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The Development of Piezoelectric Materials and the New Perspective

December 2017

In book: Advanced Piezoelectric Materials (pp.1-92)

Authors:

Pennsylvania State University

Certain materials produce electric charges on their surfaces as a consequence of applying mechanical stress. The induced charges are proportional to the mechanical stress. This is called the direct piezoelectric effect and was discovered in quartz by Pierre and Jacques Curie in 1880. Materials showing this phenomenon also conversely have a geometric strain proportional to an applied electric field. This is the converse piezoelectric effect, discovered by Gabriel Lippmann in 1881.

A and B compares observed impedance curves of rod-shaped samples for a typical k material (PZT 5H, k 33 ¼ 0.70) and a high-k material (PZN-PT single crystal, k 33 ¼ 0.90). Note a large separation between the resonance and antiresonance peaks in the high-k material, leading to the condition almost f A ¼ 2 f R. To the contrary, a regular PZT sample exhibits f A ¼ 1.3 f R. The bandwidth of the piezotransducer is defined by (Δf/f R ), leading to 100% for the PZN-PT sample and only 30% for PZT 5H.

…

A mixed-mode ultrasonic motor incorporating a torsion coupler: (A) structure of the entire motor and (B) motion of the torsion coupler.

…

Typical designs for ceramic actuators: multilayer, moonie, and bimorph.

…

Calculation of the input electrical and output mechanical energy: (A) load mass model for the calculation, (B) electric field versus induced strain curve, (C) stress versus strain curve, and (D) electric field versus polarization curve.

…

+38

A) Principle of a biosensor, where the antibody/phage is coated on a single crystal quartz oscillator. Once particular bacteria are captured selectively by the antibodies (B), the surface mass of the oscillator is increased.

…

Figures - uploaded by Kenji Uchino

Content may be subject to copyright.

Content uploaded by Kenji Uchino

Content may be subject to copyright.

CHAPTER

The Development of

Piezoelectric Materials and the

New Perspective

K. Uchino

The Pennsylvania State University, State College, PA, United States

Abstract

Certain materials produce electric charges on their surfaces as a consequence of apply-

ing mechanical stress. The induced charges are proportional to the mechanical stress.

This is called the direct piezoelectric effect and was discovered in quartz by Pierre and

Jacques Curie in 1880. Materials showing this phenomenon also conversely have a

geometric strain proportional to an applied electric field. This is the converse piezoelec-

tric effect, discovered by Gabriel Lippmann in 1881.

This article first reviews the historical episodes of piezoelectric materials in the

sequence of quartz, Rochelle salt, barium titanate, PZT, lithium niobate/tantalate,

relaxor ferroelectrics, PVDF, Pb-free piezoelectrics, and composites. Then, the detailed

performances are described in the following section, which is the introduction to each

chapter included in this book. Third, since piezoelectricity is utilized extensively in the

fabrication of various devices such as transducers, sensors, actuators, surface acoustic

wave (SAW) devices , frequency control, etc., applications of piezoelectric materials

are also introduced briefly in conjunction with materials. The author hopes that the

reader can “learn the history aiming at creating new perspective for the future in

the piezoelectric materials.”

Keywords: Piezoelectric material, Quartz, Rochelle salt, Barium titanate, Lead

zirconate titanate, Relaxor ferroelectrics, Pb-free piezoelectrics, Electromechanical

coupling factor.

1.1 THE HISTORY OF PIEZOELECTRICS

Any material or product has a lifecycle, which is determined by four

“external” environmental forces, which can be summarized under the

acronym STEP (Social/cultural, Technological, Economic, and Political

1Advanced Piezoelectric Materials

http://dx.doi.org/10.1016/B978-0-08-102135-4.00001-1

forces).

We will observe first how these forces encouraged/discouraged

the development of piezoelectric materials.

1.1.1 The Dawn of Piezoelectrics

The Curie brothers (Pierre and Jacques Curie) discovered direct piezo-

electric effect in single crystal quartz in 1880. Under pressure, quartz gen-

erated electrical charge/voltage from quartz and other materials. The root

of the word “piezo” means “pressure” in Greek; hence the original mean-

ing of the word piezoelectricity implied “pressure electricity.” Materials

showing this phenomenon also conversely have a geometric strain pro-

portional to an applied electric field. This is the converse piezoelectric effect,

discovered by Gabriel Lippmann in 1881. Recognizing the connection

between the two phenomena helped Pierre Curie to develop pioneering

ideas about the fundamental role of symmetry in the laws of physics.

Meanwhile, the Curie brothers put their discovery to practical use by

devising the piezoelectric quartz electrometer, which could measure faint

electric currents; this helped Pierre’s wife, Marie Curie, 20 years later in

her early research.

It was at 11:45 pm on Apr. 10, 1912 that the tragedy of the sinking of the

Titanic occurred (see Fig. 1.1). As the reader knows well, this was caused

by an iceberg hidden in the sea. This would have been prevented if the

ultrasonic sonar system had been developed then. Owing to this tragic

incident (social force), there was motivation to develop ultrasonic technol-

ogy development using piezoelectricity.

FIG. 1.1 The sinking of the Titanic was caused by an “iceberg” in the sea.

21. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.1.2 World War I—Underwater Acoustic Devices

With Quartz and Rochelle Salt

The outbreak of World War I in 1914 led to real investment to accelerate

the development of ultrasonic technology in order to search for German

U-Boats under the sea. The strongest forces both in these developments

were social and political. Dr. Paul Langevin, a professor at Ecole

Sup

erieure de Physique et de Chimie Industrielles de la Ville de Paris

(ESPCI Paris Tech), who had many friends including Drs. Albert Einstein,

Pierre Curie, Ernest Ratherford, among others, started experiments on

ultrasonic signal transmission into the sea, in collaboration with the

French Navy. Langevin succeeded in transmitting an ultrasonic pulse into

the sea off the coast of southern France in 1917. We can learn most of the

practical development approaches from this original transducer design

(Fig. 1.2). First, 40 kHz was chosen for the sound wave frequency. Increas-

ing the frequency (shorter wavelength) leads to better monitoring resolu-

tion of the objective; however, it also leads to a rapid decrease in the

reachable distance. Notice that quartz and Rochelle salt single crystals

were the only available piezoelectric materials in the early 20th century.

Since the sound velocity in quartz is about 5 km/s, 40 kHz corresponds

to the wavelength of 12.5 cm in quartz. If we use a mechanical resonance

in the piezoelectric material, a 12.5/2 ¼6.25 cm thick quartz single crystal

piece is required. However, in that period, it was not possible to produce

such large high-quality single crystals.

1.0

28.7

260 mm f

5.0

0.5

Steel

Center axis

Angle dependence of

acoustic power

Quartz pellets

were arranged

FIG. 1.2 Original design of the Langevin underwater transducer and its acoustic power

directivity.

31.1 THE HISTORY OF PIEZOELECTRICS

In order to overcome this dilemma, Langevin invented a new trans-

ducer construction; small quartz crystals arranged in a mosaic were sand-

wiched by two steel plates. Since the sound velocity in steel is in a similar

range to quartz, with 6.25 cm in total thickness, he succeeded to set the

thickness resonance frequency around 40 kHz. This sandwich structure

is called Langevin type and remains popular even today. Notice that quartz

is located at the center, which corresponds to the nodal plane of the thick-

ness vibration mode, where the maximum stress/strain (or the minimum

displacement) is generated in the resonance mode.

Further, in order to provide a sharp directivity for the sound wave, Lan-

gevin used a sound radiation surface with a diameter of 26 cm (more than

double of the wavelength). The half-maximum-power angle ϕcan be eval-

uated as ϕ¼30 λ=2aðÞdegree



, (1.1)

where λis the wavelength in the transmission medium (not in steel) and ais

the radiation surface radius. If we use λ¼1500 (m/s)/40 (kHz) ¼3.75 cm,

a¼13 cm, we obtain ϕ¼4.3 degree for this original design. He succeeded

practically in detecting the U-Boat 3000 m away. Moreover, Langevin also

observed many bubbles generated during his experiments, which seems to

be the “cavitation” effect that was utilized for ultrasonic cleaning systems

some 60 years later.

Though the mechanical quality factor is significantly high (i.e., low loss)

in quartz, its major problems for this transducer application include its

low electromechanical coupling k, resulting in (1) low mechanical under-

water transmitting power and receiving capability, and in (2) narrow fre-

quency bandwidth, in addition to the practical fact that only Brazil

produced natural quartz crystals at that time. Thus, US researchers

used Rochelle salt single crystals, which have a superior electromechanical

coupling factor (kis close to 100% at 24°C!) with a simple synthesizing

process. Nicholson,

Anderson, and Cady undertook research on the pie-

zoelectric underwater transducers during World War I. General Electric

Laboratory (Moore

) and Brush Company produced large quantities of

crystals in the early 1920s. The detailed history on Rochelle salt can be

found in Ref. 5.

Rochelle salt is sodium potassium tartrate [NaKC

4H

O], and it

has two Curie temperatures at 18°Cand24°C with a narrow operating

temperature range for exhibiting ferroelectricity; this leads to high electro-

mechanical coupling at 24°C and, however, rather large temperature

dependence of the performance. It was used worldwide for underwater

transducer applications until barium titanate and lead zirconate titanate

(PZT) were discovered. Since this crystal is water-soluble, it is inevitable

that it is degraded by humidity. However, the most delicate problem is its

weakness to dryness. Thus, no researcher was able to invent the best coating

technology for the Rochelle salt devices to achieve the required lifetime.

Many efforts to discover alternative piezoelectrics of Rochelle salt with

better stability/reliability continued after WWI. Potassium dihydrogen

41. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

phosphase (KH

or KDP) was discovered by Georg Busch in 1935.

Knowing the ferroelectricity of Rochelle salt, and guessing the origin to be

from the hydrogen bonds in the crystal, Busch searched hydrogen bond crys-

tals systematically and found KDP as a new ferroelectric/piezoelectric.

Though many piezoelectric materials (such as Rochelle salt, barium titanate,

and PVDF) were discovered accidentally through “serendipity,” KDP is an

exceptional example of discovery created by the perfectly planned systematic

approach. Following KDP, ADP, EDT, and DKT, amongst others, were dis-

covered continuously and examined. However, most of the water-soluble

single crystal materials have been forgotten because of the performance and

preparation improvements in synthetic quartz and perovskite ceramics

(BT, PZT).

1.1.3 World War II—Discovery of Barium Titanate

Barium titanate (BaTiO

, BT) ceramics were discovered independently

by three countries, the United States, Japan, and Russia, during World

War II: Wainer and Salomon

in 1942, Ogawa

in 1944, and Vul

1944, respectively. Compact radar system development required compact

high capacitance “condensers” (the term “condenser,” rather than “capac-

itor,” was used at that time). Based on the widely used “Titacon” (titania

condenser) composed of TiO

-MgO, researchers doped various oxides to

find higher permittivity materials. According to the memorial article

authored by Ogawa and Waku,

they investigated three dopants, CaO,

SrO, and BaO, in a wide fraction range. They found a maximum permit-

tivity around the compositions CaTiO

, SrTiO

and BaTiO

(all were iden-

tified as perovskite structures). In particular, the permittivity, higher than

1000, in BaTiO

was enormous (10 times higher than that in Titacon) at that

time, as illustrated in Fig. 1.3.

BaO

1000

800

600

400

200

BaTiO3

TiO2MgO

(

)

FIG. 1.3 Permittivity contour map on the MgO-TiO

-BaO system, and the patent coverage

composition range (dashed line).

51.1 THE HISTORY OF PIEZOELECTRICS

It should be pointed out that the original discovery of BaTiO

was not

related with piezoelectric properties. Equally important are the indepen-

dent discoveries by R. B. Gray at Erie Resister (patent applied for in 1946)

and by Shepard Roberts at MIT (published in 1947)

that the electrically

poled BT exhibited “piezoelectricity” owing to the domain realignment.

At that time, researchers were arguing that the randomly oriented “poly-

crystalline” sample should not exhibit piezoelectricity, but the secondary

effect, “electrostriction.” In this sense, Gray is the “father of piezocera-

mics,” since he was the first to verify that the polycrystalline BT exhibited

piezoelectricity once it was electrically poled.

The ease in composition selection and in manufacturability of BT

ceramics prompted Mason

and others to study the transducer appli-

cations with these electroceramics. Piezoelectric BT ceramics had a reason-

ably high coupling coefficient and nonwater solubility, but the bottlenecks

were (1) a large temperature coefficient of electromechanical parameters

because of the second phase transition (from tetragonal to rhombohedral)

around the room temperature or operating temperature, and (2) the aging

effect due to the low Curie temperature (phase transition from cubic to

tetragonal) around only 120°C. In order to increase the Curie temperature

higher than 120°C, and to decrease the second transition temperature

below 20°C, various ion replacements such as Pb and Ca were studied.

From these trials, a new system PZT was discovered.

It is worth noting that the first multilayer capacitor was invented

by Sandia Research Laboratory engineers under the Manhattan Project

with the coating/pasting method for the switch of the Hiroshima nuclear

bomb (Private Communication with Dr. Kikuo Wakino, Murata Mnfg).

1.1.4 Discovery of PZT

1.1.4.1 PZT

Following the methodology taken for the BT discovery, the perovskite

isomorphic oxides such as PbTiO

, PbZrO

, and SrTiO

and their solid

solutions were intensively studied. In particular, the discovery

of “antiferroelectricity” in lead zirconate

and the determination of the

Pb(Zr,Ti)O

system phase diagram

by the Japanese group, E. Sawaguchi,

G. Shirane, and Y. Takagi, are noteworthy. Fig. 1.4 shows the phase dia-

gram of the Pb(Zr,Ti)O

solid solution system reported by E. Sawagu-

chi—which was read and cited worldwide—and triggered the PZT era.

A similar discovery history as the barium titanate was repeated for the

lead zirconate titanate system. The material was discovered by the Japa-

nese researcher group, but the discovery of its superior piezoelectricity

was conducted by a US researcher, Bernard Jaffe, in 1954. Jaffe worked

at the National Bureau of Standards at that time. He knew well about

the Japanese group’s serial studies on the PZT system, and he focused

on the piezoelectric measurement around the MPB (morphotropic phase

61. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

boundary) between the tetragonal and rhombohedral phases; he found

enormous electromechanical coupling around that composition range.

His patent had a significant effect on the future development strategies

of Japanese electroceramic industries. It is important to remember two

important notions for realizing superior piezoelectricity: (1) Pb-included

ceramics and (2) MBP compositions.

1.1.4.2 Clevite Corporation

As mentioned above, Brush Development Company manufactured

Rochelle salt single crystals and their bimorph components for phono-

graph applications in 1930s, and in the 1940s they commercialized piezo-

electric quartz crystals by using a hydrothermal process. There was a big

piezoelectric group in Brush, led by Hans Jaffe. However, in 1952 the Cle-

vite Corporation was formed by merging the Cleveland Graphite Bronze

Corporation and Brush, and H. Jaffe welcomed B. Jaffe from NBS to Cle-

vite and accelerated the PZT business. Their contribution to developing

varieties of PZTs (i.e., hard and soft PZT’s) by doping acceptor (Mn)

and donor (Nb) ions is noteworthy. By the way, PZT was the trademark

of Clevite, and it had not been used by other companies previously. Also,

500

400

300 300

250

200

160

10001 2345

200

100

0020

40 60 80 100

PbTiO3

Atomic percent of PbTiO3

PbZrO3

T (°C)

°C

FIG. 1.4 Phase diagram for the Pb(Zr,Ti)O

solid solution system proposed by

Sawaguchi.

We now know another ferroelectric phase below the F

phase.

71.1 THE HISTORY OF PIEZOELECTRICS

Hans Jaffe and Bernard Jaffe were not related at all. These episodes are

described in their famous book, Piezoelectric Ceramics.

Clevite first concentrated on high quality military and commercial

piezoelectric filters. In the mid-1960s, they tried to develop consumer

filters for AM radios, especially automobile radios, but this was not com-

mercially viable initially. However, after 1967, they successfully started

mass-production of 10.7 MHz ceramic filters for FM automobile radios,

and they delivered them to Philco-Ford. Clevite was bought by Gould

Inc. in 1969, and it was resold to Vernitron in 1970. These drastic business

actions terminated the promising piezoelectric filter program initiated by

Clevite.

1.1.4.3 Murata Manufacturing Company

The Murata Manufacturing Co., Ltd. was founded by A. Murata in

1944. He learned ceramic technology from his father who was the

Chairman of the former Murata Pottery Manufacturing Co. Murata

Manufacturing Company began with 10 employees that produced

electroceramic components. After World War II, under the guidance of

Prof. Tetsuro Tanaka, who was one of the promoters of Barium Titanate

Study Committee during WWII, Murata started intensive studies on

devices based on barium titanate ceramics. The first products with

barium titanate ceramics were 50-kHz Langevin-type underwater trans-

ducers for fish-finders in Japan.

The second products were mechanical

filters.

In 1960, Murata decided to introduce PZT ceramics by paying a royalty

to Clevite Corporation. As already mentioned in the previous section,

because of the disappearance of Clevite from the filter business, Murata

increased the worldwide share in the ceramic filter products market.

1.1.4.4 Ternary System

Since the PZT was protected by Clevite’s US patent subsequently,

ternary solid solutions based on PZT with another perovskite phase were

investigated intensively by Japanese ceramic companies in the 1960s.

Examples of these ternary compositions are the following: PZTs in a solid

solution with Pb(Mg

1/3

2/3

(Matsushita-Panasonic), Pb(Zn

1/3

2/3

)

(Toshiba), Pb(Mn

1/3

2/3

, Pb(Co

1/3

2/3

, Pb(Mn

1/3

2/3

Pb(Ni

1/3

2/3

(NEC), Pb(Sb

1/2

, Pb(Co

1/2

, and Pb

(Mg

1/2

(Du Pont), all of which were patented by different compa-

nies (almost all composition patents have already expired). The ternary

systems with more material-designing flexibility exhibited better perfor-

mance in general than the binary PZT system, which created advantages

for the Japanese manufacturers over Clevite and other US companies.

81. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.1.5 Lithium Niobate/Tantalate

Lithium niobate and tantalate have the same chemical formula, ABO

as BaTiO

and Pb(Zr,Ti)O

. However, the crystal structure is not perov-

skite, but ilmenite. Ferroelectricity in single crystals of LiNbO

(LN)

and LiTaO

(LT) was discovered in 1949 by two researchers in Bell

Telephone Laboratories, Matthias and Remeika.

Since the Curie temper-

atures in these materials are high (1140°C and 600°C for LN and

LT, respectively), perfect linear characteristics can be observed in

electro-optic, piezoelectric, and other effects at room temperature. Though

fundamental studies had been conducted, particularly into their electro-

optic and piezoelectric properties, commercialization was not accelerated

initially because the figure of merit was not very attractive in comparison

with perovskite ceramic competitors. [Cb (columbium) was the former

name of the chemical element niobium in the 1950s.]

Since Toshiba, Japan started mass production of LN single crystals after

the 1980s, dramatic production cost reductions were achieved. Murata

commercialized filters, SAW filters, by using the SAW mode on the LN

single crystal. Recent developments in electro-optic light valves, switches,

and photorefractive memories, which are encouraged by optical commu-

nication technologies, can be found in Ref. 20.

1.1.6 Relaxor Ferroelectrics—Ceramics and Single Crystals

After the discovery of barium titanate and PZT, in parallel to the PZT-

based ternary solid solutions, complex perovskite structure materials

were intensively synthesized and investigated in the 1950s. In particular,

the contributions by the Russian researcher group led by G. A. Smolenskii

were enormous. Among them, huge dielectric permittivity was reported

in Pb(Mg

1/3

2/3

(PMN)

and Pb(Zn

1/3

2/3

(PZN).

PMN-

based ceramics became major compositions for high dielectric constant

k(10,000) capacitors in the 1980s.

It is noteworthy to introduce two epoch-making discoveries in the late

1970s and early 1980s, relating to electromechanical couplings in relaxor

ferroelectrics: electrostrictive actuator materials and high electromechan-

ical coupling factor k(95%) piezoelectric single crystals.

Cross, Jang, Newnham, Nomura, and Uchino

reported extraordi-

narily large secondary electromechanical coupling, in other words, elec-

trostrictive effect, with the strain level higher than 0.1% at room

temperature, exhibiting negligible hysteresis during rising and falling

electric field, in a composition of 0.9 PMN-0.1 PbTiO

(see Fig. 1.5).

Every phenomenon has primary and secondary effects, which are some-

times recognized as linear and quadratic phenomena, respectively.

