Electrostrictive effect in ferroelectrics: An alternative approach to improve piezoelectricity

TLDR: In this paper, the electrostrictive effect of perovskite solid solutions was systematically surveyed and the techniques for measuring the effect of electrostriction on the piezoelectric activity of these materials were presented.

Abstract: Electrostriction plays an important role in the electromechanical behavior of ferroelectrics and describes a phenomenon in dielectrics where the strain varies proportional to the square of the electric field/polarization. Perovskite ferroelectrics demonstrating high piezoelectric performance, including BaTiO3, Pb(Zr1-xTix)O3, and relaxor-PbTiO3 materials, have been widely used in various electromechanical devices. To improve the piezoelectric activity of these materials, efforts have been focused on the ferroelectric phase transition regions, including shift the composition to the morphotropic phase boundary or shift polymorphic phase transition to room temperature. However, there is not much room left to further enhance the piezoelectric response in perovskite solid solutions using this approach. With the purpose of exploring alternative approaches, the electrostrictive effect is systematically surveyed in this paper. Initially, the techniques for measuring the electrostrictive effect are given and compa...

Figures

FIG. 4. Schematic figure of domain reorientation effect on determination of longitudinal electrostrictive coefficient Q33, where 90 and 180 domain reorientations are considered. In figure (a), the d33, E, and PS are piezoelectric coefficient, coercive field, and spontaneous polarization, respectively. The S3 and S1 are the spontaneous strain along c and a crystallographic axes, respectively.

FIG. 3. The polarization-electric field, strain-electric field, and strainpolarization loops for nonlinear dielectrics (taking [001] oriented PMN crystal as example).

FIG. 2. The polarization-electric field, strain-electric field, and strainpolarization loops for linear dielectrics. Reprinted with permission from G. Viola, T. Saunders, X. Wei, K. B. Chong, H. Luo, M. J. Reece, and H. Yan, J. Adv. Dielectr. 3, 1350007 (2013). Copyright 2013 World Scientific Publishing Company.27

FIG. 16. The temperature-dependent properties, (a) piezoelectric coefficient d15, (b) dielectric constant e11, (c) spontaneous polarization Ps, and (d) electrostrictive coefficient Q1313 for single domain PMN-0.28PT, PMN-0.32PT, and PMN-0.37PT crystals. The coefficients of rhombohedral, orthorhombic, and tetragonal crystals were measured in the standard coordinates of 3m, mm2, and 4mm symmetries, respectively. The PPTs of PMN-0.28PT, PMN-0.32PT, and PMN-0.37PT crystals are 93, 80, and 45 C, respectively. Reprinted with permission from Appl. Phys. Lett. 102, 152910 (2013). Copyright 2013 AIP Publishing LLC.26

FIG. 15. The temperature dependence of electrostrictive coefficient Q of Bi0.5(Na0.82K0.18)0.5TiO3 and PZT ceramics. After Refs. 83 and 87.

FIG. 26. Dielectric constant e 33=e0 and Q 33e 33=e0 as a function of electrostrictive coefficient Q 33 for domain engineered PMN-xPT crystals. Solid circles indicate the experimental data listed in Table VI, while the hollow circles are predicted data. By linear fitting of logðQ 33Þ vs. logðe 33=e0Þ, the dielectric constants e 33=e0 and Q 33e 33=e0 for PMN-PT crystal system were predicted with coefficient Q 33 being 0.09 (typical value of PT crystal) and 0.11 m4/C2 (typical value of BT crystal), respectively.

Full text

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Electrostrictive effect in ferroelectrics: An alternative approach to improve
piezoelectricity
Fei Li, Li Jin, Zhuo Xu, and Shujun Zhang
Citation: Applied Physics Reviews 1, 011103 (2014); doi: 10.1063/1.4861260
View online: http://dx.doi.org/10.1063/1.4861260
View Table of Contents: http://scitation.aip.org/content/aip/journal/apr2/1/1?ver=pdfcov
Published by the AIP Publishing
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05:21:27

