Electric field induced polarization and strain of Bi-based ceramiccompositesDae Su Lee, Soon Jong Jeong, Min Soo Kim, and Jung Hyuk Koh Citation: J. Appl. Phys. 112, 124109 (2012); doi: 10.1063/1.4770372 View online: http://dx.doi.org/10.1063/1.4770372 View Table of Contents: http://jap.aip.org/resource/1/JAPIAU/v112/i12 Published by the AIP Publishing LLC. Additional information on J. Appl. Phys.Journal Homepage: http://jap.aip.org/ Journal Information: http://jap.aip.org/about/about_the_journal Top downloads: http://jap.aip.org/features/most_downloaded Information for Authors: http://jap.aip.org/authors

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Electric field induced polarization and strain of Bi-based ceramic composites

Dae Su Lee,1,2,a) Soon Jong Jeong,1 Min Soo Kim,1 and Jung Hyuk Koh3

1Korea Electrotechnology Research Institute, Changwon 641-120, South Korea2National Core Research Center, Pusan National University, Pusan 609-735, South Korea3Department of Electronic Materials Engineering, Kwangwoon University, Seoul 139-701, South Korea

(Received 25 May 2012; accepted 19 November 2012; published online 21 December 2012)

The ferroelectric properties and strain behaviors of 0-3-type-ceramic composites were investigated.

(100-x)Bi0.5(Na0.75K0.25)TiO3-xBiAlO3 (x¼ 5, 6, and 7: abbreviated as 95BNKT-5BA, 94BNKT-

6BA, and 93BNKT-7BA, respectively, and the three compositions are altogether designated as

BNKT-BA) were chosen as a matrix materials, and ferroelectric Bi0.5Na0.5TiO3 (f-BNT),

Bi0.5(Na0.8K0.2)0.5TiO3 (f-BNKT), and 98.5Bi0.5(Na0.8K0.2)0.5TiO3-1.5BiAlO3 (f-BNKTBA) grains

as inclusions. Large f-BNT, f-BNKT, and f-BNKTBA grains strongly affect the ferroelectric

properties and strain behaviors of the BNKT-BA matrix in the composite. In 95BNKT-5BA with

f-BNT and f-BNKT, negative strain was observed, indicating that the ferroelectric phase is formed

and stabilized. 93BNKT-7BA with f-BNT, f-BNKT and f-BNKTBA showed an increase in positive

strain, which is associated with low field-induced phase transition. It was found from the strain

curve that two contributions, ferroelectric phase stabilization and phase transition activation, were

involved in the strain behaviors of the ceramic composites. VC 2012 American Institute of Physics.

[http://dx.doi.org/10.1063/1.4770372]

I. INTRODUCTION

Piezoelectric/electrostrictive materials and actuators have

been widely used in optics, astronomy, fluid control, and preci-

sion machining systems, due to their high generative force,

accurate displacement, and fast response to external electric

fields.1 Practical materials with a large piezoelectric/electro-

strictive strain are mainly lead-based ferroelectric single crys-

tals, and ceramics, such as Pb(Mg1/3Nb2/3)O3–PbTiO3, Pb(Zn1/3

Nb2/3)O3-PbTiO3, and Pb(Zr,Ti)O3 with some dopants.1–3 In

Pb-based antiferroelectric ceramics, such as Pb0.98La0.02(Zr0.66

Ti0.10Sn0.24)0.995O34 and Pb0.98La0.02(Zr0.70Hf0.30)TiO3,5 large

strain is the result of a field-induced transition from an antifer-

roelectric to a ferroelectric phase. The development of actua-

tors based on ceramic materials that undergo such a phase

transition under an electric field has attracted great interest in

the past decade.

In view of the current demand for global environmental

protection, lead-free materials are an important topic in stud-

ies of piezoelectric materials. Sodium-potassium-niobate

(K,Na)NbO36 and bismuth-sodium-titanate (Bi0.5Na0.5)TiO3

7

systems are promising ceramic families, which might soon

replace lead-based systems.

Among lead-free systems, the (Bi0.5Na0.5)TiO3-BaTiO3-

(K0.5Na0.5)NbO3 (BNT-BT-KNN)8 system shows a large

strain comparable to that of Pb(Zr,Ti)O3 (PZT), which is

attributed to the phase transition from an antiferroelectric or

relaxor (because the exact nature of the former phase has not

been fully explained, this phase is hereafter referred to as

relaxor), to ferroelectric phases. The material delivers an

electric-field induced strain as large as 0.45%, with an elec-

tric field of 8 kV/mm, which is proposed to be related to the

electric field-induced phase transition.9–13 This field is higher

than the field used to achieve maximum polarization and

strain in typical soft PZT systems, which remains a drawback

in piezoelectric applications.8

If the critical electric field required for the phase transi-

tion can be decreased to below 3�4 kV/mm, the material can

be used for practical applications. We have proposed the

concept that the field is reduced by modifying the micro-

structure of bismuth-based ceramics.14 In typical bismuth-

based ceramics, a phase transition can be induced by apply-

ing an external field for relaxor grains (Fig. 1(a)). This case

requires high field application. In the present study, we intro-

duce a microstructure, consisting of ferroelectric grains and

relaxor grains (Fig. 1(b)). The ferroelectric phase has a high

dielectric constant, and the relaxor phase has a low dielectric

constant. Because of the dielectric constant difference

between the two grains, most of the total voltage is initially

distributed across the relaxor phase regions, creating a higher

internal electric field strength in the relaxor phase regions

than the average field strength applied to the total material.

