THE INTERNAL
At room temperature, CDP is monoclinic and belongs to the P2,/m space symmetry group with two formula units per a unit cell [ 141. The PO, ions are joined through the shorter hydrogen bond (2.48 a) into chains running along the b-axis (which is the ferroelectric one). These chains are crosslinked by the longer hydrogen bond (2.54 A) to form (100) layers. The longer hydrogen bond is already ordered in the paraelectric phase, but the shorter one is disordered with a proton statistically distributed between two offcenter equivalent sets [ 141. Below T, (153 K for CDP and 267 K for DCDP) the protons in the shorter hydrogen bond are ordered to the one oxygen atom (0;) of the PO4 group, disturbing the PO4 ion configuration and lowering its symmetry from C, (in the paraelectric phase) to C1 (in the ferroelectric phase). Little or no change is expected in the P-O, and P-O2 distances since O1 and O2 are involved with the already ordered H,(D,) bond system. This was born out in a comparison of distances calculated on the one hand from the crystallographic positions in the paraelectric phase and on the other, after applying the atomic displacement parameters in the ferroelectric phase for CsD2P04 [ 141. In both cases (paraelectric and ferroelectric phase) = 1.49 a (where the close association of D1 is = 1.57 a and dp-o, dP-0, with 0,). However, the two P-Q bonds, being crystallographically equivalent with a length of 1.53 A (calculated from structural data), become
17
unequal in the displaced calculation, dp-O; = 1.61 A and dp__O, = 1.47 A (where 0; designates the oxygen with which Dz becomes associated). As there are no data for the protonated crystal, we assume these distances also to be valid for the CsH2P0, crystal. Thus, the Td symmetry of the free PO4 ion should be disturbed by the crystal field and become lowered to C, in the paraelectric and to C1 in the ferroelectric phase. This lowering of the symmetry should lead to splitting of the F2 and E modes into three and two different components, respectively, and these should appear at different wave numbers in the spectra. Also taking into account the coupling effects of the neighbouring groups in the unit cell, the number of bands should be doubled. Hence, 9 bands should be expected for the PO, internal modes in the oriented gas model approximation (site symmetry) or 18 bands in the approximation of the unit cell symmetry (factor group) for both paraelectric and ferroelectric phases. However, the internal modes should belong to different symmetry species in the paraelectric and the ferroelectric phase, so that their polarization properties should also differ. BAND
ASSIGNMENT
AND
DISCUSSION
The orthophosphate ion in aqueous solution is known to have tetrahedral symmetry (Td) and its fundamental modes appear at 1020 cm-’ (v3(F2)), 940 cm-’ (v1(A3)), 560 cm-’ (vJF?)) and 420 cm-’ (v,(E)) [15]. Tables 1 and 2 present the selection rules in the paraelectric and ferroelectric phases as well as bands observed in both infrared and Raman spectra, assigned on the basis of their symmetry to the proper vibrations. It is difficult to consider the selection rules by taking into account simultaneously the infrared and the Raman spectra, as they appear to follow different rules. For example, the region of the asymmetric stretching mode v3(FZ) in the Raman spectrum could be explained by considering the site symmetry only so that the triple degenerated mode at 1020 cm-’ splits into three bands at 1130 (Ag), 990 (A,, Be) and 920 cm-’ (Ag, Bg). However, in the infrared spectra the correlation field coupling should be considered because six broad bands are observed at 1150 (B,), 1130 (A,), 1080 (B,), 1025 (A,), 970 (II,) and 940 cm-’ (A,). The symmetric stretching mode yields two infrared bands of different polarization at 870 cm-’ (11b) and 890 cm-’ (lb) instead of the single band expected. The appearance of six infrared asymmetric stretching bands instead of three and of two totally symmetric stretching bands instead of one favours the CZ instead of the CZh factor group even in the paraelectric phase. This means that the skeletal stretching modes do not see the crystallographic Ci symmetry and are managed rather by the rules of the CZ group. For the deformation modes, in the paraelectric phase the vq bands fit neither the CZh nor the CZ factor group symmetry in both infrared and Raman spectra. In the ferroelectric phase the infrared spectra fit the CZ group symmetry yielding three A-species bands (560, 540 and 470 cm-‘) and three
18
-
-2A
V&G
-
v#‘,)
qtA,LlA<;
v~(F,)
3A
3A
Factor group symmetry Cl
for the PO,
Ib
Ilb
2A
2B
lb
Ilb
E
lb
Ilb
YY.