APPLIED PHYSICS REVIEWS—FOCUSED REVIEW
Electrostrictive effect in ferroelectrics: An alternative approach to improve
piezoelectricity
Fei Li,
1
Li Jin,
1
Zhuo Xu,
1
and Shujun Zhang
2,a)
1
Electronic Materials Research Laboratory, Key Laboratory of the Ministry of Education and International
Center for Dielectric Research, Xi’an Jiaotong University, Xi’an 710049, China
2
Materials Research Institute, Pennsylvania State University, University Park, Pennsylvania 16802, USA
(Received 14 July 2013; accepted 2 October 2013; published online 15 January 2014)
Electrostriction plays an important role in the electromechanical behavior of ferroelectrics and
describes a phenomenon in dielectrics where the strain varies proportional to the square of the
electric field/polarization. Perovskite ferroelectrics demonstrating high piezoelectric performance,
including BaTiO
3
,Pb(Zr
1-x
Ti
x
)O
3
, and relaxor-PbTiO
3
materials, have been widely used in various
electromechanical devices. To improve the piezoelectric activity of these materials, efforts have been
focused on the ferroelectric phase transition regions, including shift the composition to the
morphotropic phase boundary or shift polymorphic phase transition to room temperature. However,
there is not much room left to further enhance the piezoelectric response in perovskite solid solutions
using this approach. With the purpose of exploring alternative approaches, the electrostrictive effect
is systematically surveyed in this paper. Initially, the techniques for measuring the electrostrictive
effect are given and compared. Second, the origin of electrostriction is discussed. Then, the
relationship between the electrostriction and the microstructure and macroscopic properties is
surveyed. The electrostrictive properties of ferroelectric materials are investigated with respect to
temperature, composition, phase, and orientation. The relationship between electrostriction
and piezoelectric activity is discussed in detail for perovskite ferroelectrics to achieve new
possibilities for piezoelectric enhancement. Finally, future perspectives for electrostriction studies are
proposed.
V
C
2014 AIP Publishing LLC.[http://dx.doi.org/10.1063/1.4861260]
TABLE OF CONTENTS
I. INTRODUCTION ............................ 2
II. THE DETERMINATION OF THE
ELECTROSTRICTIVE COEFFICIENTS........ 2
A. Electrostrictive coefficients measured by
strain versus the polarization/electric field . . 3
B. Electrostrictive coefficients measured using
the dielectric permittivity versus the applied
stress .................................. 4
C. Electrostrictive coefficients determined
using the piezoelectric coefficients. ........ 5
D. Electrostrictive coefficients determined
from the lattice parameters . .............. 6
E. Electrostrictive coefficients determined from
the dielectric permittivity under a DC-
biased electric field . ..................... 6
III. THE ORIGIN OF ELECTROSTRICTION. . . . . . 6
IV. ELECTROSTRICTION WITH RESPECT TO
THE MICROSCOPIC AND MACROSCOPIC
CHARACTERISTICS . . ..................... 8
A. Microscopic characteristics versus the
electrostrictive effect . . .................. 8
B. Macroscopic characteristics versus the
electrostrictive effect . . .................. 9
1. Dielectric and elastic responses versus
the electrostrictive effect . . . . . . . . . . . . . . 9
2. Thermal expansion versus the
electrostrictive effect . . ............... 10
V. ELECTROSTRICTION IN PEROVSKITE
FERROELECTRICS . . . ...................... 11
A. Electrostrictive effect versus ferroelectric
phase transitions . . ...................... 12
1. Polymorphic phase transition (PPT,
phase transitions induced by
temperature) . . . ...................... 12
2. Morphotropic phase boundary (MPB,
phase transitions induced by
composition) . . . ...................... 13
B. Orientation dependence of electrostriction . . 14
C. Electrostrictive coefficient Q versus the
electromechanical properties . . . . . . . . . . . . . . 15
1. Electrostrictive coefficient Q versus the
electric field-induced strain . . . . . . . . . . . . 15
2. Electrostrictive coefficient Q versus
piezoelectric activity .................. 16
a)
Author to whom correspondence should be addressed. Electronic mail:
soz1@psu.edu; shujunzhang@gmail.com.
0021-8979/2014/1(1)/011103/21/$30.00
V
C
2014 AIP Publishing LLC1, 011103-1
APPLIED PHYSICS REVIEWS 1, 011103 (2014)
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05:21:27

