Zuo-Guang. Ye Advanced Dielectric Piezoelectric and Ferroelectric Materials: Synthesis, Characterisation and Applications

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Handbook of dielectric, piezoelectric and ferroelectric materials260

The electromechanical coupling factor

in the rotated orientation is then

given by

9.23

Because we are particularly interested in the

and

for these crystals,

their rotated values are plotted in Figs 9.5 and 9.6, respectively. In both

figures, (a) is the orientational dependence of the amplitude in 3D and (b) is

a particular 2D cross section of (a). The distance between the origin and a

point on the surface in Figs 9.5(a) and 9.6(a) or a point on the curve in Figs

9.5(b) and 9.6(b) represents the absolute value of the constant in the

corresponding direction. The maximum values of

and

can be obtained

in the 63.0° and 70.8° directions, respectively, from the dipolar direction, in

which the maximum effective piezoelectric constant

reaches 2411 pC/N

and the electromechanical coupling factor

reaches 0.94. In fact, if one

uses the single domain data set to directly calculate the properties along

[001] (54.74° from the dipolar direction), the effective values are

= 2316

pC/N and

= 0.93, which are almost the same as those directly measured

values for multi-domain PMN–33%PT single crystals. The effective

along the [001] direction decreases to 134 pC/N, which is very close to the

measured

=143 pC/N in the multi-domain system. Such a good match is

quite amazing considering the single domain data were measured under bias,

while the bias field can cause some properties to degrade, particularly the d

value.

As shown in Fig. 9.5(b) and 9.6(b), in terms of the rhombohedral coordinates,

the maximum value of effective d

occurs in the directions 152.9° and

332.9°, respectively, from the [010]

of the rhombohedral coordinates while

the maximum value of k

occurs in directions 160.8° and 340.8°, respectively,

from the [010]

. One can also see that these two quantities do not change

significantly with orientation near their maximum values, particularly the

value; therefore, the [001] direction poled crystals can give almost the

optimum electromechanical coupling coefficient k

and piezoelectric

coefficient d

The calculated values are based purely on the property rotation. Hence,

we may conclude that the main portion of the superior effective d

in the

multi-domain state comes from the orientational conversion of the super-

large shear piezoelectric constant d

of the single domain state.

9.5 Summary

The intensive research on domain engineered PMN–PT and PZN–PT single

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Full-set material properties and domain engineering principles 261

crystals in recent years not only has given us a new category of piezoelectric

materials that could lead to a new generation of electromechanical devices,

it has also produced a new physical means to enhance functional properties

(b)

2500

2000

1500

1000

500

1000

1500

2000

2500

270

300

330

0 [112]

120

150

180

210

240

[111]

[001]

dmax

= 152.9°

(a)

–2000

–1000

1000

2000

–4000

–2000

2000

4000

[111]

–1500

–1000

–500

500

1000

1500

[112]

[110]

9.5

(a) Orientational dependence of piezoelectric constant

(in

units of 10

–12

C/N). (b) The cross-section of (a) in the

[112]

–[111]

plane.

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Handbook of dielectric, piezoelectric and ferroelectric materials262

of ferroelectric materials. The basic idea of domain engineering of ferroelectric

crystals is to re-direct the field-induced displacement of a certain mode to

other modes through the manipulation of domain structures. Such domain

manipulation is different from the conventional sense of increasing ‘extrinsic

contributions’, which refers to the additional electromechanical activities

9.6

(a) Electromechanical coupling coefficient

. (b) The cross-

section of (a) in the

[112]

–[111] plane.

1.0

0.8

0.6

0.4

0.2

0.0

0.2

0.4

0.6

0.8

1.0

[112]

330

300

270

240

210

180

150

120

[001]

dmax

= 160.8°

(b)

–0.5

–1

0.5

–1

–0.5

0.5

[112]

[110]

(a)

–0.5

–1

0.5

[111]

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Full-set material properties and domain engineering principles 263

produced by the movement of domain walls. Here, the domain patterns form

a new class of mesoscopic structures that have their own symmetries and

their unique properties, which can be quite different from the properties of

the underlying crystal structure. Obviously, not all ferroelectric crystals can

be ‘domain engineered’ to achieve high piezoelectric properties. At least one

of the piezoelectric coefficients in the single domain state must be very large

in order for the re-directing scheme to work.