In actuator materials, these correspond to the piezoelectric and electro-

strictive effects.

91.1 THE HISTORY OF PIEZOELECTRICS

When the author started actuator research in the the mid-1970s,

precise “displacement transducers” (we initially used this terminology)

were required in the Space Shuttle program, particularly for “deformable

mirrors,” for controlling the optical pathlengths over several wavelengths

(1 micron). Conventional piezoelectric PZT ceramics were plagued by hys-

teresis and aging effects under large electric fields; this was a serious prob-

lem for an optical positioner. Electrostriction, which is the secondary

electromechanical coupling observed in centrosymmetric crystals, is not

affected by hysteresis or aging.

Piezoelectricity is a primary (linear)

effect, where the strain is generated in proportion to the applied electric

field, while the electrostriction is a secondary (quadratic) effect, where

the strain is in proportion to the square of the electric field (parabolic strain

curve). Their response should be much faster than the time required for

domain reorientation in piezoelectrics/ferroelectrics. In addition, electric

poling is not required. However, at that time, most people believed that

the secondary effect would be minor and could not provide a larger con-

tribution than the primary effect. Of course, this may be true in most cases,

but the author’s group actually discovered that relaxor ferroelectrics, such

as the lead magnesium niobate-based solid solutions, exhibit enormous

electrostriction. This discovery, in conjunction with the author’s multi-

layer actuator invention (1978), accelerated the development of piezoelec-

tric actuators after the 1980s.

Dr. S. Nomura’s group was interested in making single crystals of PZT

in the 1970s, in order to clarify the crystal orientation dependence of

−25 −20 −15 −10 −5

−1

−2

(A) (B) (A)

−3

−4

Strain S2×10−4

+5+10

Electric field in KV/cm−1

+15 +20 +25

FIG. 1.5 Transverse strain in ceramic specimens of 0.9PMN-0.1PT (A) and a typical hard

PZT 8 piezoceramic (B) under varying electric fields.

10 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

the piezoelectricity. However, it was difficult to prepare large single crystals

around the MPB compositions (52/48). Thus, we focused on the Pb

(Zn

1/3

2/3

-PbTiO

solid solution system, which has a phase diagram

similar to the PZT system, but large single crystals are easily prepared. See

the MPB between the rhombohedral and tetragonal phases in Fig. 1.6,in

comparison with Fig. 1.4.

Fig. 1.7 shows changes of electromechanical

coupling factors with a mole fraction of PT in the Pb(Zn

1/3

2/3

-PbTiO

solid solution system, reported by Kuwata, Uchino, and Nomura in 1982,

which was best cited in 1998. Note that the MPB composition, 0.91 PZN-0.09

PT, exhibited the maximum for all parameters, as expected, but the highest

values in electromechanical coupling factor k

* and the piezoelectric con-

stant d

* reached 95% and 1600 pC/N. (Superscript * was used because the

poling direction was not along the spontaneous direction.) When a young

PhD student, J. Kuwata, reported to the author first, even the author could

not believe the large numbers. Thus, the author and Dr. Kuwata worked

together to re-examine the experiments. When the author saw the antireso-

nance frequency almost twice of the resonance frequency, the author

needed to believe the incredibly high k value. The author still remembers

that the first submission of our manuscript was rejected because the referee

could not “believe this large value.” The maximum k

in 1980 was about

72% in PZT-based ceramics. The paper was published after a year-long

communication by sending the raw admittance curves, etc. However, the

original discovery was not believed or not required for applications until

the mid-1990s.

Economic recession and aging demographics (average age reached

87 years old) in Japan accelerated medical technologies, and high-kpiezo-

electric materials have focused on in medical acoustics since the mid-

1990s. Toshiba started reinvestigation of PZN-PT single crystals, with a

Cubic

Tetragonal

Rhombohedral

Transition temperature (°C)

0 0.1

−100

100

200

PZN PT→

0.2

FIG. 1.6 Phase diagram for the Pb(Zn

1/3

2/3

)

-PbTiO

solid solution system.

111.1 THE HISTORY OF PIEZOELECTRICS

15 d33

−k31

−d33

d33

d31

k33

s33

E//[111] E//[001]

s33

s11

k33

k33, −k31 dij(´10−10 CN−1)l3(´10−4 Cm−2K−1)

sij(´10−10 m−2N−1)

d33

1.0

0.5

000.1 0.2

PZN x

5 :Rhombo. :Tetr.

e3 (´103)

PT→

FIG. 1.7 Changes of electromechanical coupling factors with mole faction of PT in the Pb

(Zn

1/3

2/3

-PbTiO

solid solution system.

12 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

strong crystal manufacturing background of lithium niobate in the 1980s.

These data reported 15 years earlier have been reconfirmed, and impr-

oved data were obtained, aiming at medical acoustic applications.

In parallel, Park and Shrout

at The Penn State University demonstrated

the strains as large as 1.7% induced practically for the PZN-PT solid solu-

tion single crystals. There is considerable interest at present in the appli-

cation of these single crystals, sponsored by the US Navy. The single

crystal relaxor ferroelectric is one of the rare examples, where interest

has been revived 15 years after the original discovery.

It is notable that the highest values are observed for a rhombohedral

composition only when the single crystal is poled along the perov-

skite [0 0 1] axis, not along the [1 1 1] spontaneous polarization axis.

Fig. 1.8 illustrates an intuitive principle model in understanding this

piezoelectricity enhancement depending on the crystal orientation in

perovskite ferroelectrics. The key is the largest electromechanical coup-

ling for the d

shear mode in perovskite structures (i.e., d

because there is easy rotation of the oxygen octahedron, in comp-

arison with the squeeze deformation of the octahedron. The reader

can refer to the theoretical paper (Ref. 28) authored by X. H. Du,

U. Belegundu, and K. Uchino, which was also one of the most cited papers

in 1998.

Strain

[100]

[001]

[010]

d15

d33

d33eff

FIG. 1.8 The intuitive principle model in understanding the piezoelectricity enhancement

depending on the crystal orientation in perovskite ferroelectrics.

131.1 THE HISTORY OF PIEZOELECTRICS

1.1.7 Polyvinylidene Difluoride

In 1969, the piezoelectricity of polyvinylidene difluoride, PVDF, was

discovered by Kawai

at Kureha. The piezoelectric coefficients of poled

thin films of the material were reported to be as large as 6–7 pCN

1

:10

times larger than that observed in any other polymer.

PVDF has a glass transition temperature (T

) of about 35°C and is typ-

ically 50%–60% crystalline. To give the material its piezoelectric proper-

ties, it is mechanically stretched to orient the molecular chains and then

poled under tension. Unlike other popular piezoelectric materials, such

as PZT, PVDF has a negative d

value. Physically, this means that PVDF

will compress instead of expand or vice versa when exposed to the same

electric field. PVDF-trifluoroethylene (PVDF-TrFE) copolymer is a well-

known piezoelectric, which has been popularly used in sensor applica-

tions such as keyboards.

Bharti et al. reported that the field induced strain level can be signifi-

cantly enhanced up to 5% by using a high-energy electron irradiation onto

the PVDF films.

1.1.8 Pb-Free Piezoelectrics

The 21st century is called the “century of environmental management.”

We are facing serious global problems such as the accumulation of toxic

wastes, the greenhouse effect on Earth, contamination of rivers and seas,

and lack of energy sources, oil, natural gas etc. In 2006, the European Com-

munity started RoHS (restrictions on the use of certain hazardous sub-

stances), which explicitly limits the usage of lead (Pb) in electronic

equipment. The net result is that we may need to regulate the usage of lead

zirconate titanate (PZT), the most famous piezoelectric ceramic, in the

future. Governmental regulation on PZT usage may be introduced in

Japan and Europe in the next 10 years. RoHS seems to be a significant

threat to piezoelectric companies who have only PZT piezoceramics.

However, this also represents an opportunity for companies that are pre-

paring alternative piezoceramics for the piezoelectric device market.

Pb (lead)-free piezoceramics started to be developed after 1999. Fig. 1.9

shows statistics of various lead-free piezoelectric ceramics. The share of

the papers and patents for bismuth compounds (bismuth layered type

and (Bi,Na)TiO

type) exceeds 61%. This is because bismuth compounds

are easily fabricated in comparison with other compounds. Fig. 1.10 shows

the current best data reported by Toyota Central Research Lab, where

strain curves for oriented and unoriented (K,Na,Li) (Nb,Ta,Sb)O

ceramics are shown.

Note that the maximum strain reaches up to

150010

6

, which is equivalent to the PZT strain.

14 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Tungsten

bronze type

compound

13% Bi-layered type

compound

34%

(Na,K)NbO3 type

compound

20%

(Bi1/2Na1/2)TiO3 type

compound

27%

Other

FIG. 1.9 Patent disclosure statistics for lead-free piezoelectric ceramics. (Total number of

patents and papers is 102).

2000

1000

800

600

400

200

0050100

(A)

(

)

Temperature (°C)

Electric field (V/mm)

Oriented LF4

Strain (10-6)Smax/Emax (pm/V)

Unoriented LF4

150 200

0 500 1000 1500

PZT-D

2000

1500

1000

500

FIG. 1.10 Strain curves for oriented and unoriented (K,Na,Li) (Nb,Ta,Sb)O

ceramics.

1.1.9 Composites

1.1.9.1 Composite Effects

Kitayama and Sugawara,

Nippon Telegraph and Telephone, reported

on piezoceramic:polymer composites at the Japan IEEE Conference in

1972, which would appear to be the first paper of the piezoelectric-based

composites. As shown in Fig. 1.11, their paper dealt with the hot-rolled

composites made from PZT powder and PVDF, and they reported on

the piezoelectric and pyroelectric characteristics. Flexibility similar to

PVDF, but higher piezoelectric performance than PVDF, was obtained.

Newnham’s

contribution to establishing the composite connectivity

concept, and the summary of sum, combination, and product effects,

promoted the systematic studies in piezocomposite field. In certain cases,

the average value of the output of a composite exceeds both outputs of

Phase 1 and Phase 2. Let us consider two different outputs, Yand Z,

for two phases (i.e., Y

). When a figure of merit (FOM) for

an effect is provided by the fraction (Y/Z), we may expect an extra-

ordinary effect. Suppose that Yand Zfollow the concave and convex

type sum effects, respectively, as illustrated in Fig. 1.12; the combi-

nation value Y/Zwill exhibit a maximum at an intermediate ratio of

FIG. 1.11 The first report on piezoelectric composites by Kitayama and Sugawara in 1972.

16 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

phases—that is, the average FOM is higher than either end member

FOMs (Y

or Y

). This was called a “combination effect.” Newnham’s

group studied various connectivity piezoceramic/polymer composites,

which exhibited a combination property of g(the piezoelectric voltage

constant); this is provided by d/ε

ε(d: piezoelectric strain constant, and

ε: relative permittivity), where dand εfollow the concave and convex

type sum effects.

1.1.9.2 Magnetoelectric Composites

When Phase 1 exhibits an output Ywith an input X, and Phase 2

exhibits an output Zwith an input Y, we can expect for a composite that

exhibits an output Zwith an input X. A completely new function is created

for the composite structure, called a “product effect.” Philips developed a

magnetoelectric material based on the product effect concept,

which

exhibits electric voltage under the magnetic field application, aiming at

a magnetic field sensor. This material was composed of magnetostrictive

CoFe

and piezoelectric BaTiO

mixed and sintered together. Fig. 1.13A

shows a micrograph of a transverse section of a unidirectionally solidified

rod of the materials with an excess of TiO

. Four finned spinel dendrites

CoFe

are observed in a BaTiO

bulky whitish matrix. Fig. 1.13B shows

the magnetic field dependence of the magnetoelectric effect in an arbitrary

unit measured at room temperature. When a magnetic field is applied on

this composite, cobalt ferrite generates magnetostriction, which is trans-

ferred to barium titanate as stress, finally leading to the generation of a

charge/voltage via the piezoelectric effect in BaTiO

Phase 1 : X ® Y1/Z1

Phase 2 : X ® Y2/Z2

Phase 2

Phase 1

Improvement

Phase 2Phase 1

X ® (Y/Z)*

Y1/Z1Y2/Z2

FIG. 1.12 Basic concept of the performance improvement in a composite via a combina-

tion effect.

171.1 THE HISTORY OF PIEZOELECTRICS

Ryu et al.

extended the magnetoelectric composite idea into a lami-

nate structure (2–2 composites). We used Terfenol-D and high gsoft

PZT layers, which are much superior to the performances of cobalt ferrite

and BT, respectively. However, due to the difficulty in cofiring of these

two materials, we invented the laminated structures. This idea now forms

the basis of the magnetoelectric sensor designs in the microelectromecha-

nical systems (MEMS) area.

1.1.9.3 Piezoelectric Dampers

An intriguing application of PZT composites is as a passive mechanical

damper. Consider a piezoelectric material attached to an object whose

vibration is to be damped. When vibration is transmitted to the piezoelec-

tric material, the vibration energy is converted into electrical energy by the

piezoelectric effect, and an AC voltage is generated. If a proper resistor is

connected, however, the energy converted into electricity is consumed in

Joule heating of the resistor, and the amount of energy converted back into

mechanical energy is reduced so that the vibration can be rapidly damped.

Indicating the series resistance as R, the capacitance of the piezoelectric

material as C, and the vibration frequency as f, damping takes place most

rapidly when the series resistor is selected in such a manner that the imped-

ance matching condition, R¼1/2πfC, is satisfied.

Being brittle and hard, ceramics are difficult to assemble directly into a

mechanical system. Hence, flexible composites can be useful in practice.

When a composite of polymer, piezoceramic powder, and carbon black

is fabricated (Fig. 1.14), the electrical conductivity of the composite is

greatly changed by the addition of small amounts of carbon black.

properly selecting the electrical conductivity of the composite (i.e., electri-

cal impedance matching), the ceramic powder effectively forms a series

Hmax

(

)(

)

Hdc

FIG. 1.13 (A) Micrograph of a transverse section of a unidirectionally solidified rod of

mixture of magnetostrictive CoFe

and piezoelectric BaTiO

, with an excess of TiO

(B) Magnetic field dependence of the magnetoelectric effect in a CoFe

: BaTiO

composite

(at room temperature).

18 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

circuit with the carbon black, so that the vibration energy is dissipated

effectively. The conductivity of the composite changes by more than 10

orders of magnitude around a certain carbon fraction called the “percola-

tion threshold,” where the carbon powder link starts to be generated. This

eliminates the use of external resistors. Note that the damper material

exhibits a selective damping performance for a certain vibration fre-

quency, depending on the selected resistivity of the composite, which

can be derived from the electrical impedance matching between the per-

mittivity and resistivity.

1.1.10 Other Piezoelectric-Related Materials

1.1.10.1 Photostrictive Materials

The phtostriction phenomenon was discovered by Dr. P. S. Brody and

the author independently, and almost at the same time, in 1981.

38,39

principle, the photostrictive effect arises from a superposition of the

“bulk” photovoltaic effect, in other words, generation of large voltage

from the irradiation of light, and the converse-piezoelectric effect, in other

words, expansion or contraction under the applied voltage.

In certain

ferroelectrics, a constant electromotive force is generated with exposure

of light, and a photostrictive strain results from the coupling of this

bulk photovoltaic effect with converse piezoelectricity. A bimorph unit

has been made from PLZT 3/52/48 ceramic doped with a slight addition

of tungsten.

The remnant polarization of one PLZT layer is parallel to

the plate and in the direction opposite to that of the other plate. When a

violet light is irradiated to one side of the PLZT bimorph, a photovoltage

of 1 kV/mm is generated, causing a bending motion. The tip displace-

ment of a 20 mm bimorph 0.4 mm in thickness was 150 μm, with a

response time of 1 s.

A photo-driven micro walking device, designed to begin moving by

light illumination, has been developed.

As shown in Fig. 1.15, it is simple

PZT ceramic Carbon Polymer

Piezoelectricity Conductivity Mechanical

flexibilit

FIG. 1.14 Piezoceramic:polymer: carbon black composite for vibration damping.

191.1 THE HISTORY OF PIEZOELECTRICS

in structure, having neither lead wires nor electric circuitry, with two

bimorph legs fixed to a plastic board. When the legs are irradiated alter-

nately with light, the device moves like an inchworm with a speed of

100 μm/min. In pursuit of thick film type photostrictive actuators for

space structure applications, in collaboration with Jet Propulsion Labora-

tory, Penn State investigated the optimal range of sample thickness and

surface roughness dependence of photostriction. 30-μm thick PLZT films

exhibit the maximum photovoltaic phenomenon.

1.1.10.2 Monomorphs

The “monomorph” is defined as a single uniform material that can bend

under an electric field. A semiconductive piezoelectric plate can generate

this intriguing bending phenomenon, discovered by Uchino’s group.

When attending a basic conference of the Physical Society of Japan, the

author learned about a surface layer generated on a ferroelectric single crys-

tal due to formation of a Schottky barrier. It was not difficult to replace some

of the technical terminologies with our words. First polycrystalline piezo-

electric samples were used, with reduction processes to expand the

Schottky barrier thickness. Uchino’s group succeeded in developing

a monolithic bending actuator. A monomorph device has been devel-

oped to replace the conventional bimorphs, with simpler structure and

manufacturing process. A monomorph plate with 30 mm in length and

0.5 mm in thickness can generate a 200 μm tip displacement, an equal mag-

nitude to that of the conventional bimorphs. The “rainbow” actuator by

Aura Ceramics

is a modification of the above-mentioned semiconductive

piezoelectric monomorphs, where half of the piezoelectric plate is reduced

so as to make a thick semiconductive electrode to cause a bend.

FIG. 1.15 Photo-driven walking machine.

20 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

In the following sections, the author provides the reader with the nec-

essary fundamental knowledge on piezoelectricity and the present status

of materials.

1.2.1 Piezoelectric Figures of Merit

There are five important figures of merit in piezoelectrics: the piezo-

electric strain constant d, the piezoelectric voltage constant g, the electromec-

hanical coupling factor k, the mechanical quality factor Q

, and the acoustic

impedance Z.

1.2.1.1 Piezoelectric Strain Constant d

The magnitude of the induced strain xby an external electric field

Eis represented by this figure of merit (an important figure of merit

for actuator applications):

x¼dE:(1.2)

1.2.1.2 Piezoelectric Voltage Constant g

The induced electric field Eis related to an external stress Xthrough the

piezoelectric voltage constant g(an important figure of merit for sensor

applications):

E¼gX:(1.3)

Taking into account the relation, P¼dX, we obtain an important rela-

tion between gand d:

g¼d=ε0ε:ε:relative permittivity



(1.4)

1.2.1.3 Electromechanical Coupling Factor k

The terms electromechanical coupling factor,energy transmission coefficient,

and efficiency are sometimes confused.

All are related to the conversion

rate between electrical energy and mechanical energy, but their defini-

tions are different.

(a) The electromechanical coupling factor k

k2¼Stored mechanical energy=Input electrical energy



(1.5)

k2¼Stored electrical energy=Input mechanical energy



(1.6)

Let us calculate Eq. (1.5), when an electric field Eis applied to a

piezoelectric material. See Fig. 1.16A, left. Since the input electrical

211.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

energy is (1/2) ε

(ε

: permittivity under stress free condition)

per unit volume and the stored mechanical energy per unit volume

under zero external stress is given by (1/2) x

¼(1/2) (dE)

: elastic compliance under short-circuit condition), k

can be

calculated as the following:

k2¼1=2ðÞdEðÞ

2=sE

=1=2ðÞε0εXE2



¼d2=ε0εXsE:

(1.7)

(b) The energy transmission coefficient λ

max

Not all the stored energy can be actually used, and the actual

work done depends on the mechanical load. With zero mechanical

load or a complete clamp (no strain), no output work is done. The

energy transmission coefficient is defined by

λmax ¼Output mechanical energy=Input electrical energy



max (1.8)

or equivalently,

PSPS

Piezo-actuator

Mass

(1.7)

(1.9)

Output mechanical

energy

Input electrical

energy

(A) (B)

(

)(

)

xxdE

dE+sX

e0eE+dX

−dE/s

FIG. 1.16 Calculation of the input electrical and output mechanical energy: (A) load mass

model for the calculation, (B) electric field versus induced strain curve, (C) stress versus strain

curve, and (D) electric field versus polarization curve.

22 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

λmax ¼Output electrical energy=Input mechanical energy



max (1.9)

The difference of the above from Eqs. (1.5), (1.6) is “stored” or

“spent.”

