Specfrochimico Acm, Vol. 4OA, No. I I/12, pp. 1063-1069. 1984 058468539/84 $3.00 + 0.00 Printed in Great Britain. 0 1984 Pergamon Press Ltd.

Raman spectra and phase transitions in single crystal

ANSHU AGARWAL, M. B. PATEL, MAHENDRA PAL and H. D. BIST Department of Physics, Indian Institute of Technology, Kanpur 208 016, India

(Receioed 13 June 1983; infinalform 23 May 1984)

Abstract-Raman spectra of single crystal (NH.&ZnCI, at 300 and 105 K at different polarizations are reported and analysed in view of previously reported structural data. The experimental observations suggest that the free oriented gas model is applicable for group theoretical analysis of the vibrational modes in this system at room temperature. It is also concluded that the space group for the room temperature phase III is C,’ instead of CzO. The temperature dependence of thermosensitive bands shows discontinuities at 267 and 194K. The structure in the new phase VI below 194 K is suggested to be triclinic.

1. INTRODUCTION

Recently much attention has been paid to crystals having the general formula AZBXI; where A = NH.,, N(CH&, K, Rb, Cs; B = Zn, Co, Fe, Mn and X = Cl, Br, I; most of them show ferroelectricity, ferroelas- ticity, incommensurability etc. Usually these crystals exhibit the following sequence of phase transitions: from the initial paraelectric phase with space group D$ into an incommensurate phase and then into a ferroelectric phase (Cz,) with tripled lattice parameter along the pseudohexagonal axes [ 11. However, am- monium tetrachlorozincate (ATCZ) with the formula (NH&ZnC14 follows a different scheme of phase transitions, viz. phase I (T > 406K) is normal with C = Co and space group 0:: [2], phase II (406 > T > 319 K) is paraelectric with C = 4C, and space group C:, [2], phase III (319 > T > 271 K) is antiferroelec- tric with C = 4C, and space group Cf [2,3] or Cz, [4,5], phase IV (271 > T > 266 K) is incom- mensurate [6] and phase V (266 K > T) is ferroelectric with C = 3C, and space group Cz, [7]. Our pre- liminary Raman investigation of the polycrystalline ATCZ indicates the presence of a new phase below 194K[8]. However, the mechanism of the phase transition could not be well understood due to the ambiguities in the assignments of the bands and in the observed site symmetry and/or factor group splittings on lowering the temperature. Further, the crystal structure at room temperature (RT) is still con- troversial. Earlier MIKHAIL [4] and WARCZEWSKI [S] proposed the Cz, space group for the RT phase III, whereas recently MATSUNAGA [2] and KONINGSVELD [3] suggested C: space group (mono- clinic) though the angles between the three axes were each 90” in KONINGSVELD’S data. To elucidate the above ambiguities we have investigated the Raman spectra of ATCZ single crystal at different polariz- ations at RT as well as 105 K while monitoring some of the thermosensitive bands.

2. CRYSTAL STRUCTURE AND GROUP THEORETICAL

ANALYSIS

The crystal structure of ATCZ at RT was earlier reported by MIKHAIL[~] to be orthorhombic, Cz, with Z = 16, a = 37.172, b = 7.221 and c = 12.643A. The crystal consists of isolated ZnCl:- tetrahedra connected with NH: ions in rows. Recently KONINGSVELD [3] reinvestigated the crystal structure of ATCZ at RT and suggested that it was monoclinic Cf with 2 = 16, a = 12.620, b = 7.211, c = 37.098A, b = 90” and exhibited twinning by pseudomerohedry. He argued that the apparent mmm symmetry was caused by twinning and by the pseudo-orthorhombic symmetry of the lattice, due to which an erroneous space group C& had been assigned to ATCZ [4].

For both the factor groups C, and C2”, one expects from group theory [9] six different spectra correspon- ding to XX, Yx ZZ, X Y, YZ and XZ polarizations. The first four belong to A’ species and the latter two to A” species under the factor group C,, whereas XX, YY, ZZ belong to A,, XY to A2, XZ to B, and YZ belongs to B, species under the factor group C2”. The free ZnCli- and NH: ions have Td molecular symmetry and the nine internal vibrational modes for each ion are distributed as Al (R) + E(R) + 2Fz (R, i.r.) [ 10,111. The distribution of these normal modes among the factor group species could be found using (i) the crystal spectrum model and (ii) the free oriented gas model [12, 131.

