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

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Handbook of dielectric, piezoelectric and ferroelectric materials180

background diffusion) of Gaussian function. The two distinct peaks for (111)

and the dominant peak for (200)

are the signature of the rhombohedral

symmetry, indicating the formation of the R3m phase for x = 0.35.

Based on the above analysis, we conclude that the solid solution of

(1–x)PSN–xPT with compositions in the MPB region exhibits a complex

phase mixture with the monoclinic phase that appears as the major phase for

0.37 ≤ x ≤ 0.42, and a small amount of the tetragonal phase. This observation

is in agreement with the report by Haumont et al. (2003), who evidenced a

monoclinic phase (of Pm or Cm symmetry) as the ground state combined

with some amount of the tetragonal phase for the composition x = 0.43.

7.2.3 Dielectric properties

The dielectric permittivity as a function of temperature at various frequencies

(from 10 to 100 kHz) was measured from 400 °C down to 10 °C at 2–3 °C

intervals for the (1–x)PSN–xPT ceramics with the compositions x = 0.35,

0.37, 0.38, 0.39, 0.40, 0.41, 0.42, 0.45, and 0.50 by means of an Alpha High

Resolution Dielectric/Impedance Analyzer (NovoControl). The real permittivity

is shown in Fig. 7.4 for the frequency f = 100 kHz. The spectral features

depend on the compositions. For x = 0.45 and x = 0.50, only one anomaly

appears at T

≈ 286 °C and T

≈ 305 °C, respectively, corresponding to the

phase transition from the paraelectric cubic to the ferroelectric tetragonal

phase. For the compositions of 0.35 ≤ x ≤ 0.42, however, the permittivity

spectrum clearly shows two anomalies. In addition to the sharp peak at T

another shoulder-like anomaly appears at a lower temperature, named T

MPB

indicating a second transition from the ferroelectric tetragonal phase into

another ferroelectric phase(s). As Ti content decreases, T

moves to a lower

temperature, while T

MPB

shifts to a higher temperature. The two anomalies

are nearly merged for x = 0.35. The appearance of T

MPB

and the associated

phase transition in (1–x)PSN–xPT indicate the typical features of the

morphotropic phase boundary behaviour, as previously observed in the PZT,

PMN–PT, and PZN–PT systems (Kuwata et al., 1981; Shrout et al., 1990;

Noheda et al., 1999; Ye et al., 2001; Ohwada et al., 2003).

7.2.4 Thermal analysis by differential scanning

calorimetry (DSC)

The temperature dependences of the heat flow of the (1–x)PSN–xPT ceramics

(x = 0.35, 0.37, 0.38, 0.39, 0.40, 0.41, 0.42, 0.45, and 0.50) were measured

on a differential scanning calorimeter (DSC6200, Seiko Exstar). Figure 7.5

shows the DSC measurement for the 0.50PSN–0.50PT ceramics as an example.

Thermal anomalies with an endothermic peak on heating and an exothermic

peak on cooling are observed. The thermal events show an onset temperature

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

181

= 0.38

= 0.37

= 0.35

MPB

40035030025020015010050

10000

20000

30000

40035030025020015010050

MPB

40000

30000

20000

10000

40035030025020015010050

MPB

50000

40000

30000

20000

10000

= 0.41

= 0.40

= 0.39

40035030025020015010050

MPB

20000

10000

30000

20000

10000

40000

30000

20000

10000

Real permittivity

= 0.50

= 0.45

= 0.42

Temperature (°C)

40035030025020015010050

MPB

20000

30000

10000

20000

30000

10000

30000

20000

10000

7.4

Real permittivity of the (1–

)Pb(Sc

1/2

−

PbTiO

ceramics as a function of temperature for the compositions

= 0.35, 0.37, 0.38, 0.39, 0.40, 0.41, 0.42, 0.45, and 0.50 at the frequency

= 100 kHz.

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Handbook of dielectric, piezoelectric and ferroelectric materials182

of 306 °C upon heating and 310 °C upon cooling, indicating a normal thermal

hysteresis. The peak temperature is in good agreement with the permittivity

peak temperature of 0.50PSN–0.50PT (304 °C). The same measurements

and analysis were performed on the ceramic samples of different compositions,

as shown in Fig. 7.6 for the heating data.

