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

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Handbook of dielectric, piezoelectric and ferroelectric materials280

slightly distorted to become rhombohedral or monoclinic. However, at present,

the origin of this birefringence is unknown. In the ‘F’ region, the coexistence

of the bright state without the domain walls and the fine domain state was

observed. In the ‘G’ region, only the fine domain structure was clearly observed,

all the domain walls of which were assigned to 90° of the {110}

planes.

In the ‘A’, ‘B’, ‘C’ and ‘D’ regions, these symmetries were assigned on

the basis of some reports.

18,20–22

However, there is no information about the

‘E’, ‘F’ and ‘G’ regions. Thus, these symmetries were measured using the in

situ Raman scattering measurement, which was combined with the polarizing

microscopic observation. As a result, the change from ‘D’ to ‘G’ by E-field

was assigned to an E-field induced phase transition from the cubic to tetragonal

phase.

100 µm

10.14

Various domain configurations in (A) the ‘A’ region, (B) the ‘B’

region, (C) the ‘C’ region, (D) the ‘D’ region, (E) the ‘E’ region, (F) the

‘F’ region and (G) the ‘G’ region as shown in Fig. 10.13. P and A on

each graph indicate the crossed polarizer and analyzer.

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Domain wall engineering in piezoelectric crystals 281

10.5.2 Domain size dependence of the piezoelectric

property using 31 resonators

On the basis of the result of the domain size dependence on the E-field and

temperature, various kinds of domain size were induced in the [111]

oriented

BaTiO

single crystals with the engineered domain configuration. The

engineered domain BaTiO

crystal with a large domain size was poled at just

below the Curie temperature (T

) while that with the finer domain size was

poled at just above T

. Figure 10.15 shows the BaTiO

single crystals with

four kinds of domain sizes, i.e. (a) over 40 µm, (b) of 13.3 µm, (c) of 6.5 µm

and (d) of 5.5 µm. All of the domains observed in Fig. 10.15 were assigned

to 90° domain walls of {110}

planes. The domain configurations for all the

resonators prepared in this study were composed of the same 90° domain

walls,

and the difference between these domain configurations was just

domain size, i.e. domain wall density, as shown in Fig. 10.16.

Using these 31 resonators with the different domain sizes, the piezoelectric

properties were measured at 25 °C by a conventional resonance–antiresonance

200 µm

(a)

(b)

(c)

(d)

[111]

[110]

[112]

[110]

[112]

[111]

[110]

[112]

[111]

[110]

[112]

10.15

Engineered domain configurations of the [111]

oriented BaTiO

single crystals with the different average domain sizes of (a) greater

than 40 µm, (b) 13.3 µm, (c) 6.5 µm and (d) 5.5 µm.

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Handbook of dielectric, piezoelectric and ferroelectric materials282

method

using a weak ac E-field of 125 mV/mm. Figures 10.17 and 10.18

show the frequency dependence of the impedance and the phase for the 31

resonators with a domain size over 40 µm and that with a domain size of 6.5

µm, respectively. If the poling treatment is completely successful, the phase

between resonance and antiresonance frequencies should be close to +90°.

However, in these figures, the maximum phase angle was only +50° and

+15°, respectively. These low phase angles suggested an insufficient poling

treatment. Using these resonance and antiresonance frequencies, the

piezoelectric-related constants were estimated. Table 10.1 shows the domain

size dependence of the properties using these 31 resonators. The d

of the

[001]

oriented BaTiO

single-domain crystal was reported as –33.4 pC/N

while the effective d

of the [111]

oriented BaTiO

single-domain crystal

calculated using the d

of 90 pC/N, d

of –33.4 pC/N and d

of 564 pC/N

reported by Zgonik et al.

was –62 pC/N. On the other hand, the d

of the

[111]

poled BaTiO

single crystal with a domain size over 40 µm was estimated

[112]

[110]

[111]

= 40 µm

= 13.3 µm

= 6.5 and 5.5 µm

10.16

Schematic 31 resonators composed of the engineered domain

configuration with different domain sizes.