YZ
xz
2.2, xz
z.z,
.zZ, xz
XY, YZ
xx, yy,zz xz
XY,
xx, YY,
yz
xx, xy,
YZ
XY,
xx, YY,
420 390dep
435 390dep
440 390
390
565 545 530 470 385
485
810
1160 1030*20 960
Ilb
IR
470
480dep
(870~~)
1005m dep 925"s
1135 990sdep 925
Raman
540 530
555 520 505
900sn
116Ch1210 1080~s 960
lb
crystal
CsD,PO,
phase of the CsH,PO,
560 540
870
1140s 1010 940
Ilb
IR
IR Raman
in the ferroelectric
CsH,PO,
vibrations
Activity
ion internal
3B
3A
3A
--c
Site ISOUP symmetry Cl
Free ion symmetry Td
diagram
chart
2
Correlation
TABLE
430 385
540 530 500
890
vs
1170--1220 1075sb 970
lb
(425 dep) 385dep
(425dep) 385dep 360
485
535 520
545 535dep (500) 485
890 880 1 88Ovw
(llSOw?) 1155 1025 920
(1180 w ?) 1155 1025 920
Raman
-
20
B-species bands (at 555, 520 and 505 cm-‘). However the number of the Raman v4 bands remains unaltered at 4 in the low temperature spectra, although some bands alter their position slightly. The room temperature spectra yield one depolarized infrared band (at 390 cm-‘) and two Raman bands (at 390 and 430 cm-‘) in the region of the v2 mode. Thus no apparent preferences for either the CZh or CZ groups in regard to the skeletal bending modes in the paraelectric phase are evident. These anomalies of the paraelectric phase for the selection rules can be explained by considering the disorder character of the short hydrogen bond. As mentioned before the proton (deuteron) H,(D,) is statistically distributed between two equivalent off-center positions. If the proton is considered to jump between them on the time scale, the inverse of the band frequencies for the stretching vibrations v 1 and u3 could be comparable with the time rp which the proton spends in each position. Hence the stretching vibrations distinguish the two different PO4 configurations and see the proton as ordered in one of them, implying CZ group symmetry. However, the inverse frequencies for the deformation vibrations are neither low enough to distinguish these sets, nor high enough to treat them as completely indistinguishable. Thus the skeletal bending modes v2 and v4 do fit neither the CZh nor the CZ space symmetry group. The changes observed in the band position and intensity (Fig. 1) especially for the skeletal stretching vibrations with changes in the electric vector orientation or by deuteration suggest coupling effects between the internal vibrations. We will discuss this problem in detail. (i) The very significant intensity changes by different electric vector orientations of the &-components of the u1 and v3 modes prompted a search for a possible coupling effect inside the PO4 ion. In the paraelectric phase coupling between the P-O1 and P-O2 bonds (involved in the longer hydrogen bond) and the P-O3 and P-0; bonds (involved in the shorter hydrogen bond) seemed to be logical bearing in mind the equal P-O3 distances of the bonds. However, in the ferroelectric phase coupling between the elongated bonds P--O1(nl) and P-O& (involving oxygens to which the protons are ordered) as well as between the two other shorter bonds PY02 and P-O3 seemed more logical. The correlation of the calculated direction co? (Table 3) for both cases with the infrared dichroism of the v1 and v3 bands confirms the second model. Thus, the four modes in the skeletal stretching region may be regarded as largely made up by the P-(0,), P-(O), symmetrical and P-(O), symmetrical, P-( OH)Z asymmetrical, asymmetrical modes in order of increasing frequencies. Thus, the bands at 900 cm-’ (v,P-(On),) and 1080 cm-’ (v,P-(0),) are the most intensive by small magnitudes of the angle* (II (Fig. l), whereas the band at 950 cm-’ (v,,P-(On),) shows the greatest intensity in spectra measured for 45” < (Y *01 is the angle between the crystallographic axis c and the direction of the incident light measured clockwise in the (010) plane.
of the electric
vector
21
50"
i
J
LA
800
1200
Fig. 1. IR spectra of the PO, stretching region measured using different orientations of the electric vector in the (010) plane. (Y is the angle between the electric vector of the incident light and c-axis. T = 20 K.
However, in the direction (Y= (125”-135” ) only one band (1180 cm-‘) originating from v,, P-(O), appears in the spectra, which agrees very well with the structural considerations. (ii) Beside the inside ion coupling for the PO4 stretching vibrations described, inter-ion couplings between the neighbouring PO, groups inside the primitive cell are inferred from the A-B (Davydov) splitting seen in the infrared spectra. (iii) The deuteration mass effects and the band position shifts depending
< 70".
22
TABLE 3 The calculated direction cos’ of the transition dipole stretching modes in the CsH,PO, crystal Type of mode
moments
of the PO, internal
a*
b
C
@.na
Paraelectric phase VPO(1) VPO(2) v,PO(l)O(2) v,PO(l)O(2) VPO(3) VPO(4) v,PO(3)0(4) v,PO(3)0(4)
0.56 0.22 0.03 0.97 0.29 0.29 0.00 0.89
0.00 0.00 0.00 0.00 0.67 0.67 1.00 0.00
0.44 0.78 0.97 0.03 0.04 0.04 0.00 0.11
42 152 170 100 109 109
Ferroelectric ~,PO(l)O(4) ~,PW)O(4) ~w2m(3) ~w2)0(3)
0.65 0.03 0.36 0.00
0.26 0.46 0.24 0.58
0.09 0.51 0.40 0.42
70 13 136 6
109
phase
aa is the angle between the -c direction and the projections of the transition dipole moments on the (010) plane. With O(l), O(2), O(3) and O(4) are assigned the 0,, 0,, 0, and 0; from the text.
on OLcorrelated with the dipole moment directions of the proton vibrations and support resonance coupling between the internal vibrations of the PO4 group and the hydrogen bonds. The most prominent band position changes are found for the v,P(O)~ mode which shifts from 1130 cm-’ up to 1220 cm-’ in different orientations (see the curve in Fig. 2). The lowest wavenumber position (in the a! = 125”--135” direction) seems to correspond to the pure vibration because no absorption from the vzOH vibration occurs in this
O0
30'
60“
I I, 90"
I I a 1, 150" 120"
I
a
I
1806
Fig. 2. The frequency of the v,PO, IR mode as a function of the electric vector (E) orientation. oi is the angle between the E and -c direction.
