ISSN 1063�7834, Physics of the Solid State, 2013, Vol. 55, No. 10, pp. 2065–2070. © Pleiades Publishing, Ltd., 2013.Original Russian Text © N.M. Olekhnovich, A.V. Pushkarev, Yu.V. Radyush, 2013, published in Fizika Tverdogo Tela, 2013, Vol. 55, No. 10, pp. 1950–1955.

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1. INTRODUCTION

Bismuth�containing systems with a perovskitestructure have attracted the particular attention ofresearchers, which is associated with the active searchfor new ferroelectric and piezoelectric materials con�taining no environmentally harmful lead and satisfy�ing modern technical requirements. It is in this direc�tion that there have been developed investigations ofsolid solutions based on (NaBi)1/2TiO3 (NBT),(KBi)1/2TiO3 (KBT) [1], and other bismuth�contain�ing compounds with ferroelectric properties. TheNBT compound at room temperature has a rhombo�hedrally distorted perovskite structure (space groupR3c) and undergoes a sequence of temperature phasetransitions with a change in the character of the dipoleordering [2]. It is known that there are systems ofNBT�based solid solutions with the morphotropicphase boundary near which the permittivity andpiezoelectric coefficients reach high values (see [3]and references therein). Solid solutions of the systemsNBT–BaTiO3 [4], NBT–PbZrO3 [5], NBT–La(MgTi)1/2O3 [6], and NBT–Bi(ZnTi)1/2O3 [7]exhibit properties of relaxor ferroelectrics. The KBTcompound at room temperature has a tetragonally dis�torted perovskite structure (space group P4mm). TheNBT–KBT solid solutions undergo a sequence of

concentration phase transitions associated with achange in the type of ordered distortions in the crystallattice [8].

This paper presents the results of the investigationinto the characteristics of the dielectric response ofperovskite ceramics with the 0.9(Na1 – xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 compositions lying near the mor�photropic phase boundary. The perovskite phase of theBi(ZnTi)1/2O3 (BZT) compound, which is formed athigh pressures and temperatures, has a tetragonallydistorted structure [9]. In the (1 – x)NBT–xBZT sys�tem at normal pressure, solid solutions are formed in alimited region of compositions (x < 0.2) [10]. Accord�ing to their structural and dielectric characteristics,these solid solutions differ significantly from the endcompound NBT.

2. SAMPLE PREPARATION AND EXPERIMENTAL TECHNIQUE

The initial reagents for the synthesis of0.9(Na1 ⎯ xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 solid solu�tions were the high�purity oxides Bi2O3, TiO2, andZnO, as well as the carbonates Na2CO3 and K2CO3.The synthesis was carried out in three stages accordingto the conventional ceramic technology. In the first

FERROELECTRICITY

Dielectric Characteristics of the Relaxor State of the Perovskite Ceramics 0.9(Na1 – xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3

near the Morphotropic Phase Boundary N. M. Olekhnovich*, A. V. Pushkarev, and Yu. V. Radyush

Scientific�Practical Materials Research Centre, National Academy of Sciences of Belarus,ul. P. Brovki 19, Minsk, 220072 Belarus

* e�mail: olekhnov@ifttp.bas�net.by Received March 20, 2013

Abstract—X�ray diffraction investigations have revealed that, in the system of solid solutions0.9(Na1 ⎯ xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3, there is a morphotropic phase boundary in the potassium con�centration range of x ≈ 0.25, which separates the regions of compositions with rhombohedral (R3c) and tet�ragonal (P4mm) structures. It has been shown that, in the vicinity of this boundary, ceramic samples of thestudied system exhibit properties of relaxor ferroelectrics. The results of the investigation into the dielectricproperties of relaxor ceramics of the composition x = 0.3 with the use of the impedance spectra measured inthe frequency range from 25 to 106 Hz at temperatures from 100 to 900 K have been presented. It has beenfound that, in the temperature region of the existence of the relaxor state lying below the temperature corre�sponding to the maximum of the real part of the permittivity ( = 550 K), the dielectric polarization isdetermined by the sum of the contributions from the matrix and dipole clusters. The temperature dependenceof the contribution from the clusters, which is determined by the kinetics of their formation and freezing, ischaracterized by a curve with the maximum at approximately 400 K. The process of freezing of dipole clustersoccurs over an extended temperature range of more than 200 K.

