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

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Handbook of dielectric, piezoelectric and ferroelectric materials400

(≈ 80K) of Pb(Mg

1/3

2/3

and of PMN is indicative of the strong influence

of the Nb(Ta)–O chemical bonds. However, only one of the B cation is a

ferroactive atom, and it was admitted that Mg in PMN, Sc in PSN or Zr in

PZT are less involved in the ferroelectricity (Chen et al., 1995, and references

therein) and that the associated oxygen octahedra are only weakly distorted

(if any). Besides, Nb cations are known to be displaced along the <111>

directions with respect to their oxygen octahedra (about 0.1Å) from extended

X-ray absorption fine structure (EXAFS) (Prouzet et al., 1993). However

results from nuclear magnetic resonance (NMR) measurements (Laguta

et al., 2003) seem to be contradictory as they indicate that Sc is the ferroactive

ions. Ti cations are also considered to be displaced but there are more ‘versatile’

in their direction than Nb cation. Indeed it was shown in Pb(ZrTi)O

(PZT)

(Grinberg et al., 2002) and PbSc

1/2

–PT (PST–PT) (Frenkel et al.,

2004) that the direction of Ti cations gradually changes from [111], as in

BaTiO

, to [001] direction, as in PbTiO

, with increase of Ti. In a way Ti

plays the same role as the polarisations in MPB systems by rotating from a

rhombohedral-like direction to a tetragonal-like one (see below). Actually

the displacement of Pb cations, which are considered as the most active ions,

are somewhat governed by the B cation distribution via coupling through the

oxygen cages. A Pb cation inside an ordered distribution of B cation should

be displaced differently from when these B cations are randomly distributed

(Grinberg et al., 2002). The role of B cation is thus also very important.

It is interesting to observe that inside the ferroelectric rhombohedral phase

of PSN and PMN–PT, the [100], i.e. tetragonal-like displacement of lead

atoms, together with the [111], i.e. rhombohedral-like displacement of B

cation (Fig. 6), composes a global polarisation which stands evidently out of

the [111] and [100] directions and inside a plane of symmetry corresponding

to a monoclinic Cm phase: the local polar order of the ferroelectric phase

results from a competition between both types of displacements associated

[001]

Polarisaton

of lead

Polarisation of

Ti/B

cations

[111]

[110]

14.6

Schematic decomposition of local polarisation in PSN and PMN–

: the polarisation due to [100] displacements of lead atoms and the

polarisation of B cations along [111] rhombohedral direction

compose into a resulting polarisation inside a

monoclinic plane.

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From the structure of relaxors to the structure of MPB 401

to the cations and prefigures the long-range monoclinic polar phase which is

observed in the MPB phase, as we discuss below.

From this set of experiments we obtain this preliminary physical picture:

at high temperatures isotropic but highly anharmonic dynamical displacements

of lead are observed along a spherical shell. Upon cooling, these displacements

gradually slow down and begin to correlate below the so-called Burns

temperature T

: it is tempting to call PNRs these ‘regions’ of correlation,

forgetting a possible discussion about the pertinence of this notion of well-

delimited domains with abrupt boundaries, etc.

Keeping this idea in mind, we have to consider that whereas the PNRs

result from the intra-correlation of displacements, close to T

, the inter-

correlation between the PNRs is weak. When these correlations get strong

enough at lower temperature, dynamical displacements are evidenced which

are no more along a spherical shell but get more and more anisotropic along

the <100> direction and the associated diffuse scattering appears in the

diffraction experiments below a T* temperature. T* may correspond to a

local order–disorder phase transition related to Pb atoms (Dkhil et al., 2002),

and, by analogy with magnetic systems, may be related to a crossover from

a Heisenberg to an Ising-like transformation (Stock et al., 2004).

In the case of PMN these displacements freeze below T

(∼200K), the

intensity of the associated diffuse scattering becomes constant (Fig. 14.7a),

and no long-range polarisation appears. In the case of PSN and PMN with

5% and higher concentration of PT, the temperature evolution of the diffuse

scattering intensity gets a critical evolution (Fig. 14.7b): a [111] long-range

polarisation appears below a critical temperature T

. The same feature was

also evidenced in PZN (Bing et al., 2005). However below T

the short-

range component of the polarisation (perpendicular to (111)) manifests itself

by a non-zero intensity of the diffuse scattering at the lowest temperature.

