Materials for Noise Control: Paper ICA2016-535
100 years of piezoelectric materials in acoustics: From a
sonar to active metasurfaces
Pavel Mokrý(a)
(a)
Institute of Mechatronics and Computer Engineering, Technical University of Liberec,
Studentská 2, 46117 Liberec, Czech Republic, [email protected]
Abstract
Since the discovery of the quartz ultrasound generator by Paul Langevin in 1917, piezoelectric
materials has been successfully applied to many acoustic devices, which have greatly improved
our lives. Nowadays, the piezoelectric transducers can employ a vast set of piezoelectric materials such as single crystals, ceramics, polymers, biopolymers, macro fiber composites, ferroelectrets, flexoelectric materials and some others. In this Paper, a brief review of the use of
piezoelectric materials in electroacoustic transducers will be given. Emphasis will be put on the
modern applications of piezoelectric materials to the acoustics, especially on the method of active
control of their elastic properties by means of active shunt circuits. The recent application of this
method allowed the construction of so called active acoustic metamaterials (AAMM) and metasurfaces. The AAMMs based on the piezoelectric transducers offer the fabrication of efficient
sound shielding structures with a low weight, a large area and a small thickness compared to the
wavelength of a sound wave. It is evident that such sound-isolation structures may be applicable
in devices with severely restricted weight constraints. It has been recently discovered that the
great sound isolation efficiency of the AAMM is obtained in the regime of a negative acoustic
impedance. Stability of the AAMM operating in the regime of a negative acoustic impedance will
be analyzed and discussed.
Keywords: piezoelectric transducer, active elasticity control, active acoustic metasurface
100 years of piezoelectric materials in acoustics: From
a sonar to active metasurfaces
1
Introduction
The “electrical activity" of certain crystalline materials has been known to a mankind for several
hundreds of years. Only in the 19th century the electro-mechanical phenomena in crystals has
been studied with the required scientific rigour. In 1880 Jacques and Pierre Curie discovered
that the compression of tourmaline single crystal samples along certain directions yielded the
presence of electrical charge on the sample surface [4]. The essential feature of the discovered
phenomenon is the linear relationship between generated charge and the applied force. Few
months later, Jonas Ferdinand Gabriel Lippmann suggested the existence of the inverse effect,
i.e. existence of strain due to applied electric field. This phenomenon was immediately demonstrated experimentally again by Jacques and Pierre Curie in 1881 [5]. These phenomena have
been called the piezoelectric effect after Hankel since 1881.
Since the discovery of piezoelectricity, the piezoelectric properties of a large number of materials have been demonstrated and applied to many electromechanical and electroacoustic
devices. Section 2 presents a brief review of piezoelectric materials used in acoustics. The
noise suppression by means of the active elasticity control in piezoelectric transducers is introduced in Sec. 3. Section 3.5 presents our recent development of planar structures with
negative values of specific acoustic impedance.
2
Piezoelectric materials in acoustics
2.1 Quartz and Rochelle salt
The materials, where the piezoelectric effect was discovered afterwards, were quartz and
Rochelle salt. It is rather difficult to trace the specific years of the first reports on the piezoelectricity in these materials. However, earliest references to their piezoelectric properties are
by Voigt in 1910 [19]. In the early years, the piezoelectricity was considered only as a laboratory curiosity and a challenge for crystalography physicists and mathematicians working in the
group and tensor theories.
The situation changed completely in 1920s, when the scientific teams from the Allied countries
during the WWI have been working on the submarine detection system. In 1917, Paul Langevin
and Constantin Chilowsky filled a patent [3] of a device for ultrasonic detection of submarines.
Their ultrasonic transducer consisted of the array of quartz crystals sandwiched between two
steel plates. The structure, which is shown in fig. 1, had the resonant frequency of 50 kHz.
