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

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Handbook of dielectric, piezoelectric and ferroelectric materials80

Table 3.1

Property uniformity in (001) wafers

(001) Wafer SB-BIII-01 SB-BIII-11 SB-BIII-08

from <111>-boule <110>-boule <001>-boule

Area A B A B Whole

Property

(pC/N) (pC/N) (pC/N) (pC/N) (pC/N)

Average 6523 1974 5619 1700 5695 2298 5463 1993 5888 1889

Std dev. 711 156 168 104 293 141 293 96 117 31

Coef. var.% ±10.9 ±7.9 ±3.0 ±6.1 ±5.2 ±6.2 ±5.4 ±4.8 ±2.0 ±1.6

Max. var.% ±23.3 ±18.2 ±5.1 ±12.0 ±9.9 ±11.9 ±8.3 ±7.4 ±3.8 ±3.7

Coefficient variation = standard deviation/average

Maximum variation = (maximum-minimum)/(2×average)

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Recent developments and applications of piezoelectric crystals 81

and composition. Lateral uniformity analysis indicates that the property

variation is not only strongly related to the growth direction, but also to the

sample cutting direction. Cutting perpendicular to the composition gradient,

which is always along the crystal growth direction, will give much less

property variation. Since (001) wafers cut from <001>-oriented boule are

perpendicular to the composition gradient, less than ±2% variation of both

the piezoelectric and dielectric properties has been achieved for (001) wafers

cut from <001> grown boules.

3.2.3 Innovative zone-melting growth of

PMN–PT crystal

Although the Bridgman method is a very promising technique, the composition

segregation issue has to be addressed for commercial production of PMN–

PT crystal. Since PMN–PT is a complete solid solution system as shown by

its high-temperature phase diagram, it inevitably exhibits an inhomogeneous

composition distribution along crystal boules grown by Bridgman method

[12], resulting in variation of dielectric and piezoelectric properties along

the growth orientation. Even though the composition variation along the

growth direction can be restrained to some degree by applying higher growth

rate and a lower axial temperature gradient across the solid–liquid interface,

it can never be eliminated due to the thermodynamic nature of the solid

solution system [12]. The existence of such a composition and property

variation is one of the main disadvantages of Bridgman growth. As mentioned

before, PMN–PT exhibits the highest piezoelectric response along the <001>

orientation [2]. Although the <001>-oriented Bridgman growth can produce

desirable (001) wafers with very high lateral uniformity in each wafer, it

cannot eliminate the wafer-to-wafer variation, resulting in only about one-

third of the length in each boule with the required PT composition range

with desired piezoelectric and dielectric properties and a reasonable property

variation (typically ± 3 to 5%).

Owing to the inevitable composition segregation in Bridgman growth,

alternative crystal growth techniques have to be sought to further improve

the longitudinal composition uniformity along the growth direction and to

extend the portion of as-grown boules which has optimal piezoelectric

properties. Zone leveling, a type of zone-melting methods, which has been

shown to produce a uniform, or level, distribution of solute in polycrystals

and single crystals in many applications [19] has been proposed as an alternative

method to prevent composition segregation in PMN–PT crystal growth [10].

In single-pass zone leveling, the composition distribution along the

solidification direction can be described by the following equation [19]:

cc k

kgl

–/

= (1 – (1 – )e

3.2

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Handbook of dielectric, piezoelectric and ferroelectric materials82

where g is the distance from the point at which the first solid freezes and l

is the length of melting zone. The equation is valid in all but the last melting

zone. Theoretically, zone leveling can produce a flat composition distribution

except for the initial and ending regions.

The zone melting growth of PMN–PT crystals was initially demonstrated

in an RF induction heated furnace by self-seeded and <111>-seeded growth

[20]. Recently, <110>-oriented PMN–PT single crystals have also been grown

by a modified zone melting process in a three-zone resistance heated furnace.

One of the boules grown by this modified zone melting method is shown in

Fig. 3.5(a) and the Ti concentration along the growth direction in this boule

Zm (ZM-06-02)

Bridgman (SB-BII-05)

Simulation (Bridgman)

0 20406080100

Position in percentage (from the seed)

(b)

Ti concentration (%)

3.5

Photo of a boule grown by a modified zone melting method (a)

and Ti concentration along the growth direction in this boule in

comparison with that in a boule grown by Bridgman method (b).