Another fundamental principle for domain engineering is to use domain

interactions to create structural instabilities. It is known that the lattices in

the domain wall regions are distorted. When high domain wall density is

introduced in the crystal, they could lower the phase transition temperature

since the domain walls are natural nucleation sites to induce phase transitions.

The piezoelectric and dielectric properties can become very large due to

such domain pattern-induced instabilities.

Domain pattern formation not only depends on the characteristics poling

field, such as the field level, direction and duration time, but also depends on

the environment temperature and boundary conditions of the sample.

Considering the unique feature of domain engineered crystals, the

characterization work must be conducted with extreme care. Not all the

traditional characterization methods can give reasonable values since some

of them will cause the change of domain patterns, which in turn leads to

property changes. It is also important to understand the error propagation

mechanism and develop ways to reduce the measurement errors when the

system has very large piezoelectric coefficients and high electromechanical

coupling coefficients.

9.6 References

1. H. Ouchi, K. Nagano and S. Hayakawa, ‘Piezoelectric properties of Pb(Mg

1/3

2/3

–PbTiO

solid solution ceramics’, J. Am. Ceram. Soc., 48, pp. 630–635

(1965).

2. S. Nomura, T. Takahashi and Y. Yokomizo, ‘Ferroelectric properties in the system

Pb(Zn

1/3

2/3

–PbTiO

’, J. Phys. Soc. Jpn., 27, pp. 262–267 (1969).

3. J. Kuwata, K. Uchino and S. Nomura, ‘Dielectric and piezoelectric properties of

0.91Pb(Zn

1/3

2/3

–0.09PbTiO

single crystals’, Jpn. J. Appl. Phys., 21, pp. 1298–

1320 (1982).

4. S. E. Park and T. R. Shrout, ‘Ultrahigh strain and piezoelectric behavior in relaxor

based ferroelectric single crystals’, J. Appl. Phys., 82, pp. 1804–1811 (1997).

5. S. E. Park and T. R. Shrout, ‘Characteristics of relaxor-based piezoelectric single

crystals for ultrasonic transducers’, IEEE Trans. UFFC, 44, pp. 1140–1147 (1997).

6. J. Fousek, D. B. Litvin and L. E. Cross, ‘Domain geometry engineering and domain

average engineering of ferroics’, J. Phys. Condens. Matter, 13, L33–38 (2001).

7. J. Fuksa and V. Janovec, ‘Macroscopic symmetries and domain configurations

of engineered domain structures’, J. Phys. Condens. Matter, 14, pp. 3795–3812

(2002).

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Handbook of dielectric, piezoelectric and ferroelectric materials264

8. D. Hatch, H. T. Stokes and W. Cao, ‘Allowed mesoscopic point group symmetries

in domain average engineering of perovskite ferroelectric crystal’, J. Appl. Phys.,

94, pp. 5220–5227 (2003).

9. Z. G. Ye and M. Dong, ‘Morphotropic domain structures and phase transitions in

relaxor-based piezo-/ferroelectric (1 – x)Pb(Mg

1/3

2/3

–xPbTiO

single crystals’,

J. Appl. Phys., 87, pp. 2312–2319 (2000).

10. J. Yin and W. Cao, ‘Effective macroscopic symmetries and materials properties of

multi-domain PZN–PT single crystals’, J. Appl. Phys., 92, pp. 444–448, (2002).

11. J. Han and W. Cao, ‘Interweaving domain configurations in [001] poled rhombohedral

phase 0.68Pb(Mg

1/3

2/3

–0.32PbTiO

single crystals’ Appl. Phys. Lett., 83, pp.

2040–2042 (2003).

12. A. F. Devonshire, ‘Theory of barium titanate’, Phil. Mag., 40, pp. 1040–1050

(1949).

13. J. Erhart and W. Cao, ‘Effective symmetry and physical properties of twinned perovskite

ferroelectric crystals’, J. Mater. Res., 16, pp. 570–577 (2001).

14. J. Erhart and W. Cao, ‘Permissible symmetries of multi-domain configurations in

perovskite ferroelectric crystals’, J. Appl. Phys., 94, pp. 3436–3445 (2003).