23
direction (**OS*** 0; is in the direction (Y= 52”). However, in the infrared spectra of the shorter hydrogen bond, the symmetric and asymmetric VP(O), modes resonate slightly with the v20H vibration which pushes them to higher frequencies. Addition resonance couplings of vB,P(0), with the in-plane deformation hIOH (originating from the longer bond) and very likely also with 6,OH (originating from the shorter bond) caused it to shift to 1220 cm-’ (in directions closed to their dipole moment orientations (Y= 90”) (Figs. 1 and 2). The v,P(O& and vasP(O& modes appear to be quite pure in the spectra of the protonated compound as they are far from the OH stretching and the in-plane deformation regions. The out-of-plane yOH bending modes do not affect other vibrations. However in the spectra of the deuterated crystal the 610D and &OD modes are in the range 800-1000 cm-’ and disturb the vP(O& modes. On the other hand the v,P(O), and v,,P(O), modes shift to higher frequencies because the v, OD absorption shifts down. The deformation skeletal modes seem to resonate slightly with the out-ofplane rzOD modes since they shift on deuteration. However no obvious trends are seen in this region. TEMPERATURE DEPENDENCE OF THE BAND FREQUENCY HALF-WIDTH OF THE PO:- STRETCHING MODES
AND BAND
The Raman spectra of both CDP and DCDP were studied over a range of temperatures. Results are given in Figs. 3-7. Figure 3 presents the band position and the half-width of the v3 modes at 990 cm-’ (in CDP) vs. temperature. These dependences are almost the same as those reported in ref. 3 yielding an abrupt change in the vicinity of T,. The out-of-plane r,OH mode also lies in this region and becomes active in the ferroelectric phase (Fig. 4). However, the half-width of the v3 mode (at 1130 cm-‘) rapidly increases with increasing temperature in the paraelectric phase (140-220 K), but its band position remains almost unaltered (Fig. 5). For the spectra of the D-compound, the temperature functions of the band parameters (D and AU) for the four skeletal stretching modes are presented in Fig. 6 (from the x-spectra) and Fig. 7 (from the xx-spectra). The v3 bands at 920 cm-’ and 1025 cm-’ (a counterpart of the band at 990 cm-’ in CDP) shows a nearly linear increase of half-width (Au) with temperature up to 247 K, followed by an abrupt decrease and then a further increase. The third v3 band at 1153 cm-’ (a counterpart of the v3 band at 1130 cm-’ in CDP) implies also a linear characteristic with a half-width remaining almost unchanged till 247 K and then rapidly increasing with increasing temperature in the paraelectric phase. The band frequency seems to be unvarying for v3 at 1025 cm-’ and continuously decreases for v3 at 920 cm-’
**o
s---O;
is the hydrogen
bond of a shorter
distance
(ref. 1).
(a)
.
. . . .
.
7
.
.
( b)
1005
* *
1000
9901
’
’ ’ 100
’
’
’
’
200
’
’
’
’
’
300 T/K
*
Fig. 3. Temperature dependence of the band parameters of the v,PO, mode (at 990 cm-‘) in the zz-Raman spectrum (a* (cc)21 geometry) of the CsH,PO, crystal: (a) band halfwidth; (b) band position.
with the increase of the temperature up to 240 K, where an abrupt reduction is observed. All these anomalous changes for the v3P04 modes take place in the range of the phase transition, but it is likely that the transition temperature is lowered to 247 K due to incomplete deuteration. It should be mentioned that the shape of the half-width curve for the band at 920 cm-’ observed in the region 120-180 K is caused by both in-plane-deformation modes (hlOD at 904 cm-’ and &OD at 940 cm-‘) broadening with increasing temperature, so that they become mixed with the v3 mode and finally become obscured by it, disturbing its linear character. However, the halfwidth Au vs. T characteristic of the totally symmetric stretching mode u1 (at 880 cm-‘) is linear in the range from 20 K to 105 K and from 100 K to 250 K, with a slight bend in the vicinity of 100 K. It is difficult to explain the anomalous behaviour with changing temperature of the bands at 920 and 990 cm-’ (which change abruptly in the vicinity of T,), and at 1130 cm-’ (giving a rapid increase with temperature higher than T,). It is possible that this could be an intrinsic characteristic of a given mode indicated by the correlation of the ion vibrations with each other (by phonon propagation other than that in the (a*~) plane) as was suggested by Aoki et al. [3]. But if this is accepted, such an abrupt temperature dependence should be expected (i) for all stretching vibrations, which is not
25
95K
65 50 35 15 1200
1100
RAMAN
900
1000
10
SHIFT
Fig. 4. Raman peratures.
spectra
of CsH,PO,
crystal
measured
in the v) PO, region at different
tem-
r(a’
CiJ ‘4 _ 16-
00
00
15 1413-
0
12-
0 0
11i
00
0
,
00
00
000 0
“25’
/
4
80
’
’
’
’
’
’
200
’
’
’
’
’
300
’
8
‘0
T/K
Fig. 5. Temperature dependence the zz-Raman spectra (a* (cc)b (b) band frequency.
of the band parameters of the v, mode (at 1130 cm-‘) in geometry) of the C.&PO, crystal: (a) band half-width;
26
30.
2O-e..9! . . .
