Hindawi Publishing CorporationISRN CeramicsVolume 2013 Article ID 369670 12 pageshttpdxdoiorg1011552013369670

Research ArticleElectrical Conduction in (Na05Bi05)1minus119909Ba

119909TiO3 (0 le 119909 le 1)

Ceramic by Complex ImpedanceModulus Spectroscopy

Ansu Kumar Roy Kamal Prasad and Ashutosh Prasad

University Department of Physics TM Bhagalpur University Bhagalpur 812007 India

Correspondence should be addressed to Ashutosh Prasad apdphygmailcom

Received 30 December 2012 Accepted 18 February 2013

Academic Editors S-Y Chu O Dymshits and S Marinel

Copyright copy 2013 Ansu Kumar Roy et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The present work describes the piezoelectric impedance and conductivity studies of (Na05Bi05)1minus119909Ba119909TiO3 (1 minus 119909)BNT-119909BT(0 le 119909 le 1) ceramicsThe ceramics were prepared by conventional ceramic fabrication technique X-ray diffraction data confirmedthe formation of a pure compound in all the compositions Williamson-Hall plot yielded the apparent crystallite sizes sim26ndash52 nm and SEM micrograph showed grain sizes ranging between 18ndash35 120583m for the material samples Values of longitudinalpiezoelectric charge coefficients of the samples poled under a dc electric field of about 25 kVmmat 80∘C15min indicated that theirpiezoelectric properties near the MPB are rather sensitive to the phase composition and reach preferred values at 119909 = 008 wherethe relative content of the tetragonal phase is significantly higher than that of the monoclinic phase Complex impedancemodulusspectroscopic analyses indicated the presence of grain-boundary effect along with the bulk contribution and also confirmed thepresence of non-Debye type ofmultiple relaxations in thematerialsThe temperature dependent electrical conductivity data suggestthe negative temperature coefficient of resistance behaviour The activation energy studies allow insight into the nature of theconduction mechanisms occurring in the materials system which are explained on the basis of hopping model of charge carriers

1 Introduction

Till date the most widely used piezoelectric materials arePbTiO

3-PbZrO

3- (PZT)based ceramics because of their

excellent piezoelectric properties In view of harmful effectsfor the mankind as well as for the other living creatureson the earth due to possible lead toxicity spreading duringprocessing the use recycling and disposal of devices con-taining PZT a global interest has arisen in developing piezo-electric materials that are biocompatible and environment-friendly Therefore it is necessary to investigate and developenvironment-friendlymaterials to replace PZT-based ceram-ics with comparable properties Recently lead-free piezo-electric ceramic materials with perovskite structure and Bi-layered structure oxides as viable alternatives to PZT havebeen reported Among these materials bismuth sodiumtitanate Bi

05Na05TiO3(BNT) first reported by Smolenskii

et al [1] is considered to be a viable candidate to replacethe widely used lead-based perovskite materials due to itshigh remnant polarization (119875

119903= 38 120583Ccm2) Nevertheless

the applications of BNT are limited by its high coercive field

(119864119888= 73 kVmm) and high conductivity It is an A-site

substituted distorted perovskite compound (ABO3) Its

dielectric properties reveal two anomalies The well-knownfirst one corresponds to the antiferroelectric-paraelectrictransition at about 320∘C [2]The other one at sim150∘Cndash200∘Cis frequency-dependent (called the depolarization tempera-ture 119879

119889) and is not yet well understood since no structural

transition is observed at that temperature In order to improvethe poling process and enhance the piezoelectric propertiesof the BNT ceramics a number of BNT-based solid solu-tions such as BNT-BaTiO

3(BT) [3 4] BNT-Bi

05K05TiO3

[5] BNT-(Ba Sr)TiO3[6] BNT-SrTiO

3-Bi05Li05TiO3[7]

BNT-Bi05K05TiO3-Bi05Li05TiO3

[8] BNT-Bi05K05TiO3-

BiFeO3[9] BNT-BT-Bi

05K05TiO3[10] BNT-BT-KNbO

3

[11] Bi2O3doped BNT-BT [12] BNT-NaNbO

3[13] BNT-

BiFeO3[14] BNT-Bi

2O3-Sc2O3[15] BNT-La

2O3[16] and

BNT-Ba(W12

Cu12

)O3[17] and so forth have been devel-

oped and studied in recent years It is found that the dielectricand piezoelectric properties of these ldquomodifiedrdquo BNT-basedmaterials were effectively enhanced when the morphotropicphase boundary (MPB) composition (inwhich coexistence of

2 ISRN Ceramics

(rhombohedralmonoclinic) tetragonal phases was assumed)was attained Many of the researchers from all over the worldhave reported the MPB composition to lie within 119909 = 005ndash008 for (1 minus 119909)BNT-119909BT A recent literature has reportedan exhaustive study on (1 minus 119909)BNT-119909BT [18] However inview of some of the important and yet untouched aspectsand properties of the (1 minus 119909)BNT-119909BT ceramic system thepresentwork is aimed at studying the piezoelectric propertiesimpedancemodulus spectroscopy and conductivity of the(1 minus 119909)BNT-119909BT(119909 = 0 002 004 005 006 008 010 and10) ceramic system By knowing the conduction mechanismwithin a material system we can tune their properties andcan use them for particular applications In this contextthe present study of (Na

05Bi05)1minus119909

Ba119909TiO3(1 minus 119909)BNT-119909BT

(0 le 119909 le 1) ceramics is assumed worthwhile in probingthe conduction mechanism in detail which may be helpful intailoring the electrical characteristics for desired applications

2 Experimental

Polycrystalline samples having the nominal formula(Bi05Na05)1minus119909

Ba119909TiO3 (1 minus 119909)BNT-119909BT were prepared

by a high temperature solid-state reaction technique usingoxides Bi

2O3 Na2CO3 BaCO

3and TiO

2(HiMedia) (having

a purity of more than 995 for each of them) in a suitablestoichiometryThe above ingredients weremixed thoroughlyfirst in air and then in methanol medium using agate mortarand pestle The oxide mixtures were calcined at an optimizedtemperature of 1170∘C for about 3 h in an alumina crucibleThen by adding a small amount of polyvinyl alcohol (PVA)as a binder to the calcined powder circular and rectangulardisk-shaped pellets were fabricated for different compositionsby applying uniaxial pressure of 4ndash6 tons per square inchThe pellets were subsequently sintered at an optimizedtemperature of 1180∘C for about 2 h The XRD spectra weretaken on calcined powders of (1 minus 119909)BNT-119909BT with anX-ray diffractometer (XrsquoPERT-PRO Pan Analytical USA)at room temperature using CuK

120572radiation (120582 = 15405 A)

over a wide range of the Bragg angles (20∘ le 2120579 le 80∘)

The microstructure of the sintered pellets was observedat room temperature from the micrographs obtained byusing a scanning electron microscope (JEOL-JSM840A)Thetemperature-dependent dielectric constant (1205761015840) loss tangent(tan120575) impedance and phase values at various frequencieslike 100Hz 1 kHz 10 kHz 100 kHz and 1MHzwere evaluatedusing the capacitance impedance and phase data obtainedfrom a computer-controlled LCR Hi-Tester (HIOKI 3532-50Japan) on a symmetrical cell of type AgceramicAg whereAg is a conductive paint coated on either side of the pelletLongitudinal piezoelectric charge coefficients (119889

33) of the

poled (1 minus 119909)BNT-119909BT ceramic samples were measuredunder an electric field of about 25 kVmm at 80∘C15minin a silicone oil bath using a PM3500 119889

3311988931

meter (KCFTechnologies USA)

3 Results and Discussion

31 Structural Study Figure 1 shows the XRD patterns ofcalcined (1 minus 119909)BNT-119909BT powder A standard computer

program (POWD) was utilized for the XRD-profile analy-sis Good agreement between the observed and calculatedinterplanar spacing without any trace of extra peaks dueto the constituent oxides was found thereby suggesting theformation of a biphasic pure compound All the reflectionpeaks of the XRD pattern of the samples were indexed andthe lattice parameters were determined in the monoclinicas well as in tetragonal system of crystals The presence ofmonoclinic and tetragonal phases in the compositions having119909 le 006 and 119909 ge 006 possibly due to its constituentsBNT and BT respectively is endorsed by the splitting ofpeaks 445∘ndash475∘ into two peaks (200) and (002) in the XRDpatterns as shown in Figures 1(a) and 1(b) This splittingbecomes increasingly prominent with the further addition ofBT for 092 BNT-008 BT 090 BNT-010 BT aswell as for purebarium titanate (BT) The apparent particle size and latticestrain of (1minus119909)BNT-119909BT were estimated by analyzing the X-ray diffraction peak broadening using the Williamson-Hallapproach [19]

120573Cos 120579 = 2(Δ120585120585) sin 120579 + 119870120582

119863 (1)

where119863 is the crystallite size 120573 is the diffraction peak widthat half intensity (FWHM) Δ120585120585 is the lattice strain and 119870the Scherrer constant (sim089)However these results have notbeen shown in the paper for brevity sake

32 Tolerance Factor In general the perovskite structure isstable in the region 0880 lt 119905 lt 1090 [18] and the stabilityis higher as the 119905-value is closer to 1 For example the 119905-valueof a cubic SrTiO

3(= 1001) is closer to 1 than that for the

orthorhombic CaTiO3(= 0966)The 119905-value also provides an

indication about how far the atoms can deviate from the idealpacking positions and be still ldquotoleratedrdquo in the perovskitestructure Calculated values of tolerance factors for different(1 minus 119909)BNT-119909BT compositions (119909 = 0 0 02 0 04 005006 008 and 1) using the Goldschmidt formula [20] are veryclose to 1 (lying between minimum = 0985 for BNT andmaximum = 1058 for 090 BNT-010 BT) thus indicating agood stability for all the test samples of the present work

33 Microstructural Study Figure 2 shows the SEM micro-graph of (1 minus 119909)BNT-119909BT (119909 = 0 0 02 004 005 006 008and 1) compositions Grain shapes are clearly visible therebyindicating the existence of polycrystalline microstructureGrains of unequal sizes with less porosity appear to bedistributed throughout the samples The average grain sizewas found with the help of linear intercept method Grainsizes for the chosen compositions were found to range 18ndash35 120583m generally decreasing with increasing barium titanatecontent as detailed in Table 1 Of these the 096 BNT-004 BTcomposition (whose SEM image is shown in Figure 2(c))showed the highest porosity and irregular shaped unequalsized grains as compared with those of others The SEMmicrograph of 094 BNT-006 BT (Figure 2(e)) also showsslight porosity and inequality in grain size Here it would notbe inopportune tomention that BT has been fabricated undera different condition than that for (1 minus 119909)BNT-119909BT [21] and

ISRN Ceramics 3

20 25 30 35 40 45 50 55 60 65 70 75 80

1

0100080060050040020

Peak position (deg)

119909

(a)

445 45 455 46 465 47 475

1

x

01

008

006

005

004

002

0

Peak position (deg)

(b)

Figure 1 (a) X-ray diffraction patterns and (b) expanded X-ray diffraction patterns of (Bi05Na05)1minus119909

Ba119909TiO3ceramics (119909 = 00 002 004

005 006 008 010 and 10)

119909 = 0

(a)

119909 = 002

(b)

119909 = 004

(c)

119909 = 005

(d)

119909 = 006

(e)

119909 = 008

(f)

119909 = 01

(g)

119909 = 1

(h)

Figure 2 SEM micrographs of (Na05Bi05)1minus119909

Ba119909TiO3(119909 = 0 002 004 005 006 008 010 and 10) compositions

Table 1 The values of density grain size dielectric constant (120576119903) loss tangent (tan 120575) and piezoelectric coefficient (119889

33) at room temperature

of (Bi05Na05)1minus119909Ba119909TiO3 samples

Samples Density (gcm3) Grain size (120583m) 120576119903(RT10 kHz) tan 120575 (RT10 kHz) 119889

33(pCN)

BNT 485 351 673 026 17098BNT-002BT 5008 182 672 032 22096BNT-004BT 5078 297 545 011 50095BNT-005BT 5144 308 724 047 95094BNT-006BT 5234 301 871 008 124092BNT-008BT 5248 24 951 011 112090BNT-010BT 5382 276 1110 009 103BT 602 16 1200 003 101 plusmn 5

