ISSN 1063�7842, Technical Physics, 2013, Vol. 58, No. 11, pp. 1608–1613. © Pleiades Publishing, Ltd., 2013.Original Russian Text © M.V. Talanov, A.V. Turik, L.A. Reznichenko, 2013, published in Zhurnal Tekhnicheskoi Fiziki, 2013, Vol. 83, No. 11, pp. 60–66.

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INTRODUCTION

The study of reversible permittivity ε measured in aweak ac electric field during the application of a dc orslowly changing electric field E gives important infor�mation on the physics of polar dielectrics and the pos�sibility of their practical application. As a result, onecan determine tunability K = (ε(E = 0) – ε(E ≠0))/ε(E = 0), which is one of the basic functionalparameters of the materials used in microwave devices,e.g., radars and communication systems [1–3]. More�over, the understanding of the processes of domainswitching in ferroelectrics is necessary to create prom�ising samples of energy�independent ferroelectric ran�dom access memory (FRAM).

One of the specific features of ε(E) dependences forferroelectrics is the presence of minima, which mani�fest themselves when E increases (after a change in theE direction). Drougard and Young [4] were the first todetect these anomalies when studying tetragonal (T)BaTiO3 crystals. Their formation was related to themechanical compression of antiparallel domains, thenumber of which is maximal near coercive field Ec.Similar anomalies were observed during the investiga�tion of the reversible characteristics of orthorhombic(O) BaTiO3 crystal [5], ceramics based on the (1 –x)PbZrO3–xPbTiO3 (PZT) system [6–10], (011) ori�ented (1 – x)PbMg1/3Nb2/3O3(PMN)–xPbTiO3(PT)crystal at x = 0.32 [11], and lead�free ceramics basedon the system (1 – x)(Na,K,Li,Ba)(Nb0.9Ta0.1)O3–xSrZrO3 [12].

In [13], we considered the evolution of the revers�ible characteristic during an increase in the concen�tration of classical ferroelectric PT in the multicom�

ponent system PMN–PbNi1/3Nb2/3O3(PNN)–PbZn1/3Nb2/3O3(PZN)–PT (Fig. 1). At low PT con�centrations (below 0.30), we did not detect clearanomalies in the ε(E) dependences. An increase in thePT concentration beginning with 0.30 led to theappearance of a plateau in the range E = 3.0–7.0 kV/cm, which is close to the values of Ec deter�mined from dielectric hysteresis loops. At PT concen�trations >0.35, the plateau in the forward ε(E) curvestransformed into pronounced ε maxima typical of clas�sical ferroelectrics [4–10]. In this case, plateau�likesegments in the ε(E) dependences were detected forheterophase (T + pseudocubic (Psc)) samples and min�ima in ε(E) were detected for single�phase T samples.

Several models exist to explain the appearance ofminima in the ε(E) dependences of rhombohedral(Rh), T, and heterophase ceramics: they are based onthe contributions to ε of 180° and 90° domain switch�ing (for T samples) and 71° and 109° domain switch�ing (for Rh samples) [6, 9]. Nevertheless, these modelscannot explain the plateau�like segments in the ε(E)dependences of heterophase ceramics [13].

Apart from the switching processes caused by E,induced phase transitions, which result in substantialchanges in the macroscopic properties of materials,can occur. For example, the appearance of a plateau inthe ε(E) dependences of an (001) oriented (1 –x)PZN–xPT (x = 0.08) crystal was attributed to anelectric�field�induced phase transition into the Tphase [14], which was supported later [15]. Anincrease in E in the case of morphotropic composi�tions (1 – x)PMN–xPT (x ≈ 0.27–0.32) and (1 –x)PZN–xPT (x ≈ 0.07–0.09) leads to a complex

