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

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Handbook of dielectric, piezoelectric and ferroelectric materials390

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14.1 Introduction

Very good reviews have already addressed relaxors (Bokov and Ye, 2006)

and the structural aspects of morphotropic phase boundary (MPB) systems

(Noheda, 2002; Noheda and Cox, 2006) and therefore it is not the intent of

this chapter to repeat this difficult work. Instead here we would like to focus

on the connection between two features of this issue which are usually

treated in a separate manner but which are, in our opinion, connected: relaxor

compounds and MPB systems.

For a long time, numerous studies have pointed out the need of a structural

knowledge at the nanoscale for understanding the physical properties of

these fascinating materials. Recently it has been shown that the local chemical

composition deeply determines the polar ordering. Keeping this fact in mind

will make it easy for the reader, with the help of some simplistic pictures, to

understand the basic ideas about the structure of a relaxor, why it is already

a ‘potential’ or ‘virtual’ MPB and what changes are needed to make it behave

like a ‘true’ MPB compound.

Several groups around the world have contributed to and continue to

work on these topics; in particular the contribution of researchers doing

modelling has grown impressively recently. It is obviously impossible to

make an extensive bibliography and we will not pretend to have read everything.

In the following we will restrict ourselves to experimental results mainly

from diffraction and diffuse scattering by X-ray, neutron and Raman techniques.

This chapter is mainly an informal discussion, suitable for a wide readership

with many ideas and basic sketches showing the crossover from relaxor

towards MPB through their structure on a nanoscale. Moreover, for the sake

of clarity we have focused our description on perovskite-like structure and

especially lead-based complex perovskite as it is the most widely studied

family.

Therefore this chapter is organised as follows: On Section 14.2 we will

make a brief historical introduction, through two simple sets of experimental

From the structure of relaxors to the

structure of MPB systems

J-M KIAT and B DKHIL, Ecole Centrale Paris, France

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observations stressing the two basic ingredients we shall use throughout this

chapter, namely the polar nano-regions (PNRs) and chemically ordered regions

(CORs). In Section 14.3 we will discuss the question of order and disorder

as it has been studied from structural measurements in archetypal relaxors

PbMg

1/3

2/3

(PMN) and PbSc

1/2

(PSN). Section 14.3.1 deals

with the question of long-range and short-range polar order; the concept of

PNRs will be addressed; in Section 14.3.2 we will discuss the question of

chemical order and in Section 14.3.3 we will focus on the interaction between

both entities. At this point the reader will have, we hope, a simplistic but

adequate physical picture of the structure of a relaxor.

In Section 14.4 we will move towards the MPB compounds by studying

the influence of titanium substitution, using the same basic ingredients of

chemical and polar orders. The rotation of polarisation is discussed in different

systems in Section 14.4.1; in Section 14.4.2 the progressive crossover from

short (local) range to long-range (macroscopic phase) monoclinic order is

discussed. Those experimental results are also connected to the results from

ab-initio modelling in Section 14.4.3. In Section 14.4.4 the concept of local

chemical composition is discussed more deeply in relation to cationic ordering.

At the end of this section the relationship between the structure of a relaxor

and the structure of the morphotropic phases will be displayed through simplistic

sketches to make it, we again hope, clear for the reader.

In this framework, Section 14.5 will present some selected experimental

results on the effects of electric field (14.5.1), pressure (14.5.2), grain size

reduction (14.5.3) and in thin films (14.5.4) in connection with the ideas

developed before. Finally Section 14.6 will conclude by summarizing in a

table and schematic figures all the ideas discussed in this text.

14.2 Historical context

Smolenskii (1984) and his group make the pioneering studies of ‘textbook’

relaxor compound PbMg

1/3

2/3

(PMN) using dielectric measurements.

