Structural and electrical studies in La-substituted SrBi2Nb2O9 ferroelectric ceramics

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Physica B 371 (2006) 337–342 Structural and electrical studies in La-substituted SrBi 2 Nb 2 O 9 ferroelectric ceramics Vaibhav Shrivastava a , A.K. Jha a, , R.G. Mendiratta b a Department of Applied Physics, Delhi College of Engineering, Delhi 110042, India b School of Applied Sciences, Netaji Subhas Institute of Technology, Delhi 110075, India Received 26 January 2005; received in revised form 20 October 2005; accepted 23 October 2005 Abstract In this paper, structural and electrical studies of A-site lanthanum-substituted Sr 1x La x Bi 2 Nb 2 O 9 ; x ¼ 0:020:5 ceramics are reported. The introduction of lanthanum produces pore-free microstructure upto x ¼ 0:3. A diffuse ferroelectric to paraelectric phase transition is observed in the doped samples and positive temperature coefficient of resistance (PTCR) is observed in x ¼ 0:0, 0.4 and 0.5 samples whereas x ¼ 0:120:3 samples show negative temperature coefficient of resistance (NTCR). Curie temperature decreases continuously with increase in lanthanum content. r 2005 Elsevier B.V. All rights reserved. Keywords: Donor doping; Space-charge polarisation; DC conductivity; Dielectric loss 1. Introduction Bismuth-layered SrBi 2 Nb 2 O 9 (SBN) and SrBi 2 Ta 2 O 9 (SBT) ceramics have drawn attention of researchers due to their excellent fatigue characteristics as compared to those of Pb(Zr,Ti)O 3 (PZT) ceramics [1,2]. Therefore, doping in SBN- and SBT-type layered ceramics to improve the electrical and structural properties have been a matter of interest [3,4]. These ceramics show high values of Curie temperature and fatigue resistance, but suffer from high dielectric loss and low dielectric constant for which presence of space-charge in the structure is believed to be the cause [5]. In SBN and SBT ceramics role of donor type dopants can play a significant role due to their nature to deliver free charge in the structure while occupying the desired sites. Forbess et al. [6] have reported an increase in Curie temperature on doping 0.1 off-valent lanthanum. The unavailability of sufficient literature on these studies and their significance led us to carryout this research. In this paper, the effects of A-site lanthanum substitution on the structural and electrical properties of Sr 1x La x Bi 2 Nb 2 O 9 ceramics are reported for x ¼ 0:020:5. The work is also aimed at providing an idea of optimum composition for better NvRAM, capacitor and other applications. 2. Experimental Samples were prepared using solid-state reaction method taking SrCO 3 , La 2 O 3 , Bi 2 O 3 and Nb 2 O 5 (all from Aldrich) in stoichiometric proportions. The powders were thor- oughly mixed and passed through sieve of appropriate size. Mixtures were calcined at 900 1C in air. Polyvinylalcohol (Aldrich) 2 wt.% solution was mixed in all powdered samples in proportions and then molded into disc shape pellets by applying pressure of 270 MPa. Pellets were sintered in air at 1150 1C for 2 h. X-ray diffractograms were taken for all the calcined and sintered samples on Philips X-ray diffractometer PW 1710 using CuKa radiation of wavelength 1.54439 A ˚ in the range 101p2yp701 at a scanning rate of 0.051/s. The micrographs of fractured surfaces of a few sintered pellets were recorded on a Cambridge Stereo Scan 360 scanning electron microscope (SEM). All pellets were coated with silver paste and cured at 600 1C for half an hour. Dielectric measurements were taken on an HP 4192A Impedance Analyser operating at oscillation level of 1 V in the frequency range 50 Hz–1 MHz ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.10.131 Corresponding author. Tel.: +91 11 30972376; fax: +91 11 27871023. E-mail address: [email protected] (A.K. Jha).

Transcript of Structural and electrical studies in La-substituted SrBi2Nb2O9 ferroelectric ceramics

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0921-4526/$ - se

doi:10.1016/j.ph

�CorrespondiE-mail addre

Physica B 371 (2006) 337–342

www.elsevier.com/locate/physb

Structural and electrical studies in La-substituted SrBi2Nb2O9

ferroelectric ceramics

Vaibhav Shrivastavaa, A.K. Jhaa,�, R.G. Mendirattab

aDepartment of Applied Physics, Delhi College of Engineering, Delhi 110042, IndiabSchool of Applied Sciences, Netaji Subhas Institute of Technology, Delhi 110075, India

Received 26 January 2005; received in revised form 20 October 2005; accepted 23 October 2005

Abstract

In this paper, structural and electrical studies of A-site lanthanum-substituted Sr1�xLaxBi2Nb2O9; x ¼ 0:020:5 ceramics are reported.

