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

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Handbook of dielectric, piezoelectric and ferroelectric materials270

would be expected for lead-free ferroelectrics. BaTiO

single crystal is one

of the typical lead-free ferroelectrics and has the tetragonal 4mm symmetry

at room temperature.

The piezoelectric properties were investigated using

the [111]

oriented tetragonal BaTiO

single crystals, as shown in

Fig. 10.4.

20–22

It should be noted that the piezoelectric constant d

was

directly measured from the strain vs. E-field curves. Two kinds of engineered

domain configurations were formed, i.e. (a) the [111]

poled tetragonal

engineered domain configuration and (b) the [111]

poled orthorhombic

[100]

[001]

[011]

[010]

E-field

[010][001]

[111]

E-field

[110]

[100][010]

[001]

[112]

10.3

Schematic model of the engineered domain configurations for

the [011]- and [111]-poled tetragonal

4mm

ferroelectric crystals.

OrthorhombicTetragonal

E-field

[111]

[110]

[112]

[001]

[100]

[010]

[111]

54.7°

<100>

203 pC/N 295pC/N

[111]

<100>

35.3°

E-field

[111]

[–110]

[11–2]

[110]

[101]

[011]

10.4

Two engineered domain configurations for the [111]

poled

(a) tetragonal and (b) orthorhombic BaTiO

single crystals.

WPNL2204

Domain wall engineering in piezoelectric crystals 271

engineered domain configuration (Fig. 10.4). This is because for the tetragonal

BaTiO

crystals, the higher E-field drive over 10 kV/cm along the [111]

direction led to the E-field induced phase transition from the tetragonal

4mm to orthorhombic mm2 phase. The original d

below 10 kV/cm was

203 pC/N while the d

in the induced phase above 10 kV/cm reached 295

pC/N. It is known that the d

value of the [001]

poled tetragonal BaTiO

single crystals was 90 pC/N.

Therefore, the d

of the [111]

poled tetragonal

BaTiO

was almost twice, and the d

of the [111]

poled orthorhombic

BaTiO

was almost three times, as large as that of the [001]

poled tetragonal

BaTiO

20,22

We must consider the difference between the d

values of 203 and

295 pC/N. As shown in Fig. 10.4, both the [111]

poled tetragonal and

orthorhombic engineered domains were composed of three kinds of domains,

but the angle θ between the polar direction and the E-field direction were

quite different, i.e. θ = 54.7° for the d

of 203 pC/N, while θ = 35.3° for the

of 295 pC/N. It is very important to clarify whether this angle θ is effective

for the piezoelectric performance or not. Thus, the piezoelectric properties

of BaTiO

single crystals were investigated as a function of the crystallographic

orientations of [001]

and [111]

, and the crystal structures of tetragonal,

orthorhombic and rhombohedral phases, as shown in Fig. 10.5.

20,22

The

temperature was changed from –100 to 200 °C. It should be noted that the

piezoelectric properties were measured by two kinds of methods, i.e. (a)

measurement under a high E-field over 100 V/cm (estimation of piezoelectric

3 domains1 domain 3 domains No domain

–90°C5°C 132°C

Orthorhombic

mm2

Rhombohedral

Tetragonal

4mm

Cubic

m-3m

E-fieldE-field E-field [111]

4 domains4 domains 1 domain No domain

E-fieldE-field E-field [001]

<111>

<110>

35.3°

<100>

54.7°

<100>

45.0°

<110>

<111>

54.7°

10.5

Expected domain configurations for the [111]

and [001]

poled

BaTiO

single crystals with three kinds of the crystal structures.

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Handbook of dielectric, piezoelectric and ferroelectric materials272

constants from the strain vs. E-field curves) and (b) resonance–antiresonance

measurement under a low ac E-field below 10 V/cm (estimation of piezoelectric

properties from the impedance vs. frequency curves).

10.4.1 Piezoelectric properties measured under high

E-field

[001]

oriented BaTiO

single crystals

Under high E-fields, the strain vs. E-field curves of the [001]

oriented

BaTiO

single crystals were measured from –100 to 200 °C.

18,21

On the basis

of the slope of the strain behaviors over 20 kV/cm, the piezoelectric constant

was calculated directly, as shown in Fig. 10.6. It should be noted from

Fig. 10.6 that for the [001]

oriented orthorhombic BaTiO

single crystals,

the maximum d

of 500 pC/N was obtained at 0 °C. This is a very large

value that is almost comparable to that of PZT ceramics. The d

of the

[001]

poled orthorhombic BaTiO

single crystals was much higher than that

of the [001]

poled rhombohedral BaTiO

single crystals. When the E-field

was applied along the [001]

direction, two kinds of engineered domain

configurations could be formed, i.e. (a) the [001]

poled orthorhombic BaTiO

crystal with four equivalent domains and a θ of 45.0° and (b) the [001]

poled rhombohedral BaTiO

crystal with four equivalent domains and a θ

of 54.7°.

