Pergamon Solid State Communications, Vol. 103, No. 4. pp. 243-248, 1997 Q 1997 Elsevier Science Ltd

Printed in Great Britain. All rights reserved 00x3- IO98/97 $17.OO+.Ou

PII: SOO38-1098(97)00144-0

INFLUENCE OF THE RATE OF TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF SINGLE CRYSTAL Rb2CoC14

Jose-Maria Martin, Jaime de1 Cerro and Saturio Ramos

Instituto Mixto de Ciencia de Materiales, CSIC-Universidad de Sevilla, P.O. Box 1065, E41080 Seville, Spain

(Received 18 November 1996; accepted 27 March 1991 by G. Bastard)

The influence of very small rates of temperature change on the dielectric permittivity of incommensurate crystal Rb$oCld was studied. It is shown that in the commensurate phase the permittivity excess depends on the cooling rate and the tail is present even for rates as low as 0.002 K min-‘. Relaxation processes of the permittivity were studied in both the temperature range where C and IC phases coexist and at temperatures where the discommensurations are not stable. Results are compared with data of RbzZnC14 and K2ZnC14. Data suggest that the dielectric tail is more stable in Rb2CoC14 than in K2ZnC14 and is a consequence of revival discommensurations. 0 1997 Elsevier Science Ltd

Keywords: incommensurate phases, hysteresis phenomena, dielectric properties, A2BX4 family.

1. INTRODUCTION

The Rb&oCle crystal belongs to the family of A2BX4 insulating compounds. On cooling it reveals the same

sequence of paraelectric(P)-incommensurate(IC)- commensurate(C) structural phase transitions observed in RbzZnC14, which is one of the most widely studied crystals of this family. The P-IC phase transition

temperature is T, = 292 K and the IC-C phase transition

temperature is T, = 195 K. These temperatures are

similar to those of RbzZnC14; unit cell dimensions are also similar so the difference in chemical properties of Co and Zn seem to have little effect on the transition. The

crystal structure of RbzCoClb is orthorhombic and its space group is Pnma, the modulation of IC phase is

90 = a*( l/3 - S) and it locks at a*/3 in the C phase

(Pna2 ,). This sequence of transitions can be explained on the

basis of a Landau-type theory [l] with a two-component order parameter of modulus p and phase 4. Near to T, the structure of the IC phase may be regarded as a sinusoidal inhomogeneous distribution of the order parameter [2]. With decreasing temperature, higher harmonics become significant and the structure evolves to a sequence of quasidomain regions of homogeneous values of pa and 4, [3] where 4, represents one of the six equilibrium values of 4 in the C phase.

These commensurate domains are, typically, 10 nm in width [4] and are separated by narrow domain walls

called discommensurations (DC) in which 6 changes by an increment of 2~16. When cooling the width of the regions is increased and therefore the density of DC decreases. At T,, the density should reduce to zero [5] when the C phase nucleates. In reality, DC nucleate into ferroelectric domain walls (DW) by a mechanism in which six DC meet and disappear. The (commensurate)

regions grow to the size of a ferroelectric domain ( lo3 nm) [4].

The dielectric properties of the family of A2BX4 crystals are mainly due to the properties of DC and DW. The dielectric properties of the IC phase are well

understood on the basis of a Landau-type theory which leads to Curie-Weiss law behaviour [6,7] near to T, due to the coupling of DC to electric field. In any case, the single measurement of the static dielectric constant does not tell us very much about the IC-C phase transition; simultaneous measurements of birefringence [8] or relaxation frequency [9] together with the permittivity show that, for standard quality crystal, the phase transition occurs below the peak of permittivity and thus, both phases coexist in a range of 1 K below the peak of permittivity. Global hysteresis phenomena are found in the IC-phase and are ascribed to the influence of defects on motion and diffusion of DC [4, 101.

