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

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Handbook of dielectric, piezoelectric and ferroelectric materials230

Kuwata J, Uchino K and Nomura S (1982), Dielectric and piezoelectric properties

of 0.91Pb(Zn

1/3

2/3

–0.09PbTiO

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Handbook of dielectric, piezoelectric and ferroelectric materials232

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Part II

Field-induced effects and domain

engineering

233

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235

9.1 Introduction

Relaxor ferroelectric materials have demonstrated superior dielectric properties

and they can form solid solutions with ferroelectric materials to produce

larger piezoelectric response. The investigation of relaxor-based ferroelectric

ceramics and single crystals began in the 1960s.

1,2

Interesting electromechanical

phenomena were observed in 0.91Pb(Zn

1/3

2/3

–0.09PbTiO

single crystals

in the 1980s, which can produce high electromechanical coupling coefficient

of k

> 90% when being poled along [001] of cubic phase direction.

The

phenomena were further explored in the late 1990s when better and larger

crystals were fabricated.

4,5

It was demonstrated that single crystals

(1 – x)Pb(Mg

1/3

2/3

–xPbTiO

(PMN–PT) and (1–x)Pb(Zn

1/3

2/3

–

xPbTiO

(PZN–PT) poled along [001] of cubic phase coordinates can produce

very large piezoelectric coefficient (d

> 2000 pC/N) and very high

electromechanical coupling coefficient (k

> 90%).

4,5

With the improvement

of fabrication techniques, the size of the crystals and the compositional

uniformity have now met the requirements for practical applications. The

method of intentionally off-polar direction poling to produce desired domain

patterns in order to obtain large piezoelectric response is referred as ‘domain

engineering’.

In order to use computer simulations to design devices that can utilize

these advanced piezoelectric crystals, one must know the complete set of

material parameters for input in the design software. For such a purpose, it

is insufficient to know only the d

and k

coefficients since the materials

are very anisotropic. An accurate, complete set of material properties can

provide useful comparison among different composition crystals in order to

select the best crystals for particular applications. In addition, such

complete information is also needed for theoretical analysis to understand

the fundamental principle of domain engineering method and to find the

physical origin of such super-large d

and k

coefficients in domain engineered

crystals.

Full-set material properties and domain

engineering principles of ferroelectric

single crystals

W C A O, The Pennsylvania State University, USA

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Handbook of dielectric, piezoelectric and ferroelectric materials236

There are two critical issues involved in the property characterization of

these multi-domain single crystals. First, because the material properties are

anisotropic, we must identify the effective symmetries of these multi-domain

systems in order to define the material constant matrices. Unlike single

domain single crystals, for which the macroscopic symmetry is the same as

the microscopic crystal symmetry, the macroscopic symmetry of a domain

engineered single crystal is the effective symmetry of the engineered

domain patterns, which can be very different from the crystal symmetry.

Because several energetically degenerated domain states exist in the

structure and several domain wall orientations are allowed, the engineered

domain patterns can be quite complicated and the symmetries of such

patterns need to be analyzed for different combinations of domains and

domain walls.

The second issue is the self-consistency of the full matrix data. Based on

symmetry analysis, there are only a fixed number of independent material

constants for a given symmetry. Therefore, one must be able to correlate the

data from different types of measurements using symmetry constraints and

constitutive relations. Experimental measurements showed that material

properties could be substantially different for different geometry samples of

the same composition because the domain patterns being generated are strongly

influenced by the geometry and boundary conditions. In addition, uncertainties

of some derived quantities can be very large due to the unstable nature of

some constitutive relations. Unstable relations refer to those mathematical

formulas that can enlarge the error through error propagation as discussed in

more details below.

In this chapter, we will discuss these two issues and provide a

collection of full-set property data for PMN–PT and PZN–PT single

crystals that have been measured up to date. The chapter is arranged as

follows: in Section 9.2, the challenges involved in the characterization of

these domain engineered crystals are discussed and the methodologies

used to overcome these difficulties are described. In Section 9.3, a list is

provided of available full set material properties, including [001] and [011]

direction poled PZN–PT and PMN-PT multi-domain single crystals in the

rhombohedral phase, as well as single domain rhombohedral and tetragonal

phase PMN–PT single crystals. In Section 9.4, the correlation between

single domain and multi-domain data is described and the orientation

effect that constitutes the basic principle of domain engineering is discussed

briefly. Section 9.5 provides some general remarks for using domain

engineering methods to enhance the functional properties of ferroelectric

materials.

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Full-set material properties and domain engineering principles 237

9.2 Technical challenges and characterization

methods

9.2.1 Effective symmetries of multi-domain single

crystal systems

Theoretically speaking, different domain states are energetically degenerated

in the ferroelectric phase. However, if two or more domains are put together

they can form interesting domain configurations depending on domain wall

orientations as well as their relative volume ratios.

In multi-domain crystals, the effective macroscopic symmetry is determined

by the spatial distribution of domains, not by the lattice structure. Domain

pattern symmetry describes the collective microstructure of domains and

domain walls, while the permissible domains and domain walls depend on

the underlying crystal lattice symmetry of the ferroelectric phase and its

relationship with the symmetry of the paraelectric phase. Hence, crystal

symmetry and domain pattern symmetry are interrelated but quite different.