Let us consider the case where an electric field Eis applied to a

piezoelectric under constant external stress X(<0, because a

compressive stress is necessary to work to the outside). This

corresponds to the situation that a mass is put suddenly on the

actuator, as shown in Fig. 1.16A. [Note that when the load is gradually

applied on the actuator, 1/2 needs to be multiplied in the following

energy discussion.] Fig. 1.16B shows two electric-field versus

induced-strain curves, corresponding to two conditions: under the

mass load and no mass. Because the area on the electric field-strain

domain does not mean the energy, we should use the stress-strain

and electric field-polarization domains in order to discuss the

mechanical and electrical energy, respectively. Fig. 1.16C illustrates

how to calculate the mechanical energy. Note that the mass shrinks

the actuator first by sX (s: piezo-material’s compliance, and X<0).

This mechanical energy sX

is a sort of “loan” to the actuator credited

from the mass, which should be subtracted later. This energy

corresponds to the hatched area in Fig. 1.16C. By applying the step

electric field, the actuator expands by the strain level dE under a

constant stress condition. This is the mechanical energy provided from

the actuator to the mass, which corresponds to jdEXj. Like paying

back the initial “loan,” the output work (from the actuator to the mass)

can be calculated as the area subtraction (shown by the dotted area

in Fig. 1.16C):

ZXðÞdx ¼ dE +sXðÞX:(1.10)

Fig. 1.16D illustrates how to calculate the electrical energy. The

mass load Xgenerates the loan electrical energy by inducing P¼dX

(see the hatched area in Fig. 1.16D). By applying a sudden electric

field E, the actuator (like a capacitor) receives the electrical energy

of ε

εE

. Thus, the total energy is given by the area subtraction

(shown by the dotted area in Fig. 1.16D):

ZEðÞdP ¼ε0εE+dXðÞE:(1.11)

It is obvious that mechanical output/work energy is zero under a

no-load condition (i.e., X¼0), and it is also zero under a completely

clamped condition (i.e., x¼0) of the actuator. Thus, we need to choose

a proper load to maximize the energy transmission coefficient. From the

maximum condition of

231.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

λ¼ dE +sXðÞX=ε0εE+dXðÞE, (1.12)

we can obtain

λmax ¼1=kðÞ

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1=k2

ðÞ1



¼1=kðÞ+ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1=k2

ðÞ1



2

:(1.13)

Refer to Ref. 45 for the detailed derivation process. Notice that

k2=4<λmax <k2=2, (1.14)

depending on the kvalue. For a small k,λ

max

¼k

/4, and for a large k,

max

¼k

/2. We neglected the extreme case of k0.95, when λ

max

approaches to k

It is also worth noting that the maximum condition stated above

does not agree with the condition that provides the maximum output

mechanical energy. The maximum output energy can be obtained

when the dotted area in Fig. 1.16C becomes the maximum under the

constraint of the rectangular corner point tracing on the line (from dE

on the vertical axis to dE/son the horizontal axis). Therefore, the

load should be a half of the maximum generative stress (or “blocking”

stress) and the mechanical energy: [dE s(dE/2s)](dE/2s)¼(dE)

4s. In this case, since the input electrical energy is given by [ε

εE+d

(dE/2s)] E,

λ¼1=22=k2



1



, (1.15)

which is close to the value λ

max

when kis small, but it has a different

value when kis large; that is predicted theoretically.

η¼Output mechanical energy



=Consumed electrical energy



(1.16)

η¼Output electrical energy



=Consumed mechanical energy



:(1.17)

The difference of the efficiency definition from Eqs. (1.8), (1.9)

is “input” energy and “consumed” energy in the denominators. In a

work cycle (e.g., an electric field cycle), the input electrical

energy is transformed partially into mechanical energy and the

remainderisstoredaselectricalenergy (electrostatic energy like a

capacitor) in an actuator. In this way, the ineffective electrostatic

energy can be returned to the power source with a designed circuit,

leading to near 100% efficiency if the loss is small. Typical

values of dielectric and elastic losses in PZT are about 1%–3%.

A driving power supply can be coupled with an inductive

component L(or negative capacitance) to collect the remaining

electric energy from the capacitive piezo-actuator.

24 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.2.1.4 Mechanical Quality Factor Q

The mechanical quality factor, Q

, is a parameter that characterizes the

sharpness of the electromechanical resonance spectrum. When the

motional admittance Y

is plotted around the resonance frequency ω

the mechanical quality factor Q

is defined with respect to the full width

[2Δω]atYm=ﬃﬃﬃ

p(or 3 dB-down) as

QM¼ω0=2Δω:(1.18)

Also note that Q

1

is equal to the mechanical loss (tan ϕ

). When we

define a complex elastic compliance, s

¼s

–js

, the mechanical loss tan-

gent is provided by tan ϕ

¼s

. The Q

value is very important in

evaluating the magnitude of the resonant displacement and strain. The

vibration amplitude at an off-resonance frequency (dEL,L: length of

the sample) is amplified by a factor proportional to Q

at the resonance

frequency. For example, a longitudinally vibrating rectangular plate

through the transverse piezoelectric effect d

generates the maximum dis-

placement given by (8/π

EL. Refer to Ref. 45 for the detailed der-

ivation process.

Another important note: Q

1

(¼tan ϕ

) generates the heat primarily in

the piezo-sample when driven at its resonance mode.

1.2.1.5 Acoustic Impedance Z

The acoustic impedance Zis a parameter used for evaluating the acous-

tic energy transfer between two materials. It is defined, in general, by

Z2¼pressure=volume velocity



:(1.19)

In a solid material,

Z¼ﬃﬃﬃﬃﬃ

ρc

p, (1.20)

where ρis the density and cis the elastic stiffness of the material.

In more advanced discussions, there are three kinds of impedances:

specific acoustic impedance (pressure/particle speed), acoustic imped-

ance (pressure/volume speed), and radiation impedance (force/speed).

See Ref. 48 for details.

1.2.2 Piezoelectric Resonance

1.2.2.1 The Piezoelectric Constitutive Equations

When an electric field is applied to a piezoelectric material, deforma-

tion (ΔL) or strain (ΔL/L) arises. When the field is alternating, mechanical

vibration is caused, and if the drive frequency is adjusted to a mechanical

resonance frequency of the device, a large resonating strain is generated.

This phenomenon can be understood as a strain amplification due to

251.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

accumulating input energy with time (i.e., amplification in terms of time),

and it is called piezoelectric resonance. The amplification factor is propor-

tional to the mechanical quality factor Q

. Piezoelectric resonance is very

useful for realizing energy trap devices, actuators, etc. The theoretical

treatment is as follows.

If the applied electric field and the generated stress are not large, the

stress Xand the dielectric displacement Dcan be represented by the fol-

lowing equations, using elastic compliance sij E, absolute permittivity εmkX

(not “relative”), and piezoelectric constant d

xi¼sijEXj+dmi Em, (1.21)

Dm¼dmiXi+εmk XEk:(1.22)

(i,j¼1,2,…,6; m,k¼1,2,3)

These are called the piezoelectric constitutive equations. The number

of independent parameters for the lowest symmetry trigonal crystal is

21 for sijE, 18 for d

, and 6 for εmkX. The number of independent

parameters decreases with increasing crystallographic symmetry. Con-

cerning the polycrystalline ceramics, the poled axis is usually denoted

as the z-axis and the ceramic is isotropic with respect to this z-axis (Curie

group C

∞v

(∞m)). The number of nonzero matrix elements in this case is

10 s11E,s12 E,s13E,s33E,s44E,d31,d33 ,d15,ε11X, and ε33 X



1.2.2.2 Electromechanical Coupling Factor

Next, let us introduce the electromechanical coupling factor k,which

corresponds to the rate of electromechanical transduction. The internal

energy Uof a piezoelectric vibrator is given by summation of the mechanical

energy UM¼ZxdX



and the electrical energy UE¼ZDdE



.Uis

calculated as follows, when linear relations Eqs. (1.21), (1.22) are applicable:

U¼UM+UE

¼1=2ðÞ

i,j

sijEXjXi+1=2ðÞ

m,i

dmiEmXi

+1=2ðÞ

m,i

dmiXiEm+1=2ðÞ

k,m

εmkXEkEm

¼UMM +2UME +UEE

¼1=2ðÞ

i,j

sijEXjXi+21=2ðÞ

m,i

dmiEmXi+1=2ðÞ

k,m

εmkXEkEm:

(1.23)

The sand εterms represent purely mechanical and electrical energies

and U

), respectively, and the dterm denotes the energy

26 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

transduced from electrical to mechanical energy, or vice versa, through

the piezoelectric effect (U

). The electromechanical coupling factor kis

defined by the following:

k¼UME=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

UMM UEE

p:(1.24)

Note that this definition is equivalent to the definition provided in

Section 1.2.1:

k2¼UME=UE¼Stored mechanical energy=Input electrical energy



k2¼UME=UM¼Stored electrical ene rgy=Input mechanical energy



It is not obvious that the electromechanical coupling factor kis the same

under a static (Eq. 1.7) and dynamic condition (Eq. 1.24).

The kvalue var-

ies with the dynamic vibration mode (even in the same ceramic sample),

and can it have a positive or negative value (see Table 1.1). From Table 1.1,

it can be seen that jk

jratio around 0.47 originates from the jd

ratio around 0.43. The kvalue is governed primarily by the contributing

piezoelectric d constant for that vibration mode.

1.2.2.3 Longitudinal Vibration Mode

Let us consider the longitudinal mechanical vibration of a piezoceramic

plate through the transverse piezoelectric effect (d

), as an example

(Fig. 1.17) for demonstrating that the dynamic coupling factor kat the

resonance is the same as the static one. If the polarization is in the z-

direction and x-yplanes are the planes of the electrodes, the extensional

vibration in the xdirection is represented by the following dynamic equa-

tion (when the length Lis more than 4–6 times of the width wor the thick-

ness b, we can neglect the coupling modes with width or thickness

vibrations):

@2u=@ t2



¼F¼@X11=@xðÞ+@X12=@yðÞ+@X13=@zðÞ, (1.25)

where uis the displacement of the small volume element in the ceramic

plate in the x-direction. The relations between stress, electric field (only

exists due to the electrodes), and the induced strain are given by the

following:

x1¼s11EX1+s12 EX2+s13EX3+d31E3,

x2¼s12EX1+s11 EX2+s13EX3+d31E3,

x3¼s13EX1+s13 EX2+s33EX3+d33E3,

x4¼s44EX4,

x5¼s44EX5,

x6¼2s11Es12 E



X6:(1.26)

271.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

TABLE 1.1 Several Shapes of the Piezoelectric Resonator and Their Electromechanical Coupling Factors

Coupling factor Elastic boundary conditions Resonator shape Definition

X16¼0, X2¼X3¼0

x16¼0, x26¼0, x36¼0

1d31

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

11 εX

X1¼X2¼0, X36¼0

x1¼x26¼0, x36¼0

Fundamental mode

3d33

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

33 εX

X1¼X26¼0, X3¼0

x1¼x26¼0, x36¼0

Fundamental mode

k31 ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1σ

X1¼X26¼0, X36¼0

x1¼x2¼0, x36¼0

Thickness mode

k33 ﬃﬃﬃﬃﬃﬃ

εx

0X1¼X26¼0, X36¼0

x1¼x26¼0, x3¼0

Radial mode

3kpAk33

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1A2

pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1k2

28 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

0X16¼0, X26¼0, X3¼0

x16¼0, x2¼0, x36¼0

Width mode

2k31

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1k2

qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1+σ

1σ

00 X16¼0, X2¼0, X36¼0

x16¼0, x26¼0, x3¼0

Width mode

k31 Bk33

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1k2

000 X16¼0, X26¼0, X36¼0

x16¼0, x2¼0, x3¼0

Thickness mode

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

kpAk33



1A2k31 Bk33

ðÞ

1k2

33 k31 Bk33

ðÞ

0X16¼0, X2¼0, X36¼0

x1¼0, x26¼0, x36¼03

Width mode

1k33 Bk31

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

1B2

ðÞ1k2



¼k

X1¼X2¼X3¼0, X46¼0

x1¼x2¼x3¼0, x46¼0

d15

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

εX

11 sE

Here :A¼ﬃﬃﬃ

ps13E

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s33Es11 E+s12E

ðÞ

p,B¼s13E

ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s11Es33 E

291.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

When the plate is very long and thin, X

and X

may be set to equal to

zero through the plate. Since shear stress will not be generated by the elec-

tric field E

(¼E

), Eq. (1.26) is reduced to only one equation:

X1¼x1=s11Ed31 =s11E



Ez:(1.27)

Introducing Eq. (1.27) into Eq. (1.25), and allowing for x

¼@u/@x(non-

suffix xcorresponds to the Cartesian coordinate, and x

is the strain along

the 1 (x) direction) and @E

/@x¼0 (due to the equal potential on each elec-

trode), leads to a harmonic vibration equation:

ω2ρs11Eu¼@2u=@x2:(1.28)

Here, ωis the angular frequency of the drive field, and ρis the density.

Substituting a general solution u¼u

(x)e

jωt

(x)e

jωt

into Eq. (1.27), and

with the boundary condition X

¼0atx¼0 and L(sample length) (due to

the mechanically free condition at the plate end), the following solution

can be obtained:

@u=@x¼x1¼d31 Ezsin ωLxðÞ=v+ sin ωx=vðÞ½=sin ωL=vðÞ

¼d31 Ez

cos ωL2xðÞ



cos ωL



(1.29)

Here, vis the sound velocity in the piezoceramic along the length, which

is given by

v¼1=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ρs11E

p:(1.30)

When the specimen is utilized as an electrical component such as a filter

or a vibrator, the electrical admittance [(induced current/applied voltage)

FIG. 1.17 Longitudinal vibration through the transverse piezoelectric effect (d

) in a rect-

angular plate (L≫w≫b).

30 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

ratio] plays an important role. The current flow into the specimen is

described by the surface charge increment, @D

/@t, and the total current

is given by the following:

i¼jωwZL

D3dx ¼jωwZL

d31X1+ε33 XEz



¼jωwZL

d31 x1=s11Ed31 =s11E





+ε33XEz



dx:

(1.31)

Using Eq. (1.29), the admittance Yfor the mechanically free sample is

calculated:

Y¼i=VðÞ¼i=EztðÞ¼jωwL=WzbðÞ

d312=s11 E



cos ωL2xðÞ



cos ωL



AEz

+ε33Xd31 2=s11E



Ez#dx

¼jωwL=bðÞε33LC½1+ d312=ε33 LCs11E



ðtan ωL=2vðÞ=ωL=2vðÞ,

(1.32)

where wis the width, Lis the length, bis the thickness of the rectangular

piezo-sample, and Vis the applied voltage. ε33LC is the permittivity in a

longitudinally clamped sample, which is given by

ε33LC ¼ε33 Xd312=s11E



:(1.33)

You will find below that ε33LC ¼ε33 x1¼ε33X1d31 2

s11Eε33 X

!"#

ε33X1k31 2



, which is called “damped” permittivity, purely electrostatic

capacitance. The piezoelectric resonance is achieved where the admittance

becomes infinite or the impedance (Z¼1/Y) is zero. The resonance fre-

quency f

is calculated from Eq. (1.32) (by putting ωL/2v¼π/2), and

the fundamental frequency is given by

fR¼ωR=2π¼v=2L¼1=2Lﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ρs11E



:(1.34)

311.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

On the other hand, the antiresonance state is generated for zero admit-

tance or infinite impedance:

ωAL=2vðÞcot ωAL=2vðÞ¼d312=ε33 LCs11E¼k312=1k312



:(1.35)

The final transformation is provided by the following definition:

k31 ¼d31=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s11Eε33 X

p:(1.36)

The resonance and antiresonance states are both mechanical resonance

state with amplified strain/displacement states, but they are very differ-

ent from the driving viewpoints. The mode difference is described by the

following intuitive model.

In a high electromechanical coupling material

with kalmost equal to 1, the resonance or antiresonance states appear for

tan(ωL/2v)¼∞or 0 [i.e., ωL/2v¼(m1/2)πor mπ(m: integer)], respec-

tively, by neglecting the damped capacitance term. The strain amplitude

distribution for each state [calculated using Eq. (1.29)] is illustrated

in Fig. 1.18. In the resonance state, large strain amplitudes and large capac-

itance changes (called motional capacitance) are induced, and the current

can easily flow into the device. In contrast, at the antiresonance, the large

strains are induced locally at nodal line regions in the device, but compen-

sate completely in total, resulting in no capacitance change, and the cur-

rent cannot flow easily into the sample. Thus, for a high k

plate the first

antiresonance frequency f

should be twice as large as the first resonance

frequency f

. Both resonance and antiresonance states are in the mechan-

ical resonances excited under low voltage/high current or high voltage/

low current, which can create large strain in the sample under minimum

input electrical energy. The stress X

at the plate ends (x¼0 and L) is sup-

posed to be zero in both cases. However, though the strain x

at the plate

ends is zero for the resonance, the strain x

is not zero (actually the max-

imum) for the antiresonance. This means that there is only one vibration

node at the plate center for the resonance (top-left in Fig. 1.18), and there

are two additional nodes close at both plate ends for the antiresonance

(top-right in Fig. 1.18). This occurs because of the antiresonance drive,

in other words, high voltage/low current (minimum power) drive due

to the high impedance. The converse piezo-effect strain under Edirectly

Resonance Antiresonance

Low coupling High coupling

m=1 m=1

m=2 m=2

FIG. 1.18 Strain distribution in the resonant and antiresonant states.

32 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

via d

(uniform strain in the sample) superposes on the mechanical res-

onance strain distribution (distributed strain with nodes in the sample),

two strains of which have exactly the same level theoretically at the anti-

resonance for k

¼1.

In a typical case, where k

¼0.3, the antiresonance state varies from

the previously mentioned mode and becomes closer to the resonance

mode (top-center in Fig. 1.18). The low-coupling material exhibits an

antiresonance mode where the capacitance change due to the size change

(motional capacitance) is compensated by the current required to charge up

the static capacitance (called damped capacitance). Thus, the antiresonance

frequency f

will approach the resonance frequency f

The general procedure for calculating the piezoelectric parameters (k

,s11E,andε33X) from the admittance/impedance spectrum measure-

ment is described below:

(1) The sound velocity vin the specimen is obtained from the resonance

frequency f

(see Fig. 1.17), using Eq. (1.34):f

¼v/2L.

(2) Knowing the density ρ, the elastic compliance s11Ecan be calculated from

the sound velocity v:v¼1=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

ρs11E

(3) The electromechanical coupling factor k

is calculated from the vvalue

and the antiresonance frequency f

through Eq. (1.35). Especially in low-

coupling piezoelectric materials, the following approximate equation is

useful:

k312=1k31 2



¼π2=4



Δf=fR

ðÞΔf¼fAfR

ðÞ(1.37)

(4) Knowing the permittivity ε33Xfrom the independent measurement

under an off-resonance condition, the d

is calculated from k

through

Eq. (1.36):k31 ¼d31=ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s11Eε33 X

Fig. 1.19A and B compares observed impedance curves of rod-shaped

samples for a typical kmaterial (PZT 5H, k

¼0.70) and a high-kmaterial

(PZN-PT single crystal, k

¼0.90). Note a large separation between the

resonance and antiresonance peaks in the high-kmaterial, leading to

the condition almost f

¼2f

. To the contrary, a regular PZT sample

exhibits f

¼1.3 f

. The bandwidth of the piezotransducer is defined by

(Δf/f

), leading to 100% for the PZN-PT sample and only 30% for PZT 5H.

1.2.3 Overview of Piezoelectric Materials

This section summarizes the current status of piezoelectric materials:

single-crystal materials, piezoceramics, piezopolymers, composites and

piezofilms. Table 1.2 shows the piezoelectric material parameters.

Quartz, with the highest mechanical quality factor, is used for low loss

transducers. The PZT family shows high dand ksuitable for high power

331.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

transducers. Sm-doped lead titanates exhibit extremely high mechanical

coupling anisotropy k

, suitable for medical transducers. Piezopolymer

PVDF has small permittivity, leading to a high piezo gconstant, in addition

to mechanical flexibility, suitable for pressure/stress sensor applications.

k33 = 0.70

k33 = 0.90

fA= 465 kHz

fA= 584 kHz

= 1.3 fR

=2 fR

fR= 360 kHz

fR= 295 kHz

Frequency

(A)

)

Frequenc

1/wC0

ImpedanceImpedance

FIG. 1.19 (A) Impedance curves for a reasonable kmaterial (PZT 5H, k

¼0.70), and (B) a

high-kmaterial (PZN-PT single crystal, k

¼0.90).