3. Can piezoelectric activity be improved
with electrostriction? .................. 17
VI. CONCLUSIONS AND FUTURE
PERSPECTIVES............................ 18
I. INTRODUCTION
Electrostriction is a basic electromechanical phenom-
enon in all insulators or dielectrics. It describes the electric
field/polarization-induced strain (S
ij
) that is proportional to
the square of electric field (E
i
)/polarization (P
i
), expressed in
the following equations:
S
ij
¼ Q
ijkl
P
k
P
l
;
S
ij
¼ M
ijkl
E
k
E
l
;
(1)
where Q
ijkl
and M
ijkl
are electrostrictive coefficients.
Electrostriction is a four-rank tensor property; thus it can be
observed in all crystal symmetries.
1
The strain induced by the electrostrictive effect is gener-
ally small when compared with that induced by piezoelectric-
ity. Consequently, there has been limited attention focusing on
the electrostrictive effect. In the 1980s, a systematic study on
electrostriction was carried out on relaxor ferroelectrics
with perovskite structures, such as Pb(Mg
1/3
Nb
2/3
)O
3
(PMN),
Pb(Zn
1/3
Nb
2/3
)O
3
(PZN), and 0.9Pb(Mg
1/3
Nb
2/3
)O
3
-0.1PbTiO
3
(PMN-0.1PT) single crystals/ceramics, in which a high electro-
strictive strain was observed because of the high dielectric
response of the relaxors.
2–7
Relaxors offer several advantages
over ferroelectric materials, including low hysteresis in the
strain-field response (excellent displacement accuracy), no
remnant strain, reduced aging effects, and they do not require
poling.
3
Compared with classical ferroelectric ceramics, these
materials are believed to have potential for use in actuator
applications such as inchworms, micro-angle adjusting devi-
ces, and bistable optical devices, where reproducible and
non-hysteretic deformation responses are required.
3
In addi-
tion, in the 1990s, investigations on electrostriction were per-
formed on polymers,
8–15
including ferroelectric polymers,
dielectric elastomers, and polymer composites. Ultra-high elec-
trostrictive strains were observed in these polymeric materials
(>4% for polyvinylidene fluoride [PVDF] and >40% for sili-
cone), giving them potential for use in actuator applications.
15
On the other hand, ferroelectrics are the mainstay mate-
rials for piezoelectric transducer and actuator applications
and have been reported to possess much higher piezoelectric
responses when compared with non-ferroelectric materials.
16
Typical ferroelectric single crystals and ceramics, including
barium titanate (BaTiO
3
, BT) (reported in the 1940s),
17
lead
titanate zirconate (Pb(Zr
1-x
Ti
x
)O
3
, PZT) polycrystalline
ceramics (reported in the 1950s),
17
and relaxor-PT based sin-
gle crystals (reported in the 1980s to 1990s),
18–23
exhibited
piezoelectric responses that are two to three orders higher
than Quartz crystals (first piezoelectric crystal 2 pC/N).
Similar to inorganic ferroelectrics, ferroelectric polymers
such as PVDF also possess a higher piezoelectric response
than their nonferrous counterpart.
24,25
Thus, it is desirable to
understand the origins of high piezoelectric activity in ferro-
electrics. For ferroelectrics whose paraelectric phase is cen-
trosymmetric, the piezoelectric coefficient d
mij
can be
expressed as a derivative of strain to electric field
d
mij
¼
@S
ij
@E
m
¼
Q
ijkl
P
k
@P
l
@E
m
þ
Q
ijkl
P
l
@P
k
@E
m
¼ Q
ijkl
P
k
e
lm
þ Q
ijkl
P
l
e
km
; (2)
where e
ij
is the dielectric permittivity, and i, j, k, l, and
m ¼1, 2, or 3. Equation (1) is used as the expression of strain
(S
ij
). Equation (2) indicates that the piezoelectric coefficients
of these ferroelectrics originate from the electrostrictive
effect, spontaneous polarization, and the dielectric response.
Figure 1 shows that the piezoelectric coefficients can be
recognized as the slope of the electrostrictive strain versus
the electric field. Thus, we can conclude that the high piezo-
electric response in ferroelectrics is established on the
electrostrictive effect and is associated with a large “bias
polarization” (spontaneous polarization). The electrostrictive
effect plays a key role in the electromechanical behavior in
ferroelectrics, investigations on which will benefit the explo-
ration of high-performance piezoelectrics. In this paper, the
investigations on the electrostrictive effect are surveyed, fo-
cusing on ferroelectric-related materials. First, the measure-
ment methods of the electrostrictive effect are given and
compared. Second, the origin of electrostriction is discussed
for ionic crystals. Then, the relationshi ps between the elec-
trostriction and the crystal structure, dielectric response,
elastic pr operty and thermal expansion are surveyed. The
electrostrictive properties of the ferroelectric materials are
investigated with respect to temperature, composition, ferro-
electric phase, and orientation. Finally, the contribution of
electrostriction to the piezoelectric activity is discussed in
detail for perovskite ferroelectrics, and we outline a possible
approach for improving the piezoelectricity through the elec-
trostrictive effect.
II. THE DETERMINATION OF THE
ELECTROSTRICTIVE COEFFICIENTS
To determine the electrostrictive coefficients, five
approaches have been proposed in the literature. These are
based on the strain-polarization/electric field curves, dielec-
tric permittivity-stress curves, the piezoelectric effect for the
FIG. 1. Schematic plot of the relationship between electrostriction and pie-
zoelectric effects. Due to the high “bias polarization,” an ac electric field
can induce ac strain with the same frequency of electric field.
011103-2 Li et al. Appl. Phys. Rev. 1, 011103 (2014)
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Frequently asked questions

