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Proton magnetic relaxation study of cation dynamics in TMACA
Solid State Communications, Printed in Great Britain.
Vol. 86, No. 12, pp. 803-806, 1993.
PROTON MAGNETIC
RELAXATION
0038-1098/93 $6.00 + .OO Pergamon Press Ltd
STUDY OF CATION DYNAMICS
IN TMACA
B. Jagadeesh, PK. Rajan, K. Venu and V.S.S. Sastry School of Physics, University of Hyderabad,
Hyderabad
500 134, India
(Received 17 December 1992 by C.N.R. Rao)
tris(trimethylammonium) Cation dynamics in nonachlorodiantimonate, which shows different phases as a function of temperature, is studied through proton spin lattice relaxation measurements at five Larmor frequencies. Results show a clear signature of the para-ferroelectric phase transition at 363 K and the existence of dynamically inequivalent trimethylammonium cations and methyl groups, both in the ratio of 1: 2. Various activation energies associated with the dynamics of the cations and methyl groups&e calculated.
1. INTRODUCTION IN RECENT years there has been considerable interest in alkylammonium halogenates, particularly with cations containing methyl compounds ammonium groups. These systems exhibit a series of structural phase transitions and motions of the cation groups are found to be relevant in understanding the nature of these transitions. The alkylammonium halogenates of general formula [NH4_n(CH3)n]3Y2X9 (n = 1 to 4); Y = Sb, Bi; X = Cl, Br, I are recently reported to be having sequences of phase transitions and have interesting polar properties [l-3]. Tris(trimethylammonium) nonachlorodiantimonate (TMACA), ~H(CHs)&Sb$l,, crystallizes at room temperature in the polar P, space group of monoclinic system (0 = 90.17”, Z = 2) [4]. It has been reported that one (TMA)+ cation among three in the molecule occupies the free space in a twelve membered (-Sb-Cl-)6 ring due to its weak bifurcated bond, suggesting structural inequivalence in the (TMA)+ positions in the ratio of 1 : 2. Dielectric and DSC studies [5] on this system show that this undergoes a first order phase transition at around 363 K from para to a low temperature ferroelectric phase, which exists at least down to 120K. Raman and Brillouin light scattering experiments [6] have indicated that this phase transition is of order-disorder type and that it might be connected with the disordering of cation. Proton trimethylammonium (TMA) spin lattice relaxation time (Ti) and the second moment (Mz) measurements at 90MHz were reported earlier on this compound [7]. However,
the analysis of this data, based on the model proposed therein, does not indicate the presence of inequivalent TMA groups. To elucidate the dynamics of the cation further, possibly with a more refined model, protonspin lattice relaxation times (Ti) have been measured in the present study at lower freof quencies, which show a better resolution the relaxation behavior with temperature. These measurements are made at five frequencies to help proposing a consistent model for the cation dynamics, and a more elaborate model [8] which takes all types of possible dynamics into consideration, including the lone proton contribution, (which was taken as only a scaling factor in the model considered by Idziak et al. [7]), is proposed for this dynamics. An interesting outcome of these experiments is the observation of dynamically inequivalent TMA groups, in contrast to what has been reported earlier using the same technique [7]. 2. EXPERIMENTAL
DETAILS
The TMACA crystals were obtained by slow evaporation of aqueous solution of stoichiometric mixture of (CH,),NHCl and SbC13 with excess HCl. Polycrystalline sample of the dried substance was evacuated at around lop5 torr and was sealed in a 6mm diameter glass tube. Ti measurements were made on home made pulsed NMR spectrometer at five frequencies (4, 10, 20, 29.8 and 39.8 MHz) using saturation burst and inversion recovery sequences over a temperature range 83 K to 400 K with 0.1 K stability. A gas flow
803
PROTON MAGNETIC
804
type cryostat is used to control the temperature of the sample. The Ti measurements are accurate to within 5%.
