Materials for Noise Control: Paper ICA2016-535

100 years of piezoelectric materials in acoustics: From asonar to active metasurfaces

Pavel Mokrý(a)

(a) Institute of Mechatronics and Computer Engineering, Technical University of Liberec,Studentská 2, 46117 Liberec, Czech Republic, pavel.mokry@tul.cz

Abstract

Since the discovery of the quartz ultrasound generator by Paul Langevin in 1917, piezoelectricmaterials has been successfully applied to many acoustic devices, which have greatly improvedour lives. Nowadays, the piezoelectric transducers can employ a vast set of piezoelectric ma-terials such as single crystals, ceramics, polymers, biopolymers, macro fiber composites, fer-roelectrets, flexoelectric materials and some others. In this Paper, a brief review of the use ofpiezoelectric materials in electroacoustic transducers will be given. Emphasis will be put on themodern applications of piezoelectric materials to the acoustics, especially on the method of activecontrol of their elastic properties by means of active shunt circuits. The recent application of thismethod allowed the construction of so called active acoustic metamaterials (AAMM) and meta-surfaces. The AAMMs based on the piezoelectric transducers offer the fabrication of efficientsound shielding structures with a low weight, a large area and a small thickness compared to thewavelength of a sound wave. It is evident that such sound-isolation structures may be applicablein devices with severely restricted weight constraints. It has been recently discovered that thegreat sound isolation efficiency of the AAMM is obtained in the regime of a negative acousticimpedance. Stability of the AAMM operating in the regime of a negative acoustic impedance willbe analyzed and discussed.

Keywords: piezoelectric transducer, active elasticity control, active acoustic metasurface

100 years of piezoelectric materials in acoustics: Froma sonar to active metasurfaces

1 IntroductionThe “electrical activity" of certain crystalline materials has been known to a mankind for severalhundreds of years. Only in the 19th century the electro-mechanical phenomena in crystals hasbeen studied with the required scientific rigour. In 1880 Jacques and Pierre Curie discoveredthat the compression of tourmaline single crystal samples along certain directions yielded thepresence of electrical charge on the sample surface [4]. The essential feature of the discoveredphenomenon is the linear relationship between generated charge and the applied force. Fewmonths 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 demon-strated experimentally again by Jacques and Pierre Curie in 1881 [5]. These phenomena havebeen called the piezoelectric effect after Hankel since 1881.

Since the discovery of piezoelectricity, the piezoelectric properties of a large number of ma-terials have been demonstrated and applied to many electromechanical and electroacousticdevices. Section 2 presents a brief review of piezoelectric materials used in acoustics. Thenoise suppression by means of the active elasticity control in piezoelectric transducers is in-troduced in Sec. 3. Section 3.5 presents our recent development of planar structures withnegative values of specific acoustic impedance.

2 Piezoelectric materials in acoustics2.1 Quartz and Rochelle salt

The materials, where the piezoelectric effect was discovered afterwards, were quartz andRochelle salt. It is rather difficult to trace the specific years of the first reports on the piezo-electricity in these materials. However, earliest references to their piezoelectric properties areby Voigt in 1910 [19]. In the early years, the piezoelectricity was considered only as a labora-tory curiosity and a challenge for crystalography physicists and mathematicians working in thegroup and tensor theories.

The situation changed completely in 1920s, when the scientific teams from the Allied countriesduring the WWI have been working on the submarine detection system. In 1917, Paul Langevinand 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 twosteel 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-SubmarineDivision of the British Naval Staff. In the same year 1917, Boyle and Albert Beaumont Woodproduced the first working prototype of the underwater active sound detection apparatus. By1918, both Britain and France have manufactures prototype systems, which were successfullytested. The serial production of sonars started in 1922 and they were used for measurements

2

Cable, heavily insulated

Iron pipe for support

Copper casing

Thin mica

Steel plate

Quartz

Steel plate

Insulating andwaterproof mixture

(a)

suspension board

ring

base

earpad

piezoelectric polymerdiaphragm

polyurethane foam backing

framework

(b)

shield case piezoelectric polymerdiaphragm

polyurethane foam backing

(c)

Figure 1: Scheme of the first practical application of the piezoelectric material to acous-tics. It is the quartz electroacoustic transducer designed by Robert William Boyle andlater patented by Chilowsky and Langevin [3] (a). Early applications of PVDF polymer inelectroacoustic devices: cross-sectional view of a headphone (b) and a microphone (c) byTamura et al. [18].

of the see depth.