15. D. A. Berlincourt, D. R. Curran and H. Jaffe, ‘Piezoelectric and piezomagnetic

materials and their function in transducers’, in Physical Acoustics, ed. W. P. Mason,

vol 1, Part A, Academic Press, New York, pp. 169–267 (1964).

16. IEEE Standard on Piezoelectricity, ANSI/IEEE STD 1987 (1987).

17. S. Zhu, B. Jiang and W. Cao, ‘Characterization of piezoelectric materials using

ultrasonic and resonant techniques’, Proceedings of SPIE, 3341, pp. 154–162 (1998).

18. W. Jiang, R. Zhang, B. Jiang and W. Cao, ‘Characterization of piezoelectric materials

with high piezoelectric and electromechanical coupling coefficients’, Ultrasonics,

41, pp. 55–63 (2003).

19. J. Yin, B. Jiang and W. Cao, ‘Elastic, piezoelectric and dielectric properties of

0.955Pb(Zn

1/3

2/3

) O

–0.045PbTiO

single crystal with designed multi-domains’,

IEEE Trans. UFFC, 47, pp. 285–291 (2000).

20. R. Zhang, B. Jiang, W. Cao and A. Amin, ‘Complete set of material constants of

0.93Pb(Zn

1/3

2/3

–0.07PbTiO

domain engineered single crystal’, J. Mater. Sci.

Lett., 21, pp. 1877–1879 (2002).

21. R. Zhang, B. Jiang, W. Jiang and W. Cao, ‘Complete set of properties of 0.92Pb

(Zn

1/3

2/3

–0.08PbTiO

single crystal with engineered domains’, Mater. Lett.,

57, pp. 1305–1308 (2003).

22. R. Zhang, B. Jiang and W. Cao, ‘Elastic, dielectric and piezoelectric coefficients of

domain engineered 0.70Pb(Mg

1/3

2/3

–0.30PbTiO

single crystal’, AIP Conference

Proceedings, 626, pp. 188–197 (2002).

23. R. Zhang, B. Jiang and W. Cao, ‘Elastic, piezoelectric and dielectric properties of

multi-domain 0.67Pb(Mg

1/3

2/3

–0.33PbTiO

single crystal’, J. Appl. Phys., 90,

pp. 3471–3475 (2001).

24. H. Cao, V. Hugo Schmidt, R. Zhang, W. Cao and H. S. Luo, ‘Elastic, piezoelectric

and dielectric properties of 0.58Pb(Mg

1/3

2/3

–0.42PbTiO

single crystal’, J.

Appl. Phys., 96, pp. 549–554 (2004).

25. R. Zhang, B. Jiang, W Jiang and W. Cao, ‘Complete set of elastic, dielectric and

piezoelectric coefficients of 0.93Pb(Zn

1/3

2/3

–0.07PbTiO

single crystal poled

along [011]’, Appl. Phys. Lett., 89, pp. 242908-1–242908-3 (2006).

26. J. F. Nye, Physical Properties of Crystals, Oxford University Press, London

(1957).

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Full-set material properties and domain engineering principles 265

27. R. Zhang, B. Jiang and W. Cao, ‘Single-domain properties of 0.67Pb(Mg

1/3

2/3

)

–0.33PbTiO

single crystals under electric field bias’, Appl. Phys. Lett., 82, pp.

787–789 (2003).

28. R. Zhang and W. Cao, ‘Transformed material coefficients for single domain

0.67Pb(Mg

1/3

2/3

–0.33PbTiO

single crystal under differently defined coordinate

systems’, Appl. Phys. Lett., 85, pp. 6380–6382 (2004).

29. E. A McLaughlin and H. C. Robinson, ‘Shear mode properties of single crystal

ferroelectrics’, J. Acoust. Soc. Am., 114, pp. 2322 (2003).

30. W. G. Cady, in Piezoelectricity, Dover Publications, Inc., New York (1964).

31. R. Zhang, B. Jiang and W. Cao, ‘Orientation dependence of piezoelectric properties

of single domain 0.67Pb(Mn

1/3

2/3

–0.33PbTiO

Crystals’, Appl. Phys. Lett.,

82, pp. 3737–3739 (2003).