Reversible Permittivity of MulticomponentPMN–PT–Based Ceramics

M. V. Talanov, A. V. Turik, and L. A. ReznichenkoResearch Institute of Physics, Southern Federal University, pr. Stachki 194, Rostov�on�Don, 344090 Russia

e�mail: tmikle�man@mail.ruReceived December 25, 2012

Abstract—The reversible permittivity of Ba�doped ceramics of the multicomponent system mPMN–nPNN–yPZN–xPT (m = 0.1298–0.4844, n = 0.1266–0.4326, y = 0.0842–0.130, x = 0.25–0.40) is studied.The reversible permittivities of cubic, heterophase, and tetragonal ceramics are analyzed under various exper�imental conditions, such as the measuring ac electric field frequency and the time of residence in a dc biaselectric field. The transformation of permittivity minima into a plateau and the subsequent disappearance ofall anomalies as the lead titanate concentration decreases are assumed to be related to a change in the initialdomain structure of the material. A diagram illustrating the dependence of the tunability coefficient on thelead titanate concentration is plotted, and the ceramic compositions that correspond to the characteristicdependences of reversible permittivity are determined.

DOI: 10.1134/S1063784213110261

PHYSICAL SCIENCEOF MATERIALS

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REVERSIBLE PERMITTIVITY OF MULTICOMPONENT PMN–PT–BASED CERAMICS 1609

sequence of phase transitions [16–18]. Based on abinitio calculations, Fu and Cohen [19] showed that thesource of the giant piezoelectric effect in these materi�als can be a polarization–rotation mechanism relatedto the rotation of a polarization vector during the Rh–T phase transitions through an intermediate phase(phases). The authors of [20] used the eight�orderLandau–Ginzburg–Devonshire potential and pre�dicted the existence of two different monoclinic (M)phases with space groups Cm (MA, MB) and Pm (MC)that can serve as a structural bridge during E�inducedphase transitions apart from the O phase [21]. Thesephases were experimentally detected during the inves�tigation of morphotropic solid solutions (SSs) PMN–PT [22, 23], PZN–PT [24, 25], and PZT [26, 27].Moreover, it was shown in a number of works thatsome of these phases can exist near a morphotropicphase boundary [28, 29], which complicates thedomain structure and, hence, affects the macroscopicproperties [30, 31].

The purpose of this work is to reveal the causes ofthe plateau in the ε(E) dependences of heterophaseceramics based on relaxor ferroelectrics and PT.

EXPERIMENTAL

Ba�doped ceramics of the multicomponent systemmPMN–nPNN–yPZN–xPT with m = 0.1298–

0.4844, n = 0.1266–0.4326, y = 0.0842–0.130, andx = 0.25–0.40 were prepared by solid�phase synthesisusing columbite method elements [32] from prelimi�narily synthesized zinc, nickel, and magnesium nio�bates. Sintering was performed according to a stan�dard ceramic technology at T = 1180–1220°C. Theprocedure of sample preparation was described indetail in [33]. The samples to be tested were 1�mm�thick disks 10 mm in diameter. Metallization was car�ried out by double baking of a silver�containing paste.

The ε(E) dependences of unpoled samples weremeasured at room temperature in the ac measuringelectric field range 0.1–100 kHz on a test bed includ�ing an Agilent 4263B LCR�meter. The measurementswere carried out using reversible changes in the dc fieldstrength in the range from –20 to +20 kV/cm. Thevoltage was applied stepwise at residence time τ from1 s to 10 min.

RESULTS AND DISCUSSION

Figure 1 shows the ε(E) dependences of the ceram�ics under study with various PT concentrations x. As isseen From Fig. 1a, samples with a high PT concentra�tion (x = 0.40) are characterized by the ε(E) depen�dences that are typical of normal ferroelectrics. Thedecrease in the ε(E) curve is not related to 180°domain switching, the coarsening of a domain struc�

10

8

6

4

7.5

6.0

4.5

3.04.5

4.0

3.5

3.0

2.4

2.2

2.0

−15 −10 −5 0 5 10 15

10

8

6

4

6

5

4

3

2

3.0

2.7

2.4x = 0.400

x = 0.375

x = 0.325

x = 0.300

x = 0.275

x = 0.250

ε ×

10−

3ε ×

10−

3

ε ×

10−

3ε ×

10−

3

E, kV/cm

10

8

6

4

2

0 5 10 15 20E, kV/cm

ε ×

10−

3

x = 0.250 (C)x = 0.275 (Psc)x = 0.300 (Psc+T)x = 0.325 (Psc+T)x = 0.350 (Psc+T)x = 0.345 (Psc+T)x = 0.400 (T)

(a)

(b)

Fig. 1. ε(E) dependences of ceramics with various PT concentrations x at a measuring electric field frequency of 1 kHz and τ = 2 min:(a) loops and (b) forward runs (not initial) on the same scale [13].

