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Dielectric dispersion behavior of BaZrxTi1xO3 solid solutions with aquasiferroelectric state

Shanming Ke,1 Huiqing Fan,2,a Haitao Huang,3,a Helen L. W. Chan,3 and Shuhui Yu41State Key Laboratory of Solidification Processing, School of Materials Science, Northwestern PolytechnicalUniversity, Xian 710072, Peoples Republic of China and Department of Applied Physics andMaterials Research Center, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong,Peoples Republic of China2State Key Laboratory of Solidification Processing, School of Materials Science, Northwestern PolytechnicalUniversity, Xian 710072, Peoples Republic of China3Department of Applied Physics and Materials Research Center, The Hong Kong Polytechnic University,Hung Hom, Kowloon, Hong Kong, Peoples Republic of China4Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences, Shenzhen 518067, PeoplesRepublic of ChinaReceived 22 March 2008; accepted 4 June 2008; published online 8 August 2008

The temperature dependence of dielectric permittivity was investigated for the barium zirconiumtitanate solid solution system BZT, BaZrxTi1xO3 0.25x0.5. The dielectric relaxationbehavior was observed in these ferroelectrics with diffused phase transition. In contrast to thecanonical relaxors such as PbMg1/3Nb2/3O3, the diffused phase transition of BZT could not be welldescribed by the popular modified CurieWeiss law. Quasiferroelectric state theory was introducedto explain the dielectric results of the BZT relaxors. 2008 American Institute of Physics.DOI: 10.1063/1.2964088

I. INTRODUCTION

Relaxor ferroelectrics relaxors have been attractingmuch interest because of their superior physical properties,such as giant dielectric constant, extraordinary piezoelectric-ity, ultrahigh strain, and so on. The characteristic feature ofcanonical relaxors is that there is a large, diffusing, andfrequency-dispersive maximum in the temperature depen-dence of dielectric permittivity. This broad dielectric peak isbelieved to originate from the polarization of nanosize re-gions, i.e., the polar nanoregions PNRs see Refs. 1 and 2for a review of the structure and properties of relaxors. Be-sides the canonical relaxors, including PbMg1/3Nb2/3O3PMN Ref. 3 and PbSc1/2Ta1/2O3,4 the relaxor behaviorcould also been observed in the systems where paraelectricphase such as BaZrxTi1xO3 BZT Ref. 5 andBaSnxTi1xO3 Ref. 6 is embedded in a ferroelectric ma-trix or vice versa.

1xBaTiO3xBaZrO3 BZT system was identified asan infinite solid solution in the 1950s.7 BZT exhibits apinched phase transition at x0.15, that is, all the three-phase transitions corresponding to pure BaTiO3 are mergedinto one broad peak.8 Further increases of Zr concentrationwould result in a ferroelectric relaxor behavior similar to thatof the canonical relaxors.9 The ferroelectric-relaxor cross-over composition of BZT has been claimed to be at x=0.25.9Recently, BZT has shown great potential for the applicationin tunable microwave devices,10,11 due to its large dielectricnonlinearity i.e., the dependence of permittivity on dc elec-tric field and low dielectric loss. However, unlike the ca-nonical relaxors such as PMN, an electric field does not

seem to induce a long-range polar order in BZT relaxors.12On the other hand, there are several evidences, which revealthat BZT might well occupy a peculiar niche in perovskite-type relaxors. The high-pressure Raman scattering investiga-tions showed that BaZr0.35Ti0.65O3 BZT35 behaves underhigh pressure similar to normal ferroelectrics, not to canoni-cal relaxors.13 It has been reported that PMN shows a largeheat capacity anomaly as well as a large broad dielectricpeak due to the formation of PNRs.14 There is no heat ca-pacity anomaly observed in BZT35, which implies a differ-ent relaxor state from that of PMN.15 Bokov et al. suggestedthat this should be a quasiferroelectric state by taking intoaccount nanoscale inhomogeneities of quasiferroelectricstructure in which the ferroelectric regions separated bysmall nonpolar Zr-rich regions.16 In this work, we present theresults of dielectric studies on the solid solutions betweenBaTiO3 and nonferroelectric BaZrO3.