RELAXATION
Vol. 86, No. 12
STUDY
protons in the three methyl groups. In such a case the total relaxation time is written as [8]
3. RESULTS AND DISCUSSION The variation of the Ti as a function of temperature (T) at typical frequencies is shown in the Fig. 1. In the high temperature region above 285K the relaxation times are independent of frequency. There is a discontinuity in the Ti data at 363K. There seems to be a shallow minimum appearing in Ti, manifesting as a shoulder in the Ti vs T-’ plot for 4, 10, 20, 29.8MHz at 182K, 189K, 213 K, 222K respectively and this feature is prominent at lower frequencies due to a better dispersion of T, data with temperature. On further cooling, the results show a broad minimum at each frequency. The values of these minima are 3.3, 8.6, 14, 21 and 29ms at 4, 10, 20, 29.8 and 39.8 MHz respectively. Also the recovery of magnetization at 83 K is found to be non-exponential, giving rise to two T, values. The spin lattice relaxation of proton in a molecule like trimethyl ammonium group is due to the modulation of various proton-proton dipolar interactions by the random reorientations of CHs groups about their three fold symmetric axes (characterized by the correlation time rf) and three fold rotations of TMA cations around the protonnitrogen (Cj) axis (characterized by the correlation time r,i). A given proton in a methyl group can interact with two other protons in the same methyl group, six protons in the other two methyl groups, and one lone proton outside the methyl groups. Further, the lone proton interacts with nine a-4MHz . - 10 MHz
P
o - 39.8 MHz lOOO-
Q 2
loo -
5 6
1
+
-&@
kn
2
kn
n=l
+
(~0)~
(lone proton)
1
(1)
’
with k, = r, k2 = r+ R, k3 = R, k4 = 2r, and k5 = 2r + R. Here r = 7;’ and R = 7,1’. The d’) s L@) s and M(,‘1)s in equation (1) are relaxation constan& which are calculated knowing various proton-proton distances and the gyromagnetic ratio of protons. Assuming that these motions are thermally activated, the variation of the correlation time rc with the temperature can be written in the Arrhenius form as rc =
70 exp(-%lW,
(2)
where E, is the activation energy associated with the motion. The data should, in principle, contain two well resolved minima, at WT,= 0.616 and WT,~= 0.616 corresponding to the CHs and (TMA)+ dynamics respectively, if rc and rcl are sufficiently different and the coupling between the two dynamics is neglected. The values of the minima calculated from this model at different frequencies, assuming that the minima are well separated, are given in Table 1. However, the observed T, minima do not match either with that of CHs group or of TMA group (Table 1). In fact, they are higher than the expected values due to CH3 group, and lower than the expected minima due to TMA group at all frequencies. Normally, inequivalence of these molecular groups is responsible for such discrepancies, and such Table 1. Expected values of T, minima based on the model of Sjiblom and Punkkinen (1975)
10-
0’
(inter)
(intra)
’
2
’
3
’
4
’
5
’
6
’
7
’
8
’
9
’
10
’
11
’
12
1000/T(“K-l)
Fig. 1. Proton spin lattice relaxation time (T,) as a function of inverse temperature (1 /T) at three Larmor frequencies. The solid lines are the best fit curves.