The thermal events detected by the DSC measurements indicate a structural

phase transition for all the samples studied. The temperature of the phase

transition is in good agreement with the Curie temperature T

obtained by

the permittivity measurements. An additional weak anomaly is observed on

the low-temperature side of the major DSC peak for x = 0.35, which corresponds

to the morphotropic phase transition temperature T

MPB

observed in the dielectric

permittivity measurements. This transition should appear in some other

compositions, but the thermal events are too weak to be detected.

7.2.5 Morphotropic phase diagram of the

(1–

)Pb(Sc

1/2

–

PbTiO

solid

solution system

Based on the above XRD, DSC, and dielectric results, a phase diagram for

the solid solution of (1–x)PSN–xPT is established with more details in and

around the MPB, as shown in Fig. 7.7. The para-/ferroelectric phase transition

temperature T

is in good agreement with the data previously reported by

Tennery et al. (1968). The most important feature of this phase diagram is

that the MPB region is identified as a mixture of the monoclinic (M) phase

= 0.50

310°C

306°C

1500

1000

500

DDSC (µW/min)

Temperature (°C)

360340320300280260240220

–1300

–1200

–1100

–1000

–900

–800

–700

–600

–500

DSC (µW)

7.5

DSC measurement of 0.50Pb(Sc

1/2

−0.50PbTiO

ceramics

as a function of temperature on heating and cooling.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

183

the (majority) and some of the tetragonal (T) phase for 0.35 < x < 0.42 at or

around room temperature. With x increasing from 0.42 to 0.50, the T phase

becomes the major phase, with the monoclinic phase persisting in a small

amount. Therefore, as the PT content (x) increases, the (1–x)PSN–xPT solid

solution undergoes a sequence of structural changes from the rhombohedral

(R) phase (x ≤ 0.35), to the monoclinic (M) phase mixed with a small amount

of the tetragonal phase (+δT) (0.35 < x <0.45), then to the tetragonal T phase

mixed with a small amount of the monoclinic phase (+δM) (0.45 ≤ x ≤ 0.50)

and finally to the pure tetragonal (T) phase (x > 0.50). (Note that the pure

tetragonal phase was observed by Haumont et al. (2003) for x ≥ 0.55 only.)

More importantly, in Fig. 7.7, the morphotropic phase boundary region is

well defined by a curved upper limit, which indicates the temperatures of the

morphotropic phase transition T

MPB

. Upon cooling through T

MPB

, (1–x)PSN–

xPT transforms from a tetragonal phase into either a mixture of the monoclinic

and the tetragonal phases (for 0.37 ≤ x ≤ 0.42) or to the rhombohedral phase

(for 0.35 ≤ x < 0.37). The curvature of the MPB upper limit indicates the

dependence of the morphotropic phase transition temperature on the

composition. Interestingly, the (1–x)PSN–xPT compositions of 0.35 ≤ x ≤

0.39 exhibit both a higher T

MPB

(> 175 °C) and a higher T

(> 200 °C) than

Temperature (°C)

330300270240210

Heat flux (arbt. units)

= 0.35

= 0.37

= 0.38

= 0.39

= 0.40

= 0.50

= 0.45

= 0.42

= 0.41

7.6

DSC measurements for the (1–

)Pb(Sc

1/2

−

PbTiO

ceramics with compositions of

= 0.35, 0.37, 0.38, 0.39, 0.40, 0.41,

0.42, 0.45, and 0.50.

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Handbook of dielectric, piezoelectric and ferroelectric materials184

the PMN–PT and PZN–PT systems, making them a more interesting relaxor-

based material system for high-temperature piezoelectric applications.

7.2.6 Ferroelectric and piezoelectric characterizations

The ferroelectricity of the (1–x)PSN–xPT samples of MPB compositions is

confirmed by polarization–electric field hysteresis loops displayed at room

temperature. Typical hysteresis loops for 0.60PSN–0.40PT at different applied

electric fields (±7.5 kV/cm and ±12 kV/cm) are shown in Fig. 7.8(a). The

remnant polarization reaches P

≈ 22

C/cm

under a drive field of E ≈

±12 kV/cm with a coercive field of E

≈ 5 kV/cm.

Figure 7.8(b) shows the variation of strain as a function of bipolar electric

field for the same sample. It displays a symmetric ‘butterfly’ loop, resulting

from the bipolar ferroelectric switching behaviour. A peak-to-peak strain

value of 0.15% is obtained at E = ± 10kV/cm.

The dielectric constants and the piezoelectric coefficients d

at room

temperature are plotted as a function of compositions and shown in Fig. 7.9.

