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Processing and Application of Ceramics 8 [3] (2014) 145–153 DOI: 10.2298/PAC1403145B Frequency and temperature dependence behaviour of impedance, modulus and conductivity of BaBi 4 Ti 4 O 15 Aurivillius ceramic Tanmaya Badapanda 1,, Ranjan Kumar Harichandan 2 , Sudhasu Sekhar Nayak 2 , Avinna Mishra 3 , Sahid Anwar 3 1 Department of Physics, C.V. Raman College of Engineering, Bhubaneswar, Odisha, 752054, India 2 Department of Physics, Centurion University of Technology & Management, Bhubaneswar, Odisha, 751020, India 3 Polytechnics Colloids & Materials Chemistry, Institute of Minerals and Materials Technology, Bhubaneswar, Odisha, 751013, India Received 8 August 2014; Received in revised form 24 September 2014; Accepted 27 September 2014 Abstract In this work, we report the dielectric, impedance, modulus and conductivity study of BaBi 4 Ti 4 O 15 ceramic synthesized by solid state reaction. X-ray diraction (XRD) pattern showed orthorhombic structure with space group A 21 am confirming it to be an m = 4 member of the Aurivillius oxide. The frequency dependence dielec- tric study shows that the value of dielectric constant is high at lower frequencies and decreases with increase in frequency. Impedance spectroscopy analyses reveal a non-Debye relaxation phenomenon since relaxation frequency moves towards the positive side with increase in temperature. The shift in impedance peaks towards higher frequency side indicates conduction in material and favouring of the long range motion of mobile charge carriers. The Nyquist plot from complex impedance spectrum shows only one semicircular arc representing the grain eect in the electrical conduction. The modulus mechanism indicates the non-Debye type of conductivity relaxation in the material, which is supported by impedance data. Relaxation times extracted using imaginary part of complex impedance (Z ′′ ) and modulus (M ′′ ) were also found to follow Arrhenius law. The frequency de- pendent AC conductivity at dierent temperatures indicates that the conduction process is thermally activated. The variation of DC conductivity exhibits a negative temperature coecient of resistance behaviour. Keywords: Aurivillius compound, impedance spectroscopy, grain boundary, electric modulus, dielectric relaxation, AC conductivity I. Introduction Aurivillius bismuth-layer structure ferroelectrics pose attractive electrical properties (BLSFs) such as ex- cellent fatigue endurance, fast switching speed, good polarization retention, relatively high Curie tempera- ture, low aging rate and low operating voltage. Due to their excellent properties these materials are com- mercially applicable as ferroelectric non-volatile ran- dom access memory (FRAM) storage devices, high tem- perature piezoelectric device and sensor applications [1,2]. Bismuth layered structure ferroelectrics belong to a multilayer family of so-called Aurivillius phase with a general chemical formula (Bi 2 O 2 ) 2+ (A m-1 B m O 3m+1 ) 2– , Corresponding author: tel: +91 674 2113593, mob: +91 9437306100, e-mail: [email protected] where A is a combination of one or more mono-, di- and trivalent ions with 12-fold coordinated cation; B is a combination of tetra-, penta-, and hexavalent ions with 6-fold coordinated cation and m refers to the number of BO 6 octahedra between neighboring Bi 2 O 2 layers along the c-axis [3–5]. These BO 6 octahedra exhibit sponta- neous polarization and (Bi 2 O 2 ) 2+ layers act as the insu- lating paraelectric layers and mainly control the electri- cal response such as electrical conductivity, while the ferroelectricity arises mainly in the perovskite blocks [6]. Majority of these oxides are normal ferroelectrics with fairly high Curie temperatures as a consequence of three main distortions from the prototype high tem- perature paraelectric phase, namely tilting of octahe- dra around the a- and c-axes and cationic displacement along the polar a-axis. Very few of these ceramics shows 145

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Page 1: Frequency and temperature dependence behaviour of ... › publikacije › PAC › pdf › PAC 25 05.pdfFrequency and temperature dependence behaviour of impedance, modulus and conductivity

Processing and Application of Ceramics 8 [3] (2014) 145–153

DOI: 10.2298/PAC1403145B

Frequency and temperature dependence behaviour of impedance,

modulus and conductivity of BaBi4Ti4O15 Aurivillius ceramic

Tanmaya Badapanda1,∗, Ranjan Kumar Harichandan2, Sudhasu Sekhar Nayak2,Avinna Mishra3, Sahid Anwar3