(i) Crystal spectrum model

This model has two approaches, viz. a unit cell approach and a site symmetry approach, both of which are now well known[9]. The unit cell approach is difficult and tedious, but gives a unique distribution of modes among the factor group species. The site symmetry approach is rather simple and yields a distribution of modes exactly the same as given by the unit cell approach provided the correct site symmetry

1063

1064 ANSHU AGARWAL et al.

Table 1. Correlation between the species ofthe point group Td and the factor groups C, and Czv: direct (--) and through the site symmetry C1 (---)

Factor group Site group Cl” C,

Point group Td

Site group Cl

Factor group C,

Table 2. Distribution of modes* in different polarizations under the factor groups C,, and C,

Factor group Symmetry species Polarizabilities

Modes VI (A,) ~2 (E) vj(F,) ~4 (F, 1

16(4) O(4) O(4) O(4) 16(8) O(8) 16(8) 16(8) ‘X8) O(8) 16(16) 16(16) 16(12) O(l2) 16(12) 16(12) 32(24) 16(24) 16(12) O(l2) 16(12) 16(12) 32(24) 16(24)

*Numbers outside oarantheses corresoond to direct correlation of point group to the factor group and those inside the parantheses to site symmetry correlation.

is chosen out of the several possibilities for that space group. In the present case, however, only one site (C,) is available for both the space groups (Cf and C,‘,) under consideration. Therefore, the unit cell approach is not needed. The correlation between the species of point group 7” and the factor groups CzU and C, through the site symmetry C1 are given by the broken lines in Table 1. The distributions of the four internal modes v, (A, ), v2 (E), v3 (F,) and v4 (F2) of the ZnCl:- ion among different symmetry species under the factor groups CzU and C; are given by the numbers inside parentheses in Table 2. For the NH: ion, the number of modes under each symmetry species would be doubled as there are twice as many NH: ions as ZnCli- ions in the unit cell. In order to get a clear picture of Tables 1 and 2, we reproduce the correlation diagram for the totally symmetric stretching vibration vI (A 1 ) of ZnCl:- both for the Czv and C, factor groups through the site C1 in Table 2(A). It is evident that this mode would appear in all the six polarization geomet- ries under both the space groups. Thus no conclusion regarding the correct space group could be drawn in the present case with the crystal spectrum model.

(ii) Free oriented gas model

This model is applicable only in the cases where crystalline field effects are relatively weak and, hence, it is possible to analyse the vibrational spectra of the solid by assuming that the behaviour is that of a gas, whose molecules remain oriented in space just as they are in the crystal [12, 131. MUNCH et al. [13] have

Table 2(A). Correlation diagram fdr the species A, of the point group&and the species of the factor groups Czy and C,

through site symmetry C,

Factor Site Point Site Factor group symmetry group symmetry group c Z” CI Td C, C,

2 A’

2 A”

2 A’

2 A”

oa 4A

Table 2(B). Correlation of the species A, of point group Td directly to the species of factor groups CfU and C,

Factor group C2”

Point group G

Factor group C,

Raman spectra and phase transitions in (NH,),ZnCI, 1065

applied this model to analyse the vibrational spectra of stearic acid crystal which is built from hydrogen bonded molecular pairs (with weak dynamic coupling) placed on sites with Ci symmetry. In this approach the symmetry of the site, at which the ions might be situated in the crystal, is ignored. Consequently, one gets a different distribution of symmetry species

depending only on the correlation between the molec- ular (i.e., the free ionic) point group and the factor group of the crystal. Recently, SEETHARAM et al. [14] applied this procedure, instead of the normal site symmetry and factor group approach, for the analysis of the vibrational spectra of NaVO,. A correlation between the species of the point group Td and the factor groups Czv and C, is given in Table 1 (solid lines). The distribution of modes, as yielded by this model, for the

factor groups Czv and C, are given in Table 2 by the numbers outside the parentheses. We have reproduced the distribution of the 16 v1 modes of ZnCl:- in the unit cell species of the factor groups Czv and C, in Table 2(B). It reveals that the totally symmetric vI mode would appear only in three polarizations for the Czv factor group, but would appear in four polariz- ations if the factor group is C,. The distributions of the other modes too into different polarizations by the free oriented gas model turn out to be different for the two space groups (cf. Table 2), thus making the distinction between the two space groups possible. The validity of this model in the present case is discussed in section 4.