Independently, Robert William Boyle was working on the similar system at the Anti-Submarine
Division of the British Naval Staff. In the same year 1917, Boyle and Albert Beaumont Wood
produced the first working prototype of the underwater active sound detection apparatus. By
1918, both Britain and France have manufactures prototype systems, which were successfully
tested. The serial production of sonars started in 1922 and they were used for measurements
2
suspension board
Cable, heavily insulated
shield case
piezoelectric polymer
diaphragm
Iron pipe for support
ring
Copper casing
base
Thin mica
earpad
Steel plate
Quartz
piezoelectric polymer
diaphragm
Steel plate
Insulating and
waterproof mixture
(a)
polyurethane foam backing
framework
(b)
polyurethane foam backing
(c)
Figure 1: Scheme of the first practical application of the piezoelectric material to acoustics. It is the quartz electroacoustic transducer designed by Robert William Boyle and
later patented by Chilowsky and Langevin [3] (a). Early applications of PVDF polymer in
electroacoustic devices: cross-sectional view of a headphone (b) and a microphone (c) by
Tamura et al. [18].
of the see depth.
In the early sonar systems both quartz and Rochelle salt were used. Quartz had better mechanical properties, which was advantageous in the fabrication process. On the other hand,
Rochelle salt had better piezoelectric response.
The greatest advantage of quartz is the possibility to prepare cuts, which have almost temperature independent resonant frequency. Such a feature is beneficially used even today in watch
and other resonators, which require a high temperature stability.
2.2 Barium titanate and lead zirconate titanate
The practical reasons and further development in the sonar construction after WWII required
the reduction of the resonance frequency down to 5 kHz. Such a requirement could not be
reached with quartz crystals. So in the early 1950s, the barium titanate piezoelectric systems
were developed. Barium titanate is a ferroelectric-ferroelastic material, where the electromechanical response is amplified by the movements of so called ferroelastic domain walls. As
a result, the barium titanate samples have about two orders of magnitude larger electromechanical response. On the other hand, the irreversible movement of ferroelactic domain walls
introduces a strong hysteresis into the piezoelectric response. It may yield to the considerable
signal distortion, higher harmonic generation in the output acoustic signal, and heating of the
transducer due to dielectric losses. These phenomena should be considered during the design
of the electronics part of the electroacoustic system.
A breakthrough in the construction of electromechanical and electroacoustic transducers was
the discovery of ferroelectric-ferroelastic solid solution of lead zirconate titanate (PZT). PZT
belongs to the same family of materials as barium titanate. The greatest advantage of PTZ
is that it can be prepared in the form of a ceramic sample. This greatly simplifies the sample
preparation and greatly reduces the prize of the transducers. Their piezoelectric response can
3
be controlled by doping. Niobium-doped PZT (so called soft-PZT) have increased piezoelectric
response and large actuator displacement can be achieved at moderate electric fields. Irondoped (hard-PZT) is characterized by smaller hysteresis in the piezoelectric response. Anyway,
the piezoelectric response is about one order of magnitude larger than the response of barium
titanate.
Unfortunately, the presence of lead in the compound makes PZT the subject of RoHS regulation. Since the regulators have the opinion that lead can be leached (e.g. by acid rains) from
its PbO oxide, which is contained in PZT, equally easily as it can be diffused from shot gun
pellets, the researchers in the field of material science are intensively searching for a lead-free
replacement for PZT. However, without a much success yet.
2.3 Piezoelectric polymers and biopolymers
The single crystal or ceramic piezoelectric transducers are very efficient in the ultra sound
generation in water, which is caused by the comparable magnitudes of their specific acoustic
impedance. Unfortunately, their efficiency in the air-borne electroacoustic transducers is greatly
reduced due to the difference in values of their specific acoustic impedance. In order to increase the efficiency of electroacoustic transducer, the light enough and highly piezoelectric
material should be used.
