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

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Handbook of dielectric, piezoelectric and ferroelectric materials460

material with 0.4 µm presents the transition at 65 and 56 °C on heating and

cooling, respectively. Therefore, a shift towards lower temperatures has

occurred. There is still hysteresis in the sharpness of Young’s modulus minima

and, so, in the kinetics of the transition. This allows one to narrow the

temperature interval in which the slowing down takes place, from 71–61 to

65–61 °C. The material with 0.15 µm presents a broad mechanical anomaly

at ∼30 °C with negligible hysteresis, neither in the temperatures nor in its

sharpness. This suggests that the transition has further shifted down to lower

temperatures, and that its kinetics is always slow. This is consistent with the

slowing down occurring in the 65–61 °C interval, which is therefore size

independent. The size effect is thus to decrease the transition temperature,

and as a consequence, there is a size range between 0.4 and 0.15 µm, for

which the transition is shifted below the temperature of its slowing down,

between 65 and 61 °C, and the kinetics becomes very slow (Jiménez et al.,

in preparation).

The room temperature ferroelectric hysteresis loops for ceramics with 4,

0.4 and 0.15 µm grain size are shown in Fig. 15.8. The saturation polarisation

for the ceramics with 4 and 0.4 µm is similar, 25–22µC/cm

, though the

remnant polarisation is significantly decreased from 21 to 11 µC/cm

with

size decrease. The material with 0.15µm only presents incipient switching.

The room temperature phases have been studied by Rietveld analysis of

XRD data. The agreement factors of the Rietveld analysis along with the cell

parameters are given in Table 15.2. Only those for Cm monoclinic and R3m

rhombohedral phases are included because they always gave the best factors,

though monoclinic Pm, orthorhombic Bmm2, tetragonal P4mm, cubic Pm3m,

and phase mixing were also considered. The Rietveld results indicate that

ceramics with 4 and 0.4 µm are monoclinic, while that with 0.15 µm is

rhombohedral. The spontaneous polarisation was calculated from the Rietveld

results (errors between 5 and 29 µC/cm

) and values of 58 with a dispersion

of 12 µC/cm

were obtained with no size dependence (Carreaud et al., 2006).

Table 15.1

Parameters of the Vogel–Fulcher behaviour for the relaxor

state in the PMN–PT system

Size

(°C)

(meV)

PMN

Single crystal –56 79

0.9PMN–0.1PT

Ceramic 18 41

0.8PMN–0.2PT

4 µm7730

0.4 µm7537

0.15 µm75 44

0.65PMN–0.35PT 0.15 µm 167 3

Viehland

et al.

(1991).

Viehland

et al.

(1990).

Jiménez

et al.

(in preparation).

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Size effects on the macroscopic properties 461

This indicates that the size effect on the saturation and remnant polarisation

is associated with the domain configuration rather than with the spontaneous

polarisation. Domain size that must be strongly linked with the kinetics of

the relaxor to ferroelectric transition would, thus, strongly influence ferroelectric

switching, this being hindered by small sizes (Jiménez et al., in preparation).

The increase of the monoclinic domain size has been proposed to be the

origin of the higher remnant polarisation for coarse-grained 0.7PMN–0.3PT

(also included in Fig. 15.8) as compared with 0.8PMN–0.2PT ceramics, both

with Cm symmetry (Jiménez et al., 2006).

15.6 Size effects on the macroscopic properties of

0.65Pb(Mg

1/3

2/3

–0.35PbTiO

0.65PMN–0.35PT is located at the core of the MPB region, and it is the

composition for which the electromechanical properties are better for bulk

ceramics. The temperature dependence of permittivity measured on heating

at five frequencies for a coarse-grained ceramic with 4 µm grain size is

shown in Fig. 15.9. A well-defined anomaly typical of a first-order ferroelectric

phase transition is observed. Hysteresis is also illustrated for the reciprocal

permittivity at 10 kHz. Transition occurs at 169 and 164 °C on heating and

4 µm

0.4 µm

0.15 µm

0.8 PMN–0.2 PT

0.7 PMN–0.3 PT: 4 µm

0.1 Hz

–2 –1012

Electric field,

(kV mm

–1

)

Electric displacement,

(µC/cm

)

–20

–40

15.8

Room temperature ferroelectric hysteresis loops for the

0.8PMN–0.2PT ceramics with decreasing grain size. The loop for a

coarse-grained 0.7PMN–0.3PT material is included for comparison.