TABLE 1.2 Piezoelectric Properties of Representative Piezoelectric Materials

49,50

Parameter Quartz BaTiO

PZT

(Pb,Sm)

TiO

PVDF-

TrFE

(pC/N) 2.3 190 289 593 65 33

(10

3

Vm/N) 57.8 12.6 26.1 19.7 42 380

0.09 0.38 0.51 0.50 0.50 0.30

0.33 0.58 0.65 0.03

/ε

5 1700 1300 3400 175 6

>10

500 65 900 3–10

(°C) 120 328 193 355

34 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.2.3.1 Single Crystals

Although piezoelectric ceramics are widely used for a large number of

applications, single crystal materials retain their utility, being essential for

applications such as frequency-stabilized oscillators and surface acoustic

devices. The most popular single-crystal piezoelectric materials are

quartz, lithium niobate (LiNbO

), and lithium tantalate (LiTaO

). The sin-

gle crystals are anisotropic, exhibiting different material properties

depending on the cut of the materials and the direction of bulk or surface

wave propagation.

Quartz is a well-known piezoelectric material. α-Quartz belongs to the

triclinic crystal system with point group 32 and has a phase transition at

537°C to its β-form, which is not piezoelectric. Quartz has a cut with a zero

temperature coefficient. For instance, quartz oscillators, operated in the

thickness shear mode of the AT-cut, are used extensively for clock sources

in computers, and frequency stabilized ones in TVs and VCRs. On the

other hand, an ST-cut quartz substrate with X-propagation has a zero tem-

perature coefficient for SAW, so it is used for SAW devices with highly

stabilized frequencies. Another distinguished characteristic of quartz is

an extremely high mechanical quality factor, Q

>10

Lithium niobate and lithium tantalate belong to an isomorphous crystal

system and are composed of oxygen octahedron. The Curie temperatures

of LiNbO

and LiTaO

are 1210 and 660°C, respectively. The crystal sym-

metry of the ferroelectric phase of these single crystals is 3 m, and the

polarization direction is along the c-axis. These materials have high elec-

tromechanical coupling factors for SAWs. In addition, large single crystals

can easily be obtained from their melt using the conventional Czochralski

technique. Thus, both materials occupy very important positions in the

SAW device application field.

Single crystals of Pb(Mg

1/3

2/3

(PMN), Pb(Zn

1/3

2/3

(PZN),

and their binary systems with PbTiO

(PMN-PT and PZN-PT) with

extremely large electromechanical coupling factors are discussed in the

following section.

1.2.3.2 Polycrystalline Materials

Barium titanate, BaTiO

, is one of the most thoroughly studied and

most widely used ferroelectric materials. Just below the Curie temp-

erature (130°C), the vector of the spontaneous polarization points in the

[0 0 1] direction (tetragonal phase), below 5°C it reorients in the [0 1 1]

(orthorhombic phase) and below 90°C in the [1 1 1] direction (rhombo-

hedral phase). The dielectric and piezoelectric properties of ferroelectric

ceramic BaTiO

can be affected by its own stoichiometry, microstructure,

and by dopants entering onto the Aor Bsite in solid solution. Modified

ceramic BaTiO

with dopants such as Pb or Ca ions have been developed

351.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

to stabilize the tetragonal phase over a wider temperature range and

have been used as commercial piezoelectric materials. After the discovery

of PZT, BT’s role in piezoelectric devices ceased, and it is primarily used

in capacitors at present. However, in these 10 years, once Pb usage will

be strictly regulated, interest in BT based piezoceramics may revive.

Piezoelectric Pb(Ti,Zr)O

solid solutions (PZT) ceramics discovered in

the 1950s are widely used nowadays because of their superior piezoelectric

properties. The phase diagram for the PZT system (PbZr

1x

)is

shown in Fig. 1.20. The crystalline symmetry of this solid-solution system

is determined by the Zr content. Lead titanate also has a tetragonal ferroelec-

tric phase of a perovskite structure. With increasing Zr content, x, the tetrag-

onal distortion decreases and at x>0.52 the structure changes from the

tetragonal 4mm phase to another ferroelectric phase of rhombohedral 3 m

symmetry.The line dividing these two phases is called the morphotropic phase

boundary (MPB). The boundary composition is considered to have both

tetragonal and rhombohedral phases coexisting together. Fig. 1.21 shows

the dependence of several piezoelectric dconstants on composition near

the MPB. The dconstants have their highest values near the MPB. This

enhancement in piezoelectric effect is attributed to the increased ease of

reorientation of the polarization under an applied electric field.

Doping the PZT material with donor or acceptor ions changes its prop-

erties dramatically. Donor doping with ions such as Nb

or Ta

provides

“soft” PZTs, such as PZT-5, because of the facility of domain motion due

to the resulting Pb-vacancies. On the other hand, acceptor doping with

or Sc

leads to “hard” PZTs, such as PZT-8, because the oxygen

vacancies will pin the domain wall motion.

PZT in a ternary solid solution with another perovskite phase has been

investigated intensively by Japanese ceramic companies. Examples of

these ternary compositions are the following: PZTs in a solid solution

with Pb(Mg

1/3

2/3

(Panasonic), Pb(Zn

1/3

2/3

(Toshiba), Pb

(Mn

1/3

2/3

, Pb(Co

1/3

2/3

, Pb(Mn

1/3

2/3

, Pb(Ni

1/3

2/3

)

(NEC), Pb(Sb

1/2

, Pb(Co

1/2

, and Pb(Mg

1/2

(Du Pont)—all of which were patented by different companies (almost

all composition patents have already expired).

Table 1.3 summarizes piezoelectric, dielectric, and elastic properties

of typical PZTs: “soft” PZT-5H, semihard PZT-4, and “hard” PZT-8. Note

that soft PZTs exhibit high k, high d, and high ε, in comparison with

hard PZTs, while Q

is quite high in hard PZTs. Thus, soft PZTs should

be used for off-resonance applications, while hard PZTs are suitable to

the resonance applications.

The end member of PZT, lead titanate has a large crystal distortion.

PbTiO

has a tetragonal structure at room temperature with its tetragon-

ality c/a¼1.063. The Curie temperature is 490°C. Densely sintered PbTiO

ceramics cannot be obtained easily, because they break up into a powder

36 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

when cooled through the Curie temperature due to the large spontaneous

strain. Lead titanate ceramics modified by adding a small amount of addi-

tives exhibit a high piezoelectric anisotropy. Either (Pb,Sm)TiO

351

or (Pb,

Ca)TiO

352

exhibits an extremely low planar coupling, that is, a large k

ratio. Here, k

and k

are thickness-extensional and planar electromechan-

ical coupling factors, respectively. Since these transducers can generate

500

400

300

200

100

001020

Tetragonal Morphotropic

phase boundary

Rhombohedral

Cubic

PSPS

aaa

30 40 50 60 70 80 90 100

PbTiO3PbZrO3

Mole % PbZrO3

Temperature (°C)

FIG. 1.20 Phase diagram of lead zirconate titanate (PZT).

800

600

400

200

48 50 52 54

Mole % PbZrO3

dij (´10−12 C/N)

−d31

d33

d15

56 58 60

FIG. 1.21 Dependence of several dconstants on composition near the morphotropic phase

boundary in the PZT system.

371.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

purely longitudinal waves through k

associated with no transverse waves

through k

, clear ultrasonic imaging is expected without a “ghost” caused

by the transverse wave. (Pb,Nd)(Ti,Mn,In)O

ceramics with a zero temper-

ature coefficient of the SAW delay have been developed as superior sub-

strate materials for SAW device applications.

TABLE 1.3 Piezoelectric, Dielectric, and Elastic Properties of Typical PZTs

Soft PZT-5H Semi-Hard PZT-4 Hard PZT-8

EM coupling factor

0.65 0.58 0.51

0.39 0.33 0.30

0.75 0.70 0.64

0.68 0.71 0.55

Piezoelectric coefficient

(10

12

m/V) 274 122 97

593 285 225

741 495 330

(10

3

Vm/N) 9.1 10.6 11.0

19.7 24.9 25.4

26.8 38.0 28.9

Permittivity

33X

/ε

3400 1300 1000

11X

/ε

3130 1475 1290

Dielectric loss (tan δ) (%) 2.00 0.40 0.40

Elastic compliance

11E

(10

12

/N) 16.4 12.2 11.5

12E

4.7 4.1 3.7

13E

7.2 5.3 4.8

33E

20.8 15.2 13.5

44E

43.5 38.5 32.3

Mechanical Q

65 500 1000

Density ρ(10

kg/m

) 7.5 7.5 7.6

Curie temp (°C) 193 325 300

38 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.2.3.3 Relaxor Ferroelectrics

Relaxor ferroelectrics can be prepared either in polycrystalline form

or as single crystals. They differ from the previously mentioned normal

ferroelectrics in that they exhibit a broad phase transition from the

paraelectric to ferroelectric state, a strong frequency dependence of the

dielectric constant (i.e., dielectric relaxation) and a weak remanent polari-

zation. Lead-based relaxor materials have complex disordered perovskite

structures.

Relaxor-type electrostrictive materials, such as those from the lead

magnesium niobate-lead titanate, Pb(Mg

1/3

2/3

-PbTiO

(or PMN-

PT), solid solution are highly suitable for actuator applications. This

relaxor ferroelectric also exhibits an induced piezoelectric effect. That

is, the electromechanical coupling factor k

varies with the applied

DC bias field. As the DC bias field increases, the coupling increases and

saturates. Since this behavior is reproducible (no hysteresis), these

materials can be applied as ultrasonic transducers that are tunable by

the bias field.

Single-crystal relaxor ferroelectrics with the MPB composition show

tremendous promise as ultrasonic transducers and electromechanical

actuators. Single crystals of Pb(Mg

1/3

2/3

(PMN), Pb(Zn

1/3

2/3

)

(PZN) and binary systems of these materials combined with

PbTiO

(PMN-PT and PZN-PT) exhibit extremely large electromechanical

coupling factors.

25,55

Large coupling coefficients and large piezoelectric

constants have been found for crystals from the MPBs of these solid

solutions. PZN-8%PT single crystals were found to possess a high k

value of 0.94 for the (0 0 1) perovskite crystal cuts; this is very

high compared to the k

of around 0.70–0.80 for conventional PZT

ceramics.

1.2.3.4 Polymers

Polyvinylidene difluoride, PVDF or PVF2, is piezoelectric when

stretched during fabrication. Thin sheets of the cast polymer are then

drawn and stretched in the plane of the sheet, in at least one direction

and frequently also in the perpendicular direction, to transform the mate-

rial to its microscopically polar phase. Crystallization from the melt forms

the nonpolar α-phase, which can be converted into the polar β-phase by a

uni-axial or bi-axial drawing operation; the resulting dipoles are then reor-

iented through electric poling (see Fig. 1.22). Large sheets can be manufac-

tured and thermally formed into complex shapes. The copolymerization

of vinylidene difluoride with trifluoroethylene (TrFE) results in a random

copolymer (PVDF-TrFE) with a stable, polar β-phase. This polymer need

not be stretched; it can be poled directly as formed. A thickness-mode

391.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

coupling coefficient of 0.30 has been reported. Piezoelectric polymers have

the following characteristics:

(a) small piezoelectric dconstants (for actuators) and large gconstants

(for sensors), due to small permittivity

(b) light weight and soft elasticity, leading to good acoustic impedance

matching with water or the human body

, allowing for a broad resonance

band width

Such piezoelectric polymers are used for directional microphones and

ultrasonic hydrophones.

1.2.3.5 Composites

Piezo-composites comprising piezoelectric ceramic and polymer

phases are promising materials because of their excellent and readily tai-

lored properties. The geometry for two-phase composites can be classified

according to the dimensional connectivity of each phase into 10 structures:

0–0, 0–1, 0–2, 0–3, 1–1, 1–2, 1–3, 2–2, 2–3, and 3–3.

A1–3 piezo-composite,

such as the PZT-rod:polymer composite, is one of the most promising con-

figurations. The advantages of this composite are high coupling factors,

low acoustic impedance, good matching to water or human tissue,

mechanical flexibility, broad bandwidth in combination with a low

mechanical quality factor, and the possibility of making undiced arrays

by structuring the electrodes. The thickness-mode electromechanical cou-

pling of the composite can exceed the k

(0.40–0.50) of the constituent

ceramic, approaching almost the value of the rod-mode electromechanical

coupling, k

(0.70–0.80) of that ceramic.

The electromechanical coupling

factor of the composites is much superior to the pure polymer piezoelec-

trics. Acoustic impedance is the square root of the product of its density

and elastic stiffness. The acoustic match to tissue or water (1.5 Mrayls)

[CH2CF2]n

Carbon

Fluoride

Hydrogen

FIG. 1.22 Structure of polyvinylidene difluoride (PVDF).

40 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

of the typical piezoceramics (20–30 Mrayls) is significantly improved by

forming a composite structure, that is, by replacing some of the heavy, stiff

ceramic with a light, soft polymer. Piezoelectric composite materials are

especially useful for underwater sonar and medical diagnostic ultrasonic

transducer applications. Fujifilm unveiled their bendable and foldable 0:3

composites (PZT fine powder was mixed in a polymer film) through a

news release; its superior acoustic performance seems to be promising

for flat-speaker applications.

1.2.4 Thin-Films

Both zinc oxide (ZnO) and aluminum nitride (AlN) are simple binary

compounds with a Wurtzite-type structure, which can be sputter-

deposited as a c-axis oriented thin film on a variety of substrates. Since

ZnO has reasonable piezoelectric coupling, thin films of this material are

widely used in bulk acoustic and SAW devices. The fabrication of highly

oriented (along c) ZnO films have been studied and developed extensively.

However, the performance of ZnO devices is limited, due to their low pie-

zoelectric coupling (20%–30%). PZT thin films are expected to exhibit

higher piezoelectric properties. At present the growth of PZT thin films

is being carried out for use in microtransducers and microactuators.

1.2.4.1 Thin Film Preparation Technique

Techniques for fabrication of oxide thin films are classified into phys-

ical and chemical processes:

(a) Physical processes

electron beam evaporation

RF sputtering, DC sputtering

ion beam sputtering

ion plating

(b) Chemical processes

sol-gel method (dipping, spin coating etc.)

chemical vapor deposition (CVD)

MOCVD

liquid phase epitaxy, melting epitaxy, capillary epitaxy, etc.

Sputtering has been most commonly used for ferroelectric thin films

such as LiNbO

, PLZT, and PbTiO

.Fig. 1.23 shows the principle of a mag-

netron sputtering apparatus. Heavy Ar plasma ions bombard the cathode

(target) and eject its atoms. These atoms are deposited uniformly on the

substrate in an evacuated enclosure. Choosing a suitable substrate and

deposition condition, single crystal-like epitaxially deposited films can

be obtained. The sol-gel technique has also been employed for processing

411.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

PZT films. Applications of thin film ferroelectrics include memories, SAW

devices, piezo sensors and micromechatronic or MEMS (micro electrome-

chanical system) devices.

As was discussed with regard to Fig. 1.8 in the previous section, (0 0 1)

epitaxially oriented PZT rhombohedral composition films are most

suitable from the application viewpoint.

Kalpat et al. demonstrated

(0 0 1) and (1 1 1) oriented films on the same Pt-coated Si substrate by

changing the rapid thermal annealing profile.

Fig. 1.24A and B shows

the PZT (70/30) films with (0 0 1) and (1 1 1) orientations.

1.2.4.2 MEMS Application

The micromachining process used by the author’s group to fabricate the

PZT micropump is illustrated in Fig. 1.25. The etching process for the sil-

icon:PZT unit is shown on the left-hand side of the figure and that for the

glass plate is shown on the right-hand side. A schematic of the micropump

for a blood tester is pictured in Fig. 1.26.

The blood sample and test che-

micals enter the system through the two inlets, shown in Fig. 1.26, are

mixed in the central cavity, and finally are passed through the outlet

for analysis. The movement of the liquids through the system occurs

through the bulk bending of the PZT diaphragm in response to the drive

potential provided by the interdigital surface electrodes.

Gas

Heater

Holder

Substrate

Magnetic

field

Vacuum pump

Target

Plasma

High f power supply

FIG. 1.23 Principle of a magnetron sputtering apparatus.

42 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

(

)(

)

200

400

600

800

0 20 40 60 80 100

PZT(100)

PZT(111)

Annealing time (s) 2q

Temperature (°C)

20 25 30 35 40 45 50

CPS (abritrary units)

PZT(100) PZT(200)

PZT(111)

FIG. 1.24 Epitaxially grown rhombohedral (70/30) PZT films with (0 0 1) and (1 1 1) ori-

entations: (A) optimum rapid thermal annealing profiles and (B) X-ray diffraction patterns

for films grown according to these profiles.

Pt/Ti/Silicon on

insulator wafer (SOI)

PZT thin film sputtering

Top electrode Au/Ti deposition

Top electrode patterning

(photolithography and lift-off)

Deep reactive Ion-etching (DRIE)

membrane formation

Anodic bonding to silicon

wafer

Masking and wet etching

formation of cavity in glass

Bottom glass plate

FIG. 1.25 The micromachining process used to fabricate a PZT micropump.

Glass

wafer

Inlet Inlet

Outlet

SiO2/Si

Top

electrode Bottom

electrode

PZT IDTs

FIG. 1.26 A schematic diagram of the structure of a PZT micropump.

Actual size:

4.5 mm4.5 mm2 mm.

431.2 PIEZOELECTRIC MATERIALS—PRESENT STATUS

1.2.4.3 Constraints in Thin/Thick Films

The thin film structure is inevitably affected by four significant

parameters:

(1) Size constraints: Similar to a powder sample, there may exist a

critical film thickness below which the ferroelectricity would

disappear.

(2) Stress from the substrate: Tensile or compressive stress is generated due

to thermal expansion mismatch between the film and the substrate,

sometimes leading to a higher coercive field for domain reorientation.

Curie temperature is also modified with a rate of 50°C per 1 GPa. We

may manipulate the Curie temperature to increase or decrease,

theoretically owing to the induced stress.

(3) Epitaxial growth: Crystal orientation dependence should be also

considered, similar to the case of single crystals. An example can be

found in a rombohedral composition PZT, which is supposed to

exhibit the maximum performance when the P

direction is arranged

57 degree cant from the film normal direction (i.e., (0 0 1)

crystallographic orientation).

(4) Preparation constraint: Si substrate requires a low sintering

temperature of the PZT film. Typically 800°C for a short period is

the maximum for preparing the PZT, which may limit the

crystallization of the film, leading to the reduction of the properties.

A metal electrode on a Si wafer such as Pt also limits the

crystallinity of the PZT film.

1.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW

OF APPLICATIONS

1.3.1 Pressure Sensors/Accelerometers/Gyroscopes

One of the basic applications of piezoelectric ceramics is a gas igniter.

The very high voltage generated in a piezoelectric ceramic under applied

mechanical stress can cause sparking and ignite the gas. There are two

means to apply the mechanical force: either by a rapid, pulsed application

or by a more gradual, continuous increase.

Piezoelectric ceramics can be employed as stress sensors and accelera-

tion sensors, because of the direct piezoelectric effect.Fig. 1.27 shows a 3D

stress sensor designed by Kistler. By combining an appropriate number

of quartz crystal plates (extensional and shear types), the multilayer

device can detect 3D stresses.

Fig. 1.28 shows a cylindrical gyroscope commercialized by NEC-Tokin

(Japan).

The cylinder has six divided electrodes, one pair of which is

44 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

used to excite the fundamental bending vibration mode, while the other

two pairs are used to detect the acceleration. When the rotational acceler-

ation is applied about the axis of this gyro, the voltage generated on the

electrodes is modulated by the Coriolis force. By subtracting the signals

between the two sensor electrode pairs, a voltage directly proportional

to the acceleration can be obtained.

1.3.2 Piezoelectric Vibrators/Ultrasonic Transducers

1.3.2.1 Piezoelectric Vibrators

In the use of mechanical vibration devices such as filters or oscillators,

the size and shape of a device are very important, and both the vibra-

tional mode and the ceramic material must be considered. The resonance

+++++

–––––

+++++

–––––

++++

–––––

––––

++++

––––

++++

––––

FIG. 1.27 3D stress sensor (by Kistler).

Support

Holde

Vibrator

Lead

FIG. 1.28 Cylindrical gyroscope (by NEC-Tokin).

451.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

frequency of the bending mode in a centimeter-size sample that ranges

from 100 to 1000 Hz, which is much lower than that of the thickness

mode (100 kHz). For these vibrator applications the piezoceramic should

have a high mechanical quality factor (Q

) rather than a large piezoelec-

tric coefficient d; that is, hard piezoelectric ceramics are preferable.

