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

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Handbook of dielectric, piezoelectric and ferroelectric materials330

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Handbook of dielectric, piezoelectric and ferroelectric materials332

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333

12.1 Introduction

Relaxor ferroelectrics include as their best-known type perovskites with

ABO

-type unit cell which are crystals in which unlike-valence cations

belonging to a given site (A or B) are present in the correct ratio for charge

balance, but are situated randomly on these cation sites (Cross, 1987). These

randomly different cation charges give rise to random fields, which tend to

make the phase transitions ‘diffuse’ instead of sharp as in normal ferroelectrics

(Westphal et al., 1993; Ye, 1998). Lead magnesium niobate, Pb(Mg

1/3

2/3

)

(PMN), is one of the most interesting relaxor ferroelectric (FE) materials.

PMN has a disordered complex structure in which the Mg

and Nb

cations

exhibit only some short range order on the B-site. PMN has cubic symmetry

at room temperature with space group Pm3m, whereas below 200K a small

rhombohedral distortion (pseudocubic) was observed (Cross, 1987; Shebanov

et al., 1984). Near 280K the PMN crystal undergoes a diffuse transition

characterized by a broad frequency-dependent dielectric maximum. An extra

dielectric peak was observed at T

∼ 212 K in the field-heating result, and

was attributed to the percolating clusters due to the suppression of the random

fields (Westphal et al., 1993). The normal FE crystal PbTiO

(PT) has a

tetragonal symmetry with space group P4mm at room temperature and has a

normal FE phase transition taking place at T

= 760K with a long-range FE

order occurring below T

(Jona, 1962).

The relaxor-based FE crystals Pb(Mg

1/3

2/3

)

1–x

(PMN–PT) are

expected to show properties of both relaxor ferroelectric PMN and normal

ferroelectric PT. PMN–PT has a morphotropic phase boundary (MPB) in the

range of ∼28 to ∼36mol% of PT (Shrout et al., 1990). As temperature

decreases, the solid solution crystals PMN–xPT (0.28 ≤ x ≤ 0.36) have successive

phase transitions: cubic paraelectric (PE) phase→tetragonal FE

phase→rhombohedral FE phase. However, the phase diagram is not unique

and depends on many physical parameters, such as poling strength and

Electric field-induced domain structures and

phase transitions in PMN–PT single crystals

V H SCHMIDT and R R CHIEN, Montana State

University, Bozeman, USA and C-S TU,

Fu Jen Catholic University, Taiwan

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Handbook of dielectric, piezoelectric and ferroelectric materials334

crystallographic orientation. Dielectric and piezoelectric properties of PMN–

PT are sensitive to Ti content, E-field strength, crystallographic orientation,

mechanical stress (from slicing or external pressure), thermal treatment,

sample thickness, and acquisition process (Tu et al., 2004; Davis et al., 2006).

The ultra-high piezoelectricity has been theoretically attributed to polarization

rotations between tetragonal (T) and rhombohedral (R) phases through

monoclinic (M) or orthorhombic (O) symmetry (Fu and Cohen, 2000).

Morphotropic domain structures and phase transitions in PMN–PT crystals

have been systematically studied by using polarizing microscopy (Ye and

Dong, 2000; Bokov and Ye, 2004; Chien et al., 2005b, 2006). From domain

observations, R→M

→T

001

and R→M

→T→M

→R

111

transition sequences

were evidenced respectively at room temperature in (001)-cut PMN–24%PT

and (111)-cut PMN–33%PT crystals as the E field increases (Tu et al., 2003b;

Chien et al., 2004). A field-induced R→O transition through an M

-type M

phase was suggested for a (110)-cut PMN–30%PT crystal (Viehland and Li,

2002). The synchrotron X-ray diffraction of (001)-cut PMN–35%PT crystal

after poling (E = 43kV/cm) shows an M

-type M phase, but the weakly

poled sample exhibits an average R symmetry (Ye et al., 2001). A coexistence

of R and M phases was observed in (001)-cut PMN–33%PT crystals at room

temperature (Xu et al., 2002).