4 ISRN Ceramics

the XRD data and SEM image for barium titanate have alsobeen taken from the previousworks of our group [21] and thevalue of longitudinal piezoelectric charge coefficient (119889

33) for

it has been taken from the literature [22] for comparison sake

34 Piezoelectric Study Minimum and maximum valuesof longitudinal piezoelectric charge coefficient (119889

33) of the

ceramic samples poled under an electric field of about25 kVmm in a silicone oil bath at 80∘C15min were foundto be sim17 pCN and 124 pCN for BNT and 094 BNT-006 BTcompositions respectively as given in Table 1 A high valueof 11988933

for 094 BNT-006 BT may be supposed to be dueto the presence of morphotropic phase boundary (MPB)composition (where both monoclinic and tetragonal phasesare supposed to coexist) as detailed before

35 Complex Impedance Spectroscopic Analysis Compleximpedance spectroscopy (CIS) is a powerful tool for char-acterizing many of the electrical properties of materials andtheir interfaces with electronically conducting electrodesIt may be used to investigate the dynamics of bound ormobile charges in the bulk or interfacial regions of anykind of solid or liquid material ionic semiconductingmixed electronic-ionic and even insulators (dielectrics) Anequivalent circuit based on impedance and electric modulusspectra provides the physical processes occurring inside thesample Most of the real ceramics contain grains and grain-boundary regions which individually have very differentphysical properties These regions are well observed in theimpedance and modulus spectra The electrical propertiesof the present material system have been investigated usingCIS technique Electrical ac data may be presented in any ofthe four interrelated formalism relative permittivity (120576lowast) =1205761015840minus 11989512057610158401015840 impedance (119885lowast) = 1198851015840 minus 11989511988510158401015840 = 1119895120596119862

0120576lowast electric

modulus (119872lowast) = 1198721015840+ 119895119872

10158401015840= 1120576

lowast admittance (119884lowast) =1198841015840+ 11989511988410158401015840= 119895120596119862

0120576lowast and tan 120575 = 120576

101584010158401205761015840= 119872

101584010158401198721015840=

119885101584011988510158401015840= 119884101584010158401198841015840 where 120596 (= 2120587119891) is the angular frequency

1198620= 1205760119860119905 is the geometrical capacitance 119895 = radic minus 1 120576

0is

the permittivity of free space (= 8854 times 10minus12 Fmminus1) 119905and119860 are the thickness and area of the pellet respectively andrelative permittivity (1205761015840) = 119862

1199011198620 Here 119862

119901is the parallel

capacitance and 120575 the loss angle is the complementary(=90 minus 120579) to the phase angle (120579) both of which are directlyobserved by the LCR Hi-Tester The modulus (|119885|) of thecomplex impedance (119885lowast) is directly observed by the LCRHi-Tester so that 119885cos120579 (= 1198851015840) and 119885sin120579 (= 11988510158401015840) respectivelygive the real and imaginary parts of the impedance (119885lowast) Thefrequency dependence of1198851015840 for (1minus119909)BNT-119909BT (119909 = 0 002004 005 006 008 and 1) ceramics at several temperaturesbetween ambient temperature and 450∘C is observed (butnot shown by plots for brevity sake) At lower tempera-tures 1198851015840 decreases monotonically with increasing frequencyup to a certain frequency and then becomes frequency-independent Only at the highest chosen temperature that isat 450∘C 1198851015840(119891) plots tend to provide peaks below the lowestmeasurement frequency range that is 100Hz The highervalues of 1198851015840 at comparatively lower frequencies and lowertemperatures mean that the polarization in the test material

is larger under the aforesaid conditions The temperaturewhere this change occurs varies with frequency in differentmaterialsThis also means that the resistive grain-boundariesbecome conductive at these temperatures This also showsthat the grain-boundaries are not relaxing even at very highfrequencies and higher temperatures 11988510158401015840(119891) plots (althoughnot shown in the present paper for brevity sake) showedalmost identical monotonically decreasing type of variationup to a certain frequency limit beyond which they mergetogether to show frequency-independent nature of variationextending up to the highest frequency limit at all the chosentemperatures except at the highest one that is at 450∘Cin which case all the 11988510158401015840(119891) plots give peaks in the limitingfrequency range of sim122Hzndash364Hz for 094 BNT-006 BTandBNT respectively as shown in Figure 3However bariumtitanate (dopant) concentration-dependent shifting of11988510158401015840(119891)either towards higher or lower frequency side could not beclearly affirmed from the plots Further no peaks were seenfor 096 BNT-004 BT and 090 BNT-010 BT compositionsThe merger of 11988510158401015840 (as well as of 1198851015840) at higher frequen-cies for all the temperatures indicates possible release ofspace charge polarizationaccumulation at the boundariesof homogeneous phases in the applied external field Atlower temperatures 11988510158401015840 decreases monotonically therebysuggesting that the relaxation in the material system at lowertemperatures is absent This means that relaxation speciesare immobile defects and the orientation effects may beassociated Also the magnitude of 1198851015840 and 11988510158401015840 decreases withincreasing frequencies This would imply that relaxation inthe material system is temperature-dependent and thereis apparently not a single relaxation time The electricalbehavior of the system has been studied over a wide rangeof temperature 35ndash450∘C and frequency 100Hzndash1MHz Inorder to study the contribution of various microscopicelements such as intragrain intergrain electrode effect andrelaxation process we have used the Cole-Cole plots analysisFigures 4(a) through 4(g) shows the Cole-Cole plots of thecompounds at different temperatures only 375ndash450∘C and theplot corresponding to 450∘C for different (1 minus 119909)BNT-119909BTcompositions is shown in Figure 4(h) From the data it isapparent that at low temperatures when the resistivities ofthe samples are too high a small portion of the impedancedispersion profile can be detected in the measured frequencyrange and thus making data analysis impossible Since theimpedance measurements performed for all the samplesbelow 375∘C did not present a complete semicircle theycould not be considered for equivalent circuit modelingin this study It can be seen that the semicircles exhibittheir depressed centers below the abscissa representing thedistribution of relaxation timesThis nonideal behavior couldbe attributed to the several factors such as grain orientationgrain-boundary stress-strain phenomena and atomic defectdistribution A series array of two parallel RC combinations[(119877119892 119862119892) (119877gb 119862gb)] in series with a resistor (119877119904) (though the

data of119877119904for any of the samples are not shown in the table for

brevity sake)was found to best fit the experimental data for allthe samples thereby indicating the contribution fromgrain ofthe sample in the high frequency region and from the grain-boundaries in the low frequency region No other relaxation

ISRN Ceramics 5

Table 2 Grain (bulk)(grain-boundary) resistances (119877119892119877gb) capacitances (119862119892119862gb) and the corresponding relaxation times (120591

119892120591gb) at

450∘C for (1 minus 119909)BNT-119909BT ceramic

Composition 119877119892

Rgb 119862119892

119862gb 120591119892

120591gb

BNT 028MΩ 047MΩ 112 nF 114 nF 034ms 054ms098BNT-002BT 068MΩ 097MΩ 069 nF 082 nF 047ms 080ms096BNT-004BT 891MΩ mdash mdash mdash mdash mdash095BNT-005BT 016MΩ 029MΩ 003 nF 173 nF 400 120583s 050ms094BNT-006BT 022MΩ 049MΩ 062 nF 246 nF 014ms 117ms092BNT-008BT 018MΩ 032MΩ 0003 nF 264 nF 047120583s 086ms090BNT-010BT 035MΩ 063MΩ 211 nF 216 nF 074ms 136ms

mechanism such as the electrode effects is identified in thestudied frequency range Table 2 shows the barium titanate(dopant) concentration dependent variation of grain (bulkor intrinsic) and grain-boundary related relaxation times 120591

119892

(= 119877119892lowast 119862119892) and 120591gb(= 119877gb lowast 119862gb) for (1 minus 119909)BNT-119909BT

compositions 119877119892and 119877gb at the specified temperature are

evaluated from the intercepts of the corresponding semicir-cles on the1198851015840-axis that is from the semicircle diameter while119862119892and 119862gb are evaluated from the values of frequency at the

peaks (= 119891max) in the 11988510158401015840(119891) plots by using the relation 120596119898120591119898

= 1 that is 120596max = 1RC because 119891max corresponds to therelaxation frequency Evaluated parameters using the aboverelations show thatfor BNT and 098 BNT-002 BT both thetime periods tend to increase while they decrease in the caseof 095 BNT-005 BT 120591

119892continuously increases to reach a

maximum value of 074ms for 090 BNT-010 BT composi-tion and 120591gb also reaches a maximum value of 136ms for090 BNT-010 BT composition but for the compositions inbetween 095 BNT-005 BT and 090 BNT-010 BT it showsan increasing decreasing and then again increasing trendswith increasing concentration of dopant (barium titanate) indifferent compositions

36 Complex Modulus Analysis Complex modulus formal-ism is a very important and convenient alternative toolfor impedance spectroscopy with additional advantages ascompared to those in complex impedance spectroscopy (CIS)in determining analyzing and interpreting the dynamicalaspects of electrical transport phenomena (ie parameterssuch as carrierion hopping rate and conductivity relaxationtime) It provides an insight into the electrical processes char-acterized by the smallest capacitance of the material In orderto analyze and interpret experimental data it is essentialto have a model equivalent circuit that provides a realisticrepresentation of the electrical properties The modulusrepresentation suppresses the unwanted effects of extrinsicrelaxation often used in the analysis of dynamic conductivi-ties of ionically conducting glasses and is also frequently usedin the analysis of dielectric data of ionic conductors [23] Theadvantage of adopting complex electrical modulus spectrais that it can discriminate against electrode polarization andgrain-boundary conduction process Using electric modulusanalysis it is easier to relate this phenomenon to otherproperties especially the dynamical mechanical modulusand can be written as a single function of conductivity

01 1 10 100 1000

0

02

04

06

08

1

12

Frequency (kHz)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

119885998400998400

(MΩ

)

Figure 3 Frequency dependence of 11988510158401015840 of (1 minus 119909)BNT-119909BT (119909 = 0002 004 005 006 008 and 1) ceramics at 450∘C

Moynihan et al [24] and Moynihan [25] have given detailedanalyses of the electric modulus formalism and applicationof the Kohlrausch decay functionThe Kohlrausch-Williams-Watts (KWW) function which in our case will be theKohlrausch electrical relaxation function is given by 120593(119905) =exp [minus(119905120591)120573] with 0 lt 120573 lt 1 For a realistic assessmentof the modulus formalism it is important to realize thatit is based on the description of electric response of thesample in terms of the macroscopic field decay function 120593(119905)Empirically the KWW function is a convenient choice for120593(119905) and the nonexponential parameter 120573 is suitably variedto fit the dataThe peak position of frequency in lossmodulusspectra gives the most probable relaxation time from thecondition 120596

119898120591119898= 1 as detailed under the section of CIS

The most probable relaxation time also obeys the Arrheniusrelation 120596

119898= 120596oexp(minus119864119886119896119861119879) From the spectra it can be

observed that below the Curie temperature bulk propertiesof ceramic samples come from the grain capacitance of thematerials Semicircles were drawn by fitting the data pointsmanually Two distinguished semicircles could be drawn

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

2 ISRN Ceramics

(rhombohedralmonoclinic) tetragonal phases was assumed)was attained Many of the researchers from all over the worldhave reported the MPB composition to lie within 119909 = 005ndash008 for (1 minus 119909)BNT-119909BT A recent literature has reportedan exhaustive study on (1 minus 119909)BNT-119909BT [18] However inview of some of the important and yet untouched aspectsand properties of the (1 minus 119909)BNT-119909BT ceramic system thepresentwork is aimed at studying the piezoelectric propertiesimpedancemodulus spectroscopy and conductivity of the(1 minus 119909)BNT-119909BT(119909 = 0 002 004 005 006 008 010 and10) ceramic system By knowing the conduction mechanismwithin a material system we can tune their properties andcan use them for particular applications In this contextthe present study of (Na

05Bi05)1minus119909

Ba119909TiO3(1 minus 119909)BNT-119909BT

(0 le 119909 le 1) ceramics is assumed worthwhile in probingthe conduction mechanism in detail which may be helpful intailoring the electrical characteristics for desired applications

