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Compare raman study of the phase transitions in K2ZnCl4 and Rb2ZnCl4, Rb2ZnBr4, K2SeO4
M. Quilichini, J.P. Mathieu, M. Le Postollec, N. Toupry
To cite this version:
M. Quilichini, J.P. Mathieu, M. Le Postollec, N. Toupry. Compare raman study of the phase transitions in K2ZnCl4 and Rb2ZnCl4, Rb2ZnBr4, K2SeO4. Journal de Physique, 1982, 43 (5), pp.787-793.
�10.1051/jphys:01982004305078700�. �jpa-00209452�
Compared Raman study of the phase transitions in K2ZnCl4
and Rb2ZnCl4, Rb2ZnBr4, K2SeO4
M. Quilichini (*), J. P. Mathieu, M. Le Postollec and N. Toupry
Laboratoire de Recherches Physiques, Université Pierre et Marie Curie, 4, place Jussieu, Tour 22, 75230 Paris Cedex 05, France
(Reçu le 17 septembre 1981, révisé le 21 décembre, accepte le 26 janvier 1982)
Résumé. 2014 Les spectres de diffusion Raman de monocristaux de K2ZnCl4 ont été étudiés dans un domaine de
température qui comprend les températures de transition de phase successives de ce composé (Ti = 553 K, TL = 403 K), et qui s’étend jusqu’à 10 K. Un mode d’amplitude est observé dans la phase incommensurable (T Ti). Une nouvelle phase est détectée par l’observation d’un mode mou pour T T0. Des mesures de biré- fringence faites en fonction de la température confirment l’existence de cette phase basse température dans K2ZnCl4
et Rb2ZnBr4 et permettent de déterminer le point de transition T0 (T0 = 175 K et 107 K pour K2ZnCl4
et Rb2ZnBr4 respectivement). Des arguments de théorie des groupes sont appliqués aux résultats Raman obtenus pour T T0 et ne sont pas suffisants pour faire une attribution certaine du groupe d’espace de la phase basse température observée dans K2ZnCl4, Rb2ZnCl4, Rb2ZnBr4. Le mécanisme de la transition de la phase para-
électrique vers la phase incommensurable est discuté sur la base des résultats obtenus au voisinage de Ti par diffusion inélastique cohérente de neutrons et de la lumière.
Abstract. 2014 The Raman spectra of K2ZnCl4 single crystals have been measured over the temperature range cover-
ing the successive phase transitions at Ti = 553 K, TL = 403 K down to 10 K. An amplitude mode is detected
below Ti. Evidence for a new phase below T0 is given by the observation of a soft phonon mode. The measured temperature dependence of the birefringence clearly confirms the existence of this low temperature phase in K2ZnCl4 and Rb2ZnBr4 at T0 = 175 K and 107 K respectively. It is shown that group theoretical considerations
applied to experimental Raman data of Rb2ZnCl4 are not sufficient to assign the space group of this low tempera-
ture phase in K2ZnCl4, Rb2ZnCl4 and Rb2ZnBr4. The mechanism of the transition from the paraelectric phase to
the incommensurate phase is discussed for the four compounds K2SeO4, K2ZnCl4, Rb2ZnCl4 and Rb2ZnBr4
on the basis of Raman and neutron data obtained in the vicinity of Ti ; the possibility of a crossover between a displacive regime and an order disorder regime is emphasized.
Classification
Physics Abstracts
78.30
1. Introduction. - In the present paper we report Raman and birefringence measurements on K2ZnC’4
known to exhibit successive phase transitions similar to those of K2SeO4. In this respect, K2Seo4 appears to be the prototype of this series of A2MX4 compounds.