The areas of different phase components are marked to highlight the

composition and phase dependence of the properties. It can be seen that the

highest values of ε′ and d

appear in the ceramics of compositions within

the MPB region.

(ε′)

(DSC)

C (pm3m)

MPB

(P4mm)

(R3m)

M + δT T + δM

(1 –

)Pb(Sc

1/2

–

PbTiO

0.700.650.600.550.500.450.400.350.300.250.20

–100

–50

100

150

200

250

300

350

400

450

Temperature (°C)

7.7

Phase diagram for the (1–

)Pb(Sc

1/2

−

PbTiO

solid

solution around its MPB established based on the results of this

work. Solid circles are the boundary between the tetragonal phase

(at high temperature) and M + δT phase(s) at low temperature, which

represents the upper limit of the MPB region with the monoclinic

phase in majority.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

185

7.3 Growth of relaxor ferroelectric

Pb(Sc

1/2

and

(1–

)Pb(Sc

1/2

–

PbTiO

single

crystals

This section describes the growth of relaxor ferroelectric PSN and (1–x)PSN–

xPT solid solution single crystals and Section 7.4 describes the characterization

of the physical properties of the grown crystals.

Electric field (kV/cm)

(a)

PSN–PT ceramic (

= 0.40)

Polarization (µC/cm

)

–30

–20

–10

–12 –9 –6 –3 0 3 6 9 12

Electric field (kV/cm)

(b)

PSN–PT ceramic (

= 0.40)

Strain (%)

–9 –6 –3 0 3 6 9

–0.12

–0.08

–0.04

0.00

–0.0

0.08

7.8

Typical hysteresis loops (a) and strain-electric field variation (b)

for 0.60Pb(Sc

1/2

−0.40PbTiO

ceramics under a bipolar drive

(solid circle: ±12 kV/cm; open square: ±7.5 kV/cm).

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Handbook of dielectric, piezoelectric and ferroelectric materials186

7.3.1 Crystal growth

Because of the high melting points of PSN and (1–x)PSN–xPT (>1400 °C),

the use of a flux is necessary for the crystal growth in order to lower the

temperature limits. Previous work has revealed that the mixture of (PbO +

δB

) is an effective solvent for the growth of the PMN–PT and PZN–PT

piezocrystals because it combines the advantage of both the borate and the

PbO solvent (Dong and Ye, 2000; Zhang et al., 2000). Therefore, similar

flux composition and growth conditions are applied for the growth of PSN

and (1–x)PSN–xPT. Table 7.1 lists the melting points of PSN (Yanagisawa et

al., 1998), PbTiO

(Eisa et al., 1980), PbO (Geller and Bunting 1937), and

PT content (%)

PSN-PT ceramics

34 36 38 40 42 44 46 48 50 52

ε′

2400

2000

1600

1200

800

R3m M2+δT M1 + δT T + δM

PT content (%)

PSN-PT ceramics

5250484644424038363432

500

400

300

200

100

R3m M2+δT M1 + δT T + δM

7.9

Room temperature dielectric constants and piezoelectric

coefficients

as a function of composition and phase component

for the (1–

)Pb(Sc

1/2

−

PbTiO

ceramics. R stands for the

rhombohedral

R3m

phase; M1: the monoclinic

phase; M2: the

monoclinic

phase; and T: the tetragonal

P4mm

phase.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

187

(Levin, 1966). It can be seen that the melting point of PSN is much

higher than PT, a character that is very similar to the PMN–PT binary system.

As a result, a similar phase segregation problem is expected in the grown (1–

x)PSN–xPT crystals, as described in the following sections.

A double crucible setup (Dong and Ye, 2000) was used for the crystal

growth. From the spontaneous nucleation process upon slow cooling from

1180 to 1000 °C, most of the crystals were nucleated and grown on the

bottom and walls of the crucibles (Fig. 7.10), probably because of heat

dissipation through the walls of the container. The X-ray powder diffraction

shows that the grown crystals exhibit a pure perovskite phase.

Table 7.1

Melting points of Pb(Sc

1/2

(PSN),

PbTiO

, PbO, and B

Compounds Melting point (°C)

PSN 1425

PbTiO

1285

PbO 886

450

7.10

Top-view of an as-cooled crucible from growth of (1–

)Pb(Sc

1/2

−

PbTiO

single crystals, showing the growth by

spontaneous nucleation around the crucible walls.