2 Experimental

Polycrystalline samples having the nominal formula(Bi05Na05)1minus119909

Ba119909TiO3 (1 minus 119909)BNT-119909BT were prepared

by a high temperature solid-state reaction technique usingoxides Bi

2O3 Na2CO3 BaCO

3and TiO

2(HiMedia) (having

a purity of more than 995 for each of them) in a suitablestoichiometryThe above ingredients weremixed thoroughlyfirst in air and then in methanol medium using agate mortarand pestle The oxide mixtures were calcined at an optimizedtemperature of 1170∘C for about 3 h in an alumina crucibleThen by adding a small amount of polyvinyl alcohol (PVA)as a binder to the calcined powder circular and rectangulardisk-shaped pellets were fabricated for different compositionsby applying uniaxial pressure of 4ndash6 tons per square inchThe pellets were subsequently sintered at an optimizedtemperature of 1180∘C for about 2 h The XRD spectra weretaken on calcined powders of (1 minus 119909)BNT-119909BT with anX-ray diffractometer (XrsquoPERT-PRO Pan Analytical USA)at room temperature using CuK

120572radiation (120582 = 15405 A)

over a wide range of the Bragg angles (20∘ le 2120579 le 80∘)

The microstructure of the sintered pellets was observedat room temperature from the micrographs obtained byusing a scanning electron microscope (JEOL-JSM840A)Thetemperature-dependent dielectric constant (1205761015840) loss tangent(tan120575) impedance and phase values at various frequencieslike 100Hz 1 kHz 10 kHz 100 kHz and 1MHzwere evaluatedusing the capacitance impedance and phase data obtainedfrom a computer-controlled LCR Hi-Tester (HIOKI 3532-50Japan) on a symmetrical cell of type AgceramicAg whereAg is a conductive paint coated on either side of the pelletLongitudinal piezoelectric charge coefficients (119889

33) of the

poled (1 minus 119909)BNT-119909BT ceramic samples were measuredunder an electric field of about 25 kVmm at 80∘C15minin a silicone oil bath using a PM3500 119889

3311988931

meter (KCFTechnologies USA)

3 Results and Discussion

31 Structural Study Figure 1 shows the XRD patterns ofcalcined (1 minus 119909)BNT-119909BT powder A standard computer

program (POWD) was utilized for the XRD-profile analy-sis Good agreement between the observed and calculatedinterplanar spacing without any trace of extra peaks dueto the constituent oxides was found thereby suggesting theformation of a biphasic pure compound All the reflectionpeaks of the XRD pattern of the samples were indexed andthe lattice parameters were determined in the monoclinicas well as in tetragonal system of crystals The presence ofmonoclinic and tetragonal phases in the compositions having119909 le 006 and 119909 ge 006 possibly due to its constituentsBNT and BT respectively is endorsed by the splitting ofpeaks 445∘ndash475∘ into two peaks (200) and (002) in the XRDpatterns as shown in Figures 1(a) and 1(b) This splittingbecomes increasingly prominent with the further addition ofBT for 092 BNT-008 BT 090 BNT-010 BT aswell as for purebarium titanate (BT) The apparent particle size and latticestrain of (1minus119909)BNT-119909BT were estimated by analyzing the X-ray diffraction peak broadening using the Williamson-Hallapproach [19]

120573Cos 120579 = 2(Δ120585120585) sin 120579 + 119870120582

119863 (1)

where119863 is the crystallite size 120573 is the diffraction peak widthat half intensity (FWHM) Δ120585120585 is the lattice strain and 119870the Scherrer constant (sim089)However these results have notbeen shown in the paper for brevity sake

32 Tolerance Factor In general the perovskite structure isstable in the region 0880 lt 119905 lt 1090 [18] and the stabilityis higher as the 119905-value is closer to 1 For example the 119905-valueof a cubic SrTiO

3(= 1001) is closer to 1 than that for the

orthorhombic CaTiO3(= 0966)The 119905-value also provides an

indication about how far the atoms can deviate from the idealpacking positions and be still ldquotoleratedrdquo in the perovskitestructure Calculated values of tolerance factors for different(1 minus 119909)BNT-119909BT compositions (119909 = 0 0 02 0 04 005006 008 and 1) using the Goldschmidt formula [20] are veryclose to 1 (lying between minimum = 0985 for BNT andmaximum = 1058 for 090 BNT-010 BT) thus indicating agood stability for all the test samples of the present work

33 Microstructural Study Figure 2 shows the SEM micro-graph of (1 minus 119909)BNT-119909BT (119909 = 0 0 02 004 005 006 008and 1) compositions Grain shapes are clearly visible therebyindicating the existence of polycrystalline microstructureGrains of unequal sizes with less porosity appear to bedistributed throughout the samples The average grain sizewas found with the help of linear intercept method Grainsizes for the chosen compositions were found to range 18ndash35 120583m generally decreasing with increasing barium titanatecontent as detailed in Table 1 Of these the 096 BNT-004 BTcomposition (whose SEM image is shown in Figure 2(c))showed the highest porosity and irregular shaped unequalsized grains as compared with those of others The SEMmicrograph of 094 BNT-006 BT (Figure 2(e)) also showsslight porosity and inequality in grain size Here it would notbe inopportune tomention that BT has been fabricated undera different condition than that for (1 minus 119909)BNT-119909BT [21] and

ISRN Ceramics 3

20 25 30 35 40 45 50 55 60 65 70 75 80

1

0100080060050040020

Peak position (deg)

119909

(a)

445 45 455 46 465 47 475

1

x

01

008

006

005

004

002

0

Peak position (deg)

(b)

Figure 1 (a) X-ray diffraction patterns and (b) expanded X-ray diffraction patterns of (Bi05Na05)1minus119909

Ba119909TiO3ceramics (119909 = 00 002 004

005 006 008 010 and 10)

119909 = 0

(a)

119909 = 002

(b)

119909 = 004

(c)

119909 = 005

(d)

119909 = 006

(e)

119909 = 008

(f)

119909 = 01

(g)

119909 = 1

(h)

Figure 2 SEM micrographs of (Na05Bi05)1minus119909

Ba119909TiO3(119909 = 0 002 004 005 006 008 010 and 10) compositions

Table 1 The values of density grain size dielectric constant (120576119903) loss tangent (tan 120575) and piezoelectric coefficient (119889

33) at room temperature

of (Bi05Na05)1minus119909Ba119909TiO3 samples

Samples Density (gcm3) Grain size (120583m) 120576119903(RT10 kHz) tan 120575 (RT10 kHz) 119889

33(pCN)

BNT 485 351 673 026 17098BNT-002BT 5008 182 672 032 22096BNT-004BT 5078 297 545 011 50095BNT-005BT 5144 308 724 047 95094BNT-006BT 5234 301 871 008 124092BNT-008BT 5248 24 951 011 112090BNT-010BT 5382 276 1110 009 103BT 602 16 1200 003 101 plusmn 5

4 ISRN Ceramics

the XRD data and SEM image for barium titanate have alsobeen taken from the previousworks of our group [21] and thevalue of longitudinal piezoelectric charge coefficient (119889

33) for

it has been taken from the literature [22] for comparison sake

34 Piezoelectric Study Minimum and maximum valuesof longitudinal piezoelectric charge coefficient (119889

33) of the

ceramic samples poled under an electric field of about25 kVmm in a silicone oil bath at 80∘C15min were foundto be sim17 pCN and 124 pCN for BNT and 094 BNT-006 BTcompositions respectively as given in Table 1 A high valueof 11988933

for 094 BNT-006 BT may be supposed to be dueto the presence of morphotropic phase boundary (MPB)composition (where both monoclinic and tetragonal phasesare supposed to coexist) as detailed before

35 Complex Impedance Spectroscopic Analysis Compleximpedance spectroscopy (CIS) is a powerful tool for char-acterizing many of the electrical properties of materials andtheir interfaces with electronically conducting electrodesIt may be used to investigate the dynamics of bound ormobile charges in the bulk or interfacial regions of anykind of solid or liquid material ionic semiconductingmixed electronic-ionic and even insulators (dielectrics) Anequivalent circuit based on impedance and electric modulusspectra provides the physical processes occurring inside thesample Most of the real ceramics contain grains and grain-boundary regions which individually have very differentphysical properties These regions are well observed in theimpedance and modulus spectra The electrical propertiesof the present material system have been investigated usingCIS technique Electrical ac data may be presented in any ofthe four interrelated formalism relative permittivity (120576lowast) =1205761015840minus 11989512057610158401015840 impedance (119885lowast) = 1198851015840 minus 11989511988510158401015840 = 1119895120596119862

0120576lowast electric

modulus (119872lowast) = 1198721015840+ 119895119872

10158401015840= 1120576

lowast admittance (119884lowast) =1198841015840+ 11989511988410158401015840= 119895120596119862

0120576lowast and tan 120575 = 120576

101584010158401205761015840= 119872

101584010158401198721015840=

119885101584011988510158401015840= 119884101584010158401198841015840 where 120596 (= 2120587119891) is the angular frequency

1198620= 1205760119860119905 is the geometrical capacitance 119895 = radic minus 1 120576

0is

the permittivity of free space (= 8854 times 10minus12 Fmminus1) 119905and119860 are the thickness and area of the pellet respectively andrelative permittivity (1205761015840) = 119862

1199011198620 Here 119862

119901is the parallel

capacitance and 120575 the loss angle is the complementary(=90 minus 120579) to the phase angle (120579) both of which are directlyobserved by the LCR Hi-Tester The modulus (|119885|) of thecomplex impedance (119885lowast) is directly observed by the LCRHi-Tester so that 119885cos120579 (= 1198851015840) and 119885sin120579 (= 11988510158401015840) respectivelygive the real and imaginary parts of the impedance (119885lowast) Thefrequency dependence of1198851015840 for (1minus119909)BNT-119909BT (119909 = 0 002004 005 006 008 and 1) ceramics at several temperaturesbetween ambient temperature and 450∘C is observed (butnot shown by plots for brevity sake) At lower tempera-tures 1198851015840 decreases monotonically with increasing frequencyup to a certain frequency and then becomes frequency-independent Only at the highest chosen temperature that isat 450∘C 1198851015840(119891) plots tend to provide peaks below the lowestmeasurement frequency range that is 100Hz The highervalues of 1198851015840 at comparatively lower frequencies and lowertemperatures mean that the polarization in the test material

is larger under the aforesaid conditions The temperaturewhere this change occurs varies with frequency in differentmaterialsThis also means that the resistive grain-boundariesbecome conductive at these temperatures This also showsthat the grain-boundaries are not relaxing even at very highfrequencies and higher temperatures 11988510158401015840(119891) plots (althoughnot shown in the present paper for brevity sake) showedalmost identical monotonically decreasing type of variationup to a certain frequency limit beyond which they mergetogether to show frequency-independent nature of variationextending up to the highest frequency limit at all the chosentemperatures except at the highest one that is at 450∘Cin which case all the 11988510158401015840(119891) plots give peaks in the limitingfrequency range of sim122Hzndash364Hz for 094 BNT-006 BTandBNT respectively as shown in Figure 3However bariumtitanate (dopant) concentration-dependent shifting of11988510158401015840(119891)either towards higher or lower frequency side could not beclearly affirmed from the plots Further no peaks were seenfor 096 BNT-004 BT and 090 BNT-010 BT compositionsThe merger of 11988510158401015840 (as well as of 1198851015840) at higher frequen-cies for all the temperatures indicates possible release ofspace charge polarizationaccumulation at the boundariesof homogeneous phases in the applied external field Atlower temperatures 11988510158401015840 decreases monotonically therebysuggesting that the relaxation in the material system at lowertemperatures is absent This means that relaxation speciesare immobile defects and the orientation effects may beassociated Also the magnitude of 1198851015840 and 11988510158401015840 decreases withincreasing frequencies This would imply that relaxation inthe material system is temperature-dependent and thereis apparently not a single relaxation time The electricalbehavior of the system has been studied over a wide rangeof temperature 35ndash450∘C and frequency 100Hzndash1MHz Inorder to study the contribution of various microscopicelements such as intragrain intergrain electrode effect andrelaxation process we have used the Cole-Cole plots analysisFigures 4(a) through 4(g) shows the Cole-Cole plots of thecompounds at different temperatures only 375ndash450∘C and theplot corresponding to 450∘C for different (1 minus 119909)BNT-119909BTcompositions is shown in Figure 4(h) From the data it isapparent that at low temperatures when the resistivities ofthe samples are too high a small portion of the impedancedispersion profile can be detected in the measured frequencyrange and thus making data analysis impossible Since theimpedance measurements performed for all the samplesbelow 375∘C did not present a complete semicircle theycould not be considered for equivalent circuit modelingin this study It can be seen that the semicircles exhibittheir depressed centers below the abscissa representing thedistribution of relaxation timesThis nonideal behavior couldbe attributed to the several factors such as grain orientationgrain-boundary stress-strain phenomena and atomic defectdistribution A series array of two parallel RC combinations[(119877119892 119862119892) (119877gb 119862gb)] in series with a resistor (119877119904) (though the

data of119877119904for any of the samples are not shown in the table for

brevity sake)was found to best fit the experimental data for allthe samples thereby indicating the contribution fromgrain ofthe sample in the high frequency region and from the grain-boundaries in the low frequency region No other relaxation

