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

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Handbook of dielectric, piezoelectric and ferroelectric materials190

while keeping the same ratio of PSNT/flux as in Batch 1, results in a significant

reduction of the percentage yields in the same temperature interval,

corresponding to a relatively flat temperature curve. Increasing the ratio of

PSNT/flux in Batch 4, while keeping the same ratio of PbO/B

as in Batch

2, increases the yields of (1–x)PSN–xPT crystals and hence the slope of its

temperature variation. Therefore, by changing the chemical compositions,

the solubility of (1–x)PSN–xPT can be appropriately adjusted to achieve a

more stable growth.

Based on the analysis of crystal growth mechanism (Bing and Ye, 2003),

the growth parameters were optimized, which has resulted in a significant

improvement both in the morphology and the quality of the grown (1–x)PSN–

xPT crystals. Figure 7.12 shows a crystal that exhibits pseudo-cubic

Table 7.2

Summary of the various growth parameters and the yields of

the grown (1–

)Pb(Sc

1/2

–

PbTiO

single crystals for selected trials

Batch Ratio of PSNT/ Ratio of PbO/ Yields of grown

flux (mol%) B

(mol%) PSNT crystals (%)

1 15/85 75/25 85 ± 5

2 15/85 70/30 22 ± 2

3 25/75 70/30 64 ± 2

4 25/75 70/30 62 ± 2

7.12

Crystal of (1–

)Pb(Sc

1/2

−

PbTiO

solid solution exhibiting

the pseudo-cubic morphology.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

191

morphology, indicating that an appropriate saturation was achieved at the

solid/liquid interface and remained almost constant during the growth.

7.4 Properties of Pb(Sc

1/2

and

(1–

)Pb(Sc

1/2

–

PbTiO

single crystals

This section describes the dielectric, ferroelectric and piezoelectric properties

and the optical domain structure of the PSN and (1–x)PSN–xPT single crystals.

Figure 7.13 shows the typical samples used for those characterizations. The

(001)

cub

-oriented platelets were mirror polished for optical measurements

first and then sputtered with gold layers for the subsequent dielectric and

ferroelectric measurements. The rod sample was used for piezoelectric

resonance measurements.

7.4.1 Dielectric properties of Pb(Sc

1/2

crystals

The PSN crystals studied exhibit the typical character of a disordered structure,

similar to that reported for the disordered PSN ceramics with a stoichiometric

Pb content (Chu et al., 1994). Figure 7.14 shows the temperature dependences

7.13

Typical crystal samples of (1–

)Pb(Sc

1/2

−

PbTiO

used

for electrical and optical measurements (the (001)

cub

-oriented plate

sample for dielectric, ferroelectric and optical measurements, the

(001)

cub

-oriented rod sample used for piezoelectric resonance

measurements).

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Handbook of dielectric, piezoelectric and ferroelectric materials192

of the real and imaginary parts of dielectric permittivity for a (001)-oriented

PSN crystal measured at different frequencies. Upon cooling, a maximum

permittivity was observed at temperature T

max

, which is 103 °C for the real

part and 99 °C for the imaginary part (at 1 kHz). It shows frequency dispersion

with T

max

shifting to a high temperature as frequency increases, suggesting

the typical relaxor ferroelectric behaviour. A remarkable sharp drop of the

permittivity can be observed in both real and imaginary parts at the same

temperature T

= 97 °C, accompanied by a strong attenuation of the frequency

dispersion. This sharp decrease in dielectric permittivity immediately below

max

corresponds to the spontaneous relaxor to ferroelectric phase transition,

which is consistent with that reported for PSN ceramics (Chu et al., 1994).

7.4.2 Dielectric properties of

(1–

)Pb(Sc

1/2

–

PbTiO

crystals

Figure 7.15 shows the temperature dependence of the real permittivity

(dielectric constant, ε′) at various frequencies of a (001)

cub

(1–x)PSN–xPT

400 kHz

100 kHz

64 kHz

10 kHz

4 kHz

1 kHz

0.7 kHz

0.1 kHz

(a)

(b)

= 97°C

max.