Frequency (MHz)
T, min due to methyl group (ms)
T1 min due to TMA group (ms)
10 20 29.8 39.8
5 10 14.9 19.9
10.90 21.80 32.48 43.38
Vol. 86, No. 12
PROTON MAGNETIC
a situation has been predicted for (TMA)+ ions by X-ray studies [4]. Assuming that these structurally inequivalent (TMA)+ ions (in 1 : 2 ratio) may also be dynamically inequivalent with different correlation times (~ii and ri: with corresponding parameters E$ and ri,, Z$: and T,‘: respectively), the data are fitted to the equation. As a first step to incorporate this suggestive clue, a model with inequivalent (TMA) ions in the ratio of 1 : 2, but with only dynamically equivalent methyl groups has been tried out to explain the observed data, using r;’
=f(T;‘)‘+;(T;‘)“,
(3)
where (TIP’)’ and ( Ti-l)ll are given by equation (1) with appropriate correlation times for the TMA groups. This model however, was not found satisfactory to account for the experimental results at all frequencies, consistently. Further refinement of the model is effected by proposing that the methyl groups are also inequivalent in the same 1 : 2 ratio with parameters (Ei and -& Z$’ and 7:’ respectively). The observed T, minimum value corresponding to the broad minimum observed in the data corresponds to two thirds of methyl groups and two thirds of TMA group (methyl group II and TMA group II) giving a minimum approximately at the same place. Similarly, the shoulder observed in the data at higher temperatures corresponds to a minimum due to one third of TMA groups (TMA group I) and there is no other minimum appearing in the temperature range (83-400K) covered. However, according to the above model, a minimum due to the remaining methyl groups (methyl group I) is expected and is perhaps outside the temperature region of observation. The data, then, are fitted to equation (3) without taking into account methyl group I. A reduction factor of 0.85 was used in both the terms in equation (3) to take into account the averaging of dipolar interaction which normally takes place in symmetric molecular groups [8]. This model has been found to account for the data well at all the frequencies consistently, i.e. yielding “70” and “Ea” values to within 10% and 5% accuracy, respectively: Ei, = 4.3 f 0.1 kcal mol-‘, T;, = (2.3 f 0.2) x lo-i3 s, E”al = 3.7 f 0.1 kcal mol-’ , 7;; = (l.l*o.l)
x 10-l%,
Eil = 2.4 f 0.1 kcal mol-’ and
# = (1 .l f 0.2) x lo-l2 s.
RELAXATION
STUDY
805
It may be noted that none of these parameters agree with those calculated in the earlier 90MHz work [7], which assumes a model without dynamical inequivalence for the different molecular groups. It is to be pointed out that the specific features of variation of T, with temperature brought out by this study at lower frequencies cannot be accounted for, in principle, by the model proposed earlier. The magnetization recovery at 83 K, is found to be non-exponential and can be analyzed to yield two different Ti values (at each frequency, at each temperature), say Ti, and T,? The slower component, Z’i,, thus obtained falls on the calculated curve for the above mentioned model and Fig. 1 depicts this value at the lowest temperature. T,,., on the other hand, is relatively shorter (35 ms, 600 ms, 2 s at 4, 10 and 39.8 MHz respectively) and this could perhaps be due to the methyl groups-I, whose minimum might be appearing well below 77K. Well separated correlation times of these methyl groups-I, compared to the other molecular groups in this system, could in such a case be giving rise to the observed non exponentiality in the magnetization recovery. The discontinuous downward jump observed in Ti at 363 K correlates well with the reported structural transition at this temperature. From the slope of ln( Ti) vs l/T plot, the activation energy was found to be 2.1 