The field concentration in the relaxor phase region easily

induces the phase transition. This composite concept was

realized in a previous study.14 Although the concept has been

proven to be effective in Bi-based composite, questions still

remain of how the ferroelectric phase can affect the phase

transition in the relaxor phase. An assumption proposed in the

previous report should be clarified: only the dielectric con-

stant difference of two phases leads to a concentration of

electric field in the relaxor phase, and to resultant strain

behavior. Analogous to other phase transformation/phase

transition composites, where inclusions help the nucleation

and growth of a second heterogeneous phase in the matrix,15

there is also the curious matter of whether the existing large

a)Author to whom correspondence should be addressed. Electronic mail:

leeds@keri.re.kr.

0021-8979/2012/112(12)/124109/11/$30.00 VC 2012 American Institute of Physics112, 124109-1

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ferroelectric grains may serve as preferential sites of the

phase transition to a ferroelectric phase when an electric field

is applied. To confirm the questions, three ferroelectric mate-

rials were prepared to mix with a relaxor material exhibiting

phase transition upon field application. We chose BNKT-BA

as phase transition materials, because they have a relatively

low critical electric field for the phase transition.16 For the

choice of ferroelectric materials, we considered two extreme

cases; ferroelectric ceramic with a high coercive field and a

large remnant polarization (in this case, f-BNT), and ferro-

electric ceramics with a low coercive field and a low remnant

polarization (in this case, f-BNKT17 and f-BNKTBA16).

In this study, we have investigated electric field depend-

ent polarization and strain behavior of the ceramic compo-

sites, in order to demonstrate the realization of the composite

concept proposed in the previous report.14 The microstruc-

tural evolution in the composite, and its impact on the polar-

ization and strain were evaluated. In addition, the role of

ferroelectric f-BNT, f-BNKT, and f-BNKTBA in the com-

posite was studied. To do so, three types of composite mate-

rials, BNKT-BAþBNT, BNKT-BAþBNKT, and BNKT-

BAþBNKTBA, were fabricated. Also, the ferroelectric and

piezoelectric properties of the composites were measured.

II. EXPERIMENTAL PROCEDURE

To construct the inhomogeneous microstructure, large

ferroelectric f-BNT, f-BNKT, and f-BNKTBA single par-

ticles and BNKT-BA powders were prepared. f-BNT par-

ticles with a grain size over 5 lm were fabricated by a

molten salt method.18,19 In the first reaction, Bi2O3 (Cerac

Co., 99.9%) and TiO2 (Cerac Co., 99.9%) powders were

reacted in a NaCl and KCl (Cerac Co., 99.9%) flux at

1100 �C for 30 min, to obtain plate-like Bi4Ti3O12 precursor

particles. In the second reaction, the BNT single particles

were formed by reacting plate-like Bi4Ti3O12, Bi2O3,

Na2CO3, and TiO2 powders in a KCl and NaCl flux at

1100 �C for 30 min. Here, to reduce Pr and Ec of f-BNT,

0.5 mol. % BiAlO3 doping was performed. As a result,

BiAlO3-doped f-BNT exhibits higher Pr and Ec values

(almost 1.5 times larger) than that of f-BNKT. Residual al-

kali ions and chlorine were removed from the f-BNT single

particles, by repeated washing in deionized hot water. The

large f-BNKT and f-BNKTBA particles were also fabricated

by a molten salt method.

The BNKT-BA powders were prepared by a conven-

tional solid state reaction process. Bi2O3, Na2CO3, K2CO3,

TiO2, and Al2O3 were used as raw materials (99.9% purity).

These raw powders were ball-milled for 24 h in ethanol with

12 mm diameter zirconia balls. After drying, the mixed pow-

ders were calcined at 800 �C. The powders were then mixed

with f-BNT, f-BNKT and f-BNKTBA single particles, with

volume ratios of 10% and 20%. The mixed powders were

pressed into a disk of 12 mm diameter and 2 mm thickness.

The green compacts were sintered at 1150 �C for 12 h.