(a)

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Recent developments and applications of piezoelectric crystals 83

analyzed by EPMA is presented in Fig. 3.5(b) and compared with that in a

boule grown by Bridgman method. It is apparent from the data that the zone

melting method improved the longitudinal composition uniformity of the

boule by leveling the Ti concentration in the middle part of the boule. The

circled area in Fig. 3.5b corresponds to the location of the crucible where

minor leakage of the melt occurred, which might be the cause of the sharp

decrease of Ti concentration in the same area. Although preliminary studies

have been carried out to explore the feasibility of zone melting growth of

PMN–PT crystal, more effort is needed before it becomes competitive to the

well-developed Bridgman growth method.

3.3 Dynamic performance of piezoelectric crystals

with frequency and dc bias

Piezoelectric single crystals used in electromechanical devices are in many

cases exposed to high electric field, high dynamic stress, high frequency or

any combination of these. For PMN–PT single crystals, use is limited to less

than 90° due to a strongly curved MPB, and a dc bias field must often be

used to prevent depoling for high ac drive applications. So it is desirable to

get detailed information about the dielectric and piezoelectric behavior under

different frequency and dc bias fields.

3.3.1 Dielectric behavior with frequency

The frequency dependence of dielectric permittivity as a function of temperature

for [001] oriented 0.69Pb(Mg

1/3

2/3

–0.31PbTiO

(PMNT31) and

0.61Pb(Mg

1/3

2/3

–0.39PbTiO

(PMNT39) single crystals has been

characterized in the frequency range of 100Hz to 100kHz (Fig. 3.6). Several

dielectric anomalies below T

are observed in Fig. 3.6 for rhombohedral

PMNT31 and only one peak is found at T

for tetragonal PMNT39. The two

dielectric anomalies in the low temperature range, around 75 and 86°C,

correspond to ferroelectric phase transitions between rhombohedral and

monoclinic phases and monoclinic and tetragonal phases, respectively [21].

The dielectric peak located at 154°C is the temperature of maximum dielectric

permittivity (T

) of PMNT31 crystals. It is also observed that frequency

dispersion of dielectric permittivity occurs when the temperature is below

86°C and over 151 °C, while the dielectric permittivity is frequency independent

in the temperature range 86–151°C. A transition between the normal

ferroelectric and relaxor states is indicated by the appearance of a frequency

dispersive shoulder slightly below the T

and an abrupt disappearance of the

frequency dispersion at a lower temperature. This temperature is described

as T

~151°C in Fig. 3.6, which reflects the decay of a macrodomain state to

a microdomain state driven by thermal agitation [23–23], while no evident

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Handbook of dielectric, piezoelectric and ferroelectric materials84

frequency-dependent dielectric behavior was found for tetragonal PMNT39,

with a T

around 187°C.

3.3.2 Dielectric behavior with dc bias

Figure 3.7 shows the dielectric permittivity and dielectric loss as a function

of temperature for [001] oriented and poled PMNT31 single crystals that are

measured on heating at 100kHz frequency with an applied field [24]. The dc

bias is increased from 0 to 20 kV/cm in 1kV/cm incremental steps. As

shown in Fig. 3.7, when the dc bias is larger than 1kV/cm, the maximum

dielectric permittivity peak becomes sharper and higher then subsequently

lowers and becomes more diffuse while also shifting to higher temperature

with further increases in bias. This is in good agreement with other reports

[21, 25, 26]. It should be noted that when the dc bias is small (~1kV/cm), the

is found to shift to lower temperature, and then increases when dc bias is

above 1kV/cm and increases linearly when dc bias is over 3kV/cm (as

depicted in the small inset figure). The ferroelectric phase transition

temperatures T

R-M

and T

M-T

are found to shift to lower temperature with

increasing dc bias. The dielectric peak at the rhombohedral to monoclinic

phase transition becomes more diffuse and broad when the dc bias is larger

than 4kV/cm, implying the coexistence of the rhombohedral and monoclinic

phases under this condition because of compositional fluctuations. It will

disappear when the dc bias is over 10kV/cm and only the electric-field-

induced monoclinic phase is observed at room temperature. Figure 3.8 displays

3.6

Frequency dependence of dielectric properties as a function of

temperature for [001] oriented rhombohedral PMNT31 and tetragonal

PMNT39 crystals, measured on a zero-field-heating run.