f 0.3 kcal mol-‘, which is obviously to be attributed to the dynamics of TMA group, within the proposed model this value is found to be in fair agreement with that reported by Idziak et al. [7] within experimental error. The decrease in the activation energy in the paraelectric phase compared to corresponding value of both types of (TMA)+ ions in ferroelectric phase indicates an increase in the freedom of (TMA)+ ions in the paraelectric phase. Certain dielectric anomalies were reported in TMACA [5] around 200K. However, there is no signature of these anomalies in the present data in this temperature region. It may be noted in this context that the ri data at high frequencies [7] also did not show any anomalous behavior at this temperature. Raman scattering studies show, at best, a gradual and small change in the position of the spectral lines spread over a wide temperature region and these features could not be attributed to a possible structural phase transition [6]. On the other hand the high frequency (90MHz) Ti data show a weak discontinuity at 125 K [7] which was assigned to a possible structural phase transition. But the present study does not show any anomalous behavior at this temperature at all the five Larmor frequencies. The presence of T, minima observed at these lower
806
PROTON MAGNETIC
frequencies in this temperature region may perhaps be obscuring the details of such weak discontinuities as observed at 90MHz. It may further be observed that the Raman studies [6] also do not throw any light on this possible transition. 4. CONCLUSIONS studies in relaxation Proton magnetic nonachlorodiantimonate tris(trimethylammonium) reveal dynamical inequivalence in trimethylammonium groups and methyl groups, both in 1 : 2 ratio in agreement with the X-ray results. This assignment differs from the model proposed earlier based on results at a higher frequency. The dynamic parameters associated with the rotations of different types of trimethylammonium ions about their Ci axes and random reorientations of CHs groups around their Cs axes are calculated. Acknowledgements - Financial assistance for two of the authors (from the Council of Scientific and
RELAXATION
STUDY
Vol. 86, No. 12
Industrial Research, India for B.J. and from the University Grants Commission, India for P.K.R) is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
R. Jakubas, Z. Galewski, L. Sobczyk & J. Matuszewski, J. Phys. 18, L857 (1985). R. Jakubas, Z. Czapla, Z. Galewski, L. Sobczyk, O.J. Zogal & T. Lis, Whys. Status Solidi (a) 93, 449 (1986). A. Miniewicz & R. Jakubas, Solid State Commun. 63, 1987 (1987). A. Kallel & J.W. Bats, Acta. Crystal. C41, 1022 (1985). R. Jakubas, A. Miniewicz, M. Bertault, J. Sworakowski & A. Collet, J. Phys. France 50, 1483 (1989). A. Miniewicz, R. Jakubas, C. Ecolivet & A. Girard, J. Raman Spect. 20, 381 (1989). S. Idziak & R. Jakubas, Solid State Commun. 62, 173 (1987). R. Sjiiblom & M. Punkkinen, J. Mugn. Res. 20, 484 (1975).
Vol. 86, No. 12, pp. 803-806, 1993.
PROTON MAGNETIC
RELAXATION
0038-1098/93 $6.00 + .OO Pergamon Press Ltd
STUDY OF CATION DYNAMICS
IN TMACA
B. Jagadeesh, PK. Rajan, K. Venu and V.S.S. Sastry School of Physics, University of Hyderabad,
Hyderabad
500 134, India
(Received 17 December 1992 by C.N.R. Rao)
tris(trimethylammonium) Cation dynamics in nonachlorodiantimonate, which shows different phases as a function of temperature, is studied through proton spin lattice relaxation measurements at five Larmor frequencies. Results show a clear signature of the para-ferroelectric phase transition at 363 K and the existence of dynamically inequivalent trimethylammonium cations and methyl groups, both in the ratio of 1: 2. Various activation energies associated with the dynamics of the cations and methyl groups&e calculated.