The relative densities of the ceramic disks, measured by

the Archimedes method, were higher than 96%. The crystal

structures of the sintered disks were determined by X-ray

diffractometry (Philips, X-Pert PRO MPD), using Cu Ka

radiation. Silver paste was applied on both sides of the sam-

ples to form electrodes for the measurement of electrical

properties. These specimens were poled in silicone oil, under

an electric field over 5 kV/mm at 60 �C. The specimens were

measured after 1 day of aging at room temperature. Polariza-

tion vs. electric field (P-E) hysteresis loops were measured

using Precision Premier II equipment (Radiant Technologies,

Inc.) at 100 mHz. Field-induced strains were measured using

a contact-type displacement sensor (Millitrion: Model 1240)

at 50 mHz. The piezoelectric properties were measured by

resonance-antiresonance method, using an impedance ana-

lyzer (HP4294A). The electromechanical coupling factor

was measured using the IEEE standard. To study the kinetics

of the switching in composites, the conventional square pulse

technique was employed by measuring the current flowing

through a series resistor to the sample electrodes.28 The rec-

tangular pulse was generated with a pulse generator and then

input into a high power pulse generator for power amplifica-

tion. The high power pulse generator has a maximum power

of 6 kW, and 10 A current can be supplied by the machine

under 5000 V with a pulse width of 10 ms. The rise time of

the pulse generator was shorter than 1 ls. The resistance

value of the series resistor was kept small, so that the circuit

has the resistance-capacitance (RC) time constant less than

1 ls. The tested specimens were cut with a thickness of

0.2 mm and an area of 25 mm2. The current flowing to the

sample electrode during the first pulse switching was

obtained by measuring the voltage across the series resistor.

The voltage as a function of time was stored with a digital

oscilloscope. The switching time was obtained by reading

the time at which the switching current falls to 10% of its

maximum value. The RC peaks obtained in the second pulse

were extrapolated to longer time, and the areas under the

peak were subtracted from the total areas to determine only

the switching current.

FIG. 1. Schematics of the polarization processes in (a)

polycrystalline materials, showing electric field induced

phase transition, and (b) polycrystalline materials con-

sisting ferroelectric large grains and relaxor matrix,

showing electric-field-induced phase transition.

124109-2 Lee et al. J. Appl. Phys. 112, 124109 (2012)

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III. RESULTS AND DISCUSSION

A. XRD and microstructure

The X-ray diffraction (XRD) patterns of BNKT-BA

without and with f-BNT (20%) ceramics are shown in Fig. 2.

The XRD patterns of all the ceramics indicated pure perov-

skite structure without secondary phases. Although all XRD

patterns are not shown in this paper, BNKT-BA with f-BNKT

and f-BNKTBA ceramics also exhibited perovskite structure.

Figure 3 shows the scanning electron micrographs

(SEMs) of as-sintered 94BNKT-6BA without and with

f-BNT, f-BNKT, and f-BNKTBA. The addition of f-BNT,

f-BNKT, and f-BNKTBA significantly influenced the grain

size of the 94BNKT-6BA ceramic. The 94BNKT-6BA with

f-BNT, f-BNKT, and f-BNKTBA samples exhibited a mix-

ture or composite of small 94BNKT-6BA and large f-BNT,

f-BNKT, and f-BNKTBA grains, respectively. The grain

size of 94BNKT-6BA are 0.5 lm�2 lm, and the large

f-BNT, f-BNKT, and f-BNKTBA grains are 5 lm�20 lm.

95BNKT-5BA and 93BNKT-7BA with f-BNT, f-BNKT,

and f-BNKTBA ceramics have similar microstructures.

B. Ferroelectric properties

Figure 4 displays the polarization versus electric field

for BNKT-BA with ferroelectric f-BNT, f-BNKT, and

f-BNKTBA. For comparison, the curves of Bi0.5(Na0.75

K0.25)0.5TiO3 and BNKT-BA are also included. The polariza-

tion behaviors of all composites investigated in this study

were close to that of relaxor BNKT-BA, when the applied

electric field was below 2 kV/mm. Under fields between

2 kV/mm and 4 kV/mm, the composite specimens showed an

abrupt jump in polarization, and approached that of Bi0.5

(Na0.75K0.25)0.5TiO3. This indicates that the composites have

similar polarization to the relaxor BNKT-BA at low field

application (<2 kV/mm), and then their polarization is close

to that of the ferroelectric Bi0.5(Na0.75K0.25)0.5TiO3 with high

field application, revealing that the phase transition from

relaxor to ferroelectric completes at fields less than 4 kV/mm.

The BNKT-BA with f-BNKTBA have a sharp polarization

change, in that the value of the composite matches those of

the relaxor BNKT-BA under low field, and the polarization

was almost in accordance with that of the ferroelectric

Bi0.5(Na0.75K0.25)0.5TiO3 with high field application.

Interestingly, the Pr and Ec of the BNKT-BA with

f-BNKTBA are smaller than those of the composites with

f-BNT and f-BNKT. These reductions of Pr and Ec in the

composite (see Table I) may be related to the polarization fea-

ture of f-BNKTBA. This may be because the f-BNKTBA with

low coercive field helps the BNKT-BA to be easily polarized,

more than f-BNT and f-BNKT with high coercive field.

The physical properties of f-BNKTBA, f-BNT, and

f-BNKT are listed in Table I. The piezoelectric coefficient

d33 and the electromechanical coupling factor kp decrease

with increasing amounts of BiAlO3 in the composite. When

the ferroelectric phase f-BNT, f-BNKT, and f-BNKTBA were

added to the BNKT-BA matrix, the d33 and kp increased.