Tetragonal

Rhombohedral

Frequency

1 kHz–100 kHz

50 100 150 200

Temperature (°C)

Rhombohedral PMNT31

= 154 °C;

R-M

= 75 °C;

M-T

= 86 °C

Tetragonal PMNT39

= 187 °

40 000

30 000

20 000

10 000

Dielectric permittivity

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Recent developments and applications of piezoelectric crystals 85

3.7

dc bias field dependence of dielectric permittivity and dielectric

loss as a function of temperature for [001] oriented PMNT31 single

crystals (measured at frequency of 100 kHz during heating).The thick

lines in the figures are dielectric property without dc bias. The small

inset shows the

and

M-T

as a function of dc bias (after ref. 24).

the dielectric permittivity and dielectric loss as a function of temperature for

[001] oriented and poled PMNT39 tetragonal single crystals, measured at

100kHz frequency during field-heating as the dc bias increases from 0 to

20kV/cm in 2kV/cm incremental steps. The dielectric permittivity peaks are

found to lower and broaden. The

is found to be 187°C when the dc bias

is around 2kV/cm, which is the same value as that without dc bias, then

shifts to higher temperature with increasing dc bias. Similar phenomena

were observed in other compositions in the PMNT system such as PMNT26

crystals [27] and PMNT10 ceramics [28]. It has also been reported recently

[29] that PMNT single crystals with PT content lower than 40%, at small

biases, in contrast to usual ferroelectrics, T

remains practically unchanged

or even decreases with electric field, up to a certain threshold bias (which is

considered to be the magnitude of the random field), above which T

increases.

This behavior can be well explained when considering a first-order phase

transition at the relaxor–ferroelectric phase boundary as well as the quenched

random fields and random bonds model [29, 30].

3.3.3 Piezoelectric behavior with dc bias

Figure 3.9 shows the unipolar strain as a function of electric field for a

PMNT31 crystal, in which it can be seen that the crystal transforms from the

50 100 150 200

Temperature (°C)

0.20

0.15

0.10

0.05

0.00

50 000

10 000

20 000

30 000

40 000

Dielectric permittivity

Rhombohedral PMNT31

Dielectric loss

Phase transition

temperature T

M-T

0 5 10 15 20

DC bias (kV/cm)

180

160

140

120

100

Temperature (°C)

dc bias increases to 20

kV/cm in 1 kV/cm steps

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Handbook of dielectric, piezoelectric and ferroelectric materials86

3.8

dc bias field dependence of dielectric permittivity and dielectric

loss as a function of temperature for [001] oriented PMNT39 single

crystal (measured at frequency of 100 kHz during heating). The thick

lines in the figures are dielectric behavior without dc bias. The small

inset exhibits the

as a function of dc bias.

50 100 150 200 250

Temperature (°C)

Tetragonal PMNT39

0.03

0.02

0.01

Dielectric loss

30 000

5000

10 000

15 000

20 000

Dielectric permittivity

25 000

DC bias increases to

20 kV/cm in 2 kV/cm steps

0 5 10 15 20

DC bias (kV/cm)

210

205

200

195

190

185

Temperature (°C)

= 400 pC/N

Tetragonal phase

= 1200 pC/N

Monoclinic phase

= 2100 pC/N

Rhombohedral phase

010203040

Electric field (kV/cm)

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0.0

Strain (%)

20 40 60 80

Temperature (°C)

Phase transition

bias (kV/cm)

3.9

Unipolar electric field dependence of the strain response for a

PMNT31 crystal measured up to 40kV/cm field. The small inset

shows dc bias fields for monoclinic to tetragonal phase transition at

different temperatures (after ref. 31).

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Recent developments and applications of piezoelectric crystals 87

rhombohedral phase to the monoclinic phase, and then to the tetragonal

phase with increasing electric field. The piezoelectric coefficient d

calculated from the various slopes to be 2100 pC/N for the rhombohedral

phase, 1200 pC/N for the monoclinic phase, and 400 pC/N the electric-field-

induced tetragonal phase. The small inset figure in Fig. 3.9 shows the dc bias

field required for the monoclinic to tetragonal phase transition as a function

of temperature for PMNT31 single crystals. It exhibits an exponential decay

tendency with increasing temperature for the transformation fields, which

suggests that upon heating, the polarization vector moves more easily toward

the [001] orientation under the applied dc bias [31, 32].

3.4 Single crystal piezoelectric actuators

Piezoelectric actuations have been used extensively in a broad range of

applications including precision positioning control, active damping control,

adaptive optics and adaptive structures for flap control [33–37]. Many different

types of piezoelectric actuators have been developed, including in-plane

actuators (or plate actuators), stack actuators, benders, flextensional actuators,

and piezo-motors. In-plane actuation mostly adopts the ‘31’ mode to generate

motion in plane. Its enhancement has been achieved by utilizing inter-digital

electrodes because of the low transverse piezoelectric coefficient (d

) compared

with the longitudinal counterpart (d

~ 2 for most piezo materials).

