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

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Handbook of dielectric, piezoelectric and ferroelectric materials450

the ferroelectric phase, and that a paraelectric cubic phase exists below

30 nm.

15.3 The relaxor ferroelectric

Pb(Mg

1/3

2/3

–PbTiO

solid solution

PMN is a prototype of relaxor. Its dielectric permittivity as a function of

temperature shows a broad maximum of ∼20 000ε

at –8 °C

and 1 kHz, the

position of which, T

, shifts towards higher temperatures with increasing

frequency within a range of 20 °C (the so-called Curie range) in the 100 Hz–

1 MHz interval. Below T

, the permittivity also shows dispersion; it increases

when the frequency is decreased. PMN presents slim ferroelectric hysteresis

loops that result in small remnant polarisation. The saturation and remnant

polarisation decrease when the temperature is increased, but do not vanish at

and maintain finite values up to significantly higher temperatures (Cross,

1994). No macroscopic phase transition occurs at the Curie range and the

overall symmetry remains cubic at low temperatures, even though nanometre

size polar regions (PNRs) exist within the cubic phase (Burns and Dacol,

1983; De Mathan et al., 1991; Dkhil et al., 2002). PNRs originate from site

disorder and their dynamics is responsible from the relaxor characteristics,

yet the actual mechanisms are under debate. Relaxors were proposed to be

dipolar glass-like systems (Viehland et al., 1990), for which the (interacting)

PNRs present thermally activated polarisation fluctuations above a freezing

temperature, T

, of –56 °C for PMN (Viehland et al., 1991), and evolve to a

non-ergodic glass state below T

. Frustration of polar long range order results

from competing interactions (random bonds).

This model was questioned, and random fields were proposed to be the

origin (Westphal et al., 1992) or to play a significant role (Pirc and Blinc,

1999) in the relaxor state. A large set of experiments, and also recent calculation

results, suggest a physical picture (see Chapter 14), in which local chemical

inhomogeneities (CIRs, i.e. chemical inhomogeneity regions) act as nucleation

sites for PNRs and therefore, eventually, to long-range polar order: a high

enough electric field causes a ferroelectric, rhombohedral long range order

to develop below a temperature that is field dependent (Arndt et al., 1988);

this ferroelectric phase undergoes a first-order phase transition to the relaxor

state during subsequent heating without field (Ye and Schmid, 1993; Calvarin

et al., 1995). In the case of PMN and other ‘simple’ relaxors such as PZN,

Pb(Sc

1/2

, etc., these CIRs were for a long time mainly associated

with charged regions with local B-cations ordering (CORs, i.e. charged ordered

regions). However, more recent observations in PMN as well as preservation

of relaxor behaviour when doping with titanium (which should destroy B-

cation ordering) indicate a more complex (but non-charged) cations distribution.

The temperature, composition, electric field, pressure, etc. dependence of

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Size effects on the macroscopic properties 451

physical and structural properties of relaxors should receive an interpretation

in this framework of interacting CORs with the CIRs, in which the local

chemistry and the local polarisation are intimately coupled.

From the standpoint of properties and applications, the addition of small

amounts of PT increases the Curie range to ~40 °C for 0.9PMN–0.1PT (Swartz

et al., 1984). This composition is the basis of the electrostrictive ceramic

multilayer actuators used in applications requiring no hysteresis (Nomura

and Uchino, 1982). On cooling, 0.9PMN–0.1PT presents a spontaneous

relaxor–ferroelectric transition to the rhombohedral phase (R3m space group)

below room temperature (RT). Further addition of PT causes the shift of the

relaxor state towards higher temperatures, and the rhombohedral phase is

stabilised at RT for 0.85PMN–0.15PT (Ye et al., 2003). This phase was

thought to be the room temperature phase up to ~0.65PMN–0.35PT (Noblanc

et al., 1996), at which a morphotropic phase boundary (MPB) with a tetragonal

phase (P4mm space group) had been earlier described (Choi et al., 1989).

