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

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Handbook of dielectric, piezoelectric and ferroelectric materials410

Vakhrushev et al., (2007) demonstrated that the observed anisotropic diffuse

scattering can be very well reconstructed by strain field produced by defects

of tetragonal symmetry (Fig. 14.12).

In contrast, the application of an electric field does not lead to the suppression

of the diffuse scattering

and even under a high-strength field (40kV/cm), the

‘butterfly-shape’ diffuse scattering is only partially affected (Xu et al., 2006):

a redistribution of the intensity occurs via changes in elastic constants. With

the assumption that the butterfly-shape diffuse scattering originates only in

polar nanoregions, one might expect the diffuse scattering to disappear because

the electric field is, in principle, strong enough to align these nanoregions

and to achieve a uniform polar state. The fact that this is not observed

suggests that the polar defects that are supposed to be responsible for the

anisotropic diffuse scattering are coupled to a deformation that inhibits the

alignment of the PNRs. It is this idea that has been developed in this section.

We would like to come back to the question of local symmetry of PNRs

(whether it is rhombohedral, tetragonal or monoclinic) and their mere existence

Pressure Temperature

0.1 GPA 1.5 GPA

3.6 GPA > 4.5 GPA

(reciprocal lattice unit)

0.1

0.0

0.1

0.0

–0.1

PMN (100)

10 K

500 K

250 K

650 K

0.9 1.0 1.10.9 1.0 1.1

(reciprocal lattice unit)

Electric field

= 0

[111]

(a) (b)

–0.1 0 0.1 –0.1 0 0.1

(0,

)

(H, O, O)

3.00

2.50

2.00

14.11

Diffuse scattering around <

00>; evolution with pressure in

PMN (Chaabane

et al.

, 2003a), temperature in PMN (Xu

et al.

, 2004)

and electric field in PZN (Xu

et al.

, 2005).

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From the structure of relaxors to the structure of MPB 411

as a well-delimited zone of polar correlation with an abrupt boundary. This

section shows that the reality is obviously much more complex. Indeed, a

glance at Fig. 14.13 readily shows that these questions, as well as the question

of a clear separation between PNRs and CORs, are due to the need to build

simplistic objects which should help us to understand reality: there is no

clear separation between PNRs, CORs and the monoclinic adaptative zone

(see Section 14.4.2).

To conclude this section a few words have to be added to the connection

of the structural pictures of relaxors presented here and the theoretical

background. Some years ago, in parallel to phenomenological models, random

field models with ideas issued from renormalisation theories were developed

in particular to explain the experimental observations of non-mean-field

critical exponent. The success of these types of model was important, but still

conflicting results with experiments pointed out the important part played by

the point or extended defects: there was clearly a need to take into account

these defects in the models. The notion of ‘random field’ is one way, among

several, to explain more accurately the experimental observations by taking

into account some types of defects. In the field of relaxors, the Imry and Ma

4000.00

14000.00

24000.00

–2.50

–2.60

–2.70

–2.80

–2.90

–3.00

–3.10

–3.20

–3.30

–3.40

–3.50

–0.50 –0.40 –0.30 –0.20 –0.10 0.00 0.10 0.20 0.30 0.40

14.12

Calculated 2D plot of the diffuse scattering intensity

distribution in PMN near the (003) point.

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Handbook of dielectric, piezoelectric and ferroelectric materials412

argument was used by Kleemann (1993) to explain the diffuseness of PMN

by quenched random electric field arising from charged compositional

fluctuations and inducing a nanodomain state. However, other approaches,

based on random bond interaction and giving rise to glassy behaviour, were

also developed: that is why relaxors are sometime also called glassy ferroelectrics.

The situation has been clarified by Pirc and Blinc (1999) who developed

the random bond–random field model. In this model, the PNRs not only

interact between each other as expected in classical glass-like systems

(dipolar or quadrupolar) but may also interact with random fields arising from

the compositionally chemical disorder. In this model the change with temperature

from isotropic (Heisenberg) to discrete value of the order parameter is considered.

And this is indeed what is observed from the experimental point of view (see

Fig. 14.5 for instance, showing the isotropic to anisotropic positions of lead

atoms). However, this model considers pseudospins (as PNRs) interactions

with quenched random electric fields and describes in an elegant manner

the static behaviour of relaxors but it cannot currently satisfactorily describe

the dynamic properties and, especially, the dielectric relaxation.