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Handbook of dielectric, piezoelectric and ferroelectric materials462

cooling, respectively. Note the deviation from the Curie–Weiss law above

the transition temperature that indicates the presence of a high-temperature

relaxor state. Relaxor behaviour has been observed up to 0.5PMN–0.5PT

(Bokov et al., 2005). The same results for a ceramic with a grain size of 0.15

µm are also shown in the figure. The first-order type anomaly has vanished

and, instead, the relaxor type behaviour is observed in agreement with previous

results (Carreaud et al., 2005). The parameters of the fit to the Vogel–Fulcher

relationship are included in Table 15.1. A freezing temperature of 167 °C is

obtained. These results are analogous to those obtained for 0.8PMN–0.2PT,

which were associated with the decrease of the transition temperature below

that at which the kinetics of the transition slows down. This suggests that the

temperature at which the transition slows down is higher for 0.65PMN–

0.35PT and is, thus, composition dependent. According to Ye’s model, this is

the temperature at which the volume (number and size) of PNRs reaches a

certain threshold that hinders ferroelectric fluctuations triggered by the phase

transition, and slows down its kinetics. The PNRs in PMN have been observed

to coarsen with the addition of PT (Hilton et al., 1989). This is consistent

with the threshold volume to occur at a higher temperature for 0.65PMN–

0.35PT than for 0.8PMN–0.2PT, as suggested by the results (Algueró et al.,

2007).

Table 15.2

Agreement factors and cell parameters of the Rietveld analysis of XRD

data for PMN–PT ceramics

Composition Size Symmetry

Goodness

Bragg

of fit

0.8PMN–0.2PT

R3m

6.97 1.44 5.22

(Carreaud

et al.

,4µm a = 4.0291 Å, β = 89.92°

2006)

6.71 1.39 2.73

= 5.6991 Å,

= 5.6928 Å,

= 4.0303 Å, β = 89.88°

R3m

6.22 1.33 4.26

0.4 µm a = 4.0284 Å, β = 89.97°

6.15 1.31 2.70

= 5.6982 Å,

= 5.6953 Å,

= 4.0289 Å, β = 89.94°

R3m

7.07 1.35 2.57

0.15 µm

= 4.0300 Å, β = 89.99°

7.15 1.36 2.97

a=5.6983Å, b=5.6980Å, c=4.0311 Å, β=89.99°

0.65PMN-0.35PT

P4mm

5.50 1.19 4.25

(Algueró

et al

., 4 µm 89/11 %

2007)

= 4.015 Å,

= 4.001 Å,

= 4.031 Å, β = 89.85°

P4mm

= 4.001 Å,

= 4.046 Å

P4mm

5.42 1.23 3.23

0.15 µm 95/5 %

= 4.016 Å,

= 4.012 Å,

= 4.019 Å, β = 89.92°

P4mm

= 4.005 Å,

= 4.024 Å

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Size effects on the macroscopic properties 463

0.1, 1, 10, 100, 1000 kHz

(a)

4 µm

0.15µm

0.65 PMN–0.35T

50 100 150 200 250 300

Temperature,

(°C)

Real permittivity, ε (xε

)

16 000

12 000

8000

4000

(b)

0.15µm

4 µm

Reciprocal permittivity, ε

–1

50 100 150 200 250 300

Temperature,

(°C)

15.9

(a) Dielectric permittivity measured on heating at five

frequencies for 0.65PMN–0.35PT ceramics with decreasing grain size.

(b) Thermal hysteresis of the reciprocal permittivity at 10kHz for the

same ceramics.

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Handbook of dielectric, piezoelectric and ferroelectric materials464

Ferroelectric hysteresis loops for the MPB PMN–PT ceramics with 4 and

0.15 µm grain size are shown in Fig. 15.10. High values of saturation and

remnant polarisation – 28 and 25 µC/cm

, respectively – were obtained for

the coarse-grained ceramic, while only incipient switching is observed for

the 0.15 µm material. The room temperature phases were also studied by

Rietveld analysis of XRD data. Best agreement factors were obtained for a

mixture of Pm monoclinic and P4mm phases, and are given in Table 15.2

along with the cell parameters. Rietveld results indicate that both ceramics

with 4 and 0.15 µm present coexistence of monoclinic and tetragonal phases,

with the amount of tetragonal phase decreasing from 11 to 5% with the size

decrease. Domain configuration as a function of size was studied by

transmission electron microscopy (TEM). Images for the two ceramics are

shown in Fig. 15.11. Three types of domains – micrometre-sized simple

lamellar domains, wedge-type domains with the same size, and submicrometre/

nanometre sized crosshatched domains – exist in the coarse-grained material,

while only crosshatched domains are present in the submicrometre material.

The latter domains, also referred to as tweedlike, have been proposed to be

precursors of polar long-range order (Viehland et al., 1995), which has thus

partially developed for the 4 µm ceramic but not for the 0.15 µm material.

This is consistent with the size effect on ferroelectric switching being associated

with the decrease of the monoclinic domain size. The decrease would again

0.65 PMN–0.35 PT

4 µm

0.15 µm

0.1 Hz

–2 –10 1 2

Electric field,

(kV mm)

Electric displacement, D(µC/cm

)

–20

–40

15.10

Room temperature ferroelectric hysteresis loops for the

0.65PMN-0.35PT ceramics with decreasing grain size.