For speakers or buzzers audible by humans, devices with a rather low

resonance frequency are used (100 Hz–2 kHz range). Examples are a

unimorph consisting of one piezoceramic plate bonded with a metallic

shim, a bimorph consisting of two piezoceramic plates bonded together,

and a piezoelectric fork consisting of a piezo-device and a metal fork. A

piezoelectric buzzer design has merits such as high electric power effi-

ciency, compact size, and long life. A state-of-the-art speaker has only a

0.7 mm ultra-thin thickness and a 0.4 g weight.

The power consumption

is only 1/5–2/3 compared to electromagnetic types. The piezo-speaker

has wide frequency range and high sound pressure, and in particular

no interference with credit cards (with a magnetic memory strip), which

is important nowadays.

1.3.2.2 Ultrasonic Transducers

Ultrasonic waves are now used in various fields. The sound source

is made from piezoelectric ceramics, as well as magnetostrictive mate-

rials. Piezoceramics are generally superior in efficiency and in size to

magnetostrictive materials. In particular, hard piezoelectric materials

with a high Q

are preferable because of high power generation

without heat generation. A liquid medium is usually used for sound

energy transfer. Ultrasonic washers; ultrasonic microphones; sonars for

short-distance remote control, underwater detection, and fish finding;

and nondestructive testers are typical applications of piezoelectric mate-

rials. Ultrasonic scanning detectors are useful in medical electronics for

clinical applications ranging from diagnosis to therapy and surgery.

(a) Ultrasonic imaging

One of the most important applications is based on the ultrasonic

echo field.

63,64

Ultrasonic transducers convert electrical energy into

a mechanical form when generating an acoustic pulse, and they con-

vert mechanical energy into an electrical signal when detecting its

echo. The transmitted waves propagate into a body and echoes are

generated which travel back to be received by the same transducer.

These echoes vary in intensity according to the type of tissue or body

structure, thereby creating images. An ultrasonic image represents

the mechanical properties of the tissue, such as density and elasticity.

We can recognize anatomical structures in an ultrasonic image

since the organ boundaries and fluid-to-tissue interfaces are easily

46 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

discerned. The ultrasonic imaging process can also be carried out in

real time. This means we can follow rapidly moving structures such

as the heart without motion distortion. In addition, ultrasound is

one of the safest diagnostic imaging techniques. It does not use ioniz-

ing radiation like X-rays and thus is routinely used for fetal and obstet-

rical imaging. Useful areas for ultrasonic imaging include cardiac

structures, the vascular systems, the fetus, and abdominal organs such

as the liver and kidneys. In brief, it is possible to see inside the human

body without breaking the skin by using a beam of ultrasound.

Fig. 1.29 shows the basic ultrasonic transducer geometry. The trans-

ducer is mainly composed of three layers: matching layer, piezoelec-

tric ceramic, and backing layer.

One or more matching layers are

used on the surface of the piezoceramic array to increase sound trans-

missions into tissues. The backing is added to the rear of the trans-

ducer in order to dampen the acoustic backwave and to reduce the

pulse duration. Piezoelectric materials are used to generate and detect

ultrasound. In general, broadband transducers should be used for

medical ultrasonic imaging. The broad bandwidth response corre-

sponds to a short pulse length, resulting in better axial resolution.

Three factors are important in designing broad bandwidth trans-

ducers: acoustic impedance matching,ahigh electromechanical coupling

coefficient of the transducer, and electrical impedance matching. These

pulse echo transducers operate based on thickness mode resonance

of the piezoelectric thin plate. Further, a low planar mode coupling

coefficient, k

, is beneficial for limiting energies being expended in

nonproductive lateral mode. A large dielectric constant is necessary

to enable a good electrical impedance match to the system, especially

with tiny piezoelectric sizes.

There are various types of transducers used in ultrasonic imaging.

Mechanical sector transducers consist of single, relatively large reso-

nators and can provide images by mechanical scanning such as wob-

bling. Multiple element array transducers permit discrete elements to

be individually accessed by the imaging system and enable electronic

focusing in the scanning plane to various adjustable penetration

depths through the use of phase delays. Two basic types of array trans-

ducers are linear and phased (or sector). A linear array is a collection of

elements arranged in one direction, producing a rectangular display

(see Fig. 1.30). A curved linear (or convex) array is a modified linear

array whose elements are arranged along an arc to permit an enlarged

trapezoidal field of view. The elements of these linear type array

transducers are excited sequentially group by group with the sweep

of the beam in one direction. These linear array transducers are used

for radiological and obstetrical examinations. On the other hand, in a

471.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

phased array transducer the acoustic beam is steered by signals that

are applied to the elements with delays, creating a sector display. This

transducer is useful for cardiology applications where positioning

between the ribs is necessary.

Figure 1.31 demonstrates the superiority of the PZN-PT single crys-

tal to the PZT ceramic for medical imaging transducer applications,

Piezoelectric element

Matching layer

Ultrasonic

beam

Backing

Input

pulse

FIG. 1.29 Basic transducer geometry for acoustic imaging applications.

Piezoelectric vibrato

Backing

(A)

(

)

FIG. 1.30 Linear array type ultrasonic probe: (A) vibrator element and (B) structure of an

array-type ultrasonic probe.

48 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

developed by Toshiba Corporation.

Conventionally, the medical

doctor needs to use two different frequency PZT probes, one

(2.5 MHz) for checking wider and deeper area and the other

(3.75 MHz) for monitoring the specified area with a better resolution.

The PZN-PT single crystal (with very high k

and k

) probe provides

two additional merits: (1) wide bandwidth—without changing the

probe, the doctor can just switch the drive frequency from 2.5 to

3.75 MHz— and(2) a strong signal; because of the high electromechan-

ical coupling, the receiving signal level is enhanced more than double

compared with the PZT probe.

(b) Sonochemistry

Fundamental research on “sonochemistry” is now very rapidly

occurring. With using the “cavitation” effect, toxic materials such as

dioxin and trichloroethylene can be easily transformed into innocuous

materials at room temperature. Ultrasonic distillation is also possible

at room temperature for obtaining highly concentrated Japanese sak

Unlike the regular boiling distillation, this new method gives sak

much higher alcoholic concentration, while keeping gorgeous taste

and fragrance. Fig. 1.32A shows the alcoholic concentration in the base

solution and mist. This high-quality sak

e product is now commer-

cially available.

High power ultrasonic technology is applicable to transdermal

drug delivery. The Penn State researchers are working to commercial-

ize a “needle-free” injection system of insulin by using cymbal piezo-

actuators (see Fig. 1.32B).

FIG. 1.31 Ultrasonic imaging with the two PZT ceramic probes (left) and with the PZN-PT

single crystal probe (right). Courtesy of Toshiba.

491.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

1.3.2.3 Resonators/Filters

When a piezoelectric body vibrates at its resonant frequency, it absorbs

considerably more energy than at other frequencies, resulting in a dram-

atic decrease in the impedance. This phenomenon enables piezoelectric

materials to be used as a wave filter. A filter is required to pass a certain

selected frequency band or to block a given band. The bandwidth of a

filter fabricated from a piezoelectric material is determined by the square

of the coupling coefficient k, that is, it is nearly proportional to k

The background is from the relation k31 2=1k312



¼π2=4



Δf=fR

ðÞ,

where Δf¼f

f

, and the bandwidth is provided by Δf. Quartz crystals

with a very low k value of about 0.1 can pass very narrow frequency

bands of approximately 1% of the center resonance frequency. On the

other hand, PZT ceramics with a planar coupling coefficient of about

0.5 can easily pass a band of 10% of the center resonance frequency.

The sharpness of the passband is dependent on the mechanical quality

factor Q

of the materials. Quartz also has a very high Q

of about 10

which results in a sharp cut-off to the passband and a well-defined

oscillation frequency.

A simple resonator is a thin disc type, electroded on its plane faces

and vibrating radially, for filter applications with a center frequency

ranging from 200 kHz to 1 MHz and with a bandwidth of several per-

cent of the center frequency. For a frequency of 455 kHz the disc diam-

eter needs to be about 5.6 mm. However, if the required frequency is

higher than 10 MHz, other modes of vibration such as the thickness

extensional mode are exploited, because of its smaller size. The

100

(

)(

)

Ethanol mol concentration in solution (mol %)

Boiling distillation

Ethanol mol concentration in mist (mol %)

1000

10°C 30°C 50°C

FIG. 1.32 (A) Room temperature distillation with high ultrasonic power and (B) a trans-

dermal insulin drug delivery system using cymbal transducers.

(A) Courtesy of Matsuura

Brewer and (B) Courtesy of Paul Perreault.

50 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

trapped-energy type filters made from PZT ceramics have been widely

used in the intermediate frequency range for applications such as the

10.7 MHz FM radio receiver and transmitter. When the trapped-energy

phenomena are utilized, the overtone frequencies are suppressed. The

plate is partly covered with electrodes of a specific area and thickness.

The fundamental frequency of the thickness mode of the ceramic

beneath the electrode is less than that of the unelectroded portion,

because of the extra inertia of the electrode mass. The lower-frequency

wave of the electroded region cannot propagate into the unelectroded

region. The higher-frequency overtones, however, can propagate away

into the unelectroded region. This is called the trapped-energy principle.

Fig. 1.33 shows a schematic drawing of a trapped-energy filter.Inthis

structure the top electrode is split so that coupling between the two

parts will only be efficient at resonance. More stable filters suitable

for telecommunication systems have been made from single crystals

such as quartz or LiTaO

1.3.3 SAW Devices

Asurface acoustic wave (SAW), also called a Rayleigh wave, is essentially a

coupling between longitudinal and shear waves. The energy carried by

the SAW is confined near the surface. An associated electrostatic wave

exists for a SAW on a piezoelectric substrate, which allows electroacoustic

coupling via a transducer. The advantages of SAW technology are the

following

69,70

(1) The wave can be electroacoustically accessed and trapped at the

substrate surface and its velocity is approximately 10

times slower

than an electromagnetic wave.

(2) The SAW wavelength is on the same order of magnitude as line

dimensions produced by photolithography and the lengths for both

short and long delays are achievable on reasonably sized substrates.

Electrode

Ceramic plate

Top Bottom

FIG. 1.33 Schematic drawing of a trapped-energy filter.

511.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

There is a very broad range of commercial system applications that

include front-end and IF (intermediate frequency) filters, CATV (commu-

nity antenna television) and VCR (video cassette recorder) components,

synthesizers, analyzers, and navigators. In SAW transducers, finger

(interdigital) electrodes provide the ability to sample or trap the wave,

and the electrode gap gives the relative delay. A SAW filter is composed

of a minimum of two transducers. A schematic of a simple SAW bidirec-

tional filter is shown in Fig. 1.34. A bidirectional transducer radiates

energy equally from each side of the transducer. Energy that is not asso-

ciated with the received signal is absorbed to eliminate spurious

reflection.

Various materials are currently being used for SAW devices. The most

popular single-crystal SAW materials are lithium niobate and lithium tan-

talate. The materials have different properties depending on the cut of the

material and the direction of propagation. The fundamental parameters

considered when choosing a material for a given device application are

SAW velocity, temperature coefficients of delay (TCD), electromechanical

coupling factor, and propagation loss. SAWs can be generated and

detected by spatially periodic, interdigital electrodes on the plane surface

of a piezoelectric plate. A periodic electric field is produced when an RF

source is connected to the electrode, thus permitting piezoelectric cou-

pling to a traveling surface wave. If an RF source with a frequency, f,is

applied to the electrode having periodicity, d, energy conversion from

an electrical to mechanical form will be maximum when

f¼f0¼vs=d, (1.38)

where v

is the SAW velocity and f

is the center frequency of the device.

The SAW velocity is an important parameter determining the center fre-

quency. Another important parameter for many applications is tempera-

ture sensitivity. For example, the temperature stability of the center

Input Output

SAW

Interdigital electrode

Piezoelectric substrate

FIG. 1.34 Fundamental structure of a surface acoustic wave device.

52 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

frequency of SAW bandpass filters is a direct function of the temperature

coefficient for the velocity and the delay for the material used. The first-

order temperature coefficient of delay is given by

1=τðÞdτ=dTðÞ¼1=LðÞdL=dTðÞ1=vs

ðÞdvs=dTðÞ, (1.39)

where τ¼L/v

is the delay time and Lis the SAW propagation length. The

surface wave coupling factor, ks2, is defined in terms of the change in SAW

velocity that occurs when the wave passes across a surface coated with a

thin massless conductor, so that the piezoelectric field associated with the

wave is effectively short-circuited. The coupling factor, ks2, is expressed by

ks2¼2vfvm

ðÞ=vf, (1.40)

where v

is the free surface wave velocity and v

is the velocity on the

metallized surface. In actual SAW applications, the value of ks2relates

to the maximum bandwidth obtainable and the amount of signal loss

between input and output, which determines the fractional bandwidth

as a function of minimum insertion loss for a given material and filter.

Propagation loss is one of the major factors that determines the insertion

loss of a device and is caused by wave scattering at crystalline defects and

surface irregularities. Materials that show high electromechanical cou-

pling factors combined with small temperature coefficients of delay are

generally preferred. The free surface velocity, v

, of the material is a func-

tion of the cut angle and propagation direction. The TCD is an indication

of the frequency shift expected for a transducer due to a temperature

change and is also a function of the cut angle and propagation direction.

The substrate is chosen based on the device design specifications that

include operating temperature, fractional bandwidth, and insertion loss.

Piezoelectric single crystals such as 128 °Y-X(128 °-rotated-Y-cut

and X-propagation)—LiNbO

and X-112°Y(X-cut and 112 °-rotated-Y-

propagation)—LiTaO

have been extensively employed as SAW sub-

strates for applications in VIF filters. A c-axis oriented ZnO thin film

deposited on a fused quartz, glass, or sapphire substrate has also been

commercialized for SAW devices. Table 1.4 summarizes some important

material parameters for these SAW materials.

A delay line can be formed from a slice of glass such as PbO or K

O-

doped SiO

glass in which the velocity of sound is nearly independent

of temperature. PZT ceramic transducers are soldered on two metallized

edges of the slice of glass. The input transducer converts the electrical sig-

nal to a shear acoustic wave that travels through the slice. At the output

transducer the wave is reconverted into an electrical signal delayed by

the length of time taken to travel around the slice. Such delay lines are

used in color TV sets to introduce a delay of approximately 64 μs and

are also employed in videotape recorders.

531.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Recent development for SAW actuator applications are interesting. A

liquid transportation system was developed by using a standing-wave

type SAW device.

A liquid droplet can be transported by controlling

the SAW wave.

1.3.4 Micromass Sensor

1.3.4.1 Biosensor

Quartz is not only for timers of clocks, but is also used for various

micromass sensors. Because the mechanical quality factor Q

is very

large (¼10

), the monitoring resolution of the resonance frequency reaches

Δf

¼10

6

. Thus, even a small mass change on the quartz surface can be

finely detected through the resonance frequency shift.

This micromass sensor can be utilized for a biosensor for detecting

bacteria, such as Escherichia coli and salmonella. Levels as low as

–10

cells per mL are already critical to humans in the case of sal-

monella. Quartz oscillators can be used to detect this small amount

of salmonella bacteria. Fig. 1.35A shows the principle of this bio-

sensor, where the antibody/phage is coated on a single crystal quartz

oscillator. Once particular bacteria are captured selectively by the anti-

bodies, the surface mass of the oscillator is increased (see the SEM

photo of captured bacteria in Fig. 1.35B). The sensitivity 10

cells per

mL can be obtained.

TABLE 1.4 SAW Material Properties

Material

Cut-Propagation

direction

(%)

TCD

(ppm/C) V

(m/s) ε

Single

crystal

Quartz ST-X 0.16 0 3158 4.5

LiNbO

128 degree Y-X5.5 74 3960 35

LiTaO

X112 degree-Y0.75 1 8 3290 42

(1 1 0)–<001>0.8 0 3467 9.5

Ceramici PZT-In

(Li

3/5

2/5

1.0 10 2270 690

(Pb,Nd)(Ti,Mn,

In)O

2.6 <1 2554 225

Thin film ZnO/glass 0.64 15 3150 8.5

ZnO/Sapphire 1.0 30 5000 8.5

54 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.3.4.2 Viscosity Sensor

Several companies, including Stanford Research Systems and Ulvac,

Japan, commercialized a microbalance to measure the viscosity of the liq-

uid. They used a thickness-shear mode of the AT-cut quartz for intention-

ally enhancing the resonance frequency shift by the viscosity.

1.3.5 Piezoelectric Transformers

When input and output terminals are fabricated on a piezo-device and

input/output voltage is changed through the vibration energy transfer,

the device is called a piezoelectric transformer. Piezoelectric transformers

were used in color TVs in the early 1970s, because of their compact size

in comparison with the conventional electromagnetic coil-type transfor-

mers. Since serious problems were found in terms of mechanical strength

(collapse occurred at the nodal point!) and in heat generation, the develop-

ment was terminated. However, because recent laptop computers with a

liquid crystal display require a very thin, no electromagnetic-noise

transformer to start the glow of a fluorescent back-lamp, the development

of the piezotransformer has revived, and the previous problems (mechan-

ical strength and heat generation) have been almost overcome in these

20 years.

Since the original piezotransformer was proposed by Rosen,

a variety

of such transformers has been investigated. Fig. 1.36 shows a fundamental

structure where two differently poled parts coexist in one piezoelectric

Substrate

Selectivity

Bacteria

Antibody/phage:

(

)

Antibodies/phages

Bacteria

Gold

Antibodies

(

)

Quartz

FIG. 1.35 (A) Principle of a biosensor, where the antibody/phage is coated on a single

crystal quartz oscillator. Once particular bacteria are captured selectively by the antibodies

(B), the surface mass of the oscillator is increased.

L1L2

Low voltage

input High voltage

output

FIG. 1.36 Piezoelectric transformer proposed by Rosen.

551.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

plate. A standing wave with a wavelength equal to the sample length is

excited, and a half wavelength exists on both the input (L

) and output

) parts. The voltage rise ratio r(step-up ratio) is given for the unloaded

condition by the following:

r¼4=π2



k31k33 QML2=tðÞ2ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s33E=s11 E

=1+ ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

s33D=s11 E

i

:(1.41)

The rratio is increased with increasing (L

/t), where tis the thickness.

The derivation process can be found in Ref. 20.

NEC proposed a multilayer-type transformer (Fig. 1.37) in order to

increase the step-up ratio.

Usage of the third-order longitudinal mode

is another idea to distribute the stress concentration.

Step-down transformers for adaptor applications for portable equip-

ment such as laptop computers and mobile phones have also been devel-

oped. Fig. 1.38 shows a credit-card size 35 W adaptor for a laptop

computer, developed by Face Electronics, Taiheiyo Cement, in collabora-

tion with The Penn State University.

1.3.6 Piezoelectric Actuators

Piezoelectric and electrostrictive devices have become key components

in smart actuator systems such as precision positioners, miniature ultra-

sonic motors (USMs), and adaptive mechanical dampers. This section

FIG. 1.37 Multilayer-type transformer by NEC.

56 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

reviews the developments of piezoelectric actuators with particular focus

on device designs, drive/control methods, and applications.

Piezoelectric actuators are forming an interdisciplinary field between

electronic and structural ceramics.

77–80

Application fields are classified

into three categories: positioners, motors, and vibration suppressors.

The manufacturing precision of optical instruments such as lasers and

cameras, and the positioning accuracy for fabricating semiconductor chips

that must be adjusted using solid-state actuators, are generally on the

order of 0.1 μm. Regarding conventional electromagnetic motors, tiny

motors smaller than 1 cm are often required in office or factory automation

equipment and are rather difficult to produce with sufficient energy effi-

ciency. Piezoelectric motors whose efficiency is insensitive to size are con-

sidered superior in the micromotor area. Vibration suppression in space

structures and military vehicles using piezoelectric actuators is another

promising field of application.

Solid-state displacement transducers controlled by temperature (shape

memory alloy) or a magnetic field (magnetostrictive alloy) have been pro-

posed, but they are generally inferior to the piezoelectric/electrostrictive

ceramic actuators because of current technological trends aimed at reduced

driving power and miniaturization.

The shape memory actuator is too

slow in response with a very low energy efficiency, while the magnetostric-

tor requires a driving coil that is very bulky and generates magnetic noise.

FIG. 1.38 Credit-card size laptop computer adaptor (35 W) using a piezoelectric step-

down transformer (below), in comparison with a commercial adaptor with an electromag-

netic transformer (top).

