PHYSICAL REVIEW B 1 AUGUST 1998-IVOLUME 58, NUMBER 5

Temperature-induced orientational disorder in NaClO3

Ricardo C. Zamar, Cecilia E. Gonza´lez, and Daniel J. PusiolFacultad de Matema´tica, Astronomı´a y Fısica, Universidad Nacional de Co´rdoba, Ciudad Universitaria,

5000 Cordoba, Argentina~Received 17 November 1997!

A detailed study of the temperature dependence of35Cl nuclear quadrupole spin-lattice relaxation time andresonance frequency, in a wide temperature range~77–450 K!, is used to discuss old controversial conclusionsabout the experimental behavior of low frequency dielectric permittivity, Raman spectroscopy, and nuclearquadrupole resonance, in sodium chlorate. Compatibility among experimental data coming from all thesetechniques is achieved by assuming a continuous transition of the ClO3

2 ion dynamics from vibrating around anequilibrium position forT,250 K, to exchanging between two orientations at higher temperatures. That is, thepseudoharmonic single well potential, that determines the chlorate ion dynamics at lower temperatures, mutatescontinuously with increasing temperature, to reach a symmetric two-well potential for temperatures higher than380 K. In the intermediate-temperature range the behavior of NQR parameters are explained in terms ofscattering of phonons by a distribution of disordered chlorate ions. We use the Green function formalism forcalculating the corrections to the spin-lattice relaxation time and the resonance frequency due to disorder.@S0163-1829~98!00529-3#

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I. INTRODUCTION

Crystalline sodium chlorate has been studied extensivby a variety of techniques and many of its physical propties have been characterized. However, some inconsisteconcerning the molecular dynamics of the chlorate ionsmain unexplained.

Sodium chlorate is a paraelectric material but the teperature dependence of the low-frequency dielectric pertivity e(T) resembles one of a ferroelectric system approaing an order-disorder transition1 with a Curie temperatureTC;593 K greater than its fusion temperature (TF5537 K!.This temperature dependence ofe(T) is assigned to the reorientation of the chlorate ions. Since at high temperatuthe crystal is in a highly ionized state, then chlorate iocould undergo a cooperative behavior that is characteristiferroelectric systems. Based on a Mason-Debye2 model forthe dielectric relaxation, this crystal was classified as a nferroelectric order-disorder system.

The width of a low-frequency phonon (v5130 cm21),as measured by Raman spectroscopy,2 increases exponentially with temperature. This fact indicates that the dielectresponse of the crystal is being perturbed by some kindmotion ~of the chlorate ions!, different than the lattice vibrations. To account for both the dielectric relaxation mechnism and the exponential broadening of a libration phonPrasad Raoet al.2 propose that the35Cl atom inverts its po-sition in the chlorate ion, therefore jumping in a symmetdouble well potential. The relaxation time associated to tjump ist5t0e(Ea /kBT) with Ea the activation energy~heightof the barrier! of the double well.Ea520.7 kJ/mol from theirexperiment.

In a previous work on35Cl NQR in a series of chloratesalts,3 the temperature dependence of the NQR spin-latrelaxation time of sodium chlorate also showed an occrence of a relaxation mechanism different than lattice vibtions. This behavior was ascribed to the modulation of

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electric field gradient~EFG! at the resonant nuclei site, duto the neighboring chlorate ions rotation about their threefaxis. Such a mechanism is completely different than theproposed in Refs. 1 and 2.

With the aim of disentangling this controversy, in thwork we present a detailed experimental study of the teperature dependence of35Cl NQR frequencynQ(T) andspin-lattice relaxation timeT1(T) in an extended temperaturrange 77–450 K. Our experimental data also reflect thecurrence of an additional mechanism, in agreement with pvious experimental information. We discuss our experimein terms of a model involving reorientation of chlorate ioin an asymmetric potential. We propose that for temperatubelow 250 K the chlorine atom vibrates around the equilrium position compatible with the crystalline symmetry. Athe temperature increases, the potential well develops aond, unstable equilibrium position that allows the threefoaxis of the pyramidal ion to perform 180° rotations. In thway, some degree of orientational disorder appears.usual expressions forT1(T) andnQ(T) due to lattice vibra-tions cannot describe the experimental behavior. Then,write a correction to the NQR parameters due to scatterinphonons in a weakly disordered lattice. The obtained expsion, which is valid for low concentrations of disordereions, accounts for data within the range 250,T,350 K. Forhigher temperatures the depth of the second potentialincreases and the probability of finding the ion axis rotarespect to its equilibrium orientation also grows. Near 400a symmetric two-well potential is established, and the crysbecomes totally disordered.