In the early sonar systems both quartz and Rochelle salt were used. Quartz had better me-chanical 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 temper-ature independent resonant frequency. Such a feature is beneficially used even today in watchand 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 requiredthe reduction of the resonance frequency down to 5 kHz. Such a requirement could not bereached with quartz crystals. So in the early 1950s, the barium titanate piezoelectric systemswere developed. Barium titanate is a ferroelectric-ferroelastic material, where the electrome-chanical response is amplified by the movements of so called ferroelastic domain walls. Asa result, the barium titanate samples have about two orders of magnitude larger electrome-chanical response. On the other hand, the irreversible movement of ferroelactic domain wallsintroduces a strong hysteresis into the piezoelectric response. It may yield to the considerablesignal distortion, higher harmonic generation in the output acoustic signal, and heating of thetransducer due to dielectric losses. These phenomena should be considered during the designof the electronics part of the electroacoustic system.

A breakthrough in the construction of electromechanical and electroacoustic transducers wasthe discovery of ferroelectric-ferroelastic solid solution of lead zirconate titanate (PZT). PZTbelongs to the same family of materials as barium titanate. The greatest advantage of PTZis that it can be prepared in the form of a ceramic sample. This greatly simplifies the samplepreparation 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 piezoelectricresponse and large actuator displacement can be achieved at moderate electric fields. Iron-doped (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 bariumtitanate.

Unfortunately, the presence of lead in the compound makes PZT the subject of RoHS regula-tion. Since the regulators have the opinion that lead can be leached (e.g. by acid rains) fromits PbO oxide, which is contained in PZT, equally easily as it can be diffused from shot gunpellets, the researchers in the field of material science are intensively searching for a lead-freereplacement 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 soundgeneration in water, which is caused by the comparable magnitudes of their specific acousticimpedance. Unfortunately, their efficiency in the air-borne electroacoustic transducers is greatlyreduced due to the difference in values of their specific acoustic impedance. In order to in-crease the efficiency of electroacoustic transducer, the light enough and highly piezoelectricmaterial should be used.

In the 1950’s Fukada et al. investigated piezoelectricity of highly oriented and highly crystallinebiological substances, such as collagen, bone, and silk. In the 1960’s the piezoelectricity ofsynthetic high polymers, the polypeptides, was found by Fukada et al. [7]. In 1968 the syntheticpiezoelectric high polymer, poly(γ-methyl L-glutamate) films were used as transducing elementsin experimental microphones and headphones [10], however these transducers have not beencommercialized, because the piezoelectric coefficients of those films were not large.

In 1969 the piezoelectricity of polyvinidilene fluoride (PVDF) was found by Kawai [13]. Thisdiscovery really made a breakthrough in applications of synthetic piezoelectric polymers, sincethe piezoelectric coefficient of PVDF is almost ten times larger than that of quartz. Since thattime, electroacoustic transducers that use cylindrically or spherically curved thin films madeof piezoelectric high polymer films have been constructed. The first application of piezoelectricPVDF 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 movementof the film, which is forced by the difference of acoustic pressures at the opposite sides of thefilm, into the circumferential elongation and contraction of the film. A curvature of the film isimportant to make the direct phase correspondence of the sound field changes with the electricoutput or the applied external electric field.

2.4 Piezoelectric composite transducers

The applicability of PZT is limited in some applications. PZT transducers are extremely brittleand they require special attention during handling and bonding procedures. They can easilycrack when exposed to large mechanical stresses or deformations. In addition, their conforma-bility 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 afore-mentioned drawbacks has been developed.