14.4 Towards the MPB: substitution of titanium

14.4.1 Rotation of polarisation via monoclinic phase

In this section we summarise the current situation in some MPB systems

from the standpoint of the long-range polar order. Indeed as is shown in

Section 14.4.2 the question of symmetry in these systems is a difficult one as

there is a progressive transformation of local to long-range polar order: for

instance PMN can be viewed as, ‘on average’, a cubic phase but we have

seen that at low temperature frozen PNRs exist. Moreover, a very small

(a) (b)

14.13

Snapshot of local mode polarisation in (a) PSN at 600K and

(b) PMN at 130K. More highly correlated circled regions are

chemically ordered and the more disordered matrix is chemically

disordered. From calculations by Burton

et al.

(2006).

WPNL2204

From the structure of relaxors to the structure of MPB 413

amount of titaniums doping transforms the local polar order into, ‘on average’

a rhombohedral phase in which local monoclinic regions might still manifest

themselves. These difficulties are in fact more or less identical to the question

of the exact symmetry of the PNRs in non-doped compounds as discussed

above: can they be considered as a rhombohedral polar order with a monoclinic

zone of adaptation between the tetragonal symmetry imposed by the CORs?

Again Fig. 14.13 shows the difficulty of clearly separating or even identifying

the different objects under consideration.

Before the discovery of the monoclinic phase in the MPB of PZT (Noheda

et al., 1999) the rotation of polarisation between the rhombohedral and the

tetragonal phase was explained by a complex texture of microdomains (Lucuta,

1989) as shown in Fig. 14.14. The joint experimental and theoretical works

showed that the key point for explaining the giant piezoelectric properties

inside the MPB, i.e. the huge effect of a weak electric field on the direction

and magnitude of polarisation, is the fact that in a monoclinic phase the

polarisation is no longer restricted along a linear direction ([111] or [100] for

instance) but can rotate freely in a plane. In fact, up to now several monoclinic

phases have been discussed and evidenced. These phases are easily visualised

and related to the other ferroelectric phase via a picture proposed by Fu and

Cohen (2000) (Fig. 14.15).

PZT phase diagram

The situation in PZT (Fig. 14.16) has been discussed by several authors, in

particular by Noheda (2002). A unique monoclinic phase of the M

type was

evidenced in addition to the adjacent tetragonal and rhombohedral phases.

However a distinction must be made regarding the low-temperature

rhombohedral phase in which a rotation of oxygen octahedra occurs along

the [111] direction in addition to the ferroelectric shifts of the R3m phase,

inducing an R3c phase. Persistence of superlattice reflections inside the

concentration range of the monoclinic phase raises the question of the exact

space group for these concentration: if long ranged, a Pc, instead of Cm,

(001) (111) (010) (111) (001)

14.14

Lucuta’s juxtaposition of tetragonal and rhombohedral domains

in the morphotropic phase boundary.

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Handbook of dielectric, piezoelectric and ferroelectric materials414

space group should be considered from Rietveld analysis (Ranjan et al.,

2002). Later, the same group reported that the correct space group for this

phase is in fact Cc (Hatch et al., 2002). Moreover recent models involving

mixing with Cc phase were also considered (Cox et al., 2005; Ranjan et al.,

2005). TEM observation by Woodward et al. (2005) suggests a Cc phase and

(010)

[001]

Tri

[101]

[111]

(11 0)

14.15

Different phases implied in the study of MPB compounds,

described in the pseudo-cubic cell. Monoclinic phase

is also

denoted M

, while

is also denoted M

or M

depending on the

direction of polarization above or below the diagonal direction [111].

In between the two monoclinic planes is a triclinic phase. T stands

for tetragonal, O for orthorhombic and R for rhombohedral.

Temperature (K)

1000

800

600

400

200

0.44 0.46 0.48 0.50 0.52 0.54 0.56

Ti composition

I4cm

R3m

P4mm

Pm3m

14.16

Phase diagram of PZT, from Kornev

et al.

(2006).

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From the structure of relaxors to the structure of MPB 415

underlines the ability of such phase to bridge the R3c and Cm phases. Recently

(Kornev et al., 2006) the Cc phase existence was confirmed as one of the

ground states of PZT but the oxygen octahedra in this Cc phase rotate neither

about the [001] direction nor about the [111] direction, but rather about an

axis that is between these two directions. Interestingly, for the largest Ti

concentrations, a new tetragonal phase with the I4cm space was suggested

and confirmed experimentally. This phase involves the coexistence of

ferroelectricity and rotation of oxygen octahedra, but is associated with the

tetragonal symmetry (unlike R3c and Cc). As a result, an increase in Ti

concentration from 47% to 52% results not only in the continuous rotation of

the spontaneous polarization from [111] to [001], but also in the change of

the oxygen octahedra rotation axis from [111] to [001].