However, after the discovery of the monoclinic phase (Cm space group) in

the MPB PZT, a number of studies on the structure of MPB phases in relaxor–

PT systems have reported the presence of monoclinic phases (with space

groups Cm and Pm) in the MPB region (Ye et al., 2001; Noheda et al., 2002;

Kiat et al., 2002; Singh and Pandey, 2003; Haumont et al., 2003). For the

MPB PMN–PT, Rietveld analysis of powder X-ray diffraction (XRD) and

neutron diffraction data has shown that two monoclinic phases (Cm and Pm

space groups, respectively) exist between 0.75PMN–0.25PT and 0.65PMN–

0.35PT (Singh and Pandey, 2003; Singh et al., 2006). Very recently, the

region of existence of the Cm monoclinic phase has been shown to extend

down to 0.8PMN–0.2PT (Jiménez et al., 2006). The phase transition between

the relaxor and ferroelectric states for this composition presents distinctive

features that shed light on the development of polar long-range order in the

system (Algueró et al., 2005a; Jiménez et al., 2006). The MPB PMN–PT

single crystals and textured ceramics are under consideration for the new

generation of high sensitivity and high-power piezoelectric devices because

of their ultra-high piezoelectric performance under electric field. Also, the

MPB PMN–PT ceramics can present d

piezoelectric coefficients as high as

720 pC/N (Kelly et al., 1997); that is, higher than soft PZT, and significantly

lower piezoelectric losses (Algueró et al., 2005b). Furthermore, its mechanical

response is linear across a range of stress for which PZT already presents

Rayleigh-type behaviour associated with the movement of walls (Algueró et

al., 2003). These results strongly suggest that the contribution of ferroelectric/

ferroelastic domain wall displacements to the electromechanical and mechanical

responses of this material is significantly less important than in soft PZT

and, thus, one can expect a smaller effect of the ceramic clamping on the

linear coefficients, when the domain configuration changes with the decrease

of size.

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Handbook of dielectric, piezoelectric and ferroelectric materials452

15.4 Processing of submicrometre- and

nanostructured Pb(Mg

1/3

2/3

–PbTiO

ceramics

The processing of dense, submicrometre- and nanostructured ceramics requires

the combination of techniques for the synthesis of very fine powders and

sintering procedures that enhance densification but limit grain growth, basically

involving the application of pressure. For instance, 93% density, ∼35 nm

grain size BaTiO

ceramics have been processed by hot isostatic pressing

(860 °C, 200 MPa in N

) of 10 nm particle size powders obtained by hydrolysis

and decomposition (Guo et al., 2005). Also, 97% density, ∼30 nm grain size

BaTiO

ceramics have been processed by spark plasma sintering (1000 °C,

3 min) from 10–20 nm particle size powders by solution precipitation (Buscaglia

et al., 2006).

In our case, mechanosynthesis was used for obtaining (1–x)PMN–xPT

nanocrystalline powders. This was done with a high-energy planetary mill

and tungsten carbide milling media, by mechanochemical activation of a

stoichiometric mixture of the oxides. Details of the procedure and of the

mechanisms taking place during the activation can be found elsewhere (Kuscer

et al., 2006, 2007). The final powder consists of a major nanocrystalline

perovskite phase, a ∼30 wt% of amorphous phase fully depleted of MgO,

and trace amounts of pyrochlore and crystalline MgO. Contamination levels

were controlled below 50 and 600 ppm for Co and W, respectively. A de-

agglomeration treatment was finally carried out by attrition milling in

isopropanol for 4 h. Particles with such a size distribution that the 10, 50 and

90 wt% were under 0.37, 0.84 and 5.49 µm, respectively, were obtained.

Coarse-grained ceramics of different compositions with high chemical

homogeneity and crystallographic quality have been processed from these

powders by sintering in PbO (Algueró et al., 2006), and submicrometre

grain size ceramics can be obtained with hot pressing (Algueró et al., 2004).

XRD patterns for the 0.8PMN–0.2PT and 0.65PMN–0.35PT powders

synthesised are shown in Fig. 15.1. Dense, coarse-grained 0.8PMN–0.2PT

and 0.65PMN–0.35PT ceramics with a grain size of 4 µm were obtained by

sintering at 1200 °C in a PbO atmosphere, created by burying the pellets in

PbZrO

powder inside a closed alumina crucible. XRD patterns for these

ceramics are shown in Fig. 15.2. Dense, submicrometre grain size ceramics

of the same compositions with decreasing grain size approaching the nanoscale

(∼100 nm) were obtained by hot pressing at 60 MPa and decreasing

temperatures from 1000 °C down to 700 °C. 1000 °C is the upper limit above

which PbO volatilisation is significant and it is necessary to control the

atmosphere. 700 °C is the lower limit, below which the residual pyrochlore

in the powder cannot transform into the perovskite. The XRD patterns for

the ceramics prepared by hot pressing are also shown in Fig. 15.2. In this

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Size effects on the macroscopic properties 453

temperature interval, mostly single phase, dense ceramics are obtained at all

temperatures as illustrated in Fig. 15.2 and 15.3. The density was evaluated

from weight and dimension measurements, and from porosity levels obtained

by quantitative image analysis of polished surfaces. Note that both techniques

provided consistent trends with temperature, yet slightly lower values were

obtained from the ceramic dimensions and weight. This is probably a

consequence of some systematic error introduced when an ideal disc is assumed.