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266

10.1 Introduction

Domain configurations in ferroelectric materials can determine ferroelectric

and related properties such as piezoelectricity, pyroelectricity and dielectricity.

Thus, one of the most interesting investigations for ferroelectric-related

applications is the control of the desirable domain configuration. This technique

is called domain engineering. Domain engineering is the most important

technique to obtain enhanced ferroelectric-related properties for conventional

ferroelectric materials. To date, the following domain engineering techniques

have been proposed and established:

• The inhibited domain wall motion by the acceptor doping into

Pb(Ti, Zr)O

(PZT) ceramics, i.e. ‘hard’ PZT; the hard PZT ceramics are

used for the piezoelectric transformer application.

• The enhanced domain wall motion by the donor doping into PZT ceramics,

i.e. ‘soft’ PZT; the soft PZT ceramics are used for the actuator application.

• The induction of a periodic domain-inverted structure into lithium tantalate

(LiTaO

) and lithium niobate (LiNbO

) single crystals; and this device

is used for the surface acoustic wave application

2,3

and the non-linear

optical application.

4,5

• Recently, for the T-bit memory application, the writing and reading

techniques of nanodomain on a LiTaO

single crystal plate were reported

by Cho and coworkers,

6,7

and for the 3D photonic crystal application,

the writing and etching techniques of nanodomain of a LiNbO

single

crystal plate were reported by Kitamura and coworkers.

These are very important domain engineering techniques, and through their

use enhanced ferroelectric-related properties and new properties can be

expected.

Among these domain engineering techniques, the one using crystallographic

anisotropy of the ferroelectric single crystals is known as engineered domain

configuration.

9–11

This engineered domain configuration can induce enhanced

Domain wall engineering in piezoelectric

crystals with engineered domain

configuration

S W A D A, University of Yamanashi, Japan

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Domain wall engineering in piezoelectric crystals 267

piezoelectric properties in ferroelectric single crystals. However, there are

still many unknowns such as the mechanism of the enhanced property. In

particular, it is very important to find the most suitable engineered domain

configuration for the piezoelectric applications. In this study, various engineered

domain configurations were induced in BaTiO

single crystals, and their

piezoelectric properties were investigated as a function of (1) the crystal

structure, (2) the crystallographic orientation and (3) the domain size (domain

wall density). Moreover, for the tetragonal BaTiO

crystals with engineered

domain configurations, it has recently been found that the piezoelectric

properties significantly improved with decreasing domain size (domain wall

density).

12,13

These results suggest that the domain walls in the engineered

domain configuration could contribute significantly to the piezoelectric

properties. In this chapter, it is suggested that a significant contribution of

domain wall region to piezoelectric, elastic and dielectric properties, and

engineered domain configurations can be very helpful to fix the domain wall

region in piezoelectric crystals, i.e. to prepare a composite between (a) a

distorted domain wall region and (b) a normal tetragonal domain region.

Thus, an increase in the volume fraction of the distorted domain wall region

can result in crystals with ultra-high piezoelectric properties.

10.2 History of engineered domain configuration

The engineered domain configuration was initially found in Pb(Zn

1/3

2/3

)

–PbTiO

(PZN–PT) single crystals. In [001]

oriented rhombohedral PZN-

PT single crystals, ultra-high piezoelectric activities were reported by Park

and coworkers

9,14,15

and Kuwata et al.

16,17

with a strain over 1.7%, a

piezoelectric constant d

over 2500 pC/N, a electromechanical coupling

factor k

over 93% and a hysteresis-free strain vs. electric field behavior.

The (1 – x)PZN–xPT single crystals with x < 0.08 have rhombohedral 3m

symmetry at room temperature, and their polar directions are [111]

16,17

However, the unipolar electric field (E-field) drive along the [111]

direction

showed a large hysteretic strain vs. E-field behavior, a low d

of 83 pC/N

and a low k

of 38%. To explain the above strong anisotropy in piezoelectric

properties, in situ domain observation was carried out using [111]

and [001]

oriented pure PZN and 0.92PZN–0.08PT single crystals.

10,11

The result showed

that when the E-field was applied along the [001]

direction, a very stable

domain structure appeared, and domain wall motion was undetectable under

dc-bias, resulting in the hysteresis-minimized strain vs. electric-field behavior.