Above Th = 745 K, K2Seo4 has a disordered P63/mma
structure, hereafter called phase I [1, 2] (we follow
the notations of [3]). At Th, an order-disorder tran- sition leads to a paraelectric phase with space group
Pnma (phase II). A displacive transition at Ti = 129 K
leads to an incommensurate phase (phase III) with
*
a modulation
qo = a
3 (I - 6) which locks at T L = 93 Kin a ferroelectric phase with space group Pn21 a (phase IV) and a spontaneous polarization P. parallel
to b [4]. Rb2ZnC’4 and Rb2ZnBr4 were known to present only phases II to IV ; but, more recently a
new displacive transition has been detected in these two crystals at a lower temperature To by Raman spectroscopy ; its existence has been confirmed by birefringence measurements on Rb2ZnC’4 by Giinter
et al. [5, 6]. This new phase will be labelled phase V.
Up to now, only phases II, III and IV have been
reported for K2ZnC’4 with Ti = 557 K and TL = 403 K [7].
The transition at Ti in K2ZnC’4 may be of the
displacive type; it is well known in this case that the Raman signature of this type of transition is the
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01982004305078700
788
observation of an amplitude mode in the incommen- surate phase and of an additional « pseudo-phase »
mode in the commensurate lock-in phase IV. Here
the phase mode and the amplitude mode are the two specific elementary excitations of phase III ; neverthe-
less the phase mode can only be detected either by
neutron inelastic diffusion or by Brillouin spectro- scopy [8].
The format of this paper is as follows. All experi-
mental data obtained on K2ZnC’4 are given in sec-
tion 2; in section 3 we discuss the possible structure
of the new low temperature phase V found and
studied in K2ZnC14, Rb2ZnC’4, Rb2ZnBr4 and K2Se04 ; Section 4 is devoted to a discussion of the experimental results obtained on these four
compounds near T ; ; finally, in section 5 we give the implication of the present discussion in a more
general context.
2. Experimental results in K2ZnC14. - 2.1 RAMAN
MEASUREMENTS. - They were performed as described
in [5] for Rb2ZnC’4 and Rb2ZnBr4.
2.1.1 Amplitude mode. - In the b(aa)c scattering geometry in which the amplitude mode is Raman
active, the data show a soft phonon with a frequency varying from 18 cm - 1 to 26 cm-1 as the temperature decreases from 524 K (i.e. T ; - 29 K) to 300 K (Fig. 1). As in the case of Rb2ZnC’4 and Rb2ZnBr4,
this mode appears as a small peak on a broad quasi-
elastic background. With decreasing temperature, the background vanishes and the amplitude mode is
better and better resolved. This evolution is not
affected by the lock-in transition.
2.1. 2 Pseudo phase mode. - In the ferroelectric
phase IV, below TL = 403 K, the pseudo phase
mode should be observed in the b(ab)c scattering geometry. Nevertheless the presence of a strong hard Raman peak at 19 cm-1 precludes the detection of this soft excitation.
2.1.3 On can notice that the amplitude mode in spectra b(aa)c at temperatures lower than 300 K becomes more and more intense as the temperature decreases and has an asymmetric shape on its lower
energy side. At T = 10 K the spectra shows two low energy peaks at 24 cm - I and 32 cm-1 respectively.
The c(bb)a spectra studied as a function of temperature show the occurrence of another low temperature phase (called phase V as in Rb2ZnC’4 and Rb2ZnBr4) ;
this phase is detected by the observation of a soft
phonon mode with a frequency changing from 13 cm-1
to 17 cm -1 as the temperature is decreased from 140 K to 80 K (Fig. 2). The existence of this new low temperature phase explains the behaviour mentioned above for the b(aa)c spectra. It is related to an anti-
crossing process between a low energy hard line of the
phase IV and the amplitude mode similar to the anti-
crossing process already observed in Rb2ZnC’4 and Rb2ZnBr4 [5, 10].
Fig. 1. - Raman spectrum of K,ZnCl, in the b(aa)c geometry.
2.2 BIREFRINGENCE RESULTS. - In order to confirm the existence of this transition to a phase V, and to
locate precisely the transition temperature To, we
have performed birefringence measurements on
K2ZnCI4. This experimental technique has proved to
be successful to detect and confirm in Rb2ZnCl4 the
low temperature transition at To = 75 K already reported by Francke et al. [5]. Giinter et al. [6] have
obtained data with light propagating along all three crystallographic directions. Their results show that at both transition temperatures Ti and TL the bire- fringence changes continuously; the most pronounced changes occur at To for all three directions, in spite of
the fact that the TL transition is expected to be first
order.