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TALANOV et al.

ture, and (hence) a decrease in the contribution ofdomain wall motion. The minimum in ε(E) at E ≈7.0 kV/cm is caused by the compression of antiparalleldomains [4]. A decrease in E leads to a monotonicincrease in ε, and a hysteresis between the forward andbackward ε(E) curves appears. A decrease in the PT

concentration (x < 0.40) results in the transformationof the ε minima into plateau regions (x = 0.30–0.325)and their disappearance at x < 0.30 (Fig. 1b). More�over, as the PT concentration decreases, the morpho�tropic phase transition from T to cubic (C) phase,which is characteristic of relaxor ferroelectrics SSswith PT, takes place. At x ≈ 0.30–0.375, the T and Psc(phase the symmetry of which cannot be identifiedbecause of its weak and diffuse diffraction lines) phasescoexist.

Figure 2 shows the forward (not initial) ε(E) curvesobtained at various measuring electric field frequen�cies ( f = 0.1–100 kHz) for samples with a concentra�tion x = 0.25 (Fig. 2a), 0.30 (Fig. 2b), and 040 (Fig. 2c)and symmetry C, heterophase (T + Psc), and T,respectively. To estimate the dispersion depth, we usedthe parameter Δε/ε1 = (ε1 – ε10)/ε1, where ε1 and ε10

are the permittivities measured at f = 1 and 10 kHz,respectively. In the case of sample C at E < 2 kV/cm,the dispersion of ε is significant (Δε/ε1 = 0.089), whichis characteristic of relaxor ferroelectrics (Fig. 2a). Anincrease in E leads to the suppression of the dispersionof ε: at E > 8 kV/cm, Δε/ε1 decreases more than two�fold, down to Δε/ε1 = 0.033. This is likely to be relatedto the E�induced transition from a relaxor into a nor�mal ferroelectric state [34, 35] with a macroscopicdomain structure [13]. Similar ε(E) dependences wereobserved earlier for (1 – x)PMN–xPT (x = 0.10)ceramics [36]. Moreover, the authors of [36] reporteda significant decrease in the activation energy withincreasing E and attributed this decrease to the “shutdown” of a relaxation mechanism. They also notedthat E can result in removing the degeneracy of equiv�alent states and changing the potential well depths.

For the heterophase sample, we have Δε/ε1 = 0.054at E < 2 kV/cm, which is slightly lower than in the pre�vious case (Fig. 2b). As E increases, Δε/ε1 decreases to0.025. At E = 3.0–6.0 kV/cm (which corresponds tothe ε anomalies), we have Δε/ε1 = 0.038, which is closeto Δε/ε1 of sample T in weak electric fields (Fig. 2c).This finding can indicate that the heterophase sampleat E = 3.0–6.0 kV/cm is in a state close to sample Tat E < 2 kV/cm. This assumption is supported by theX�ray diffraction results in [37], which point to theE�induced phase transition in ceramics with a con�centration x = 0.30 from the heterophase (T + Psc)into the single�phase (T) state at the values of E corre�sponding to the plateau in the ε(E) dependence.T sample is characterized by an insignificant change inΔε/ε1 with increasing E (Δε/ε1 = 0.24 at E ≈ 2 kV/cmand Δε/ε1 = 0.18 at E ≈ 11 kV/cm), which is likely tobe related to the existence of a more homogeneousdomain structure characteristic of classical ferroelec�trics in the T phase (Fig. 2c).