The introduction of lanthanum produces pore-free microstructure upto x ¼ 0:3. A diffuse ferroelectric to paraelectric phase transition is

observed in the doped samples and positive temperature coefficient of resistance (PTCR) is observed in x ¼ 0:0, 0.4 and 0.5 samples

whereas x ¼ 0:120:3 samples show negative temperature coefficient of resistance (NTCR). Curie temperature decreases continuously

with increase in lanthanum content.

r 2005 Elsevier B.V. All rights reserved.

Keywords: Donor doping; Space-charge polarisation; DC conductivity; Dielectric loss

1. Introduction

Bismuth-layered SrBi2Nb2O9 (SBN) and SrBi2Ta2O9

(SBT) ceramics have drawn attention of researchers dueto their excellent fatigue characteristics as compared tothose of Pb(Zr,Ti)O3 (PZT) ceramics [1,2]. Therefore,doping in SBN- and SBT-type layered ceramics to improvethe electrical and structural properties have been a matterof interest [3,4]. These ceramics show high values of Curietemperature and fatigue resistance, but suffer from highdielectric loss and low dielectric constant for whichpresence of space-charge in the structure is believed to bethe cause [5]. In SBN and SBT ceramics role of donor typedopants can play a significant role due to their nature todeliver free charge in the structure while occupying thedesired sites. Forbess et al. [6] have reported an increase inCurie temperature on doping 0.1 off-valent lanthanum.The unavailability of sufficient literature on these studiesand their significance led us to carryout this research. Inthis paper, the effects of A-site lanthanum substitution onthe structural and electrical properties of Sr1�xLaxBi2Nb2O9 ceramics are reported for x ¼ 0:020:5. The work

e front matter r 2005 Elsevier B.V. All rights reserved.

ysb.2005.10.131

ng author. Tel.: +9111 30972376; fax: +91 11 27871023.

ss: [email protected] (A.K. Jha).

is also aimed at providing an idea of optimum compositionfor better NvRAM, capacitor and other applications.

2. Experimental

Samples were prepared using solid-state reaction methodtaking SrCO3, La2O3, Bi2O3 and Nb2O5 (all from Aldrich)in stoichiometric proportions. The powders were thor-oughly mixed and passed through sieve of appropriate size.Mixtures were calcined at 900 1C in air. Polyvinylalcohol(Aldrich) 2 wt.% solution was mixed in all powderedsamples in proportions and then molded into disc shapepellets by applying pressure of 270MPa. Pellets weresintered in air at 1150 1C for 2 h. X-ray diffractograms weretaken for all the calcined and sintered samples on PhilipsX-ray diffractometer PW 1710 using CuKa radiation ofwavelength 1.54439 A in the range 101p2yp701 at ascanning rate of 0.051/s. The micrographs of fracturedsurfaces of a few sintered pellets were recorded on aCambridge Stereo Scan 360 scanning electron microscope(SEM). All pellets were coated with silver paste and curedat 600 1C for half an hour. Dielectric measurements weretaken on an HP 4192A Impedance Analyser operating atoscillation level of 1V in the frequency range 50Hz–1MHz

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20 30 40 50 60

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20 30 40 50 60

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[°2θ]

[°2θ]

[°2θ]

[°2θ]

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(ar

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)(1

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La 0.3 La 0.5

La 0.1

Fig. 1. X-ray diffractograms of a few sintered Sr1�xLaxBi2Nb2O9 samples.

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and a frequency of 100 kHz was chosen for measuringCurie temperatures of all samples. DC conductivity of allthe samples were measured using conventional two-probelaboratory-made setup with titanium base plate and tip. Alltemperature measurements were taken at a heating rate of3 1C/min.