DOI: 10.1134/S1063783413100247

Tm'

2066

PHYSICS OF THE SOLID STATE Vol. 55 No. 10 2013

OLEKHNOVICH et al.

stage, a mixture of reagents of the specified composi�tion was ground in a ball mill; then, the obtained pow�der was pressed into tablets and subjected to heat treat�ment in a closed corundum crucible at a temperatureof 1140 K for 0.4–1.0 h. The second and third stagesof the synthesis were performed at a temperature of1270–1320 K (2 h). After each synthesis stage, theobtained product was subjected to grinding in a ballmill, and the powder was pressed into tablets for thenext stage. The ceramic samples for dielectric mea�surements were sintered at a temperature of 1370–1390 K.

The X�ray diffraction investigations of the sampleswere carried out on a DRON�3 diffractometer in themonochromatic CuK

α�radiation.

The characteristics of the dielectric response of thesolid solution ceramics were measured using an E7�20immittance meter for samples–capacitors with silverelectrodes. The permittivity (ε') and dielectric losstangent (tanδ) were measured at fixed frequencies inthe range from 102 to 106 Hz as functions of tempera�ture. The temperature was changed at a rate of 1.5–2.0 K/min in the range from 100 to 900 K. The mea�surements were carried out during heating and cool�ing. The frequency dependences of the dielectric char�acteristics of the solid solutions were determined fromthe parameters of the complex impedance Z* mea�sured with a stepwise change in the frequency from 25to 106 Hz. At any specified temperature in the rangefrom 100 to 900 K, the modulus Z and the angle of thephase shift ϕ of the complex impedance of the testcapacitor were measured in an automatic mode. Themeasured values of Z and ϕ were used to determine thereal and imaginary parts of the permittivity (ε*) andcomplex electrical conductivity (σ*):

(1)

(2)

where ω = 2πf; ε0 is the permittivity of free space; s andl are the area and thickness of the parallel�plate capac�

itor, respectively; and j = .

The direct�current (dc) electrical conductivity σdc

of the ceramic samples at different temperatures wasdetermined from the diagram σ'–σ'' in the low�fre�quency range.

Then, the frequency dependences of the imaginarypart of the permittivity, which is related only to thedielectric polarization ( = ε'' – σdc/ε0ω, where thesubscript ac refers to the alternating�current charac�teristic), and the Cole–Cole diagrams –ε' on thecomplex plane at different temperatures were ana�lyzed.

ε* ε' ω( ) jε'' ω( )– ljε0ωs�����������Z*

1–,= =

σ* σ' ω( ) jσ'' ω( )+ ls�Z*

1–,= =

1–

εac''

εac''

3. RESULTS AND DISCUSSION

The analysis of the X�ray diffraction patterns hasrevealed that the phase diagram of the studied solidsolutions is characterized by the morphotropic phaseboundary, which lies in the composition region withxM ≈ 0.25. At a low potassium concentration in the sys�tem (x < xM), the solid solutions have a rhombohe�drally distorted crystal lattice (space group R3c), as inthe case of the (NaBi)1/2TiO3 compound. The phaselying in the composition region with x > xM has a tet�ragonally distorted crystal lattice (space group P4mm),as in the case of the (KBi)1/2TiO3 compound. The unitcell parameters of the two phases increase linearly withincreasing potassium concentration x. It is found that,in the rhombohedral phase, there are out�of�phaserotations of the octahedra around the hexagonal axis.The angle of rotation decreases with an increase in xand, as the morphotropic phase boundary isapproached, becomes relatively small.