Nevertheless, all ceramics studied here have closed porosity and a density

well above 90%. Scanning force microscopy images of the polished and

thermally etched surfaces of all the samples are shown in Fig. 15.4. Grain

sizes of ∼0.4, 0.2, 0.15 and 0.1 µm were obtained by hot pressing the 0.8PMN–

0.2PT powder at 1000, 900, 800 and 700°C, respectively, and similar results

were obtained for 0.65PMN–0.35PT. The size effects on the macroscopic

properties of this group of ceramic samples have been studied.

15.5 Size effects on the macroscopic properties of

0.8 Pb(Mg

1/3

2/3

–0.2PbTiO

0.8PMN–0.2PT is at the PMN edge of the MPB region. The phase transition

between the room temperature ferroelectric phase and the high-temperature

relaxor state has been recently described for coarse-grained ceramic samples

processed from the powders synthesised by mechanochemical activation

Intensity (a.u.)

20 30 40 50

2θ(°)

15.1

XRD patterns for the PMN–PT powders synthesised by

mechanochemical activation, used for the subsequent processing of

the ceramic materials with decreasing grain size (Pe: perovskite, Py:

pyrochlore).

0.65 PMN–0.35 PT

0.8 PMN–0.2 PT

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Handbook of dielectric, piezoelectric and ferroelectric materials454

(Algueró et al., 2005a; Jiménez et al., 2006). The material presents a transition

between the monoclinic Cm ferroelectric phase and the non-ergodic relaxor

state with well-defined, different transition (

= 71 °C and

= 61 °C on

heating and cooling, respectively) and freezing (T

= 77 °C) temperatures.

20 30 40 50

2θ(°)

20 30 40 50

2θ(°)

Intensity (a.u.)Intensity (a.u.)

HP at 700 °C

HP at 800 °C

HP at 900 °C

HP at 1000 °C

1200 °C in PbO

HP at 700 °C

HP at 800 °C

HP at 900 °C

HP at 1000 °C

1200 °C in PbO

0.65 PMN–0.35 PT

0.8 PMN–0.2 PT

15.2

XRD patterns for the PMN–PT ceramic materials processed from

the mechanosynthesised powders (Pe: perovskite, Py: pyrochlore).

Sintering conditions aimed at obtaining decreasing grain sizes are

indicated (HP: hot pressing).

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Size effects on the macroscopic properties 455

The transition also presents thermal hysteresis in the kinetics that is much

slower on cooling than on heating. This indicates that quite a sharp slowing

down occurs in the temperature interval between the transition temperatures

on cooling and heating.

These features were established by studying the temperature dependence

of the dielectric permittivity and the Young´s modulus across the transition

in combination with thermal expansion measurements. The dielectric

permittivity measured on heating at five frequencies is shown in Fig. 15.5

for a ceramic with 4 µm grain size. Note the sharp increase between 67 and

77 °C, and the relaxor-type characteristics above the latter temperature. This

corresponds to the freezing temperature T

, obtained by the fit of the frequency

dependence of the temperature of the maximum dielectric permittivity, T

to the Vogel–Fulcher relationship, as shown in Fig. 15.6. The permittivity

presents a clear thermal hysteresis, as illustrated in Fig. 15.7 for the same

ceramics at 10 kHz. A sharp decrease is not observed on cooling at any

temperature. The thermal hysteresis of the Young´s modulus is shown in the

same figure. The minima are associated with the phase transition, which is

much sharper on heating than on cooling, reflecting the slowing down of the

phase transition within the temperature interval between the transition on

heating and cooling: 71 and 61 °C. The slowing down can be interpreted

Weight and volume

Quantitative microscopy

0.8 PMN-0.2PT

96.3%

98.5%

97.3%

95.2%

93%

95%

94%

90%

700 800 900 1000

Hot pressing temperature,

(°C)

Density (g/cm

)

8.1

7.8

7.5

7.2

15.3

Density measured by two different techniques for the 0.8PMN–

0.2PT ceramic materials processed by hot pressing the

mechanosynthesised powders at decreasing temperatures.