X-ray diffractograms of a few sintered samples areshown in Fig. 1. The position of peaks indicates theformation of perovskite structure. The samples with x ¼

0:020:3 show high crystallinity. The x ¼ 0:4 and 0.5 wereless crystalline as evident from the disappearance of a fewpeaks of low intensity. The intensity of a few peaks isobserved to decrease regularly with increase in lanthanumcontent. An increase in the width of a few peaks indiffractograms of x ¼ 0:4 and 0.5 samples is observed.From the observed reduction in the intensities of majorpeaks upto x ¼ 0:3, suppression in the perovskite phase isestimated, as peak intensity is an indication of phaseconcentration. In addition, background noise, whichindicates the amorphous content in the structure, isobserved to increase in the samples with x ¼ 0:4 and 0.5for higher 2y values. The added lanthanum is likely to go tothe strontium site because of similar ionic radius andcoordination number. The lanthanum is not likely tooccupy the sites of bismuth and niobium due to similarreasons. The details of lanthanum occupancy and a fewstructural distortion parameters have been reported else-where [7].

Fig. 2 shows the SEM images of microstructure offractured surfaces of x ¼ 0:0, 0.1, 0.3 and 0.5 samples. Theundoped SBN shows poor microstructure with porosityand maximum grains of average size below 1 mm as in

Fig. 2a. Lanthanum as dopant in small quantities is known[8] to reduce porosity by promoting uniform grain growth;the same is observed in doped samples up to x ¼ 0:3samples with average grain size 5 mm. The microstructureof x ¼ 0:5 sample shows grains of average size below 1 mmand having irregular shape with no ordered boundary.High concentrations of lanthanum, i.e., more than30 atomic% may induce formation of defects [9] in thestructure because of high solid solubility nature andoccupancy onto other sites.Fig. 3 shows the variation of dielectric constant (e) with

frequency in the range 50Hz–1MHz at room temperaturefor all the samples. A slow decrease in dielectric constant isobserved over the studied frequency range for x ¼ 0:1, 0.2and 0.3 samples. Samples with x ¼ 0:0, 0.4 and 0.5 show arapid decrease up to 1 kHz followed by a slow decrease athigher frequencies. This rapid decrease in dielectricconstant is attributed to space-charge polarisation satura-tion. Normally the space-charge saturates up to 1 kHz,however, in a few donor-doped ceramics it may extend upto 100 kHz [10]. For frequencies higher than 1 kHz thedielectric constant increases with increase in lanthanumcontent upto x ¼ 0:3 and decreases for x ¼ 0:4 and 0.5. Allsamples show a decrease in e-values at frequencies above100 kHz, which is an indication of nearby relaxation peakof saturation. The introduction of lanthanum is known toincrease dielectric constant [11,12] because of its high ionicpolarisibility. Also, it contributes to the space-chargepolarisation by the creation of vacancies in the structureto maintain charge neutrality. The dielectric constant ofundoped sample is affected, besides other factors, by theevaporation of bismuth oxide during sample preparation.

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Fig. 2. SEM fracture photographs of x ¼ 0:0, 0.1, 0.3 and 0.5 samples.

102 103 104 105 10650

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Die

lect

ric c

onst

ant

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Fig. 3. Dielectric constant versus frequency behaviour of Sr1�xLaxBi2Nb2O9 ceramics.

Fig. 4. Dielectric constant versus temperature behaviour of Sr1�xLax

Bi2Nb2O9 ceramics.

V. Shrivastava et al. / Physica B 371 (2006) 337–342 339

This results in space-charge generation the effect of whichis felt more at lower frequencies [5]. Low e-values at higherfrequencies are also expected because of saturation ofspace-charge polarisation near 1–100 kHz. This is indicatedin Fig. 3 where large saturation of space charge occurs near1 kHz for x ¼ 0:0, 0.4 and 0.5 samples and completesaturation of the same has been shown near 100 kHz. Thex ¼ 0:2 sample does not show such a loss of space-chargepolarisation; further investigations are needed to explainthis observation.

In Fig. 4, dielectric constant versus temperature behaviorof the studied compositions is shown. The observationshave been plotted using Microcal Origin data plot. Thesemeasurements were taken at frequency 100 kHz near andabove which space-charge and orientational polarisationscease off and only ionic and electronic contributionspersists [5]. These ceramics are known to have single phasetransitions corresponding to Curie temperature wheredielectric constant is a maximum. Curie temperature andmaximum dielectric constant (emax.) both show a decreasewith increase in lanthanum content up to x ¼ 0:5. Di-electric peak is broadened with increase in x which issimilar to diffuse phase transition type behavior of

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6.38

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rago

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ie te

mpe

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Fig. 5. Tetragonal strain and Curie temperature versus composition x of

Sr1�xLaxBi2Nb2O9 ceramics.

