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

Подождите немного. Документ загружается.

Handbook of dielectric, piezoelectric and ferroelectric materials430

[111] direction above a threshold value (1.7kV/cm), PMN transforms into a

rhombohedral phase at around 230K upon field cooling (Calvarin et al.,

1995). Interestingly, when the electric field is applied below the freezing

temperature, a time-dependent phase transition occurs (Vakhrushev et al.,

1997) with nucleation of polar rhombohedral nanodomains without growth

and after an incubation time, a percolation of these domains giving rise to a

microdomain state. Since these works and the discovery of monoclinic phases

in the MPB, E–T phase diagrams have been constructed in several studies for

[111]-oriented PMN (Sommer et al., 1993; Colla et al., 1996; Ye, 1998) and

PMN–PT (Emelyanov et al., 1993; Raevski et al., 2005) crystals. It is interesting

to notice that recent NMR investigations have also demonstrated the percolation

character of the induced phase transition in PMN (Blinc et al., 2003).

Furthermore, these NMR measurements have also revealed that although the

ferroelectric phase occurs, about 50% of the crystal remains in the glassy

matrix state, suggesting the polar inhomogeneities existing in these systems.

The same situation was also reported on PSN (Laguta et al., 2004).

Other relaxors and/or other crystal orientations have also been studied.

For instance a recent investigation on PZN showed that a monoclinic phase

can be induced when the electric field is applied along the [001] direction

(Lebon et al., 2005). However, some experimental results show that this

monoclinic phase could already exist without an electric field (see pages

416–22). PSN has also been recently studied by Samara and Venturini (2006)

and Venturini et al. (2006) who showed that a biasing electric field favours

the ferroelectric phase over the relaxor state, and that above 5kV/cm the

relaxor state vanishes.

Owing to the discovery of very high piezoelectric responses, the effort

has recently been concentrated on the MPB concentrations. For instance,

application of an electric field along the [001] direction on PZN–8%PT

induces the following phase sequence: rhombohedral → M

→ M

→

tetragonal. Interestingly, when the field is removed, the reverse sequence is

T → M

→ O. In PMN–35%PT a phase transformation sequence of cubic →

tetragonal → orthorhombic was found for E//110, whereas a sequence of

cubic → tetragonal → M

for E//001 was evidenced (Cao et al., 2006).

Recently Kutnjak et al. (2006) have shown that the giant electromechanical

response in PMN–29.5%PT and potentially in other ferroelectric relaxors is

the manifestation of a critical point inside the electrical field–temperature

phase diagram. They describe how, close to the critical point, both the energy

cost and the electric field necessary to induce ferroelectric polarization rotations

decrease significantly, thus explaining the giant electromechanical response

of these relaxors. This points out the extreme importance of these studies for

the understanding of the electromechanical properties of these materials for

technological applications.

WPNL2204

From the structure of relaxors to the structure of MPB 431

14.5.2 External pressure effect

A very good review paper by Samara and Venturini (2006) on this subject

has already been published. Among the results it is pointed out that at moderate

value (15kbar), the hydrostatic pressure is known to amplify the relaxor

behaviour of PMN by decreasing the correlation length associated with the

PNRs. In PZN–9.5%PT, up to 3kbar the main influence of pressure is a

decrease of T

but above 3kbar a ferroelectric to relaxor crossover is induced.

At higher pressure the structure is strongly changed in both systems with, at

a first stage, the disappearance of the polar behaviour as expected by the

continuous decrease of the correlation length of the polar regions. In the case

of the relaxor PZN (Janolin et al., 2006), which is characterised by a disordered

rhombohedral polar R3m phase, a homogeneous state is achieved at a pressure

of p

≈ 5GPa. The new high pressure phase is consistent with a non-polar

R-3c space group associated with antiphase tilting of the oxygen octahedra,

similarly to PMN (Kreisel et al., 2002; Chaabane et al., 2003b) or PZN–

4.5%PT (Ahart et al., 2005), and is related to the appearance of new

superstructures on the diffraction patterns and a narrow peak at around

350 cm

–1

in the Raman spectra (Chaabane et al., 2004). It is noticeable that

the oxygen tilting appears only when the system becomes homogeneous.