4:
'a-
2'
300
200
100
20
V K
100
200
300 T/K
Fig. 6. Temperature dependence of the band parameters of the vP0, stretching modes in the zz-Raman spectra (a*(cc)b geometry) of the CsD,PO, crystal: (a) the band half-width of the v,PO, mode at 880 cm-’ (x) and for the v,PO, mode at 920 cm-’ (B). Dashed line represents the s,OD mode at 904 cm-‘. Solid line represents the 6,OD mode at 941 cm-‘. (b) The band half-width of the v,PO, mode at 1025 cm-’ (*) and at 1150 cm-’ (0); (c) the band position for the v,PO, mode at 920 cm-‘; (d) the band position for the v,PO, mode at 1025 cm-‘.
5 1030t
(a)
(a)
0
1020t
O
O
0
0 0
0
1010 'L'
40
&*‘B’a.
(bl
lb)
J *yz 30
0
2040 -200
0
220
0
0
00
240
260
280
0
300
320 T/K Fig. 7. Temperature dependences of the band parameters of the v,PO, mode at 1025 cm-’ in the xx-Raman spectrum (c(a*a*)b geometry) of the CsD,PO, crystal: (a) the band position; (b) the band half-width.
27
observed experimentally (for v1 mode); (ii) by each phonon propagation other than that in the (010) plane. However, in Fig. 7 are presented the Au = f(T) and 0 = f(T) characteristics for the v3 mode (at 1025 cm ’ in DCDP) in the geometry c(a*a*)b, i.e. with a scattering vector in the direction of the b-axis, where no abrupt changes were observed. On the other hand a possible reason for the observed anomalies in the v3P04 mode characteristics could be some resonance coupling between the skeletal stretching modes and the deformation vibrations (610D and 6,OD for the band at 920 cm-’ or a10H for that at 990 cm-‘). As far as the v1 (at 880 cm-‘) and v3 (at 1130 cm-‘) modes are concerned, they lie rather far from the deformation modes and the plotted diagrams are thought to imply their intrinsic properties. Thus, the problem of the anomalous behaviour of the band parameters (Av and U) vs. temperature in the vicinity of T, observed for some skeletal stretching modes in the zz-Raman spectral still remains open to discussion REFERENCES 1 V. Videnova-Adrabinska and J. Baran, J. Mol. Struct., 156 (1986) 1. 2 B. Marchon and A. Novak, J. Chem. Phys., 78 (1983) 2105. 3 M. Aoki, M. Kasahara and I, Tatsuzaki, J. Raman Spectrosc., 15 (1984) 97. 4 S. S. Ti, S. Rumble and F. Ninio, Solid State Commun., 44 (1982) 129. 5 J. Baran, Ph. D. Thesis, University of Wrodaw, 1976. 6 V. Videnova, Ph. D. Thesis, University of Wroctw, 1979. 7 H. Ratajczak, J. Mol. Struct., 3 (1969) 27. 8 H. Ratajczak, J. Mol. Struct., 11 (1972) 267. 9 R. P. Lowndes, N. E. Tornberg and R. C. Leung, Phys. Rev. B, 10 (1974) 911. 10 N. E. Tornberg and R. P. Lowndes, J. Mol. Struct., 19 (1973) 555. 11 E. V. Chisler, I. T. Savatinova and V. Yu. Davydov, Opt. Spectrosk., 32 (1972) 544. 12 E. V. Chisler, V. Yu. Davydov and I. T. Savatinova, Fiz. Tverd. Tela, 13 (1971) 1949; 13 (1971) 1599. 13 A. C. Chapman and L. E. Thirlwell, Spectrochim. Acta, 20 (1964) 937. 14 B. C. Frazer, D. Semmingsen, W. D. Ellenson and G. Shirane, Phys. Rev. B, 20 (1979) 2745. 15 H. Schutze, N. Weinstock, A. Miiller and G. Vandrish, Spectrochim. Acta, Part A, 29 (1973) 1705.
in The Netherlands
POLARIZED INFRARED AND RAMAN SPECTRA OF MONOCLINIC CsH2P04 SINGLE CRYSTAL AND ITS DEUTERATED HOMOLOGUE CsD2P04 Part II. Internal vibrations of the PO, ion
V. VIDENOVA-ADRABINSKA
and W. WOJCIECHOWSKI
Institute of Inorganic Chemistry and Metallurgy of Rare Elements, of Wrocraw, Smoluchowskiego 23, 50-372 WrocZaw (Poland)
Technical University
J. BARAN Laboratory of Theoretical Chemistry and Chemical Physics, Institute of Chemistry, Wroctaw University, F. Joliot-Curie 14, 50-383 Wrociaw (Poland) (Received 28 May 1986)
ABSTRACT A correlation between the experimentally observed and the theoretically predicted bands of the internal orthophosphate ion vibrations was made. By measuring the infrared spectra in different orientations in the planes of the crystal axes, the problem of coupling effects was elucidated using the polarization properties and the isotopic effect for both internal PO, modes and the hydrogen bond modes. Intra-ion coupling for the PO, stretching modes, as well as interion couplings between the neighbouring PO, groups inside the primitive cell, are inferred from the infrared spectra. The observed anomalies of the paraelectric phase with respect to the selection rules are explained by the disorder character of the short hydrogen bond. The band parameters for the PO, Raman stretching modes vs. temperature were measured and the problem of the abrupt changes observed in some of these characteristics in the vicinity of the ferroelectric change temperature, T,, is discussed. INTRODUCTION
In a previous paper [l] we paid considerable attention to the vibrational properties of the strong hydrogen bonds occurring in the CsH2P04 crystal. However, there was no discussion on the internal modes of the orthophosphate ions linked in the crystal net through these hydrogen bonds. Since none of the workers who have studied the spectra of this crystal [2--41 was concerned with detailed analysis of the PO4 ion internal vibrations we decided to study this with regard to the ion symmetry in the crystal lattice. From our previous experience of investigating KDP-type crystals [5, 61 and from reported data [7-121 we have noticed considerable discrepancy between the number of bands and/or their symmetry predicted by the selection rules and the number of bands observed in the spectra measured. Attempts to explain 0022-2860/87/$03.50
0 1987 Elsevier Science Publishers B.V.