Thus, the ε(E) curves and the change in Δε/ε1 dem�onstrate that the SS in the system under study canundergo both the morphotropic (as the PT concentra�tion increases) and the E�induced (as E increases)

0 5 10 15

0 5 10 15

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9

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6

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2.4

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x = 0.250 (C)

Δε/ε1 = 0.033

Δε/ε1 = 0.089

Δε/ε1 = 0.054

x = 0.300 (Psc+T)

Δε/ε1 = 0.038

Δε/ε1 = 0.025

x = 0.400 (T)

Δε/ε1 = 0.018

Δε/ε1 = 0.24

E, kV/cm

ε ×

10−

3ε ×

10−

3ε ×

10−

3

0.1110100

kHz

0.1110100

kHz

110100

kHz

(a)

(b)

0 5 10 15

(c)

Fig. 2. ε(E) dependences obtained at an electric field fre�quency f = 0.1–100 kHz and τ = 2 min for ceramics withvarious PT concentrations: x = (a) 0.250 (C), (b) 0.300(T + Psc), and (c) 0.400 (T). The regions for which the val�ues of Δε/ε1 are given are indicated.

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transitions from a relaxor to a normal ferroelectricstate.

Figure 3 shows the forward runs (not initial) of theε(E) dependences that were obtained under variousconditions of residence of heterophase samples with aconcentration x = 0.30 in an electric field. A decreasein the residence time from τ = 10 min to 1 s leads to asignificant increase of ε (at τ < 10 s) over the entire Erange (Fig. 3a). At τ = 1 s, the ε(E) curve has a maxi�mum corresponding to the values of Ec determinedfrom a dielectric hysteresis loop. In other words,reversible ε becomes close to differential ε at the min�imum values of τ. The transformation of the ε maxi�mum into a plateau with increasing τ is thought to berelated to the fact that the switching of non�clampeddomains contributes to ε at short τ, which is reflectedas the maximum in ε. At long τ, ε is determined by thecontribution of only clamped domains, since non�clamped domains have been switched.

Figure 3b shows the time relaxation of ε after anincrease in E at τ = 10 min. The changes in the ε(E)curves are maximal for the curves recorded at times of10 s and 1 min after a change in E (at E < 4 kV/cm).At a longer time after a change in E, the ε maximumthat is characteristic of the ε(E) dependences of theferroelectrics (at E ≈ 1 kV/cm) and is related to thereverse switching of non�180° domains disappears[38, 39]. This disappearance is likely to be explainedby the relatively fast times of domain switching (lessthan 1 min). In the E range corresponding to the plateauin the ε(E) dependence, ε remains almost unchanged,which can also be explained by the E�induced shut downof a relaxation mechanism (mechanisms) [36]. A fur�ther increase in E results in insignificant discrepanciesbetween ε(E) recorded at various waiting times.

Figure 4 shows a comparison of the ε(E) depen�dence of a heterophase sample with x = 0.30 and theE dependences of its unit cell parameters obtained byX�ray diffraction in [37]. In the E range correspondingto the plateau in the ε(E) dependence, T�phase cellparameter cT (deformation along the E direction), tet�ragonality cT/aT, and T cell volume VT increasesharply. Moreover, the E�induced phase transitionfrom the heterophase (T + Psc) into the single�phase(T) state occurs at E ≈ 5 kV/cm, and it is accompaniedby the limitation of domain switching in the range E =4.5–6.3 kV/cm [37]. Thus, an increase in E stimulatesthe phase transition related to changes in the structure(T + Psc T) and dielectric properties (relaxor fer�roelectric normal ferroelectric) of the material.

The authors of [7] noted that the domain compres�sion effect can be “smeared” near a phase transition,which manifests itself in the appearance of a plateau inthe ε(E) dependences of heterophase ceramics. As wasexperimentally found in [37], significant mechanicalstresses appear in heterophase ceramics as a result ofan electric�field�induced phase transition and therelated changes in a domain structure. These stresses

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0 5 10E, kV/cm

ε ×

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−3

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−3

1 s

2 s

1 min

5 min10 min

1 s

10 s

1 min

2.5 min

5 min

7.5 min

10 min

(a)

(b)

Fig. 3. ε(E) dependences of heterophase phase with x =0.300 obtained under various conditions of residence in anelectric field: (a) various values of τ and (b) relaxation of εat τ = 10 min. The time after changing E is given.