II. EXPERIMENTAL PROCEDURE

The BaZrxTi1xO3 with compositions x=0.200.50,abbreviated as BZT100x ceramics were prepared by solidstate reaction process by mixing appropriate quantities ofhigh purity BaCO3, ZrO2, and TiO2 raw powders. The start-ing materials were ball milled for 8 h in alcohol. After dry-ing, the powders were calcined at 1200 C for 2 h. Thecalcined powders were further ball milled, dried, and pressedinto disks with 7% polyvinyl alcohol PVA addition. Thepellets were sintered at 1450 C for 16 h. For a comparativestudy, PMN ceramics were also fabricated by a columbitemethod.17

The room temperature x-ray diffraction XRD studywas carried out on all sintered ceramics of BZT which wasverified to be a single phase with the cubic perovskite struc-

aAuthors to whom correspondence should be addressed. Electronic ad-dresses: [email protected] and [email protected].

JOURNAL OF APPLIED PHYSICS 104, 034108 2008

0021-8979/2008/1043/034108/7/$23.00 2008 American Institute of Physics104, 034108-1

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ture, as shown in Fig. 1a. Data were collected on an auto-mated diffractometer XPert PRO MPD, Philips withCu K1 radiation. The microstructure evolution was studiedby scanning electron microscopy SEM JSM-6335F,JEOL. For instance, Figs. 1b and 1c display the SEMimages of BZT25 and BZT35 surfaces, respectively. The av-erage grain size of all the ceramic samples was in the rangeof 1030 m. Micro-Raman spectral measurements wereperformed on a JY HR800 Raman spectrometer under back-scattering geometry. An argon ion laser was used as the ex-citation source with an output power of 15 mw at 488 nm.Top and bottom electrodes were made by coating silver painton both sides of the sintered disks followed by a firing at650 C for 20 min. The temperature dependence of the di-electric permittivity of the samples was measured under amultifrequency LCR meter Model SR720 of Stanford Re-search System, and the frequency dependence of the dielec-tric permittivity was measured by using a frequency responseanalyzer Novocontrol Alpha-analyzer over a broad fre-quency range 0.01 Hz10M Hz.

III. RESULTS AND DISCUSSIONA. Micro-Raman scattering

The room temperature micro-Raman spectra of BZT ce-ramics are displayed in Fig. 2. By fitting the measured spec-tra and deconvolution of the fitted curves into individualLorentzian components, the peak position of each compo-nent, i.e., the natural frequency cm1 of each Raman activemode, was obtained in these samples. As shown in Fig. 2, the

seven normal modes of our BZT40 sample, including A1,A2, A3, A4, A5, E1, and E2 modes where the number isonly named for convenience at 151.5, 315.9, 517.9, 723,761.1, 230.2, and 282 cm1, respectively, are in good agree-ment with those of cubic Pm3m BZT40 thin films.18 Thedependence of the mode position on Zr concentration x issummarized in Fig. 3. In the literature, notable changes in the

FIG. 1. Color online a XRD patterns for the BZT25, BZT35, and BZT40 ceramics sintered at 1450 C. b and c show the FE-SEM images of the BZT25and BZT35 surface area, respectively.

FIG. 2. Color online Micro-Raman scattering spectra measured spectra:open circles and fitted spectra: thick solid lines for a BZT25, b BZT35,c BZT40, and d BZT45 samples.

034108-2 Ke et al. J. Appl. Phys. 104, 034108 2008


200450 cm1 spectral region of ferroelectric perovskiteshave been attributed to vibrations associated to polar BO6octahedra. The splitting of ETO2 mode into E1 and E2modes for x0.4 should be associated with an increase inthe ionic radius RTi4+=0.0745 nm, RZr4+=0.086 nm,when Ti is gradually replaced by Zr. The vibration of Tiatoms against the oxygen cage results in an ATO1 mode at180 cm1.19 Dobal et al.20 reported that the ATO1 modecould be reduced to about 129 cm1 for Zr replacing Ti sites.The A1 mode frequency of our BZT samples decreases from153.3 x=0.25 to 147.88 cm1 x=0.50 could therefore beassigned to a normal mode involving Zr atoms. The couplingbetween the A4 and A5 modes strengthens as the intensity ofthe A4 mode decreases with increasing Zr content. In addi-tion, the intensity of the A5 mode at 780 cm1 increase withincreasing Zr content, where the mode has been claimed tobe a clear signature of the relaxor phase.21