Frequency,

(kHz)

700600500

100

1000

Impedance, |

| (Ω)

Phase, θ (deg.)

–90

–60

–30

10.17

Frequency dependence of the impedance and phase for the

[111]

oriented BaTiO

single crystals with an average domain size of

greater than 40 µm, measured at 25 °C.

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Domain wall engineering in piezoelectric crystals 283

to be –97.8 pC/N while that of the [111]

poled BaTiO

single crystal with

a domain size of 6.5 µm was found to be –180 pC/N. In particular, the

31 resonator with a domain size of 5.5 µm showed much higher d

–230 pC/N and k

of 47.5% than those (d

of –171 pC/N and k

of 34.4%)

reported for soft PZT ceramics.

Therefore, the [111]

oriented engineered

domain BaTiO

crystal exhibit much higher piezoelectric properties than the

[001]

oriented BaTiO

single-domain crystal.

It had been believed that the highest piezoelectric property must be obtained

in single-domain crystals, and that it was impossible for the material constants

to be beyond the values of single-domain crystal. However, this study reveals

that the 90° domain walls in the engineered domain configuration significantly

enhance the piezoelectric effects, giving rise to much higher piezoelectric

constants than those from single-domain crystals.

In general, under a high E-field drive, the domain walls can move very

easily, and this domain wall motion makes no intrinsic contribution to the

piezoelectric properties. However, in the engineered domain configuration

shown in Fig. 10.3, the 90° domain walls cannot move with or without

unipolar dc E-field drive.

20,21

This means that in the engineered domain

configuration, the 90° domain walls can exist very stably with or without a

unipolar E-field drive. Therefore, the contribution of the domain walls to the

piezoelectric properties has been clarified for the first time using the engineered

domain configuration. In other words, the engineered domain configuration

is considered as domain wall engineering among the domain engineering

techniques.

28,29

Frequency,

(kHz)

700600500

100

1000

Impedance, |

| (Ω)

–90

–60

–30

Phase, θ (deg.)

10.18

Frequency dependence of the impedance and phase for the

[111]

oriented BaTiO

single crystals with an average domain size of

6.5 µm, measured at 25 °C.

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Handbook of dielectric, piezoelectric and ferroelectric materials284

10.5.3 Domain size dependence of the piezoelectric

property using 33 resonators

By the poling treatment at various electric fields and temperatures,

12,13

the

33 resonators of BaTiO

crystals with different domain sizes were prepared.

The average domain sizes in the engineered domain configuration (Fig.

10.3) were changed from 100 to 6 µm. The domain configurations for all the

33 resonators prepared in this study were composed of the same 90° domain

Table 10.1

Domain size dependence of piezoelectric properties for the 31 BaTiO

crystal resonators

BaTiO

single crystals

(pm

)

(pC/N)

(%)

[001]

129 7.4 –33.4 –

(single domain)

[111]

–– –62.0 –

(single domain)

[111], charged 1299 10.9 –85.3 24.1

(domain size of 80 µm)

[111], charged 2117 7.80 –98.2 25.7

(domain size of 50 µm)

[111], charged 2185 7.37 –97.8 25.9

(domain size of 40µm)

[111], charged + neutral 2117 8.30 –102.7 26.0

(domain size of 20.0 µm)

[111], charged + neutral 2186 8.20 –112.5 28.2

(domain size of 15.0 µm)

[111], charged + neutral 2087 7.68 –134.7 35.7

(domain size of 13.3 µm)

[111], charged + neutral 1921 8.20 –137.6 36.8

(domain size of 12.0 µm)

[111], charged + neutral 2239 9.30 –140.5 32.8

(domain size of 10.0 µm)

[111], charged + neutral 2238 9.10 –159.2 37.5

(domain size of 8.0µm)

[111], charged + neutral 2762 9.30 –176.2 36.9

(domain size of 7.0µm)

[111], charged + neutral 2441 8.80 –180.1 41.4

(domain size of 6.5µm)

[111], charged + neutral 2762 9.58 –230.0 47.5

(domain size of 5.5µm)

‘Soft’ PZT ceramics

1700 16.4 –171.0 34.4

0.988

(Ti

0.48

0.52

)

0.976

0.024

Measured by Zgonik

et al

. [9].