A contradiction emerges from the mere assimilation of the local order

which develops below T

to the notion of PNRs: this identification should

lead to a monoclinic symmetry for the PNRs in opposition with the model of

rhombohedral local order proposed by Mathan et al. in PMN and the intuitive

idea of nucleation from the PNRs of the rhombohedral phase observed in

PSN or in PMN–PT. It is noteworthy that when de Mathan et al. did their

modelling for the diffuse scattering they found that either the rhombohedral

or the orthorhombic symmetry may explain the diffuse scattering observed

on the diffraction patterns and thus the PNRs, but at this time, as it was

known that an electric field induces a rhombohedral phase at low temperature

in PMN, it was admitted that the PNRs should be of rhombohedral symmetry

and the orthorhombic symmetry was discarded. Another observation related

to this question is the existence of a (long-range) rhombohedral phase in

PMN at low temperature when an electric field is applied above a critical

value (see Section 14.6). This phase arises from nucleation (Vakhrushev

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Handbook of dielectric, piezoelectric and ferroelectric materials402

et al., 1997) and percolation of nanodomains which could be identical to the

PNRs. We will see in Section 14.3.3. that this question is rather complex and

in fact not completely understood, but for the moment we ignore these facts

and consider the PNRs to be the local polar order evidenced by the experiments

described in this section.

Intensity (arb. units)

600

500

400

300

200

100

100 150 200 250 300 350 400 450 500

Temperature (K)

100 150 200 250 300 350 400 450 500

Temperature (K)

800

700

600

500

400

300

200

100

14.7

(a) Diffuse scattering in PMN: below a (extrapolated)

temperature

* the diffuse scattering appears; it saturates below a

temperature. (b) Diffuse scattering in PMN–10%PT: below

* the

diffuse scattering gets a critical behaviour at

; below

it gets a

non-zero saturated value.

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From the structure of relaxors to the structure of MPB 403

Raman experiments by Toulouse and coworkers (Svitelskiy et al., 2003,

2005) as well as neutron inelastic experiments by Shirane and coworkers

(see references in text below), Vakhrushev and coworkers (Naberezhnov et

al., 1999) and Hlinka et al. (2003) showed above T

a soft TO mode with

increasing (when cooling) couplings to local mode associated to spherical

displacement of lead and tunnelling of niobium atoms. This soft mode could

condense at T ≈T*, but below T

a drop of the transverse optic (TO) phonon

branch into the transverse acoustic (TA) one at a non-zero wave vector q and

its strong damping below a sufficiently small q vector were related to the

condensation of the PNRs. This condensation inhibits the propagation of the

long-wavelength TO polar modes when the phonon wavelength is comparable

to the size of the PNRs. This anomaly has been called the ‘waterfall effect’

(Gehring et al., 2000; Wakimoto et al., 2002). A central peak appears

(Naberezhnov et al., 1999), associated to the PNRs, i.e. polar correlated

atomic fluctuation below T

, which progressively couple between each other

and slow down, becoming static below T

The PNRs being polar, they couple to the polar TO phonon mode, which

in turn can serve as a microscopic probe of the PNRs. However, based on

analogous experimental observations on the classic ferroelectric BaTiO

(Shirane et al., 1970) and reinvestigation of neutron experiments, some doubt

on the connection of the PNRs and the waterfall effect was expressed (Hlinka

et al., 2003). An explanation based on classic interference of line shape

anomalies due to the coupled acoustic and optic branches without any ad hoc

assumption was proposed (Hlinka et al., 2003). This controversy is complicated

by the fact that different probes are used to investigate the soft mode: neutron

vs. infra red and Raman techniques. Indeed these techniques use phonons

with different wave-vectors; therefore, the TO and TA modes, their over-

and/or under-damping and their possible coupling in neutron data are not

necessary similar to those of IR for instance. In order to reconcile the

observations, the ‘phase-shifted model’ (Hirota et al., 2002) was introduced.

In this model, a PNR consists of two components. The first one corresponds

to the polar soft mode and thus gives rise to the spontaneous polarisation

within the PNRs. The second one is associated with the acoustic mode and

corresponds to a uniform displacement of all atoms inside the PNR; a TO–

TA coupling is therefore possible. In Section 14.3.3 we will see that this

picture is consistent with the mechanism proposed from diffuse scattering

experiments.