With further increasing pressure, the octahedral tilt angle increases and the

R-3c structure is destabilised above p

≈ 10GPa towards a monoclinic non-

polar C2/c structure, the tilt system being essentially conserved. Above p

≈ 23GPa, a polar state reappears and is described by a monoclinic structure

with Cc space group which combines both ferroelectric and antiferrodistortive

instabilities (Janolin et al., 2006). The re-entrance of the polar state is similar

to recent observations for PbTiO

and is due to a new kind of ferroelectricity

(Kornev et al., 2005), that is driven by an original electronic effect, and can

be considered as a general feature of perovskites and related materials. The

monoclinic Cc phase has also been reported in such MPB systems as PZT

(Rouquette et al., 2005), with lower symmetries as triclinic P1 and

The fact that the monoclinic phase is obtained in these systems at high

pressure suggests that this monoclinic phase may store an important strain

(energy), a key point for the understanding of the giant piezoelectric properties.

14.5.3 Grain size reduction effect

The question of ferroelectricity when size is reduced is an old problem which

has recently been revived owing to the experimental observation of polarisation

in nanocrystal of BaTiO

with a size as small as 70nm (Scott, 2006), in

contradiction with previous experimental and theoretical reports. Regarding

relaxors, we have recently addressed the question of reduction of size grains

in the ceramics (Carreaud et al., 2005) of PMN in which the dielectric

relaxation at size below around 30nm was found to disappear (Fig. 14.26).

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials432

The compounds of PMN–20%PT, which is just at the border of the MPB

region, and PMN–35%PT have also been studied. In the former, a path of

rotation from M

to M

is observed and below a critical value of ~200nm a

rhombohedral structure is stabilised (Carreaud et al., 2006), whereas the

latter displays a destruction of ferroelectric domain states toward PNRs with

typical sizes equal to the size of the grains below 200nm (Fig. 14.26b).

These effects are also discussed in connection with pressure experiments

and strain/field effects.

The sensibility to the reduction of size appears to be extreme. Although

not discussed in this chapter, it probably explains the so-called ‘X phase’

related to a probable skin effect, which has been well documented in BaTiO

for a long time. For further information the reader may consult the chapter

in this book on the grain size effect by Algueró et al., Chapter 15.

14.5.4 Rotation of polarisation in thin films

Evidently the study of thin films is going to take increasing interest in the

field of relaxor/MPB compounds. Several authors have studied temperature

dependence of dielectric properties in the thin films of PMN, PMN–PT, PSN

and PZT but up to now the question of structural evolution has only mainly

addressed in simple perovskites such PbTiO

and BaTiO

. We have recently

studied (Haumont et al., 2006b; Janolin, 2007) the thin films of PSN and

PSN–PT43% (i.e. inside the MPB) of various thickness, deposited on STO

and MgO substrates. In the former compound we have evidenced at room

temperature a polar tetragonal phase instead of the rhombohedral phase; this

raises the question of the existence of monoclinic phases for MPB PSN-PT

films, as in this case both PSN and PT have a polar tetragonal phase. However,

in the latter compound a single monoclinic Pm (M

) phase is nevertheless

observed whereas in bulk material this phase is mixed with a tetragonal

phase; this indicates that the origin of the monoclinic phase in films of

PSN-PT with morphotropic concentration is different from that of bulk

materials and is directly associated to the strains induced by the changing on

substrate. Depending on the substrate and the thickness, different domains

configuration are obtained (Fig. 14.27). Nevertheless, even in the polydomain

configurations observed in the thicker films, the stress is never completely

relaxed and induces complex structural evolution with temperature completely

different from that of bulk compound: in case of the MPB compound, at high

temperature, a succession of transformations toward a tetragonal non-polar

phase is observed and the cubic phase never reaches 95K.

14.6 Conclusions and future trends

In conclusion, we propose some simplistic pictures which summarise the

main ideas developed in this chapter.

WPNL2204

From the structure of relaxors to the structure of MPB 433

PMN

0.65 PMN–0.35PT

≈ 200 nm in PMN–35% PT

0 1000 2000 3000

(nm)

(b)

≈ 30 nm in PMN

∆

max

(K)

–1

14.26

(a) Temperature and grain size dependence of dielectric

constant in PMN (left) and in PMN–35%PT (right). Plain, dotted and

dashed lines correspond to frequency ranges between 1 and 100kHz

(b) Grain size dependence of dielectric relaxation, defined by

∆

max

(

) =

(ε

max(f=100 kHz)

) –

(ε

max(f=10 kHz)

) for PMN and PMN–35%PT.