On the other hand, the static dielectric constants er of the

relaxor BNKT-BA were higher than those of the ferroelectric

phases. This difference in dielectric constant is contrary to

the concept that the electric field would be concentrated on

the relaxor grains, when the dielectric constant of the relaxor

phase is lower than that of ferroelectric phase. In normal fer-

roelectric materials, the small signal static dielectric constant

is contributed by reversible polarization, i.e., ionic, elec-

tronic polarization, and ferroelectric domain switch. This

dielectric constant is an attribute of polarization in normal

ferroelectric materials. However, the phase transition devel-

oped in this study is associated with irreversible polariza-

tion.20,21 Therefore, reversible and irreversible polarizations

are the ferroelectric feature in the phase transition material.

The degree of the reversible and irreversible polarizations is

expressed with the dielectric coefficient,22,23 determined by

average slope of the polarization-electric field loop.23

Figure 5 shows the dielectric coefficient as a function

of electric field for BNKT-BA, f-BNT, f-BNKT, and

f-BNKTBA. The dielectric coefficients of f-BNT and

f-BNKT are lower than those of BNKT-BA in the fields

below 3 kV/mm (Figs. 5(a) and 5(b)). When the field is inFIG. 2. X-ray diffraction patterns of BNKT-BA without and with f-BNT

(20%). The XRD pattern of BNKT and f-BNT are included.

FIG. 3. Scanning electron microscopy images of as-sintered 94BNKT-6BA

without and with f-BNT (20%), f-BNKT (20%), and f-BNKTBA (20%).

124109-3 Lee et al. J. Appl. Phys. 112, 124109 (2012)

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the range of 3 kV/mm to 5 kV/mm, the dielectric coefficient

of BNKT-BA is lower than that of f-BNT and f-BNKT

(Figs. 5(a) and 5(b)). As a consequence, the field applied on

BNKT-BA is less than the field on f-BNT and f-BNKT at

E< 3 kV/mm, and in the range of 3 kV/mm < E< 5 kV/mm,

a higher field would be applied on the BNKT-BA. The

dielectric coefficient of f-BNKTBA is lower than that of

BNKT-BA in the fields below 2 kV/mm (Fig. 5(c)), whereas

BNKT-BA has a lower value than f-BNKTBA at 2�5 kV/

mm. These results imply that composites with f-BNKTBA

experience phase transition at lower electric field than com-

posites with f-BNT and f-BNKT.

C. Field induced strains

The strain behaviors of the composite were investigated.

The composite exhibited larger strain than relaxor BNKT-BA.

The strain behavior of the composites varies with the compo-

sition of matrix and the ferroelectric materials. Figure 6 shows

the plots of bipolar strains versus electric field for BNKT-BA

without and with f-BNT, f-BNKT, and f-BNKTBA.

95BNKT-5BA has increases in total strain (Stot) and negative

strain (Sneg) with the addition of f-BNT. Here, Sneg denotes a

result obtained from zero field strain to minimum values of

strain curves (see curve on the left-hand side of Fig. 6(a)).

94BNKT-6BA with 10% f-BNT showed total strain increase,

as well as positive strain (Spos). Spos is the value from the max-

imum strain to zero field strain. However, 94BNKT-6BA with

20% f-BNT has increment in negative strain. 93BNKT-7BA

with f-BNT has increased positive strain with slight increment

in negative strain.

The effects of f-BNKT and f-BNKTBA on the strain of

BNKT-BA specimens were also investigated. 95BNKT-5BA

with f-BNKT and f-BNKTBA show negative strain increase

with increasing ratio of ferroelectric grain, as shown in

Figs. 6(b) and 6(c). Other specimens, 94BNKT-6BA and

93BNKT-7BA with f-BNKT and f-BNKTBA, have only

positive strain increase with the addition of ferroelectric

grains. In 95BNKT-5BA, the total and negative strain

increases with increasing ratio of f-BNKT. The addition of

10% f-BNKT to 95BNKT-5BA brought increases in total

and positive strain. With further increases in the ratio of fer-

roelectric f-BNKT (20%), negative strain was observed. The

composite with f-BNKTBA showed increment in total and

positive strain, regardless of the BNKT-BA matrix. In addi-

tion, the 94BNKT-6BA þ 20% BNKTBA had a large bipo-

lar strain, with a relatively narrow hysteresis curve.

FIG. 4. Polarization-electric field curves of BNKT-BA with f-BNT (20%), f-BNKT (20%), and f-BNKTBA (20%). The curves of BNKT and BNKT-BA are

included.

124109-4 Lee et al. J. Appl. Phys. 112, 124109 (2012)

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D. Discussions

In ferroelectric materials, two mechanisms are involved

in generating strain when subjected to an external field:

relaxor-to-ferroelectric phase transition, and ferroelectric do-

main switching.24–27 Phase transition gives rise to only posi-

tive strain in bipolar strain behavior, whereas domain

switching generates negative strain, as well as positive strain

upon bipolar field application. In addition, the materials expe-

riencing field-induced ferroelectric phase transition (relaxor-

to-ferroelectric) have low Pr or no Pr, and low Ec. Domain

switching in ferroelectric materials has high Pr and Ec in

polarization behavior. These features have been described

many times in the literatures for lead-based ceramics24,25 and

bismuth-based ceramics.26,27 Negative strain and Pr are mac-

roscopic characteristics that explain the difference between

ferroelectric phase transition, and domain switching upon

bipolar field application. The composite, compromising

relaxor matrix (phase transition by field application), and

ferroelectric grain or filler (domain switching), exhibited

complicated polarization and strain behavior. Therefore, the

mechanism of the composite was evaluated by observing the

negative strain and Pr.