In the 1950’s Fukada et al. investigated piezoelectricity of highly oriented and highly crystalline
biological substances, such as collagen, bone, and silk. In the 1960’s the piezoelectricity of
synthetic high polymers, the polypeptides, was found by Fukada et al. [7]. In 1968 the synthetic
piezoelectric high polymer, poly(γ-methyl L-glutamate) films were used as transducing elements
in experimental microphones and headphones [10], however these transducers have not been
commercialized, because the piezoelectric coefficients of those films were not large.
In 1969 the piezoelectricity of polyvinidilene fluoride (PVDF) was found by Kawai [13]. This
discovery really made a breakthrough in applications of synthetic piezoelectric polymers, since
the piezoelectric coefficient of PVDF is almost ten times larger than that of quartz. Since that
time, electroacoustic transducers that use cylindrically or spherically curved thin films made
of piezoelectric high polymer films have been constructed. The first application of piezoelectric
PVDF film as a microphone and headphone was made by Tamura et al. [18] [see Fig. 1 (b) and
(c)]. Principle function of these devices is based on a transformation of the radial movement
of the film, which is forced by the difference of acoustic pressures at the opposite sides of the
film, into the circumferential elongation and contraction of the film. A curvature of the film is
important to make the direct phase correspondence of the sound field changes with the electric
output or the applied external electric field.
2.4 Piezoelectric composite transducers
The applicability of PZT is limited in some applications. PZT transducers are extremely brittle
and they require special attention during handling and bonding procedures. They can easily
crack when exposed to large mechanical stresses or deformations. In addition, their conformability to curved surfaces is extremely poor [17]. Therefore, the concept of active piezoceramic
4
composite transducers (PCT) containing PZT and some flexible adhesive to eliminate the aforementioned drawbacks has been developed.
A typical PCT is made of an active layer sandwiched between two thin soft encapsulating
layers. The first generation of PCT actuators were manufactured using a layer of cylindrical
piezoceramic fibers embedded in a protective polymer matrix material. They were called Active
Fiber Composite (AFC) and were introduced by Hagood and Bent [11] as an alternative to
monolithic piezoceramic wafers for structural actuation applications. Strain energy density was
improved by utilizing interdigital electrodes (IDEs) to produce electrical fields in the plane of the
actuator [12]. In order to increase the contact area of the PZT fiber with the electrodes, the
new type of PCT actuator with PZT fibers with rectangular cross-section, called Macro Fiber
Composite (MFC) actuator was developed at NASA Langley Research Center. Nowadays, both
of these types of actuators are produced by Smart Materials Corp.
2.5 Piezoelectrets
Piezoelectrets represent a very promising group of piezoelectric substances with electromechanical response comparable to PZT [2]. Today, piezoelectrets are made of porous polymer films prepared by double-expansion process and corona poling, which introduces immobile
free charge carriers on the surface of the voids inside the polymer matrix made of polypropylene. The charges on the surface of the voids form a texture of electric dipoles, so that the
piezoelectret has a nonzero macroscopic polarization, which is sensitive to the applied uniform
electric field. This makes the piezoelectret extremely flexible, lightweight, with a low acoustic impedance. In addition, piezoelectrets can be produced inexpensively and environmentally
friendly. These properties of piezoelectrets allow the construction of light, flat, and sensitive
electroacoutic transducers.
3
Noise suppression by means of active elasticity control
The greatest advantage of piezoelectric materials is the linear relationship between electrical
and mechanical state quantities in the piezoelectric actuator. This makes it possible to fabricate the electroacoustic transducers with an extremely simple construction, a low cost, a fast
response without distortion of the transmitted signal, and many other advantages.
The aforementioned fundamental properties of piezoelectric material allow the construction of
extremely simple noise and vibration suppression devices by means of the method called active elasticity control of piezoelectric materials. Its fundamental principles and applications are
presented in this section.