1Department of Physics, C.V. Raman College of Engineering, Bhubaneswar, Odisha, 752054, India2Department of Physics, Centurion University of Technology & Management, Bhubaneswar, Odisha, 751020,

India3Polytechnics Colloids & Materials Chemistry, Institute of Minerals and Materials Technology, Bhubaneswar,

Odisha, 751013, India

Received 8 August 2014; Received in revised form 24 September 2014; Accepted 27 September 2014

Abstract

In this work, we report the dielectric, impedance, modulus and conductivity study of BaBi4Ti4O15 ceramicsynthesized by solid state reaction. X-ray diffraction (XRD) pattern showed orthorhombic structure with spacegroup A21am confirming it to be an m = 4 member of the Aurivillius oxide. The frequency dependence dielec-tric study shows that the value of dielectric constant is high at lower frequencies and decreases with increasein frequency. Impedance spectroscopy analyses reveal a non-Debye relaxation phenomenon since relaxationfrequency moves towards the positive side with increase in temperature. The shift in impedance peaks towardshigher frequency side indicates conduction in material and favouring of the long range motion of mobile chargecarriers. The Nyquist plot from complex impedance spectrum shows only one semicircular arc representing thegrain effect in the electrical conduction. The modulus mechanism indicates the non-Debye type of conductivityrelaxation in the material, which is supported by impedance data. Relaxation times extracted using imaginarypart of complex impedance (Z′′) and modulus (M′′) were also found to follow Arrhenius law. The frequency de-pendent AC conductivity at different temperatures indicates that the conduction process is thermally activated.The variation of DC conductivity exhibits a negative temperature coefficient of resistance behaviour.

Keywords: Aurivillius compound, impedance spectroscopy, grain boundary, electric modulus,

dielectric relaxation, AC conductivity

I. Introduction

Aurivillius bismuth-layer structure ferroelectricspose attractive electrical properties (BLSFs) such as ex-cellent fatigue endurance, fast switching speed, goodpolarization retention, relatively high Curie tempera-ture, low aging rate and low operating voltage. Dueto their excellent properties these materials are com-mercially applicable as ferroelectric non-volatile ran-dom access memory (FRAM) storage devices, high tem-perature piezoelectric device and sensor applications[1,2]. Bismuth layered structure ferroelectrics belong toa multilayer family of so-called Aurivillius phase witha general chemical formula (Bi2O2)2+(Am-1BmO3m+1)2–,

∗Corresponding author: tel: +91 674 2113593,mob:+91 9437306100, e-mail: [email protected]

where A is a combination of one or more mono-, di-and trivalent ions with 12-fold coordinated cation; B isa combination of tetra-, penta-, and hexavalent ions with6-fold coordinated cation and m refers to the number ofBO6 octahedra between neighboring Bi2O2 layers alongthe c-axis [3–5]. These BO6 octahedra exhibit sponta-neous polarization and (Bi2O2)2+ layers act as the insu-lating paraelectric layers and mainly control the electri-cal response such as electrical conductivity, while theferroelectricity arises mainly in the perovskite blocks[6]. Majority of these oxides are normal ferroelectricswith fairly high Curie temperatures as a consequenceof three main distortions from the prototype high tem-perature paraelectric phase, namely tilting of octahe-dra around the a- and c-axes and cationic displacementalong the polar a-axis. Very few of these ceramics shows

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relaxor behaviour, such as BaBi2Nb2O9, BaBi2Ta2O9,BaBi4Ti4O15 (BBT) etc. [7,8]. BaBi4Ti4O15 is a m =

4 member of bismuth layered-structured ferroelectric,which shows four slabs of perovskite layers separatedby one slab of fluorite layer. BBT has Ba and Bi ions oc-cupying A sites and Ti ions in the B sites of perovskite([Am-1BmO3m+1]2–) block and it shows a diffuse phasetransition from 390 °C to 440 °C.