= 99°C @ 1kHz

max.

= 103°C @ 1kHz

Temperature (°C)

20015010050

50000

40000

30000

20000

10000

5000

4000

3000

2000

1000

Real part of permittivity

Imaginary part of permittivity

7.14

Real (a) and imaginary (b) parts of permittivity of

Pb(Sc

1/2

single crystals, as a function of temperature (upon

cooling) at different frequencies.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

193

crystal platelet with nominal composition at x = 0.425, measured from 300 °C

down to 10 °C at 2–3 °C intervals in the frequency range from 10 to 100 kHz.

The dielectric constant shows a sharp peak at T

max

= 213 °C, corresponding

to the ferroelectric Curie temperature T

, with a very high maximum value

of 60 000. No frequency dispersion is found near T

max

, suggesting a normal

ferroelectric behaviour.

It can be seen from the measured transition temperature that the actual

composition (estimated to be x ≈ 0.28) of the grown (1–x)PSN–xPT single

crystals differs significantly from the nominal composition (x = 0.425). This

suggests that a severe phase (or composition) segregation occurs during the

crystallization of the solid solution compound. This problem was encountered

in the growth of PMN–PT crystals, as well as in many other solid solution

systems. The high-temperature phase diagram of the PMN–PT solid solution

has recently been established (Gao, 2003). It quantitatively describes the

separation of the solidus and liquidus lines which is the origin of the segregation

problem. Since the melting point of PSN (>1425 °C) is higher than that of

PbTiO

, we can expect a qualitatively similar phase segregation phenomenon

to appear, giving rise to the same trend, i.e. the composition of the grown

100 kHz

10 kHz

1 kHz

= 213°C

@ 1kHz

Temperature (°C)

300250200150100500

70000

60000

50000

40000

30000

20000

10000

0.10

0.08

0.06

0.04

0.02

0.00

Loss

Real permittivity

7.15

Real dielectric permittivity and loss of a (001)

cub

-oriented

(1–

)Pb(Sc

1/2

−

PbTiO

single crystal with nominal

composition

= 0.425.

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Handbook of dielectric, piezoelectric and ferroelectric materials194

(1–x)PSN–xPT crystals should contain a lower concentration of PbTiO

than

the nominal composition.

Based on the qualitatively estimated phase segregation trend, the (1–

x)PSN–xPT crystals with compositions within the MPB region have been

grown from an adjusted nominally charged composition. Figure 7.16 shows

the dielectric permittivity measured on the (1–x)PSN–xPT crystals with nominal

composition of x = 0.51 upon cooling. It reveals two anomalies at T

250°C and T

MPB

= 219 °C, respectively, which are typical of the MPB behaviour

of the ferroelectric solid solutions. According to the T

–composition

relationship shown in the MPB phase diagram of Fig. 7.7, the actual

composition of this (1–x)PSN–xPT crystal is located at x = 0.37. Therefore,

the effective phase segregation coefficient is found to be k = 0.73. Such a

smaller-than-unity coefficient indicates that the Ti concentration in the grown

crystals is indeed lower than in the liquid of the loaded composition (Eq.

7.1), which is consistent with the estimated phase segregation trend. Similar

segregation behavior has been reported for the PMN–PT system (Luo et al.,

2000; Zawilski et al., 2003).

In order to investigate the phase symmetry of this MPB crystal in detail,

the powder X-ray profiles of the pseudocubic (111)

cub

and (200)

cub

reflections

of this crystal are analyzed using the Lorentzian fitting procedure and the

results are shown in Fig. 7.17 together with the experimental data from the

(1–x)PSN–xPT ceramic with composition at x = 0.37. Both the (111)

cub

and

(200)

cub

reflections can be well fitted with three peaks. The phase analysis of

100 kHz

10 kHz

1 kHz

0.1 kHz

250°C

Shoulder

219°C

Temperature (°C)

350300250200150100500

60000

50000

40000

30000

20000

10000

Real permittivity

7.16

Variation of the real part of permittivity of (1–

)Pb(Sc

1/2

−

PbTiO

single crystals with composition within the MPB, as function

of temperature, measured upon cooling.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

195

2θ (deg.)