II. EXPERIMENT

A. Apparatus and techniques

Polycrystalline samples of NaClO3 were prepared by recrystallization of the commercial Merck Co. product fromsaturated solution with tridistilled water. The water evapo

2476 © 1998 The American Physical Society

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PRB 58 2477TEMPERATURE-INDUCED ORIENTATIONAL DISORDER . . .

tion rate was regulated to get crystallite sizes of aboumillimeter. The sample was packed in a 12 mm diameter20 mm long PTFE cylindrical sample holder.

We used a pulsed, broadband and fully computer ctrolled, home-made NQR spectrometer. It is equipped witPTS 310 frequency synthesizer, a Kalmus LP 1000 potransmitter, and a Doty LN-2L signal preamplifier. Data aquisition was made with a Thurlby 625 digitizer. Phase ccling of the rf and quadrature detection were available. Tcontrol and automatic measurement computer programdeveloped in our laboratory.

The temperature of the sample was stabilized better t0.1 K in the whole range. The probehead was located ina temperature controlled thermal bath. The home-made tperature control device, covering the range 80–450 K, csists of four coaxial and partially insulated copper cylindimmersed in a cooling bath~liquid nitrogen for temperaturelower than room temperature and preheated oil for higtemperatures!. The temperature control was effectiveachieved by heating inner cylinders with electronicadriven heaters. Cu-constant on thermocouples and FMod. 510 chopper amplifiers give input voltage to propotional temperature regulation.

The resonance frequency, defined as the center of theresponding spectrum, was measured by fast Fourier trform of the NQR free induction decay~FID!. The spin-latticerelaxation time was measured at each temperature in~care-fully checked! resonance peak saturation condition. Mesurements ofT1 were made by the standard two-pulse squence (p/22t2p/2); the delay time between pulsevarying from 1 ms to 5T1. T1 values were obtained by fitting the expression

S~t!5S0F12aexpS 2t

T1D G

which relates the amplitude of the sample responseS(t) atthe irradiation frequency~Fourier transform from the FIDafter the second pulse! to the delay timet. Each fit ofS(t)involved a set of 20 to 32 experimental data points. All tmeasurements here reported were performed going utemperature and then confirmed lowering the temperatur

B. Spin-lattice relaxation time

Figure 1 shows the measuredT1(T) in an extended temperature range. At low temperatures, 165 K,T,250 K, apower law fits toT1 data:4

T1vib21 5ATl, ~1!

with A51.731028 s21 andl52.46. This temperature dependence is typical of relaxation mechanisms due to fluctions of the lattice vibrations related with the anharmonicof the crystal field and with pseudoharmonic processes~suchas first order phonon-phonon Raman processes!.5 It is worthpointing out that this value ofl, noticeably greater than 2indicates a certain degree of anharmonicity of the lattpotential.6 Equation~1! gives the dotted curve in Fig. 1. Fotemperatures higher than 300 K, the experimental dclearly fall below this curve. More precisely, data dispersabout Eq.~1! shows that near 250 K the vibrational modalone cannot explain the experimental trend. The differe

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between the experimental data and the lower temperaturbecomes resolutely exponential. The data can be fittedadding an exponential term to the relaxation mechandriven by vibrational fluctuations:

T1215T1vib

21 1Be2U/T, ~2!

with B58268 s21 andU526.461 kJ/mol.The data follow this trend~long dash curve of Fig. 1! for

T<340 K. An exponential temperature dependence suchthis one cannot be related to vibrational processes~neitherquasiharmonic nor anharmonic!.4–6 It is worth remarkingthat this second mechanism becomes appreciable inT1(T)for the same temperature range where a low-frequency pnon is anomaly broadened.2 For temperatures higher tha340 K there is a further drop inT1, and for T;440 K, aminimum inT1(T) is suggested by the data. Due to the poS/N ratio T1 could not be measured for higher temperatur

C. 35Cl NQR frequency

Figure 2 shows the experimental temperature dependeof the peak frequency. This smooth behavior indicates t

FIG. 1. Temperature dependence of the spin-lattice relaxatime T1(T) and the fitting curves from different models for relaation.