ISRN Ceramics 5

Table 2 Grain (bulk)(grain-boundary) resistances (119877119892119877gb) capacitances (119862119892119862gb) and the corresponding relaxation times (120591

119892120591gb) at

450∘C for (1 minus 119909)BNT-119909BT ceramic

Composition 119877119892

Rgb 119862119892

119862gb 120591119892

120591gb

BNT 028MΩ 047MΩ 112 nF 114 nF 034ms 054ms098BNT-002BT 068MΩ 097MΩ 069 nF 082 nF 047ms 080ms096BNT-004BT 891MΩ mdash mdash mdash mdash mdash095BNT-005BT 016MΩ 029MΩ 003 nF 173 nF 400 120583s 050ms094BNT-006BT 022MΩ 049MΩ 062 nF 246 nF 014ms 117ms092BNT-008BT 018MΩ 032MΩ 0003 nF 264 nF 047120583s 086ms090BNT-010BT 035MΩ 063MΩ 211 nF 216 nF 074ms 136ms

mechanism such as the electrode effects is identified in thestudied frequency range Table 2 shows the barium titanate(dopant) concentration dependent variation of grain (bulkor intrinsic) and grain-boundary related relaxation times 120591

119892

(= 119877119892lowast 119862119892) and 120591gb(= 119877gb lowast 119862gb) for (1 minus 119909)BNT-119909BT

compositions 119877119892and 119877gb at the specified temperature are

evaluated from the intercepts of the corresponding semicir-cles on the1198851015840-axis that is from the semicircle diameter while119862119892and 119862gb are evaluated from the values of frequency at the

peaks (= 119891max) in the 11988510158401015840(119891) plots by using the relation 120596119898120591119898

= 1 that is 120596max = 1RC because 119891max corresponds to therelaxation frequency Evaluated parameters using the aboverelations show thatfor BNT and 098 BNT-002 BT both thetime periods tend to increase while they decrease in the caseof 095 BNT-005 BT 120591

119892continuously increases to reach a

maximum value of 074ms for 090 BNT-010 BT composi-tion and 120591gb also reaches a maximum value of 136ms for090 BNT-010 BT composition but for the compositions inbetween 095 BNT-005 BT and 090 BNT-010 BT it showsan increasing decreasing and then again increasing trendswith increasing concentration of dopant (barium titanate) indifferent compositions

36 Complex Modulus Analysis Complex modulus formal-ism is a very important and convenient alternative toolfor impedance spectroscopy with additional advantages ascompared to those in complex impedance spectroscopy (CIS)in determining analyzing and interpreting the dynamicalaspects of electrical transport phenomena (ie parameterssuch as carrierion hopping rate and conductivity relaxationtime) It provides an insight into the electrical processes char-acterized by the smallest capacitance of the material In orderto analyze and interpret experimental data it is essentialto have a model equivalent circuit that provides a realisticrepresentation of the electrical properties The modulusrepresentation suppresses the unwanted effects of extrinsicrelaxation often used in the analysis of dynamic conductivi-ties of ionically conducting glasses and is also frequently usedin the analysis of dielectric data of ionic conductors [23] Theadvantage of adopting complex electrical modulus spectrais that it can discriminate against electrode polarization andgrain-boundary conduction process Using electric modulusanalysis it is easier to relate this phenomenon to otherproperties especially the dynamical mechanical modulusand can be written as a single function of conductivity

01 1 10 100 1000

0

02

04

06

08

1

12

Frequency (kHz)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

119885998400998400

(MΩ

)

Figure 3 Frequency dependence of 11988510158401015840 of (1 minus 119909)BNT-119909BT (119909 = 0002 004 005 006 008 and 1) ceramics at 450∘C

Moynihan et al [24] and Moynihan [25] have given detailedanalyses of the electric modulus formalism and applicationof the Kohlrausch decay functionThe Kohlrausch-Williams-Watts (KWW) function which in our case will be theKohlrausch electrical relaxation function is given by 120593(119905) =exp [minus(119905120591)120573] with 0 lt 120573 lt 1 For a realistic assessmentof the modulus formalism it is important to realize thatit is based on the description of electric response of thesample in terms of the macroscopic field decay function 120593(119905)Empirically the KWW function is a convenient choice for120593(119905) and the nonexponential parameter 120573 is suitably variedto fit the dataThe peak position of frequency in lossmodulusspectra gives the most probable relaxation time from thecondition 120596

119898120591119898= 1 as detailed under the section of CIS

The most probable relaxation time also obeys the Arrheniusrelation 120596

119898= 120596oexp(minus119864119886119896119861119879) From the spectra it can be

observed that below the Curie temperature bulk propertiesof ceramic samples come from the grain capacitance of thematerials Semicircles were drawn by fitting the data pointsmanually Two distinguished semicircles could be drawn

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Ceramics 3

20 25 30 35 40 45 50 55 60 65 70 75 80

1

0100080060050040020

Peak position (deg)

119909

(a)

445 45 455 46 465 47 475

1

x

01

008

006

005

004

002

0

Peak position (deg)

(b)

Figure 1 (a) X-ray diffraction patterns and (b) expanded X-ray diffraction patterns of (Bi05Na05)1minus119909

Ba119909TiO3ceramics (119909 = 00 002 004

005 006 008 010 and 10)

119909 = 0

(a)

119909 = 002

(b)

119909 = 004

(c)

119909 = 005

(d)

119909 = 006

(e)

119909 = 008

(f)

119909 = 01

(g)

119909 = 1

(h)

Figure 2 SEM micrographs of (Na05Bi05)1minus119909

Ba119909TiO3(119909 = 0 002 004 005 006 008 010 and 10) compositions

Table 1 The values of density grain size dielectric constant (120576119903) loss tangent (tan 120575) and piezoelectric coefficient (119889

33) at room temperature

of (Bi05Na05)1minus119909Ba119909TiO3 samples

Samples Density (gcm3) Grain size (120583m) 120576119903(RT10 kHz) tan 120575 (RT10 kHz) 119889

33(pCN)

BNT 485 351 673 026 17098BNT-002BT 5008 182 672 032 22096BNT-004BT 5078 297 545 011 50095BNT-005BT 5144 308 724 047 95094BNT-006BT 5234 301 871 008 124092BNT-008BT 5248 24 951 011 112090BNT-010BT 5382 276 1110 009 103BT 602 16 1200 003 101 plusmn 5

4 ISRN Ceramics

the XRD data and SEM image for barium titanate have alsobeen taken from the previousworks of our group [21] and thevalue of longitudinal piezoelectric charge coefficient (119889

33) for

it has been taken from the literature [22] for comparison sake

34 Piezoelectric Study Minimum and maximum valuesof longitudinal piezoelectric charge coefficient (119889

33) of the

ceramic samples poled under an electric field of about25 kVmm in a silicone oil bath at 80∘C15min were foundto be sim17 pCN and 124 pCN for BNT and 094 BNT-006 BTcompositions respectively as given in Table 1 A high valueof 11988933

for 094 BNT-006 BT may be supposed to be dueto the presence of morphotropic phase boundary (MPB)composition (where both monoclinic and tetragonal phasesare supposed to coexist) as detailed before

35 Complex Impedance Spectroscopic Analysis Compleximpedance spectroscopy (CIS) is a powerful tool for char-acterizing many of the electrical properties of materials andtheir interfaces with electronically conducting electrodesIt may be used to investigate the dynamics of bound ormobile charges in the bulk or interfacial regions of anykind of solid or liquid material ionic semiconductingmixed electronic-ionic and even insulators (dielectrics) Anequivalent circuit based on impedance and electric modulusspectra provides the physical processes occurring inside thesample Most of the real ceramics contain grains and grain-boundary regions which individually have very differentphysical properties These regions are well observed in theimpedance and modulus spectra The electrical propertiesof the present material system have been investigated usingCIS technique Electrical ac data may be presented in any ofthe four interrelated formalism relative permittivity (120576lowast) =1205761015840minus 11989512057610158401015840 impedance (119885lowast) = 1198851015840 minus 11989511988510158401015840 = 1119895120596119862

0120576lowast electric

modulus (119872lowast) = 1198721015840+ 119895119872

10158401015840= 1120576

lowast admittance (119884lowast) =1198841015840+ 11989511988410158401015840= 119895120596119862

0120576lowast and tan 120575 = 120576

101584010158401205761015840= 119872

101584010158401198721015840=

119885101584011988510158401015840= 119884101584010158401198841015840 where 120596 (= 2120587119891) is the angular frequency

1198620= 1205760119860119905 is the geometrical capacitance 119895 = radic minus 1 120576

0is

the permittivity of free space (= 8854 times 10minus12 Fmminus1) 119905and119860 are the thickness and area of the pellet respectively andrelative permittivity (1205761015840) = 119862

1199011198620 Here 119862

119901is the parallel

capacitance and 120575 the loss angle is the complementary(=90 minus 120579) to the phase angle (120579) both of which are directlyobserved by the LCR Hi-Tester The modulus (|119885|) of thecomplex impedance (119885lowast) is directly observed by the LCRHi-Tester so that 119885cos120579 (= 1198851015840) and 119885sin120579 (= 11988510158401015840) respectivelygive the real and imaginary parts of the impedance (119885lowast) Thefrequency dependence of1198851015840 for (1minus119909)BNT-119909BT (119909 = 0 002004 005 006 008 and 1) ceramics at several temperaturesbetween ambient temperature and 450∘C is observed (butnot shown by plots for brevity sake) At lower tempera-tures 1198851015840 decreases monotonically with increasing frequencyup to a certain frequency and then becomes frequency-independent Only at the highest chosen temperature that isat 450∘C 1198851015840(119891) plots tend to provide peaks below the lowestmeasurement frequency range that is 100Hz The highervalues of 1198851015840 at comparatively lower frequencies and lowertemperatures mean that the polarization in the test material

is larger under the aforesaid conditions The temperaturewhere this change occurs varies with frequency in differentmaterialsThis also means that the resistive grain-boundariesbecome conductive at these temperatures This also showsthat the grain-boundaries are not relaxing even at very highfrequencies and higher temperatures 11988510158401015840(119891) plots (althoughnot shown in the present paper for brevity sake) showedalmost identical monotonically decreasing type of variationup to a certain frequency limit beyond which they mergetogether to show frequency-independent nature of variationextending up to the highest frequency limit at all the chosentemperatures except at the highest one that is at 450∘Cin which case all the 11988510158401015840(119891) plots give peaks in the limitingfrequency range of sim122Hzndash364Hz for 094 BNT-006 BTandBNT respectively as shown in Figure 3However bariumtitanate (dopant) concentration-dependent shifting of11988510158401015840(119891)either towards higher or lower frequency side could not beclearly affirmed from the plots Further no peaks were seenfor 096 BNT-004 BT and 090 BNT-010 BT compositionsThe merger of 11988510158401015840 (as well as of 1198851015840) at higher frequen-cies for all the temperatures indicates possible release ofspace charge polarizationaccumulation at the boundariesof homogeneous phases in the applied external field Atlower temperatures 11988510158401015840 decreases monotonically therebysuggesting that the relaxation in the material system at lowertemperatures is absent This means that relaxation speciesare immobile defects and the orientation effects may beassociated Also the magnitude of 1198851015840 and 11988510158401015840 decreases withincreasing frequencies This would imply that relaxation inthe material system is temperature-dependent and thereis apparently not a single relaxation time The electricalbehavior of the system has been studied over a wide rangeof temperature 35ndash450∘C and frequency 100Hzndash1MHz Inorder to study the contribution of various microscopicelements such as intragrain intergrain electrode effect andrelaxation process we have used the Cole-Cole plots analysisFigures 4(a) through 4(g) shows the Cole-Cole plots of thecompounds at different temperatures only 375ndash450∘C and theplot corresponding to 450∘C for different (1 minus 119909)BNT-119909BTcompositions is shown in Figure 4(h) From the data it isapparent that at low temperatures when the resistivities ofthe samples are too high a small portion of the impedancedispersion profile can be detected in the measured frequencyrange and thus making data analysis impossible Since theimpedance measurements performed for all the samplesbelow 375∘C did not present a complete semicircle theycould not be considered for equivalent circuit modelingin this study It can be seen that the semicircles exhibittheir depressed centers below the abscissa representing thedistribution of relaxation timesThis nonideal behavior couldbe attributed to the several factors such as grain orientationgrain-boundary stress-strain phenomena and atomic defectdistribution A series array of two parallel RC combinations[(119877119892 119862119892) (119877gb 119862gb)] in series with a resistor (119877119904) (though the

data of119877119904for any of the samples are not shown in the table for

brevity sake)was found to best fit the experimental data for allthe samples thereby indicating the contribution fromgrain ofthe sample in the high frequency region and from the grain-boundaries in the low frequency region No other relaxation