(b)

(200)

(111)

(200)

(111)

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

(arb. units)

47.046.546.045.545.044.544.043.543.042.5

PScNT ceramics (

= 0.37)PScNT single crystal

37.6 37.8 38.0 38.2 38.4 38.6 38.8 39.0 39.2 39.4 39.6

2θ (deg.)

(a)

(arb. units)

0.0

0.2

0.4

0.6

0.8

1.0

0.0

0.2

0.4

0.6

0.8

1.0

42.5 43.0 43.5 44.0 44.5 45.0 45.5 46.0 46.5 47.0

37.6 37.8 38.0 38.2 38.4 38.6 38.8 39.0 39.2 39.4 39.6

7.17

Analysis of the X-ray profiles of 0.63Pb(Sc

1/2

−

0.37

PbTiO

single crystals and ceramics (open circles:

experiment data; solid lines: fitting results).

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Handbook of dielectric, piezoelectric and ferroelectric materials196

the MPB crystal in Fig. 7.17(a) indicates that a monoclinic phase is present

as the major phase which is mixed with a small amount of the tetragonal

phase. Comparing the XRD data and fitting results of the crystals with those

of the 0.63PSN–0.37PT ceramics (Fig. 7.17b), it can be seen that the phase

symmetry and phase components of both samples are in good agreement

with each other, confirming the MPB composition and phase behavior of the

grown crystals.

The phase transition of the MPB crystal at T

appears as a sharp peak

without frequency dispersion. This suggests that as the Ti content increases

to 37%, the crystal behaves like a normal ferroelectric with a non-dispersive

and sharp phase transition. A slight ‘shoulder-like’ anomaly was observed at

about 265 °C for all frequencies in Fig. 7.16, which could be due to the

nucleation of precursor domains of the ferroelectric phase (Bing and Ye,

2005).

7.4.3 Calorimetric analysis of Pb(Sc

1/2

crystals

Differential scanning calorimetry (DSC) analysis was carried out on PSN

crystals. As shown in Fig. 7.18, PSN exhibits a sharp anomaly at 98 °C in the

variation of heat flow as a function of temperature, indicating a structure

phase transition. This temperature is in good agreement with the temperature

at which the sharp decrease in dielectric permittivity occurs.

7.4.4 Ferroelectricity

Well-developed ferroelectric hysteresis loops are displayed under the moderate

bipolar electric field for the (001)

cub

-oriented PSN and (1–x)PSN–xPT crystals

Temperature (°C)

101°C

98°C

1751501251007550

–300

–200

–100

DSC (µW)

7.18

Differential scanning calorimetry (DSC) measurements of Pb(Sc

1/2

single crystals, upon heating and cooling.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

197

at room temperature, as shown in Fig. 7.19, indicating the ferroelectricity. In

PSN, the saturation of the polarization is achieved at an electric field of ±18

kV/cm with a maximum polarization of 25

C/cm

and a relatively small

coercive electric field of E

≈ 2.5 kV/cm. Such a hysteresis loop with almost

vertical lines and flat electric field dependence indicates a sharp switching of

macrodomains and a fairly stable domain state when the electric field is

removed. In (1–x)PSN–xPT (x = 0.425), the saturation of the polarization

is achieved at an electric field of ±10kV/cm. The remnant polarization

reaches P

≈ 25

C/cm

under a bipolar drive of E = ±12kV/cm with a

coercive electric field of E

≈ 4kV/cm, slightly larger than that of the PSN

crystals.