FIG. 2. Experimental35Cl nQ(T) behavior of NaClO3. Full linerepresents the fit with Eq.~4!. A noticeable departure from thevibrational model is observed in the high-temperature region. Twindow shows the exponential behavior ofDnQ(T) for T.245 K.

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2478 PRB 58ZAMAR, GONZALEZ, AND PUSIOL

no first order phase transition occurs in the studied tempture range. The line is narrow and Lorentzian shaped, ofkHz width, forT,380 K. The only anomaly we observed foT.400 K is the occurrence of a low-amplitude, broad baground but the narrow central line remains always obseable.

In absence of phase transitionsnQ is temperature dependent because~i! the local EFGq at the 35Cl resonant nucleisite, is time averaged by molecular fluctuations and~ii ! themean square amplitudeu2& of the angular displacement othe maximum principal axis of the EFG relative to its eqlibrium direction, is also temperature dependent.7 The corre-sponding expression for the temperature dependence ofnQ isgiven by

nQ~T!5e2Q

2hq0S 12

3

2^u2& D , ~3!

where Q is the nuclear quadrupole moment andq0 is theensemble average EFG at the nuclear sites, at a refertemperature.

A simplified form for nQ(T) due to lattice vibrations inthe quasiharmonic approximation is given by10

nQ~T!vib5n0~12bT!

3F12P

v0~12gT!cothS \v0~12gT!

2kBT D G , ~4!

with n0 the frequency of a hypothetical rigid lattice atT500 K, P a fitting parameter representing the sum overvibration modes over the whole Brillouin zone,v0 an aver-age mode frequency,g the linear coefficient giving the phonon frequency shift due to the lattice anharmonicity, andbthe correction ton0 due to thermal expansion.8,9

Equation~4! can be fitted to our experimental data withthe restricted temperature range 80,T,245 K. The fittingparameters aren0530867 kHz, P/v057.1231023, g54.631024 K21, v0569 cm21, andb5431025 K21.

A noticeable departure from this trend occurs in thigher-temperature region. The window in Fig. 2 showsfrequency differenceDnQ(T) between experimental data anEq. ~4!. A better fit of the temperature dependence is otained by adding an exponential term as follows:

nQ~T!5nQ~T!vib1Ce2U/T. ~5!

The best fit yields the parameters:C553104 s21 and U5(26.760.1) kJ/mol. Notice the similarity of theU valuesin both n(T) andT1(T) experiments.

III. DISCUSSION

A. Fitting to standard models

It is well known that an exponential behavior in the NQvariablesnQ(T) and T1(T) is neither related to quasihamonic lattice vibrations,10 nor to anharmonicity.6 That is,phonons alone cannot account for such behavior. It insteagenerally assigned10 to thermally activated molecular reorentation or to hindered rotations of the whole molecule opart of it. The chlorate ion is a highly symmetric moleculgroup; it is a flat trigonal pyramid with three oxygen atomon its base and a chlorine atom at the remaining vertex

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NaClO3, exponential behaviors innQ(T) andT1(T) such asthose of Eqs.~2! and ~5! could in principle be associatewith ~i! hindered rotations of the oxygen atoms about thzaxis perpendicular to the oxygen plane, as suggested in3 or ~ii ! chlorate ion reorientation about an axis containedthe oxygen plane, as suggested in Refs. 1 and 2. The rotaof oxygen atoms does not affect directly the electric fiegradient at the site of the resonant nuclei~top of the pyramid!but could modulate the EFG at the Cl sites of neighborions.3 Therefore this mechanism could conceivably contrute to T1(T). However, this kind of motion alone cannoexplain Raman ande(T) measurements from Refs. 1 andsince it has no influence on the electric dipole moment ofchlorate ion. The contribution to the NQR spin-lattice relaation time predicted by a model for the intermolecular EFmodulation is4

T1mod21 5

2

3

vQ2 tc

~11vQ2 tc

2!S q8

q D 2

, ~6!

with the correlation timetc5t0eU/T, t05h/kBT, U the acti-vation energy of the reorientation~in the present case, thbarrier in the three well potential!, andq8/q the ratio of theEFG at the resonant nucleus produced by the neighbogroup motion to the principalz component of the EFG tensoof the molecular ion.

Accordingly, if molecular vibrations and intermoleculaEFG modulation are considered as independent procesthen

1

T15

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T1vib1

1

T1mod, ~7!

with T1vib21 from Eq. ~1! andT1mod

21 , from Eq.~6!. The formerexpression gives a curve having qualitative similarity wdata and the best fit parameters are

vQt051.331024,

U536.6 kJ/mol, ~8!

q8/q52.531025.