12000

8000

4000

1500

1000

500

125

115

105

100 200 300 400

Temperature (K)

PMN PMN–PT35

900 nm

Relaxor

75 nm

Relaxor

15 nm

Non-relaxor

21 500

11500

1500

1200

1000

800

600

260

220

180

140

325 425 525

Temperature (K)

Non-ferroelectric

phase

15 nm

Relaxor

50 nm

Non-relaxor

675 nm

(a)

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials434

14.27

(a) θ/2θ scans of (004) peak for PSN–PT film on MgO substrate

(300nm) and for two films of PSN–PT on STO with a 50nm and 300

nm thickness. (b) Temperature dependence of inter-reticular distance

of the

phase for different films.

Intensity (arb. units)

800

700

600

500

400

300

200

100

85.0 85.5 86.0 86.5 87.0 87.5 88.0 88.5

2θ(°)

(a)

PSN–PT/STO

50 nm

PSN–PT/MgO

300 nm

PSN–PT/STO

300 nm

4.080

4.070

4.060

4.050

4.040

4.030

4.020

200 300 400 500 600 700 800 900 1000

(K)

(b)

00L

H00 PSNPT on STO 300 nm

0K0

H00 – PSNPT on MgO 300 nm

00L – PSNPT on STO 50 nm

WPNL2204

From the structure of relaxors to the structure of MPB 435

14.6.1 Temperature evolution of the structure of relaxors

The physical situation can be roughly summarized by Table 14.1 and the

captions to Figs 14.28–14.31. We have reviewed some main experimental

results, even though many others, not described in this paper have been

reported. A ‘snap-shot’ close to and below the Burns temperature could

therefore give the schematic pictures, as shown in Fig. 14.28. Figure 14.29

Physical

pictures

Main

experimental

evidences

described in

this text

≤

• Complete

freezing of

PNRs in the

form of local

polar order,

coexisting with

eventual long-

range polar

order

• Lattice

parameter

anomaly

• Anisotropic

minimum in

agreement

factor versus

shifts

• Diffuse

scattering

• Vanishing of

dielectric peak

≤

• PNRs strongly

correlated, some

become static

• Lattice

accommodation

(monoclinic)

between CORs

(tetragonal) and

PNRs

(rhombohedral )

• Eventually at

with

* :

appearance of

long-range polar

order (PSN,

PMN–PT and

other related

systems)

• Lattice

parameter

anomaly

• Raman

anomalies

• Anisotropic

minimum in

agreement

factor versus

shifts

• Diffuse

scattering with

eventual critical

component

• Dielectric

maximum,

relaxation with

max(ω)

* <

• At

displacements

gradually have

slow down

and correlate,

forming

dynamic PNRs

weakly

correlated

• CORs/CIRs

may act as

nucleation

centre for the

PNRs

• Lattice

parameter

anomaly

• Raman

anomalies

• Anharmonic

thermal

parameter,

isotopic

minimum in

agreement

factor versus

shifts

Table 14.1

Brief and simplistic summary of the temperature evolution of the

structure of a relaxor.

• Isotropic but

highly

anharmonic

dynamical

displacements

of the lead

along a

spherical shell

• Chemical

ordered regions

(CORs/CIRs)

with local

composition

different from

the bulk exist in

the samples

(whatever

is)

• Anharmonic

thermal

parameter,

isotropic

minimum in

agreement

factor versus

shifts

• Superstructure

peaks (CORs)

whatever

• Raman

scattering

(CORs/CIRs)

(whatever

is)

= freezing temperature;

* = temperature when diffuse scattering appears on cooling;

critical temperature (for compounds with phase transition);

= Burns temperature when

PNRs are created.

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials436

Chemical inhomogeneity

Accommodation region

Short-range polar region

Paraelectric matrix

≈

(a)

Chemical inhomogeneity

Short-range polar region

Paraelectric matrix

(b)

14.28

Schematic picture of the ‘structure’ of a relaxor close to

and

close to

*. The arrows symbolise the correlations. Note that many

details are not addressed in this picture, in particular the questions

of dynamic versus static displacements.