Q1. What are the contributions in "Electrostrictive effect in ferroelectrics: an alternative approach to improve piezoelectricity" ?

With the purpose of exploring alternative approaches, the electrostrictive effect is systematically surveyed in this paper. 

Q2. What are the advantages of relaxors over ferroelectric materials?

2–7 Relaxors offer several advantages over ferroelectric materials, including low hysteresis in the strain-field response (excellent displacement accuracy), no remnant strain, reduced aging effects, and they do not require poling. 

Q3. What is the definition of the strain in a polymer?

Ultra-high electrostrictive strains were observed in these polymeric materials (>4% for polyvinylidene fluoride [PVDF] and >40% for silicone), giving them potential for use in actuator applications. 

Q4. What is the role of the electrostrictive effect in ferroelectrics?

The electrostrictive effect plays a key role in the electromechanical behavior in ferroelectrics, investigations on which will benefit the exploration of high-performance piezoelectrics. 

Q5. What is the effect of the strain on the ferroelectrics?

Similar to inorganic ferroelectrics, ferroelectric polymers such as PVDF also possess a higher piezoelectric response than their nonferrous counterpart. 

Q6. What is the strain of a relaxor?

16 Typical ferroelectric single crystals and ceramics, including barium titanate (BaTiO3, BT) (reported in the 1940s), 17 lead titanate zirconate (Pb(Zr1-xTix)O3, PZT) polycrystalline ceramics (reported in the 1950s),17 and relaxor-PT based single crystals (reported in the 1980s to 1990s),18–23 exhibited piezoelectric responses that are two to three orders higher than Quartz crystals (first piezoelectric crystal 2 pC/N). 

Q7. What are the electrostrictive properties of ferroelectrics?

The electrostrictive properties of the ferroelectric materials are investigated with respect to temperature, composition, ferroelectric phase, and orientation. 

Q8. What is the dmij coefficient for ferroelectrics?

For ferroelectrics whose paraelectric phase is centrosymmetric, the piezoelectric coefficient dmij can be expressed as a derivative of strain to electric fielddmij ¼ @Sij @Em ¼ QijklPk@Pl @Em þ QijklPl@Pk @Em¼ QijklPkelm þ QijklPlekm; (2)where eij is the dielectric permittivity, and i, j, k, l, and m¼ 1, 2, or 3. 

Q9. What is the definition of the term?

It describes the electric field/polarization-induced strain (Sij) that is proportional to the square of electric field (Ei)/polarization (Pi), expressed in the following equations:Sij ¼ QijklPkPl; Sij ¼ MijklEkEl;(1)where Qijkl and Mijkl are electrostrictive coefficients. 

Q10. What is the definition of the strain induced by the relaxor ferroelectrics?

In the 1980s, a systematic study on electrostriction was carried out on relaxor ferroelectrics with perovskite structures, such as Pb(Mg1/3Nb2/3)O3 (PMN), Pb(Zn1/3Nb2/3)O3 (PZN), and 0.9Pb(Mg1/3Nb2/3)O3-0.1PbTiO3 (PMN-0.1PT) single crystals/ceramics, in which a high electrostrictive strain was observed because of the high dielectric response of the relaxors. 

Q11. What is the eij of the piezoelectric coefficients of ferroelectric?

Equation (2) indicates that the piezoelectric coefficients of these ferroelectrics originate from the electrostrictive effect, spontaneous polarization, and the dielectric response. 

Q12. What is the effect of the electrostrictive effect on ferroelectrics?

the authors can conclude that the high piezoelectric response in ferroelectrics is established on the electrostrictive effect and is associated with a large “bias polarization” (spontaneous polarization).