The first parameter is consistent with the values ofn0 @fromEq. ~4!# and t0. The fittedU is a reasonable value for thikind of motions.10 On the contrary, the expected value f(q8/q) ranges4 from 1021 to 1022. The fitted value is severaorders of magnitude smaller. The extremely low fitted vais meaningless: if modulation were so effective in makithe EFG more symmetric, no NQR signal should be oserved. Then, even when this model provides a functiontemperature that can be fitted to data, the obtained pareters are not acceptable for explaining the experimentalhavior. Because this rotation cannot be identified ascause of the temperature behavior of the dielectric permitity constant either, we conclude that this motion alone isresponsible for the observed experimental trends.

We now consider the second proposition: chlorate iontation about an axis contained in the oxygen plane. Whdealing with the temperature dependence of NQR variabof a system of nuclei subject to a random two site excha

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PRB 58 2479TEMPERATURE-INDUCED ORIENTATIONAL DISORDER . . .

~2SE!—as this problem appears to be—the transition prability per unit time between energy levelsp and q of anunperturbed HamiltonianH0, due to a time-dependent peturbation is11

Wpq52tcuvpqu2

11vpq2 tc

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with uvpqu the matrix elements of the perturbation in thbasis ofH0.

The former approach is based on the assumption thatime dependence of the spin Hamiltonian can be represeby a function of timef (t) that randomly exchanges betweetwo values

H~ t !5H01 f ~ t !H1 .

The probability thatf (t) retains its initial value after a timetis P(t)5e2t/tc and^ f (t)&50. Therefore, the nucleus is presumed to spend, in the average, the same time at eachThis picture is then equivalent to the double well potenmodel proposed by Prasad Raoet al.2 for explaining Ramanexperiments.

In the particular case of spin-3/2 nuclei the contributionrelaxation due to reorientation is11

1

T1~2SE!5(

pqWpq54tc

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~11vQ2 tc

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whereB andC are the off-diagonal elements of the pertubation HamiltonianH1 andtc has the same definition as iEq. ~6!. Considering molecular vibrations and reorientatioas independent relaxation mechanisms, we analyzedT1(T)data with

1

T15

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T1vib1

1

T1~2SE!. ~11!

Equation ~10! has the same temperature dependenceEq. ~6!, therefore the fitting parameters are the same shoin Eq. ~8! but one of them has a different meaning. The fittactivation energy is noticeably greater than the value ofkJ/mol reported in Ref. 2 and assigned to the height oftwo well potential barrier.

Although the symmetric double well potential modcould explain the ferroelectriclike behavior ofe(T) ~Ref. 1!and the anomalies in the Raman spectrum,2 some contradic-tions should be pointed out. If chlorate ions fluctuatedsymmetric potentials, the probabilities of occupying eithequilibrium position should be the same~because the transition probabilities from one well to the other would be equa!.Raising the temperature would just shorten the lifetimeeach well~or increase the reorientation frequency!. The two-site exchange model would suggest that the system iscompletely disordered state in the sense that the chloratecan either point the direction compatible with the cryssymmetry or the opposite one with the same probability.our knowledge no such kind of disorder has been reportedcrystallographic studies~at least for the crystal phase attaiable in the temperature range studied here!.

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Concerning NQR resonance frequency, within the 2model,11 one should expectnQ to be shifted from its value avery long correlation times in a quantity

DnQ5vQtc

2

p

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~11vQ2 tc

2!. ~12!

Using the parameters from the fitting curve toT1(T) data,we obtain DnQ,50 Hz in the whole temperature rangwhile the measured frequency shift ranges up to 100 k~about three orders of magnitude greater!, as shown in Fig. 2.In addition,nQ(T) data do not follow the trend predicted bEq. ~12! either.

Within this model, and using the fitted activation energyUfor calculating the correlation time, one sees thattc rangesfrom 1 s at 150 K to 1028 s near 450 K. Thentc.1/vQ inthe whole temperature range, that is, reorientations wonot be very frequent within the time scale of the NQR eperiment. Under this condition one could consider thatdisorder in orientations is static, within the time scale pvided by our NQR experiment. Accordingly, for very lowreorientation rates, i.e.,T,250 K in this experiment, oneshould expect an inhomogeneously broadened NQR strum or eventually a splitting of the line corresponding to tinequivalent positions of the resonant nuclei. However,such features were detected here.