In order to explain the huge spread (compared with conventional ferroelectric,

see Fig. 14.1) in the temperature dependence of the dielectric permittivity,

they proposed the first structural model of PMN, introducing the concept of

‘diffuse phase transition’. Indeed up to that time, maximum of the temperature

dependence of dielectric permittivity ε(T) was associated with critical behaviour

at ferroelectric phase transitions with Curie–Weiss law close to critical

temperature T

. They considered the relaxation of isolated polar regions and

relaxation or resonance of the boundaries of these regions to be at the origin

of the anomalous dielectric permittivity, which is still recognized by most

modern researchers. Other authors suggested that owing to chemical

inhomogeneities, different local concentrations of cations induce ferroelectric

phase transition with concentration-dependent critical temperature T

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From the structure of relaxors to the structure of MPB 393

observation of the diffuseness should therefore be due to convolution of

multiple ε(T)-curves.

It is noteworthy that, nevertheless, these chemical inhomogeneities alone,

even if they explain the broad dielectric anomaly, are not enough to understand

the so-called ‘relaxor’ behaviour described by the frequency-dependence of

the maximum value of dielectric permittivity ε

max

) with a non-Debye

evolution.

Much later, our group was the first to make a structural investigation of

PMN at different temperature by combined X-ray and neutron diffraction

(Bonneau et al., 1989, 1991; Mathan et al., 1990, 1991). The first surprise

was the observation down to 5K of very high thermal parameters, indicating

some kind of disorder from the ideal perovskite structure, whereas no long-

range deviation from a cubic, i.e. non-ferroelectric phase, is observed, consistent

with previous observations (Cross, 1987). Statistic displacements of atoms

out of cubic special positions allowed us to improve the quality of the structure

refinement and the thermal parameters recovered more standard values. The

second surprise during the same set of experiments was the observation in

the powder patterns of very strong diffuse scattering on the basis of the line

profile of Bragg peaks which progressively grows from high temperature.

These sets of results were explained by introducing the concept of polar

1 kHz

10 kHz

100 kHz

1000 kHz

PbMg

1/3

2/3

3(PMN)

BaTiO

100 150 200 250 300 350 400 450

Temperature (K)

Dielectric constant ε′

2.5×10

2.0×10

1.5×10

1.0×10

5000

14.1

Real part of dielectric permittivity of PMN compared with BaTiO

(

of which is 393K, the temperature scale has been shifted).

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Handbook of dielectric, piezoelectric and ferroelectric materials394

nano-regions (PNRs), at high temperature and in the vicinity of the T

max

temperature (the exact range of temperature is given below). At low temperature

when the situation appears to be frozen, a structural model for the local polar

order with rhombohedral symmetry was proposed by de Mathan et al. (1991)

to take into account the additional diffuse scattering.

Let us now turn back to the chemical inhomogeneities introduced by

Smolenskii. Indeed besides the polar feature of relaxors, another common

local characteristic concerns the intrinsic compositional disorder of non-

isovalent ions (on the B-site of the perovskite). This random distribution of

heterovalent ions is expected to give rise to random fields (RFs) which in

turn may influence the polar properties (Westphal et al., 1992; Kleemann,

1993). Besides this random arrangement and following Smolenskii’s ideas,

Krause et al. (1979) observed cations ordering in PMN in the form of chemically

ordered regions (CORs). Indeed, in addition to Bragg peaks and diffuse

scattering, superstructure peaks indicating local change in the average

composition are easily observed in diffraction experiments ( Fig. 14.2). This

peculiar chemical arrangement through CORs is of huge interest in the

understanding of relaxors, as we shall see later.

At this time the two basic concepts for the understanding of relaxors – as

well as MPB compounds – were introduced. Numerous studies followed and

14.2

X-ray diffraction Q-scan showing both superstructure peaks and

diffuse scattering in a single crystal of PMN at 10K.

(1/2 1/2 1/2)

(3/2 3/2 1/2)

(5/2 5/2 1/2)

(7/2 7/2 1/2)

Diffuse

diffusion

0.5 1 1.5 2 2.5 3 3.5 4

Lattice reciprocal direction (h h 1/2)

Intensity (arb. unit)

50000

40000

30000

20000

10000

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From the structure of relaxors to the structure of MPB 395

progressively the idea emerged that the connection between these two sets of

basic experimental observations, i.e. atomic shift disorder and PNRs on one

side and chemical disorder and CORs or RFs on the other, was the key to

understanding relaxor behaviour.