B. Dielectric behavior

The temperature dependence of and the imaginarypart of the dielectric constant at various frequencies forthe BZT25, BZT35, and BZT40 samples are shown in Fig. 4.Only one broad dielectric peak is observed for all the BZTcompositions. At x=0.25, slight frequency dispersion in starts to appears, A stronger frequency dispersion is observedfor BZT35 and BZT40. Similar to a typical ferroelectric re-laxor, as the frequency increases, decreases and the tem-perature Tm corresponding to the dielectric maxima shiftsto higher values. In the same manner, the temperature of theimaginary part maxima increases with the increase of fre-quency, while the peak value increases unlike that of . Thedecrease in Tm and the maximum dielectric constant withincreasing Zr content can be well understood by phenomeno-logical theory.22 Since Zr4+ has larger ionic size as comparedto Ti4+, the addition of Zr increases the chemical pressureimposed on the surrounding lattice and therefore results inlower Tm and lower maximum dielectric constant.

C. Characterization of the peakSince Smolenskys work,3 the feature of the temperature

dependence of the dielectric constant, above Tm, has beenwidely studied with various models as an important featureto characterize the dielectric relaxation behavior of a relaxor.For a normal ferroelectric, the CurieWeiss CW law is fol-

lowed in the paraelectric region. However, for relaxors, thedielectric constant follows CW law only above the Burnstemperature TB, which is much higher than Tm and belowwhich the PNRs appear.

A modified CW law was usually used to describe the peak on the high temperature side and the diffuseness of thephase transition23

FIG. 5. Power law Eq. 1 fit of the reciprocal dielectric constant of BZT.

FIG. 3. Color online Deconvoluted active Raman mode frequencies as afunction of Zr concentration x for BZT-x samples.

FIG. 4. Temperature dependences of the dielectric permittivity of aBZT25, b BZT35, and c BZT40 at various frequencies.



1/ 1/m = T Tm/C . 1

The value of 12 is the expression of the degree ofdielectric relaxation in a ferroelectric. When =1, Eq. 1expresses the CW behavior of the normal ferroelectrics,while =2 reduces to the quadratic dependence,3 which isvalid for a canonical relaxor ferroelectric experientially. Inthis study, the obtained values of from the experimentaldata at 1 kHz, fitted by Eq. 1 for BZT compositions, andthe fitting curves are shown in Fig. 5. It is apparent in Fig. 5that with the increase of Zr content there is a systematicdecrease in . Interestingly, the value decreases to 1.53with the increase in Zr concentration, which evidently showsthe evolution of ferroelectric relaxations from canonical re-laxor to the normal ferroelectric behavior. However, the di-electric spectra Fig. 4 and the micro-Raman scattering re-sults Fig. 2 show more and more clearly a relaxor behaviorfrom BZT25 to BZT45. This phenomenon leads to a conclu-sion that is not a good parameter to express the degree ofdielectric relaxation in BZT, even in BaTiO3-based ferroelec-trics or relaxors with diffuse phase transition DPT. Further-more, Eq. 1 contains frequency-dependent quantities Tmand m. As a result, the parameters and C, which define theshape of the function, also depend on frequency and therebyare not fully appropriate for describing the frequency-

independent high temperature slope of the dielectric peak.These parameters and C appear to be different sometimesin different temperature intervals for the same material.24 ForBZT25, decreases to 1.83 in a smaller temperature intervalin our study.

Bokov et al. recently proposed a Lorenz-type formula todescribe the dependence of the dielectric constant on tem-perature at TTm in relaxors,

25

A

= 1 +

T TA2

22, 2

where the temperature TA and the magnitude A of theLorenz height generally differ from the Tm and A of theexperiments. The parameter , which is frequency-independent at high enough frequencies, characterizes thediffuseness of the peak. The behavior of the dielectric con-stant peak on the high temperature side predicted by Eq. 2has been found in a number of relaxor ferroelectrics,25,26 aswell as in our prepared BZT25, BZT35, and BZT40. Excel-lent fits are achieved above Tm. The result of fitting is shownin Fig. 6 by solid line and the best-fit parameters are listed inTable I. Note that the increase of with increasing Zr con-centration in BZT from 71.7 to 170.2 in this study indicatesan increased degree of diffuseness of the dielectric peak. It

FIG. 6. Color online Temperaturedependences of the dielectric constantof BZT25, BZT35, BZT40, and PMNat 10 kHz. The solid lines are the fit-ting curves by using Eq. 2.

TABLE I. Curve fitting results for BZT and PMN.