1. INTRODUCTION IN RECENT years there has been considerable interest in alkylammonium halogenates, particularly with cations containing methyl compounds ammonium groups. These systems exhibit a series of structural phase transitions and motions of the cation groups are found to be relevant in understanding the nature of these transitions. The alkylammonium halogenates of general formula [NH4_n(CH3)n]3Y2X9 (n = 1 to 4); Y = Sb, Bi; X = Cl, Br, I are recently reported to be having sequences of phase transitions and have interesting polar properties [l-3]. Tris(trimethylammonium) nonachlorodiantimonate (TMACA), ~H(CHs)&Sb$l,, crystallizes at room temperature in the polar P, space group of monoclinic system (0 = 90.17”, Z = 2) [4]. It has been reported that one (TMA)+ cation among three in the molecule occupies the free space in a twelve membered (-Sb-Cl-)6 ring due to its weak bifurcated bond, suggesting structural inequivalence in the (TMA)+ positions in the ratio of 1 : 2. Dielectric and DSC studies [5] on this system show that this undergoes a first order phase transition at around 363 K from para to a low temperature ferroelectric phase, which exists at least down to 120K. Raman and Brillouin light scattering experiments [6] have indicated that this phase transition is of order-disorder type and that it might be connected with the disordering of cation. Proton trimethylammonium (TMA) spin lattice relaxation time (Ti) and the second moment (Mz) measurements at 90MHz were reported earlier on this compound [7]. However,
the analysis of this data, based on the model proposed therein, does not indicate the presence of inequivalent TMA groups. To elucidate the dynamics of the cation further, possibly with a more refined model, protonspin lattice relaxation times (Ti) have been measured in the present study at lower freof quencies, which show a better resolution the relaxation behavior with temperature. These measurements are made at five frequencies to help proposing a consistent model for the cation dynamics, and a more elaborate model [8] which takes all types of possible dynamics into consideration, including the lone proton contribution, (which was taken as only a scaling factor in the model considered by Idziak et al. [7]), is proposed for this dynamics. An interesting outcome of these experiments is the observation of dynamically inequivalent TMA groups, in contrast to what has been reported earlier using the same technique [7]. 2. EXPERIMENTAL
DETAILS
The TMACA crystals were obtained by slow evaporation of aqueous solution of stoichiometric mixture of (CH,),NHCl and SbC13 with excess HCl. Polycrystalline sample of the dried substance was evacuated at around lop5 torr and was sealed in a 6mm diameter glass tube. Ti measurements were made on home made pulsed NMR spectrometer at five frequencies (4, 10, 20, 29.8 and 39.8 MHz) using saturation burst and inversion recovery sequences over a temperature range 83 K to 400 K with 0.1 K stability. A gas flow
803
PROTON MAGNETIC
804
type cryostat is used to control the temperature of the sample. The Ti measurements are accurate to within 5%.
RELAXATION
Vol. 86, No. 12
STUDY
protons in the three methyl groups. In such a case the total relaxation time is written as [8]
3. RESULTS AND DISCUSSION The variation of the Ti as a function of temperature (T) at typical frequencies is shown in the Fig. 1. In the high temperature region above 285K the relaxation times are independent of frequency. There is a discontinuity in the Ti data at 363K. There seems to be a shallow minimum appearing in Ti, manifesting as a shoulder in the Ti vs T-’ plot for 4, 10, 20, 29.8MHz at 182K, 189K, 213 K, 222K respectively and this feature is prominent at lower frequencies due to a better dispersion of T, data with temperature. On further cooling, the results show a broad minimum at each frequency. The values of these minima are 3.3, 8.6, 14, 21 and 29ms at 4, 10, 20, 29.8 and 39.8 MHz respectively. Also the recovery of magnetization at 83 K is found to be non-exponential, giving rise to two T, values. The spin lattice relaxation of proton in a molecule like trimethyl ammonium group is due to the modulation of various proton-proton dipolar interactions by the random reorientations of CHs groups about their three fold symmetric axes (characterized by the correlation time rf) and three fold rotations of TMA cations around the protonnitrogen (Cj) axis (characterized by the correlation time r,i). A given proton in a methyl group can interact with two other protons in the same methyl group, six protons in the other two methyl groups, and one lone proton outside the methyl groups. Further, the lone proton interacts with nine a-4MHz . - 10 MHz