243

244 TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF Rb2CoC14 Vol. 103, No. 4

On the other hand, the experimental dielectric properties of the C-phase cannot be explained on the basis of an equilibrium theory. The ground state of the C-phase must be single domain; so, on cooling, we should expect a drop of the permittivity to the back- ground equilibrium value (roughly 18) passing through some intermediate value in which the transition occurs. Instead of this, a large tail is observed extending over 20 K. The remanent excess of permittivity (hereafter the tail) on cooling has been related to the oscillations of remanent chaotic discommensurations [ 1 l- 141 or,

alternatively, to oscillations of ordinary domain walls as in normal ferroelectrics [ 15, 161.

On the contrary, on heating from far below T, the permittivity remains at the background value and a sudden increase is observed close to T,. Thermal hysteresis on the value of T, is observed; this hysteresis ranges from 3 K to 0.2 K depending on the quality of the sample [5].

In K2ZnC14, a crystal isomorphous to RbzCoCld, comprehensive experiments have been carried out on ageing phenomena in the C-phase [II, l&20].

Mashiyama et al. 1193 showed that the permittivity relaxed to the background value in several days fulfilling an exponential law

where E,~ is the equilibrium value and 7 is the relaxation time. The equilibrium value was shown to be that of the heating branch and the relaxation time was around 50 h. In this experiment it took 8 days for the permittivity to

drop to the value of the heating branch. It was also shown that the width of the tail depends on the temperature rate, dT/dt 1201 and it was observed that the tail practically

disappears for dT/dt = - 0.006 K min-‘. These results show the metastable character of the tail.

Similar ageing phenomena were reported for unpurified [4] and purified [211 RbzZnC14 crystal. The tail was also dependent on dT/dt [16, 211 although there is no evidence that the tail disappears on cooling at very low rate. The relaxation process was ascribed to several different mechanisms [21] and subsequently the proposed behaviour was a stretched exponential law

where 7 is the mean relaxation time and a is close to 0.5. However an important factor must be taken into account: the experimental difficulty in keeping T constant for the time necessary for the permittivity to drop to the equilibrium value.

As expected from the phenomenological theory, no ageing phenomena were observed on the heating branch

for either on K2ZnC14 or on RbzZnClb crystals because on heating from far below T, both crystals are in equilibrium states.

On the other hand no relaxation experiment has ever been reported on RbzCoCld although we can expect behaviour qualitatively similar to that of K2ZnC14 and RbzZnClc

In this paper we study the influence of small

temperature rates on the permittivity tail of Rb2CoC14 crystal and its relaxation process. The results are

compared with those of K2ZnC14 and Rb2ZnC14 crystals.

2. EXPERIMENTAL

A crystal of RbzCoCld was grown using an improved method [22] which reduces significantly the thermal hysteresis on T, from 12 K [22] to 4 K [23], however this value of hysteresis is significatively larger than that obtained in highly purified RbaZnCld [5] thus we think that the crystal can be considered as standard quality and defects are present in some extent. The sample was 50 mm2 in cross section and 3.1 mm in height along its

ferroelectric axis. Gold electrodes were evaporated on the sample.

The dielectric permittivity, E, was measured with a capacitance bridge ES1 SP5240, working at a frequency of 2 kHz. Several experiments were performed at different temperature rates of cooling and heating. We will label these experiments as A (for the experiment taken at 0.002 K min-I), B (at 0.02 K min-‘), C (at 0.2 K min-‘), D (at 1.0 K min-‘).

Experiment C and D were carried out in a con- ventional chamber filled with N2 gas. The chamber was cooled with liquid nitrogen while the temperature of the sample was controlled by a Eurotherm P812 temperature

controller. The precision of the controller was 0.1 K

while the sensitivity of the running rate was 0.01 K min-‘.