14.3 Structure of archetypal relaxors PbMg

1/3

2/3

(PMN) and PbSc

1/2

(PSN)

The two main features for the understanding of relaxor structures, i.e. PNR

and COR, were introduced in the last section; this section is devoted to a

deeper experimental investigation of these basic ideas. To this purpose we

focus our description on both relaxors PbMg

1/3

2/3

(PMN) and PbSc

1/2

(PSN) which are representative of the two main families of lead-

based relaxors, namely the 1/3:2/3 and 1/2:1/2 compounds. (1/3:2/3 and

1/2:1/2 refer to the ion distribution on the B-site of the perovskite.) Their

common characteristics and differences will be discussed in the following

sections.

14.3.1 Polar order

Whereas the dielectric properties of PMN and PSN are quite similar, their

low temperature structures differ significantly. Indeed whereas PMN does

not exhibit any ‘true’, i.e. long-ranged, ferroelectric transition but short-

range polar order, PSN (as well as PMN–PT with concentration close and

above ~5% of PT (Ye et al., 2003) displays a rhombohedral R3m, i.e.

ferroelectric, phase with clear and weakly first-order anomalies whereas the

behaviour of PMN appears to be more complex (Fig. 14.3), with several

characteristic temperatures that are explained below. The situation of

PbZn

1/3

2/3

(PZN), which is also considered as a model relaxor, displays

similar changes to that of PSN, although it is a 1/3:2/3-type compound (it

will be briefly analysed in Section 14.4.1).

It is well known that inside the high-temperature cubic phase not all

atoms of lead-based relaxor compound are sited at their cubic special positions:

the first observation in PMN was reported by Bonneau et al. (1991). Several

attempts have been made to model such behaviour in different lead-based

compounds: in particular split-ion (Malibert et al., 1997), rotator (spherical

layer) (Vakhrushev et al., 1994), and anharmonic Graham–Charlier expansion

(Kiat et al., 2000); interesting results have also been obtained via pair

distribution function analysis but will not be discussed here; we refer the

reader to the book by Egami and Billinge (2003).

In all cases the parameters describing the displacement of ions from their

undistorted positions were found to be temperature dependent. The Graham–

Charlier expansion which is based on a high-order (i.e. anharmonic)

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Handbook of dielectric, piezoelectric and ferroelectric materials396

max

100 200 300 400

100 200 300 400 500 600

(a)

20000

15000

10000

5000

4.050 Å

4.045 Å

4.092 Å

4.086 Å

4.078 Å

2000

1600

1200

800

400

100 200 300 400 500 600 700 800

(b)

280 300 320 340 360380 400 420

(K)

14.3

Comparison of temperature dependence of the lattice parameter

with temperature dependence of real part of dielectric permittivity in

(a) PMN and (b) PSN.

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From the structure of relaxors to the structure of MPB 397

development of thermal parameters, seems to be the more versatile way to

model the disorder of the cubic phase.

The lead atoms appears to play a more significant role in the local non-

cubic behaviour. For instance in PMN at 673K (Fig. 14.4) lead atoms stand

on a highly anharmonic potential and are never at their special position but

on a spherical shell. This situation is strongly different for instance from that

in for PbTiO

where this situation is observed only in the very close vicinity

of T

(Malibert et al., 1997; Kiat et al., 2000); in the case of lead-free perovskites

such as BaTiO

and KNbO

, this situation for barium and potassium atoms

respectively is never observed (Kiat et al., 2000). In PMN in cooling, the

potential deep increases and anharmonicity is stronger; in fact at room

temperature (Fig. 14.4) it is so strong that Graham–Charlier approximations

is no more valid and one is faced with more simplistic treatments. For

instance disordered displacements are introduced via split-atoms in the

structural refinements and possible decrease of agreement factor between

the calculated–experimental difference are researched. At high-temperature

(for instance 523K) in PMN–PT10% (Fig. 14.5), shifting the lead atoms,

along any directions, induces better agreement factor and diminishes the

abnormal high-temperature factor (harmonic) (Dkhil et al., 2002). This situation

corresponds to the spherical shell disorder; at lower temperature (300K) but

still in the cubic phase, i.e. above the critical temperature T

, the shifts are

no more isotropic but rather along the <001> direction (Fig. 14.5). This

situation persists down to the lowest temperature in the case of the (on

average) paraelectric PMN.