Let us compare the phase diagram of the0.9(Na1 ⎯ xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 solid solu�tions with the phase diagram of the(Na1 ⎯ xKxBi)1/2TiO3 solid solution. It is known that, inthe phase diagram of the (Na1 – xKxBi)1/2TiO3 solidsolutions at room temperature, there are three regionsof compositions differing in their crystal lattice symme�tries [8]. In the region with x ≤ 0.45, the solid solution ofthis system has a rhombohedral structure characterizedby out�of�phase rotations of the octahedra. In theregion with x ≥ 0.7, there exists the P4mm phase with atetragonally distorted crystal lattice. In the intermediateregion 0.45 < x < 0.7, the solid solution has an R3mrhombohedral structure in which there is no rotation ofthe octahedra. From the comparison of the phase dia�grams of the systems 0.9(Na1 ⎯ xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 and (Na1 ⎯ xKxBi)1/2TiO3 it followsthat, when the (Na1 ⎯ xKxBi)1/2TiO3 system is dopedwith zinc, the region of the existence of the R3m phaseis almost completely degenerate, whereas the region ofthe existence of the R3c phase is significantly narrowed.

3.1. Temperature Dependence of the Dielectric Characteristics of the Ceramics in the Relaxor State

The results of the investigations have demonstratedthat the ceramic samples of the 0.9(Na1 – xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 solid solutions with the composi�tions lying in the morphotropic phase boundary regionexhibit properties of relaxor ferroelectrics, whereasoutside of this region, they have properties of ferro�electrics with a diffuse phase transition. Below, wepresent the results of the investigations of the solidsolution ceramics in the relaxor state.

Based on the performed investigations, we deter�mined the character of the temperature dependences ofthe real (ε') and imaginary (ε'') parts of the permittivityand dielectric loss tangent (tanδ) of the solid solution

PHYSICS OF THE SOLID STATE Vol. 55 No. 10 2013

DIELECTRIC CHARACTERISTICS OF THE RELAXOR STATE 2067

ceramics near the morphotropic phase boundary. Forillustration, we analyze the obtained results for thecomposition with x = 0.3 (Fig. 1). It can be seen fromthis figure that the temperature dependence ε'(T) has amaximum whose position ( ) weakly depends on thefrequency of the measuring field. The temperature ofthe maximum lies in the range of 550 K. The ceramicsample in the vicinity of the temperature is charac�terized by a small value of tanδ.

The character of the temperature dependence ε'(T)in the range < T < Tm + 220 corresponds a diffuseferroelectric phase transition and is described by therelationship [11]

(3)

where the parameter γ is approximately equal to 1.9. Inthe general case, the parameter γ, which characterizesthe degree of diffuseness of the phase transition, canvary within the range 1 ≤ γ ≤ 2. The observed high valueof γ indicates that the studied ceramics are character�ized by a high degree of diffuseness of the phase tran�sition. At temperatures above approximately 770 K,the temperature dependence ε'(T) at high frequencies,where the effect of electrical conduction is small, cor�responds to the Curie–Weiss law. The Curie tempera�ture determined by extrapolating the dependence of1/ε' on T is equal to 580 K.

In the temperature range of 200–500 K, the curvesε'(T) are characterized by a “hump” with an increaseddispersion. Moreover, the curves of the temperaturedependences ε''(T) and tanδ(T) in the aforemen�tioned temperature range contain a maximum thatshifts toward higher temperatures with an increase inthe frequency of the measuring field. In this case, thevalues of ε'' and tanδ at the maximum increase. A sim�ilar behavior of the temperature dependences of thecharacteristics of the dielectric response is known forother bismuth�containing perovskites [6, 12]. Theobserved character of the behavior of the parametersε', ε'', and tanδ in this temperature range suggests atransition of the system to the relaxor ferroelectricstate. The observed frequency dependence of the tem�perature of the maximum of the imaginary part of thepermittivity ( ) is described by the Vogel–Fulcherrelationship [13]

(4)

where f is the frequency at which the maximum of ε'' isobserved at the temperature ; Ea and Tf are the activa�tion energy and the temperature of freezing of polar clus�ters, respectively; and f0 is the characteristic frequency.

The performed analysis has demonstrated that theobserved dependence ( f ) is described by relation�ship (4) for the following parameters: Tf = 270 K, Ea =0.07 eV, and f0 = 7.4 × 105 s–1.