Experiments A and B were carried out in a conduc- tion calorimeter previously described [24]. The sample was placed between two identical heat fluxmeters with electrodes. These fluxmeters are symmetrically placed in a calorimetric block surrounded by several adiabatic shields. The assembly is placed in a hermetic case where a high vacuum can be reached, thus obtaining great temperature stability (thermal fluctuations are less than 1 mK), moreover, the temperature gradient in the sample can be considered as negligible. Dielectric permittivity and thermal properties can be simultaneously measured with this device; the thermal study is now in progress and it will be published later. The vessel is in thermal contact with a large amount of alcohol whose temperature is controlled by an Eurothenn P812 temperature controller. The temperature controller can

Vol. 103, No. 4 TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF RbQCl, 245

impose a constant temperature change rate on the alcohol, the precision of the controller is 0.1 K while its temperature change rate sensitivity was 0.01 K h-‘. The temperature of the sample follows the alcohol temperature change rate after some initial time which is not relevant. Experiment A was performed under high- vacuum conditions ( 10e5 mbar) while experiment B was performed in Nr atmosphere.

At last, two experiments were performed at fixed temperature. These experiments were carried out in the calorimetric vessel and the temperature was fixed by dissipating a electric power on the block. The power was manually controlled during few hours so as the temperature to be constant within 0.1 K of amplitude.

3. RESULTS

Data of dielectric permittivity for the cooling expcri- ments are presented in Fig. 1.

The temperature of maximum permittivity, T,,,,, shows no systematic dependence on dTldt and is around 195 K. The maximum value of permittivity ranges between 120 for experiments C and D and 70 for A and B. Although other experimental factors such as dT/dt or temperature gradient may also modify the value of the peak to some extent, the strong difference in the height of the peak of permittivity must be ascribed to the different annealing process due to features of the different experimental devices.

Experiments C and D were carried out after ten hour’s annealing at 300 K and it took only about one hour to reach the decreasing temperature rate near T,. Due to the high thermal inertia of the calorimeter, it took more than two days to reach the temperature rates of experiments A and B, thus, we can expect a loss of annealing information in these last experiments. The influence of annealing conditions on K2ZnC14 were reported by Zhang et al. [ll]. They observed that the maximum of permittivity varied from 80 to 30 by varying the annealing time from ten hours to one hour. This could explain the rather variable data on the maximum of permittivity observed in several papers. In any event, our data agree substantially with those previously reported for both RbzCoClt [9, 221 and RbzZnCl, [8].

In Fig. 2, data on dielectric permittivity for experiment A are presented during cooling and heating scan. To our knowledge, the temperature rate of experiment A is the lowest ever used on these kind of crystals; it is even three times lower than the experiment reported by G. Niquet et al. [20] at 0.006 K min-’ on KzZnC14 where the tail practically disappears. In contrast we show in Fig. 2 that the tail is still observed and its shape is similar to that of experiments B, C and D. We must point out that in this experiment the system took

160 ,

120

E

80

40

0 I I I I

‘92 T/K 196 200

Fig. 1. Temperature dependence of the dielectric permittivity of RbrCoC14 single crystal near the IC-C phase transition during cooling scan. (A) ]dT/dt) = 0.002 K min-‘, (0) (dT/dt( = 0.02 K min-‘, (0) IdTldt! = 0.2 K min-‘, (m) IdTldtl = 1.0 K min-‘.

seven days from the peak of permittivity to reach T1 in Fig. 2, where the tail is still clearly present. If Rb2CoC14 behaved like K2ZnC14, the permittivity might have relaxed to the value of the heating scan. So

80(

60

E

40

20

0 I II ’ I

160 T/K

200

Fig. 2. Temperature dependence of the dielectric permittivity of RbzCoCld single crystal during cooling (bold) and heating (light) scans in a wide range of temperature, IdTldtl = 0.002 K min-‘. The time needed for the crystal to take T1 from the temperature of the peak was seven days.

246 TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF Rb2CoC14 Vol. 103, No. 4

according to our data, the relaxation time of the permittivity in RbzCoCld seems to be higher than in K2ZnC14.

From the value of the maximum of permittivity which lies around 75, both on cooling and on heating

scans and its thermal hysteresis which is around 1 K, we confirm that the purity of the sample is not high. This value is less than those previously published for

standard quality crystal (2-4 K) [4, 221 due to the small temperature change rate of the experiment, however it remains greater than those obtained for purified RbzZnCIJ samples (0.2 K) [5].