14.3.2 Chemical order

As pointed out in the introduction it was recognized very early that ‘textbook’

PMN was not chemically homogeneous and the first model of explanation

for diffusivity of dielectric properties was based on a T

dependence of the

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Handbook of dielectric, piezoelectric and ferroelectric materials404

local chemistry. Later observations by electronic microscopy (Krause et al.,

1979; Randall et al., 1986) were reported: the absence of temperature

dependence of superstructure intensities assigned a chemical origin and these

peaks were interpreted as arising from nanodomains with a non-stochiometric

composition Pb(Mg

1/2

. This local composition results in negative

unbalanced charge which have to be compensated by rich Nb zones with

positive charge in order to get a global Pb(Mg

1/3

2/3

concentration.

The size of these nanoregions should result from equilibrium between

elastic and electric energies. The associated static charges induce the creation

of random electric fields which are at the origin of modern interpretations

for the non-growing of polar order at low temperature in PMN. A simple

picture of cationic distribution was straightforward (Fig. 14.8) and was denoted

the 1:1 model due to the alternating Nb or Mg [111] planes in the structure.

Latter, observation of equivalent superstructure peaks in PSN seemed to

confirm this structural model because in this compound it is more ‘natural’

since the global 1/2:1/2 stochiometry instead of 1/3:2/3 does not imply an

unbalanced charge.

However, an alternative structural model in PMN proposed by Davies and

Akbas (2000) and Chen et al. (1989) was inspired from the structure of

compounds such as Ba(Mg

1/3

2/3

and, Sr(Mg

1/3

2/3

in which the

ordered

Pb(B B )O

1/2 1/2

′′′

regions are electrically neutral due to random

occupation of B

and B

on the B′ site whereas the B″ site is only occupied

by B

, leading to a global formula

Pb[(B B ) ]O

2/3

1/3

1/2

12/

. With such a

model, a global 1:2 stoichiometry of B cation is retained within the sample.

The explanation for nanometric size of these ordered domains within this

model is based (Viehland and Li, 1993) on the competition of stability between

perovskite ABO

and pyrochlore structure A

: above a nanometric critical

B′

[111]

14.8

Ordered structure 1:1, perpendicular to [111] direction, of

PbB′B″O

; only B cations are shown.

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From the structure of relaxors to the structure of MPB 405

size the ordered perovskite region transforms into parasitic pyrochlore

phase.

In the case of PSN the situation appears to be simpler. Indeed since

pioneering work by Setter and coworkers (Chu et al., 1995a,b), it is well

known that due to a high-temperature (1510K) order–disorder phase transition

Sc/Nb can diffuse through the structure and arranges in a structural scheme

probably identical to that depicted in Fig. 14.8. This is due to cationic radius

and valency with close values (0.74Å, 0.69Å and III, V for Sc and Nb,

respectively), as systematic investigations of cationic order of PbBB′O

oxide

have shown. Ordered PSN displays much lowest value of real permittivity

with lowest relaxation than disordered compounds (Fig. 14.9). The lead

vacancies as well as the substitution of barium for lead (6% on Fig. 14.9)

strongly increase the diffusivity of the dielectric behaviour. Notice, however,

that in all cases considered, a well-defined cubic–rhombohedral transition is

found.

Persistence of relaxation in an ordered compound is against the intuitive

idea on the need of disorder for the dielectric relaxation to appear. TEM and

ε′

20000

16000

12000

8000

4000

100 150 200 250 300 350 400 450

(K)

Ordered PSN

PBSN

PSN vacancies

PSN disordered

14.9

Temperature dependence of real permittivity in disordered PSN

(

= 380(±5)K), ordered PSN (

= 350(±5)K), lead vacancies PSN

(

= 365(±7)K) and PSN with 6% of Ba on Pb site (

= 375(±6) K);

is deduced from X-ray measurements.

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Handbook of dielectric, piezoelectric and ferroelectric materials406

X-ray diffraction have shown that the so-called ‘ordered’ or ‘disordered’

PSN is only an unrealistic limit case: indeed, measurement of {h + 1/2,

k + 1/2, l + 1/2} superstructure peaks intensity allows one to calculate a

simplistic coefficient:

surst

Bragg

observed

surst

Bragg

S=1

























where (I

surst

Bragg

)

S=1

is a calculated value with hypothesis of a totally ordered

compound, whose value is roughly the same whatever the model of order

one considers. S is therefore a rough measurement of volumic ratio of ordered

regions.