ISRN Ceramics 5

Table 2 Grain (bulk)(grain-boundary) resistances (119877119892119877gb) capacitances (119862119892119862gb) and the corresponding relaxation times (120591

119892120591gb) at

450∘C for (1 minus 119909)BNT-119909BT ceramic

Composition 119877119892

Rgb 119862119892

119862gb 120591119892

120591gb

BNT 028MΩ 047MΩ 112 nF 114 nF 034ms 054ms098BNT-002BT 068MΩ 097MΩ 069 nF 082 nF 047ms 080ms096BNT-004BT 891MΩ mdash mdash mdash mdash mdash095BNT-005BT 016MΩ 029MΩ 003 nF 173 nF 400 120583s 050ms094BNT-006BT 022MΩ 049MΩ 062 nF 246 nF 014ms 117ms092BNT-008BT 018MΩ 032MΩ 0003 nF 264 nF 047120583s 086ms090BNT-010BT 035MΩ 063MΩ 211 nF 216 nF 074ms 136ms

mechanism such as the electrode effects is identified in thestudied frequency range Table 2 shows the barium titanate(dopant) concentration dependent variation of grain (bulkor intrinsic) and grain-boundary related relaxation times 120591

119892

(= 119877119892lowast 119862119892) and 120591gb(= 119877gb lowast 119862gb) for (1 minus 119909)BNT-119909BT

compositions 119877119892and 119877gb at the specified temperature are

evaluated from the intercepts of the corresponding semicir-cles on the1198851015840-axis that is from the semicircle diameter while119862119892and 119862gb are evaluated from the values of frequency at the

peaks (= 119891max) in the 11988510158401015840(119891) plots by using the relation 120596119898120591119898

= 1 that is 120596max = 1RC because 119891max corresponds to therelaxation frequency Evaluated parameters using the aboverelations show thatfor BNT and 098 BNT-002 BT both thetime periods tend to increase while they decrease in the caseof 095 BNT-005 BT 120591

119892continuously increases to reach a

maximum value of 074ms for 090 BNT-010 BT composi-tion and 120591gb also reaches a maximum value of 136ms for090 BNT-010 BT composition but for the compositions inbetween 095 BNT-005 BT and 090 BNT-010 BT it showsan increasing decreasing and then again increasing trendswith increasing concentration of dopant (barium titanate) indifferent compositions

36 Complex Modulus Analysis Complex modulus formal-ism is a very important and convenient alternative toolfor impedance spectroscopy with additional advantages ascompared to those in complex impedance spectroscopy (CIS)in determining analyzing and interpreting the dynamicalaspects of electrical transport phenomena (ie parameterssuch as carrierion hopping rate and conductivity relaxationtime) It provides an insight into the electrical processes char-acterized by the smallest capacitance of the material In orderto analyze and interpret experimental data it is essentialto have a model equivalent circuit that provides a realisticrepresentation of the electrical properties The modulusrepresentation suppresses the unwanted effects of extrinsicrelaxation often used in the analysis of dynamic conductivi-ties of ionically conducting glasses and is also frequently usedin the analysis of dielectric data of ionic conductors [23] Theadvantage of adopting complex electrical modulus spectrais that it can discriminate against electrode polarization andgrain-boundary conduction process Using electric modulusanalysis it is easier to relate this phenomenon to otherproperties especially the dynamical mechanical modulusand can be written as a single function of conductivity

01 1 10 100 1000

0

02

04

06

08

1

12

Frequency (kHz)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

119885998400998400

(MΩ

)

Figure 3 Frequency dependence of 11988510158401015840 of (1 minus 119909)BNT-119909BT (119909 = 0002 004 005 006 008 and 1) ceramics at 450∘C

Moynihan et al [24] and Moynihan [25] have given detailedanalyses of the electric modulus formalism and applicationof the Kohlrausch decay functionThe Kohlrausch-Williams-Watts (KWW) function which in our case will be theKohlrausch electrical relaxation function is given by 120593(119905) =exp [minus(119905120591)120573] with 0 lt 120573 lt 1 For a realistic assessmentof the modulus formalism it is important to realize thatit is based on the description of electric response of thesample in terms of the macroscopic field decay function 120593(119905)Empirically the KWW function is a convenient choice for120593(119905) and the nonexponential parameter 120573 is suitably variedto fit the dataThe peak position of frequency in lossmodulusspectra gives the most probable relaxation time from thecondition 120596

119898120591119898= 1 as detailed under the section of CIS

The most probable relaxation time also obeys the Arrheniusrelation 120596

119898= 120596oexp(minus119864119886119896119861119879) From the spectra it can be

observed that below the Curie temperature bulk propertiesof ceramic samples come from the grain capacitance of thematerials Semicircles were drawn by fitting the data pointsmanually Two distinguished semicircles could be drawn

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

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Journal ofNanomaterials

4 ISRN Ceramics

the XRD data and SEM image for barium titanate have alsobeen taken from the previousworks of our group [21] and thevalue of longitudinal piezoelectric charge coefficient (119889

33) for

it has been taken from the literature [22] for comparison sake

34 Piezoelectric Study Minimum and maximum valuesof longitudinal piezoelectric charge coefficient (119889

33) of the

ceramic samples poled under an electric field of about25 kVmm in a silicone oil bath at 80∘C15min were foundto be sim17 pCN and 124 pCN for BNT and 094 BNT-006 BTcompositions respectively as given in Table 1 A high valueof 11988933

for 094 BNT-006 BT may be supposed to be dueto the presence of morphotropic phase boundary (MPB)composition (where both monoclinic and tetragonal phasesare supposed to coexist) as detailed before

35 Complex Impedance Spectroscopic Analysis Compleximpedance spectroscopy (CIS) is a powerful tool for char-acterizing many of the electrical properties of materials andtheir interfaces with electronically conducting electrodesIt may be used to investigate the dynamics of bound ormobile charges in the bulk or interfacial regions of anykind of solid or liquid material ionic semiconductingmixed electronic-ionic and even insulators (dielectrics) Anequivalent circuit based on impedance and electric modulusspectra provides the physical processes occurring inside thesample Most of the real ceramics contain grains and grain-boundary regions which individually have very differentphysical properties These regions are well observed in theimpedance and modulus spectra The electrical propertiesof the present material system have been investigated usingCIS technique Electrical ac data may be presented in any ofthe four interrelated formalism relative permittivity (120576lowast) =1205761015840minus 11989512057610158401015840 impedance (119885lowast) = 1198851015840 minus 11989511988510158401015840 = 1119895120596119862

0120576lowast electric

modulus (119872lowast) = 1198721015840+ 119895119872

10158401015840= 1120576

lowast admittance (119884lowast) =1198841015840+ 11989511988410158401015840= 119895120596119862

0120576lowast and tan 120575 = 120576

101584010158401205761015840= 119872

101584010158401198721015840=

119885101584011988510158401015840= 119884101584010158401198841015840 where 120596 (= 2120587119891) is the angular frequency

1198620= 1205760119860119905 is the geometrical capacitance 119895 = radic minus 1 120576

0is

the permittivity of free space (= 8854 times 10minus12 Fmminus1) 119905and119860 are the thickness and area of the pellet respectively andrelative permittivity (1205761015840) = 119862

1199011198620 Here 119862

119901is the parallel

capacitance and 120575 the loss angle is the complementary(=90 minus 120579) to the phase angle (120579) both of which are directlyobserved by the LCR Hi-Tester The modulus (|119885|) of thecomplex impedance (119885lowast) is directly observed by the LCRHi-Tester so that 119885cos120579 (= 1198851015840) and 119885sin120579 (= 11988510158401015840) respectivelygive the real and imaginary parts of the impedance (119885lowast) Thefrequency dependence of1198851015840 for (1minus119909)BNT-119909BT (119909 = 0 002004 005 006 008 and 1) ceramics at several temperaturesbetween ambient temperature and 450∘C is observed (butnot shown by plots for brevity sake) At lower tempera-tures 1198851015840 decreases monotonically with increasing frequencyup to a certain frequency and then becomes frequency-independent Only at the highest chosen temperature that isat 450∘C 1198851015840(119891) plots tend to provide peaks below the lowestmeasurement frequency range that is 100Hz The highervalues of 1198851015840 at comparatively lower frequencies and lowertemperatures mean that the polarization in the test material

is larger under the aforesaid conditions The temperaturewhere this change occurs varies with frequency in differentmaterialsThis also means that the resistive grain-boundariesbecome conductive at these temperatures This also showsthat the grain-boundaries are not relaxing even at very highfrequencies and higher temperatures 11988510158401015840(119891) plots (althoughnot shown in the present paper for brevity sake) showedalmost identical monotonically decreasing type of variationup to a certain frequency limit beyond which they mergetogether to show frequency-independent nature of variationextending up to the highest frequency limit at all the chosentemperatures except at the highest one that is at 450∘Cin which case all the 11988510158401015840(119891) plots give peaks in the limitingfrequency range of sim122Hzndash364Hz for 094 BNT-006 BTandBNT respectively as shown in Figure 3However bariumtitanate (dopant) concentration-dependent shifting of11988510158401015840(119891)either towards higher or lower frequency side could not beclearly affirmed from the plots Further no peaks were seenfor 096 BNT-004 BT and 090 BNT-010 BT compositionsThe merger of 11988510158401015840 (as well as of 1198851015840) at higher frequen-cies for all the temperatures indicates possible release ofspace charge polarizationaccumulation at the boundariesof homogeneous phases in the applied external field Atlower temperatures 11988510158401015840 decreases monotonically therebysuggesting that the relaxation in the material system at lowertemperatures is absent This means that relaxation speciesare immobile defects and the orientation effects may beassociated Also the magnitude of 1198851015840 and 11988510158401015840 decreases withincreasing frequencies This would imply that relaxation inthe material system is temperature-dependent and thereis apparently not a single relaxation time The electricalbehavior of the system has been studied over a wide rangeof temperature 35ndash450∘C and frequency 100Hzndash1MHz Inorder to study the contribution of various microscopicelements such as intragrain intergrain electrode effect andrelaxation process we have used the Cole-Cole plots analysisFigures 4(a) through 4(g) shows the Cole-Cole plots of thecompounds at different temperatures only 375ndash450∘C and theplot corresponding to 450∘C for different (1 minus 119909)BNT-119909BTcompositions is shown in Figure 4(h) From the data it isapparent that at low temperatures when the resistivities ofthe samples are too high a small portion of the impedancedispersion profile can be detected in the measured frequencyrange and thus making data analysis impossible Since theimpedance measurements performed for all the samplesbelow 375∘C did not present a complete semicircle theycould not be considered for equivalent circuit modelingin this study It can be seen that the semicircles exhibittheir depressed centers below the abscissa representing thedistribution of relaxation timesThis nonideal behavior couldbe attributed to the several factors such as grain orientationgrain-boundary stress-strain phenomena and atomic defectdistribution A series array of two parallel RC combinations[(119877119892 119862119892) (119877gb 119862gb)] in series with a resistor (119877119904) (though the

data of119877119904for any of the samples are not shown in the table for

brevity sake)was found to best fit the experimental data for allthe samples thereby indicating the contribution fromgrain ofthe sample in the high frequency region and from the grain-boundaries in the low frequency region No other relaxation