Tm'

Tm'

Tm'

1/ε' 1/εm'– T Tm'–( )γ/C,=

Tm''

f f0 Ea/k Tm'' Tf–( )–( ),exp=

Tm''

Tm''

3.2. Characteristics of the Dielectric Polarization Relaxation in the Temperature Region

of the Relaxor State

In order to evaluate the characteristics of the relax�ation of the dielectric polarization of the solid solu�tions ceramics in the region of the existence of therelaxor state, we analyzed the frequency dependencesof the imaginary part of the permittivity, which isrelated only to the dielectric polarization ( = ε'' –

σdc/ε0ω), and the diagrams –ε' on the complexplane. It was found that the dc electrical conductivityof the ceramic samples exponentially increases with anincrease in the temperature (σdc =σdc0exp(⎯ΔEdc/kT)). The activation energy of charge

carriers (ΔEdc) in the temperature range T < isequal to 0.3 eV. According to the performed analysis,the dc electrical conductivity σdc in the temperatureregion of the existence of the relaxor state of theceramic samples is relatively small. For example, atroom temperature it does not exceed approximately10–11 S/m. The contribution of the conductivity σdc tothe imaginary part of the permittivity ε'' at T < 450 Kwas found to be relatively small and, hence, wasignored.

εac''

εac''

Tm'

4000

2000

102 Hz103 Hz104 Hz105 Hz106 Hz

0

200

0

400

0.05

0

0.10

0.15

200 400 600 800T, K

Fig. 1. Temperature dependences of the real (ε') and imag�inary (ε'') parts of the permittivity and the dielectric losstangent (tanδ) for the solid solution with x = 0.3.

ε'

ε''

tanδ

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PHYSICS OF THE SOLID STATE Vol. 55 No. 10 2013

OLEKHNOVICH et al.

The frequency dependences of and the dia�

grams –ε' at different temperatures in the range T <

are presented in Figs. 2 and 3, respectively. From theanalysis of the presented data it follows that the dielec�tric response of the studied ceramics is determined bythe sum of two components. One component is relatedto the dielectric polarization of dipole clusters, whereasthe other component is the contribution of the matrixitself (ferroelectric domains). The dipole clusters makea contribution predominantly in the high�frequencyrange. This is indicated by the increase in height of themaximum in the curve ε''(T) with an increase in the fre�quency (Fig. 1). At low frequencies, the dielectricpolarization is primarily determined by the contribu�tion of the matrix. The ratio of the contributionsdepends on the temperature. As the temperatureincreases to approximately 400–420 K, the contribu�tion from dipole clusters first increases, but, then, witha further increase in the temperature T, it decreases.

The dielectric response of the studied ceramics wasdescribed using the equivalent circuit shown in theinset to Fig. 2, where the CPE is a constant�phase ele�ment with the admittance written as Y = A–1( jω)α.The subscript c refers to the dipole clusters, and thesubscript d relates to the matrix.

εac''

εac''

Tm'

From the analysis of the considered equivalent cir�cuit, we derived the expression that allows one todescribe, in accordance with the well�known Cole–Cole relationship [14], the frequency dependence ofthe complex permittivity of a system consisting of twosubsystems (in our case, the matrix and dipole clus�ters) with a broad spectrum of relaxation times of thedielectric polarization

(5)

where τ is the average relaxation time and α is theparameter determining the width of the spectrum ofrelaxation times of the corresponding subsystem.

The analysis of the curves of the frequency depen�dence (Fig. 2) and the diagrams –ε' (Fig. 3) hasshown that the average relaxation time of the dielectricpolarization of the matrix is rather large (ωτd � 1).Then, the real and imaginary parts of the permittivityof dipole clusters ( and ), according to relation�ship (5), can be represented in the form

(6)

where B = .

Using expressions (6) and the variational method, wedetermined the parameters B and αd, at which the dia�

grams –(ε∞ + ) on the complex plane are described

by a circular arc (the Cole–Cole diagram [14]).