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Size effects on the macroscopic properties 465

be a consequence of the decrease of the transition temperature below that of

the slowing down of its kinetics (Algueró et al., 2007).

Poling was carried out at 3 kV mm

–1

and 150 °C for 15 min. Ceramics

were then cooled to 50 °C with the field kept on. A d

of 525 ± 15 and 290

± 15 pC/N was achieved for the materials with a size of 4 and 0.15 µm,

respectively, which was measured with a Berlincourt meter. It is remarkable

that the 0.15 µm ceramic presents a piezoelectric coefficient as high as

∼300 pC/N, in spite of the limited ferroelectric switching observed at room

temperature. This could be a consequence of the high field under which the

material undergoes the relaxor to ferroelectric transition during the poling,

which might speed up the kinetics of the transition and result in a larger

domain size. The room temperature strain under unipolar field is shown in

(a) (b)

(c)

100 nm

200 nm1 µm

15.11

TEM images for the 0.65PMN-0.35PT ceramics with (a) 4 µm

and (b, c) 0.15 µm grain size. (c) Illustration of typical crosshatched

domains.

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Handbook of dielectric, piezoelectric and ferroelectric materials466

Fig. 15.12. The electromechanical behaviour for the coarse-grained material

is typical of a PZT-based ceramic, with an initial high slope of ∼1100 pC/N

associated with extensive domain wall movement and hysteresis. The slope

continuously decreases when the field increases down to a saturation value

of ∼350 pC/N at high field, when hysteresis vanishes. Strain under field for

the submicrometre-structured material is quite different. Though the initial

slope is low, strain readily increases, so that values at high field that are

comparable to those of the coarse-grained material; ∼1.2×10

–3

(average d

of ∼700 pC/N) are obtained. Saturation is not observed and large hysteresis

exists. These characteristics that somehow resemble those of electrostrictive

materials, yet hysteretic, are most probably linked to the growth of the

monoclinic domains under the field and the change in their configuration

from crosshatched to micrometre-sized bands.

These results show that the MPB PMN–PT ceramics with 0.15 µm grain

size are highly sensitive materials with low field piezoelectric coefficients of

∼300 pC/N, and high field-effective coefficients of ∼700 pC/N. Thus, this

MPB material presents promising down scaling properties.

15.7 Final remarks and future trends

The study of the macroscopic properties in combination with advanced

structural analysis and polar domain characterisation has allowed us to

15.12

Room temperature strain under high unipolar field for the

0.65PMN–0.35PT ceramics with decreasing grain size.

µm

0.15

µm

0.65MN–0.35PT

Electric field,

(kV mm

–1

)

2.01.51.00.50.0

0.0

0.5

1.0

1.5

Strain,

(×10

–3

)

WPNL2204

Size effects on the macroscopic properties 467

characterise and discuss the size effects in the PMN–PT system. In the range

investigated, which spanned the submicrometre range approaching the

nanoscale (∼100 nm), the size effects seem to be strongly linked to the

mechanisms of development of polar long-range order and kinetic aspects.

The primary size effect is the shift of the ferroelectric-relaxor transition

towards lower temperatures, and large effects on the properties turn up when

it is shifted below the temperature at which the transition slows down. Once

this occurs, the kinetics becomes slow and as a result, the size of the monoclinic

domains decreases and the ferroelectric switching is hindered. This is very

different from the case of PZT, for which size effects mainly originate from

the clamping of the ferroelectric/ferroelastic domain walls. Despite these

effects, high-sensitivity PMN–PT materials with a grain size of 0.15 µm can

be obtained by the application of a high electric field during the transition

from the relaxor to the ferroelectric state.

These results are not only relevant for bulk ceramic technology, but also

for thick and thin films in Si-integrated technologies. As a matter of fact, the

PMN–PT films prepared on Si-based substrates by chemical solution deposition

show very low retention of polarisation, i.e. saturation polarisation much

higher than remnant polarisation, as compared with bulk ceramics of the

same compositions (Park et al., 2001, Calzada, 2007).

Interest in alternative (to PZT) MPB materials is high. Lead-free, niobate-

based MPB ceramic materials have recently been developed as an

environmentally friendly alternative to PZT (Saito et al., 2004), and novel,

high Curie temperature MPB systems based on Bi perovskites are under

intense research for high-temperature applications (Zhang et al., 2003). The

behaviour of the properties on down-scaling, not only the properties themselves,

needs to be considered when novel materials are devised and assessed. This

involves understanding the size effects.

15.8 References

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Handbook of dielectric, piezoelectric and ferroelectric materials468

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Size effects on the macroscopic properties 469

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