P
o - 39.8 MHz lOOO-
Q 2
loo -
5 6
1
+
-&@
kn
2
kn
n=l
+
(~0)~
(lone proton)
1
(1)
’
with k, = r, k2 = r+ R, k3 = R, k4 = 2r, and k5 = 2r + R. Here r = 7;’ and R = 7,1’. The d’) s L@) s and M(,‘1)s in equation (1) are relaxation constan& which are calculated knowing various proton-proton distances and the gyromagnetic ratio of protons. Assuming that these motions are thermally activated, the variation of the correlation time rc with the temperature can be written in the Arrhenius form as rc =
70 exp(-%lW,
(2)
where E, is the activation energy associated with the motion. The data should, in principle, contain two well resolved minima, at WT,= 0.616 and WT,~= 0.616 corresponding to the CHs and (TMA)+ dynamics respectively, if rc and rcl are sufficiently different and the coupling between the two dynamics is neglected. The values of the minima calculated from this model at different frequencies, assuming that the minima are well separated, are given in Table 1. However, the observed T, minima do not match either with that of CHs group or of TMA group (Table 1). In fact, they are higher than the expected values due to CH3 group, and lower than the expected minima due to TMA group at all frequencies. Normally, inequivalence of these molecular groups is responsible for such discrepancies, and such Table 1. Expected values of T, minima based on the model of Sjiblom and Punkkinen (1975)
10-
0’
(inter)
(intra)
’
2
’
3
’
4
’
5
’
6
’
7
’
8
’
9
’
10
’
11
’
12
1000/T(“K-l)
Fig. 1. Proton spin lattice relaxation time (T,) as a function of inverse temperature (1 /T) at three Larmor frequencies. The solid lines are the best fit curves.
Frequency (MHz)
T, min due to methyl group (ms)
T1 min due to TMA group (ms)
10 20 29.8 39.8
5 10 14.9 19.9
10.90 21.80 32.48 43.38
Vol. 86, No. 12
PROTON MAGNETIC
a situation has been predicted for (TMA)+ ions by X-ray studies [4]. Assuming that these structurally inequivalent (TMA)+ ions (in 1 : 2 ratio) may also be dynamically inequivalent with different correlation times (~ii and ri: with corresponding parameters E$ and ri,, Z$: and T,‘: respectively), the data are fitted to the equation. As a first step to incorporate this suggestive clue, a model with inequivalent (TMA) ions in the ratio of 1 : 2, but with only dynamically equivalent methyl groups has been tried out to explain the observed data, using r;’
=f(T;‘)‘+;(T;‘)“,
(3)
where (TIP’)’ and ( Ti-l)ll are given by equation (1) with appropriate correlation times for the TMA groups. This model however, was not found satisfactory to account for the experimental results at all frequencies, consistently. Further refinement of the model is effected by proposing that the methyl groups are also inequivalent in the same 1 : 2 ratio with parameters (Ei and -& Z$’ and 7:’ respectively). The observed T, minimum value corresponding to the broad minimum observed in the data corresponds to two thirds of methyl groups and two thirds of TMA group (methyl group II and TMA group II) giving a minimum approximately at the same place. Similarly, the shoulder observed in the data at higher temperatures corresponds to a minimum due to one third of TMA groups (TMA group I) and there is no other minimum appearing in the temperature range (83-400K) covered. However, according to the above model, a minimum due to the remaining methyl groups (methyl group I) is expected and is perhaps outside the temperature region of observation. The data, then, are fitted to equation (3) without taking into account methyl group I. A reduction factor of 0.85 was used in both the terms in equation (3) to take into account the averaging of dipolar interaction which normally takes place in symmetric molecular groups [8]. This model has been found to account for the data well at all the frequencies consistently, i.e. yielding “70” and “Ea” values to within 10% and 5% accuracy, respectively: Ei, = 4.3 f 0.1 kcal mol-‘, T;, = (2.3 f 0.2) x lo-i3 s, E”al = 3.7 f 0.1 kcal mol-’ , 7;; = (l.l*o.l)
