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

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Handbook of dielectric, piezoelectric and ferroelectric materials440

The final conclusion of this overview is that the notion of MPB in the

sense of a confined concentration region where the polarisation rotates from

the rhombohedral [111] direction to the tetragonal [001] direction in a definite

region of the phase diagram should probably be replaced by the notion of

morphotropic phase region (MPR).

14.7 Acknowledgements

Our group has worked on the understanding of the relaxor and related material

for almost 20 years and many researchers and students have contributed to

these studies, as can be seen from the references. We would like also to thank

Serguey Vakhrushev from Ioffe Institute for many illuminating discussions.

Many figures in this chapter are from or adapted from Raphael Haumont’s

thesis.

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15.1 Introduction

Ferroelectric perovskite, morphotropic phase boundary (MPB) Pb(Zr,Ti)O

(PZT)-based ceramics are the basis of a wide range of piezoelectric

technologies, such as sensors, actuators, smart systems, ultrasound generation

and sensing and underwater acoustics (Setter, 2002). Their high

electromechanical activity is associated with the presence of a monoclinic

phase in the MPB region, between the rhombohedral and tetragonal phases

(Noheda, et al. 2000), and the mechanism of polarisation rotation among the

phases (Guo et al., 2000). This is the same mechanism responsible for the

ultra-high piezoelectricity, d

coefficient > 1500 pC/N, of the rhombohedral

Pb(Zn

1/3

2/3

–PbTiO

(PZN–PT) and Pb(Mg

1/3

2/3

–PbTiO

(PMN–

PT) single crystals (Park and Shrout, 1997) and textured ceramics (Kwon et

al., 2005) near or in their respective MPBs (Noheda et al., 2001). The

commercial PZT based ceramics with the highest sensitivity are the so-

called soft PZT, for which the d

piezoelectric coefficient is raised from

∼200 pC/N up to ∼600 pC/N by composition engineering of the Curie

temperature and domain wall mobility (Takahashi, 1982). Piezoelectric devices

are not oblivious to the current miniaturisation trends in ceramic technology

for microelectronics. Multilayer ceramic capacitors (MLCC) are being down-

scaled (Pithan et al., 2005), and an analogous trend can be anticipated for

multilayer ceramic actuators (MLCA) and for other piezoelectric device

configurations (Uchino, 1998). This technological trend benefits from the

scaling behaviour of piezoelectricity: longitudinal deformation under a given

voltage does not depend on size and thus, the down-scaling of a MLCA does

not affect the piezoelectric response. Also, the total displacement is proportional

to the number of layers and so, there is a general driving force to reduce the

thickness. With the ceramic layers in MLCC approaching the thickness of 1

µm, reliability requires five to ten grains per layer and thus, submicrometre

grain sizes close to the 100 nm limit are necessary. Similar and even lower

sizes are involved in Si integrated thick (Gentil et al., 2004) and thin (Trolier-

Size effects on the macroscopic properties

of the relaxor ferroelectric

Pb(Mg

1/3

2/3

–PbTiO

solid solution

M ALGUERÓ, J RICOTE, P RAMOS and

R JIMÉNEZ, Instituto de Ciencia de Materiales de Madrid,

CSIC, Spain, J CARREAUD, J-M KIAT and

B DKHIL, Ecole Centrale Paris, France and J HOLC and

M KOSEC, Institute Jozef Stefan, Slovenia

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Handbook of dielectric, piezoelectric and ferroelectric materials448

McKinstry and Muralt, 2004) film piezoelectric technologies. This raises the

issue of how properties are affected by the size reduction. In this chapter, we

review our work on the size effects in the PMN–PT solid solution. This MPB

system shows distinctive features that point to a better down-scaling behaviour

than PZT in terms of the electromechanical properties.

Firstly, current knowledge of size effects in ferroelectrics is briefly reviewed.

Emphasis is put on polycrystals and on the macroscopic properties, not only

because they are the basis for the functionality of the materials, but also as

a means of addressing some fundamental issues, e.g. the size effect on the

ferroelectric phase transition. Secondly, background on the PMN–PT relaxor–

ferroelectric solid solution is also reviewed. The relevance of this system for

its fundamental and applied interests is emphasised. Next, procedures used

for the processing of PMN–PT submicro- and nanostructured ceramics are

described, and the ceramic materials studied, their density and grain size are

introduced. Then, size effects on the macroscopic properties, the electric,

mechanical and electromechanical properties of 0.8PMN–0.2PT and 0.65PMN–

0.35PT ceramics are successively presented. Based on these results, the size

effects on the transition between the relaxor and ferroelectric states, the

room temperature phases, the polar domain structure, and the functionality

of the materials will be discussed. The chapter ends with a section devoted

to final remarks and future trends.