The Stot, Sneg, and Pr measured in Figs. 4 and 6 are

plotted in Fig. 7. High negative strains and high Pr were

observed for 95BNKT-5BA with f-BNT and f-BNKT, and

94BNKT-6BA with f-BNT. This means that the ferroelectric

phase is formed upon field application, and it is switched

upon reverse field application. Low negative strains were

observed for 94BNKT-6BA with f-BNKT and f-BNKTBA

(Fig. 7(b)), and 93BNKT-7BA with f-BNT, f-BNKT, and

f-BNKTBA (Fig. 7(c)). Meanwhile, the existence of high pos-

itive strain and low Pr, for 94BNKT-6BA with f-BNKTBA

and 93BNKT-7BA with f-BNT, f-BNKT, and f-BNKTBA, is

an indication of relaxor-to-ferroelectric phase transition and

ferroelectric-to-relaxor phase transition, with external field

application and removal.

Among all the specimens, the three composite speci-

mens of 94BNKT-6BA with 20% f-BNT, 20% f-BNKT, and

TABLE I. Ferroelectric and piezoelectric characteristics (er: Relative dielectric constant, Pr: Remnant polarization, Ec: Coercive field, Pmax: Maximum polar-

ization (at 5 kV/mm), d33: Piezoelectric constant, and kp: Electromechanical coupling factor).

er Pr (lC/cm2) Ec (kV/mm) Pmax (lC/cm2) d33 (pC/N) kp (%)

B0.5(N0.75K0.25)0.5TiO3 1166 25.3 2.5 34.6 128 18.3

f-BNT 354 41.8 4.3 40.3 83 15.8

f-BNKT 1143 37.3 2.9 43.5 151 19.0

f-BNKTBA 1459 22.8 1.4 33.0 56 16.2

95BNKT-5BA 1556 10.9 0.9 33.5 18 14.5

95BNKT-5BA þ 10% f-BNT 1440 22.1 1.3 36.5 142 17.3

95BNKT-5BA þ 10% f-BNKT 1483 22.8 1.2 39.7 150 16.8

95BNKT-5BA þ 10% f-BNKTBA 1532 16.6 1.1 36.8 24 14.2

95BNKT-5BA þ 20% f-BNT 1333 31.5 1.5 40.4 205 28.4

95BNKT-5BA þ 20% f-BNKT 1429 29.5 1.4 41.6 195 19.3

95BNKT-5BA þ 20% f-BNKTBA 1513 20.5 1.3 38.9 54 15.1

94BNKT-6BA 1534 7.12 0.8 31.2 17 13.6

94BNKT-6BA þ 10% f-BNT 1526 21.2 1.7 37.5 33 14.6

94BNKT-6BA þ 10% f-BNKT 1533 19.1 1.1 38.7 40 16.2

94BNKT-6BA þ 10% f-BNKTBA 1540 11.1 1.0 36.2 21 14.2

94BNKT-6BA þ 20% f-BNT 1421 24.3 1.4 39.5 65 15.5

94BNKT-6BA þ 20% f-BNKT 1483 15.0 1.3 39.9 58 15.1

94BNKT-6BA þ 20% f-BNKTBA 1530 13.0 1.2 38.9 30 14.9

93BNKT-7BA 1564 6.9 0.9 29.7 11 12.8

93BNKT-7BA þ 10% f-BNT 1530 9.9 1.4 34.7 22 14.4

93BNKT-7BA þ 10% f-BNKT 1545 10.8 1.4 36.3 21 14.3

93BNKT-7BA þ 10% f-BNKTBA 1568 8.9 1.0 32.9 19 13.4

93BNKT-7BA þ 20% f-BNT 1452 14.8 1.2 39.1 42 14.6

93BNKT-7BA þ 20% f-BNKT 1504 14.8 1.2 40.2 36 14.9

93BNKT-7BA þ 20% f-BNKTBA 1553 10.2 1.2 35.9 26 14.0

FIG. 5. Field dependence of the dielectric coefficient

for various BNKT-BA: (a) f-BNT, (b) f-BNKT, and (c)

f-BNKTBA.

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20% f-BNKTBA showed distinct strain behaviors, positive

strain and negative strain, which were related to the polariza-

tion behaviors. To evaluate the polarization and strain of the

composites, the three composite specimens were chosen and

compared with a polarization model proposed by Miller

et al.29–31

Several models describing the P-E loop of the ferroelec-

tric composites have been proposed and employed to explain

their properties.29–31 Miller’s model is effective in the evalu-

ation of lead-based layered composites without detailed

physical understanding. This model can be used for under-

standing the polarization behavior of the composites even if

there is a lack of physical analysis for the polarization

mechanism.