Our birefringence measurements have been done
using a setting slightly different from the one described in [6]. We used a Hg lamp as source. The 5 461 A
Fig. 2. - Raman spectrum of K,ZnCl, in the c(bb)a geometry showing the observed soft mode in the low tem-
perature phase (V).
emission line was selected by a differential filter. The
sample was in the shape of a platelet and was mounted
in an He-gas cryostat; we assumed that the thickness,
e, does not change with temperature; we are however
aware, as Günter et al., of the relative softness of this
compound. The cryostat plus a ÀI4 plate were placed
between a polarizer and a shadow analyser. Figure 3
Fig. 3. - Plot of P = 7c Anj e as a function of temperature for K,ZnCl,. (1 = 5 461 A, e is the thickness of the sample
cut perpendicular to the acute bissectrice of the angle of the optical axes, Onij is the birefringence with i, j = a, b, c.)
shows fi =
y-r
2 Aðnllc as a function of temperature for light propagating along the a axis. This curve showsa low temperature transition at To = 175 K; this
agrees with the value extrapolated from the tempera-
ture dependence of the new soft mode in phase V. One
can also notice than An does not change sign at To,
in opposition to the case of Rb2ZnC’4’
3. Discussion of the low temperature phase. -
3. l. INTRODUCTION. - i) The birefringence measu-
rements described above for K2ZnC’4 were repeated
on Rb2ZnBr4. Figure 4 shows the plot of
fJ(T) = 1 ;
An.b vs. T and gives a phase IV-phase Vtransition temperature To = 106 K, in good agree- ment with the value obtained from the Raman data [5]. Moreover this curve shows a birefringence
behaviour different from the one observed in Rb2ZnC’4
for the same geometry.
ii) In a recent paper by Lopez Echarri et al. [3],
evidence for a new phase transition in K2Seo4 at T6 = 56 K was obtained by specific heat measure-
ments. We therefore performed on this crystal the
same Raman experiments as on K2ZnCI4, Rb2ZnCl4
and Rb2ZnBr4 to know whether the phase V could be
detected by the observation of a soft phonon mode.
For KZSe04 no soft mode was observed. Nevertheless
birefringence measurements with light propagating along the three principal axes of the crystal are pre-
Fig. 4. - Plot of P as a function of temperature for Rb2ZnBr4’
790
Fig. 5. - Low temperature spectra of Rb,ZnC’4. a) a(bb)c, b(cc)a, b(aa)c : T = 10 K. b) b(ab)c, «pseudo-phase»
mode geometry : T = 13 K. c) b(ca)c, b(cb)c : T = 10 K.
sently in progress in order to see whether the behaviour
of K2Se04 is the same as the one observed for the three other compounds. If differences are found in bire-
fringence as in Raman results, this would suggest that the low temperature phase transition at 56 K does not lead of the same phase V as in Rb2ZnC’4, K2ZnC’4
and Rb2ZnCl4. The use of Tb (instead of To) for the temperature transition is meant for this possibility.
iii) The structure of phase V is not yet known.
Preliminary diffraction neutron measurements made
on a powder sample of Rb2ZnC’4 [9] have shown
that this phase has a structure different from the ferroelectric IV one. The data obtained at 4 K are
refined in space group Pn21 a with a R factor of 5.6 %.
This correct R value is due to the fact that no new
Bragg line was detected for T To. However the refined atomic coordinates do not follow the trend observed through the 353 K, 160 K and 110 K results.