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Handbook of dielectric, piezoelectric and ferroelectric materials456

within the two-stage model for the development of ferroelectric long-range

order in relaxor systems, as recently proposed by Ye et al. (2003). In the first

stage, PNRs start condensing at high temperature. Their number and size

increase as the temperature is decreased until the temperature of the phase

transition is reached. Then, the second stage begins that is characterised by

the onset of ferroelectric fluctuations. The model proposes that the kinetics

of the transition is controlled by the number of PNRs at the onset of the

ferroelectric fluctuations, which depends on temperature. Therefore, the slower

the kinetics, the lower the temperature of the transition. The thermal hysteresis

0.8 PMN-0.2PT

200 nm 400 nm

(a) HP at 700 °C (a) HP at 800 °C

800 nm 400 nm

(d) HP at 1000 °C (c) HP at 900 °C

15.4

Atomic force microscopy images of polished and thermally

etched surfaces of the 0.8PMN–0.2PT ceramic materials processed by

hot pressing (HP) the mechanosynthesised powders at decreasing

temperatures.

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Size effects on the macroscopic properties 457

4 µm

0.4 µm

0.15 µm

0.8 PMN–0.2 PT

4 µm

0.4 µm

0.15 µm

0.1, 1, 10, 100, 1000 kHz

–200 –150 –100 –50 0 50 100 150 200 250

Temperature,

(°C)

Real permittivity, ε (xε

)

30000

20000

10000

Real permittivity, ε (xε

)

15000

10000

5000

Real permittivity, ε (xε

)

9000

6000

3000

15.5

Dielectric permittivity measured on heating at five frequencies

for 0.8PMN–0.2PT ceramics with decreasing grain size. Curves at 10

kHz are directly compared in the inset.

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Handbook of dielectric, piezoelectric and ferroelectric materials458

in the kinetics of the transition for 0.8PMN–0.2PT would then be a consequence

of the hysteresis in the temperature of the transition, and of the transition

being slowed down in this interval.

The same macroscopic properties for ceramics with 0.4 and 0.15 µm grain

size are also shown in Figs 15.5–15.7. Note the absence of dielectric dispersion

above T

for the submicrometre size ceramics (see Fig. 15.5). This indicates

the absence of Maxwell–Wagner type polarisation at the grain boundaries,

which is associated with the presence of segregated second phases or defects

(Buscaglia et al., 2006). The permittivity still presents a sharp, yet less

pronounced, increase on heating for the ceramic with a grain size of 0.4 µm,

but not for the sample with a size of 0.15µm. A direct comparison of the

permittivity values of all materials with different grain sizes is given in the

inset of Fig. 15.5 at 10 kHz. The broadening and depression of the maximum

with the decrease in size is similar to that observed in BaTiO

(Zhao et al.,

2004) and is thus most probably a boundary effect. Note that ceramics present

similar permittivity values at 250 °C in spite of the large difference in the

density of boundaries, which further indicates the good quality of the materials

processed. The high-temperature relaxor state exists for all sizes. Fits to the

Vogel–Fulcher relationship for the submicrometre-structured materials are

also given in Fig. 15.6. The parameters of the fits are given in Table 15.1. No

size effect was observed on either the freezing temperature or the activation

energy. The thermal hysteresis of permittivity and Young’s modulus for the

ceramics with submicrometre grain sizes are also shown in Fig. 15.7. The

4 µm

0.4 µm

0.15 µm

V-F fit

0.8 PMN–0.2 PT

In (ω)

88 92 96 100 104

(°C)

15.6

Temperature of the maximum dielectric permittivity,

, as a

function of frequency, and fit to the Vogel–Fulcher relationship for

the 0.8PMN–0.2PT ceramics with decreasing grain size.

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Size effects on the macroscopic properties 459

15.7

Thermal hysteresis of the dielectric permittivity at 10kHz and

Young’s modulus across the transition for the 0.8PMN–0.2PT

ceramics with decreasing grain size.

0.8 PMN–0.2 PT

4 µm

0.4 µm

0.15 µm

Real permittivity, ε (xε

)

30000

20000

10000

Real permittivity, ε (xε

)

15000

10000

5000

Real permittivity, ε (xε

)

7500

5000

2500

0 50 100 150

Temperature,

(°C)

TTT

0 50 100 150

Young’s modulus,

(GPa)

260

220

180

140

100

Young’s modulus,

(GPa)

230

200

170

140

100

Young’s modulus,

(GPa)

TTT

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