Impedance spectroscopy is a powerful technique toolfor investigation of complex electrical properties. De-pending on the chemical composition, various ferroelec-tric/antiferroelectric or paraelectric phases with slightlydifferent dielectric properties and crystal structures ofdifferent type are formed. In all ferroelectrics the studyof electrical conductivity is very important to realizethe associated physical properties and nature of con-ductivity in these materials. It is well known that theinterior defects such as A site vacancies, space chargeelectrons or oxygen vacancies have great influence onferroelectric fatigue or ionic conductivity of the mate-rial. Considering that the solid defects play a decisiverole in all of these applications, it is very important togain a fundamental understanding of their conductivemechanism. Various kinds of defects are always sug-gested as being responsible for the dielectric relaxationsat high temperature range. The AC impedance analy-sis is a powerful tool to separate the grain boundaryeffects. It is also useful to establish dependence of itsrelaxation mechanism on the grain and grain boundaryeffects by considering the different values of resistanceand capacitance. The AC impedance is a non-destructiveexperimental technique for the characterization of mi-cro structural and electrical properties of different elec-tronic material. The technique is based on the analy-sis of response of a system towards the input AC andthe calculation of impedance as a function of the fre-quency. The frequency dependent properties of a mate-rial can be described as complex permittivity (ε∗), com-plex impedance (Z∗), complex admittance (Y∗), com-plex electric modulus (M∗) and dielectric loss or dis-sipation factor (tan δ). The phenomenon of impedancespectroscopy is applied to the dielectric materials, i.e.solid or liquid non-conductors whose electrical charac-teristics involve dipolar rotation, and to materials withelectronic conduction [8,9].

Recently, there have been many reports on the synthe-sis and characterization of BBT with regard to its struc-tural, dielectric and ferroelectric properties [10–14]. Inour earlier work, we have reported the detail structural,ferroelectric and relaxor behaviour with a detailed anal-ysis of relaxor and diffuse behaviour of BBT ceramic[15]. But there are very few reports on the dielectricdispersion and conduction mechanism of BBT ceramic.Recently Kumar et al. [16] have reported the dielectricrelaxation of BBT ceramics mostly within the ferroele-cetric region (30–470 °C). In this paper we report the di-electric dispersion and conduction mechanism of BBTceramics in the paraelecteric region (486–786 °C) by

employing the impedance spectroscopy. Electric mod-ulus and the relaxation behaviour have been studied byanalysing the complex impedance. The resistivity andcapacitance associated with grains were determined.

II. Experimental details

The stoichiometric ratio of starting chemicals BaCO3(99.9%), TiO2 (99.9%) and Bi2O3 (99.9%) (E. MerckIn-dia Ltd.) was weighed for the composition BaBi4Ti4O15.The weighed powders were ball milled in a laboratoryball milling machine for 8 h using high purity zirconiaballs and acetone as a medium. After drying, calcinationwas done in a high purity alumina crucible at 1000 °Cfor 2 h in a conventional programmable furnace. Thecalcined powders were grinded using an agate mortarand then pressed into discs using pressure of 250 MPain a hydraulic press with 5 wt.% PVA solution addedas a binder. The discs were sintered at 1100 °C for 1 hwith 5 °C/min heating rate. The phase purity of the cal-cined powders was confirmed by the X-ray diffractome-ter. X-ray diffraction analysis of the samples was carriedout using a Philips diffractometer model PW-1830 withCu-Kα (λ = 1.5418 Å) radiation in a wide range of 2θ(20°< 2θ <70°) at a scanning rate of 0.5°/min. For elec-trical measurements, silver electrodes were applied onthe opposite disk faces and were heated at 700 °C for5 min. The frequency (1 Hz–1 MHz) and temperature(486–786 °C) dependent dielectric measurement werecarried out using a N4L-NumetriQ (model PSM1735)connected to PC.

III. Results and discussion

3.1. X-ray diffraction

Figure 1 shows the XRD pattern of BaBi4Ti4O15 ce-ramic calcined at 1000 °C for 2 h and sintered at 1100 °Cfor 2 h. The X-ray diffraction patterns could be indexedas a pure Bi-layered perovskite structure with m = 4. Noimpurity peaks corresponding to any other secondary

Figure 1. XRD pattern of BBT powder calcined at 1000 °Cfor 2 h and pellet sintered at 1100 °C for 2 h

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phase were found in the XRD patterns which confirmsthe single phase nature of the compositions. So the ob-tained phase was indexed using the orthorhombic spacegroup A21am which is in close agreement with the earlierreports [17–19]. The detail structural analysis and lat-tice parameters were obtained from Rietveld refinementstudy which has been reported in our earlier report [16].