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Fig. 6. Dielectric loss versus frequency behaviour of Sr1�xLaxBi2Nb2O9

ceramics.

Fig. 7. Dielectric loss versus temperature behaviour of Sr1�xLaxBi2Nb2O9

ceramics.

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relaxors. Such transition behavior is explained on the basisof the formation of micro-polar regions [13,14], which havetheir respective transition temperatures. A decrease inCurie temperature with increase in lanthanum content isattributed to the overall decrease in tetragonal lattice strain[15]. The lead-doped samples have also shown similarbehavior. The observed values of tetragonal strain withCurie temperature as a function of composition are shownin Fig. 5.

Fig. 6 shows the dielectric loss as a function of frequencyat room temperature. The undoped SBN sample showshuge loss, which decreases with frequency up to 80 kHz andthereafter increases again; a known dielectric dispersionbehaviour [16]. Among the doped samples, x ¼ 0:3 sampleshows minimum loss at low frequencies which increasesappreciably after about 100 kHz. The x ¼ 0:4 and 0.5samples show large loss values before and after about

100 kHz, similar to undoped sample. Sample with x ¼ 0:2shows greater loss for frequencies less than 1 kHzcompared to x ¼ 0:1 and 0.3 samples but it shows acontinuous decrease in loss value up to 1MHz. Theincrease in loss values beyond 100 kHz is attributed torelaxation losses due to ion jump or electron hopping [17]in samples with x ¼ 0:0, 0.1, 0.3, 0.4 and 0.5. The frequency80 kHz at which all the samples show minimum loss issignificant, and after this loss is higher for x ¼ 0:4 and 0.5samples compared to x ¼ 0:0 sample. The x ¼ 0:4 and 0.5samples are possibly defect structures as indicated bydisappeared peaks in X-ray diffractograms. At higherfrequencies more energy should be dissipated during therotation of dipoles in a defect structure therefore highdielectric loss is expected in x ¼ 0:4 and 0.5 samples. Thehigher loss values of x ¼ 0:0 sample are attributed to thepresence of space-charge due to the evaporation of bismuthoxide during sintering which is also possibly the cause forrelatively higher dielectric constant values up to 1 kHz.Dielectric loss versus temperature behaviour of the

studied samples is shown in Fig. 7. The samples areobserved to possess dielectric loss peaks at differenttemperatures. The peaks in samples with x ¼ 0:1, 0.2 and0.3 are observed in a wide temperature range whereasx ¼ 0:0, 0.4 and 0.5 samples show peaks at small intervalsof temperature. The dielectric loss values show peaks withrespect to temperature due to the following reasons: (i) if adielectric is a mixture of two or more polar substances and(ii) due to different character of losses in chemicallyindividual dielectric like dipolar and structural, etc. Themaximum dielectric loss is expected at a temperature nearwhich phase transition occurs, i.e., in the neighbourhood ofCurie temperature. In the present work, observations ofdielectric loss are in accordance with that of Curie

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Table 1

Activation energy and high temperature conductivity of samples

Composition (x) in

Sr1�xLaxBi2Nb2O9

DC (eV) PE

phase

s (� 10�8 S/cm)

DC (at RT) DC (600 1C)

0.0 1.05 0.83 425

0.1 1.29 0.84 464

0.2 1.15 0.87 487

0.3 0.85 0.97 515

0.4 0.25 0.82 577

0.5 0.47 0.79 1672

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temperature measurements. From Fig. 7a, where measureddielectric loss values for x ¼ 0:0, 0.4 and 0.5 are plotted, itis clear that the loss increases with temperature only forx ¼ 0:0 and 0.4 samples but for x ¼ 0:5 insignificantchanges are observed. The peaks observed in x ¼ 0:1 to0.3 samples are possibly relaxational peaks [7,18] atdifferent temperatures, the reasons for such behaviourhave been described earlier. The x ¼ 0:2 sample showsalmost similar behaviour but its first peak is of less heightcompared to x ¼ 0:1 and 0.3 the reason for which ispossibly less space-charge in this sample compared to x ¼