Compositions

f kHz Tm K m

TA K A K

TL Ka b a b a b

BZT25 10 232.5 6474.4 230 233.3 6751 6364 64 72 203BZT35 10 152.6 3237.3 150.4 147.6 4232 3081 82.6 114.4 143BZT40 10 136.1 1142.9 133.1 120.4 1836 1040 103.3 166.7 120PMN 10 267.7 10986 271.1 250.6 11225 11954 48.9 103.6 264.3



should be mentioned that Eq. 2 not only could be used todescribe the high temperature side of the dielectric peak, butalso the low temperature side of the dielectric peak, as shownin Fig. 6.

D. Characterization of the extent of dielectricdispersion

In Fig. 4 we note that frequency dispersion is observedfor BZT ceramics, especially for BZT35 and BZT40 withhigher Zr concentrations. The parameter =1100 KHz /1 KHz was employed to characterize the extent ofthe dielectric dispersion in BaSnxTi1xO3 in the previousstudy by the other researchers.27 A bigger implies muchmore dielectric dispersion. Figure 7a shows temperaturedependency of the extent of dielectric dispersion forBZT25, BZT35, and BZT40, respectively. The values of for BZT35 and BZT40 show rapid decrease from about 100to 160 K and decline to almost zero after 190 K. The valuesof for BZT25 show more slowly decrease first and alsodecline to Zero at last. These phenomena indicate that somekinds of relaxation polarization exist in both samples ofBZT35 and BZT40, which are different from BZT25. Figure7b plots the differential coefficient derived from Fig. 7a.In Fig. 7b, we could get the characteristic temperature TLlisted in Table I of , which implies the highest changingrate.

For comparison, Fig. 8 plots the temperature dependenceof dielectric constant, and d /dT of PMN ceramics. It canbe seen that the TL of PMN locates at the temperature rangearound Tm, but TL of BZT is 1030 C smaller than Tm, aspresented in Table I. This phenomenon indicates that the dy-namic processes of PNRs in PMN and BZT are different.

E. Universal relaxor dielectric response in BZT

As shown above, in relaxor ferroelectrics both BZT andPMN, the dielectric dispersion in the high-temperature slopeof permittivity maximum TTm is very weak 0 incomparison with the relaxation at TTm. As a result, thephenomenon was much less pronounced and had seldombeen considered. Bokov and Ye28 first found that at the tem-peratures above Tm the dielectric dispersion inPbMg1/3Nb2/3O3-PbTiO3 PMN-PT exactly follows theuniversal dielectric response law. Figure 9 shows the fre-quency dependence of the real and imaginary part of thedielectric permittivity of BZT35 around and above Tm, whichis similar to those reported for PMN crystal in the earlierworks.28,29 As can be seen in Fig. 9, two processes coexist.The first one gives rise to the f maximum, which isclearly seen at T=133 K indicated by arrow and themaxima move out of the measurement frequency windowupon increasing temperature. The f related to the secondprocess decreases monotonically with increasing frequencylow frequency, guided by solid lines, which is more clearlyshown in the ac conductivity plots f0.

FIG. 7. Color online a The dielectric dispersion strengths =1100 KHz /1 KHz for BZT25, BZT35, and BZT40 samples. b The d /dTof BZT25, BZT35, and BZT40.

FIG. 8. Color online Temperature dependences of the dielectric constantdashed line, the dielectric dispersion strength solid gray line, andd /dT dot line of PMN ceramics.

FIG. 9. Color online Frequency dependences of the real and imaginarypart of BZT35 at temperatures around Tm. Solid line only guides the eyes.



Figure 10 displays the frequency dependence of the realpart of ac conductivity of BZT35 at various temperatures.Obviously, it could be described by the so-called universaldielectric response law,

f = dc + 0fs, 3where dc is the dc bulk conductivity and f is the frequency.Equation 3 is typical of thermally assisted tunneling be-tween localized states. This law describes one phenomenonthat is associated with many-body interactions betweencharges and dipoles. By using Eq. 3, we get the exponent sas shown in the inset of Fig. 10. It can be found that sdecreases rapidly with increasing temperature below 195 K,above which it gets to a plateau value. Consequently, thehigh-temperature dielectric dispersion of BZT tends to dis-appear above this temperature, which is similar to those re-ported by Bokov and Ye.28 It is worth noting that the value ofdielectric constant contributed by the universal relaxationprocess is much less than that of the conventional relaxorprocess.