WPNL2204

From the structure of relaxors to the structure of MPB 437

14.29

Schematic picture of temperature-dependence of the ‘structure’

of a PMN-like relaxor (a) and a PSN-like ferroelectric relaxor (b).

100 200 300 400 500 600 700 800

Complete freezing Strongly Weakly Uncorrelated

of PNRs and correlated correlated dynamical

macroscopic dynamical and dynamical motions of

polarisation static PNRs PNRs individual atoms

4.092 Å

4.086 Å

4.078 Å

280

300

320

340

360

380

400

420

T(K)

2000

1600

1200

800

400

(b)

max

20000

15000

10000

5000

100 200 300 400

4.050 Å

4.045 Å

100 200 300 400 500 600

Complete Strongly correlated Weakly correlated Uncorrelated

freezing dynamical and dynamical PNRs dynamical motion

of PNRs static PNRs of individual atoms

(a)

WPNL2204

Handbook of dielectric, piezoelectric and ferroelectric materials438

shows the comparative evolution of PMN and PSN (and other relaxors with

ferroelectric phase).

Of course these pictures should not be taken as being exact and definitive,

in particular, regarding the accuracy of the different temperatures as well as

the notion of PNRs or CORs with well defined ‘domains’ and sharp boundaries.

Indeed, at a ‘zero’ level diffraction/diffuse scattering experiments do not

allow us to differentiate a ‘cake with grapefruit’ model (as depicted in Figs

14.30 and Fig. 14.31), implying nanodomains with sharp boundaries inside

a matrix) from a ‘cake with grape flavour’ model, i.e. a situation in which the

polar order does not form a boundary but is characterised by a correlation

length exponentially decaying and penetrating the whole sample. In fact, the

situation appears to be probably much more complex than these two extreme

(limiting) cases. Indeed by the careful fittings of diffuse scattering profiles,

‘fractal’ or ‘hierarchical’ organisation of the PNRs is possible. Clarification

of the situation is left for the future.

Many other questions are still unsolved, among them the coexistence and

the structure of the ‘frozen’ PNRs inside the ferroelectric domain states

which is probably much more complicated than a simple rhombohedral or

monoclinic local symmetry. One proposal is to use below the freezing

temperature T

, the term SPNRs (static polar nanoregions) instead of PNRs.

14.6.2 The concentration evolution of MPB systems:

MPB or morphotropic phase region?

We have discussed in the above sections that the monoclinic polar order already

exists in ‘pure’ relaxors in the form of PNRs or in connection with PNRs

(SPNRs). When doping with PT this polar order progressively develops in the

form of long-range ferroelectrics phases. We have seen that the CORs which

act as nucleation centres for the PNRs also transforms into chemical

inhomogeneous regions (CIRs) characterised by very local fluctuation or

segregation of titanium which may act as nucleation centres for the monoclinic

MPB phases. How the CORs transform into the CIRs when doping with titanium

is a question that is not yet clearly understood. So, although further experiments

are clearly needed to understand the nanoscale cation distribution, a possible

global simplistic picture of polar and chemical distributions with increasing

content of PT can be drawn to summarise what has been discussed (Fig. 14.30).

This picture points out the important fact that the relaxors and the MPB

systems are highly inhomogeneous and may be viewed as some kind of

composite materials (Fig. 14.31) in which nanoregions of local compositions

and of ferroelectric displacements coexist, forming self-organised nanostructured

systems. The notion of a matrix of average composition and average symmetry

that embeds these nanoregions is probably not correct as discussed above, but

it remains important at least for getting a rough picture of these systems.

WPNL2204

From the structure of relaxors to the structure of MPB 439

Cubic or

rhombohedral

matrix

PMN, PSN, PZN

Microscopic mechanism

PbTiO

Tetragonal matrix

Monoclinic regions

Increasing

amount of

titanium

Local monoclinic

distortion (region

under constraint)

Ordered 1:1 region

Ordered

nanoregions

Ti segregation

charged regions

Monoclinic

symmetry

Tetragonal

regions

14.30

Low-temperature structure versus the concentration of the titanium of MPB relaxors/compounds.

WPNL2204