3. EXPERIMENTAL

Single crystals of ATCZ were prepared by slow evapor- ation of an aqueous solution of NH,CI and ZnCI, taken in stoichiometric proportions. The sample was purified by repeated recrystallizations from aqueous solutions. The freshly prepared crystals, being deliquescent, were dried in a vacuum desiccator.

The crystals of the pure sample grew in the form of rectangular plates elongated along the c axis (or a axis) with respect to the monoclinic Cz (or orthorhombic Cz,) system according to the international crystallographic convention. A crystal of the size 1.5 x 3.0 x 8.0mm3 (a x b x c) was chosen for the investigation. The x, y and z axes are fixed parallel to these a, b and c axes, respectively, which correspond to the monoclinic system. For Raman studies at RT the single crystal was mounted on a goniometer, whereas for Raman spectra at low temperature the crystal was mounted on the cold finger of a home made variable temperature cell. The sample was excited with 514.5nm line (_ 1OOmW power at the sample) obtained from a Spectra Physics Ar+ laser. The scattered radiations were analysed on a Spex 1403 double monochromator and recorded on a linear chart recorder coupled with Digital Photon Counting system DPC-2 and monochromator through Compudrive using a thermoelectri- cally cooled photomultiplier tube as a detector.

4. RESULTS AND DISCUSSION

(i) General remarks

Raman spectra of a single crystal of ATCZ at RT for the six different polarizations are shown in Fig. 1. The observed band positions are presented in Table 3. The regions for the four internal vibrations (i.e. vl, v2, vj

Wavenumber (cd)

Fig. 1. Raman spectra in different polarizations of (NH4)2ZnC14 single crystal at room temperature (300K). Dotted curves have been taken with 10 times higher sensi- tivity with respect to the corresponding continuous line

curves.

and vq of species A,, E, F2 and FZ, respectively) of free NHf [lo] and ZnCl$- [ 1 l] are well known. To distin-

guish the modes of NH: (or ZnCl:-) a superscript “N” (or “Z”) is used. Since E x E = A, + A2 +E, ExF, =F,+F2 and FzxF1=A1+E+F,+F2 one may expect that in a free molecule v1 will resonate with 2v, and 2v,, and v3 will resonate with v2 + vq and 2v,. Thus a number of two-phonon bands may appear in the stretching regions of NH: and ZnClt- with the corresponding resonating fundamentals.

(ii) Vibrational assignment at RT

(a) Infernal modes of NH: . The bands appearing in all polarizations at 1412 and 1658 cm- 1 are unambigu- ously assigned to bending modes of NH:, vy and VP, respectively [lo]. The strongest band in the diagonal polarizations at 3154cm-’ (which appears weekly in XY polarization also) is easily assigned to NH totally symmetric stretch, vfl. Besides this, a number of weak bands are observed in the NH stretching region. The weak bands at 3194 and 3168cm-’ appearing in cross polarizations, which are quite far off from the expected two-phonon band positions, are assigned to NH asymmetric stretch, v$’ [lo]. The appearance of vr as a doublet in XZ polarization may be due to factor group splitting.

The inherent Raman intensities of Raman active vr and v!$ modes are very weak and their overtones and combination modes would be still weaker. Therefore, these two-phonon bands will not show up unless they resonate with some of the fundamental modes falling

1066 ANSHU AGARWAL et a/.

Table 3. Band positions (in cm-‘) of the bands observed in Raman spectra in different polarizations of ammonium tetrachlorozincate at room temperature (300K) and at liquid nitrogen temperature (105 K) along with their vibrational

assignment

300K 105 K A’ A ”

Z(XX)Y Z( YY)X X(ZZ)Y Z(X Y)X Z(XZ)X Z( YZ)X Z( YY)X Z(XY)X Z(XZ)X Z(YZ)X Assignment

3310w 3312 w 33lOw - - 3334w - - - 2# - - - - 3252 w 3260~ -

3196sh 3194sh 3194w 3232sh - - 3240 VW vr 3168~ - - 3196m 3184~ 3186m

3154s 3154s 3154s 3154w - 3168s 3168~ - 3170m - - - - 3123s 3130m 3132m 3127m VP - - - - - 3093 s 3093 m 3093 m 3094 m