The comparison between the measurement of our speci-

mens and the calculation of the model was performed in

understanding the change in Pr, Ps, and Ec, which gives a

clue to evaluate the field-induced phase transition and strain

for the composite. The modified Miller’s model was con-

structed under an assumption that the P(C) (polarization of

composite) ¼ P(F) (polarization of ferroelectric phase) ¼P(R) (polarization of relaxor phase).32

According to the Miller’s model,29 the polarization of

ferroelectric phase is divided into polarization of the positive

and negative switching cycles. The dipole polarization

Pþ(E) of the positive domain switching cycle can be

expressed with Eq. (1).

pþðEÞ ¼ PsattanhE� EC

b

� �n

;with b ¼ Ec ln1þ Pr

Psat

� �1n

1� Pr

Psat

� �1n

264

375�1

;

(1)

Pr, Psat, and Ec are the positive remnant polarization, satura-

tion polarization, and coercive field of the hysteresis loop,

respectively. The negative switching cycle of dipole polar-

ization, P�(E), was determined with P�(E)¼�Pþ(�E).

With this model, the calculations for ferroelectric f-BNT, f-

BNKT, and f-BNKTBA were plotted in Fig. 8.

FIG. 6. Bipolar strains as a function of electric field of BNKT-BA, and with f-BNT, f-BNKT, and f-BNKTBA.

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The experimental P-E loop model for the relaxor mate-

rial, experiencing relaxor-to-ferroelectric phase transition,

consists of three equations in three regimes. The high-field

hysteresis portions of the double loops were defined by

functions similar to those for the ferroelectric material.

However, for the phase transition materials, the hysteresis

was offset by an electric field Eo, and a polarization Po.

These offsets corresponded to the local origins or centers of

the hysteresis portions of the loops. Parameters (Table II)

for the hysteresis loop equations in the phase transition ma-

terial (94BNKT-6BA in this case) are also shown in Fig.

8(d). In the quadrant I (þP, þE) region, the hysteresis loops

of the relaxor (R)-to-ferroelectric (F) transitions were deter-

mined by

PþðEÞ ¼ ðPsat � PoÞ tanhðE� E0Þ � Ec

2b

� �n

þ Po: (2)

The loop for the F to R reversion was expressed by

P�ðEÞ ¼ ðPsat � PoÞ tanh�ðE� E0Þ � Ec

2b

� �n

þ Po: (3)

Similarly, in quadrant III (�P, �E) region, the hystere-

sis loop was expressed by

PþðEÞ ¼ �ðPsat � PoÞ tanh�ðEþ EoÞ � Ec

2b

� �n

� Po ðfor R-F transitionÞ; and P�ðEÞ

¼ �ðPsat � PoÞ tanhðEþ EoÞ � Ec

2b

� �n

� Poðfor F-R reversionÞ: (4)

In the linear II regime, the loop was determined by

P 6 ðEÞ ¼ dP

dE6 Pð0Þ: (5)

FIG. 7. The Stot, Sneg, and Pr for composites plotted as a function of f-BNT, f-BNKT, and f-BNKTBA.

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From the equations of the two phases with a condition

of P(C)¼P(F)¼P(R), the P-E loop model for the composite

was calculated and then plotted in Fig. 9. The calculated P-E

loops from the model were compared with the measured

loops of the composites and 94BNKT-6BA. In the case of

low electric field E< 3 kV/mm, for the three different com-

posite cases, all calculated polarizations were in fairly good

agreement with the measured values. In addition, the calcu-

lated and the measured Pr coincide with each other.

Comparison between the composites and the 94BNKT-

6BA defines how the existence of the ferroelectric grains

allows the polarization and strain behaviors to change in the

composites. The P-E of the 94BNKT-6BA was expressed

with division into three regimes defined above: two small

loops are formed in the quadrant I and III regions, and the

linear relation of P to E in between them. In region I, Po and

Eo are defined as the polarization and field corresponding to

the center of a small loop.32 Therefore, these Po and Eo have

equivalent meanings to P(E¼ 0) and Ec in a typical ferro-

electric loop, respectively (corresponding to the switching or

removal of ferroelectric domains). That is, the Po and Eo are

the points which characterize the removal of the existing fer-

roelectric phase/domains in the phase transition material.

Accordingly, if the Pr of composite is above the Po of the

pure phase transition material, the existing ferroelectric

domain is likely to be stable even when the applied field is

removed.

The Pr of each composite was compared with the Po

of relaxor 94BNKT-6BA, and the results are shown as

below: for the composite of 94BNKT-6BA and f-BNT, Po

(94BNKT-6BA)¼ 17 lC/cm2 < Pr (94BNKT-6BA þ 20%

BNT)¼ 22 lC/cm2 < Pr (94BNKT-6BA)¼ 24 lC/cm2; for

the composite of 94BNKT-6BA and f-BNKT, Pr (94BNKT-

6BA þ 20% BNKT)¼ 14 lC/cm2 < Po (94BNKT-6BA)

¼ 17 lC/cm2 < Pr (94BNKT-6BA)¼ 24 lC/cm2; for the

composite of 94BNKT-6BA and f-BNKTBA, Pr (94BNKT-

6BA þ 20% BNKTBA)¼ 8 lC/cm2 < Po (94BNKT-6BA)

¼ 17 lC/cm2 < Pr (94BNKT-6BA)¼ 24 lC/cm2.