Figure 2. Frequency dependent real part of dielectricconstant at different temperatures

Figure 3. Frequency dependent imaginary part of dielectricconstant at different temperatures

3.2. Frequency dependence of dielectric study

Figure 2 shows the variation of dielectric constant(ε′) of the BBT ceramic at different temperatures asthe function of angular frequency (ω = 2π f ). Thefrequency dependent complex dielectric permittivity isgiven by:

ε∗ − εα

εs − εα=

11 + jωτ

(1)

where εs and εα are low and high frequency dielec-tric constants and τ is the time constant. It is observedfrom Fig. 2 that the dielectric constants sharply decreasewith increasing frequency (<1 kHz), and the rate of de-crease levels off in a certain frequency range (>1 kHz).But, at relatively low frequency, the dielectric constantstrongly depends on frequency, evidently showing a di-electric dispersion [15]. Such a strong dispersion seemsto be a common feature in ferroelectric materials con-cerned with ionic conductivity, which is referred as low-frequency dielectric dispersion. When the frequency in-creases, the relative effect of ionic conductivity becomessmall and as a result, the frequency dependence of di-electric constant becomes weak. At lower frequencies,the dipolar complexes will be able to keep up with theapplied field and reorient with each half cycle. The fulleffect of the polarization reversal will contribute to thedielectric constant [14].

Figure 3 plots the frequency dependence of imagi-nary dielectric constant ε′′ of BBT at various temper-atures. Similar to the behaviour of dielectric constantwith frequency, the dielectric loss increases with in-creasing temperature. No loss peak was observed inthe ε′′ spectra. The high values of ε′′ at high temper-atures and the large drop of ε′′ with increase in fre-quency seem to indicate the influence of conductivityand space charge polarization. This indicates the ther-mally activated nature of the dielectric relaxation of thesystem. The fast rising trend of ε′′ at low frequenciesmay be due to the polarization mechanism associatedwith the thermally activated conduction of mobile ionsand/or other defects. High values of dielectric permittiv-ity are observed only at very high temperature and verylow frequencies which is may be due to the free chargebuild up at interfaces within the bulk of the sample (in-terfacial Maxwell-Wagner (MW) polarization) [20] andat the interface between the sample and the electrodes(space-charge polarization).

3.3. Impedance spectroscopy study

In order to understand the observed dielectric disper-sion, we carried out the complex impedance analysis.Figure 4 shows the variation of real part of impedance(Z′) with the corresponding frequency at different tem-peratures. The value of Z′ for all temperatures coincidesat high frequency. This behaviour is due to the reductionof barrier with increase in temperature due to which theAC conductivity is increased. At low frequency, Z′ valuedecreases with rise in temperature indicating the nega-tive temperature coefficient of resistance (NTCR). Fig-ure 5 shows the graph of imaginary parts of impedanceZ′′ versus frequency at temperatures between 486 °Cand 786 °C. The graph showed that Z′′max shifts to higherfrequency with the increase in temperature representinga relaxor behaviour within the ceramic [12–14]. A sig-nificant broadening of the peaks with increasing tem-perature suggests the presence of electrical processes inthe material with spread of relaxation time. This may

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Figure 4. Frequency dependent real part of impedanceat different temperatures

Figure 5. Frequency dependent imaginary part of impedanceat different temperatures

Figure 6. Scaled Z′′(ω,T) versus logω [i.e., Z′′(ω,T)/Z′′max

and log (ω/ωmax)]

be due to the presence of immobile species at low tem-peratures and defects at high temperatures. Since theseobservations are made at higher temperatures some re-laxation species, such as defects, may be responsible forelectrical conduction in the material by hopping of elec-trons/oxygen ion vacancies/defects among the availablelocalized sites. The heights of peaks are found to de-crease gradually with the increase in frequency and tem-perature, and finally, they merge in the high frequencydomain. It indicates the presence of space charge polar-ization at lower frequencies and disappearance at higherfrequencies. Figure 6 shows the plot of scaled Z′′(ωT )versus logω, i.e. Z′′(ωT )/Z′′max and log(ω/ωmax), whereωmax corresponds to the peak frequency of the Z′′ ver-sus logω plots. It can be seen that the Z′′ data coalescedinto a master curve. These observations indicate that thedistribution function for relaxation times is nearly tem-perature independent with nonexponential conductivityrelaxation.