It was expected that if the number of the equivalent domains constructing

the engineered domain configuration is the same, the smaller angle θ can

Temperature,

(°C)

–150 –100 –50 0 50 100 150

4mmmm23m

(pC/N)

500

400

300

200

100

10.6

Relationship between the

and temperature for the [001]

oriented BaTiO

single crystals from –100 to 150 °C.

WPNL2204

Domain wall engineering in piezoelectric crystals 273

cause larger piezoelectric properties. The result in Fig. 10.6 supported the

above hypothesis. Therefore, when the E-field was applied along the [001]

direction of BaTiO

single crystals, the orthorhombic phase was very important

for the higher piezoelectric performance.

[111]

oriented BaTiO

single crystals

The strain vs. E-field curves of the [111]

oriented BaTiO

single crystals

were also measured from –100 to 200 °C.

18,21

On the basis of the slope of the

strain behaviors below 10 kV/cm, the piezoelectric constant d

was calculated

and shown in Fig. 10.7. The strain vs. E-field curves at 25 °C underwent

discontinuous changes owing to two kinds of the E-field induced phase

transitions, i.e. (1) the first transition from tetragonal to orthorhombic phase

around 4–6 kV/cm and (2) the second transition from orthorhombic to

rhombohedral phase around 30 kV/cm.

20–22

In Fig. 10.7, it should be noted

that for the [111]

oriented orthorhombic BaTiO

single crystals, the maximum

of 260 pC/N was obtained at –70 °C. As mentioned above, the d

of the

[111]

poled orthorhombic BaTiO

crystal over 10 kV/cm was 295 pC/N at

25 °C (Fig. 10.4). We believe that this discrepancy in d

(35 pC/N) may be

caused by the temperature difference. Moreover, in Fig. 10.7, the d

(–74 °C) of the [111]

poled orthorhombic BaTiO

single crystals was higher

than that (20 °C) of the [111]

poled tetragonal BaTiO

single crystals. In

Fig. 10.5, when the E-field was applied along the [111]

direction, two kinds

of the engineered domain configurations could be obtained, i.e. (a) the [111]

poled orthorhombic BaTiO

crystal with the three equivalent domains and θ

Temperature,

(°C)

4mmmm23m

–150 –100 –50 0 50 100 150

500

400

300

200

100

(pC/N)

10.7

Relationship between the

and temperature for the [111]

oriented BaTiO

single crystals from –100 to 150 °C.

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Handbook of dielectric, piezoelectric and ferroelectric materials274

of 35.3° and (b) the [111]

poled tetragonal BaTiO

crystal with the three

equivalent domains and θ of 54.7°. Therefore, it was confirmed that when

the number of the equivalent domains constructing the engineered configuration

is the same, a smaller angle θ can cause larger piezoelectric properties.

Therefore, when the E-field was applied along [111]

direction of BaTiO

single crystals, the orthorhombic phase was also very important for the

higher piezoelectric performance.

Crystal structure and crystallographic orientation for the best engineered

domain configuration in BaTiO

single crystals

The above discussions suggested that of the factors that can be responsible

for the piezoelectric performance, the following two are the most important:

(1) the number of the equivalent domains constructing the engineered domain

configuration and (2) the angle θ between the polar direction and the E-field

direction.

Based on Fig. 10.5, we use the piezoelectric constants in Figs

10.6 and 10.7 to check these factors. As mentioned above, when the number

of the equivalent domains constructing the engineered domain configuration

was the same, the smaller angle θ caused larger piezoelectric properties.

Next, the role of the number of the equivalent domains constructing the

engineered domain configuration can be clarified by comparing the [001]

poled rhombohedral BaTiO

crystal that had four equivalent domains and θ

of 54.7° with the [111]

poled tetragonal crystal that had three equivalent

domains and the same θ of 54.7°. The d

of the [001]

poled rhombohedral

BaTiO

crystal was about 400 pC/N, which is twice as high as that of the

[111]

poled tetragonal BaTiO

crystal (about 200 pC/N). This suggests that

the effect of the number of the equivalent domains on the piezoelectric

properties is significantly larger than that of θ.