Calculated using the values measured by Zgonik

et al

. [9].

Measured by Jaffe

et al

. [1].

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Domain wall engineering in piezoelectric crystals 285

walls,

and the difference between these domain configurations was just the

domain size, as shown in Fig. 10.19.

The piezoelectric properties were measured at 25 °C using a weak ac E-

field of 50 mV/mm. Table 10.2 shows the domain size dependence of

piezoelectric-related properties using these 33 resonators. As a reference, the

calculated d

piezoelectric constant for the [111]

oriented BaTiO

single-

domain crystal using the material constants reported by Zgonik et al.

was

also listed. All the piezoelectric-related properties increased with decreasing

domain size. The most surprising thing is the fact that the piezoelectric

[112]

[110]

[111]

= 100 µm

= 22 µm

= 6 µm

10.19

Schematic of 33 resonators composed of the engineered

domain configuration with different domain sizes.

Table 10.2

Domain size dependence of piezoelectric properties for the 33 BaTiO

crystal resonators

BaTiO

single crystals

(pm

/N)

(pC/N)

(%)

[001]

(single domain) –– 90 –

[111]

(single domain) –– 224 –

[111], neutral 1984 10.6 235 54.4

(domain size of 100 µm)

[111], neutral 1959 10.7 241 55.9

(domain size of 60 µm)

[111], neutral 2008 8.8 256 64.7

(domain size of 22 µm)

[111], neutral 2853 6.8 274 66.1

(domain size of 15 µm)

[111], neutral 1962 10.8 289 66.7

(domain size of 14 µm)

[111], neutral 2679 10.9 331 65.2

(domain size of 6 µm)

Measured by Zgonik

et al

. [19].

Calculated using the values measred by Zgonik

et al

. [19].

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Handbook of dielectric, piezoelectric and ferroelectric materials286

properties significantly depend on the domain size regardless of the 31 or 33

mode. Thus, we must consider the possible effect of non-180° domain walls

on the piezoelectric property. Liu et al. proposed a model for the role of

domain walls in the engineered domain configurations.

Here, we consider

this useful model to explain the enhanced piezoelectric property with increasing

non-180° domain wall density.

10.6 Role of non-180° domain wall region on

piezoelectric properties

It is well known that a region near the 90° domain walls is gradually distorted

to relax the strain between domains with different polar directions, as shown

in Fig. 10.20.

31–35

Moreover, for BaTiO

crystals, the crystal structure near

the 90° domain walls gradually changed from normal tetragonal, with a c/a

ratio of 1.011, to tetragonal, with a c/a ratio close to 1.0. Thus, it can be

expected that the region near the 90° domain walls with pseudo-cubic structure

exhibits the material constants of BaTiO

single crystals near T

, as reported

by Budimir et al.

In this study, the BaTiO

crystals with engineered domain

configuration were regarded as a composite of (a) normal tetragonal region

and (b) distorted 90° domain wall region. On the basis of this two-phase

model, a volume fraction of the distorted domain wall region over the normal

tetragonal region was estimated as follows. To simplify the calculation, one-

dimensional model was applied.

First, the thickness of the distorted 90°

domain wall region (W

) was assumed using various sizes from 1 to 100

nm.

31–35

Next, using this thickness (W

) and the domain size (W

), the

Charged 90° domain wall Neutral 90° domain wall

[111]

Distorted

region

Distorted

region

[111]

10.20

Schematic of structure near the 90° domain walls for BaTiO

crystals.