Dielectric relaxation measurements are usually per-formed in the frequency domain and the data can berepresented on the complex impedance plane by usingthe Cole-Cole function. Figure 7 shows the compleximpedance spectrum for the BBT ceramic measured atdifferent temperatures. One depressed semicircle is ob-served within the studied temperature range, represent-ing the grain effect in the material. It is also observedthat with the increase in temperature the radius of thesemicircles decreases representing decrement in the re-sistivity. All the semicircles exhibit some depression de-gree instead of a semicircle centred at real axis Z′ due tothe distribution of relaxation time. The bulk resistanceof the material is obtained by fitting the experimental re-sponse to that of an equivalent circuit, which is usuallyconsidered to comprise a series of one parallel Resistor-CPE (R-CPE) elements as shown in Fig. 7 (inset). Thecircuit parameters fitting was done by ZView softwarewith the modelled circuits. The experimental value ofbulk resistance (Rb) at different temperatures has been

Figure 7. Nyquist plot of BBT ceramic measured at varioustemperatures and Inset shows the appropriate equivalent

electrical circuit

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obtained from the intercept of the semicircular arc onthe real axis (Z′). The depression of the semicircle isconsidered further evidence of polarization phenomenawith a distribution of relaxation times. This can be re-ferred to as the non-Debye type of relaxation in whichthere is a distribution of relaxation times [21,22]. Thisnon-ideal behaviour can be correlated to several factors,such as grain orientation, grain boundary, stress-strainphenomena and atomic defect distribution. This modi-fication leads to the Cole-Cole empirical behaviour de-scribed by the following equation:

Z∗ =R

1 + ( jω/ω0)1−n(2)

where n represents the magnitude of the departure ofthe electrical response from an ideal condition and canbe determined from the location of the centre of theCole-Cole circles. Least squares fitting to the compleximpedance data give the value of n > 0 at all the tem-peratures, suggesting the dielectric relaxation to be ofpoly-dispersive non-Debye type. This type of depressedsemicircle represents a constant phase element (CPE) inthe equivalent circuits. In solid materials, a distributionof relaxation times is usually observed and the capaci-tance is replaced by a CPE, which represents more accu-rately the behaviour of the grain interior, grain boundaryand electrode processes [23]. From Fig. 7 it is clear thatthe value of Rb decreases with rise in temperature. Thisshows the negative temperature coefficient of resistivity(NTCR) like that of a semiconductor. The capacitances(Cg) due to these effects can be calculated using the re-lation:

ωmaxRC = 1 (3)

where ωmax (=2π fmax) is the angular frequency at themaxima of the semicircle. Table 1 shows the tempera-ture variation of Cg obtained from Cole-Cole plots (us-ing Rg) at different temperatures.

Table 1. Grain resistance and capacitance from Nyquist plot

Temperature [°C] Resistance [Ω] C [nF]486 286077.3 1.94E-09536 102754.3 1.21E-09586 39049.3 8.85E-10636 14526.9 7.45E-10686 7130.2 5.40E-10736 2838.7 4.25E-10

3.4. Modulus analyses

The electric modulus is the reciprocal of complexpermittivity and was introduce by Macedo to study thespace charge relaxation process. The complex electricmodulus spectrum represents the measure of the dis-tribution ion energies or configuration in the structureand it also describes the electrical relaxation and micro-scopic properties. Physically the electric modulus cor-responds to the relaxation of the electric field in the

material when electric displacement remains constant.The electrical response can be analysed through com-plex electric modulus formalism. The complex electricmodulus (M∗) has been calculated by using the relation:

M∗(ω) = M′ + jM′′ = jωC0Z∗ (4)

where

M′(real part) = ωC0Z′′ (5)

and

M′′(imaginary part) = ωC0Z′ (6)

where

C0 =ε0A

t(7)

where ε0 is permittivity in free space, A is area of elec-trode surface and t is thickness.

Figures 8 and 9 display the frequency (angular) de-pendence of M′(ω) and M′′(ω) for BBT as a functionof temperature. M′′(ω) shows a dispersion tending to-ward M∞ (the asymptotic value of M′(ω) at higher fre-quencies) (Fig. 8). In the low temperature region, thevalue of M′(ω) increases with the increase in frequencyand decreases with the rise in temperature with slowrate. While in the high-temperature region, the value ofM′(ω) increases rapidly with the increase in both thetemperature and frequency [23]. It may be contribut-ing to the conduction phenomena due to the short rangemobility of charge carriers. This implies the lack of arestoring force for flow of charge under the influence ofa steady electric field.