16
these anomalies have been made in different ways [8]. It is essential to consider that the PO4 ions vibrate in the crystal field perturbed by very strong hydrogen bonds. Changes in the PO4 stretching region due to the lowering of the ion symmetry from Td to CsV (or less) and to CzV (or less) in different orthophosphates in H,O and DzO solutions and correlations with some crystal spectra were reported in ref. 13. Since the CsH2P04 single crystal has a relatively low symmetry P2Jm in the paraelectric phase and P21 in the ferroelectric phase, it appears to be appropriate for studying the problem of the phosphate group skeletal vibrations. Our main intentions were: (i) to correlate the experimentally-observed bands with the theoretically-predicted values and to explain any discrepancy; (ii) to ascertain or to reject the possible resonance coupling between the skeletal modes and the hydrogen bond modes. Significant changes in the intensity and the frequency, mainly for the skeletal stretching bands, by different orientations of the electric vector were observed and inspired the present study. Using the polarization properties and the isotopic effect for both the internal modes of PO4 ions and the hydrogen bonds and measuring spectra in different orientations in the planes of the crystal axes we were able to obtain useful information which explained the interference effects and clarified the influence of the surrounding neighbourhood. The experimental conditions used have been reported [l] . CRYSTAL STRUCTURE AND SELECTION VIBRATIONS OF THE ORTHOPHOSPHATE
RULES ION
FOR THE INTERNAL
At room temperature, CDP is monoclinic and belongs to the P2,/m space symmetry group with two formula units per a unit cell [ 141. The PO, ions are joined through the shorter hydrogen bond (2.48 a) into chains running along the b-axis (which is the ferroelectric one). These chains are crosslinked by the longer hydrogen bond (2.54 A) to form (100) layers. The longer hydrogen bond is already ordered in the paraelectric phase, but the shorter one is disordered with a proton statistically distributed between two offcenter equivalent sets [ 141. Below T, (153 K for CDP and 267 K for DCDP) the protons in the shorter hydrogen bond are ordered to the one oxygen atom (0;) of the PO4 group, disturbing the PO4 ion configuration and lowering its symmetry from C, (in the paraelectric phase) to C1 (in the ferroelectric phase). Little or no change is expected in the P-O, and P-O2 distances since O1 and O2 are involved with the already ordered H,(D,) bond system. This was born out in a comparison of distances calculated on the one hand from the crystallographic positions in the paraelectric phase and on the other, after applying the atomic displacement parameters in the ferroelectric phase for CsD2P04 [ 141. In both cases (paraelectric and ferroelectric phase) = 1.49 a (where the close association of D1 is = 1.57 a and dp-o, dP-0, with 0,). However, the two P-Q bonds, being crystallographically equivalent with a length of 1.53 A (calculated from structural data), become
17
unequal in the displaced calculation, dp-O; = 1.61 A and dp__O, = 1.47 A (where 0; designates the oxygen with which Dz becomes associated). As there are no data for the protonated crystal, we assume these distances also to be valid for the CsH2P0, crystal. Thus, the Td symmetry of the free PO4 ion should be disturbed by the crystal field and become lowered to C, in the paraelectric and to C1 in the ferroelectric phase. This lowering of the symmetry should lead to splitting of the F2 and E modes into three and two different components, respectively, and these should appear at different wave numbers in the spectra. Also taking into account the coupling effects of the neighbouring groups in the unit cell, the number of bands should be doubled. Hence, 9 bands should be expected for the PO, internal modes in the oriented gas model approximation (site symmetry) or 18 bands in the approximation of the unit cell symmetry (factor group) for both paraelectric and ferroelectric phases. However, the internal modes should belong to different symmetry species in the paraelectric and the ferroelectric phase, so that their polarization properties should also differ. BAND
ASSIGNMENT
AND
DISCUSSION
The orthophosphate ion in aqueous solution is known to have tetrahedral symmetry (Td) and its fundamental modes appear at 1020 cm-’ (v3(F2)), 940 cm-’ (v1(A3)), 560 cm-’ (vJF?)) and 420 cm-’ (v,(E)) [15]. Tables 1 and 2 present the selection rules in the paraelectric and ferroelectric phases as well as bands observed in both infrared and Raman spectra, assigned on the basis of their symmetry to the proper vibrations. It is difficult to consider the selection rules by taking into account simultaneously the infrared and the Raman spectra, as they appear to follow different rules. For example, the region of the asymmetric stretching mode v3(FZ) in the Raman spectrum could be explained by considering the site symmetry only so that the triple degenerated mode at 1020 cm-’ splits into three bands at 1130 (Ag), 990 (A,, Be) and 920 cm-’ (Ag, Bg). However, in the infrared spectra the correlation field coupling should be considered because six broad bands are observed at 1150 (B,), 1130 (A,), 1080 (B,), 1025 (A,), 970 (II,) and 940 cm-’ (A,). The symmetric stretching mode yields two infrared bands of different polarization at 870 cm-’ (11b) and 890 cm-’ (lb) instead of the single band expected. The appearance of six infrared asymmetric stretching bands instead of three and of two totally symmetric stretching bands instead of one favours the CZ instead of the CZh factor group even in the paraelectric phase. This means that the skeletal stretching modes do not see the crystallographic Ci symmetry and are managed rather by the rules of the CZ group. For the deformation modes, in the paraelectric phase the vq bands fit neither the CZh nor the CZ factor group symmetry in both infrared and Raman spectra. In the ferroelectric phase the infrared spectra fit the CZ group symmetry yielding three A-species bands (560, 540 and 470 cm-‘) and three
18
-
-2A
V&G
-
v#‘,)
qtA,LlA<;
v~(F,)
3A
3A
Factor group symmetry Cl
for the PO,
Ib
Ilb
2A
2B
lb
Ilb
E
lb
Ilb
YY.