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TALANOV et al.

can limit domain switching, in particular, 90° domainswitching, which is also supported by the presence ofplateau�like anomalies in the E dependences of thelongitudinal strain of heterophase ceramics [40].Thus, the transformation of ε minima into a plateauand the subsequent disappearance of any anomalieswhen the PT concentration decreases can be associ�ated with a change in the initial domain structure ofthe material. The ε minima that are detected at highPT concentrations and caused by a relatively narrowEc distribution of domains are explained by mechani�cal clamping of domains. As the PT concentrationdecreases, the Ec distribution of domains becomeswider. Moreover, heterophase ceramics undergo astructural phase transition, which results in significantmechanical stresses that can limit domain switching.Ceramics with a low PT concentration has no classicdomain structure. As a result, an increase in E does notlead to the appearance of any ε anomalies related tomechanical clamping processes.

Figure 5 shows the diagram reflecting the dependenceof tunability coefficient K (at E = 20 kV/cm) on thePT concentration in ceramics prepared at various T.The PT concentration regions that correspond to themost typical ε(E) dependences are indicated. They arecharacterized by high values of K (~0.8) that weaklydepend on x and ε (~10000), anhysteretic ε(E) depen�dences, and the absence of pronounced ε anomalies

(region I, x < 0.3); medium values of K (0.35–0.8) andε (3000–8000), hysteretic ε(E) dependences, and theformation of plateau�like segments and implicit εmaxima with increasing E (region II, 0.3 ≤ x < 0.375);low values of K (~0.3) and ε (2500–3000), a pro�nounced hysteresis in ε(E) dependences, and the for�mation of pronounced ε minima with increasing E(region III, x ≥ 0.375).

An analysis of the diagram shows that the ceramicsof group I have the best parameters for application intunable devices. The maximum values of K for theseceramics were obtained at T = 1180 and 1220°C. Theapplication of the ceramics of groups II and III in suchdevices can be complicated because of low values of Kand ε and the presence of ε anomalies. It should benoted that the appearance of a plateau in the ε(E)dependences and longitudinal deformation can nega�tively affect the operation of destination drives, in par�ticular, actuators.

CONCLUSIONS

We studied the ε(E) dependences of Ba�dopedceramics of the multicomponent system mPMN–nPNN–yPZN–xPT (m = 0.1298–0.4844, n =0.1266–0.4326, y = 0.0842–0.130, x = 0.25–0.40)and found the following.

(1) The anomalies in the ε(E) dependencesinduced by a change in the PT concentration in thesystem were shown to undergo evolution: the localminima in the case of T samples transform into a pla�teau in the ε(E) dependences of heterophase samplesand are absent in the ε(E) dependences of cubic SSs.

(2) The appearance of a plateau in the ε(E) depen�dences is assumed to be caused by the E�inducedphase transition from a heterophase into a single�

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16.14

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4.035

4.0304.025

4.015

4.0100 2 4 6 8 10 12

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3

E, kV/cm

VT,

Å3

a Psc

, Å

c T,

Åa T

, Å

4.020(c

T/a

T −

1)

× 1

0−3 ,

Å

Fig. 4. Effect of E on ε, the unit cell volume, and the unitcell parameters of a sample with x = 0.300 [37].

0.8

0.6

0.4

0.25 0.30 0.35 0.40 x

1180°C1200°C1220°C

K

Fig. 5. Diagram reflecting controllability coefficient K (atE = 20 kV/cm) calculated for ceramics with various PTconcentrations synthesized at T = 1180–1220°C. Theceramic compositions that correspond to the most charac�teristic ε(E) dependences are indicated.

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REVERSIBLE PERMITTIVITY OF MULTICOMPONENT PMN–PT–BASED CERAMICS 1613

phase state (T + Psc T) and by the transition froma relaxor state with a pronounced dispersion of ε to anormal ferroelectric state.

(3) The manifestation of the anomalies of reversibleε of heterophase samples was analyzed at various τ,and the role of the limitation of domain switching inthe formation of a plateau in the ε(E) dependences wasconsidered.

(4) Based on an analysis of the dependence of tun�ability coefficient K on the PT concentration inceramics, we separated the SS compositions with themaximum values of K. It was shown that the ceramicsof group I prepared at T = 1180 and 1220°C have thebest parameters for application in tunable devices.

ACKNOWLEDGMENTS

This work was supported by state contractno. 16.513.11.3032.

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Translated by K. Shakhlevich