Electric field (kV/cm)

(a)

Electric field (kV/cm)

(b)

–15 –10 –5 0 5 10 15

Polarization (µC/cm

)

–30

–20

–10

–30 –20 0 20 30–10 10

–30

–20

–10

Polarization (µC/cm

)

7.19

Polarization vs. electric field (P–E) loops for a (001)

cub

-oriented

Pb(Sc

1/2

crystal (a) and (1–

)Pb(Sc

1/2

−

PbTiO

(

0.425) crystal (b) at room temperature, indicating the ferroelectricity.

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Handbook of dielectric, piezoelectric and ferroelectric materials198

7.4.5 Piezoelectricity

Figure 7.20 shows the strain–electric field relation for the (001)

cub

-oriented

(1–x)PSN–xPT (x = 0.425) sample under a bipolar drive. A peak-to-peak

strain value of 0.07% has been reached at E ≈ ±18kV/cm.

The longitudinal electromechanical coupling factor k

was determined

by the measurements of the resonance (f

) and antiresonance (f

) frequencies

for a (001)

cub

-oriented (1–x)PSN–xPT crystal rod. The rod sample is pre-

poled along the <100>

cub

length direction by applying an electric field of 20

kV/cm at a temperature above 150°C, and then cooled to room temperature

with the electric field kept on. The typical profile of the resonance (f

) and

antiresonance (f

) frequencies at room temperature gives rise to the values of

the longitudinal electromechanical coupling factor k

in the range of 73–

80%. The d

values measured by Berlincourt d

meter are found in the

range of 300–500 pC/N.

7.4.6 Domain structure

The domain structure and its evolution as a function of temperature in the

(001)

cub

-oriented PSN single crystals and the (001)

cub

-oriented (1–x)PSN–

xPT single crystals with different compositions have been observed and

examined by cross polarized light microscopy (Olympus BX60) in a

temperature range between –180 °C and 250 °C. Figure 7.21 shows a typical

domain pattern in the (001)

cub

PSN plate. The domain pattern at room

temperature is composed of fine birefringent domains, indicating a macro-

domain state. When the sample was rotated in such a way that the <001>

cub.

Electric field (kV/cm)

–20 –15 –10 –5 0 2015105

Strain (%)

–0.06

–0.04

–0.02

0.00

0.02

0.04

0.06

7.20

The bipolar strain vs. electric field for the (001)

cub

-oriented (1–

)Pb(Sc

1/2

−

PbTiO

(

= 0.425) single crystal.

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Piezo- and ferroelectric (1–

)Pb(Sc

1/2

–

PbTiO

199

direction of crystal forms an angle of 45° with the directions of the polarizer

(namely 45° position hereafter), most areas of the crystal became dark,

indicating a rhombohedral symmetry at room temperature as the major phase.

A sharp phase transition can be observed upon heating with a full extinction

at any angles with respect to the crossed polarizers, which is in agreement

with the cubic symmetry. The birefringent domains reappear upon cooling

through T

In the (1–x)PSN–xPT crystals, the long-range ferroelectric states are

evidenced by distinct birefringent domains. However, the crystals with different

dielectric T

max

show very different domain patterns. The domain patterns for

the crystals grown from two different nominal compositions that show the

different dielectric T

max

are shown in Fig. 7.22. The crystal with a dielectric

max

around 210 °C (estimated to be x ≈ 0.26) exhibits birefringent domains

(Fig. 7.22 a) with a fine structure and is in full extinction when the crystal is

at the 45° position, indicating a rhombohedral symmetry at room temperature.

On the other hand, the crystal that shows a dielectric maximum at 243°C

(with x ≈ 0.36) displays spindle-like domains (Fig. 7.22 b). The crystals with

composition close to or within MPB show only partially extinction while the

other parts remain birefringent in a particular position. Such a complex

domain structure indicates the coexistence of multiple phases of different

symmetry, reflecting the nature of the MPB.

7.21

Domain structure of the (001)

cub

-oriented Pb(Sc

1/2

—single crystals under cross polarized light microscopy at room

temperature.

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