3112sh - - - - - - ? - 3066sh 3066sh - 3044w 3046~ - #+v,N

2820~~ 2824~~ 2824~~ 2820~~ 2824~~ 2820~~ 2832~ 2832 w 2830~ 2830~ 2vp 1658 w 1658 w 1650~~ 1658~~ 1658,~ 1658~~ 166Om 166Om 1664w 1662 w

- - 1645w - - #

- - 1428 w 143ow 143ow - 1412 w 1412~ 1412~~ 1410~ 1412~~ 1412~~ 1408m 1405 m 1408~ 1408m VP

292 vs 292 vs 292 vs 292m - 292 vs 292 vs 292 s 292 s Vf 280~ 284~ 276 sh 278 sh 278 sh 278sh v$

- - 242 m 244w 248 w - - 132s 155sh 157s 156s

244w LN 154m

- 135s - 137s 135sh - 133w 126s 125s _ _ _ _ _ _ _ vZ

- - 117m 115w 112s 115m 118m 108sh - - 106s 107m - - - -1

Vf

- - - - 1OOsh - 102 sh 108sh LN - 89m - - 89m - - 89 VW 66vw - - 68vw - - - -

47 VW 47m - 5ow 52m 52vw - - - LZ - 35sh - - -

28vw - - - - - - - Ii

Abbreviations used in this table are: v-very; s-strong; m-medium; w-weak; sh-shoulder; L--lattice mode; N-NH: ; Z-ZnCI: -

in that region. For a free NH: ion vr will resonate with

2vy and 2~: and vy will resonate with 2~: and vr + vt. If crystal field effects are to be considered, the crystal spectrum model would lead to the prediction that vr and vr might resonate with each of the three two- phonon bands. As a consequence the two-phonon bands would show up in all the six polarizations by resonating with either vr or v$’ or both. But this is not the case as observed. In fact, in each of the three diagonal polarizations two overtones at 3310 and 2824cm- ’ are observed which correspond to 2vr and 2$, respectively. The 2vr band also appears in the cross polarizations due to resonance with the vr mode. The combination band of v$’ and v!j is expected to fall at 3066cm-’ which appears only in the XZ and YZ polarizations. These observations support the free NHf ion picture suggesting that the crystal field perturbations are quite small in ATCZ. One can, then, neglect the site group splitting of the modes and approximately analyse the spectra of the solid by correlating the species of point group (free ion sym- metry) to those of factor group (the free oriented gas model) [13].

Table 2(B) predicts that the totally symmetric stret- ching vibration of NH; and ZnCli- would appear only in XX, YYand ZZ polarizations under the factor

group C,,,whereas they are expected to appear in XX, Yx ZZ and X Y polarizations under the factor group C,. The appearance of this mode for NH: and ZnCl: - (see section 4 (ii.b) below) in XX, YY, ZZ and XY polarizations favours the prediction of factor group C, for ATCZ. The appearance of vr and vy modes in all the polarizations further supports the C, symmetry, as for C2” symmetry vr;’ should not appear in XZ and 22 polarizations and vy in X Y polarization (cf. Table 2).

(b) Internal modes of ZnCl:-. The modes of ZnCl:- are assigned on the same basis as for NH:. A strong band at 292 cm _ ’ and a weak band at 280cm- ’ are assigned to vf and v$, respectively. To assign the modes of ZnCL- for the orthorhombic system (0::) BEATTIE et al. [ 151 have suggested theoretically that v: and v$ should appear intensely in diagonal polariz- ations whereas v$ and v$ should appear intensely in cross polarizations. ATCZ is a special case of mono- clinic systems (i.e. /3 = go”), therefore one may expect the intensity behaviour of the modes of ZnCl:- in ATCZ similar to that in orthorhombic systems. In the present case 6 and v3 show similar behaviour as predicted above, so the same predictions can be applied for v$ and v$ also and one can assign the bands at 107 and 126cm-’ to these modes, respectively. A strong band at 132cm-’ appearing in XZ polarization may

Raman spectra and phase transitions in (NH,),ZnCl, 1067

be a component of vf or an external mode of NH:. The above suspicion is completely removed by moni- toring the temperature behaviour of this band. The band shifts to 156 cm- ’ at 10.5 K. Such a large shift in the internal modes of ZnCl:- is not expected. Thus the band at 132cm- ’ is an external mode of NH:.