F. Dielectric behavior with applied electric field

The dielectric permittivity and for BZT25, stud-ied at various frequencies under 0 and 15 kV/cm dc biases,are shown in Fig. 11. It is evident in the figure that there is astrong response of dielectric permittivity to the applied elec-tric field. Note that under a dc bias field of 15 kV/cm, thephase transition peak becomes much broader. Moving tohigher temperatures and dielectric frequency dispersion issuppressed around the peak. However, unlike PMN andPb1y/4LayZrxTi1xO3 PLZT, an electric field does notseem to induce a long-range polar order.

G. Discussion

Based on the above results and analysis, it is found thatBZT x0.25 systems posses the basic characteristics ofrelaxors. The peak of T is very diffusing, with a strongdispersion at the low temperature side of Tm. Our dielectricstudy on BZT shows a strong deviation from the CW law,

indicating the existence of PNRs at TTm. The XRD Ref.12 and Raman spectra results13 confirmed the absence of astructure phase transition around the Tm in BZT. Similar toPMN, the dielectric permittivity of BZT also has two maincontributors: conventional relaxor dielectric response anduniversal relaxor dielectric response.23 However, BZT alsoshows very different dielectric properties from that of thecanonical relaxors. The most popular formula Eq. 1 is notsuitable to describe the diffuseness of the DPT of BZT. Thedielectric dispersion behavior of BZT is different from ca-nonical relaxors such as PMN. Moreover, BZT relaxors dis-play very different electric filed tunable behavior comparedwith PMN. The reported high-pressure Raman spectra ofBZT relaxors were reminiscent of features that have beenobserved for pure BaTiO3, but different from PMN.13

Although the step for understanding the physical phe-nomenon of relaxor ferroelectrics has still been going on, incanonical relaxors such as PMN, the relaxor behavior is as-signed to the non-homogeneous distribution of the Mg2+ andNb5+ cations over the B-site of the perovskite structure.13 Incontrast, for BZT, the B-sites cations have the same chargeand cannot induce such a kind of charge imbalanced order-disorder. However, an inhomogeneous distribution should beat the origin of relaxor behavior. For canonical relaxor,Moriya et al.14 found a broad heat capacity anomaly in PMNand PbMg1/3Ta2/3O3 PMT, which was not detected inBZT relaxors.15 The heat capacity anomaly in PMN andPMT showed order-disorder type mechanism for formationof PNRs in the crystal. In the case of BZT, the mechanismhas been suggested not to be the order-disorder type, butdisplacive type.15 This explanation implies that there is noglassy freezing in BZT relaxors, which is in agreement witha dielectric investigation by Bokov et al.16 In the frameworkof the random bond-random field theory, freezing shouldlead to a decrease of entropy and then to an anomaly in thetemperature dependence of heat capacity.14,30 Because of thespecial state in BZT, Bokov et al. proposed that the state ofBZT relaxors should be called a quasiferroelectric state,

FIG. 10. Color online Frequency dependence of the real part of ac con-ductivity for BZT35. The inset shows the evolution of the exponent s theT is also shown as a reference FIG. 11. Color online Temperature dependences of the dielectric permit-tivity at various frequencies for BZT25 solid line. The dielectric permit-

tivity under applied dc bias of 15 kV/cm is also shown dashed line.



which can be considered as a mixture of the randomly dis-tributed large static and small dynamic PNRs and thenonpolar Zr-rich nanoregions.16 The quite different proper-ties between BZT and canonical relaxors can be then relatedto the change of dynamic PNR number. The changing rate of for BZT25 show more slowly decrease compared to that ofBZT35 and BZT40, which also can be attributed to the dif-ferent number of static and dynamic PNRs, as the differentconcentration of nonpolar Zr-rich nanoregions.

IV. CONCLUSION

In summary, we have prepared the BaZrxTi1xO30.25x0.5 ceramics by conventional solid state reactionroute. Through the dielectric study of this system, we haveobserved an obviously different relaxor behavior in BZT sys-tem compared with the canonical relaxors. The BZT relaxorsdisplay very different dielectric dispersion behavior to that ofPMN. The popular modified CW law is not suitable to de-scribe the dielectric peak of BZT but a Lorenz-type law does.A quasiferroelectric state explanation considering static anddynamic PNRs is in agreement with the experiment results.

ACKNOWLEDGMENTS

This work has been supported by the National NatureScience Foundation of China 50672075, the RFDP20050699011, the 111 project B08040 of MOE, and theAeronautic Science Foundation of China 2006ZF53068, aswell as by the Research Grants Council of the Hong KongSpecial Administrative Region, China Project No.PolyU5166/05E.

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