15.2 Size effects in ferroelectrics

Most of the studies on size effects in polycrystals have focused on tetragonal

BaTiO

as the basis of MLCC. The room temperature dielectric permittivity

of BaTiO

ceramics presents a distinctive variation with grain size that is

associated with the evolution of the ferroelectric domain configuration (Arlt

and Sasko, 1980; Arlt et al. 1985; Arlt 1990a). Above 10µm, a three-

dimensional ferroelectric/ferroelastic 90° domain configuration is formed

that fully relaxes stresses caused by ceramic clamping. Between ∼0.3 and

10 µm, a banded configuration is formed that is capable of relaxing the stress

only in two dimensions. Below 0.3 µm, the decrease in elastic energy by

twinning does not compensate the surface energy of the wall, and 90° domains

are not formed. The dielectric permittivity, like the piezoelectric and elastic

coefficients, comprises a contribution from domain wall mobility, and so it

is dependent on the density of walls. This density does not change above

10 µm, and the permittivity does not depend on size in this size range. Below

10 µm, domain size varies with the square root of the grain size, which

causes wall density, and thereby the permittivity to increase when the size

decreases. However, permittivity does not continuously increase until 0.3 µm,

but presents a maximum at 0.8–1 µm. This is the size at which the structural

distortion of the perovskite starts decreasing, most probably as a consequence

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Size effects on the macroscopic properties 449

of the increasing stresses caused by the clamping. These stresses reduce the

domain wall mobility (Demartin and Damjanovic, 1996). Therefore, the

decrease of permittivity below 0.8–1 µm results from the decrease in wall

mobility. The stresses reach their highest levels with the disappearance of

the 90° domain walls at ∼0.3 µm.

Non-linear thermodynamic theory shows that the clamping modifies the

room temperature phase of the single domain crystals, so as to have a

coexistence of rhombohedral and orthorhombic phases, instead of the tetragonal

phase, at room temperature (Zembilgotov et al., 2005). Polarisation switching

is also affected by the changes in the domain configuration with size reduction,

and the remnant polarisation of the hysteresis loops decreases when the

banded structure is formed (Arlt, 1990b), and is further reduced when the

90° domains disappear, and only 180° switching is possible (Hungría et al.,

2005). It is expected that there is a size limit below which ferroelectricity is

lost (Li et al., 1997). This would set a lower limit for the down-scaling of

piezoelectric ceramic technologies.

Dense BaTiO

ceramics with a grain size of 20 nm still present the anomaly

associated with the transition between the ferroelectric and paraelectric states

in the temperature dependence of the dielectric permittivity (Deng et al.,

2006). This anomaly shows significant broadening and flattening for

nanostructured materials as compared with coarse-grained ceramics, which

has been shown to be a boundary effect (Bratkovsky and Levanyuk, 2005).

The actual values of permittivity are very sensitive to the nature of the grain

boundary, which acts as a low dielectric permittivity coating that decreases

the permittivity (Zhao et al., 2004). Figures as high as 1600 have been

reported for ceramics with a size of 30 nm and tailored boundaries (Buscaglia

et al., 2006). Ferroelectric switching was not observed for the previous

ceramics, which was proposed to be caused by the pinning of transgranular

180° domain walls at the grain boundaries, yet local switching was demonstrated

by piezoresponse force microsocopy.

Less attention has been paid to MPB materials and their electromechanical

properties. The d

piezoelectric coefficient of soft PZT ceramics

continuously decreases with grain size from 550 pC/N for 4 µm, down to

350 pC/N for 0.17 µm, which was associated with the decrease of the

ferroelectric/ferroelastic domain wall mobility because of the clamping (Randall

et al., 1998). The non-linear thermodynamic theory predicts a wide region of

coexistence of rhombohedral and tetragonal phases with the disappearance

of the domains (Zembilgotov et al., 2005). In relation to the size limit of

ferroelectricity, ferroelectric switching has been observed in thin film compacts

of 9 nm size PZT particles (Seol and Takeuchi, 2004). Recently, the size

effects were studied in the MPB PMN–PT (Carreaud et al., 2005). Structural

characterisation and dielectric properties of bulk compacts indicate that a

room temperature relaxor state is present for sizes below 0.2 µm, instead of

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