YZ
xz
2.2, xz
z.z,
.zZ, xz
XY, YZ
xx, yy,zz xz
XY,
xx, YY,
yz
xx, xy,
YZ
XY,
xx, YY,
420 390dep
435 390dep
440 390
390
565 545 530 470 385
485
810
1160 1030*20 960
Ilb
IR
470
480dep
(870~~)
1005m dep 925"s
1135 990sdep 925
Raman
540 530
555 520 505
900sn
116Ch1210 1080~s 960
lb
crystal
CsD,PO,
phase of the CsH,PO,
560 540
870
1140s 1010 940
Ilb
IR
IR Raman
in the ferroelectric
CsH,PO,
vibrations
Activity
ion internal
3B
3A
3A
--c
Site ISOUP symmetry Cl
Free ion symmetry Td
diagram
chart
2
Correlation
TABLE
430 385
540 530 500
890
vs
1170--1220 1075sb 970
lb
(425 dep) 385dep
(425dep) 385dep 360
485
535 520
545 535dep (500) 485
890 880 1 88Ovw
(llSOw?) 1155 1025 920
(1180 w ?) 1155 1025 920
Raman
-
20
B-species bands (at 555, 520 and 505 cm-‘). However the number of the Raman v4 bands remains unaltered at 4 in the low temperature spectra, although some bands alter their position slightly. The room temperature spectra yield one depolarized infrared band (at 390 cm-‘) and two Raman bands (at 390 and 430 cm-‘) in the region of the v2 mode. Thus no apparent preferences for either the CZh or CZ groups in regard to the skeletal bending modes in the paraelectric phase are evident. These anomalies of the paraelectric phase for the selection rules can be explained by considering the disorder character of the short hydrogen bond. As mentioned before the proton (deuteron) H,(D,) is statistically distributed between two equivalent off-center positions. If the proton is considered to jump between them on the time scale, the inverse of the band frequencies for the stretching vibrations v 1 and u3 could be comparable with the time rp which the proton spends in each position. Hence the stretching vibrations distinguish the two different PO4 configurations and see the proton as ordered in one of them, implying CZ group symmetry. However, the inverse frequencies for the deformation vibrations are neither low enough to distinguish these sets, nor high enough to treat them as completely indistinguishable. Thus the skeletal bending modes v2 and v4 do fit neither the CZh nor the CZ space symmetry group. The changes observed in the band position and intensity (Fig. 1) especially for the skeletal stretching vibrations with changes in the electric vector orientation or by deuteration suggest coupling effects between the internal vibrations. We will discuss this problem in detail. (i) The very significant intensity changes by different electric vector orientations of the &-components of the u1 and v3 modes prompted a search for a possible coupling effect inside the PO4 ion. In the paraelectric phase coupling between the P-O1 and P-O2 bonds (involved in the longer hydrogen bond) and the P-O3 and P-0; bonds (involved in the shorter hydrogen bond) seemed to be logical bearing in mind the equal P-O3 distances of the bonds. However, in the ferroelectric phase coupling between the elongated bonds P--O1(nl) and P-O& (involving oxygens to which the protons are ordered) as well as between the two other shorter bonds PY02 and P-O3 seemed more logical. The correlation of the calculated direction co? (Table 3) for both cases with the infrared dichroism of the v1 and v3 bands confirms the second model. Thus, the four modes in the skeletal stretching region may be regarded as largely made up by the P-(0,), P-(O), symmetrical and P-(O), symmetrical, P-( OH)Z asymmetrical, asymmetrical modes in order of increasing frequencies. Thus, the bands at 900 cm-’ (v,P-(On),) and 1080 cm-’ (v,P-(0),) are the most intensive by small magnitudes of the angle* (II (Fig. l), whereas the band at 950 cm-’ (v,,P-(On),) shows the greatest intensity in spectra measured for 45” < (Y *01 is the angle between the crystallographic axis c and the direction of the incident light measured clockwise in the (010) plane.
of the electric
vector
21
50"
i
J
LA
800
1200
Fig. 1. IR spectra of the PO, stretching region measured using different orientations of the electric vector in the (010) plane. (Y is the angle between the electric vector of the incident light and c-axis. T = 20 K.
However, in the direction (Y= (125”-135” ) only one band (1180 cm-‘) originating from v,, P-(O), appears in the spectra, which agrees very well with the structural considerations. (ii) Beside the inside ion coupling for the PO4 stretching vibrations described, inter-ion couplings between the neighbouring PO, groups inside the primitive cell are inferred from the A-B (Davydov) splitting seen in the infrared spectra. (iii) The deuteration mass effects and the band position shifts depending
< 70".