Moreover some of the calculated Zn-Cl distances are
anomalously short or long. Then no definite conclu- sion can be drawn, although these refinements clearly suggest some structural rearrangement below To.
iv) From their birefringence measurements, Gfnter
et al. suggest that the new transition in Rb2ZnC’4 is
ferroelastic with polar axis along b, leading to a pos- sible monoclinic space group P1211 [6]. This is in good
agreement with the result obtained by Wada on Rb2ZnC’4 by spontaneous polarization measurements for T To [10], Wada also proposes that this transi- tion is induced by a doubly degenerate phonon at the
Brillouin zone boundary (B.Z.B.) of the Pn21 a ferro-
electric phase IV of Rb2ZnCI4. In a very recent study
of dielectric constants and of the spontaneous polari-
zation Unruh et al. [16] show that at To the crystal
transforms to another ferroelectric state : there is a
continuous onset of a spontaneous polarization parallel to the pseudo-hexagonal a axis, while the component of PS parallel to the b axis starts to decrease
with decreasing temperature (as observed by Wada).
Also a group theory analysis proposed by Dvorak
Fig. 6. - Plot of wampl. as a function of I1TIT¡ for K2Se04, K2ZnCI4, Rb2ZnC14, Rb2ZnBr4. Dashed lines are extrapo- lated curves outside the experimental data points range.
et al. [17] shows that the possible space groups of this phase V are either Pc11 (phase 1) or Bl la (phase 2)
or PI (phase 3). In agreement with the experimental data, these authors pointed out that the phase tran-
sition IV-V may be continuous because there are
neither cubic invariants nor Lifshits invariants in the
thermodynamic potential describing the phase tran-
sitions into the phases II, III, IV, the transition would be induced by the crystal instability against two degenerate modes in the phase II.
3. 2 DiscussioN. - We will now discuss the Raman results [5, 10] obtained on the phase V of Rb2ZnC’4
and see whether they can lead to a confirmation of the transition mechanism, and, thus of the space group of this phase. As far as the experimental results are
concerned we agree with the data obtained by Wada;
however we would like to make further comments.
We observe for Rb2ZnC’4 (as well as for Rb2ZnBr4)
a totally symmetric soft phonon below To in the three
« diagonal » scattering geometries b(aa)c, a(bb)c and b(cc)a ; this was also found by Wada. At T = 10 K
this phonon reaches 14 cm-1 and an anticrossing with
a hard peak (at 9 cm-1 ) is clearly observed in the
a(bb)c geometry when the temperature is decreased from To to 10 K (Fig. 5).
Wada also reported another soft mode «VB»
observed in the scattering geometry b(ab)c where the pseudo phase mode of the ferroelectric phase IV
is also active. In his data, both the VB and the pseudo phase mode are detected as a single shoulder on the Rayleigh line for T = 70 K (in phase V); the two
lines are resolved at T = 7 K. In our own spectra the pseudo phase mode is already visible in phase IV
at T = 90 K where it appears as a weak peak at 6 cm-1. As the temperature is decreased this peak
remains weak in phase IV and becomes broader, asymmetric and more intense in phase V (e.g. at
T = 61 K its frequency is 7.5 cm-’). At T = 15 K
two well resolved lines are obtained at 8.5 cm-1 and 13 cm- 1 respectively.
We can analyse these data by taking into account
the fact that below To, the structure is supposed to be monoclinic, the point group being either C2 or C.,.
In both cases, there are in phase V two q = 0 irredu-
cible polar representations and the Raman activity
may be written in the Pnma frame.
It is obvious that phase (2) allows a coherent interpre-
tation of all the experimental data described above.
There are two soft modes : the S mode is the totally symmetric mode visible in the b(aa)c, a(bb)c, b(cc)a
and b(ab)c scattering geometries. The other soft mode A is observed in the b(cb)c geometry, by a
careful analysis of the evolution of this Raman spec- trum with temperature. In phase IV at T = 130 K a peak at 11 cm-1 emerges from a broad quasielastic background. In phase V this peak becomes broader and asymmetric; as the temperature is decreased down
to 10 K, the mean frequency of this double structure
approaches 19 cin-’ and remains unresolved.
Thus from the Raman data, we are able to propose
a space group of the phase V. A structure determina-
tion is nevertheless necessary to ascertain these
experimental and theoretical6conclusions.