(c) External modes oj’NH,’ and ZnCli-. A number of bands at 28,35,47,66,89 and 132cm- ’ are observed in the lattice region. The bands can be separated as the lattice modes of NH: and ZnCL- by comparing the band positions observed in the Raman spectra of

CNU-WUnCL WI. (iii) Vibrational assignment at 105 K

The Raman spectra of ATCZ at 105 K in YY X Y YZ and XZ polarizations are shown in Fig. 2. The ob- served bands with their assignment are also given in Table 3. The bands are assigned with the analogy of RT spectra. A very strong band at 292cm-i in YY polarization, whose position remains unchanged in going to 105K from RT, is assigned as vf. The appearance of v-1_ as a strong band in cross polariz- ations may be either due to enhancement of site effects or ATCZ going to triclinic structure.

In the N-H stretching region, three strong bands at 3168,3123 and 3093cm-’ are observed in YY polariz- ation. None of these bands corresponds to any of the two-phonon modes. With the help of the temperature dependence of these bands (Fig. 3) these are assigned to the totally symmetric vy mode, corresponding to the three different types of NH: ions present in this phase VI (cf. section 4(iv)). The three distinct sites for the NH: ion cannot arise due to enhanced site effects without a change in the crystal structure. The nearly equal intensities of v$ as well as of different com- ponents of vy in ail the cross polarizations suggest that the structure of ATCZ in the low temperature phase may be triclinic.

I-II 1

3 J’ / 5:

Wovenumber 1 em -’ 1

Fig. 2. Raman spectra in YY, XZ, X Yand YZ polarizations of (NH&ZnCl, single crystal at 105 K.

235

K

255

265

270

273

I I I I I I 3400 2960

Wovenumber (cm-‘)

Fig. 3. Temperature dependence of the bands in N--H stretching region in YY polarization.

The bending mode v$J of NH; appears as a doublet in the YY polarization. The v,” mode shows a doublet in all polarizations. One component corresponding to each mode is more intense and broad relative to the other respective component. The strong components at 1660 and 1408 cm- ’ corresponding to v$’ and VP, respectively, are being associated with the two types of NH: , while the weaker ones at 1645 and 1430 cm- ’ to the respective bands of the third type of NH: ion.

(iv) Phase transitions

To characterize the phase transitions in ATCZ we have monitored the temperature dependence of the thermosensitive bands in the N-H stretching region in YY polarization as shown in Fig. 3. As the temperature is lowered below 266 K, a new band at 3126cm- I appears at the lower frequency side of vii’. This band gains intensity on further reducing the temperature. At h 194K its intensity becomes nearly one third of the intensity of the parent band. The above obser- vation suggests that there are two distinguishable sites available for NH; ions. One of the sites has ap- proximately the same environment as in RT phase III since the nature of the parent band (3154cm-‘) remains almost unchanged. The nominal and continu- ous variation in the position of this band (Fig. 4(a)) may be due to changes in the hydrogen bonding. Below

1068 ANWU AGARWAL~~ al.

Temperature IK)

Fig. 4. (a) The variation of the band positions of N-H symmetric stretching mode, vfi, with temperature in YY’ polarization. (b) The variation of peak intensity of ZnCl symmetric stretching mode, VP, with temperature in W

polarization.

194K the parent band (shifted to 3168cm-‘) again splitsinto twocomponentsat 3146and 3176cm-‘.A11 the three components have approximately equal in- tensities at 105 K. Thus it is concluded that at 105 K the NH: ions are equally distributed in three distinguish- able sites.

The variation of peak intensity of v: in YY polariz- ation also supports the existence of phase transitions at 266 and 194K as depicted in Fig. 4(b). The peak position of v4 remains unchanged in going to low temperature (105 K). The X-ray data of ATCZ at low temperature are not available in the literature but the appearance of vf as a strong band in cross polariz- ations suggests that the structure of ATCZ in phase VI (below 194K) may be triclinic. The decrease in in- tensities of totally symmetric stretching modes of NH: and ZnCl:- on reducing the temperature sug- gests that both the ions are more distorted from their point group symmetries Td at low temperature.