ISRN Ceramics 5

Table 2 Grain (bulk)(grain-boundary) resistances (119877119892119877gb) capacitances (119862119892119862gb) and the corresponding relaxation times (120591

119892120591gb) at

450∘C for (1 minus 119909)BNT-119909BT ceramic

Composition 119877119892

Rgb 119862119892

119862gb 120591119892

120591gb

BNT 028MΩ 047MΩ 112 nF 114 nF 034ms 054ms098BNT-002BT 068MΩ 097MΩ 069 nF 082 nF 047ms 080ms096BNT-004BT 891MΩ mdash mdash mdash mdash mdash095BNT-005BT 016MΩ 029MΩ 003 nF 173 nF 400 120583s 050ms094BNT-006BT 022MΩ 049MΩ 062 nF 246 nF 014ms 117ms092BNT-008BT 018MΩ 032MΩ 0003 nF 264 nF 047120583s 086ms090BNT-010BT 035MΩ 063MΩ 211 nF 216 nF 074ms 136ms

mechanism such as the electrode effects is identified in thestudied frequency range Table 2 shows the barium titanate(dopant) concentration dependent variation of grain (bulkor intrinsic) and grain-boundary related relaxation times 120591

119892

(= 119877119892lowast 119862119892) and 120591gb(= 119877gb lowast 119862gb) for (1 minus 119909)BNT-119909BT

compositions 119877119892and 119877gb at the specified temperature are

evaluated from the intercepts of the corresponding semicir-cles on the1198851015840-axis that is from the semicircle diameter while119862119892and 119862gb are evaluated from the values of frequency at the

peaks (= 119891max) in the 11988510158401015840(119891) plots by using the relation 120596119898120591119898

= 1 that is 120596max = 1RC because 119891max corresponds to therelaxation frequency Evaluated parameters using the aboverelations show thatfor BNT and 098 BNT-002 BT both thetime periods tend to increase while they decrease in the caseof 095 BNT-005 BT 120591

119892continuously increases to reach a

maximum value of 074ms for 090 BNT-010 BT composi-tion and 120591gb also reaches a maximum value of 136ms for090 BNT-010 BT composition but for the compositions inbetween 095 BNT-005 BT and 090 BNT-010 BT it showsan increasing decreasing and then again increasing trendswith increasing concentration of dopant (barium titanate) indifferent compositions

36 Complex Modulus Analysis Complex modulus formal-ism is a very important and convenient alternative toolfor impedance spectroscopy with additional advantages ascompared to those in complex impedance spectroscopy (CIS)in determining analyzing and interpreting the dynamicalaspects of electrical transport phenomena (ie parameterssuch as carrierion hopping rate and conductivity relaxationtime) It provides an insight into the electrical processes char-acterized by the smallest capacitance of the material In orderto analyze and interpret experimental data it is essentialto have a model equivalent circuit that provides a realisticrepresentation of the electrical properties The modulusrepresentation suppresses the unwanted effects of extrinsicrelaxation often used in the analysis of dynamic conductivi-ties of ionically conducting glasses and is also frequently usedin the analysis of dielectric data of ionic conductors [23] Theadvantage of adopting complex electrical modulus spectrais that it can discriminate against electrode polarization andgrain-boundary conduction process Using electric modulusanalysis it is easier to relate this phenomenon to otherproperties especially the dynamical mechanical modulusand can be written as a single function of conductivity

01 1 10 100 1000

0

02

04

06

08

1

12

Frequency (kHz)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

119885998400998400

(MΩ

)

Figure 3 Frequency dependence of 11988510158401015840 of (1 minus 119909)BNT-119909BT (119909 = 0002 004 005 006 008 and 1) ceramics at 450∘C

Moynihan et al [24] and Moynihan [25] have given detailedanalyses of the electric modulus formalism and applicationof the Kohlrausch decay functionThe Kohlrausch-Williams-Watts (KWW) function which in our case will be theKohlrausch electrical relaxation function is given by 120593(119905) =exp [minus(119905120591)120573] with 0 lt 120573 lt 1 For a realistic assessmentof the modulus formalism it is important to realize thatit is based on the description of electric response of thesample in terms of the macroscopic field decay function 120593(119905)Empirically the KWW function is a convenient choice for120593(119905) and the nonexponential parameter 120573 is suitably variedto fit the dataThe peak position of frequency in lossmodulusspectra gives the most probable relaxation time from thecondition 120596

119898120591119898= 1 as detailed under the section of CIS

The most probable relaxation time also obeys the Arrheniusrelation 120596

119898= 120596oexp(minus119864119886119896119861119879) From the spectra it can be

observed that below the Curie temperature bulk propertiesof ceramic samples come from the grain capacitance of thematerials Semicircles were drawn by fitting the data pointsmanually Two distinguished semicircles could be drawn

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Ceramics 5

Table 2 Grain (bulk)(grain-boundary) resistances (119877119892119877gb) capacitances (119862119892119862gb) and the corresponding relaxation times (120591

119892120591gb) at

450∘C for (1 minus 119909)BNT-119909BT ceramic

Composition 119877119892

Rgb 119862119892

119862gb 120591119892

120591gb

BNT 028MΩ 047MΩ 112 nF 114 nF 034ms 054ms098BNT-002BT 068MΩ 097MΩ 069 nF 082 nF 047ms 080ms096BNT-004BT 891MΩ mdash mdash mdash mdash mdash095BNT-005BT 016MΩ 029MΩ 003 nF 173 nF 400 120583s 050ms094BNT-006BT 022MΩ 049MΩ 062 nF 246 nF 014ms 117ms092BNT-008BT 018MΩ 032MΩ 0003 nF 264 nF 047120583s 086ms090BNT-010BT 035MΩ 063MΩ 211 nF 216 nF 074ms 136ms

mechanism such as the electrode effects is identified in thestudied frequency range Table 2 shows the barium titanate(dopant) concentration dependent variation of grain (bulkor intrinsic) and grain-boundary related relaxation times 120591

119892

(= 119877119892lowast 119862119892) and 120591gb(= 119877gb lowast 119862gb) for (1 minus 119909)BNT-119909BT

compositions 119877119892and 119877gb at the specified temperature are

evaluated from the intercepts of the corresponding semicir-cles on the1198851015840-axis that is from the semicircle diameter while119862119892and 119862gb are evaluated from the values of frequency at the

peaks (= 119891max) in the 11988510158401015840(119891) plots by using the relation 120596119898120591119898

= 1 that is 120596max = 1RC because 119891max corresponds to therelaxation frequency Evaluated parameters using the aboverelations show thatfor BNT and 098 BNT-002 BT both thetime periods tend to increase while they decrease in the caseof 095 BNT-005 BT 120591

119892continuously increases to reach a

maximum value of 074ms for 090 BNT-010 BT composi-tion and 120591gb also reaches a maximum value of 136ms for090 BNT-010 BT composition but for the compositions inbetween 095 BNT-005 BT and 090 BNT-010 BT it showsan increasing decreasing and then again increasing trendswith increasing concentration of dopant (barium titanate) indifferent compositions

36 Complex Modulus Analysis Complex modulus formal-ism is a very important and convenient alternative toolfor impedance spectroscopy with additional advantages ascompared to those in complex impedance spectroscopy (CIS)in determining analyzing and interpreting the dynamicalaspects of electrical transport phenomena (ie parameterssuch as carrierion hopping rate and conductivity relaxationtime) It provides an insight into the electrical processes char-acterized by the smallest capacitance of the material In orderto analyze and interpret experimental data it is essentialto have a model equivalent circuit that provides a realisticrepresentation of the electrical properties The modulusrepresentation suppresses the unwanted effects of extrinsicrelaxation often used in the analysis of dynamic conductivi-ties of ionically conducting glasses and is also frequently usedin the analysis of dielectric data of ionic conductors [23] Theadvantage of adopting complex electrical modulus spectrais that it can discriminate against electrode polarization andgrain-boundary conduction process Using electric modulusanalysis it is easier to relate this phenomenon to otherproperties especially the dynamical mechanical modulusand can be written as a single function of conductivity

01 1 10 100 1000

0

02

04

06

08

1

12

Frequency (kHz)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

119885998400998400

(MΩ

)

Figure 3 Frequency dependence of 11988510158401015840 of (1 minus 119909)BNT-119909BT (119909 = 0002 004 005 006 008 and 1) ceramics at 450∘C

Moynihan et al [24] and Moynihan [25] have given detailedanalyses of the electric modulus formalism and applicationof the Kohlrausch decay functionThe Kohlrausch-Williams-Watts (KWW) function which in our case will be theKohlrausch electrical relaxation function is given by 120593(119905) =exp [minus(119905120591)120573] with 0 lt 120573 lt 1 For a realistic assessmentof the modulus formalism it is important to realize thatit is based on the description of electric response of thesample in terms of the macroscopic field decay function 120593(119905)Empirically the KWW function is a convenient choice for120593(119905) and the nonexponential parameter 120573 is suitably variedto fit the dataThe peak position of frequency in lossmodulusspectra gives the most probable relaxation time from thecondition 120596

119898120591119898= 1 as detailed under the section of CIS

The most probable relaxation time also obeys the Arrheniusrelation 120596

119898= 120596oexp(minus119864119886119896119861119879) From the spectra it can be

observed that below the Curie temperature bulk propertiesof ceramic samples come from the grain capacitance of thematerials Semicircles were drawn by fitting the data pointsmanually Two distinguished semicircles could be drawn

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

6 ISRN Ceramics

0 03 06 09 12 15 180

03

06

09

12

15

18119885998400998400

(MΩ

)

119885998400 (MΩ)

(a)

0 05 1 15 20 250

05

1

15

20

25

119885998400 (MΩ)

(b)

0 02 04 06 08 1 12 140

02

04

06

08

1

12

14

119885998400 (MΩ)

(c)

0 02 04 06 08 10

02

04

06

08

1

119885998400998400

(MΩ

)

119885998400 (MΩ)

(d)

0 01 02 03 04 05 06 070

01

02

03

04

05

06

07

119885998400 (MΩ)

(e)

0 02 04 06 080

02

04

06

08

119885998400 (MΩ)

(f)

0 02 04 06 080

02

04

06

08

119885998400998400

(MΩ

)

119885998400 (MΩ)

375∘C400∘C

425∘C

450∘C

(g)

0 02 04 06 08 1 120

02

04

06

08

1

12

119885998400998400

(MΩ

)

119885998400 (MΩ)

450∘C

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

(h)

Figure 4 (a)ndash(g) Complex impedance plots for (1 minus119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1) ceramics at different temperaturesand (h) corresponding plots at 450∘C

above the Curie temperature specifically at 450∘C for allthe test material system (as depicted in Figures 5(a) through5(f) except for the case of 098 BNT-002 BT as shown inFigure 5(b) in which a lone semicircle corresponding to thegrain-boundary was observed) In this type of formulismthe left semicircle represents the grain-boundary while theright one corresponds to the bulk or the grains inside thetest material These semicircles indicate that both grainand grain-boundary capacitance started active role in theconduction mechanism above the Curie temperature that is

in the paraelectric phase of the material system Howeverno modulus spectrum could be drawn for 096 BNT-004 BTpossibly due to the inhomogeneous and porous nature ofthe sample as evidenced by the SEM image too Under thesaid condition we could not perform the fitting analysisfor the data points in the light of KWW function becauseno prominent peaks for frequency-dependent imaginarypart of electric modulus (11987210158401015840(119891)) spectra correspondingto different temperatures except at sim400ndash450∘C were seenfor our test material system in the specified measurement

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Ceramics 7

998400(times10minus4)