4. Discussion of the vicinity of 1;. - In this last part,
we will compare the presently known Raman and
Neutron results for K2SeO4, Rb2ZnCI4 and Rb2ZnBr4
with those of K2ZnC’4 (essentially Raman data); we
will first analyse the dynamical experiments, then
the structural information, i.e. the variation of 6
versus T.
Among these four substances K2SeO4 appears to be the best representative of a displacive type transi- tion. Nevertheless, even in this case, one is far from an
ideal situation. Although as small as in Raman scattering, the amplitude mode appears with
it emerges from the central peak only for At > 0.06 and hardens from M = 11.5 cm-1 (At = 0.057) to
36 cm- I (At = 0.92). Furthermore, in the neutron
data of Iizumi et al. [4], for T > T ;, the soft mode dispersion curve is very anisotropic in q space, being
very flat and softening as a whole along a* as T -+ T;.
When T; is approached, the critical scattering has an
unusual width in the wings of the energy profile, suggesting that there is more than one relaxation time, and that this spectrum consists of a narrow central peak plus some overdamped phonons. Finally,
the phason mode has never been detected although
there is no reason not to detect it in a neutron scatter-
ing experiment.
All these results suggest that in K2SeO4 the soft
mode does not really reach m = 0 at T; and that some
crossover between a displacive and an order-disorder
regime could appear in the vicinity of T;.
This last aspect seems to be more evident for the two rubidium salts. First the Raman visibility of the amplitude mode starts at At = 0.228 for Rb2ZnC’4
and at At = 0.245 for Rb2ZnBr4 ; in these two cases
this mode slowly emerges from a broad central peak
which may be related to a low frequency phonon density of states made visible in Raman scattering and
due to some atomic disorder. Except for this important aspect, the amplitude mode dynamics in these two crystals seem to be very similar to that of K2Seo4’
Indeed, if one plots S(At) = co(At)lco(At = 1) one
obtains very similar results for the three salts (table I).
792
Table I. - Experimental data used or curves of figure 6 are given as Wexp( = Wamplitudon).At = I
-Tis
thereduced temperature. W = (Oexp is the normalized frequency shift; (,o(At -+ 1) has been extrapolated from
curves of figure 6. For K2ZnCI4, Rb2ZnCI4 and Rb2ZnBr4, .,refers to the frequency shift which is calculated by a ro(A2ZnX4)
.
proper scaling based on the
ratio w(K2Se04)
determined at At = 0.3.(o(K2SeO4)
Note that due to the existence of the phase V, m(At = 1)
is only obtained as an extrapolation.
Fig. 7. - Plot of 03B4 (with q03B4 = (t - 6) a*) as a function of
T/T; for Rb2ZnBr4, Rb2ZnC14, K2ZnC14, K2Se04.
Secondly, for T in the vicinity of T ;, neutron measu-
rements made on Rb2ZnC’4 [13] and Rb2ZnBr4 [14]
failed to reveal any soft branch. Careful analysis on
the Cl salt neutron data seem however to suggest that a very flat low frequency branch could exist in the a* direction at lower temperature. This, again,
tends to support a much larger crossover region for a
more likely order-disorder behaviour.
The difference between the Rb salts and K2Seo4
also appears in a plot of the incommensurate modula- tion as a function of T/T; (Fig. 7). For both Rb2ZnCl4
and Rb2ZnBr4 in a large temperature region, 6
remains nearly or very flat respectively before finally locking for TITI - 0.6 (one has to notice the hyste-
resis which appears for Rb2ZnBr4 in the vicinity of rj. In K2SeO4 on the contrary, 6 locks around TITI = 0.7 and drops continuously with T. K2ZnC’4
is in two respects rather similar to K2SeO4. First, the b(T/T;) curves for the two compounds have clearly
some common features : the continuous drop with T
and nearly identical values for the lock-in tempera-
ture. Secondly, from our Raman data the amplitude
mode appears at approximately the same At value.
Nevertheless, w(åt = 0.05) is 18 cm-1 and Z(At)
is clearly different for the two crystals as is apparent in figure 6. It is thus not clear if the central peak of figure 1
has the same origin as in Rb2ZnC’4 and Rb2ZnBr4.