According to the comparison of Po and Pr (Table III),

the ferroelectric domains of the composite of 94BNKT-6BA

þ 20% BNT remains even after a positive field cycle in

which the field was applied and then removed. This leads to

the observation of negative strain in the S-E curve.

Meanwhile, the composites of 94BNKT-6BA þ 20%

BNKT and 94BNKT-6BA þ 20% BNKTBA showed the

complete removal of the existing ferroelectric domains with

a decrease of the applied field to zero. This results in the pos-

itive strain behavior.

As a consequence, in the composite of high Pr, the ferro-

electric phase still exists in the matrix even when the applied

FIG. 8. Measured and calculated P-E

loops of (a) f-BNT, (b) f-BNKT, (c)

f-BNKTBA, and (d) 94BNKT-6BA by a

modified Miller’s model.

TABLE II. Coercive field, polarization characteristics, and other factors of f-BNT, f-BNKT, f-BNKTBA, and 94BNKT-6BA with respect to the design of the

modified Miller’s model.

Psat (lC/cm2) Pr (lC/cm2) Ec (kV/mm) b n Eo (kV/mm) Po (lC/cm2) P(0) (lC/cm2) dP/dE

f-BNT 45 43 5 0.59 0.7 … … … …

f-BNKT 35 24.6 2.55 1.007 0.6 … … … …

f-BNKTBA 35 23.4 1.8 1.185 1.2 … … … …

94BNKT-6BA 32 24 3.2 … 1 2.2 17 7 …

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field decreased to zero. The composite of ferroelectric inclu-

sions with high Pr has negative strain in bipolar S-E curves.

Meanwhile, in case of specimens with the ferroelectric inclu-

sions of low Pr, at E¼ 0, ferroelectric domains are unstable

and the complete ferroelectric-to-relaxor phase reversion

takes place. This allows the observation of only positive

strain in S-E curves.

For E> 3 kV/mm, the experimental polarization devi-

ates from the calculated result. This polarization difference

is not solely due to the difference of dielectric constant but

to other factors.

Another possibility is related to the nucleation of ferro-

electric domains and their growth in relaxor matrix. The

existing ferroelectric phase has a high polar characteristic and

thus would serve as a preferential nucleation site for the ferro-

electric domain in the relaxor matrix when relaxor-to-ferro-

electric phase transition takes place upon field application.

The nucleation and growth of ferroelectric domains (phase)

are expected to occur in a region of the matrix, being near

large ferroelectric grains. This possibility was evaluated with

a modified Kolmogorov-Avrami-Ishibashi (K-A-I) model33,34

and polarization reversal which has been widely used to

understand the kinetics of ferroelectric phase transition in fer-

roelectric materials, especially thin films and composites.

Both processes, nucleation and growth, are related to the

applied electric field, in that the applied electric field energy

can activate both process.35 We have estimated an average

domain wall velocity v as well as the nucleation rate R as a

function of the electric field E. For the polarization reversal

in ferroelectric materials, the switching time under a low

field level is controlled by the nucleation of new domains or

ferroelectric phase. The switching time ts and the maximum

switching current Imax can be expressed by the following

relations under low electric field:

Imax � e�a

Eapplied

� �and

1

ts� e

�a

Eapplied

� �; (6)

where a is the so-called activation field or threshold field.

Under a high field, the switching is controlled by phase wall

motion. The switching time and Imax can be expressed by the

following relations with the applied field:

Imax � KEapplied and1

ts� KEapplied; (7)

where K is a constant, being a measure of the ease with

which the phase walls move.

When Imax or 1/ts is plotted against E, an exponential

relation holds in the low field region within which the nucle-

ation of new phase controls the switching and a linear rela-

tion holds in the high field region within which the phase

wall motion controls the switching. On the other hand, when

ln(Imax) or ln(1/ts) is plotted against 1/E, a linear relation

should hold in the low field region, within which nucleation

of the new ferroelectric domain controls the switching, but

not in the high field region, within which the wall growth

controls the switching.

Figure 10 shows the plots of switching current (I) versus

time (t), maximum switching current (Imax) versus electric

field (E), and the switching time inverse (1/ts) versus electric

field (E) for the 94BNKT-6BA þ 20% BNKT composite and

the 94BNKT-6BA relaxor. The switching current-time

curves are plotted in the Fig. 10(a). Increase in switching

current with electric field was obtained along with the obser-

vation of the maximum current at the shorter time as the

increase in the field. This is the same tendency of switching

in polarization reversal of normal ferroelectric materials.36,37

Imax versus E and 1/ts versus E curves are displayed in the

FIG. 9. Measured and calculated P-E loops for composites of 94BNKT-6BA with (a) f-BNT, (b) f-BNKT, and (c) f-BNKTBA.

TABLE III. Coercive field and polarizations of 94BNKT-6BA and composites.