Besides this, notice that though in the limit of long corrlation times, Eq.~10! becomes 1/T1}exp(2U/T), the valueof U that fits data in the higher-temperature range mustdrasticallydecreasedto get a good fit for lower temperatureThis means that Eq.~2! cannot be considered as the loncorrelation time-limit of Eq.~10!. Summarizing, the symmetric two-well potential model for the chlorate ion reorienttion predicts a temperature dependence of both the NQRquency and the line shape which are very different fromexperimental results.

B. The asymmetric two-well model

We work out an alternative explanation that removescontradictions commented above. Let us now proposethe reorientation of the three fold axis of the chlorate ioccurs in anasymmetriclocal potential. The chlorate ion axican attain a stable equilibrium orientation~let us call itA)compatible with the crystal symmetry and an unstable eqlibrium orientationB, 180° opposite to the one suggestedthe site symmetry. In such a way, it spends a much lontime in the stable equilibrium orientation than in the othe

We can make an analogy with a two level magnetic stem by identifying the chlorate ion with a spin 1/2 variablean external magnetic field. At low temperatures the equirium population of the lower energy level is much greathan the upper level population and it is possible to descthis situation in terms of a concentrationC of disorderedions, defined as the ratio of the population of disordered ito the total number of them. For sufficiently low tempertures this concentration is

C~T!>P~B!

P~A!5e~EA2EB!/T[e2E/T.

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2480 PRB 58ZAMAR, GONZALEZ, AND PUSIOL

If the disordered ions are homogeneously distributhrough the sample, all the local configurations compatiwith the equilibrium populations are equally probable athe system takes one or another at random. The lifetimeach particular configuration is short or at least much shothan the lifetime of a given ion in its stable orientation. Thall the measured equilibrium quantities are configuratioaverages, over all configurations compatible with a givconcentration of homogeneously disordered ions.

Now we make an estimate of the effect that such a disbution of disordered ions has on the temperature dependof the NQR parameters. Disorder alters the rotational dynics of the chlorate ion and hence the mean square displment^u2& of Eq. ~4!. It also has influence onT1 through theautocorrelation functionsu(t)u* & and ^u2(t)u2* &.4,6 As afirst approximation, we can consider the effect of disorderindependent of the normal vibrations of the lattice. The mdifference between our proposal and the others mentioabove is that here we just account for theindirect effect ofdisorder in the EFG averaging. It is not thedirect effect ofreorientations but the change in the EFG averaging dueperturbation in the phonons of the lattice.

At this stage we can identify the problem of a distributiof orientationally disordered ions with the one of a distribtion of defects or impurities. The consequence of perturbthe perfect, harmonic lattice with this kind of impuritiesthe broadening of the phonons,12 which amounts in a changin the EFG averaging and in the fluctuation spectrum.

By expressingu(t) in terms of phonon operators6 we canrelate the Fourier transform of the time correlation functiof the angular displacements to Green’s functions. The meffects of the disorder on the NQR parameters comthrough the perturbation of the rotational motions of tchlorate ion. For the sake of simplicity we assume thatangular displacement coincides with a molecular-rotationordinate of the chlorate. We also suppose that the vibratiodynamics of the chlorate ion can be well described in terof a harmonic lattice. According to this assumption, we cdirectly write

F$^u~ t !u* &%522

12eb\vIm Gr

R~v! , ~13!

where ImGrR(v) is the imaginary part of the retarded Gre

function of the harmonic torsional oscillator. Since we asume low concentration~LC! of disordered ions, we can usa perturbative method for calculatingGr

R(v). The Green’sfunction for a perturbed crystal satisfies the Dyson equatrelating it with the ordered crystal Green’s functionGr

o(v).Neglecting any explicit influence among impurities,Gr(v)can be approximated by a perturbative expansion, keepinto linear terms in the concentration of impurities:12

^Gr~v!&5Gro~v!1C~T!(

iGr

o~v!t i~v!Gro~v!, ~14!

where the brackets mean the configurational average bestated andt i(v) is the matrix representing the local distotion due to thei th defect. In this picture each impurity can bthought as a lattice-wave scatterer.