571.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

1.3.6.1 Actuator Designs

Two of the most popular actuator designs are the multilayers

and

bimorphs (see Fig. 1.39). The multilayer, in which roughly 100 thin piezo-

electric ceramic sheets are stacked together, has the advantages of low

driving voltage (100 V), quick response (10 μs), high generative force

(1 kN), and high electromechanical coupling. But the displacement, on

the order of 10 μm, is not sufficient for some applications. This contrasts

with the characteristics of the bimorph, which consists of multiple piezo-

electric and elastic plates bonded together to generate a large bending dis-

placement of several hundred μm, but it has relatively low response time

(1 ms) and generative force (1 N).

A 3D positioning actuator with a stacked structure was proposed by a

German company, Physik Instrumente, where shear strain was utilized to

generate the xand ydisplacements.

Polymer-packed PZT bimorphs

have been commercialized by ACX for vibration reduction/control appli-

cations in smart structures.

The market research conducted in 1998 by Japan Technology Transfer

Association clarified that the actual demands on the actuators are as fol-

lows: 100 μm displacement, 100 N force, and 100 μs response. Because

neither the multilayer nor the bimorph can satisfy the actual demand,

Moonie

Multilayer

Bimorph

Single plate

FIG. 1.39 Typical designs for ceramic actuators: multilayer, moonie, and bimorph.

58 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

composite actuator structures called “moonie” and “cymbal” have been

developed to provide characteristics intermediate between the multi-

layer and bimorph actuators. This transducer exhibits an order of mag-

nitude larger displacement than the multilayer, and a much larger

generative force with a quicker response than the bimorph.

The device

consists of a thin multilayer piezoelectric element and two metal plates

with a narrow moon-shaped or cymbal-shaped cavity bonded together

as shown in Fig. 1.39. The moonie with a size of 552.5 mm

can gen-

erate a 20 μm displacement under 60 V, eight times as large as the gen-

erative displacement produced by a multilayer of the same size.

This

compact actuator has been utilized in a miniaturized laser beam

scanner.

1.3.6.2 Drive/Control Techniques

Piezoelectric actuators may be classified into two categories, based on

the type of driving voltage applied to the device and the nature of

the strain induced by the voltage (Fig. 1.40): (1) rigid displacement devices

for which the strain is induced unidirectionally along the direction of

the applied DC field and (2) resonating displacement devices for

which the alternating strain is excited by an AC field at the mechanical

resonance frequency (USMs). The first can be further divided into

two types: servo displacement transducers (positioners), controlled by

a feedback system through a position-detection signal, and pulse drive

motors operated in a simple on/off switching mode, exemplified by

inkjet printers.

The material requirements for these classes of devices are somewhat

different, and certain compounds will be better suited to particular appli-

cations. The USM, for instance, requires a very hard piezoelectric with a

high mechanical quality factor Q

, to suppress heat generation. Note that

the resonating strain/displacement is amplified by a factor of Q

, in com-

parison with the off-resonance strain/displacement (i.e., dEL).

Driving

the motor at the antiresonance frequency, rather than at resonance, is also

an intriguing technique to reduce the load on the piezoceramic and the

power supply.

The servo displacement transducer suffers most from

strain hysteresis and, therefore, a PMN electrostrictor is used for this pur-

pose. The pulse drive motor requires a low permittivity material aimed at

quick response with a certain power supply (a high-power supply is

expensive from the practical device application viewpoint!) rather than

a small hysteresis, so soft PZT piezoelectrics are preferred rather than

the high-permittivity PMN for this application.

Pulse drive techniques for ceramic actuators are very important for

improving the response of the device.

88,89

Fig. 1.41 shows transient vibra-

tions of a bimorph excited after a pseudostep voltage is applied. The rise

time is varied around the resonance period (n is the time scale with a unit

591.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Servo

drive

On/off

drive

Electrostrictive

material

(Hysteresis-free)

Soft piezoelectric

material

(Low permittivity)

Hard piezoelectric

material

(High Q)

Feedback

Rigid

strain

Servo

Displacement

Transducer

Pulse drive

motor

Ultrasonic

motor

Resonant

strain

Pulse

Sine

FIG. 1.40 Classification of piezoelectric/electrostrictive actuators.

Electric field

displacement

Tip

Electric field

10 m

displacement

Tip

(a) n = 1

(b) n = 2

Electric field

displacement

Tip

FIG. 1.41 Transient vibration of a bimorph excited after a pseudostep voltage applied.

Here, nis a time scale with a unit of 1/2 of the resonance period (i.e., 2n¼the resonance

period).

60 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

of T

/2, where T

stands for the resonance period). It is concluded that the

overshoot and ringing of the tip displacement is completely suppressed

when the rise time is precisely adjusted to the resonance period of the

piezo-device (i.e., for n¼2).

A flight actuator was developed using a

pulse-drive piezoelectric element and a steel ball. A 5-μm rapid displace-

ment induced in a multilayer actuator can hit a 2-mm steel ball up to

20 mm in height. A dot-matrix printer head has been developed using a

flight actuator.

By changing the drive voltage pulse width, the move-

ment of the armature was easily controlled to realize no vibrational ring-

ing or double hitting.

1.3.6.3 Servo Displacement Transducers

A typical example of a servo displacement transducer is found in a

space truss structure proposed by the Jet Propulsion Laboratory.

stacked PMN actuator was installed at each truss nodal point and oper-

ated so that unnecessary mechanical vibration was suppressed immedi-

ately. A Hubble Telescope has also been proposed using multilayer

PMN electrostrictive actuators to control the phase of the incident light

wave in the field of optical information processing (Fig. 1.42).

The

PMN electrostrictor provided superior adjustment of the telescope image

because of negligible strain hysteresis.

The United States Army is interested in developing a rotor control

system in helicopters. Fig. 1.43 shows a bearingless rotor flexbeam with

attached piezoelectric strips.

Various types of PZT-sandwiched beam

structures have been investigated for such a flexbeam application and

for active vibration control.

1.3.6.4 Pulse Drive Motors

A dot matrix printer is the first widely commercialized product using

ceramic actuators. Each character formed by such a printer was originally

composed of a 24 24 dot matrix. A printing ribbon is subsequently

impacted by a multiwire array. A sketch of the printer head appears in

Fig. 1.44A.

The printing element is composed of a multilayer piezoelec-

tric device, in which 100 thin ceramic sheets 100 μm in thickness were

stacked, together with a sophisticated magnification mechanism

(Fig. 1.44B). The magnification unit is based on a monolithic hinge lever with

a magnification of 30 , resulting in an amplified displacement of 0.5 mm

and energy transfer efficiency >50%.

Fig.1.45 illustrates the recent inkjet printer produced by Seiko Epson,

which PZT thin plates were laminated with vibration,chamber, and commu-

nicationplates to create a unimorph actuationmechanism. Using thecofiring

technique with PZT and ZrO

elastic parts for manufacturing this, ML chips

head (MACH), Epson achieved superior stability in ink chamber vibration

611.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

FIG. 1.42 Hubble Telescope using three PMN electrostrictive multilayer actuators for

optical image correction.

Lag pin

Pitch link

Blade

Torque tube

Hub

Piezoelectric

crystals

Flexbeam

FIG. 1.43 Bearingless rotor flexbeam with attached piezoelectric strips. A slight change in

the blade angle provides for enhanced controllability.

Head

element

Platen

Paper

Ink ribbon

Guide

Wire

Stroke amplifier

Wire

Wire guide

(

)(

)

Piezoelectric

actuator

FIG. 1.44 (A) Structure of a dot-matrix printer head (NEC) and (B) a differential-type pie-

zoelectric printer-head element. A sophisticated monolithic hinge lever mechanism amplifies

the actuator displacement by 30 times.

62 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

and for various inks. In addition, more importantly, the manufacturingcost

reduced dramatically by adopting this cofiring technique.

Toyota developed a Piezo TEMS (Toyota Electronic Modulated Suspen-

sion), which is responsive to each protrusion on the road in adjusting the

damping condition, and installed it on a Celcio (equivalent to a Lexus,

internationally) in 1989.

In general, as the damping force of a shock

absorber in an automobile is increased (i.e., “hard” damper), the control-

lability and stability of a vehicle are improved. However, comfort is sacri-

ficed because the road roughness is easily transferred to the passengers.

The purpose of the electronically controlled shock absorber is to obtain

both controllability and comfort simultaneously. Usually the system is

set to provide a low damping force (“soft”) so as to improve comfort,

and the damping force is changed to a high position according to the road

condition and the car speed to improve the controllability. In order to

respond to road roughness, a very high response of the sensor and actu-

ator combination is required.

Fig. 1.46 shows the structure of the electronically controlled shock

absorber. The sensor is composed of 5 layers of 0.5 mm thick PZT disks.

The detecting speed of the road roughness is about 2 ms and the resolution

of the up-down deviation is 2 mm. The actuator is made of 88 layers of

0.5 mm thick disks. Applying 500 V generates a displacement of about

50 μm, which is magnified by 40 times through a piston and plunger

pin combination. This stroke pushes the change valve of the damping

force down then opens the bypass oil route, leading to the decrease of

the flow resistance (i.e., “soft”).

The up-down acceleration and pitching rate were monitored when the

vehicle was driven on a rough road. When the TEMS system was used, the

MLChips

Upper electrode

Lower electrode

Vibration plate

Chamber plate

Communication plate

Nozzle

Ink chamber

Ink pass

0.5 mm

Ink supply hole

Adhesive layer

Stainless plate

PZT

FIG. 1.45 MACH Ink-jet printer head developed by Seiko Epson.

631.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

up-down acceleration was suppressed to as small as the condition fixed at

“soft,” providing comfort. At the same time, the pitching rate was also

suppressed to as small as the condition fixed at “hard,” leading to better

controllability.

In order to increase the diesel engine efficiency, high pressure fuel and

quick injection control are required. For this purpose, piezoelectric actu-

ators, specifically ML types, were adopted. The highest reliability of these

devices at an elevated temperature (150°C) for a long period (10 years) has

been achieved. Common-rail type injection valves have been widely com-

mercialized by Siemens, Bosch, and Denso Corp (Fig. 1.47).

Fig. 1.48 shows a walking piezomotor with four multilayer actuators

developed by Philips.

Two shorter actuators function as clamps and

the longer two provide the movement by an inchworm mechanism. A

major drawback of this inchworm design is the mechanical noise created

by the on-off drive (audible frequency due to the requirement lower than

the mechanical resonance of the system).

1.3.7 Ultrasonic Motors

The USM is one of the piezoelectric actuator categories. However, since

it has been maturing as an industry already, the author uses a different

section for its discussion.

FIG. 1.46 Toyota Electronic modulated suspension (TEMS) with a multilayer piezoelec-

tric actuator and a sensor.

64 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Electromagnetic motors were invented more than one hundred years

ago. While these motors still dominate the industry, a drastic improvement

cannot be expected except through new discoveries in magnetic or super-

conducting materials. Electromagnetic motors smaller than 1 cm exhibit an

energy efficiency <1% (more than 90% input electrical energy is spent for

heat generation in a wristwatch motor at present!). Therefore, the ultrasonic

motor with a piezoceramic, whose efficiency is insensitive to size, is gaining

widespread attention in the micromotor area. Fig. 1.49 shows the basic con-

struction of most USMs, which consist of a high-frequency power supply, a

Piezoelectric actuator

Control valve

Injector body

Nozzle

Displacement

amplification unit

FIG. 1.47 Common rail-type diesel injector with a piezoelectric multilayer actuator. Cour-

tesy by Denso Corp.

FIG. 1.48 Walking piezo motor using an inchworm mechanism with four multilayer pie-

zoelectric actuators by Philips.

651.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

vibrator, and a slider. The vibrator is composed of a piezoelectric driving

component and an elastic vibratory part, and the slider is composed of

an elastic moving part and a friction coat.

Although there had been some earlier attempts, the first practical USM

was proposed by Barth of IBM in 1973.

100

Various mechanisms based on

virtually the same principle were proposed by Lavrinenko et al.

101

and

Vasiliev

102

in the former USSR. Because of difficulty in maintaining con-

stant vibration amplitude with temperature rise and wear and tear, the

motors were not of much practical use at that time.

In the 1980s, with increasing chip pattern density, the semiconductor

industry began to demand much more precise and sophisticated posi-

tioners that would not generate magnetic field noise. This urgent need

accelerated the development of USMs. Another advantage of USMs over

conventional electromagnetic motors with expensive copper coils is the

improved availability of piezoelectric ceramics at a reasonable cost. Japa-

nese manufacturers are currently producing piezoelectric buzzers at

about 30–40 cents per unit.

Let us summarize the merits and demerits of the USM:

Merits

1. Low speed and high torque

Direct drive

2. Quick response, wide velocity range, hard brake, and no backlash

Excellent controllability

Fine position resolution

3. High power/weight ratio and high efficiency

Electrical

input

High frequency

power supply

Piezoelectric

driver

Stator

Elastic vibrator

piece

Friction

coat

Slider/rotor

Elastic sliding

piece

Mechanical

output

FIG. 1.49 Fundamental construction of an ultrasonic motor.

66 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

4. Quiet drive (driven at an inaudible frequency for humans)

5. Compact size and light weight

6. Simple structure and easy production process

7. Negligible effect from external magnetic or radioactive fields, and also

no generation of these fields

Demerits

8. Necessity for a high frequency power supply

9. Less durability due to frictional drive

10. Drooping torque vs. speed characteristics

1.3.7.1 Classification and Principles of USMs

The standing-wave type is sometimes referred to as a vibratory-coupler

type or a “woodpecker” type, where a vibratory piece is connected to a

piezoelectric driver and the tip portion generates an elliptical movement.

Fig. 1.50 shows a simple model proposed by Sashida.

103

A vibratory piece

is attached to a rotor or a slider with a slight cant angle θ. Take the x-ycoor-

dinate so that the xaxis is normal to the rotor face. When a vibration

displacement,

ux¼u0sin ωt+αðÞ (1.42)

is excited at the piezoelectric vibrator, the vibratory piece generates bend-

ing because of restriction by the rotor, so the tip moves along the rotor face

between A!Band freely between B!A. If the vibratory piece and the

piezovibrator are tuned properly, they form a resonating structure, and

if the bending deformation is sufficiently small compared with the length,

the tip locus during the free vibration (B!A) is represented by

Oscillator

Piezoelectric vibrator

(

)

Vibratory

piece

Rotor

FAFr

(

)

B¢

A¢d

FIG. 1.50 Vibratory coupler type motor (A) and its tip locus (B).

671.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

x¼u0sin ωt+αðÞ,

y¼u1sin ωt+βðÞ,(1.43)

which composes an elliptical locus. Therefore, only the duration A!B

provides a unidirectional force to the rotor through friction and, therefore,

an intermittent rotational torque or thrust. However, because of the inertia

of the rotor, the rotation speed ripple is not observed to be large. The

standing-wave type, in general, is low in cost (one vibration source)

and has high efficiency (up to 98% theoretically), but it lacks control in

both the clockwise and counterclockwise directions, in general.

By comparison, the propagating-wave type (a surface-wave or “surfing”

type) combines two standing waves with a 90 degree phase difference

both in time and in space. The principle is illustrated in Fig. 1.51. A surface

particle of the elastic body draws an elliptical locus due to the coupling of

longitudinal and transverse waves. This type requires, in general, two

vibration sources (i.e., sine and cosine) to generate one propagating wave,

leading to low efficiency (not more than 50%), but it is controllable in both

rotational directions by exchanging the driving voltage phase.

1.3.7.2 Standing Wave-Type Motors

Sashida developed a rotary-type motor similar to the fundamental

structure in Fig. 1.50.

103

Four vibratory pieces were installed on the edge

face of a cylindrical vibrator and pressed onto the rotor. This is one of the

prototypes that triggered the present active development of USMs. A rota-

tion speed of 1500 rpm, torque of 0.08 Nm, and an output of 12 W (effi-

ciency 40%) were obtained under an input of 30 W at 35 kHz. This type

of USM can provide a speed much higher than the inchworm types,

because of its high operating frequency and amplified vibration displace-

ment at the resonance frequency.

Slider

Moving direction

Propagation direction

Elastic body

A⬘

FIG. 1.51 Principle of the propagating wave type motor.

68 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Hitachi Maxell significantly improved the torque and efficiency by using

atorsion coupler replacing Sashida’s vibratory pieces (Fig. 1.52), and by

increasing the pressing force with a bolt.

104

The torsion coupler looks like

an old-fashioned TV channel knob, consisting of two legs, which transform

longitudinal vibration generated by the Langevin vibrator to a bending

mode of the knob disk, and a vibratory extruder. Notice that this extruder

is aligned with a certain cant angle to the legs, which transforms the bending

to a torsion vibration. This transverse moment coupled with the bending up-

down motion leads to an elliptical rotation on the tip portion, as illustrated in

Fig. 1.52B. The optimum pressing force to get the maximum thrust is

obtained, when the ellipse locus is deformed roughly by half. A motor

30 mm60 mm in size and with a 20–30 degrees in cant angle between

the leg and vibratory piece can generate torques as high as 1.3 N m with

an efficiency of 80%. However, this type provides only unidirectional rota-

tion. Note also that even though the drive of the motor is intermittent, the

output rotation becomes very smooth because of the inertia of the rotor.

In collaboration with Samsung Electro-Mechanics, Korea, The Penn

State University developed a zoom mechanism with two micro rotary

motors.

105–107

A micro motor called “metal tube type” consisting of a

metal hollow cylinder and two PZT rectangular plates was used as basic

micro actuators (see Fig. 1.53A). When we drive one of the PZT plates,

Plate X, a bending vibration is excited basically along the x0axis. However,

because of an asymmetric mass (Plate Y), another hybridized bending

mode is excited with some phase lag along the y0axis, leading to an

elliptical locus (“wobbling” vibration) in a clockwise direction, like a

Torsion coupler

Propeller

Al horn

Spacer

Al cylinder

Piezoelectric

disk

(

)(

)

FIG. 1.52 A mixed-mode ultrasonic motor incorporating a torsion coupler: (A) structure

of the entire motor and (B) motion of the torsion coupler.

691.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Hula-Hoop motion. In order to obtain a counterclockwise rotation, one

Plate Y is now driven. The rotor of this motor is a cylindrical rod with a

pair of stainless ferrule pressed with a spring. The assembly is shown

in Fig. 1.53B. The metal cylinder motor 2.4 mm in diameter and 12 mm

in length was driven at 62.1 kHz in both rotation directions. A no-load

speed of 1800 rpm and an output torque up to 1.8 mN m were obtained

for rotation in both directions under an applied root-mean-square (rms)

voltage of 80 V. A quite high maximum efficiency of about 28% for this

small motor is a noteworthy feature.

The world’s smallest camera module at the time, with both optical

zooming and auto focusing mechanisms for a cellular phone application,

was developed in 2003 (see Fig. 1.54).

107

Two micro USMs with 2.4 mm

diameter and 14 mm length were installed to control zooming and focus-

ing lenses independently in conjunction with screw mechanisms.

Nakamura et al. proposed a two-vibration-mode coupled-type motor

(Fig. 1.55), that is, a torsion Langevin vibrator was combined with three

multilayer actuators to generate larger longitudinal and transverse surface

displacements of the stator, as well as to control their phase difference.

108

The phase change can change the rotation direction.

Uchino et al. invented a π-shaped linear motor.

109

This linear motor is

equipped with a multilayer piezoelectric actuator and fork-shaped metal-

lic legs as shown in Fig. 1.56. Since there is a slight difference in the

mechanical resonance frequency between these two legs, the phase differ-

ence between the bending vibrations of both legs can be controlled by

changing the drive frequency. The walking slider moves in a way similar

to a horse using its fore and hind legs when trotting. A test motor,

20205mm

in dimension, exhibits a maximum speed of 20 cm/s

and a maximum thrust of 0.2 kgf (¼2 N) with a maximum efficiency of

20%, when driven at 98 kHz at 6 V (actual power ¼0.7 W). This motor

has been employed in a precision X-Ystage.

Plate Y

(

)(

)

Plate X

Elastic hollow

cylinder

FIG. 1.53 “Metal tube motor” using a metal tube and two rectangular PZT plates:

(A) Schematic structure and (B) photo of the world’s smallest motor (at the time) (1.5 mmϕ).

70 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.3.7.3 Propagating Wave-Type Motors

Sashida and Ueha et al. manufactured a linear motor as illustrated in

Fig. 1.57.

110,111

Two piezoelectric vibrators installed at both ends of a steel

transmission rod excite and receive the traveling transverse wave (anti-

symmetric fundamental Lamb wave mode). Adjusting a load resistance

in the receiving vibrator leads to a perfect traveling wave. Exchanging

the roles of the transmitting and receiving piezocomponents results in a

reversal of the movement.