998400 (times

10minus4)

4

35

3

25

2

15

1

05

00 05 1 15 2 25 3 35 4

119872

119872

(a)

998400(times10minus4)0 25 50 75 100

0

25

50

75

100

998400998400(times

10minus4)

119872

119872

(b)

50

40

30

20

10

050403020100

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(c)

25

30

20

15

10

5

03020 25151050

998400(times10minus5)

998400998400(times

10minus5)

119872

119872

(d)

4

35

3

25

2

15

1

05

043 352 251505 10

998400(times10minus4)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(e)

25

20

15

10

5

020 25151050

998400(times10minus5)

450∘C⨀

998400998400(times

10minus4)

119872

119872

(f)

Figure 5 (a)ndash(f) The Nyquist plots in the complex electric modulus plane for (1 minus 119909)BNT-119909BT (119909 = 0 002 004 005 006 008 and 1)ceramic samples corresponding to the data for1198721015840 and11987210158401015840 at 450∘C

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

8 ISRN Ceramics

ranges of temperature and frequency From the Nyquist plotsin the complex electric modulus plane corresponding to450∘C it transpired that for undoped BNT grain-boundariesand grains exhibit almost equal contributions and with anincrease in the content of the dopant barium titanate thegrain contribution appears to diminish with simultaneousenhancement in grain-boundary contribution and this effectcontinues up to the case of 092 BNT-008 BT that is near theMPB composition beyond which again an enhancement incontribution due to grains is seen (as depicted in Figure 5(f))Further the two semicircles appear most separated fromeach other for the case of 095 BNT-005 BT (as shown inFigure 5(c))

37 Conductivity Analysis The real part of ac conductivity iscalculated by using the expression

1205901015840

ac = 1205761015840120576∘120596 tan 120575 (2)

where 120596 (= 2120587119891) is the cyclic frequency f (being thefrequency of measurement) 120576

0is the free space permittivity

(= 885times10minus12 Fmminus1) 1205761015840 is the dielectric constant (=1198621199011198620 as

detailed earlier under CIS section) and tan120575 is the dielectricloss tangent for the test material sample Figures 6(a)ndash6(g)show the log-log plot of ac electrical conductivity (1205901015840ac)versus frequency at different temperatures It is observedfrom these plots (Figure 6) that in the low temperatureregime ac conductivity increased with increase in frequencythereby indicating dispersion of conductivity with frequencyWith increase in temperature dispersion in conductivitynarrowed down and all the curves for different frequenciesappeared to merge at high temperatures although they didnot merge completely The activation energy for conductionwas obtained using the Arrhenius relationship

120590ac = 120590119900 exp(minus119864119886

119896119861119879) (3)

A linear least-squares-fit of the conductivity data to (3) givesthe value of the apparent activation energy 119864

119886 The ac acti-

vation energies were calculated in two different temperatureregions at different frequencies and the values are givenin Table 3 The activation energy values for ac conductivityare found to increase with the increase in temperature It isalso observed that ac conductivity-based activation energycalculated at higher frequencies is lower than that at lowerones in the same temperature range for all the compositionsalbeit not shown in the present work for brevity sake This isdue to the fact that at low frequencies the overall conductivityis due to the mobilitytransportation of charge carriersover long distance rather than from relaxationorientationalmechanism in which case charge mobilitytransportation isrestricted to only the nearest neighbouring lattice sites Theconductivity of the materials has been found to increase withincrease in temperature and merging of the conductivitycurves in the higher temperature region results with therelease of space charge thereby endorsing the results derivedfrom the complex impedance spectroscopic analyses In thelow temperature region (35ndash300∘C) the activation energies

for (1 minus 119909)BNT-119909BT system (where 119909 = 0 002 004 005006 008 and 1) are in the range of 0015ndash016 eV In thisregion conductivity is almost independent of temperatureand this low value of activation energy corresponds tothe intrinsic conduction in the test material system Theactivation energies sim011ndash047 eV in the second temperatureregion (325ndash450∘C) were slightly increased with an increasein temperature thereby suggesting that the conductivity maybe the result of defects and associated charge carriers ofmetal ions such as Na+ Bi3+ and Ba2+ At high sinteringtemperatures bismuth ions are the first to get evaporatedand thereby oxygen vacancies are created for charge neutral-ization Defects such as bismuth 119881Bi

∙∙∙ and oxygen vacancies119881119874

∙∙ are considered to be themostmobile charges and play animportant role in polarization fatigue and conduction [26]The estimated activation energies of the material system maycorrespond to the motion of oxygen vacancies in the octahe-dron of the perovskite structures The dc conductivity studycan help to illustrate not only the effects of grain orientationbut also the nature of charge carriers Approximate values ofdc conductivity of the test materials were evaluated from theextrapolation of the available plateaus of the 120590ac(120596) plots upto 120596 = 0 corresponding to 350∘C 400∘C and 450∘C For thestudy of temperature-dependent variation of dc conductivitythe following formula was used

120590dc = (120590119900

119879) exp(

minus119864119886

119896119861119879) (4)

The slope of the ln(120590lowastdc119879) versus 103T plots yielded the values

of activation energy for dc conductivity (119864119886) as given in

Table 3 In the high temperature regime the slopes rapidlyincreased with an increase in temperature The calculatedactivation energies of (1 minus 119909)BNT-119909BT (where 119909 = 00 002004 005 006 008 and 01) ceramics in this region are1416 1011 0539 1447 0771 1304 and 0783 eV respectivelyAs reported earlier [27 28] motion of oxygen vacancies inthe octahedron of any perovskite structure gives rise to anactivation energy sim110 eV On the basis of the above analysesit can be concluded that the dc conductivity in the highertemperature regime is due to motion of oxygen vacanciesacross the grain-boundary Thus we see that at highertemperatures dc conductivity ismore dominant in the studiedmaterial system This is reminiscent of the semiconductingbehavior of the material system as mentioned earlier

In a bid to extend our frequency-dependent ac conduc-tivity study the double power law the generalized version ofJonscherrsquos power law

120590ac = 120590119900 + 1198601205961198781+ 1198611205961198782 (5)

is to be usedHere 120590

119900is the frequency-independent (electronic or dc)

part of ac conductivity Further the exponent 1199041(0 le 119904

1le

1) characterizes the low frequency region corresponding totranslational ion hopping and the exponent 119904

2(0 lt 119904

2lt

2) characterizes the high frequency region indicating theexistence of well-localized relaxationreorientational process[29] the activation energy of which is ascribed to reori-entation ionic hopping Almond has proposed a different

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Ceramics 9

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(a)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(b)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(c)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(d)

01 1 10 100 1000Frequency (kHz)

120590ac

(Sm

)10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

(e)

01 1 10 100 1000Frequency (kHz)

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(f)

01 1 10 100 1000Frequency (kHz)

RT

100∘C

150∘C

200∘C

250∘C

300∘C

350∘C

400∘C

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(g)

01 1 10 100 1000Frequency (kHz)

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

450∘C

120590(S

m)

10minus1

10minus2

10minus3

10minus4

10minus5

10minus6

10minus7

ac

(h)

Figure 6 (a)ndash(g) Frequency dependence of real part of complex ac conductivity for ((BNT)BT)119909(119909 = 0 0 02 004 005 006 008 and 1)

ceramics at several temperatures and (h) corresponding plots at 450∘C

Table 3 acdc conductivity-based activation energy for different compositions in the low and high temperature ranges

Composition ac activation energy (eV) in lowtemp region (35∘Cndash300∘C)

ac activation energy (eV) in hightemp region (325∘Cndash450∘C)

dc activation energy (eV) in hightemp region (350∘Cndash450∘C)

BNT 0148 0144 1416098BNT-002BT 0164 0114 1011096BNT-004BT 0015 0158 0539095BNT-005BT 0112 0138 1447094BNT-006BT 0140 0316 0771092BNT-008BT 0047 0169 1304090BNT-010BT 0072 0477 0783

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

10 ISRN Ceramics

approach in which microstructural network in the systemis responsible for this power law behavior [30 31] Hoppingmodel is extensively studied over a wide range of materialslike ceramics polymers composites and so forth and cansuccessfully explain the double power law behavior theparticular case 119899 gt 1 [32] and so forth in these materialsFurther it may be inferred that the slope 119904

1is associated

with grain-boundary conductivity whereas 1199042depends on

grain conductivity [29] In the jump relaxation model (JRM)introduced by Funke [29] and extended by Elliot [33] toaccount for ionic conduction in solids there is a highprobability for a jumping ion to jump back (unsuccessfulhop) However if the neighborhood becomes relaxed withrespect to the ionrsquos position the ion stays in the new siteThe conductivity in the low frequency region is associatedwith successful hops Beyond the low frequency regionmanyhops are unsuccessful and as the frequency increases morehops are unsuccessful The change in the ratio of successfulto unsuccessful hops results in dispersive conductivity Inthe perovskite type oxide materials presence of charge trapsin the band gap of the insulator is expected The JRMsuggests that different activation energies are associatedwith unsuccessful and successful hopping processes Thefrequency and temperature-dependence of ac conductivityin the (1 minus 119909)BNT-119909BT system of materials resembles thatof hopping type conduction Applying JRM to the frequencyresponse of the conductivity for the test materials experi-mental inverse temperature-dependent conductivity data asshown in Figure 7 were found to fit the double power lawas given in (5) The temperature-dependent variations of theexponents 119904

1and 119904

2 are shown in Figures 8(a) through

8(g) From the plots (Figure 8(b)) it is manifested that 1199041

assumes a maximum value sim1243 at 100∘C for 098 BNT-002 BT and 119904

2assumes a maximum value sim1746 at 450∘C

for the same composition Further peaks were seen to appearonly near 119879

119898(ie the antiferroelectricparaelectric phase

transition temperature) for almost all the material composi-tions However in some of the compositions the peaks weresharper while in some others they were flat that is plateau-like To be more specific BNT exhibits plateau both for1199041(119879) and 119904

2(119879) in the temperature range 100ndash300∘C in the

098 BNT-002 BT composition 1199042(119879) shows a monotonically

increasing trend while 1199041(119879) shows a plateau between the

same temperature limits 096 BNT-004 BT shows a troughfor 1199041(119879) at sim400∘C 095 BNT-005 BT exhibits shoulders at

sim100∘C and flat peaks at sim300∘C both for 1199041(119879) and 119904

2(119879)

Furthermore 1199041(119879) and 119904

2(119879) in 094 BNT-006 BT (assumed

MPB composition) show almost the same trend of variationas in 095 BNT-005 BT with the only difference that in thiscase the 119904

2(119879) peak shifts towards higher temperature side

while 1199041(119879) peak shifts towards opposite side and beyond the

MPB composition that is for 092 BNT-008 BT the peaksshow opposite shifting as compared with that in the MPBcomposition Lastly for 090 BNT-010 BT composition thetrends for the variation of 119904

1(119879) and 119904

2(119879) are the same

as in the MPB composition As shown in Figure 8(e) theminimum values of both 119904

1(= 0516) and 119904

2(= 0545)

are exhibited by the 094 BNT-006 BT composition at 35∘Cthat is at the temperature of ambience Due to localization

15 2 25 3 35

ln120590

minus3

minus4

minus5

minus6

minus7

minus8

minus9

minus10

minus11

10 kHz

119909 = 0119909 = 002119909 = 004119909 = 005

119909 = 006119909 = 008119909 = 01

ac

1000119879 (K)

Figure 7 Inverse temperature-dependent variation of ln (real partof complex ac conductivity) for (1 minus 119909)BNT-119909BT (119909 = 0 002 004005 006 008 and 1) ceramics at 10 kHz

of charge carriers formation of polarons takes place andthe hopping conduction may occur between the nearestneighboring sites As referred to earlier the enhancementin conductivity with temperature may be considered on thebasis that within the bulk the oxygen vacancies due to theloss of oxygen (usually created during sintering) allow thecharge compensation process to occur which follows theKroger-Vink equation [34] in the form 119874