0:1 and 0.3 samples. This observation is in accordance withFig. 3 where a steep decrease in dielectric constant value isobserved for x ¼ 0:1 and 0.3 samples at frequencies after100 kHz with an exception for x ¼ 0:2 sample, which showsless steeper curve. In x ¼ 0:4 and 0.5 samples, possiblynumber of defects is increased due to lanthanum occu-pancy onto the sites of bismuth and niobium ions such thatat low temperatures ions may participate for conduction.Therefore, insignificant loss peaks are observed whichshould be due to space-charge relaxational losses (structur-al losses) merged with dipolar relaxational losses [19]. Suchsignificant relaxational peaks are not expected to beobserved in defect structures where phase transitions areobserved in a wide range of temperature [20,21]. This seemsto be the cause for observed loss behaviour of x ¼ 0:4 and0.5 samples.

Bulk ionic DC conductivities of all the samples areplotted in Fig. 8. It is observed that room temperatureconductivity shows an increasing trend up to x ¼ 0:3followed by a decrease at higher values of x, (Table 1). Toensure that this was indeed the case the observations weretaken several times and the same trend was noticed eachtime. In Table 1, DC conductivity values at differenttemperatures are listed. The x ¼ 0:4 and 0.5 samples intheir paraelectric phase show positive temperature coeffi-

Fig. 8. DC conductivity behaviour of Sr1�xLaxBi2Nb2O9 ceramics.

cient of resistance (PTCR) in the neighbourhood of phasetransition temperature; the x ¼ 0:0 sample shows anidentical behaviour but to a much smaller extent. Suchbehaviour has been reported in BaTiO3 insulators. ThePTCR behaviour is the result of negative charge carrierconduction under the external electric field and is known asa characteristic of metals [22]. The samples with x ¼ 0:1,0.2 and 0.3 show negative temperature coefficient ofresistance NTCR throughout the temperature range, whichis a characteristic of insulators [23]. It indicates thatlanthanum addition either increases positive charge in thestructure or eases the evaporation of negative chargecarriers, i.e., oxygens from the structure. The secondpossibility is ruled out because of very high bond strengthof lanthanum with oxygen and the first possibility isreasonable due to donor nature of lanthanum. Theobserved PTCR behaviour in samples with x ¼ 0:4 and0.5 could be due to the lanthanum occupying other cationicsites available in the structure. It is not unreasonable toassume that as lanthanum concentration increases, it notonly occupies strontium sites but also other cationic sitesavailable in the structure, resulting in the formation ofunwanted heterogeneous phases [15,24]. If such multiplesite-occupancy occurs, marked changes in conductivity andmicrostructure are expected. The same is observed inpresent work for x ¼ 0:4 and 0.5 samples. This is alsosupported by the observed increased peak width in X-raydiffractograms (Fig. 1) and by the presence of micro-cracksin SEM fracture photographs (Fig. 2) for x ¼ 0:4 and 0.5samples.As lanthanum exists in stable oxidation state of +3 and

strontium in +2, substitution of two lanthanum ions ontotwo strontium sites produces one strontium vacancy in thestructure to preserve charge neutrality. These bismuth layerceramics have been reported to have oxygen vacanciesproduced during sample preparation [20]. It is also knownthat donor doped ceramics do not favour oxygen vacancyformation. The occupancy of lanthanum onto bismuthsites should not affect the conductivity of compositionsbecause of same valence state of +3, but if it occupiesniobium site of valence state +5, a decrease in conductivityis expected, which is observed (Table 1, RT column).Higher lanthanum content in studied compositions like x ¼

0:4 and 0.5 might induce bismuth and niobium ions to

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become free from their respective sites and to participate inionic conduction. Additionally, it will provide two freeelectrons to the structure, which possibly results in PTCR.DC activation energy for all the samples is calculated usingslope of obtained Arrhenius plots in the temperature rangeof paraelectric phase; obtained values are listed in Table 1.The x ¼ 0:1 sample is found to possess maximum activa-tion energy of 1.29 eV and the sample with x ¼ 0:4 shows aminimum of 0.25 eV, both in their paraelectric phase.