Ec (kV/mm) Psat (lC/cm2) Pr (lC/cm2) Eo (kV/mm) Po (lC/cm2) P(0) (lC/cm2)

96BNKT-6BA 3.2 32 24 2.2 17 7

Ec (kV/mm) Psat (lC/cm2) Pr (lC/cm2)

94BNKT-6BA þ 20% BNT 1.6 35 22

94BNKT-6BA þ 20% BNKT 2.0 35 14

94BNKT-6BA þ 20% BNKTBA 2.4 34.6 8

124109-9 Lee et al. J. Appl. Phys. 112, 124109 (2012)

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Fig. 10(b). In the composite, the relation of 1/ts versus E fol-

lows exponential law and the switching start at 3 kV/mm.

The relaxor shows the exponential relation of 1/ts versus E,

in a high field region above 3.5 kV/mm. These data also

show the 1/ts of the composite > 1/ts of the pure relaxor and

Imax of the composite > Imax of the pure relaxor. This indi-

cates that the nucleation occurs more rapidly for the compos-

ite than that for the pure relaxor.

The activation field calculated from the relation is 3 kV/

mm for the composite and 3.5 kV/mm for the pure relaxor,

respectively. The activation field for Pb0.92La0.08(Zr0.65-

Ti0.35)O3 and Nb-doped Pb(Zr,Ti)O3 ferroelectric ceramics38

have been reported to be about 0.4 kV/mm and 1 kV/mm,

respectively. The activation fields of the composite and the

pure relaxor are much higher than those observed for ferro-

electric ceramics, which indicates that the nucleation of a

new domain is more difficult than the nucleation of new

domains in normal ferroelectric ceramics.

As a consequence, the difference of polarization

between the calculation and the measurement with fields

>3 kV/mm can be explained by the following.

The real ferroelectric material does not have completely

uniform structure/media, but spatially inhomogeneous struc-

ture. This means that the ferroelectric materials possess inho-

mogeneous threshold field under an electric field in domain

kinetics. For spatially non-uniform threshold field Eth, the

switching is obtained in all regions,39 in which

ElocðnÞ ¼ EexðnÞ þ Erd þ Eb > Eth; (8)

where Eloc is the local electric field, Erd is the residual depo-

larization field produced by bound charges and partially

compensated by external screening, Eex is the external

applied field, and Eb is the internal bias field.

In this composite case, another term is included in the

Eloc;

ElocðnÞ ¼ EexðnÞ þ Erd þ Eb þ ER�F > Eth; (9)

ER-F is the local field coming from the ferroelectric grains in

the relaxor matrix. The polarization field from the ferroelec-

tric grains influences the nucleation of new ferroelectric

phase in relaxor grains, being located near the existing ferro-

electric grains. Therefore, the larger polarization was

observed under the lower applied field Eex.

The composites exhibited larger polarization and strain

with field higher than 3 kV/mm compared to the calculated

results from the modified Miller’s model. The switching cur-

rent results for the composite and pure relaxor have the

nucleation-controlled switching at high field level. The

nucleation for the composite is more rapid than that for the

pure relaxor. This is attributed to the presence of ferroelec-

tric large grains, which allows low field-induced phase tran-

sition and its associated strain.

In composite systems of ferroelectric material and

dielectric material with field-induced phase transition char-

acteristics, the selection of ferroelectric material can control

the ferroelectric and piezoelectric features. Finding ferro-

electric phases with low Pr and Ec enables the composite to

be easily polarized, and transformed from relaxor phase to

ferroelectric phase.

IV. CONCLUSION

The effects of ferroelectric phase grains on ferroelectric

and strain behaviors of a composite consisting of ferroelec-

tric and relaxor phases were investigated. Three types of fer-

roelectric phases, f-BNT, f-BNKT, and f-BNKTBA, were

prepared. They have different coercive fields Ec (f-BNT >

FIG. 10. (a) Switching current (I) versus

time (t), (b) maximum switching current

(Imax) versus electric field (E) and the

switching time inverse (1/ts) versus elec-

tric field (E) for the 94BNKT-6BA þ20% BNKT and the 94BNKT-6BA.

124109-10 Lee et al. J. Appl. Phys. 112, 124109 (2012)

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f-BNKT > f-BNKTBA), and remnant polarization Pr

(f-BNT > f-BNKT > f-BNKTBA). The existence of f-BNT,

f-BNKT, and f-BNKTBA allows low-field-induced phase

transition of the composite, which is due to the effective

dielectric coefficient difference between the two phases. In

95BNKT-5BA, negative strain was observed with the advent

of ferroelectric phase f-BNT and f-BNKT, indicating that the

ferroelectric phase was formed and stabilized. 93BNKT-

7BA with f-BNT, f-BNKT, and f-BNKTBA showed an

increase in positive strain, which is related to ferroelectric

phase transition with low field application, and the reverse

transition upon removal of the field. It was found from the

strain behaviors that two contributions were involved in the

composite of ferroelectric grains and relaxor matrix: ferro-

electric phase transition, and stabilization of the newly

formed ferroelectric phase. The ferroelectric phase stabiliza-

tion may be related to the remnant polarization of f-BNT, f-

BNKT, and f-BNKTBA.

ACKNOWLEDGMENTS

This research was supported by a grant from the collabo-

rative research program funded by the Korea Research

Council for industrial science & technology.

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