Stack actuators are featured with amplified stroke (each layer stroke times

the number of layers) and high blocking force. Benders and flextensional

actuators such as ‘Moonie’, ‘Cymbal’, ‘Thunder’ and ‘HYBAS’ are well

known with low profile and large stroke because of amplification mechanisms.

Piezomotors based on the difference of static and dynamic friction or vibration

modes are used for both rotary and linear motion control with high resolution

and position set-hold at power-off. All these piezoelectric actuators based on

piezoelectric ceramics are available on the market; however, single crystal

piezoelectric actuators with higher energy density compared with their ceramic

counterpart are still in the development stage partially because of the limited

availability of materials. Single crystal piezoelectrics based on PZN–PT or

PMN–PT exhibit large increases in strain over conventional piezoelectric

ceramics due to the ability to orient the crystals along a preferred high-strain

crystallographic direction. Due to a unique ferroelectric domain configuration,

the crystals’ piezoelectric strain remains nearly hysteresis-free up to levels

of ~ 0.5 to 0.6% depending on the crystal composition [37]. Furthermore, the

crystals have been found to retain appreciable piezoactivity to temperatures

as low as 20K, an important attribute for many cryogenic actuation applications

[38]. In this section, a couple of single crystal piezoelectric actuators developed

at TRS for deformable mirror, rotorcraft flap control and cryogenic actuation

applications are reported.

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Handbook of dielectric, piezoelectric and ferroelectric materials88

3.4.1 PMN–PT single crystal stack actuators for

deformable mirrors

Figure 3.10 shows a picture of some PMN–PT stack actuators developed at

TRS. The displacement output of a stack actuator is equal to n*d

*V, where

n is the total number of layers, d

is the longitudinal piezoelectric coefficient

and V is the driving voltage. It is known that d

of PMN–PT single crystal

is about 3–5 times of PZT ceramics, which means that PMN–PT single

crystal stack actuators are expected to yield 3–5 times the stroke of PZT

ceramic stack actuator under the same driving condition, or, the total length

of PMN–PT single crystal stack actuators is 1/5–1/3 of that of PZT ceramic

stacks if the same output stroke is required. This characteristic of single

crystal actuators is very attractive to deformable mirror applications for

either weight reduction or stroke improvement.

Figure 3.11 (a) shows the displacement vs. electric voltage for a typical

40-layer PMN–PT stack actuator (~ 21mm long), where good linearity between

displacement and driving voltage is observed. Over 50µm stroke is obtained

with a driving field of 14 kV/cm. Figure 3.11(b) shows the impedance and

phase vs. frequency of a 30-layer stack actuator (~ 16mm long). The results

from resonant measurements suggest fast response and highly efficient actuation

when single crystals are used.

Figure 3.12 shows schematically a deformable mirror (DM) structure

with stack actuators. Full aperture modeling for a 127mm (5 inch) mirror

with 289 single crystal stack actuators (5 × 5 × 21mm

) has been investigated.

3.10

Photograph of some single crystal stack actuators fabricated by

TRS.

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Recent developments and applications of piezoelectric crystals 89

The input surface has a 20µm focus error with a PV of 39.93µm, and an

RMS error of 11.52µm. After correction, the PV is 0.52µm, and the RMS

error is 0.07µm, which is very promising since no DM has been developed

for such a large focus error correction (>30λ for 632.8nm wave). The required

stroke is from –24.45µm to 13.01µm, and the force is from 1.16 N to 3.49

N. Thus, both stroke and force are within the single crystal stack actuator’s

capability. Compared with currently available electrostrictive or piezoceramic

DMs, which are used for low stroke wavefront correction (5–10µm), single

crystal piezoelectric DMs are promising for large stroke correction and also

60.0

50.0

40.0

30.0

20.0

10.0

0.0

0 500 1000

Driving voltage (V)

(a)

Displacement (µm)

0.0E+00 1.0E+05 2.0E+05 3.0E+05

Frequency (Hz)

(b)

–30

–60

–90

Phase (fegree)

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

Impedance (log) (ohm)

3.11

Stack actuator characterization: (a) displacement vs. voltage of a

PMN–PT single crystal stack (5 × 5 × 21 mm

); (b) impedance and

phase vs. frequency of a 30-layer stack (5 × 5 × 16 mm

Face

sheet

Back support

Actuators

3.12

Schematic of a deformable mirror with stack actuators.

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