There is an interesting hierarchical relationship: the symmetry of the crystal

structure determines the domain structure, while the symmetry of the domain

structure determines the macroscopic symmetry of the multi-domain crystal.

It is interesting to note that the effective domain pattern symmetry could be

either higher or lower than the symmetry of the unit cell.

6–8

The domain engineered PMN–PT and PZN–PT crystals that can give

large electromechanical properties are all in the rhombohedral phase with

the symmetry group 3m. Microscopically, the dipole in each unit cell in the

rhombohedral phase is formed along one of the eight body diagonal directions

of the paraelectric cubic unit cell at the ferroelectric phase transition. To be

consistent with the convention in this community, we always use the cubic

coordinates to label the poling field direction for the multi-domain

rhombohedral phase crystals.

An initially proposed configuration of the [001] poled rhombohedral phase

PMN–PT and PZN–PT single crystals is given in Fig. 9.1, in which the

multi-domain configuration is made of four different domains of equal volume

fractions divided by cross-intersecting (charged) domain walls oriented along

[100] and [010].

This configuration has an effective domain pattern symmetry

of tetragonal 4mm. However, optical and electron microscope images of

such domain patterns have rarely been reported in the literature. In fact,

some reports found that the observed domain walls are oriented in the <110>

family instead of the <100> family.

Therefore, researchers also propose

monoclinic m symmetry for the underlying crystal structure for these crystals

with compositions near the morphotropic phase boundary (MPB), which

will allow the <110> oriented domain walls.

There is also some experimental evidence on the non-equivalence of the

[100] and [010] directions in many domain engineered crystals, which implies

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Handbook of dielectric, piezoelectric and ferroelectric materials238

that the effective symmetry of the multi-domain structure can be lower than

tetragonal 4mm.

For rhombohedral 3m symmetry crystals, the existence of

<110> family domain walls implies that the domains form 109° twins in the

multi-domain structure. Therefore, locally, the effective symmetry of the

domain pattern is orthorhombic mm2, or even lower.

Such a symmetry

difference cannot be detected by the measurement of d

alone because the

piezoelectric d

coefficient will be the same for both symmetries.

The physical origin for the preference of 109° twins over 71° twins in the

rhombohedral phase is due to the lesser elastic deformation involved in the

109° twinning with respect to the original cubic structure. The difficulty

caused by the <110> family walls is that it is not possible to create a tetragonal

4mm symmetry domain pattern using only 109° twins like what is illustrated

for the case of <100> family walls as shown in Fig. 9.1.

This puzzle might be explained by the result of an optical study of domain

patterns in the 0.68Pb(Mg

1/3

2/3

–0.32PbTiO

(PMN–32%PT) system.

By focusing an optical polarizing microscope at different depth, it was

found that the local domain patterns only involve 2-variant twins instead of

4-variant crosshatched domain structures shown in Fig. 9.1. The twins are

interwoven along [001] to form a 3D structure that can be easily mistaken as

intersecting twin sets because of the finite focal depth of the microscope.

This situation is shown clearly in Fig. 9.2. In Fig. 9.2(a), one can see two

intersecting domain wall sets in the upper right corner with wall orientations

in [110] and [1

0], while the lower left corner has a patch of twin structure

with walls along [1

0]. From Fig. 9.2(b) to 9.2(d), the focal point is moved

deeper into the thickness direction, one can see that the upper right corner

gradually becomes a twin set with domain walls along [110] while the lower

left corner showing a crosshatched domain pattern in Fig. 9.2(d).

The twin cluster size is about 20 µm in these pictures. Therefore, strictly

speaking, the local domain pattern symmetry for this crystal, in the size of

20 µm or less, is orthorhombic mm2, which is basically a twin band consisting

of two types of domains with 109° domain walls. There is a transition region

between layers with mixed domain clusters as we move along the [001]

(010)

(001)

(100)

9.1

Possible domain configuration and associated polarization

orientation in a [001] poled PMN–PT single crystal of rhombohedral

phase.

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Full-set material properties and domain engineering principles 239

direction, which looks like crosshatched domain pattern with intersecting

domain walls oriented in [110] and [1

0]. In terms of the 3D structure as a

whole, the effective symmetry for such interwoven domain patterns is tetragonal

4mm, but only in the average sense. Such interwoven domain patterns provide

a reconciliation of the <110> family walls observed optically and the

rhombohedral crystal symmetry from the x-ray diffraction (XRD) results.

Considering the two end members of the solid solution systems, PMN–PT

and PZN–PT are tetragonal and rhombohedral, respectively, it is more

reasonable to assume a slightly distorted rhombohedral phase rather than a

true monoclinic symmetry for the solid solution near the MPB composition.

The rhombohedral symmetry is also in agreement with the theoretical results

from Landau–Devonshire theory for a ferroelectric with perovskite crystal

structure.

There are two main differences of this interwoven structure with the

proposed domain structure shown in Fig. 9.1, although both structures have

the effective domain pattern symmetry of tetragonal 4mm. First, the domain

(a)

(b)

20 µm

[010]

[100]

[010]

[100]

[010]

[100]

[010]

9.2

Domain structures of a PMN–32%PT single crystal observed by

focusing at different depths. From (a) to (d), the focusing depth

gradually increases along [001].

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