PMN–PT phase diagram

Shortly after the discovery of the monoclinic phase in PZT, the same situation

was reported in PMN–PT with, however, some discussions about the exact

symmetry. Ye et al. (2001) reported a Cm (M

) phase whereas we reported

(Kiat et al., 2002) a Pm (M

) phase. In fact it appears that both groups were

right (or wrong !) because the three monoclinic phases can appear in addition

to rhombohedral and tetragonal phases, depending on the concentration/

temperature/electric field/pressure/strain ranges; moreover with, in many

cases, the coexistence of phases (Akhilesh Kumar and Dhananjai, 2003;

Akhilesh Kumar et al., 2006; Singh et al., 2006). In fact the path of rotation

experimentally observed with two monoclinic phases when the concentration

is changed, i.e. rhombohedral → M

→ M

→ tetragonal, was predicted by

Fu and Cohen (2000) and shows how to minimise the internal energy of the

system. Recent results also show that the extent of the MPB appears to be

underestimated (Akhilesh Kumar et al., 2006; Carreaud et al., 2006), as well

as for the rhombohedral phase (Ye et al., 2003). We plot on Fig. 14.17

tentative phase diagram which includes these recent results. The question of

the average symmetry, in particular, in the low PT concentration range is still

a matter of debate: whether it can be more adequately described as an ‘average’

rhombohedral phase or a local monoclinic order is a difficult question, as

explained above. The question of an orthorhombic phase has also been raised

in this system as well as in PZN–PT: we discuss these questions more deeply

in Section 14.4.4 in relation to PSN–PT.

PZN–PT phase diagram

The observation (Lebon et al., 2002) in PZN by our group of splitting at

385K of the [111] cubic peaks as well as anomalous widening of [100] peaks

and the report of a field-induced monoclinic phase (Lebon et al., 2005)

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Handbook of dielectric, piezoelectric and ferroelectric materials416

showed that the structure of this system is at least as complex as other

relaxors. Recent results by Jeong and Lee (2006) suggest describing the

rhombohedral phase rather as a mixture of meso-scale PNRs in a disordered

lattice: their results show that in PZN, these PNRs are simply ‘larger’ at

room temperature (150 Å) (La-Orauttapong et al., 2001) than those in PMN

(20Å) so they are visible in powder diffraction measurements as a split of

Bragg peaks. Besides they propose that PZN and PMN have the same ground

state, i.e. mixed state of disordered cubic phase and rhombohedral PNRs.

Another point of view was also proposed and considers another ground state

for PZN as a lower symmetry phase which could be monoclinic rather than

rhombohedral (Bing et al., 2005).

In PZN–PT, since the optical observation by Fujishiro et al. (1998) of

heterophases in PZN–PT9% which showed a lowering of symmetry between

the rhombohedral and tetragonal domains, conflicting reports have been

published regarding the exact symmetry of the MPB. We reported a Pm (M

)

phase (Kiat et al., 2002) coexisting with the tetragonal phase whereas an

orthorhombic phase was reported whose unit cell was afterward described in

a monoclinic setting (this confusion was also made in PMN–PT, see pages

419–20). The situation has recently been clarified by Bertram et al. (2003),

who confirm the M

as the unique monoclinic MPB phase and clarify the

extent of the MPB as well as the phase coexistence (Fig. 14.18).

Temperature (K)

700

600

500

400

300

200

100

0 0.1 0.2 0.3 0.4 0.5 0.6

Composition PT (

14.17

Phase diagram of PMN–PT resulting from computation of

several works (see text).

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From the structure of relaxors to the structure of MPB 417

PSN–PT system

PSN–PT and PMN–PT phase diagrams show great similarities, with an overall

path of polarisation rotation via M

and M

monoclinic phases, and a significant

temperature and composition-dependent mixing between these phases.

The complete path of rotation with concentration in PSN–PT has been

precisely studied in our group by Haumont et al. (2003, 2005, 2006a) (Fig.

14.19). In particular, using apparent charge and the results of Rietveld analysis,

they studied the evolution of the polarisation (modulus and angle) inside the

Fu and Cohen cube.

At low temperature, five regions of concentration have been found:

(1) Rh (0 < x ≤ 0.26): The addition of titanium in PSN increases the

rhombohedral distortion as well as amplitudes of shifts of atoms out of

their cubic positions. The polarisation increases from P = 42µC.cm

(2) Rh→ M

(0.26 < x ≤ 0.37): The polarisation rotates in the (011) plane.

The symmetry becomes Cm of the M

type; the augmentation of the

amplitude of polarisation is stronger than in the R region.