This observation is confirmed

by comparing the [001]

poled orthorhombic BaTiO

crystal that had four

equivalent domains and a θ of 45.0° with the [111]

poled orthorhombic

BaTiO

crystal had three equivalent domains and a θ of 35.3°: the d

of the

former was twice as high as that of the latter.

The above discussion indicates a new direction to obtain the best engineered

domain configuration for the piezoelectric application. The first step is to

identify the engineered domain configuration with the largest number of

equivalent domains. For the normal perovskite-type ferroelectric single crystals,

only the [001]

poled orthorhombic and rhombohedral crystals can satisfy

this requirement. The second step is to find the engineered domain

configurations with the smallest angle

. For the normal perovskite-type

ferroelectric single crystals, only the [001]

poled orthorhombic crystals can

satisfy the second request. Therefore, the best engineered domain configuration

for the piezoelectric application can be found in the [001]

poled orthorhombic

single crystals. From this reasoning, potassium niobate (KNbO

) crystals

WPNL2204

Domain wall engineering in piezoelectric crystals 275

appear to be one of the promising candidates with ferroelectric orthorhombic

symmetry.

10.4.2 Piezoelectric properties measured under low

ac E-field

It was shown in the previous section that the high piezoelectric properties

can be realized in the [001]

poled orthorhombic and rhombohedral BaTiO

crystals. Using the IEEE resonance technique, other piezoelectric properties

such as the electromechanical coupling factor and dielectric constant were

measured for the [001]

oriented BaTiO

crystals.

18,21

Figures 10.8 and 10.9

show the d

and k

vs. temperature curves of the [001]

oriented BaTiO

crystals, respectively, which were measured using a low ac E-field of 1 V/cm

and a high dc E-field of 6 kV/cm. As expected, the [001]

poled orthorhombic

BaTiO

crystals exhibited the maximum d

of 415 pC/N and k

of 85% at

–5 °C. These values were much higher than those of PZT ceramics. Figure

10.10 shows the dc E-field dependence of k

at –5 °C using a low ac E-field

of 1 V/cm. Before poling treatment (start point), k

was just 70%, and during

the poling treatment at 6 kV/cm, k

increased to 85%. After poling treatment

(final point), k

still kept a high value of 79%. This result suggested that

poling treatment is very important for high piezoelectric properties. On the

other hand, Figs 10.11 and 10.12 show the d

and k

vs. temperature curves

of the [001]

oriented BaTiO

crystals. As expected, the [001]

poled

orthorhombic BaTiO

crystals exhibited the maximum d

of –280 pC/N and

of 65% at 0 °C.

Temperature,

(°C)

4mmmm23m

–150 –100 –50 0 50

(pC/N)

500

400

300

200

100

10.8

Relationship between the

and temperature for the [001]

oriented BaTiO

single crystals from –100 to 25 °C.

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Handbook of dielectric, piezoelectric and ferroelectric materials276

The above results indicated that for the BaTiO

single crystals, the

combination of the orthorhombic mm2 phase and the [001]

crystallographic

direction exhibited the best piezoelectric properties. It is well known that the

[001]

poled tetragonal BaTiO

crystals show a d

of 90 pC/N and a k

56%.

Therefore, the introduction of the best engineered domain configuration

Temperature,

(°C)

–150 –100 –50 0 50

4mmmm23m

(%)

100

10.9

Relationship between

and temperature for the [001]

oriented BaTiO

single crystals from –100 to 25 °C.

–5°C

Electric field,

(kV/cm)

86420

(%)

10.10

Relationship between the

and E-field for the [001]

oriented

BaTiO

single crystals measured at –5 °C. Arrows indicate poling

procedure.

WPNL2204

Domain wall engineering in piezoelectric crystals 277

into the BaTiO

crystals resulted in a five-fold increase in d

and a 1.5-fold

increase in k

. Moreover, if the [001]

poled orthorhombic single crystals

could be obtained at room temperature, we would expect much higher

piezoelectric properties. Thus, as mentioned previously, KNbO

may exhibit

a higher potential for piezoelectric applications because of its orthorhombic

mm2 phase at room temperature.

4mmmm23m

Temperature,

(°C)

–150 –100 –50 0 50

(pC/N)

–300

–240

–180

–120

–60

10.11

Relationship between the

and temperature for the [001]

oriented BaTiO

single crystals from –100 to 25 °C.

4mmmm23m

Temperature,

(°C)

–150 –100 –50 0 50

(%)

100

10.12

Relationship between the

and temperature for the [001]

oriented BaTiO

single crystals from –100 to 25 °C.

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials278

10.5 Domain size dependence of BaTiO

crystals

with engineered domain configurations

BaTiO

single crystals have a tetragonal P4mm phase at room temperature.