A typical PCT is made of an active layer sandwiched between two thin soft encapsulatinglayers. The first generation of PCT actuators were manufactured using a layer of cylindricalpiezoceramic fibers embedded in a protective polymer matrix material. They were called ActiveFiber Composite (AFC) and were introduced by Hagood and Bent [11] as an alternative tomonolithic piezoceramic wafers for structural actuation applications. Strain energy density wasimproved by utilizing interdigital electrodes (IDEs) to produce electrical fields in the plane of theactuator [12]. In order to increase the contact area of the PZT fiber with the electrodes, thenew type of PCT actuator with PZT fibers with rectangular cross-section, called Macro FiberComposite (MFC) actuator was developed at NASA Langley Research Center. Nowadays, bothof these types of actuators are produced by Smart Materials Corp.

2.5 Piezoelectrets

Piezoelectrets represent a very promising group of piezoelectric substances with electrome-chanical response comparable to PZT [2]. Today, piezoelectrets are made of porous poly-mer films prepared by double-expansion process and corona poling, which introduces immobilefree charge carriers on the surface of the voids inside the polymer matrix made of polypropy-lene. The charges on the surface of the voids form a texture of electric dipoles, so that thepiezoelectret has a nonzero macroscopic polarization, which is sensitive to the applied uniformelectric field. This makes the piezoelectret extremely flexible, lightweight, with a low acous-tic impedance. In addition, piezoelectrets can be produced inexpensively and environmentallyfriendly. These properties of piezoelectrets allow the construction of light, flat, and sensitiveelectroacoutic transducers.

3 Noise suppression by means of active elasticity controlThe greatest advantage of piezoelectric materials is the linear relationship between electricaland mechanical state quantities in the piezoelectric actuator. This makes it possible to fabri-cate the electroacoustic transducers with an extremely simple construction, a low cost, a fastresponse without distortion of the transmitted signal, and many other advantages.

The aforementioned fundamental properties of piezoelectric material allow the construction ofextremely simple noise and vibration suppression devices by means of the method called ac-tive elasticity control of piezoelectric materials. Its fundamental principles and applications arepresented in this section.

3.1 Piezoelectric equations of state

The electrical and mechanical state of the piezoelectric material is described by the electricfield Ei and electric displacement Di and by the strain Sij and stress Tij , respectively. Due toobvious thermodynamic reasons, one electrical and one mechanical state quantity are indepen-dent 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 piezoelec-tric actuator. Symbols U and Q are the voltage and charge on the electrodes. Symbolsl1, l2, and l3 are the dimensions of the piezoelectric actuator along x1, x2, x3 axes, respec-tively. E3 is the electric field along x3 axis. Symbols ∆l3 and ∆l1 are the elongation of thepiezoelectric actuator in the d33- and d31-mode, respectively. Symbols F3 and F1 stand forthe 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 possibilitieshow to unambiguously describe the local equilibrium state in the infinitesimal volume of thepiezoelectric 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 andelastic compliance, respectively.

The vast majority of piezoelectric electroacoustic transducers operate in two regimes, which areshown in Fig. 2. When the orientation of the applied force Fi = (0, 0, F3)i is parallel with theorientation of the applied electric field Ei = (0, 0, E3)i, the piezoelectric transducer operatesin the d33-mode (See Fig. 2(a)). When the state quantities Sij , Tij , Ei, and Di are uniform inthe transducer, it is convenient to integrate Eqs. (1) and (2) over the volume of piezoelectrictransducer, which yields:

Q = Cs U + dF3, (3)∆l3 = dU + (1/KS,33)F3, (4)

where CS = ε33 l1l2/l3, KS,33 = (1/s3333) l1l2/l3 and d = d333 are the capacitance, spring con-stant, and the piezoelectric coefficient of the whole piezoelectric transducer, which operates inthe d33-mode, respectively. Bulk piezoelectric ceramic and piezoelectret electroacustic trans-ducers operate usually in this mode.

6

(a)

40

35

30

25

20

15

10

5

Tra

nsm

issio

n L

oss (

dB

)100

2 3 4 5 6 7 8 9

10002

Frequency (Hz)

Negative capacitor: Off On

(b)

Figure 3: (a) Geometrical arrangement of the system for a control of the acoustic transmis-sion loss using the curved piezoelectric polymer membrane. (b) Measured transmissionloss TL = 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 theintegration of the uniform state quantities over the volume of piezoelectric transducer, one getsfollowing equation:

Q = Cs U + d(s) F1, (5)