For piezoelectric performance, an E-field poling has usually been performed

before application. However, how E-field poling affects thermal instability

(variation with temperature) of physical properties is still a critical issue for

long-term operation. It has been a goal to find crystals with high T

(Curie

temperature) or T

(depolarization temperature). ‘T

’ represents the temperature

where local polarization exhibits significant and sudden reduction by thermal

energy. Among high–T

piezoelectric crystals, Pb(In

1/2

)

1–x

(PIN–

PT), Pb(Yb

1/2

)

1–x

(PYN–PT) and Pb(Sc

1/2

)

1–x

(PSN–

PT) have drawn attention in recent years. The (001)-cut PIN–34%PT single

crystal (starting composition) grown by the modified Bridgman method with

a PMN-29%PT seed crystal, exhibits d

> 2000 pC/N and k

≅ 94% (Guo et

al., 2003). Domain and dielectric properties of (001)-cut PIN–xPT (x = 0.28,

0.30, 0.40) were also studied as functions of temperature and E field (Yasuda

et al., 2003; Tu et al., 2006d). PYN–50%PT, PIN–37%PT, and PSN–42%PT

ceramics have T

= 633, 593, and 533 K, respectively (Yamashita et al., 2002).

Polar nanoclusters or nanoregions (PNR) are believed to be responsible

for many physical properties in relaxor ferroelectrics. Field-cooled (FC) and

zero-field-cooled (ZFC)

207

Pb nuclear magnetic resonance (NMR) spectra of

the PMN crystal show the existence of two components – spherical glassy

matrix and ferroelectric nanoclusters (Blinc et al., 2003). About 50% of the

Pb nuclei reside in the spherical glass matrix which does not respond to the

external field, and 50% in the ferroelectric nanoclusters which can respond

to E field (> threshold field E

). Blinc et al. (2003) found a sudden intensity

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Electric field-induced domain structures and phase transitions 335

increase in the ZFC spectra of the anisotropic NMR line corresponding to

nanoclusters below T

≅ 210K, but the magnitude is two times smaller than

in the FC spectra (E > E

≅ 1.8kV/cm). These evidences indicate that PMN

is incipient ferroelectric. The time dependence of permittivity and polarization/

depolarization currents after switching on a dc field and also for zero-field

warming after different applied-field histories (Colla and Weissman, 2005)

were measured in PMN, and in PMN–PT with PT up to 12%, well below the

MPB concentration range. They suggested that coupled ferroelectric and

glassy order are required to explain their data.

Owing to low domain switching E field, high-strain piezoelectric crystals

have potential for non-linear optical applications. Refractive indices of (001)-

cut PMN–xPT (x = 0.35 and 0.38) crystals showed an obvious birefringence

after an E-field poling, but the phase-matched condition was not found yet

in PMN–PT crystals (Wan et al., 2003; Tu et al., 2005). Optical transmission

was significantly enhanced by a prior E-field poling.

In the remainder of this chapter, we present our results concerning phase

transitions of variously oriented PMN–PT crystals as functions of temperature,

frequency, and E field by means of dielectric permittivity, polarizing

microscopy, hysteresis loop, and X-ray diffraction measurements. Optical

transmission and refractive indices before and after poling are also included.

The chapter ends with an introduction to Landau free energy analysis of

stability of the various crystal phases, followed by conclusions.

12.2 Experimental methods

The PMN–PT crystals were grown using a modified Bridgman method at

H.C. Materials Corporation, Illinois, and Shanghai Institute of Ceramics,

China. Samples were cut perpendicular to the <001>, <011>, or <111> direction.

The Ti concentration (x%) was determined by using the dielectric maximum

temperature T

upon heating (without poling), i.e. x = [T

(°C) + 10]/5 (Feng

et al., 2003). For dielectric measurements, a Wayne-Kerr Precision Analyzer

PMA3260A was used to obtain capacitance and resistance. A Janis CCS-450

cold-head was used with a Lakeshore 340 controller and the ramping rate

was 1.5K/min. Before any measurement, the sample was annealed in the

cubic (C) phase above T

. Three processes were used in this study. The first

is called ‘zero-field-heated’ (ZFH) or ‘zero-field-cooled’ (ZFC), in which

the data were taken upon heating or cooling respectively without any E-field

poling. The second process is called ‘field-cooled-zero-field-heated’ (FC-

ZFH), in which the sample was first cooled from the C phase down to room

temperature with an E field, then cooled to 100 or 150K without field before

ZFH was performed. In the third process, the sample was directly poled at

room temperature before ZFH was performed starting below room temperature,

i.e. FR-ZFH. During the FC or FR, a dc E field was applied along the

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Handbook of dielectric, piezoelectric and ferroelectric materials336

oriented direction. The hysteresis loops were measured by using a Sawyer–

Tower circuit at f = 46Hz.