22
TABLE 3 The calculated direction cos’ of the transition dipole stretching modes in the CsH,PO, crystal Type of mode
moments
of the PO, internal
a*
b
C
@.na
Paraelectric phase VPO(1) VPO(2) v,PO(l)O(2) v,PO(l)O(2) VPO(3) VPO(4) v,PO(3)0(4) v,PO(3)0(4)
0.56 0.22 0.03 0.97 0.29 0.29 0.00 0.89
0.00 0.00 0.00 0.00 0.67 0.67 1.00 0.00
0.44 0.78 0.97 0.03 0.04 0.04 0.00 0.11
42 152 170 100 109 109
Ferroelectric ~,PO(l)O(4) ~,PW)O(4) ~w2m(3) ~w2)0(3)
0.65 0.03 0.36 0.00
0.26 0.46 0.24 0.58
0.09 0.51 0.40 0.42
70 13 136 6
109
phase
aa is the angle between the -c direction and the projections of the transition dipole moments on the (010) plane. With O(l), O(2), O(3) and O(4) are assigned the 0,, 0,, 0, and 0; from the text.
on OLcorrelated with the dipole moment directions of the proton vibrations and support resonance coupling between the internal vibrations of the PO4 group and the hydrogen bonds. The most prominent band position changes are found for the v,P(O)~ mode which shifts from 1130 cm-’ up to 1220 cm-’ in different orientations (see the curve in Fig. 2). The lowest wavenumber position (in the a! = 125”--135” direction) seems to correspond to the pure vibration because no absorption from the vzOH vibration occurs in this
O0
30'
60“
I I, 90"
I I a 1, 150" 120"
I
a
I
1806
Fig. 2. The frequency of the v,PO, IR mode as a function of the electric vector (E) orientation. oi is the angle between the E and -c direction.
23
direction (**OS*** 0; is in the direction (Y= 52”). However, in the infrared spectra of the shorter hydrogen bond, the symmetric and asymmetric VP(O), modes resonate slightly with the v20H vibration which pushes them to higher frequencies. Addition resonance couplings of vB,P(0), with the in-plane deformation hIOH (originating from the longer bond) and very likely also with 6,OH (originating from the shorter bond) caused it to shift to 1220 cm-’ (in directions closed to their dipole moment orientations (Y= 90”) (Figs. 1 and 2). The v,P(O& and vasP(O& modes appear to be quite pure in the spectra of the protonated compound as they are far from the OH stretching and the in-plane deformation regions. The out-of-plane yOH bending modes do not affect other vibrations. However in the spectra of the deuterated crystal the 610D and &OD modes are in the range 800-1000 cm-’ and disturb the vP(O& modes. On the other hand the v,P(O), and v,,P(O), modes shift to higher frequencies because the v, OD absorption shifts down. The deformation skeletal modes seem to resonate slightly with the out-ofplane rzOD modes since they shift on deuteration. However no obvious trends are seen in this region. TEMPERATURE DEPENDENCE OF THE BAND FREQUENCY HALF-WIDTH OF THE PO:- STRETCHING MODES
AND BAND
The Raman spectra of both CDP and DCDP were studied over a range of temperatures. Results are given in Figs. 3-7. Figure 3 presents the band position and the half-width of the v3 modes at 990 cm-’ (in CDP) vs. temperature. These dependences are almost the same as those reported in ref. 3 yielding an abrupt change in the vicinity of T,. The out-of-plane r,OH mode also lies in this region and becomes active in the ferroelectric phase (Fig. 4). However, the half-width of the v3 mode (at 1130 cm-‘) rapidly increases with increasing temperature in the paraelectric phase (140-220 K), but its band position remains almost unaltered (Fig. 5). For the spectra of the D-compound, the temperature functions of the band parameters (D and AU) for the four skeletal stretching modes are presented in Fig. 6 (from the x-spectra) and Fig. 7 (from the xx-spectra). The v3 bands at 920 cm-’ and 1025 cm-’ (a counterpart of the band at 990 cm-’ in CDP) shows a nearly linear increase of half-width (Au) with temperature up to 247 K, followed by an abrupt decrease and then a further increase. The third v3 band at 1153 cm-’ (a counterpart of the v3 band at 1130 cm-’ in CDP) implies also a linear characteristic with a half-width remaining almost unchanged till 247 K and then rapidly increasing with increasing temperature in the paraelectric phase. The band frequency seems to be unvarying for v3 at 1025 cm-’ and continuously decreases for v3 at 920 cm-’
**o
s---O;
is the hydrogen
bond of a shorter
distance
(ref. 1).
(a)
.
. . . .
.
7
.
.
( b)
1005
* *
1000
9901
’
’ ’ 100
’
’
’
’
200
’
’
’
’
’
300 T/K
*
Fig. 3. Temperature dependence of the band parameters of the v,PO, mode (at 990 cm-‘) in the zz-Raman spectrum (a* (cc)21 geometry) of the CsH,PO, crystal: (a) band halfwidth; (b) band position.