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^u2&5^u2&o1C~T!E0

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with C(T) the concentration of ions in stateB, and

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whereGro(v) is the Green’s function of the ordered crysta

associated with the rotational molecular coordinate ofmolecular group bearing the resonant nucleus. The dynamof the whole crystal and hence the collective character ofphenomenon, is introduced through the Green’s functionsour case the distortion affects the constants of force ofinteraction with the disordered neighbors. In the case whthe distortion is not too large, the integral of Eq.~15! de-pends smoothly on temperature, the temperature dependof the second term being mainly given by the concentratiThen, the difference betweennQ(T) of the disordered latticeand the one of a perfect harmonic lattice has a temperadependence given by

DnQ~T!5n0@^u2&2^u2&0#}e~2E/T!. ~16!

with E the energy difference between the bottom of tstable potential well and the unstable one. Notice that herEis not an activation energy. IdentifyingE with parameterUof Eq. ~5! we see that the experimental trend ofnQ(T) coin-cides with that of Eq.~16! in the whole temperature range,as shown in the window of Fig. 2.

In order to calculate the influence of disorder onT1(T),we analyze the effect of disorder on the Fourier transformsthe time correlation functionsu(t)u* & and ^u2(t)u2* &, in-volved in the final expression ofT1.6 Now we parallel ourproblem with the calculation of the phonon broadening dto a distribution of mass impurities in a perfect harmoncrystal by Lovesey.13 Here, the impurities are related tchanges in the force constants instead of masses. Aspected, for low concentrations of impurities, the obtainphonon broadening is again proportional to the concention. Considering that in this limit the four-phonon time corelation function can also be put in terms of the two-phonone,14 finally, the temperature dependence of the correctto T1(T) due to the orientational disorder can be expresconcisely as

T1 ~LC!21 5Be~2E/T! ~17!

with B a parameter that depends on the specific featurethe crystal lattice and the distribution of defects. Then,temperature dependence associated to lattice vibrationsion reorientations is given by Eq.~2!.

Equation~2! can account for the exponential behaviorthe relaxation time in the intermediate-temperature regibut fails in describingT1(T) for higher temperatures. Still iis consistent with the picture of an asymmetric potentialthe lower-temperature region. At higher temperaturestorque restoring the chlorate ion to its equilibrium positibecomes looser and the potential well might change its shand turn more symmetric. In that limit the random two s

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PRB 58 2481TEMPERATURE-INDUCED ORIENTATIONAL DISORDER . . .

exchange model could give a good approximation, as ialso compatible with the occurrence of a broadened sptrum.

The solid line fitting data of Fig. 1 is the curve provideby the 2SE mechanism, which, according to our analywould be valid for temperatures higher than 380 K. Tdashed and the solid lines above data represent the indivcontributions from the two models: low-concentration of impurities T1 (LC)(T) and symmetric two-well potentiaT1(2SE)(T); each one dominates relaxation in a different teperature range. We propose that the dynamics of the chloion is changing with temperature from the asymmetric wto the symmetric two-well regime. In this paper we have jdescribed two limiting situations: low concentration of ‘‘impurities’’ and complete disorder~symmetric two-well poten-tial!; the intermediate states cannot be described as theperposition of the other two because they might notconsidered as independent mechanisms.

Summarizing, the picture proposed in this work is constent with the available experimental data. The occurrencthermally activated processes involving the chlorate ionsconfirmed. Unlike previous works, we found that a simpmodel of a symmetric two-well potential for representithis process in the whole temperature range is not adequInstead, we proposed that the orientational potential un

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goes a progressive transformation, as the temperaturraised, going from an anharmonic potential for low tempetures, towards a double well potential for high temperaturIn the intermediate range, for 280 K,T,340 K, thephonons of the ordered lattice are scattered by a homoneous distribution of disordered ions. For increasing teperatures, also the disorder increases, and a simple mthat considers phonons and molecular reorientations as ipendent processes cannot account for the data. The exmental trend described above is consistent with the ideathe chlorate ions might become rotationally free and coshow a cooperative effect and hence a dielectric Cupoint—in agreement with the behavior ofe(T) ~Ref. 1!—asif the crystal were approaching to an order-disorder trantion.

ACKNOWLEDGMENTS

This work was supported by the National and ProvincResearch Councils~CONICET and CONICOR, respectively!, and SECYT Universidad de Co´rdoba. The authorsthank Dr. C. Schurrer and Lic. R. Rodrı´guez for assistancewith the high-temperature measurements. R.C.Z. is gratto Professor A. H. Brunetti for helpful discussions.

e

a-

s.

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