The heating scans of experiments B, C and D are fairly similar to that of experiment A: both the value of the peak of permittivity and the temperature of the peak are quite similar. This is explained by the fact that the crystal is in full thermal equilibrium when heating

because the state of the system is near single domain if the heating scan is started at a sufficiently low temperature (about 80 K below T,). On the contrary when, after cooling, the heating scan begins at a

temperature where the tail has not yet disappeared, RbzCoClJ shows similar behaviour to that found in other A2BX4 crystals: the permittivity remains constant at the value reached on cooling and a sudden peak is observed close to T,.

The phenomenological theory of A2BX4 crystals predicts [6] that the dielectric susceptibility in the whole IC phase behaves as a function of elliptic integrals. From this function it is deduced that the permittivity

excess (E - Q) diverges according to

e-q,O:(T-Tc)-’ (3)

as T moves towards T,. Here eb is the background value and it is accepted to be the value of the permittivity in the P-phase. The critical exponent, l, is theoretically equal to 1. This behaviour has been previously observed in RbzZnC14 crystal [6].

Using the background value eb = 18 and data of experiment A on cooling in the IC phase, we can calculate the value of T, by plotting (E - eb) - ’ vs the temperature. The value of T, is then found to be

T, = 194.3 K which is lower than but close to TM = 195.1 K as would be expected. In Fig. 3 (e - Q,- ’ is represented vs T - T, in a logarithmic plot; this allows us to obtain the critical exponent [ = 1.000 -+: 0.003 in the region 1 K < T - T, < 5 K; below this interval the Curie-Weiss behaviour fails as the transition takes places within the next few kelvins [25]. The critical exponent agrees more closely with the theoretical value than that obtained previously for Rb2ZnC14 crystal [6] (t = 1.02 2 0.01). Data obtained on heating show a similar behaviour with a critical exponent [ = 0.999 + 0.003; and experiments B, C and

I00 T-T,(K) IO+'

Fig. 3. Log-log plot of the reciprocal of dielectric permittivity vs temperature in the IC-phase of RbzCoCll single crystal; (dT/dt] = 0.002 K min-‘. Bold points indicate cooling; light points indicate heating.

D both on cooling and on heating scans also fulfils Curie-Weiss law.

So as to compare data of the dielectric tail in the C-phase we renormalized the curves by scaling E - eb with eM - eb, where ey is the maximum Vahe of permittivity. Data for AE = (E - eb)/(eM - eb) vs AT = (TM - T) are presented in Fig. 4(a). In this figure we observe that the effect of the thermal rate is a slight decrease of A.E on

decreasing JdTldtJ which reflects a dynamic relaxation of the dielectric permittivity. The renormalized permittivity

at AT = 2 K ranges between 0.76 (for curve D) and 0.70 (for curve A). Thus, by decreasing ]dT/dt( 500 times we get only an 8% decrease on At. We infer then that the dielectric tail is weakly dependent on temperature rate and an extremely small cooling rate would be necessary to reach equilibrium state.

This dynamic phenomenon is to be related to iso- thermal relaxations observed in K2ZnC14 and RbzZnCIJ which were explained as a sum over several relaxation

processes in the crystal. These processes were related to the annihilation of remaining stripples and their pinning to defects. It was concluded that there is a distribution of relaxation times and thus a stretched (mean) exponential was proposed to explain the relaxations [see equations (2) and (3)3, in accordance to that we assume that the dynamic relaxation governed by ]dT/dr] can be related to a stretched expression similar to equation (2). We try the following behaviour

AE a e - ( WkWo) - In 9 (4)

where the proportionality factor and v. depend on T.

Vol. 103, No. 4 TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF RbzCoCld 247

i W

1.0 -

AC* -

0.8 -

0.6 -

AE

0.8

0.6

I I I I I

4 3 2 AT/K '

0

Fig. 4. Behaviour of the dielectric tail near to the transition point, TM, for Rb$oClb single crystal on cooling. (a) Renormalized dielectric permittivity data vs AT = T,,., - T. (A) JdTldtJ = 0.002 K min-‘, IdTldrl = 0.02 K rnin-l, _( 0)

(0) IdT/dr( = 0.2 K min-‘,

(m) IdT/dt( = 1.0 K mm I. (b) The same data scaled with equation (4), v. = 2 X IO-’ K min-‘.