with the increase of the temperature up to 240 K, where an abrupt reduction is observed. All these anomalous changes for the v3P04 modes take place in the range of the phase transition, but it is likely that the transition temperature is lowered to 247 K due to incomplete deuteration. It should be mentioned that the shape of the half-width curve for the band at 920 cm-’ observed in the region 120-180 K is caused by both in-plane-deformation modes (hlOD at 904 cm-’ and &OD at 940 cm-‘) broadening with increasing temperature, so that they become mixed with the v3 mode and finally become obscured by it, disturbing its linear character. However, the halfwidth Au vs. T characteristic of the totally symmetric stretching mode u1 (at 880 cm-‘) is linear in the range from 20 K to 105 K and from 100 K to 250 K, with a slight bend in the vicinity of 100 K. It is difficult to explain the anomalous behaviour with changing temperature of the bands at 920 and 990 cm-’ (which change abruptly in the vicinity of T,), and at 1130 cm-’ (giving a rapid increase with temperature higher than T,). It is possible that this could be an intrinsic characteristic of a given mode indicated by the correlation of the ion vibrations with each other (by phonon propagation other than that in the (a*~) plane) as was suggested by Aoki et al. [3]. But if this is accepted, such an abrupt temperature dependence should be expected (i) for all stretching vibrations, which is not
25
95K
65 50 35 15 1200
1100
RAMAN
900
1000
10
SHIFT
Fig. 4. Raman peratures.
spectra
of CsH,PO,
crystal
measured
in the v) PO, region at different
tem-
r(a’
CiJ ‘4 _ 16-
00
00
15 1413-
0
12-
0 0
11i
00
0
,
00
00
000 0
“25’
/
4
80
’
’
’
’
’
’
200
’
’
’
’
’
300
’
8
‘0
T/K
Fig. 5. Temperature dependence the zz-Raman spectra (a* (cc)b (b) band frequency.
of the band parameters of the v, mode (at 1130 cm-‘) in geometry) of the C.&PO, crystal: (a) band half-width;
26
30.
2O-e..9! . . .
4:
'a-
2'
300
200
100
20
V K
100
200
300 T/K
Fig. 6. Temperature dependence of the band parameters of the vP0, stretching modes in the zz-Raman spectra (a*(cc)b geometry) of the CsD,PO, crystal: (a) the band half-width of the v,PO, mode at 880 cm-’ (x) and for the v,PO, mode at 920 cm-’ (B). Dashed line represents the s,OD mode at 904 cm-‘. Solid line represents the 6,OD mode at 941 cm-‘. (b) The band half-width of the v,PO, mode at 1025 cm-’ (*) and at 1150 cm-’ (0); (c) the band position for the v,PO, mode at 920 cm-‘; (d) the band position for the v,PO, mode at 1025 cm-‘.
5 1030t
(a)
(a)
0
1020t
O
O
0
0 0
0
1010 'L'
40
&*‘B’a.
(bl
lb)
J *yz 30
0
2040 -200
0
220
0
0
00
240
260
280
0
300
320 T/K Fig. 7. Temperature dependences of the band parameters of the v,PO, mode at 1025 cm-’ in the xx-Raman spectrum (c(a*a*)b geometry) of the CsD,PO, crystal: (a) the band position; (b) the band half-width.
27
observed experimentally (for v1 mode); (ii) by each phonon propagation other than that in the (010) plane. However, in Fig. 7 are presented the Au = f(T) and 0 = f(T) characteristics for the v3 mode (at 1025 cm ’ in DCDP) in the geometry c(a*a*)b, i.e. with a scattering vector in the direction of the b-axis, where no abrupt changes were observed. On the other hand a possible reason for the observed anomalies in the v3P04 mode characteristics could be some resonance coupling between the skeletal stretching modes and the deformation vibrations (610D and 6,OD for the band at 920 cm-’ or a10H for that at 990 cm-‘). As far as the v1 (at 880 cm-‘) and v3 (at 1130 cm-‘) modes are concerned, they lie rather far from the deformation modes and the plotted diagrams are thought to imply their intrinsic properties. Thus, the problem of the anomalous behaviour of the band parameters (Av and U) vs. temperature in the vicinity of T, observed for some skeletal stretching modes in the zz-Raman spectral still remains open to discussion REFERENCES 1 V. Videnova-Adrabinska and J. Baran, J. Mol. Struct., 156 (1986) 1. 2 B. Marchon and A. Novak, J. Chem. Phys., 78 (1983) 2105. 3 M. Aoki, M. Kasahara and I, Tatsuzaki, J. Raman Spectrosc., 15 (1984) 97. 4 S. S. Ti, S. Rumble and F. Ninio, Solid State Commun., 44 (1982) 129. 5 J. Baran, Ph. D. Thesis, University of Wrodaw, 1976. 6 V. Videnova, Ph. D. Thesis, University of Wroctw, 1979. 7 H. Ratajczak, J. Mol. Struct., 3 (1969) 27. 8 H. Ratajczak, J. Mol. Struct., 11 (1972) 267. 9 R. P. Lowndes, N. E. Tornberg and R. C. Leung, Phys. Rev. B, 10 (1974) 911. 10 N. E. Tornberg and R. P. Lowndes, J. Mol. Struct., 19 (1973) 555. 11 E. V. Chisler, I. T. Savatinova and V. Yu. Davydov, Opt. Spectrosk., 32 (1972) 544. 12 E. V. Chisler, V. Yu. Davydov and I. T. Savatinova, Fiz. Tverd. Tela, 13 (1971) 1949; 13 (1971) 1599. 13 A. C. Chapman and L. E. Thirlwell, Spectrochim. Acta, 20 (1964) 937. 14 B. C. Frazer, D. Semmingsen, W. D. Ellenson and G. Shirane, Phys. Rev. B, 20 (1979) 2745. 15 H. Schutze, N. Weinstock, A. Miiller and G. Vandrish, Spectrochim. Acta, Part A, 29 (1973) 1705.