For illustration, Fig. 4 shows the diagrams –

(ε∞

+ ) obtained for a system of dipole clusters atdifferent temperatures. It can be seen from this figurethat the centers of the circles describing these dia�grams are located substantially below the abscissa axis.This fact means that the parameter αc is significantlygreater than zero. The quantities Δεc and ε

∞ were

determined from the intercepts cut off by the circulararc on the abscissa axis. The parameter αc was found

ε* ε∞

Δεc

1 jωτc( )1 αc–

+����������������������������

Δεd

1 jωτd( )1 αd–

+����������������������������,+ +=

εac'' εac''

εc' εa''

ε∞ εc'+ ε'B π

2��αdtan

ω1 αd–

������������������–=

= ε∞

Δεc 1 π2��αc ωτc( )

1 αc–sin+⎝ ⎠

⎛ ⎞

1 2 π2��αc ωτc( )

1 αc–sin ωτc( )

2 1 αc–( )+ +

�������������������������������������������������������������������������,+

εc'' εac'' B

ω1 αd–

�����������–=

= Δεc

π2��αc ωτc( )

1 αc–

1 2 π2��αc ωτc( )

1 αc–sin ωτc( )

2 1 αc–( )+ +

�������������������������������������������������������������������������,

Δεdπ2��αd/τd

1 αd–cos

εc'' εc'

εc''

εc'

400

300

200

100

0

CPEc Cc

CdCPEd

C∞ 439 K

480 K

322 K

50

0

75

100

125

10 102 104103 105 106

f, Hz

245 K

Fig. 2. Frequency dependences of the imaginary part of thepermittivity ( ) for the solid solution with x = 0.3 at dif�

ferent temperatures.

εac''

εac''

PHYSICS OF THE SOLID STATE Vol. 55 No. 10 2013

DIELECTRIC CHARACTERISTICS OF THE RELAXOR STATE 2069

from the relationship cos αc = Δεc/2R, where R is the

radius of the circle.

The temperature dependences of the parametersΔεc, αc, and αd are shown in Fig. 5. As can be seen fromthis figure, the temperature dependence of Δεc is char�acterized by a curve with the maximum observed atapproximately 400 K. By extrapolating the curveΔεc(T) toward higher temperatures to the zero value, itcan be concluded that the starting temperature of thenucleation of dipole clusters lies in the vicinity of (550 K). An increase in the parameter Δεc with a

decrease in the temperature from to 400 K, obvi�ously, is associated with an increase in the number ofdipole clusters and their sizes. A decrease in this quan�tity at temperatures T < 400 K is caused by the processof freezing of dipole clusters, which occurs over a rel�atively wide temperature range. As was noted above,the freezing temperature of clusters Tf = 270 K wasdetermined using the Vogel–Fulcher relationship (4)from the temperature shift of the frequency at themaximum of ε''(T). It can be seen from Fig. 5 that thevalue of Δεc at T = Tf is an order of magnitude smallerthan that at the maximum. This fact implies that, asthe temperature decreases to Tf, the vast majority ofdipole clusters reside in the frozen states. According toestimates, the average relaxation time τc, with a

decrease in the temperature from to 400 K,increases by almost an order of magnitude and, at 400K, reaches approximately 5 × 10–7 s. In the tempera�ture range T < 400 K, the value of τc remains almostunchanged. Reasoning from the fact that the parame�ter αc increases with a decrease in the temperature to

π2��

Tm'

Tm'

Tm'

400 K, we can assume that, in this case, the spectrumof relaxation times of dipole clusters broadens. Thebroadening of the spectrum of relaxation times and theincrease in the average relaxation time τc with decreas�ing temperature in this region can be caused by anincrease in the size of dipole clusters and by a rise inthe degree of their interaction. At temperatures below400 K, the process of freezing of larger clusters domi�nates, while the increase in the average relaxation timeslows down. Taking into account the character of theconcentration phase transition occurring at a potas�sium concentration x ≈ 0.25, it can be assumed that the

0

100

200

50

100ε∞

+ ε'

ε'' c

300 400 500 600

245 K ω

322 Kω

02000

200

1000

ε'' c

3000 4000ε∞

+ ε'

400 400 K439 Kω ω

Fig. 4. Diagrams –(ε∞

+ ) on the complex plane for

a system of dipole clusters of the solid solution with x = 0.3at different temperatures.