An incommensurate phase is reported to exist between 271 and 266 K in this salt [6]. It is also known that the Raman signature of an incommensurate transition is the appearance of an amplitudon which softens as T -+ T, (incommensurate transition tempera- ture) from the lower temperature side[17] and/or a characteristic mode with anomalous intensity be- haviour in the lattice region [18]. The soft amplitudon is generally visible at all temperatures below z [ 17, 1 S]. In the Raman spectrum of ATCZ in XY polarization a band at 157cm-’ at 105 K softens to _ 144cm- ’ at _ 195 K as shown in Fig. 5. Above this temperature it merges in the band profile of a strong band at 112cm-’ and the soft mode behaviour cannot be observed any further. Thus, the existence of the incommensurate phase could not be well character- ized, though the observation of the aforementioned soft amplitudon indicates its presence at some higher

235

265

250

240 60 i

Waveru-nber (cm-‘)

Fig. 5. Raman spectra of soft mode in (NH,),ZnCI, in X Y polarization.

temperature. The peak intensity of the 112 cm- ’ band increases with temperature. A plot of peak intensity vs temperature for this band (not shown) exhibits a discontinuity in the slope at - 195K which may be due to the phase transition at this temperature, as predicted from the study of the internal modes (cf. Fig. 4).

5. CONCLUSIONS

(i) The free NH: ion picture and hence the free oriented gas model for the present system at room temperature is supported by the appearance of: (a) 2$

mode in the XX, YY and ZZ polarizations only, (b) (vy + VP) mode in XZ and YZ polarizations only and (c) all the internal modes as singlets in the appropriate polarization geometries. (ii) The main support for C: space group comes from the appearance of the vi mode (of both ZnCl:- and NH:) in XX, YY ZZ and X Y polarizations and of vr and VP modes in all the polarizations. (iii) ATCZ undergoes two phase transitions at 267 and 194 K. In the low temperature phase VI (T < 194 K), the NH: ions occupy three different sites and the structure is probably triclinic.

Raman spectra and phase transitions in (NH.&ZnCl, 1069

Acknowledgemenrs-Financial support from the Department of Science and Technology (DST), India, for establishing a Laser Raman Laboratory is gratefully acknowledged The authors are also thankful to the learned referees for their valuable suggestions for improving the previous manuscript and getting it in the present form.

REFERENCES

[1] S. V. MISYUL and J. A. BELOBROVA, Physica Status Solidi (a) 70, K167 (1980).

[2] H. MATSUNAGA, 1. phys. Sot. Japan 51,864 (1982). [3] H. V. KONINGSVELD, Acta Crystallogr. C39, 15 (1983). [4] I. MIKHAIL, Acta Crystallogr. B36, 2126 (1980). [S] J. WARCZEWSKI, Krist. Tech. 15, 667 (1980). [6] G. SMOLENSKII, I. G. SINY, S. D. PROKHOROVA, E. G.

KUZMINOV, V. D. MIKVABIA and R. LAIHO, Ferroelectrics 45, 185 (1982).

[7] H. MATSUNAGA, K. ITOH and E. NAKAMURA, Acta Cryslallogr. B38, 898 (1982).

[S] A. AGARWAL, M. PAL and H. D. BIST, Proc. nucl. Phys. Solid State Phys. Symp. 25C, (1982).

[9] G. TURRELL, Injfared and Raman Spectra ofcrystals, p. 359. Academic Press, London (1972).

[lo] G. HERZBERG, Molecular Spectra and Molecular Swucture, Vol. II. van Nostrand, New York (1945).

[1 1] H. KANNO and J. HIRAISHI, J. Raman Specwosc. 9,851 ( 1980).

[12] G. C. PIMENTEL and A. L. MCCLELLAN, J. them. Phys. 20, 270 (1952).

[13] W. MUNCH, U. FRINGELI and Hs. H. G~~NTHARD, Spectrochim. Acla 33A, 95 (1977).

[14] S. SEETHARAM, H. L. BHAT and P. S. NARAYANAN, J. Raman Spectrosc. 14, 401 (1983).

[15] I. R. BEAT-TIE, T. R. GILSON and G. A. OZIN, J. them. Sot. 534 (1969).

[16] A. M. BON, R. ALMAIRAC, P. NASSIRI, C. BENOIT and J. L. RIBET, Physica Status Sofidi (b) 101, KS7 (1980).

[ 171 M. QUILICHINI, J. P. MATHIEU, M. LE POSTOLEE and N. TOUPRY, J. Phys. 43, 787 (1982).

[18] M. BERTAULT, M. KRAUZMAN, M. LE POSTOLEE, R. M. PICK and M. Scorr, J. Phys. 43, 755 (1982).