119900rarr (12)119874

2uarr

+119881119900

∙∙+ 2119890minus1

thereby showing that free electrons are left

behind in the process making the materials 119899-type It mayfurther be opined that lower high frequency ac activationenergy than that at low frequency may possibly be due to thefact that at low frequencies the overall conductivity is dueto the mobilitytransportation of charge carriers over longdistance rather than relaxationorientational mechanism inwhich case charge mobilitytransportation is restricted toonly the nearest neighboring lattice sites Higher values ofconductivity based activation energy at lower frequenciesthan those at higher ones are obtained due to the fact thatthe energy required for relaxationorientational process islower than that required for mobility of charge carriers overa long distance In the light of the resulting frequency- andtemperature-dependent ac conductivity data for (1 minus119909)BNT-119909BT ceramic samples it may be inferred that JRM has shownits applicability in the entire frequency range for the testmaterial system

4 Conclusion

The present work describes the piezoelectric impedanceand conductivity studies of (Na

05Bi05)1minus119909

Ba119909TiO3 (1 minus

119909)BNT-119909BT (0 le 119909 le 1) ceramics X-ray diffractiondata confirmed the formation of phase pure compounds inall the compositions and the apparent crystallite (particle)

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

ISRN Ceramics 11

0 100 200 300 400 500040506070809

111

Hop

ping

par

amet

er

Temperature (∘C)

(a)

Hop

ping

par

amet

er

0 100 200 300 400 50002040608

112141618

Temperature (∘C)

(b)

Hop

ping

par

amet

er

0 100 200 300 400 50006070809

11112

Temperature (∘C)

(c)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

(d)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

14

Temperature (∘C)

(e)

Hop

ping

par

amet

er

0 100 200 300 400 500040506070809

111

Temperature (∘C)

(f)

Hop

ping

par

amet

er

0 100 200 300 400 500

04

06

08

1

12

Temperature (∘C)

11990411199042

(g)

Figure 8 (a)ndash(g) Temperature-dependence of low and high frequency hopping parameters (1199041and 1199042) for (1minus119909)BNT-119909BT (119909 = 0 002 004

005 006 008 and 1) ceramics between ambient temperature and 450∘C

sizes are in the sim26ndash52 nm range SEM micrographs showedgrain sizes ranging 18ndash35 120583m and the relative densitiesin the range of 91ndash97 of the theoretical ones in all thecompositions Values of longitudinal piezoelectric chargecoefficients of the (1 minus 119909)BNT-119909BT samples poled under adc electric field of about 25 kVmm at 80∘C15min lie inthe range of 17ndash124 pCN Complex impedance analysis inthe frequency range 100Hzndash1MHz over a wide temperaturerange 35∘Cndash450∘C indicates the presence of grain-boundaryeffect along with the bulk contribution and also confirms thepresence of the non-Debye type of multiple relaxations inthe materials Conductionmechanism in the material systemis explained on the basis of jump relaxation hopping modelof charge carriers The electrical conductivity measurementswith temperature suggest the negative temperature coefficient

of resistance behaviour for the material system The acdcconduction-based activation energies for the test materialsystem have also been estimated The present study of (1 minus119909)BNT-119909BT (0 le 119909 le 1) ceramics is assumed worthwhilein probing the conduction mechanism in detail which maybe helpful in tailoring the electrical characteristics for desiredapplications

Acknowledgments

The authors gratefully acknowledge the financial supportby the Department of Science and Technology New Delhiunder Grant noSRS2CMP-0172008 Thanks are also dueto Professor Nawal Binhayeeniyi et al for the help taken inthe present work for comparison purposes from [22]

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

12 ISRN Ceramics

References

[1] G A Smolenskii V A Isupov A I Agranovskaya and N NKrainik ldquoNew ferroelectrics of complex compositionrdquo SovietPhysics Solid State vol 2 pp 2651ndash2654 1961

[2] A Hussain C W Ahn H J Lee et al ldquoAnisotropic electricalproperties of Bi

05(Na075

K025

)05TiO3ceramics fabricated by

reactive templated grain growth (RTGG)rdquo Current AppliedPhysics vol 10 pp 305ndash310 2010

[3] D Z Zhang X J Zheng X Feng et al ldquoFerro-piezoelectricproperties of 094(Na

05Bi05)TiO3-006BaTiO

3thin film pre-

pared by metal-organic decompositionrdquo Journal of Alloys andCompounds vol 504 no 1 pp 129ndash133 2010

[4] C Ma and X Tan ldquoPhase diagram of unpoled lead-free (1-x)(Bi12Na12)TiO3-xBaTiO

3ceramicsrdquo Solid State Communica-

tions vol 150 no 33-34 pp 1497ndash1500 2010[5] Z Yang B Liu L Wei and Y Hou ldquoStructure and electrical

properties of (1minus119909)Bi05Na05TiO3-xBi05K05TiO3ceramics near

morphotropic phase boundaryrdquo Materials Research Bulletinvol 43 no 1 pp 81ndash89 2008

[6] W C Lee C Y Huang L K Tsao and Y CWu ldquoCrystal Struc-ture dielectric and ferroelectric properties of (Bi

05Na05)TiO3-

(BaSr)TiO3lead-free piezoelectric ceramicsrdquo Journal of Alloys

and Compounds vol 492 no 1-2 pp 307ndash312 2010[7] D Lin K W Kwok and H L W Chan ldquoFerroelec-

tric and piezoelectric properties of Bi05Na05TiO3-SrTiO

3-

Bi05Li05TiO3lead-free ceramicsrdquo Journal of Alloys and Com-

pounds vol 481 no 1-2 pp 310ndash315 2009[8] Z Yang Y Hou H Pan and Y Chang ldquoStructure microstruc-

ture and electrical properties of (1 minus 119909 minus 119910)Bi05Na05TiO3-

xBi05K05TiO3-yBi05Li05TiO3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 480 no 2 pp 246ndash2532009

[9] M Zou H Fan L Chen and W Yang ldquoMicrostruc-ture and electrical properties of (1 minus 119909)[082Bi

05Na05TiO3-

018Bi05K05TiO3]-xBiFeO

3lead-free piezoelectric ceramicsrdquo

Journal of Alloys and Compounds vol 495 no 1 pp 280ndash2832010

[10] S-T Zhang B Yang andW Cao ldquoThe temperature-dependentelectrical properties of Bi

05Na05TiO3-BaTiO

3-Bi05K05TiO3

near the morphotropic phase boundaryrdquo Acta Materialia vol60 no 2 pp 469ndash475 2012

[11] H Ni L Luo W Li Y Zhu and H Luo ldquoPreparation andelectrical properties of Bi

05Na05TiO3-BaTiO

3-KNbO

3lead-

free piezoelectric ceramicsrdquo Journal of Alloys and Compoundsvol 509 no 9 pp 3958ndash3962 2011

[12] M L Liu D A Yang and Y F Qu ldquoStudy on Bi2O3

doping methods and dielectric property of (1 minus 119909)BaTiO3-

x(Bi05Na05)TiO3ceramicsrdquo Journal of Alloys and Compounds

vol 496 no 1-2 pp 449ndash453 2010[13] T Takenaka T Okuda and K Takegahara ldquoLead-free piezo-

electric ceramics based on (Bi12Na12)TiO3-NaNbO

3rdquo Ferro-

electrics vol 196 no 1ndash4 pp 175ndash178 1997[14] K H Ryu T K Song M Kim et al ldquoEffect of BiFeO

3doping

on ferroelectric and piezoelectric properties of (Bi05Na05)TiO3

and BATiO3ceramicsrdquo Integrated Ferroelectrics vol 84 no 1

pp 31ndash38 2006[15] H Nagata and T Takenaka ldquoLead-free piezoelectric ceramics

of (Bi12Na12)TiO3-12(Bi

2O3sdotSc2O3) systemrdquo Japanese Journal

of Applied Physics Part 1 vol 36 no 9 pp 6055ndash6057 1997

[16] A Herabut and A Safari ldquoProcessing and electromechanicalproperties of (Bi

05Na05)(1minus15119909)

La119909TiO3ceramicsrdquo Journal of the

American Ceramic Society vol 80 no 11 pp 2954ndash2958 1997[17] X Wang H L W Chan and C L Choy ldquo(Bi

12Na12)TiO3-

Ba(Cu12W12)O3lead-free piezoelectric ceramicsrdquo Journal of

the American Ceramic Society vol 86 no 10 pp 1809ndash18112003

[18] M Rawat K L Yadav A Kumar P K Patel N Adhlakha and JRani ldquoStructural dielectric and conductivity properties of Ba2+doped (Bi

05Na05)TiO3ceramicrdquo Advanced Materials Letters

vol 3 no 4 pp 286ndash292 2012[19] C Suryanarayan and M G Nortan X-Ray Diffraction a Practi-

cal Approach Plenum Press New York NY USA 1998[20] O Muller and R Roy The Major Ternary Structural Families

Springer New York NY USA 1974[21] K AmarNath and K Prasad ldquoStructural and electrical

properties of perovskite Ba(Sm12Nb12)O3-BaTiO

3ceramicrdquo

Advances in Materials Research vol 1 no 2 pp 115ndash128 2012[22] N Binhayeeniyi P Sukvisut C Thanachayanont and S

Muensit ldquoPhysical and electromechanical properties of bariumzirconium titanate synthesized at low-sintering temperaturerdquoMaterials Letters vol 64 no 3 pp 305ndash308 2010

[23] N G McCrum B E Read and G Williams Anelastic andDielectric Effects in Polymeric Solids John Wiley amp Sons NewYork NY USA 1967

[24] C T Moynihan ldquoAnalysis of electrical relaxation in glasses andmelts with large concentrations of mobile ionsrdquo Journal of Non-Crystalline Solids vol 172ndash174 no 2 pp 1395ndash1407 1994

[25] C T Moynihan L P Boesch and N L Laberge ldquoDecayfunction for the electric field relaxation in vitreous ionicconductorsrdquo Physics and Chemistry of Glasses vol 14 no 6 pp122ndash125 1973

[26] W L Warren K Vanheusden D Dimos G E Pike and B ATuttle ldquoOxygen vacancymotion in perovskite oxidesrdquo Journal ofthe American Ceramic Society vol 79 no 2 pp 536ndash538 1996

[27] M J Forbess S Seraji Y Wu C P Nguyen and G Z CaoldquoDielectric properties of layered perovskite Sr

1minus119909A119909Bi2Nb2O9

ferroelectrics (A=La Ca and 119909 = 0 01)rdquo Applied PhysicsLetters vol 76 no 20 pp 2934ndash2936 2000

[28] A K Roy A Singh K Kumari K AmarNath A Prasadand K Prasad ldquoElectrical properties and ac conductivity of(Bi05Na05)05Ba006

TiO3ceramicrdquo ISRN Ceramics vol 2012

Article ID 854831 10 pages 2012[29] K Funke ldquoJump relaxation in solid electrolytesrdquo Progress in

Solid State Chemistry vol 22 no 2 pp 111ndash195 1993[30] D P Almond and C R Bowen ldquoAnomalous power law

dispersions in ac conductivity and permittivity shown to becharacteristic of microstructural electrical networksrdquo PhysicalReview Letters vol 92 no 15 Article ID 157601 5 pages 2004

[31] C R Bowen and D P Almond ldquoModelling the ldquouniver-salrdquo dielectric response in heterogeneous materials usingmicrostructural electrical networksrdquo Materials Science andTechnology vol 22 pp 719ndash724 2006

[32] G Bator ldquoAc and dc conductivity around the ferroelectric phasetransition in (CH

3NH3)3Bi2Br9(MABB) crystalrdquo Ferroelectrics

vol 200 no 1ndash4 pp 287ndash295 1997[33] S R Elliot ldquoAC conduction in amorphous chalcogenide andp-

nictide semiconductorsrdquo Advances in Physics vol 36 pp 135ndash217 1987

[34] F A Kroeger and H J Vink ldquoRelations between the concentra-tions of imperfections in crystalline solidsrdquo Solid State Physicsvol 3 pp 307ndash435 1956

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials

Submit your manuscripts athttpwwwhindawicom

ScientificaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CorrosionInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Polymer ScienceInternational Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CeramicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CompositesJournal of

NanoparticlesJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Biomaterials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

NanoscienceJournal of

TextilesHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Journal of

NanotechnologyHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

CrystallographyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CoatingsJournal of

Advances in

Materials Science and EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Smart Materials Research

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MetallurgyJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

BioMed Research International

MaterialsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Nano

materials

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal ofNanomaterials