These results indicate that relaxor compounds (PSN, PMN–10%, PT etc.)

that show, below a critical temperature, a long-ranged rhombohedral [111]

polarisation, display in their ferroelectric phase an additional perpendicular

disordered (in the sense of short-range) component. This additional component

composes (see the lead cuboctahedron in Fig. 14.5) with the ordered/long-

range polarisation and induces atomic displacements of lead in a direction

close to [100].

The chemical explanation of such displacement is quite obvious: looking

at the oxygen cuboctahedra around lead atoms, shifting the lead atom in the

[100] direction creates 4 shorter bonding lengths, 4 medium and 4 longer,

instead of 12 identical medium, bonds. This situation is known to be more

favourable for the stability of the structure than the situation in which the

lead stands on the barycentre of the polyhedron and is observed in simpler

lead oxides such as PbTiO

, PbO, etc. The physical origin of this effect is

related to the existence of the electronic lone pair (Le Bellac et al., 1995b).

This lone pair can occupy a steric volume equivalent to an oxygen atoms: for

instance the volumes of PbO

(anathase) and PbO

are the same. Calculations

of the lone pair extension and possible interaction have been performed in

the simplistic approximation of ionic model (Malibert, 1998). The result

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Handbook of dielectric, piezoelectric and ferroelectric materials398

Lead atoms are randomly on a sphere at high temperature

–0.6 –0.4 –0.2 0 0.2 0.4 0.6

Distance from centre (Å)

–0.6 –0.4 –0.2 0 0.2 0.4 0.6

Distance from centre (Å)

–0.6 –0.4 –0.2 0 0.2 0.4 0.6

Distance from centre (Å)

meV

100

meV

100

meV

100

= 293 K

= 673 K

= 873 K

Monte Carlo

error

estimate

Monte Carlo

error estimate

Monte Carlo

error estimate

14.4

Temperature evolution of anharmonic potential of lead atom from Graham–Charlier expansion [courtesy of

G. Baldinozzi].

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From the structure of relaxors to the structure of MPB 399

confirms the extension in both cubic and rhombohedral phases of the lone

pair in the steric volume of the oxygen cuboctahedron, but with a value

lower than in another structure such as PbO, Pb

. Moreover the interaction

between neighbouring lone pairs of lead atoms is shown to play a negligible

part in the interaction leading to the phase transition, whereas it has been

proved to be essential for other compounds (Le Bellac et al., 1995a).

Thus the Pb atom in lead-based relaxor is considered to be the key cation

involved in the relaxor-like behaviour. Nevertheless, in general, ferroelectricity

is known to be driven by the B cation in ABO

ferroelectric perovskite

(Cohen, 1992). Indeed, the strong difference between T

max

of dielectric constant

Rhombohedral angle (°)

89.86

89.88

89.90

89.92

89.94

89.96

89.98

100 200 300 400 500 600

Temperature (K)

0.9

0.8

0.7

0.6

0.5

0.4

001

⊥

〈111〉

= 300K

<100>

<111>

<110>

<123>

Reliability factor (%)

5.5

5.4

5.3

5.2

5.1

Reliability factor (%)

2.8

2.6

2.4

2.2

1.8

1.6

= 523 K

<100>

<111>

<110>

<123>

0 0.05 0.1 0.15 0.2 0.25 0.3

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35

Shift (A)

14.5

Temperature evolution of (210) Bragg peak neutron intensity and

of the rhombohedral angle of PMN. Above a

* temperature (see

text) indicated here by a change of slope in the (210) intensity,

Bragg

agreement factor versus shift of lead has an isotropic minimum

whereas at lowest temperature but above the critical temperature

indicated by the rhombohedral distortion the shifts are along (100).

Below

the lead inside its oxygen cuboctahedron is shown with the

long-ranged <111> displacements and the perpendicular short-

ranged (disordered) component which compose into <001>

displacements.

Relative intensity

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