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Handbook of dielectric, piezoelectric and ferroelectric materials188

7.3.2 Growth mechanism

During the growth of PSN and (1–x)PSN–xPT crystals, the crystals of the

pyrochlore phase of the Pb

1.5

6.5

-type appeared in several growth trials.

Interestingly, the formation of the pyrochlore phase was found to depend on

the chemical compositions and the lower limit of growth temperature, below

which the crystallization process is stopped (Bing and Ye, 2003). It is concluded

that a higher portion of flux vs. solute and a larger ratio of PbO vs. B

help

stabilize the perovskite phase down to a lower temperature. A higher amount

of B

in the flux may favour the formation of the pyrochlore phase. In other

words, the pyrochlore phase may be more stable over a wider temperature

range if the flux is richer in B

. By carefully selecting the PSNT/flux and

PbO/B

ratios in the solution, it is possible to obtain the perovskite

(1–x)PSN–xPT crystals in a certain temperature range without a pyrochlore phase.

In the growth by spontaneous nucleation, an appropriate supersaturation

is required to trigger the formation of the nuclei. On the other hand, the habit

of the crystal strongly depends on the growth parameters, e.g. the degree of

supersaturation, the temperature profile and the chemical composition (Chernov,

1984). Especially when the growth takes place in polycomponent systems,

such as [(PSN–PT) + flux] in this case, a distribution constant k for a given

component can reflect the growth mechanisms. Usually, at slow rates of

growth, the effective distribution coefficient k

eff

can be expressed as (Laudise,

1970):

eff

s(act)

l(act)

7.1

where C

s(act)

and C

l(act)

are the actual concentrations of the products in the

form of the solid and liquid. The value of k

eff

depends on the growth rate, the

diffusion constant for the materials in the melt, and the width of the diffusion

layer. For polycomponent systems, k

eff

can be greater or less than 1. The

closer is k

eff

to the unity, the easer the component would get into the bulk.

From this point of view, k

eff

is a very important parameter for the crystal

growth in a solid solution compound. As we will see later, the value of k

eff

is closely related to the segregation problem in (1–x)PSN–xPT.

The morphology of the (1–x)PSN–xPT crystals is affected by a number of

factors, including the shape and the size of the container and the chemical

ratio between flux and products. The (1–x)PSN–xPT crystals show a pseudo-

cubic form when grown on the crucible bottom, but a distorted form when

grown on the walls. The ‘ribbon’-like cellular structure was observed in the

growing crystals, arising from severe constitutional supercooling conditions

occurring during the growth. This happens when the solid/liquid interface of

growth cannot adjust itself to keep in a planar surface shape, necessary for

a stable growth (Laudise, 1970).

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

189

Appropriate ratios of PSNT/flux and PbO/B

must be kept to maintain

a stable growth. It was found that an increase in the portion of B

can

lower the temperature coefficient of solubility. However, if the level of B

is too high in the solution, the so-called skeletons or faceted growth will

appear, because the crystal is grown under an unstable boundary due to the

convex form of solid/liquid interface. The unstable growth is mainly caused

by the concentration difference between the corner and the center of the

growing cubic crystals (Saito, 1996). The growth may become less stable

when the feed is markedly deficient, and the fluctuation in the saturation at

the different parts becomes too large to keep a constant normal growth rate

over the flat surface. By adding the necessary amount of solute, i.e. by

increasing the concentration of (1–x)PSN–xPT in the solution, a more uniform

distribution of driven force is established to allow a stable growth (Lawson

and Nielsen, 1958; Chernov, 1984).

For the growth of (1–x)PSN–xPT solid solution crystals, the above discussion

can be depicted by the schematic plot of (100–yield per cent) of the grown

(1–x)PSN–xPT single crystals vs. temperature, as shown in Fig. 7.11. The

yields (percentages) of the crystallized (1–x)PSN–xPT perovskite crystals

were calculated from the ratios of the amount (weight) of the grown

(1–x)PSN–xPT crystals over that of the charged nominal (1–x)PSN–xPT

powder in the stoichiometric composition in the selected batches and are

listed in Table 7.2. Analysis of these data shows that the yields of (1–x)PSN–

xPT crystals during the growth are affected by the PSNT/flux and PbO/B

ratios. Increasing the portion of B

in the flux composition in Batch 2,

Decreasing temperature

Batch 2

Batch 4

Batch 1

100 – Yield% of PSN–PT

100

7.11

Schematic variation of (100–yield%) of the grown

(1–

)Pb(Sc

1/2

−

PbTiO

single crystals vs. temperature.

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