(3) M

→ M

(0.37 < x ≤ 0.43): The polarisation goes into the (010) plane,

not via intermediate values (which would have led to a triclinic phase)

but instead through a jump which occurs with strong phase coexistence:

(Cm + Pm). When the titanium concentration increases, the Pm proportion

of phase increases, the polarisation in the (011) plane decreases and

polarisation in the (010) plane increases.

(4) M

→ T (0.43 < x ≤ 0.55): The Cm phase has disappeared, P4mm

appears inside the Pm phase and its distortion and proportion increase

with Ti. A rotation of polarisation arises via the phase mixing Pm–

P4mm. The modulus of polarisation of the P4mm increases with Ti. The

monoclinic phase completely disappears at x close to 0.55.

Monoclinic M

Rhombohedral

Tetragonal

Volume fraction (%)

100

0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14

14.18

Extent and volume fractions of the different phases in PZN–PT,

from Bertram

et al.

(2003).

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Handbook of dielectric, piezoelectric and ferroelectric materials418

(K)

880

800

720

640

560

480

400

320

240

R3m

P4mm

Pm3m

0 0.2 0.4 0.6 0.8 1

<001>

P4mm

[001]

= 1

T 92 µC/cm

[1,37 0 1,76]

55 µC/cm

T [001] 57 µC/cm

<001>

= 0.43

<101>

(010)

(1-10)

<001>

[11 11 6] 57 µC/cm

[5 0 3] 60 µC/cm

<11

[113] 56 µC/cm

[551] 52 µC/cm

<001>

R 42 µC/cm

R3m

[111]

= 0

= 0.35

= 0.37

= 0.415

14.19

Phase diagram with corresponding rotation of polarization in PSN–PT. Notice also the phase coexistence.

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From the structure of relaxors to the structure of MPB 419

(5) T (0.55 < x ≤ 1) : The system is single phased with a polarisation which

increases in a slower way and saturates at P = 92µC/cm

–2

(PT).

Several interesting points have been noticed:

(1) No phase coexistence is found between the rhombohedral and any other

phase. The only report of such coexistence is for R3m + Cm at the

concentration x = 0.31 of PMN–PT by Noheda et al. (2002).

(2) Only 1.5% of titanium separates the two states: (Cm + Pm) and (Pm +

P4mm). An extreme weak change of concentration completely changes

the structure. Although not observed, a single Pm phase may occur at a

very specific concentration between x = 0.415 and x = 0.43. Such single

phases have been reported by Singh et al. (2003) in PMN–PT for x =

0.31 and for x = 0.35 by our group (Kiat et al., 2002).

(3) At concentration x = 0.43 the direction of polarisation of the Pm phase

is very close to the orthorhombic direction [101], but this symmetry is

definitively out of consideration because atoms clearly adopt non-

orthorhombic positions, even though the resulting polarisation stands

close to an orthorhombic direction. This orthorhombic Amm2 symmetry

has also been proposed in PZN–PT, as well as for PMN–PT but only

from a fitting profile of rocking curves, which is in our opinion not

sufficient. On the contrary a monoclinic M

phase but with a direction

of polarisation closes to the orthorhombic direction [101] is evidenced

via Rietveld analysis of x = 0.09 in PZN–PT and x = 0.35 in PMN–PT.

The real existence of a ‘true’ orthorhombic phase remains questionable

in these MPB systems.

The temperature evolution of these systems is also complex: for instance

the evolution of PSN–PT x = 0.415 compound’s phase mixing is detailed in

Fig. 14.20. Other concentration evolutions (less detailed) are also shown.

In the x = 0.415 compound, the Cm and Pm phases coexist from the

lowest temperatures up to about 400K when the progressive destabilisation

of the Cm phase is observed. Close to 435 K, the tetragonal P4mm phase was

found, coexisting with the Pm phase, while the Cm phase has vanished.

Above 480K, this tetragonal phase is observed alone up to about 545K, the

temperature at which it transforms toward the high-temperature paraelectric

Pm–3m phase. For highest concentration a coexistence of the Pm and P4mm

phases is observed at low temperature, and a pure tetragonal phase is recovered

above 0.55 concentration of Ti.

Interestingly we have also reported for x = 0.35 in PSN–PT a transition

(observed below room temperature) from a M

to a M

phase when cooling

which corresponds to a rotation of polarisation inside the (011) plane from

one side to the other side of the rhombohedral [111] direction.

The observation of the phases mentioned shows agreement with predictive

theoretical work by Vanderbilt and Cohen (2001). However, not all experimental

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