x 10-l%,
Eil = 2.4 f 0.1 kcal mol-’ and
# = (1 .l f 0.2) x lo-l2 s.
RELAXATION
STUDY
805
It may be noted that none of these parameters agree with those calculated in the earlier 90MHz work [7], which assumes a model without dynamical inequivalence for the different molecular groups. It is to be pointed out that the specific features of variation of T, with temperature brought out by this study at lower frequencies cannot be accounted for, in principle, by the model proposed earlier. The magnetization recovery at 83 K, is found to be non-exponential and can be analyzed to yield two different Ti values (at each frequency, at each temperature), say Ti, and T,? The slower component, Z’i,, thus obtained falls on the calculated curve for the above mentioned model and Fig. 1 depicts this value at the lowest temperature. T,,., on the other hand, is relatively shorter (35 ms, 600 ms, 2 s at 4, 10 and 39.8 MHz respectively) and this could perhaps be due to the methyl groups-I, whose minimum might be appearing well below 77K. Well separated correlation times of these methyl groups-I, compared to the other molecular groups in this system, could in such a case be giving rise to the observed non exponentiality in the magnetization recovery. The discontinuous downward jump observed in Ti at 363 K correlates well with the reported structural transition at this temperature. From the slope of ln( Ti) vs l/T plot, the activation energy was found to be 2.1 f 0.3 kcal mol-‘, which is obviously to be attributed to the dynamics of TMA group, within the proposed model this value is found to be in fair agreement with that reported by Idziak et al. [7] within experimental error. The decrease in the activation energy in the paraelectric phase compared to corresponding value of both types of (TMA)+ ions in ferroelectric phase indicates an increase in the freedom of (TMA)+ ions in the paraelectric phase. Certain dielectric anomalies were reported in TMACA [5] around 200K. However, there is no signature of these anomalies in the present data in this temperature region. It may be noted in this context that the ri data at high frequencies [7] also did not show any anomalous behavior at this temperature. Raman scattering studies show, at best, a gradual and small change in the position of the spectral lines spread over a wide temperature region and these features could not be attributed to a possible structural phase transition [6]. On the other hand the high frequency (90MHz) Ti data show a weak discontinuity at 125 K [7] which was assigned to a possible structural phase transition. But the present study does not show any anomalous behavior at this temperature at all the five Larmor frequencies. The presence of T, minima observed at these lower
806
PROTON MAGNETIC
frequencies in this temperature region may perhaps be obscuring the details of such weak discontinuities as observed at 90MHz. It may further be observed that the Raman studies [6] also do not throw any light on this possible transition. 4. CONCLUSIONS studies in relaxation Proton magnetic nonachlorodiantimonate tris(trimethylammonium) reveal dynamical inequivalence in trimethylammonium groups and methyl groups, both in 1 : 2 ratio in agreement with the X-ray results. This assignment differs from the model proposed earlier based on results at a higher frequency. The dynamic parameters associated with the rotations of different types of trimethylammonium ions about their Ci axes and random reorientations of CHs groups around their Cs axes are calculated. Acknowledgements - Financial assistance for two of the authors (from the Council of Scientific and
RELAXATION
STUDY
Vol. 86, No. 12
Industrial Research, India for B.J. and from the University Grants Commission, India for P.K.R) is gratefully acknowledged. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
R. Jakubas, Z. Galewski, L. Sobczyk & J. Matuszewski, J. Phys. 18, L857 (1985). R. Jakubas, Z. Czapla, Z. Galewski, L. Sobczyk, O.J. Zogal & T. Lis, Whys. Status Solidi (a) 93, 449 (1986). A. Miniewicz & R. Jakubas, Solid State Commun. 63, 1987 (1987). A. Kallel & J.W. Bats, Acta. Crystal. C41, 1022 (1985). R. Jakubas, A. Miniewicz, M. Bertault, J. Sworakowski & A. Collet, J. Phys. France 50, 1483 (1989). A. Miniewicz, R. Jakubas, C. Ecolivet & A. Girard, J. Raman Spect. 20, 381 (1989). S. Idziak & R. Jakubas, Solid State Commun. 62, 173 (1987). R. Sjiiblom & M. Punkkinen, J. Mugn. Res. 20, 484 (1975).