In PSN, the experimental value for the ordered compound is never higher

than ≈ 0.92 instead of 1. On the other hand, although the S value of disordered

PSN which results from quenching is equal to zero, a weak value is always

observed (Malibert et al., 1997). One should also take into consideration the

coherent length ξ of the local order which is easily deduced from profile

fitting of superstructure peaks and is in a simplistic way a ‘typical’ size for

ordered regions: in a so-called ‘ordered’ PSN, one gets a typical value of ξ

= 20 nm, whereas in the case of PMN (in which cation ordering cannot be

modified by thermal annealing), the typical size of ordered regions is about

5nm and S is less than 20%.

Weak (less than 5% of Bragg peak in PMN; see Fig. 14.10) supplementary

{h + 1/2, k + 1/2, 0} peaks have also been found in PMN and PSN. Moreover,

in PMN a temperature dependence of at least between 300K and 10K was

evidenced, suggesting possible structural origin from displacement correlations.

This hypothesis is reinforced by a non-monotonic evolution of intensity with

scattering vector. Moreover, a condensation of the M

phonon mode due to

the contribution of local antiferroelectric order (Takesue et al., 1999; Miao

et al., 2001) was proposed to explain these additional superstructures. In

PST (a compound that behaves very similarly to PSN, with tantalum instead

of niobium) the {h + 1/2, 0, 0} peaks were observed at room temperature by

transmission electron microscopy (TEM) (Randall et al., 1986): an

interpretation based on the existence of tetragonally distorted ordered zone

was proposed (Caranoni et al., 1992); however these peaks are absent in

both PSN (Malibert, 1998) and PMN(Dkhil, 1999) (Fig. 14.10).

The associated domain size deduced from full width at half maximum

(FWHM) is the same order of magnitude as for the {h + 1/2, k + 1/2, l + 1/2}

peaks and is about 5nm in PMN and disordered PSN. Depero and Sangaletti

(1997) have proposed a tetragonal distortion of cubic lattice cell with rotation

of octahedral to explain the existence of these superstructure peaks. In fact

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From the structure of relaxors to the structure of MPB 407

neutron experiments showed afterwards the absence of such tiltings, but the

idea of a tetragonal distortion for the regions of ordered cation appeared to

be correct and was demonstrated by careful analysis of the diffuse scattering

(see Section 14.3.3).

Intensity (arb. unit)

14000

12000

10000

8000

6000

4000

2000

1/2 1/2 0

3/2 3/2 0

5/2 5/2 0

7/2 7/2 0

= 300 K

= 10 K

16000

14000

12000

10000

8000

6000

4000

2000

= 300 K

= 10 K

0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6

–4 –3.5 –3 –2.5 –2 –1.5 –1 –0.5

14.10

Q-scan along [

0] and [

00] in PMN at

= 300K and

= 10K

(beamline ID15A at European Synchrotron Radiation Facility (ESRF)

showing the {

+ 1/2,

+ 1/2, 0} superstructure peaks; no {

+1/2,

0, 0} peaks are detected.

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Handbook of dielectric, piezoelectric and ferroelectric materials408

In summary, many observations demonstrate the existence in PMN and

disordered PSN of CORs with typical sizes of 5nm whose composition does

not change with temperature. Some other observations (see below) suggest

that, at least at 300K and below, these regions are tetragonally distorted, and

that this distortion probably disappears at higher temperature.

14.3.3 Interaction between CORs and PNRs: diffuse

scattering experiments

As noted in Section 14.2, the first observation of diffuse scattering in PMN

was carried out by X-ray and neutron powder diffraction. Afterwards

Vakhrushev et al. (1994) were the first to perform comprehensive sets of

experiments in single crystals, gaining deep insights of the origin of this

phenomenon. Later on, several other teams, in particular those of Shirane

and Toulouse, contributed to these types of study.

In particular, diffuse scattering located around <h00> reflections with

extension along 〈110〉 directions produces the so-called ‘butterfly-shape’

diffuse scattering. Such anisotropic diffuse scattering was observed in many

types of relaxors, PMN, PSN, PZN and MPB systems such as PZN–PT.