3. Conclusions

Lanthanum doping in bismuth layer SBN ceramics ontoA-site yields pore-free microstructure up to x ¼ 0:3. Thex ¼ 0:3 sample shows minimum dielectric loss values up to80 kHz; the values increase thereafter at higher frequenciesup to 1MHz. The sample with x ¼ 0:2 shows minimumdielectric loss at 1MHz and does not show dielectricfrequency relaxation up to this frequency. The x ¼ 0:2sample is therefore best suited for high frequency applica-tions. Additionally, this sample offers high dielectricconstant of 700 at Curie temperature of 336 1C. The PTCRfeature of x ¼ 0:0, 0.4 and 0.5 samples can also be utilisedfor sensor applications although these sample show highdielectric loss and low dielectric constant. Flatteneddielectric response of these ceramics provides wide rangeof applications. High ionic conductivity of x ¼ 0:4 and 0.5samples may yield high fatigue resistance for memoryapplications.

References

[1] C.A.P. de Arauzo, J.F. Scott, Science 246 (1989) 1400.

[2] C.A.P. Arauzo, J.D. Cuchlaro, L.D. Mcmillan, M.C. Scott,

J.F. Scott, Nature 374 (1995) 627.

[3] Y. Wu, M.J. Forbess, S. Seraji, S.J. Limmer, T.P. Chou, C. Nguyen,

G.Z. Cao, J. Appl. Phys. 90 (10) (2001) 5296.

[4] Y. Shimakawa, Y. Kubo, Y. Nakagawa, S. Goto, T. Kamiyama,

H. Asano, F. Izumi, Phys. Rev. B 61 (10) (2000) 6559.

[5] D.B. Dove, L.L. Hench (Eds.), Principles of Electronic Ceramics Part

A, London, 1971, p. 125, 495.

[6] M.J. Forbess, S. Seraji, Y. Wu, C.P. Nguyen, G.Z. Cao, Appl. Phys.

Lett. 76 (20) (2000).

[7] V. Shrivastava, A.K. Jha, R.G. Mendiratta, Solid State Commun.

September 2004, in review.

[8] R.C. Buchnan (Ed.), Principles of Electronic Ceramics, Marcel

Dekkar, New York, 1991, p. 154.

[9] G.H. Haertling, C.E. Land, J. Am. Ceramic Soc. 54 (1971) 1.

[10] R.C. Buchnan (Ed.), Principles of Electronic Ceramics, Marcel

Dekkar, New York, 1991, pp. 38–39.

[11] G.H. Haertling, J. Am. Ceramic Soc. 82 (4) (1999) 797–818.

[12] I. Bunget, M. Popescu (Eds.), Physics of Solid Dielectrics, Elsevier,

Amsterdam, Oxford, New York, 1984, p. 209.

[13] L.L. Hench, J.K. West (Eds.), Physics of Electronic Ceramics, Wiley,

New York, 1995, p. 277.

[14] V. Shrivastava, A.K. Jha, R.G. Mendiratta, Solid State Commun.

133 (2) (2005) 125–129.

[15] Y.H. Xu (Ed.), Ferroelectric Materials, Elsevier Science Publishers

B.V., 1991, p. 165.

[16] I.S. Zheludev (Ed.), Physics of Crystalline Dielectrics, vol. 2, Plenum

Press, New York, 1971, p. 521.

[17] G.A. Smolenski, V.A. Isupov, A.I. Agranoskaya, S.N. Popov, Sov.

Phys. Solid State 2 (1961) 2584.

[18] B. Tareev (Ed.), Physics of Dielectric Materials, Mir Publishers,

Moscow, 1971, p. 148.

[19] C. Ang, Z. Yu, P.M. Vilarinho, J.L. Baptista, Phys. Rev. B 57 (1998)

7403.

[20] Y. Wu, M.J. Forbess, S. Seraji, S.J. Limmer, T.P. Chou, G. Cao,

J. Appl. Phys. 89 (10) (2001) 5647.

[21] A. Chen, Y. Zhi, L.E. Cross, Phys. Rev. B 62 (2000) 228.

[22] Y.H. Xu (Ed.), Ferroelectric Materials, Elsevier Science Publishers

B.V., 1991, p. 193.

[23] R.C. Buchnan (Ed.), Principles of Electronic Ceramics, Marcel

Dekkar, New York, 1991, pp. 250–251.

[24] G.H. Haertling, Ferroelectrics 75 (1987) 25.