3.1 Piezoelectric equations of state
The electrical and mechanical state of the piezoelectric material is described by the electric
field Ei and electric displacement Di and by the strain Sij and stress Tij , respectively. Due to
obvious thermodynamic reasons, one electrical and one mechanical state quantity are independent in the piezoelectric material (i.e. specified by the boundary conditions) and the remaining
5
(a)
(b)
Figure 2: Scheme of the state variables in the (a) d33 - and (b) d31 - modes of the piezoelectric actuator. Symbols U and Q are the voltage and charge on the electrodes. Symbols
l1 , l2 , and l3 are the dimensions of the piezoelectric actuator along x1 , x2 , x3 axes, respectively. E3 is the electric field along x3 axis. Symbols ∆l3 and ∆l1 are the elongation of the
piezoelectric actuator in the d33 - and d31 -mode, respectively. Symbols F3 and F1 stand for
the forces applied to the piezoelectric actuator in the d33 - and d31 -mode, respectively.
two state quantities are thermodynamically dependent. It means that there exist 4 possibilities
how to unambiguously describe the local equilibrium state in the infinitesimal volume of the
piezoelectric material. One convenient example is as follows:
Di = εik Ek + dikl Tkl ,
(1)
Sij = dkij Ek + sijkl Tkl ,
(2)
where the symbols εik , dikl , and sijkl stand for the permittivity, piezoelectric coefficients and
elastic compliance, respectively.
The vast majority of piezoelectric electroacoustic transducers operate in two regimes, which are
shown in Fig. 2. When the orientation of the applied force Fi = (0, 0, F3 )i is parallel with the
orientation of the applied electric field Ei = (0, 0, E3 )i , the piezoelectric transducer operates
in the d33 -mode (See Fig. 2(a)). When the state quantities Sij , Tij , Ei , and Di are uniform in
the transducer, it is convenient to integrate Eqs. (1) and (2) over the volume of piezoelectric
transducer, which yields:
Q = Cs U + d F3 ,
∆l3 = d U + (1/KS,33 ) F3 ,
(3)
(4)
where CS = ε33 l1 l2 /l3 , KS,33 = (1/s3333 ) l1 l2 /l3 and d = d333 are the capacitance, spring constant, and the piezoelectric coefficient of the whole piezoelectric transducer, which operates in
the d33 -mode, respectively. Bulk piezoelectric ceramic and piezoelectret electroacustic transducers operate usually in this mode.
6
40
)Bd( ssoL noissimsnarT
35
30
25
20
Negative capacitor:
15
Off
On
10
5
2
3
4
5
6
7
100
8
9
2
1000
Frequency (Hz)
(b)
(a)
Figure 3: (a) Geometrical arrangement of the system for a control of the acoustic transmission loss using the curved piezoelectric polymer membrane. (b) Measured transmission
loss T L = 20 log |pi /pt | in the situation, when the negative capacitor is off (thin red) and on
(thick blue). (Data reproduced from Fukada et al. [8])
When the orientation of the applied force is perpendicular to the external electric field, i.e.
Fi = (F1 , 0, 0)i , the piezoelectric transducer operates in the d31 mode (See Fig. 2(b)). After the
integration of the uniform state quantities over the volume of piezoelectric transducer, one gets
following equation:
Q = Cs U + d(s) F1 ,
(a)
∆l1 = d
(5)
U + (1/KS,31 ) F1 ,
(6)
where KS,31 = (1/s1111 ) l2 l3 /l1 , d(s) = d311 l1 /l3 , and d(a) = d311 l3 /l1 are the spring constant,
and the sensing and actuation piezoelectric coefficients of the whole piezoelectric transducer,
which operates in the d31 -mode, respectively. Usually, thin piezoelectric polymer and piezoelectric composite transducers operate in this mode.