Here a! is set to -l/2 following the idea by Mashiyama et al. The negative sign of (Y reflects the inverse dependence of IdTldrl on time. At T,,., - T = 2 K, equation (4) is fulfilled for v. = 2 X 10 - 5 K min-‘, so this value of v. is an estimation of the cooling rate necessary for the tail to disappear and it indicates the long-lived nature of the dielectric permittivity tail in Rb2CoC14 crystal. In Fig. 4(b) it is presented the behaviour of the scaled relation

To complete this study, two relaxation processes were carried out: on cooling at a constant rate of 0.05 K min-’ the temperature of the device was kept constant at (AT), = 0.2 K and (AT)f = 7 K respectively. As the tail does not correspond to an equilibrium state, the dielectric permittivity decreases in time to reach the equilibrium value. Both experiments are shown in Fig. 5.

For (AT), = 0.2 K and within one hour the permittivity relaxes 8% but no noticeable decrease is

75

E

70

65

1 (dT),,=7K

I I I I

0 2. time/h

4

Fig. 5. Decay of permittivity with time in the C-phase. Left axis, (AT), = T, - T = 0.2 K; data can be fitted to a stretched exponential expression, equation (2), yielding 7= 10min and (Y = 0.6. Right axis, (AT)f = T,,, - T = 7 K.

observed afterwards during four hours. Data can be fitted to expression (2) and 7 = 12 min and (Y = 0.6 are obtained. This is in agreement with a previously reported experiment on unpurified Rb2ZnC14 [43, although the relaxation time is shorter than that reported for purified RbzZnC14 [21].

For (AT)f = 7 K the dielectric permittivity shows a long relaxation process. The study of this process could not be finished because the thermal inertia of the device did not allow us to keep the temperature of the block constant for a longer time period. Improvement of the device are now in progress which will allow us to complete this study. This extremely long relaxation process agrees with the low value of the cooling rate necessary for the tail to disappear which has been estimated above.

These results can be explained in the following way: Simultaneous measurement of birefringence and dielec- tric permittivity on Rb2ZnC14 crystal have characterized [5, 81 the phase transformation IC-C. This is due to the different coupling of birefringence and permittivity to the order parameter. While birefringence is directly related to p and thus is sensitive to any change in p (such as a phase transformation), permittivity is mainly sensitive to field-induced oscillations of anti-boundary walls. This dependence overcomes the anomaly of the permittivity due to the phase transition itself (i.e. to the transformation of the IC phase into the C phase). The simultaneous measurement of birefiingence and permittivity showed that the phase transition takes

TEMPERATURE CHANGE ON THE DIELECTRIC TAIL OF Rb2CoC14 Vol. 103, No. 4

place immediately after TM is reached on cooling and that in a range of 1 K below T, both phases coexist while DC are nucleated into DW. The same conclusion is

obtained by measuring simultaneously the permittivity and the relaxation frequency [9] on Rb&oCl+ Our relaxation experiment (e) lies in the phase-mixture

region; the equilibrium value of the permittivity is

related to the density of DC which exists in equilibrium at that temperature and the relaxation takes place due to the DW contribution to the permittiv- ity. This contribution relaxes in time by decreasing the total wall area and increasing the average spring constant [26]. This phenomenon has a short time constant and should be similar to that observed in normal improper ferroelectrics.

On the other hand, it has been indicated above that,

when lowering the temperature, the DC are nucleated into DW by a mechanism in which six DC meet and disappear; the permittivity should then reduce to the background value. If we assume that the relaxation time of this process is very long, the tail obtained when cooling can be attributed to the survival of unstable DC below the coexistence region and a relaxation process is

expected between the tail and the background value of the permittivity. This relaxation process is extremely slow as shown at (AT)f = 7 K and it would result in the observed anomalous high value of the permittivity (tail) which is overcome only at extremely low thermal

rates approximately equal to v. = 2 X 10v5 K min-‘.