The [001]

poled 3m crystals have four equivalent domains with four

polar vectors along the [111]

, [–111]

, [1–11]

and [–1–11]

directions because

of their polar directions being along <111>

. Therefore, the components of

each polar vector along the [001]

direction are completely equal with each

other, so that each domain wall cannot move under the E-field drive along

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Handbook of dielectric, piezoelectric and ferroelectric materials268

the [001]

direction owing to the equivalent domain energy changes.

9–11,14,15

This suggests the possibility of controlling the domain configuration in single

crystals using the crystallographic orientation, and the appearance of a new

technology in the domain engineering field. Thus, this special domain structure

in ferroelectric single crystals using the crystallographic orientation was

called the engineered domain configuration.

9–11

10.3 Effect of engineered domain configuration on

piezoelectric property

The engineered domain configuration is expected to possess the following

five features in terms of piezoelectric performance: (1) hysteresis-free strain

vs. E-field behavior owing to the inhibition of domain wall motion, (2)

higher piezoelectric constant along a non-polar direction owing to the easy

tilt of a polar vector by the E-field, (3) change of macroscopic symmetry in

crystals with engineered domain configuration,

10,11

(4) complex contribution

of other high shear piezoelectric constants such as d

, and (5) contribution

of non-180° domain wall region to piezoelectric properties. Features (1) to

(4) can be useful for both single-domain and multi-domain crystals while

feature (5) is expected only for multi-domain crystals. The engineered domain

configuration is defined as the domain structure composed of some equivalent

polar vectors along the E-field drive direction. Therefore, the engineered

domain configuration is basically multi-domain, and many kinds of engineered

domain configurations are possible depending on (a) the crystal structure

and (b) the crystallographic orientation.

For the rhombohedral 3m ferroelectric crystal with the polar directions of

<111>

, when the E-field is applied along the [001]

and [110]

directions,

the two types of the engineered domain configurations formed are shown in

Fig. 10.1. For the orthorhombic mm2 ferroelectric crystal with the polar

directions of <110>

, when the E-field is applied along the [001]

and [111]

directions, two kinds of the engineered domain configurations are formed, as

shown in Fig. 10.2. Moreover, for the tetragonal 4mm ferroelectric crystal

with the polar directions of <001>

, when the E-field is applied along [111]

and [110]

directions, two kinds of the engineered domain configurations are

formed, as shown in Fig. 10.3. In general, most of the practical ferroelectric

materials belong to the rhombohedral 3m, orthorhombic mm2 or tetragonal

4mm symmetry. Therefore, in this section, only these three crystal structures

will be considered as the conventional engineered domain configurations.

On the other hand, in each of the three crystal structures, three different

crystallographic directions of [001]

, [110]

and [111]

can be considered in

order to induce the above engineered domain configurations. However, it is

expected that the [110]

poled 3m and 4mm ferroelectric crystals may exhibit

a much smaller influence on the ferroelectric-related properties than the

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Domain wall engineering in piezoelectric crystals 269

[001]

poled 3m and mm2 ferroelectric crystals and the [111]

poled mm2

and 4mm ferroelectric crystals. This is because the engineered domain

configuration in the [110]

poled 3m and 4mm ferroelectric crystals is composed

of just two kinds of polar vectors. Thus, in this section, only the two kinds

of the crystallographic directions of [001]

and [111]

will be considered.

10.4 Crystal structure and crystallographic

orientation dependence of BaTiO

crystals with

various engineered domain configurations

If the concept of engineered domain configuration for PZN–PT single crystals

could be applied to other ferroelectric crystals, enhanced piezoelectric properties

E-field

[100]

[001]

[010]

[011]

[111]

[–111]

[001]

[100]

[010]

[111]

[1–11]

[–111]

[–1–11]

10.1

Schematic model of the engineered domain configurations for

the [001]- and [011]-poled rhombohedral

ferroelectric crystals.

E-field

[101]

[110]

[011]

[111]

[11–2]

[–110]

[100]

[010]

[001]

E-field

[101]

[011]

[–101]

[0–11]

10.2

Schematic model of the engineered domain configurations for

the [001]- and [111]-poled orthorhombic

mm2

ferroelectric crystals.

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