To induce an engineered domain configuration in the tetragonal crystals, the

E-field should be applied along the [111]

direction. The piezoelectric

measurements showed that the d

of the [111]

poled tetragonal BaTiO

crystal with the engineered domain configuration was almost 203 pC/N,

and this value was more than twice as large as the 90 pC/N of the [001]

poled BaTiO

single-domain crystal.

On the other hand, the d

of the

[001]

poled rhombohedral PZN–PT crystal with the engineered domain

configuration was almost 30 times as large as the 83 pC/N of the [111]

poled

PZN–PT single-domain crystal.

To explain the origin of this huge difference,

we consider the domain size, i.e. the domain wall density, for the engineered

domain configuration. This is because the domain structure of the [001]

poled PZN–PT crystal was composed of the fiber-like domains with a domain

length of 130 µm and a domain width of around 1 µm

10,11

while that of the

[111]

poled BaTiO

crystal was made of a very coarse domain with a wide

domain width of 300~400 µm.

This result suggested that a non-180° domain

wall region could contribute to piezoelectric properties significantly owing

to its strained region with gradient changing lattice structures. Thus, when

the fine domain structure is induced in the [111]

poled tetragonal BaTiO

crystals with the engineered domain configuration, it is possible to obtain a

much enhanced piezoelectric property. Therefore, the piezoelectric properties

of BaTiO

single crystals were investigated as a function of domain size, i.e.

domain wall density. In particular, in the [111]

oriented tetragonal BaTiO

crystals with an engineered domain configuration, the domain size dependence

on E-field and the temperature were investigated in detail.

10.5.1 Domain size dependence on E-field and

temperature

To understand domain size dependence on E-field and temperature for the

[111]

oriented BaTiO

crystals, the domain structures were observed at

various temperatures from 0 to 200 °C and various E-fields from 0 to 16

kV/cm. Prior to any domain observation, the BaTiO

crystals were heated

to 160 °C, and then cooled to the observation temperatures at a cooling rate

of 0.4 °C/min without E-field. At the constant temperature, the dc E-fields

were applied along the [111]

direction very slowly.

Figure 10.13 shows the domain size dependence on the E-field and

temperature for the [111]

oriented BaTiO

crystals with the engineered

domain configuration. Figure 10.14 shows the typical domain structures

observed in the corresponding regions A to G presented in Fig. 10.13 (P and

WPNL2204

Domain wall engineering in piezoelectric crystals 279

A indicate the crossed polarizer and analyzer). In Fig. 10.13, the ‘A’ and ‘B’

regions were assigned to the orthorhombic mm2 phase. At 25 °C, the dc E-

field drive along the [111]

direction for the tetragonal BaTiO

crystals resulted

in the E-field induced phase transition from 4mm to mm2, and this result was

consistent with previous reports.

18,20–22

Figure 10.14(A) and (B) shows that

these domain structures were composed of the fine domains. The fine domains

in the ‘A’ region were induced by a normal phase transition from the tetragonal

phase to the orthorhombic phase without E-field. On the other hand, the fine

domains in the ‘B’ region resulted from the E-field induced phase transition

from the tetragonal to orthorhombic phase. Thus, when the E-field was

removed, the domain structure in the ‘B’ region easily returned to the normal

tetragonal domain configuration as shown in Fig. 10.14(C). Thus, the fine

domain structure in the ‘A’ and ‘B’ regions cannot exist at room temperature

without the E-field. The ‘C’ region was assigned to the tetragonal 4mm

symmetry. The poling treatment in this region changed the domain structure

slightly, but the observed domain walls were all completely assigned to 90°

domain walls of the {110}

planes as shown in Fig. 10.14(c).

The ‘D’

region was assigned to the optical isotropic state with the cubic m-3m symmetry

as shown in Fig. 10.14(D). However, the ‘E’ region was very unclear and

abnormal. The same brightness in the ‘E’ region under crossed-polarizers

suggested that this domain state was not optical isotropic, but an anisotropic

state.

When the E-field was applied along the [111]

direction for the cubic

m-3m symmetry, it is expected that the cubic m-3m symmetry could be

Temperature,

(°C)

16012080400

E-field,

(kW/cm)

[100]

[010]

[001]

E-field

[111]

[110]

[112]

10.13

Schematic domain configuration map as a function of

temperature and E-field along the [111]

direction for the [111]

oriented BaTiO

single crystals with the engineered domain

configuration. Areas A through G stand for a region with different

domain configurations related to Fig. 10.14, respectively.

WPNL2204