3.2 Active elasticity control of piezoelectric actuators
Date et al. [6] have developed a method to control the elastic properties of piezoelectric actuators by connecting them to active shunt circuits. When the external capacitor of a capacitance
C is connected to the piezoelectric transducer, the macroscopic spring constant of the actuator
K = F1 /∆l1 can be expressed, when the equations of state of the piezoelectric actuator (3)-(4)
or (5)-(6) are appended with the equation for the charge Q on the electrodes of the external
capacitor:
U = −Q/C,
(7)
where C is the capacitance of the external capacitor. Combining Eqs. (5), (6), and (7), the
macroscopic value of the spring constant K is equal to
K = KS,31
1+α
,
1 − k2 + α
(8)
7
1.0
)1( tneiciffeoc noitprosbA
Negative capacitor:
0.8
Off
On 1 kHz
0.6
0.4
0.2
0.0
-0.2
-0.4
2
3
4
5
6
7
8
9
2
3
1000
Frequency (Hz)
(a)
(b)
Figure 4: (a) Geometrical arrangement of the system for an enhancement of the sound
absorption using the curved piezoelectric polymer membrane. (b) Measured absorption
coefficient α0 = 1 − |pr /pi |2 in the situation, when the negative capacitor is off (thin red)
and on (thick blue). (Data reproduced from Mokry et al. [15])
where k 2 = d(a) d(s) KS,31 /CS is the electromechanical coupling factor, and α = C/CS .
3.3 Sound isolation system
When the capacitance of the external capacitor C approaches the value −(1 − k 2 ) CS , it immediately follows from Eq. (8) that the value of the spring constant of the piezoelectric transducer
reaches quite high values. In order to achieve such a situation, the active electronic circuit
called negative capacitor has been constructed.
This can be used in the sound shielding system designed and constructed by Fukada et al. [8],
which is shown in Fig. 3(a). The system consists of the curved PVDF membrane of the thickness h = 0.05 mm, lateral dimensions L = 25 mm, and radius of curvature R = 40 mm.
Figure 3(b) shows the measured transmission loss through the thin polymer membrane in the
situation, when the negative capacitor, which is connected to the piezoelectric polymer film is
off (thin red) and on (thick blue).
3.4 Sound absorbing system
A very challenging sound absorbing system is presented in Fig. 4(a). The objective of this
system is to reduce the absorption coefficient α0 = 1 − |pr /pi |2 of the system, which consists of
the curved PVDF membrane and a hard backing with a large value of acoustic impedance Zm .
In this case it is not possible to determine the required value of the shunt negative capacitor in
the straightforward way and a more complex analysis is required [15].
Figure 4(b) shows the preliminary data reproduced from Ref. [15]. The thin red line shows the
measured value of α0 in the system, where h = 0.05 mm, R = 40 mm, and H = 20 mm. The
thick blue line shows the value of α0 increased at 1 kHz due to the action of the connected
8
negative capacitor. The negative values of α0 indicate that in this frequency range the energy
is supplied to the sound absorbing system from the negative capacitor.
3.5 Active acoustic metamaterials and metasurfaces
In 2005, it was recognized by Fukada et
its operation enter the regime of negative
elasticity control has been recognized as
tic metamaterials and metasurfaces, i.e.
impedance [14].
al. [9] that the sound shielding system may during
elasticity. After this discovery, the method of active
a simple tool for the construction of active acouslarge planar structures with the negative acoustic
Independently, several groups around the world have constructed active acoustic metamaterials
and metasurfaces, which employs the piezoelectric materials [1, 16].
4
Conclusions
The brief review of several piezoelectric materials, which can be used for the construction of
electroacoustic transducers, has been presented. Their advantages and disadvantages have
been discussed. The linear relationship between electrical and mechanical state quantities
makes it possible to construct devices with a small output signal distortion. The principles
of the active elasticity control method have been presented. We have shown that using this
method, it is possible to construct sound shielding and sound absorbing systems of a great
simplicity, extremely small weight and superb sound suppressing performance.
Acknowledgements
This work was supported by Czech Science Foundation Project No.: GA16-11965S, co-financed
from Ministry of Education, Youth and Sports of the Czech Republic in the Project No. NPU
LO1206.
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