Figure 9 shows the frequency dependence of theimaginary part of the electric modulus M′′(ω) at dif-ferent temperatures. The plot shows an asymmetric be-haviour with respect to peak maxima whose positions

Figure 8. Variation of real modulus with frequency atdifferent temperature

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Figure 9. Variation of imaginary modulus with frequency atdifferent temperature

Figure 10. Arrhenius plot of logωm from imaginary part ofimpedance and modulus

Figure 11. Frequency dependence of normalized peaks,Z′′/Z′′max and M′′/M′′

max for the BBT ceramic at 736 °C

are frequency and temperature dependent. These spec-tra also reflect the motions of the ions in the material byexhibiting two apparent relaxation regions. The left re-gions of the peak indicate the conduction process whileregions on the right of the peak are associated to the re-laxation process where the ion can make localized mo-tion within the well. The asymmetric modulus peaksshifts towards higher frequency side exhibiting the cor-relation between the motions of mobile charge carri-ers [24]. The asymmetry in peak broadening shows thespread of relaxation times with different time constantsand hence the relaxations of non-Debye type. The exis-tence of low frequency peaks suggests that the ions canmove over long distances whereas high frequency peakssuggest about the confinement of ions in their potentialwell. The nature of modulus spectra confirms the exis-tence of hopping mechanism in the electrical conductionof the materials.

The frequency ωm (corresponding to Z′′max and M′′max)gives the most probable relaxation time τm from the con-dition ωmτm = 1. The most probable relaxation time fol-lows the Arrhenius law given by:

ωm = ω0 exp(

−Ea

kBT

)

(8)

whereω0 is the pre-exponential factor and Ea is the acti-vation energy. Figure 10 shows a plot of the logωm ver-sus 1000/T , where the dots are the experimental dataand the solid line is the least-squares straight-line fit ofthe relaxation of both Z′′(ω) and M′′(ω). The activa-tion energy Ea is calculated from the least-squares fit tothe points. From Fig. 10 it can be seen that the activa-tion energy, calculated from Arrhenius relation, is Ea =

0.73 eV and 0.71 eV from the relaxation of Z′′(ω) andM′′(ω), respectively.

Going further in the description of experimental data,the variations of normalized parameters M′′(ω)/M′′max

and Z′′(ω)/Z′′max as a function of logarithmic frequencymeasured at 736 °C for BBT are shown in Fig. 11. Com-parison with the impedance and electrical modulus dataallows the determination of the bulk response in terms oflocalized, i.e. defect relaxation or non-localized conduc-tion, i.e. ionic or electronic conductivity. Overlapping ofthe peak positions of the Z′′(ω)/Z′′max and M′′(ω)/M′′max

is observed suggesting components from both long-range and localized relaxation. In order to mobilize thelocalized electron, the aid of lattice oscillation is re-quired. In these circumstances electrons are considerednot to move by them but by hopping motion activated bylattice oscillation. In addition, the magnitude of the ac-tivation energy suggests that the carrier transport is dueto the hopping conduction.

3.5. AC/DC conductivity analyses

The AC electrical conductivity was obtained by us-ing the relation σAC = d/(A · Z′), where d is the thick-ness and A is the surface area of the material. The plotof electrical conductivity versus frequency at different

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Figure 12. Variation of AC conductivity with frequency atdifferent temperature

temperatures is shown in Fig. 12. The frequency depen-dence conductivity spectrum exhibits three different re-gions, they are: a) low frequency dispersed b) an inter-mediate plateau and c) conductivity dispersion at highfrequencies. The variation of conductivity in the lowfrequency range is due to the polarisation effects [25].At very low frequencies the accumulation of charge oc-curs, hence drop in conductivity. In the intermediate fre-quency region conductivity is almost found to be fre-quency independent and equal to DC conductivity inhigh frequency region the conductivity increases withfrequency. The frequency dependence of electrical con-ductivity is explained by Jonscher’s power law given by:

σAC = σDC + Aωn (9)

where σAC is the AC conductivity, σDC is the limitingzero frequency conductivity, A is a pre-exponential con-stant, ω = 2π f is the angular frequency and n is thepower law exponent where 0 < n < 1 [26,27]. Thegraph indicates that the conductivity increases with in-creasing temperature. The conductivity is very sensitiveat higher frequency known as hopping frequency, whichis shifted towards higher frequency with rise in temper-ature. In the higher frequency the conductivity increasesdue to long range movement of charge carriers and thematerial shows the relaxor properties. It is observed thatthe conductivity spectra indicate the two different re-gions within the measured frequency range, they are a)an intermediate plateau and b) conductivity dispersionat high frequency. The intermediate plateau region cor-responds to frequency independent conductivity knownas DC conductivity. This region is obtained due to trans-port of mobile ions in response to applied electric field.The σDC is obtained by extrapolating to lower frequen-cies.

The DC conductivity estimated from the bulk re-sponse of the material has been observed as a function

Figure 13. Temperature dependence of DC conductivity forBBT ceramic (dots are the experimental points and solid line

is the least-square straight line fit)

of temperature as shown in the Fig 13. At higher tem-perature, the conductivity versus temperature responseis linear and can be explained by a thermally activatedtransport of Arrhenius type governed by the relation:

σDC = σ0 exp(

−Ea

kBT

)

(10)

where σ0, Ea and kB represent the pre-exponential fac-tor, the activation energy of the mobile charge carriersand Boltzmann constant respectively. The activation en-ergy was found to be 0.51 eV. The activation energiesobtained for grains is similar to the activation energy ofthe second ionization of oxygen vacancy in perovskites[26]. Oxygen vacancies in bismuth-layered oxides areformed by the loss of oxygen in the high-temperaturesintering process, in order to balance the charge mis-match due to the existence of bismuth vacancies. Inperovskite ferroelectric materials oxygen vacancies areconsidered to be one of the mobile charge carriers andmostly in titanates the ionization of oxygen vacanciescreate conduction electrons, a process which is definedby Kröger-Vink notation [28]. The excess electron andoxygen vacancies are formed in the reduction reaction:

OxO −−−→

12 O2 + V••O + 2 e− (11)

and they may be bond to Ti4+ in the form Ti4++e–←−−→

Ti3+. As indicated by Ihrig and Hennings [24], it is diffi-cult to determine whether the weakly bonded electronsare located near an oxygen vacancy or near a Ti ion.The exact location of the electrons depends on the de-tails of structure, temperature range, etc. It was, how-ever, shown that the oxygen vacancies lead to shallowlevel electrons. These electrons may be trapped by theTi4+ ions or by oxygen vacancies and they easily be-come conducting electrons by thermal activation. Theformation of oxygen vacancies can be due to the threedifferent charge states: neutral (Vx

O) state, which is able

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to capture two electrons and it is neutral in the lattice,mono ionized (V•O) state and double ionized (V••O ) state,which do not trap any electron, it is twofold positiveand can be thermally activated, thus enhancing the con-duction process. Double charge oxygen vacancies (V••O )are considered to be the major mobile charge in per-ovskite and play important role in conduction. Fits ofthe above results show that activation energies relatedto relaxation process are slightly higher than those re-lated to conduction in the studied temperature range.This suggests that the relaxation process does not gov-ern the electrical conduction. At high temperatures var-ious types of charge carriers contribute to the electri-cal conduction, although these may not be related tothe dielectric relaxation/polarization. For instance, theelectrons released from the oxygen vacancy ionizationwhich can be the source of the space charge polariza-tion, are easily thermally activated and become conduct-ing electrons. Also, dipoles related to the oxygen va-cancies and electrons can be trapped easily at the grainboundaries and thus block the ionic conduction acrossthem.

IV. Conclusions

Complex impedance spectroscopy has been used tostudy the dielectric dispersion and conduction mecha-nism of BaBi4Ti4O15 ceramic synthesized by solid statereaction. Impedance spectroscopy study shows a dielec-tric relaxation in the material which follows Maxwell-Wagner relaxations. Nyquists plots show both bulk andgrain boundary effect and the resistance decreases withrise in temperature, which indicates the NTCR be-haviour of the sample. The electrical relaxation processoccurring in the material has been found to be temper-ature dependent. Modulus analysis has established thepossibility of hopping mechanism for electrical trans-port processes in the system. The AC conductivity spec-trum is found to obey Jonscher’s universal power law.The frequency dependent AC conductivity at differenttemperatures indicated that the conduction process isthermally activated process.

References

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