FIG. 1.54 Camera auto zooming/focusing mechanism with two metal tube USMs in a

Samsung cellular phone.

Ball

bearing

Shaft

Spring

Rotor

Stator

head

Longitudinal

PZT

Torsional

PZT

Bottom

nut

Bolt

FIG. 1.55 Two-vibration-mode coupled-

type motor.

711.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Using the bending vibration, the wavelength λcan be chosen as short as

several mm to satisfy a stable surface contact with the slider by changing

the cross-section area or the moment of inertia of the transmission rod. In

the case of Fig. 1.57,λ¼26.8 mm. A slider, the contact face of which is

coated with rubber or vinyl resin, clamps the transmission rod with an

appropriate force. The transmission efficiency is strongly affected by

the vibration source position on the rod, and it shows a periodic variation

with the distance from the free end of the rod to the position of the vibra-

tor. Taking into account the wave phase, the vibration source should be

fixed at a distance corresponding to one wavelength λ(i.e., 26.8 mm) from

the rod end.

To oscillator

(

)(

)

dhesion

Multilayer

piezoelectric

actuator

0 T

90deg

1/4 T

2/4 T

3/4 T

1 T

Leg

Rail

FIG. 1.56 π-shaped linear ultrasonic motor: (A) construction and (B) walking principle.

Note the 90-degree phase difference of two legs similar to that associated with horse trotting.

3×6 mm

Horn ( 1: 4 )

Piezo vibrator

28 kHz

20 f

6 cm

Transmission rod

Slider

FIG. 1.57 Linear motor using a beam bending vibration.

72 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

The slider, made of a steel clamper 60 mm in length, which theoretically

covers two waves, was driven at a speed of 20 cm/s with a thrust of 50 N

at 28 kHz. A major problem with this type of motor is its low efficiency

(around 3%), because the whole rod must be excited even when only a

small portion is utilized for the output. To overcome this dilemma,

ring-type motors were invented where the whole rod can be utilized,

because the lengths of the stator and rotor are the same.

When we deform the rod discussed in the previous section to make a

ring by connecting the two ends topologically, we can make a rotary type

motor using a bending vibration. Two types of “ring” motor designs are

possible: (a) the bending mode type and (b) the extensional mode type.

112

Although the principle is similar to the linear type, more sophisticated

structures are employed with respect to the ceramic poling and the

mechanical support mechanism.

In general, when a vibration source drives one position of a closed ring

(circular or square) at a frequency corresponding to the resonance of this

ring, only a standing wave is excited, because the vibration propagates in

two directions symmetrically from the vibration source and interference

occurs. When multiple vibration sources are installed on the ring, dis-

placements can be obtained by superimposing all the waves (two waves

from each vibration source). Using the superimposition principle, we can

generate a traveling-like wave in the closed ring with the profile of the

original standing wave.

Fig. 1.58 shows the famous Sashida motor.

113

By means of the traveling

elastic wave (up-down motion) induced by a thin piezoelectric ring

(i.e., unimorph type), a ring-type slider in contact with the “rippled” surface

of the elastic body bonded ontothe piezoelectric is driven in both directions

by exchanging the sine and cosine voltage inputs. Another advantage is its

thin design, which makes it suitable for installation in cameras as an auto-

matic focusing device. Eighty percent of the exchange lenses in Canon’s

EOS camera series have already been replaced by the USM mechanism.

FIG. 1.58 Stator structure of Sashida’s motor.

113

731.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

The PZT piezoelectric ring is divided into 16 positively and negatively

poled regions and two asymmetric electrode gap regions so as to generate

a 9th-mode propagating wave at 44 kHz. A prototype was composed of a

brass ring of 60 mm in outer diameter, 45 mm in inner diameter, and

2.5 mm in thickness, bonded onto a PZT ceramic ring of 0.5 mm in thick-

ness with divided electrodes on the back. The rotor was made of polymer

coated with hard rubber or polyurethane.

Canon utilized Sashida’s “surfing” motor for a camera automatic focus-

ing mechanism, installing the ring motor compactly in the lens frame. It is

noteworthy that the stator elastic ring has many teeth, which can magnify

the transverse elliptical displacement and improve the speed. The lens

position can be shifted back and forth with a screw mechanism. The

advantages of this motor over the conventional electromagnetic motor

are the following:

1. Silent drive due to the ultrasonic frequency drive and no gear

mechanism (i.e., more suitable for video cameras with microphones).

2. Thin motor design and no speed reduction mechanism such as gears,

leading to space saving.

3. Energy saving.

A general problem encountered for these traveling wave-type motors is

the support mechanism of the stator. In the case of a standing wave motor,

the nodal points or lines are generally supported; this causes minimum

effects on the resonance vibration. A traveling wave, however, does not

have such steady nodal points or lines. Thus, special considerations are

necessary. Matsushita Electric proposed a nodal line support method

using a higher order vibration mode, where a wide ring is supported at

the nodal circular line and “teeth” are arranged on the maximum ampli-

tude circle (i.e., antinode) to get larger revolution.

114

Seiko Instruments miniaturized the USM to dimensions of 10 and 4 mm

øin diameter using basically the same principle.

115

A driving voltage of

3 V and a current of 60 mA produces 6000 rev/min (no-load) with a tor-

que of 0.1 mNm. A 10-mm motor has been installed in a wristwatch for a

silent alarm function, while a 4-mm motor is used for perpetual function

(i.e., date plate change). AlliedSignal developed USMs similar to Shinsei’s,

which are utilized as mechanical switches for launching nuclear bomb

missiles.

116

1.3.7.4 Smooth Impact Drive Mechanism

Though the principle is different from the USM, a competitive tech-

nology is an impulse motor. Konika-Minolta developed a Smooth Impact

Drive Mechanism (SIDM) using a ML piezo-element.

117

The idea comes

from the stick &slick condition of the ring object attached on a drive

rod in Fig. 1.59A. By applying a saw-shaped voltage to a multilayer

74 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

actuator, alternating slow expansion and quick shrinkage are excited on

a drive friction rod (see Fig. 1.59B). A ring slider placed on the drive

rod will stick on the rod due to friction during a slow expansion period,

while it will slide during a quick shrinkage period, so that the slider moves

from the bottom to the top. A lens is attached to this slider. In order to

obtain the opposite motion, the voltage saw shape is reversed. Compared

to the USMs, the impulse motor is simpler, but the 1/10 smaller holding

force (because of the slipping condition) may be a problem. Though the

drive frequency can be much higher than the inchworm type, it is still

lower than the resonance frequency, sometimes audible to the human.

The recent trend is to increase the drive frequency of the SIDM up to its

mechanical resonance, aiming at the improvement in speed and thrust.

We pointed out the problem in its drive method: the saw-type voltage

wave cannot generate the saw-type displacement when approaching

its resonance frequency (i.e., the displacement becomes sinusoidal!).

118

Taking into account that the “saw” wave can be expressed by a Fourier

transform as

fxðÞ¼

2+X

∞

n¼1

ancos nxðÞ+bnsin nxðÞ½

¼2X

∞

n¼1

1ðÞ

n+1

nsin nxðÞ, for xπ622πℤ,

(1.44)

Time

Piezo

Slider

Displacement

(

)

Drive friction rod f1.0×6.0 mm

Drive friction rod

Multilayer piezo f1.2×2.3 mm

Multilayer piezo

Fixture f2.5×0.6 mm

Size: f2.5×8.9 mm

(A)

Fixture

FIG. 1.59 (A) Illustration of the SIDM developed by Konica-Minolta for phone camera

zooming applications. (B) Displacements of the piezo-element and the slider to show the

“stick & slick” motion.

117

751.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Morita’s group proposed the 1st and 3rd harmonic combination drive for

exhibiting a saw-type displacement mode.

119

However, this harmonic

combination drive requires multiple voltage sources according to the

number of higher-order harmonics to consider.

In order to simplify the drive circuit and reduce the system cost,

Tuncdemir et al. proposed to use a rectangular voltage wave at the reso-

nance frequency with a variable duty ratio, as shown in Fig. 1.60.

118

A sche-

matic illustration of the principle is shown in Fig. 1.60A. Using a

translational-rotary multi degree-of-freedom (DoF) piezoelectric USM as

pictured in Fig. 1.61A, we computer-simulated and measured the tip

motion of the driving rod. The stator of this motor consists of four slanted

piezoelectric plates bonded on a metal rod. Dual function output, which

−2

−1

x 10−4

D25

D33

D50

D67

D75

(B) (C)

50 100 150 200 250

−2

−1

50 100 150 200 250

−2

−1

50 100 150 200 250

−2

−1

50 100 150 200 250

−2

−1

50 100 150 200 250

D1-D

(A)

Stator

FIG. 1.60 Resonance-type inertial motor drive with a variable duty-ratio rectangular

wave voltage. (A) Schematic illustration of the principle, (B) ATILA computer simulation

of the tip displacement, and (C) measured tip displacement for various duty ratios of the rect-

angular wave voltage.

120

76 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

is observed on the ring-shaped slider, is controlled by single source excita-

tion signal. The PZT ceramics are excited at the resonance frequency of the

first longitudinal mode (59 kHz) for translational operation, or of the first

torsional mode (34 kHz) for rotational output motion. Fig. 1.60B and C

shows the ATILA computer simulation of the tip displacement, and the

measured tip displacement for various duty ratios of the rectangular wave

voltage.

120

Practical slider motion under a drive condition of 59 kHz and

D¼67% is demonstrated in Fig. 1.61B. Note the smooth linear shift of the

average position, superposed with zig-zag vibrational displacement.

1.3.8 Piezoelectric Energy Harvesting

1.3.8.1 Piezoelectric Passive Damping to Energy Harvesting

Piezoelectric dampers were developed by the author’s group in the

1980s. In order to suppress mechanical noise vibration, Uchino et al. used

a piezoelectric, which could convert the vibration energy to electric

energy. The resistive shunt method was patented for consuming the

(A)

(B)

0.00

0.25

0.50

0.75

1.00

1.25

1.50

1.75

Displacement

Net motion

0.05 0.1 0.15

Second [ms]

Tip displacement (micron)

0.2 0.25

FIG. 1.61 (A) Translational-rotary ultrasonic motor with four slanted PZT ceramic plates.

(B) Practical slider motion of the “translational-rotary” inertial motor under a drive condition

of 59 kHz and D¼67%.

120

771.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

converted electric energy in Joule heat, so that the mechanical vibration

was dramatically damped. A piezoceramic patch was bonded on an

elastic plate with its fundamental resonance frequency around 200 Hz.

Fig. 1.62 shows the fact that there is an optimal resistance 6.6 kΩto be

connected to the piezoelectric damping device in order to obtain the

quickest damping; that is, the resistance should be chosen to be equal

to the piezo-damper impedance Z¼1/ωC(impedance matching!).

The

piezo-shunt methodologies have now been extended to a combination

of resistive, capacitive, and inductive components.

Consuming the converted electric energy in Joule heat seemed to be use-

less. Thus, Uchino et al. started to accumulate the electric energy in batteries

in the 1990s. Unused power exists in various forms such as vibrations, water

flow, wind, human motion, and shockwaves. In recent years, industrial and

academic research units have focused attention on harvesting energy from

vibrations using piezoelectric transducers. These efforts have provided the

initial research guidelines and have brought to light the problems and lim-

itations of implementing the piezoelectric transducer. There are three major

steps associated with piezoelectric energy harvesting

121

(i) Mechanical-mechanical energy transfer:

This includes mechanical stability of the piezoelectric transducer

under large stresses, and mechanical impedance matching.

FIG. 1.62 Resistive shunt piezoelectric patch for vibration damping test. Thefundamental

resonance frequency of this vibration system is around 200 Hz. Note that the resistance 6.6 kΩ

exhibits the quickest damping.

78 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

(ii) Mechanical-electrical energy transduction:

This relates with the electromechanical coupling factor in the

composite transducer structure.

(iii) Electrical-electrical energy transfer:

This includes electrical impedance matching, a DC/DC

converter to accumulate the energy into a capacitor, or a rechargeable

battery.

1.3.8.2 High Energy Harvesting (W)

Periodic vibrations generated from rotating machines or engines

are one of the most promising sources for recovering energy. Kim et al.

investigated first the capability of harvesting the electrical energy from

mechanical vibrations in a dynamic environment, such as an automobile

engine, through a “cymbal” piezoelectric transducer.

122,123

The targeted

mechanical vibration from an engine lies in the range of 50–150 Hz

with force amplitude of the order of 1 kN. It was found that under such

severe stress conditions the metal-ceramic composite transducer cymbal

is a promising rigid structure, keeping a relatively high electromech-

anical transduction rate. The metal cap enhances the endurance of the

ceramic to sustain high loads along with stress amplification. In our

study, the experiments were performed under a force of 7–70 N at a fre-

quency of 100 Hz on a cymbal with 29-mm diameter and 1-mm thickness.

At this frequency and force level, 60 mW power was generated from a

cymbal measured across a 400 kΩresistor. Fig. 1.63 illustrates the final

cymbal energy harvesting composites, in which three cymbals are emb-

edded in a triangular-shaped rubber sheet. These composite sheets are

inserted as mats below the engine. Since each cymbal can generates close

to 100 mW continuously, 1 W can be obtained in total. Note that the opti-

mal conditions for obtaining the maximum vibration damping and the

maximum energy harvesting are exactly the same; that is, we can perform

two tasks at the same time.

Charge output

PZT

Engine Bolt to support

the engine

FIG. 1.63 High power energy harvesting (1 W at 100 Hz) with cymbal piezoelectric flex-

ible composites.

791.3 PIEZOELECTRIC DEVICES—BRIEF REVIEW OF APPLICATIONS

Usually the output impedance of the harvested electrical energy with a

piezoelectric transducer is extremely high, so that the electrical impedance

mismatch provides significant reduction of efficiency for accumulating

the electric charge into a rechargeable battery, which has typically low

impedance around 10–100 Ω. To overcome this problem, the switch shunt

is most popularly used for energy harvesting purposes. A DC-DC buck

converter was designed for the above cymbal system, which allows trans-

fer of 50 mW power out of 60 mW from the cymbal (82% efficiency) to a

low impedance load of 5 kΩ, with a 2% duty cycle and at a switching fre-

quency of 1 kHz.

124

Another unique circuit design may be with a piezoelectric transformer.

The piezoelectric transformer used in the circuit has low output imped-

ance around 50 Ω, and the efficiency of the piezoelectric transformer in

the resonance shows over 95%. This low output impedance is suitable

for an impedance matching to the load (rechargeable battery).

125

1.3.8.3 Low-Energy Harvesting (mW)

Another promising vibration source is human motion. Uchino et al.

developed intelligent clothing (IC) with a piezoelectric energy harvesting

system of flexible piezoelectric textiles, aiming at a general power source

for charging portable equipment such as cellular phones, health monitor-

ing units, or medical drug delivery devices. The macro fiber composite

(MFC) is an actuator that offers high performance and flexibility in a

cost-competitive device (Smart Material Corp.). The MFC consists of rect-

angular piezoceramic rods sandwiched between layers of adhesive and

electroded polyimide film. This film contains interdigitated electrodes

that transfer the applied voltage directly to and from the ribbon-shaped

rods. This assembly enables in-plane poling, actuation, and sensing in a

sealed, durable, ready-to-use package. When embedded in a surface or

attached to flexible structures, the MFC actuator provides distributed

solid-state deflection and vibration control (see Fig. 1.64). The MFC com-

posites can generate power at the mW level.

125

Remote electric switch developed by Face/PulseSwitch Systems, LC, VA

is one of the successful products using a unimorph type (Thunder) piezo-

device.

126

Lightning switch wireless transmitters (the switch controls) use

NASA spacetechnology to generate their ownelectricity whenever the trans-

mitter button is pushed mechanically through the piezoelectricity. Their

radio signals travel 40 to 100+ feet right through walls, floors, and ceilings.

Based on the global trend for “jus in bello” (justice in war),

environment-friendly “green” weapons became mainstream in the 21st

century—that is, minimally destructive weapons with a pinpoint target

such as laser guns and rail guns. In this direction, programmable air-bust

munition (PABM) was developed successfully in 2004. The 25-mm caliber

programmable ammunition by ATK Integrated Weapon Systems, AZ and

80 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

Micromechatronics, PA

127

uses a multilayer piezo-actuator (instead of a

battery) for generating electric energy under shot impact to activate the

operational amplifiers that ignite the burst according to the command pro-

gram (see Fig. 1.65).

1.4 FUTURE PERSPECTIVES OF PIEZOELECTRICS

We will discuss five key development trends for providing the future

perspectives of researches: performance to reliability, hard to soft, macro

to nano, homo to hetero, and single to multifunctional.

Multilayer

piezo

enerator

FIG. 1.65 Twenty-five millimeters caliber pro-

grammable air-burst ammunition with a multi-

layer piezogenerator.

Charging the

electronic device

Flexible energy

harvest circuit

Flexible

piezoelectric

textile

FIG. 1.64 Intelligent clothing (IC) energy harvesting system with macro fiber

composites.

811.4 FUTURE PERSPECTIVES OF PIEZOELECTRICS

1.4.1 Performance to Reliability

1.4.1.1 Pb-Free Piezoelectrics

In 2006, the European community started RoHS (restrictions on the use

of certain hazardous substances), which explicitly limits the usage of lead

(Pb) in electronic equipment. Pb (lead)-free piezoceramics were devel-

oped after 1999, and they are classified basically into three groups, (Bi,

Na)TiO

(BNT), (Na,K)NbO

(NKN), and tungsten bronze (TB), most of

which are revival materials after the 1970s.

The share of the patents for bismuth compounds (bismuth layered type

and (Bi,Na)TiO

type) exceeds 61%. This is because bismuth compounds

are easily fabricated in comparison with other compounds. Honda

Electronics, Japan developed Langevin transducers by using the BNT-based

ceramics for ultrasonic cleaner applications.

128

Their composition—0.82

(Bi

1/2

)TiO

-0.15BaTiO

-0.03(Bi

1/2

)(Mn

1/3

2/3

—exhibits

¼110 10

12

C/N, which is only 1/3 of that of a hard PZT, but the elec-

tromechanical coupling factor k

¼0.41 is larger because of much smaller

permittivity (ε¼500) than that of the PZT. Furthermore, the maximum

vibration velocity of a rectangular plate (k

mode) is close to 1 m/s

(rms value), which is higher than that of hard PZTs.

(Na,K)NbO

systems exhibit the highest performance among the

present Pb-free materials, because of the MPB usage. Fig. 1.10 shows

the current best data reported by Toyota Central Research Lab, where

strain curves for oriented and unoriented (K,Na,Li)(Nb,Ta,Sb)O

ceramics are shown.

Note that the maximum strain reaches up to

1500 10

6

, which is equivalent to the PZT strain. Drawbacks

include their sintering difficulty and the necessity of the sophisticated

preparation technique (topochemical method for preparing flaky raw

powder).

TB types are another alternative choice for resonance applications,

because of their high Curie temperature and low loss. Taking into

account the general consumer attitude on disposability of portable

equipment, Taiyo Yuden, Japan developed micro USMs using non-Pb

multilayer piezo-actuators.

129

Their composition is based on TB ((Sr,

Ca)

NaNb

) without heavy metal. The basic piezoelectric parame-

ters in TB (d

¼55–80 pC/N, T

¼300°C) are not very attractive. How-

ever, once the c-axis oriented ceramics are prepared, the d

dramatically enhanced up to 240 pC/N. Further, since the Young’s

modulus Y33E¼140GPa is more than twice of that of PZT, the higher

generative stress is expected, which is suitable to USM applications.

Taiyo Yuden developed a sophisticated preparation technology for ori-

ented ceramics with a multilayer configuration: that is, preparation

under strong magnetic field, which is much simpler than the flaky

powder preparation.

82 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.4.1.2 Biodegradable Polymer

The above Pb-free materials are nontoxic and disposable. Murata

Manufacturing Co. is further seeking biodegradable devices by using L-

type poly-lactic acid (PLLA). PLLA is made of a vegetable (corn) base.

130

Because it exhibits pure piezoelectric without the pyroelectric effect, the

stress sensitivity is sufficient for leaf-grip remote controllers, which do

not need a very long life time.

1.4.1.3 Low-Loss Piezoelectrics

High-powered piezoelectrics with low loss have become a central

research topic from the energy efficiency improvement viewpoint; that

is to say, “real (strain magnitude) to imaginary performance (heat gener-

ation reduction).” Reducing hysteresis and increasing the mechanical

quality factor to amplify the resonance displacement is the primary target

from the transducer application viewpoint. We proposed a universal loss

characterization methodology in smart materials, piezoelectrics, and mag-

netostrictors; namely, by measuring accurately the mechanical quality fac-

tors Q

for the resonance and Q

for the antiresonance in the admittance/

impedance curve, we can derive physical losses.