Diffuse scattering arises from local departures from the average structure

and even if the correct model for this butterfly-type diffuse scattering is still

a matter of debate, it is generally attributed to the formation of polar correlations.

It has been, for instance, suggested that the rather localised rod-type

diffuse scattering indicates planar nano-domains which are oriented normal

to the 〈110〉 crystal directions and contain correlated Pb

displacements.

However, such ionic displacements cannot be described as ‘pure polarisation’

and there is a large contribution corresponding to the elastic deformation as

proposed in the phase-shifted model (Hirota et al., 2002). Taking into account

the elastic deformation the appearance of the PNRs should create severe

host-lattice elastic distortions. Therefore, the appearance of such elastic defects

should produce very strong diffuse scattering which is well known in the

case of phase precipitation through the so-called Huang scattering.

In this framework, it has been demonstrated that the observed anisotropic

diffuse scattering can be very well reconstructed by a strain field produced

by defects of tetragonal symmetry. In other words the source of the anisotropic

diffuse scattering comes from tetragonal clusters which are responsible, all

around them, of the appearance of static and elastic deformations of the host-

matrix.

It is worth noting that in contrast to previous conclusions, in the above

approach the anisotropic diffuse scattering, induced by the tetragonal clusters,

is not necessarily related to the PNRs. In fact, there is rather a clear correlation

between the anisotropic diffuse scattering and the CORs. Indeed, the weakening

of the superstructure spots by doping PMN with PbTiO

results in the

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From the structure of relaxors to the structure of MPB 409

simultaneous decrease of the intensity of the anisotropic diffuse scattering

(see Fig. 14.24 of Section 14.4.4). This observation may be understood by

considering that the tetragonal clusters are actually the CORs.

Nevertheless, one has to keep in mind that another way to describe the

anisotropic diffuse scattering is to consider PNRs through correlated lead

displacement in agreement with the structural data shown in Section 14.3.1

and recent calculations on PZN (Welberry et al., 2005) . Therefore, a possible

scenario which satisfies the above conclusions consists of coupling the CORs

to the PNRs, assuming that the PNRs coincide at least to some extent with

the CORs. Around such defect regions, strong (strain and electric) fields are

expected and as the matrix is highly deformable and polarisable, they can be

considered as the ‘embryos’ for the nucleation of PNRs. The PNRs are

therefore both pinned and driven by the chemical ordering and coexist with

the matrix, which can adopt a different symmetry. However as in the traditional

pictures of nucleation, several types of defects can be at the origin of the

low-temperature nucleus: for instance Laguta et al. (2004) observed PNRs in

disordered part of samples, which obviously do not nucleate on CORs.

This picture arises also from the recent simulations by Burton et al. (2006)

who showed that the polarisation and the polarisation fluctuations in relaxors

are strongly enhanced inside the CORs. Particularly in the temperature range

where they appear, polar nanoregions have not already grown and they are

essentially the same as CORs (Fig. 14.13 below). They also showed that

arbitrarily increasing the magnitudes of local electric fields, by increasing

the chemical disorder, broadens the dielectric peak, and reduces the ferroelectric

transition temperature, while sufficiently strong local fields suppress the

transition as in PMN.

Temperature, electric field and pressure effects are coherent with the

above scenario. In particular, the appearance on cooling of diffuse scattering

at a temperature T* well below T

(which marks the appearance of the

PNRs) shows the importance of the elastic contribution (otherwise, T* should

be equal to T

). Recent experiments in PMN conducted by our group have

associated this T* to strain released with the appearance of a static component

of the PNRs (Dul’kin et al., 2006). Furthermore Toulouse and coworkers

(Svitelskiy et al., 2005) suggested a tetragonal symmetry around T* which,

as the Raman lines are normally forbidden and arise from CORs, might

occur only inside the CORs. A plausible explanation is that the static component

of the PNRs is associated to the pinning of the dynamic PNRs by the tetragonal

CORs.

Application of pressure (Fig. 14.11) also leads to the disappearance of the

anisotropic diffuse scattering in relaxors: this is consistent with the above

scenario where the average crystal structure and the PNRs adopt the same

crystal structure, which in turn effectively suppresses the deformation between

the host-matrix and the PNRs (Chaabane et al., 2003b). In this framework,

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