Domain structures were observed by using a Nikon E600POL polarizing

microscope with a crossed polarizer/analyzer (P/A) pair. To avoid domain

overlapping, the samples were polished to a thickness of approximately 40–

70 µm or less. The edge orientations of the samples were determined by X-

ray diffraction. One of the sample edges was aligned with one of the crossed

P/A:0

axes so that the extinction angles shown in all domain micrographs

were measured from that sample edge as indicated in domain figures. For E-

field-dependent domain observation, transparent conductive films of indium

tin oxide (ITO) were deposited on sample surfaces by sputtering. The

experimental configuration is shown in Fig. 12.1. The details for using optical

extinction to distinguish various phases are discussed in Section 12.3.

For optical transmission measurements, a Varian Model Cary 5E ultraviolet–

visible–near infrared spectrophotometer (0.2–3.3µm) and a Perkin-Elmer

2000 Model Fourier transform infrared (FTIR) (3.0–27µm) were used.

Refractive indices were measured by using a Metricon Model 2010 Prism

Coupler equipped with three lasers (0.473, 0.790, and 1.323µm). The beam

diameters are about 1.2, 0.74, and 1.4mm for wavelengths 0.473, 0.790, and

1.323µm, respectively. The refractive index was determined by finding the

critical angle of total internal reflection.

12.3 Polarizing microscopy as applied to

perovskite-structure crystals

Various orientations of the polarizations and their corresponding

crystallographic symmetries (or phases) can be determined for most cases by

Ag paste

Polarizer

Cu wire

field

Analyzer

View

Transparent ITO electrode

12.1

Experimental configuration for observing domain structures

under the polarizing microscope. A dc

field was applied across the

sample.

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Electric field-induced domain structures and phase transitions 337

measuring optical extinction angles from polarizing microscopy. Principles

of the optical extinction in polarizing microscopy applied to perovskite-

structure crystals are discussed below.

In polarizing microscopy the crystal can be rotated between two crossed

linear polarizers. There are two key directions, the light propagation vector

k (perpendicular to the crystal cut plane) and the optical electric field axis E

of the incident light. The relation of E to the projection of the ferroelectric

polarization vector P onto the plane perpendicular to k is important for

interpreting the results. We display this relation by means of figures that aid

in visualizing the possible P vectors and their projections onto this plane.

Each figure consists of the projection along k of a cube aligned with the

parent-phase cubic cell axes, with symbols representing where P crosses the

visible faces of the cube. The origin of P is at the center of the cube. Some

faces with sides parallel to k are shown folded out somewhat.

Simplest, and thus shown first, is the (001)-cut projection as shown in

Fig. 12.2, with all four sides folded out. The inner square outlines the front

face of the cube. The triangles at its corners represent four R-phase P directions,

and the circles at its edge midpoints represent four O-phase P directions. The

square symbol at its center represents a T-phase domain whose P is parallel

to k. This symbol is shown in solid black to indicate that extinction occurs

[111]

[010]

[001]

[111]

[110]

[100]

12.2

Relation between the optical extinction orientations

corresponding to the ferroelectric polarization directions for various

phases and domains projected on the (001) plane. Dashed, dash-

dotted, and dotted lines represent polarization directions for M

–,

–, and M

-type monoclinic phase domains, respectively (adapted

from Chien

et al.

, 2006).

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Handbook of dielectric, piezoelectric and ferroelectric materials338

for all E directions because E is perpendicular to the optic axis for this

optically uniaxial domain.

The solid crosses in the other 24 symbols indicate the E axes for which

extinction will occur for the corresponding domains. Extinction occurs if E

is along a principal axis of the ellipse formed by the intersection of the plane

perpendicular to k with the index ellipsoid. The index ellipsoid is a surface

whose distance from the origin in a given direction is proportional to the

index of refraction n for light polarized with E in that direction. The R and

T domains are optically uniaxial, so the index ellipsoid is an ellipsoid of

revolution.

For the R and T domains, the optic axis is along P. For such domains in

the (001)-cut crystal, the intersection of the (001) plane with the index ellipsoid

forms an ellipse that has principal axes parallel and perpendicular to the

projection of P onto the (001) plane. Extinction for these R and T domains

occurs for E along the principal axis directions of these ellipses, as indicated

by the directions of the lines forming the crosses inside the triangle and

square symbols in Fig. 12.2. A concise and clear mathematical analysis for

the general extinction problem appears in Sommerfeld (1964). A detailed

treatment was published by Hartshorne and Stuart (1970).