This relaxation process may be related to the purity of the sample and the extent of this study to purified samples is now in progress.

We can conclude that the dielectric behaviour of Rb2CoClJ is similar to that found in Rbz’ZnClj and K2ZnC14 although the relaxation time of the permittivity tail in Rb&oCld is longer than in K2ZnC14. While, in the latter the tail disappears on cooling at 0.006 K min-‘, in the former it is present even at slowest cooling rates.

Thus, the influence of revival DC is stronger in RbzCoC14 than in K2ZnC14. The tail is related to the oscillation of remanent DC [ 1 l] which reflects a memory

of the past incommensurate phase at the commensurate phase; the impurity of the sample may stress this effect and further measurement should be made on purified crystals.

Acknowledgement-We thank Dr V. Dvorak for supplying the crystal.

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REFERENCES

Cummins, H.Z., Physics Reports, 185, 1990, 211. Ishibashi, Y., in Incommensurate Phase in Dielectrics II (Edited by R. Blinc and A.P. Levanyuk) North Holland Publishers, 1986. Toledano, J.-C. and Toledano, P., The Landau Theory of Phase Transitions. World Scientific, Singapore, 1987. Hamano, K., Ikeda, Y., Fujimoto, T., Ema, K. and Hirotsu, S., J. Phys. Sot. Jpn, 49, 1980, 2278. Novotna, V., Fousek, J., Kroupa, J., Hamano, K. and Havr&kova, M.. Solid State Commun., 83, 1992, 101. Levstik, A., Prelovsek, P., Filipic, C. and Zeks, B., Phys. Rev., B25, 1982, 3416. Martin, J.M., Ramos, S. and de1 Cerro, J., Proc. 8th EMF, 1995, in press. Fousek, J., Kroupa, J. and Chapelle, J., Solid State Commun., 63, 1987, 769. Novotna, V., Kabelka, H., Fousek, J., Vanek, P. and Warhanek. H., Ferroelectrics, 140, 1993, 163. Strukov. B.A., Phase Transitions, 15, 1989, 143. Zhang, G., Qui, S.L., Dutta, M. and Cummins, H.Z., Solid State Commun., 55, 1985, 275. Blinc, R., Prelovsek, P., Levstik, A. and Filipic, C., Phys. Rev., B29, 1984, 1508. Prelovsek, P. and Blinc, R., .I. Phys. C: Solid State Phys., 17, 1984, 577. Levstik, A., Unruh, H.G. and Prelovsek, P., Phys. Rev. Lett., 58, 1987, 1953. Fousek, J. and Janousek, J., Phys. Status Solidi., 13, 1966, 195. Hamano, K., Sakata, H., Yoneda, K., Ema, K. and Hirotsu, S., Phase Transition, 11, 1988, 279. Hamano, K., Sakata, H., Izumi, H., Yoneda, K. and Ema, K., Jpn. J. Appl. Phys., 24, Supp 24-2,1985,796. Ema, K., Kato, T. and Hamano, K., J. Phys. Sot. Japan, 53, 1984, 807. Mashiyama, H. and Kasatani, H., Jpn. J. Appt. Phys., 24, Supp 24-2, 1985, 802. Niquet, G., Maglian, M., Gueldry, A. and Sigoillot, V., J. Phys. I, France, 4, 1994, 1173. Novotna, V., Fousek, J., Kroupa, J. and Hamano, K., Solid State Commun., 77, 1991, 821. Gesi, K., J. Phys. Sot. Japan, 54, 1985, 2401. Smutny, F., Vanek, P. and Brezina, B., Ferroelectrics, 79, 1988, 315. de1 Cerro, J., Ramos, S. and Sanchez, J.M., J. Phys. E. Sci. Instrum., 20, 1987, 612. Martin, J.M., Ramos, S. and de1 Cerro, J., European Workshop on Calorimetric Technique. Phase Transition (in press). Novotni, V., Kabeika, H., Fousek, J., Havr&tkovi, M. and Warhanek, H., Phys. Rev., B47, 1993, 11019.