εc'' εc'

1.0

0.8

0.6

0.4

0.2

0

αc,

αd

αd

αc

500

0

1000

1500

2000

200 300 400 500T, K

Tf

Δε

c

Fig. 5. Temperature dependences of the parameters αd, αc,and Δεc.

3500 4000 4500 50000

200

400

439 K

ω

ω

480 K

12000

100

200

1500 1800 2100

ω 322 K

0

100

700

50

600 800 900 1000 1100

ω245 K

ε'

ε'

ε'

ε'' ac

ε'' ac

ε'' ac

Fig. 3. Diagrams –ε' on the complex plane for the solid

solution with x = 0.3 at different temperatures.

εac''

c

c

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PHYSICS OF THE SOLID STATE Vol. 55 No. 10 2013

OLEKHNOVICH et al.

clusters are polar nanoregions with a rhombohedralstructure.

The value of the parameter αd, which characterizesthe width of the spectrum of relaxation times of thematrix, as is seen from Fig. 5, increases with decreas�ing temperature. The rate of this increase depends onthe temperature. At higher temperatures (aboveapproximately 360 K), the rate of the increase is ratherhigh, while at lower temperatures, it is relatively low.In order to evaluate the character of the change in theaverage relaxation time of the dielectric polarization ofthe matrix, we analyzed the temperature dependenceof the quantity B(T) (6). It was found that the temper�

ature dependence of the quantity ,

which is proportional to the average relaxation time ofthe dielectric polarization of the matrix τd, has anexponential character in accordance with the Arrhe�nius equation (τ = τ0exp(ΔE/kT)).

4. CONCLUSIONS

The performed investigations have demonstratedthat the form of the phase diagram of the system ofsolid solutions (Na1 – xKxBi)1/2TiO3 doped with zinc atthe level of 0.1Bi(ZnTi)1/2O3 changes qualitatively. Inthe system of solid solutions 0.9(Na1 – xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3, the region of compositions of theR3m phase (in the undoped system, this region isextended (0.45 < x < 0.70)) is completely degenerate.The region of the existence of the tetragonal P4mmphase in this case is extended to the range 0.25 ≤ x ≤ 1,whereas the region of the existence of the rhombohe�dral R3c phase is narrowed (0 ≤ x ≤ 0.25). It has beenfound that, in the studied system of solid solutions,there is a morphotropic phase boundary lying in thecomposition region with xM ≈ 0.25, where the ceramicsexhibit properties of relaxor ferroelectrics.

The analysis of the temperature dependences of thereal and imaginary parts of the permittivity and theimpedance spectra has revealed specific features in themanifestation of the characteristics of the dielectricresponse of relaxor ferroelectric ceramics0.9(Na1 ⎯ xKxBi)1/2TiO3–0.1Bi(ZnTi)1/2O3 below andabove the temperature of the maximum of the permit�tivity ( ≈ 550 K). It has been found that, in the tem�

perature range above , the dielectric properties ofthe solid solutions correspond to a ferroelectric with adiffuse phase transition. In the temperature range T <

, the system transforms into the relaxor state. Thisstate is characterized by the maximum in the curveε''(T), which increases with an increase in the fre�quency and shifts toward higher temperatures, as wellas by the observed features in the frequency depen�

π2��αd/Bcos⎝ ⎠

⎛ ⎞1/ 1 αd–( )

Tm'

Tm'

Tm'

dence ε''( f ) and Cole–Cole diagrams. In the region ofthe existence of the relaxor state, the studied system ofsolid solutions has two polarization components, oneof which is associated with dipole clusters, whereas theother is related to the matrix. The temperature depen�dence of the contribution from the polarization ofdipole clusters is characterized by a curve with themaximum lying in the region of 400 K. A decrease inthis contribution with decreasing temperature belowthe temperature of the aforementioned maximum isdue to the process of freezing of dipole clusters, whichoccurs over an extended temperature range of morethan 200 K. The average time of relaxation of thedipole clusters increases with a decrease in the temper�ature to 400 K and remains almost constant with a fur�ther decrease in the temperature.

ACKNOWLEDGMENTS

This study was supported by the Belarusian Repub�lican Foundation for Fundamental Research (projectno. T11�052).

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Translated by O. Borovik�Romanova