131,132

There are three losses in piezoelectrics: dielectric tan δ, elastic tan ϕ, and

piezoelectric tan θ, each of which is further categorized as intensive

(observable) and extensive (material parameter) losses as defined by the

following:

εX*¼εX1jtanδ0

ðÞ,sE*¼sE1jtan ϕ0

ðÞ,d*¼d1jtan θ0

ðÞ;

κx*¼κx1+jtan δðÞ,cD*¼cD1+jtan ϕðÞ,h*¼h1+jtan θðÞ:

Though the previous researchers neglected the piezoelectric loss

(tan θ), we pointed out that piezoelectric loss has almost a comparable

magnitude with the dielectric and elastic losses, and it is essential to

explain the admittance/impedance spectrum. A universal method for

determining the piezoelectric loss is summarized for a piezoelectric sam-

ple here (e.g., k

mode):

(1) Obtain tan δ0from an impedance analyzer or a capacitance meter

at a frequency away from the resonance range.

(2) Obtain the following parameters experimentally from an

admittance/impedance spectrum around the resonance (A-type) and

antiresonance (B-type) range: ω

,ω

(from the 3 dB bandwidth

method), and the normalized frequency Ω

¼ω

l/2v.

(3) Obtain tan ϕ0from the inverse value of Q

(quality factor at the

resonance) in the k

mode.

(4) Calculate electromechanical coupling factor kfrom the ω

and ω

with

the IEEE standard equation in the k

mode:

831.4 FUTURE PERSPECTIVES OF PIEZOELECTRICS

k312

1k312¼π

ωb

ωa

tan πω

bωa

ðÞ

2ωa



; (1.45)

(5) Finally, obtain tan θ0by the following equation in the k

mode:

tan θ0¼tan δ0+ tan ϕ0

2+1

QA1



1+ 1

k31 k31



Ωb2

:(1.46)

High power characterization of Pb-free piezoelectric and PZT disk sam-

ples is shown in Fig. 1.66, where the resonance Q

and antiresonance Q

are

plotted as a function of vibration velocity.

133

Compared with the maximum

vibration velocity (defined by the velocity that generates a 20°Ctempera-

ture increase on the sample) of 0.3 m/s (rms) in hard PZT, Pb-free piezo-

electrics can exhibit a maximum vibration velocity higher than 0.5 m/s,

an energy density that is three times higher than that of a transducer.

1.4.2 Hard to Soft

We are facing the revival of the polymer era after the 1980s because of

their elastically soft superiority. Larger, thinner, lighter, and mechanically

flexible human interfaces are the current necessities in portable electronic

devices, leading to the development of elastically soft displays, electronic

circuits, and speakers/microphones.

100

1000

10,000

0.2 0.4

Vibration Velocity vrms (m/s)

QA, QB

Hard-PZT

BNT-BKT-BLT-Mn

BNT-BT-BNMN NKM-C

0.6 0.8

FIG. 1.66 High power characterization of Pb-free piezoelectrics and PZT. Maximum

vibration velocity is larger for Pb-free materials.

133

84 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

1.4.2.1 Elastomer Actuators

Dielectric elastomer actuators (nonpiezoelectric, nonferroelectric) are

based on the deformation of a soft polymer that acts as a dielectric between

highly compliant electrodes. This effect is dominated by Maxwell stresses

imposed by the compliant electrodes. Extremely high strains at low frequen-

cies have been reported by Pelrine et al.

134

In-plane strains of more than 100%

and 200% were observed in silicone and acrylic elastomers, respectively.

1.4.2.2 Electrostrictive Polymers

Polyvinylidene difluoride-trifluoroethylene (PVDF-TrFE) copolymer is

a well-known piezoelectric, which has been popularly used in sensor

applications such as keyboards. Zhang et al. reported that the field

induced strain level can be significantly enhanced up to 5% by using a

high-energy electron irradiation onto the PVDF films, leading to an elec-

trostrictive performance.

1.4.2.3 1:3 PZT Composites

Through a news release, Fujifilm unveiled their new bendable and fold-

able speakers that use a 1:3 composite (PZT fine powder was mixed in a

polymer film).

Superior acoustic performance seems to be promising for

flat-speaker applications.

1.4.2.4 Large Strain Ceramics

Pb(Zn

1/3

2/3

-PbTiO

(PZN-PT) or Pb(Mg

1/3

2/3

-PbTiO

(PMN-PT) single crystals became the focus dueto the rubber-like soft piezo-

ceramic strain 25 years after their discovery. Since the enhancement of the

induced strain level is a primary target,single crystals witha better capability

for generating larger strains are being used. In 1981, Kuwata et al. firstly

reported an enormously large electromechanical coupling factor,

¼92%–95%,and piezoelectricconstant,d

¼1500 pC/N,in solidsolution

single crystals between relaxor and normal ferroelectrics, PZN-PT.

24,25

This

discovery has been marked practically after more than 17years when high k

materials have been a focus in medical acoustics. These data have been

reconfirmed, and improved data were obtained, aiming at medical acoustic

applications.

26,27

The strains as large as 1.7% can be induced practically for

the PZN-PT solid solution single crystals. It is notable thatthe highest values

are observed for a rhombohedral composition only when the single crystal is

poled along the perovskite [0 0 1] axis, not along the [1 1 1] spontaneous

polarization axis (see Fig. 1.8).

1.4.3 Macro to Nano

In the micro (nano) electromechanical system (MEMS/NEMS) area,

piezoelectric-MEMS is one of the miniaturization targets for integrating

the piezo-actuators in a micro-scale device, aiming at bio/medical appli-

cations for maintaining the human health.

851.4 FUTURE PERSPECTIVES OF PIEZOELECTRICS

PZT thin films are deposited on a silicon wafer, which is then microma-

chined to leave a membrane for fabricating micro actuators and sensors, in

other words, micro electromechanical systems. Fig. 1.26 illustrates a blood

tester developed in the late 1990s by Penn State, in collaboration with

OMRON Corporation, Japan.

Applying voltage to two surface interdigi-

tal electrodes, the surface PZT film generates surface membrane waves,

which soak up blood and the test chemical from the two inlets, then mixes

the blood and test chemical in the center part and sends the mixture to the

monitor part through the outlet. FEA calculation was conducted to eval-

uate the flow rate of the liquid by changing the thickness of the PZT or the

Si membrane, inlet and outlet nozzle size, and cavity thickness. See Ref.

135 for the updated piezoelectric MEMS studies.

1.4.4 Homo to Hetero

Homo to hetero structure change is also a recent research trend: stress

gradient in terms of space in a dielectric material exhibits piezoelectric-

equivalent sensing capability (i.e., “flexoelectricity”), while the electric field

gradient in terms of space in a semiconductive piezoelectric can exhibit

bimorph-equivalent flextensional deformation (“monomorph”).

The space gradient of stress or electric field generates a direct or con-

verse flexoelectric effect, expressed respectively by the following:

Pl¼mijkl @xij=@xk



, (1.47)

Xij ¼mijkl @El=@xk

ðÞ, (1.48)

where P

are electric polarization, electric field; X

are elastic

stress, strain; x

is coordination in x

or E

;μ

ijkl

is denoted as a flexo-

electric coefficient, which has a 4th rank polar tensor symmetry, similar

to the electrostrictive tensor.

136

This means that even a paraelectric

material can generate charge under stress when the strain gradient is

generated artificially in the material. Cross et al.

137

demonstrated this

piezoelectric-equivalent effect in various artificial designs. A Ba

0.67

0.33-

TiO

(BST) paraelectric composition sample with a trapezoid shape

exhibited 10

7

C/m

of polarization under a strain gradient of 10

3

/m.

Conventional bimorph bending actuators are composed of two piezo-

electric plates, or two piezoelectrics and an elastic shim, bonded together.

The bonding layer in the latter, however, causes both an increase in hys-

teresis and a degradation of the displacement characteristics, as well as

delamination problems. Furthermore, the fabrication process for such

devices, which involves cutting, polishing, electroding, and bonding

steps, is rather laborious and costly. Thus, a monolithic bending actuator

(monomorph) that requires no bonding is a very attractive alternative

structure. Such a monomorph device can be produced from a single

ceramic plate.

The operating principle is based on the combined action

86 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

of a semiconductor contact phenomenon and the piezoelectric or electro-

strictive effect. When metal electrodes are applied to both surfaces of a

semiconductor plate, and a voltage is applied as shown in Fig. 1.67, the

electric field is concentrated on one side (that is, “Schottky barrier”),

thereby generating a nonuniform field within the plate. When the piezo-

electric (or electrostrictor) is slightly semiconductive, contraction along

the surface occurs through the piezoelectric effect only on the side where

the electric field is concentrated. The nonuniform field distribution gener-

ated in the ceramic causes an overall bending of the entire plate. The

energy diagram of a modified structure including a very thin insulative

layer was proposed.

138

The thin insulator layer increases the breakdown

voltage. The “rainbow” actuator by Aura Ceramics is a modification of the

basic semiconductive piezoelectric monomorph design, where half of the

piezoelectric plate is reduced so as to make a thick semiconductive elec-

trode that enhances the bending action.

139

1.4.5 Single to Multifunctional

Some new functions can be realized by coupling two effects. We devel-

oped magnetoelectric devices (i.e., voltage is generated by applying mag-

netic field) by laminating magnetostrictive Terfenol-D and piezoelectric

PZT materials, and we demonstrated photostriction by coupling photo-

voltaic and piezoelectric effects in PLZT.

1.4.5.1 Magnetoelectric Effect

Similar to nuclear radiation, magnetic irradiation cannot be easy felt by

humans. We cannot even purchase a magnetic field detector for a low

frequency (50 or 60 Hz). Penn State, in collaboration with Seoul National

University, developed a simple and handy magnetic noise sensor for these

Metal

to/2

(A)

(

)

to/2

Metal

Monomorph

n - type

−

FIG. 1.67 Schottky barrier generated at the

interface between a semiconductive (n-type)

piezoceramic and metal electrodes.

871.4 FUTURE PERSPECTIVES OF PIEZOELECTRICS

environmental monitoring purposes—for example, below a high-voltage

power transmission line. Fig. 1.68 shows a schematic structure of this

device, in which a PZT disk is sandwiched by two Terfenol-D (magnetos-

trictor) disks.

When a magnetic field is applied on this composite, Ter-

fenol expands, which is mechanically transferred to PZT, leading to an

electric charge generation from PZT. By monitoring the voltage generated

in the PZT, we can detect the magnetic field. The key to this device is high

effectiveness for a low frequency such as 50 Hz.

1.4.5.2 Photostriction

A photostrictive actuator is a fine example of an intelligent material, incor-

porating “illumination sensing” and self-production of “drive/

control voltage” together with final “actuation.” In certain ferroelectrics, a

constantelectromotive forceis generated with exposure of light,and a photo-

strictive strain results from the coupling of this bulk photovoltaic effect with

inverse piezoelectricity. A bimorph unit has been made from PLZT 3/52/48

ceramic doped with slight addition of tungsten.

The remnant polarization

of one PLZT layer is parallel tothe plate and in the direction opposite to that

of the other plate. When a violet light is irradiated to one side of the PLZT

bimorph, a photovoltage of 1 kV/mm is generated, causing a bending

motion. The tip displacement of a 20-mm bimorph with 0.4 mm in thickness

was 150 μm, with a response time of 1 s. A photo-driven micro walking

device, designed to begin moving by light illumination, was developed.

As shown in Fig. 1.15, it is simple in structure, having neither lead wires

nor electric circuitry, with two bimorph legs fixed to a plastic board. When

the legs are irradiated alternately with light, the device moves like an inch-

worm with a speed of 100μm/min. In pursuit of thick film-type photostric-

tive actuators for space structure applications, in collaboration with Jet

Propulsion Laboratory,Penn State investigated the optimal range of sample

thickness and surface roughness dependence of photostriction. 30-μmthick

PLZT films exhibit the maximum photovoltaic phenomenon.

140

We discussed five key trends in this section for providing the future per-

spectives of piezoelectric materials development: performance to reliability

(Pb-free piezoelectrics, biodegradable piezopolymer, low loss piezoelec-

trics), hard to soft (foldable piezopolymer film, PMN/PZN single crystals),

macro to nano (piezo-MEMS), homo to hetero (flexoelectricity, mono-

morph), and single to multifunctional (magnetoelectrics, photostriction).

Terfenol-D PZT

FIG. 1.68 Magnetic noise sensor consisting of a laminated

composite of a PZT and two Terfenol-D disks.

88 1. THE DEVELOPMENT OF PIEZOELECTRIC MATERIALS AND THE NEW PERSPECTIVE

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Acute or chronic myocardial damage has long been considered a tipping point for individual health and progression to heart failure. To address this issue, the popularity of electrospun nanofibrous scaffolds is increasing due to their structural resemblance to the extracellular matrix (ECM). The material used in these structures may be a natural polymer or a synthetic one of disparate materials. Each method possesses both advantages and disadvantages. Using a natural-based polymer including Alginate in the electrospinning solution does not give the scaffold enough mechanical strength, also the absence of adhesion molecules, such as RGD sequences, or transmembrane glycoproteins in alginate significantly reduces cell-alginate interactions, thereby limiting cell adhesion. Therefore, adding Polyvinyl alcohol (PVA) synthetic polymer to the Alginate enhances its mechanical properties for application on cardiac tissue electrospun scaffolds. On the other hand, Piezoelectricity aids cell growth in cardiac tissue. This article individually reviews the advantages and disadvantages of PVA, alginate, and piezo materials, and also suggests the composite electrospun as a promising scaffold in cardiac tissue engineering.

Unlocking piezoelectric potential of PVDF/Graphene coatings on melamine sponges for sensor technologies

Article

Mar 2025
MEASUREMENT

Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika

Article

Full-text available

May 1996
Russ Phys J

Sergey E. Stepanov

Invariant expansions of the electromagnetic field tensor F and its covariant derivative VF in the presence of gravity are obtained on the basis of the classical problem of elementary orthogonal group representation theory regarding the expansion of the tensor product of representations in terms of irreducible components. 1. IRREDUCIBLE REPRESENTATIONS OF AN ORTHOGONAL GROUP AND GEOMETRIC GRAVITATIONAL THEORY 1. Consider a pseudo-Riemann manifold (M, g). Its metric g specified a nondegenerate bilinear form q = gx in each tangential space E = TxM. In this case, each tensor space T~x~'tiM (@'E)|174 may be regarded as a space of representations of the orthogonal group O(q). In particular, | is such a space. Its O(q)-irreducible expansion is well known (see [1], p. 68) | = A2E~)S2E = A2E~)S~ E~) Rq, where A2E denotes the second external power of E*; So2E is the spurless component of the expansion of the space of symmetric 2-tensors S2E; Rq is the spur component of this expansion. On the basis of an analogous expansion (see [1], pp. 70-71) of the space S2A2E, an expansion is obtained for the curvature tensor R of the manifold (M, g) in terms of components corresponding to irreducible action components U, Z, and W of the group O(q). The spurless component W is the well-known Weil tensor of conformal curvature; the spur component U is equivalent to the scalar curvature s = TrgRic; and Z is the spurless part of the Ricci tensor Ric. The expansion R-I~Z~)U, together with the normal forms of the Petrov curvature tensor (see [1], pp. 134-139), are regarded as fundamental facts of the general theory of relativity. Less well known (see [1], pp. 588-589) is the irreducible-relative to the action of group O(q)-expansion of the covariant derivative vRic =Q@S.~A which, on the basis of the field equations Ric-2-1sg = T and the conservation law d*T = 0, allows the O(q)-irreducible expansion of the covariant derivative V T'= Q'~S'~A' of the energy-momentum tensor T to be obtained. In the course of this research, we f'md for the electromagnetic field tensor F the O(q)-irreducible expansion of its covariant derivative V F=~p into spurless f and spur p components. In this expansion, the condition p = 0 leads to the Maxwell equations in free space, and the condition f = 0 leads to a single special Maxwell equation in the presence of a charge. These results are given in the first part of section 2 below. 2. If space-time is regarded (see [2], p. 13) as a Lorentz manifold (M, g) together with a continuous unit time-like vector field ~ that is nowhere zero, the orthogonal expansion TxM = H~V of the tangential space at each point x of the manifold must be considered (see [3]; [1], p. 131). As a result, O(q) = O(q h) x O(qV), where qV is a positive-definite quadratic form in the rest space H (see [1], p. 131) such that q = qh~qV. In [3], it was proven that the well-known (see [4], p. 219; [5], p. 101; [6]) orthogonal expansion of the covariant derivative of the 4-velocity field ~ of a relativistic fluid is a corollary of the irreducible-relative to the action of the group O(q h) x O(q v)-expansion E*| = A2HGSJ HG Rq~O (V* | Vladimirsk State Pedagogical University.

Micro walking machine using piezoelectric actuators

Article

Full-text available

Jan 1989

Kenji Uchino

Design of Translation Rotary Ultrasonic Motor with Slanted Piezoelectric Ceramics

Article

Full-text available

Feb 2011

We designed and manufactured a multi-degree-of-freedom (MDoF) ultrasonic motor (USM) by using a single actuator. Although there have been numerous MDoF USMs reported in the literature, only a few of them cover the combined rotary and translational motions in a cylindrical-joint type configuration. Combining these two motions in one joint and controlling this combined motion through a novel USM is the main aim of this work. Here, we use smooth impact drive method (SIDM) with two distinct modes obtained at two distinct frequencies by the help of slanted ceramics and uneven square shaped excitation signals. The translational-rotary dual-mode motor can be driven by single source. The prototype of the motor (5 mm diameter, 25 mm total length) has 5 mm/s translational and 3 rad/s rotary speed under 4 mN blocking force, when the input signal is 20 Vp–p square wave.

Analysis of High Power Behavior in Piezoelectric Ceramics from a Mechanical Energy Density Perspective

Article

Full-text available

May 2016

In this work, a new methodology for comparing high power performance of different piezoelectric materials is presented. When comparing high power performance of piezoelectric materials of varying compositions and vibration modes, there exists an inherent problem in comparing the mechanical quality factor directly. Typically the behavior of the mechanical quality factor is reported as a function of tip vibration velocity of the sample. This paper shows why this approach can be inherently problematic and proposes an energy approach to characterize the mechanical quality factor as the solution. By utilizing mechanical energy density (

u_{e}

), the mass density of the material system (

\rho

), and the vibration mode shape (e.g.

k_{31}

and

k_{p}

) of the sample are accounted for. Therefore, a better method to compare high power performance of varying piezoelectric compositions is introduced. Furthermore, the new method is applied to various compositions by using data available in the literature. As a result, the high power behavior of the materials appear to be significantly different when the new "energy density approach" is used to compare the mechanical quality factor rather than vibration velocity. Also, the technique's ability to be utilized to consolidate data from different resonators to determine anisotropic loss factors is demonstrated on hard and soft PZT samples of

k_{31}

and

k_{p}

geometries.

Electrostrictive Actuators: Materials and Applications

Article

Full-text available

Apr 1986
AM CERAM SOC BULL

Kenji Uchino

Recent developments in the areas of piezoelectric and electrostrictive actuators are reviewed; historical and theoretical background, newly developed materials, applications, and future problems are discussed. New materials such as lead zirconate titanate (PZT) based and lead magnesium niobate (PMN) ceramics reveal excellent actuator characteristics especially by using the wet-chemical preparation technique. The remaining problem is reliability/durability of the actuators.

Study on Langevin type BaTiO3 ceramic vibrator

Article

Jan 1953

Acoustic Waves: Devices, Imaging, and Analog Signal Processing

Article

Jan 1987

G.S. Kino

Ferroelectricity in the Ilmenite Structure

Article

Phys Rev

DOI:https://doi.org/10.1103/PhysRev.76.1886.2

Effect of impurity doping on photostriction in ferroelectric ceramics

Article

Jan 1988

PHASE TRANSITIONS IN THE Pb(Zn//1/////3Nb//2/////3)O//3-PbTiO//3 SYSTEM.

Article

Jan 1981

Two successive phase transitions, changing the crystal symmetry from rhombohedral to tetragonal, and then to cubic on a heating process, have been investigated in single crystals with the composition near the morphotropic phase boundary. The existence of the morphotropic phase boundary has been confirmed by measuring the dielectric, piezoelectric and pyroelectric constant. Anomalously large electromechanical and piezoelectric constants are observed on the morphotropic phase boundary.

The Development of Piezoelectric Materials and the New Perspective

Abstract and Figures

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