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Domain wall engineering in piezoelectric crystals 287

volume fraction of the distorted 90° domain wall region (F) was estimated

with the following equation:

10.1

can be measured from the experiment in this study while W

is unknown.

Thus, we must use valid W

values for the above calculation. To date,

many researchers tried to estimate the domain wall thickness using Landau–

Ginzburg–Devonshire (LGD) theories and transmission electron microscopic

(TEM) observation, and their estimated values from 1 to 10 nm.

31–35

Recently,

based on the developed measurement equipment and theories, some new

methods were proposed to estimate the domain wall thickness.

36–38

In particular,

the domain wall thickness was related to point defect, and the defect was

responsible for the broadening of the domain wall thickness.

This means

that it is very difficult to determine the 90° domain wall thickness for BaTiO

Thus, in this study, F values were calculated using the various domain wall

thickness from 1 to 100 nm. Using the F values, the relationships between

and F and d

and F were plotted in Figs 10.21 and 10. 22, respectively,

in which the slope of a line indicates the piezoelectric constant expected

from the corresponding distorted 90° domain wall region. Using the estimated

90° domain wall thickness of 10 nm, d

and d

can be expressed using the

following equations:

= –82 676F – 69 10.2

= 81 744F + 227 10.3

of 1nm

of 10nm

of 20nm

of 50nm

of 100nm

0.0050 0.01 0.015 0.02

(pC/N)

–250

–200

–150

–100

–50

10.21

Relationship between

and

calculated using various

values from 1 to 100 nm.

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Handbook of dielectric, piezoelectric and ferroelectric materials288

i.e. d

and d

from the distorted 90° domain wall region are calculated to be

82 676 and 81 744 pC/N, respectively. Similarly, if the 90° domain wall

thickness is 3 nm, d

and d

from the distorted 90° domain wall region are

estimated to be 275 590 and 272 480 pC/N, respectively. If the 90° domain

wall thickness is 1 nm, d

of 826 760 and d

of 817 440 can be expected

from the distorted 90° domain wall region. The above values reveal that the

piezoelectric constants resulting from the distorted 90° domain wall region

are significantly high. Based on a recent theoretical calculation, the domain

wall width is estimated to be around 3 nm,

while the maximum domain

wall width is found from recent experiments to be 10 nm.

Therefore,

the d constants arising from domain wall region should be higher than

80 000 pC/N.

This study shows that the distorted 90° domain walls can contribute

significantly to the piezoelectric properties. When the domain wall density

continues to increase, how will the piezoelectric constants increase? The

domain size dependences of d

and d

can also be expressed as follows:

–826 760

– 69

10.4

817 440

+ 227

10.5

It should be noted that equations (10.4) and (10.5) are independent of W

Thus, using the various W

values, the relationships between d

and W

and

between d

and W

are plotted in Figs 10.23 and 10.24, respectively. It can

of 1nm

of 10nm

of 20nm

of 50nm

of 100nm

0.0020 0.004 0.006 0.008

300

250

200

(pC/N)

10.22

Relationship between

and

calculated using various

values from 1 to 100 nm.

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Domain wall engineering in piezoelectric crystals 289

be seen that above the W

of 20 µm, the piezoelectric coefficients were

almost constant at the calculated single-domain values, while below the W

of 10 µm, piezoelectric constants drastically increased with decreasing domain

sizes. Moreover, when the domain size decreased down to 1 µm, both d

and

reached around 1000 pC/N.

Park and Shrout reported that [001]

poled PZN single crystal exhibited

(×10

nm)

0.01 0.1 1 10 100 1000

–1000

–100

–10

(pC/N)

of 100nm

of 900nm

of –62pC/N

10.23

Relationship between

and

calculated using Equation

(10.4).

(×10

nm)

0.01 0.1 1 10 100 1000

of 100nm

of 1000nm

of 224pC/N

(pC/N)

1000

100

10.24

Relationship between

and

calculated using Equation

(10.5).

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