The O domains are optically biaxial. The optic axis directions are arbitrary

in a certain plane and are of no practical use in polarizing microscopy for

these crystals. Of importance are the principal axes of the index ellipsoid,

which for O domains align with the axes of the double-size (Z = 2) O unit

cell. One of these axes aligns with P and makes a 45° angle with two cubic

axes, another axis is the third cubic axis, and the third is perpendicular to the

other two. For instance, for any of the four O domains shown in Fig. 12.2

having P represented by circles near the four corners, the unit cell projection

is a rectangle (almost a square) with edges canted 45° relative to the page

edges. In the third direction, the cell edges are perpendicular to the page and

are about

shorter, that is, they coincide closely with the length of the

original primitive cubic unit cell.

For such biaxial domains, under what conditions will the index ellipsoid

intersection with the plane perpendicular to k be an ellipse with a principal

axis along the projection of P, so that extinction will occur with E along this

projection of P? There are two independent sufficient conditions. Case 1 is

if P lies in this plane. Case 2 is if an index ellipsoid principal axis is

perpendicular to E when E is aligned with the projection of P. For the (001)

cut crystal represented by Fig. 12.2, all 12 O symbols satisfy Case 2. The 4

in the central plane (circles near the corners) satisfy Case 1 also, so the

extinction directions for all 12 O domains are known to be along the axes

shown in the O symbols.

For the (001) cut we see that T domains will give extinctions at 0°

+ m90°,

where m is any integer. All angles are measured from the vertical direction,

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Electric field-induced domain structures and phase transitions 339

and we will henceforth omit m90° terms and only consider angles in the 0°

≤ φ < 90° range. We see that R domains only give extinctions at 45°, whereas

O domains give extinctions at 0° and 45°. We also see the importance of

knowing which direction is which in the plane perpendicular to k. Thus the

(001) cut is particularly useful for distinguishing situations for which only R

or only T domains exist. A mixture of R and T domains could give the same

extinction angles as a crystal with only O domains. For coexisting R and T

domains, T domains can be evidenced by 90° domain walls, i.e. stripes along

<110>, and T domains have the extinction angle along<100>, whereas R

domains have extinction along <110> (Ye and Dong, 2000).

All monoclinic phases for M domains that may exist in perovskite crystals

belong to the m point group, but only the M

phase has a Z = 1 unit cell based

on the primitive cubic unit cell. Any M

cell P lies between two adjacent T

and O P vectors (dotted lines in Fig. 12.2). The M

and M

‘phases’ in our

opinion should be called a single phase whose cell is based on the Z = 2 O

cell. The important distinction is that the M

cell has P between two adjacent

T and R P vectors (dashed lines), whereas the M

cell has P between two

adjacent R and O P vectors (dash-dot lines). If the plane of any set of three

adjacent P vectors described above includes k, extinction occurs for the M

phase for E in the same directions as for the adjacent T, R, or O phases, and

the lines representing these monoclinic P directions are shown solid to indicate

that the extinction directions are known. Otherwise, the extinction directions

are not known, and complete extinction does not occur for any E direction

because two of the three index ellipsoid principal axes change direction with

wavelength. This situation occurs for the O domains shown as open circles

in Fig. 12.3 for a (110) crystal cut. Any extinctions at angles other than 0°

(= 90°), 35°, and 55° must be from these open-circle O domains, M domains,

or triclinic (Tri) domains.

Another origin of incomplete extinction in the m monoclinic and mm2

orthorhombic point groups is the optical activity that occurs unless k lies in

a mirror plane. O domains that have incomplete extinction only because of

optical activity are shown by circles with open crosses in Fig. 12.4 for a

(111) crystal cut. These satisfy Case 1 above, whereas the O domains

represented by the other three circles satisfy Case 2.

From Figs 12.2–12.4 we see advantages for each of these crystal cuts. The

(001) cut of Fig. 12.2 clearly distinguishes R from T phases by the 45°

extinction angle difference. The (110) cut of Fig. 12.3 unambiguously

distinguishes certain R domains by a special 35.3° extinction angle relative

to T, some O, and other R domains. The (111) cut of Fig. 12.4 has the special

feature that any extinctions at angles other than 0°, 30°, 60°, etc. must be

from M or Tri domains.

Here, we describe the experimental procedure for determining the crystal

phase (symmetry) of a (001)-cut crystal from measuring the extinction angles

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