∆l1 = d(a) U + (1/KS,31)F1, (6)

where KS,31 = (1/s1111) l2l3/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 piezoelec-tric 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 actua-tors by connecting them to active shunt circuits. When the external capacitor of a capacitanceC is connected to the piezoelectric transducer, the macroscopic spring constant of the actuatorK = 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 externalcapacitor:

U = −Q/C, (7)

where C is the capacitance of the external capacitor. Combining Eqs. (5), (6), and (7), themacroscopic value of the spring constant K is equal to

K = KS,31

( 1 + α

1− k2 + α

), (8)

7

(a)

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4Ab

so

rptio

n c

oe

ffic

ien

t (1

)

2 3 4 5 6 7 8 9

10002 3

Frequency (Hz)

Negative capacitor: Off On 1 kHz

(b)

Figure 4: (a) Geometrical arrangement of the system for an enhancement of the soundabsorption using the curved piezoelectric polymer membrane. (b) Measured absorptioncoefficient 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 k2 = 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− k2)CS , it imme-diately follows from Eq. (8) that the value of the spring constant of the piezoelectric transducerreaches quite high values. In order to achieve such a situation, the active electronic circuitcalled 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 thick-ness 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 thesituation, when the negative capacitor, which is connected to the piezoelectric polymer film isoff (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 thissystem is to reduce the absorption coefficient α0 = 1−|pr/pi|2 of the system, which consists ofthe 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 inthe 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 themeasured value of α0 in the system, where h = 0.05 mm, R = 40 mm, and H = 20 mm. Thethick 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 energyis 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 al. [9] that the sound shielding system may duringits operation enter the regime of negative elasticity. After this discovery, the method of activeelasticity control has been recognized as a simple tool for the construction of active acous-tic metamaterials and metasurfaces, i.e. large planar structures with the negative acousticimpedance [14].

Independently, several groups around the world have constructed active acoustic metamaterialsand metasurfaces, which employs the piezoelectric materials [1, 16].

4 ConclusionsThe brief review of several piezoelectric materials, which can be used for the construction ofelectroacoustic transducers, has been presented. Their advantages and disadvantages havebeen discussed. The linear relationship between electrical and mechanical state quantitiesmakes it possible to construct devices with a small output signal distortion. The principlesof the active elasticity control method have been presented. We have shown that using thismethod, it is possible to construct sound shielding and sound absorbing systems of a greatsimplicity, extremely small weight and superb sound suppressing performance.

Acknowledgements

This work was supported by Czech Science Foundation Project No.: GA16-11965S, co-financedfrom Ministry of Education, Youth and Sports of the Czech Republic in the Project No. NPULO1206.

References

[1] W. Akl and A. Baz. Multi-cell active acoustic metamaterial with programmable bulk mod-ulus. Journal of Intelligent Material Systems and Structures, 21(5):541–556, Mar. 2010.WOS:000275169600005.

[2] S. Bauer, R. Gerhard-Multhaupt, and G. M. Sessler. Ferroelectrets: Soft electroactivefoams for transducers. Physics Today, 57(2):37–43, Feb. 2004.

[3] C. Chilowsky and P. Langevin. Production of submarine signals and the location of sub-marine objects, 1923.

[4] J. Curie and P. Curie. Développement, par pression, de l’électricité polaire dans lescristaux hémièdres à faces inclinées. Comptes rendus, 91:294–295, 1880.

[5] J. Curie and P. Curie. Contractions et dilatations produites par des tensions électriquesdans les cristaux hémièdres à faces inclinées. Comptes-rendus de l’Académie des Sci-

9

ences, 93:1137–1140, 1881.

[6] M. Date, M. Kutani, and S. Sakai. Electrically controlled elasticity utilizing piezoelectriccoupling. Journal of Applied Physics, 87(2):863–868, 2000.

[7] E. Fukada, M. Date, and N. Hirai. Piezoelectric Effect in Poly-gamma-methyl-L-glutamate.Nature, 211(5053):1079–1079, Sept. 1966.

[8] E. Fukada, M. Date, K. Kimura, T. Okubo, H. Kodama, P. Mokry, and K. Yamamoto. Soundisolation by piezoelectric polymer films connected to negative capacitance circuits. IEEETransactions on Dielectrics and Electrical Insulation, 11(2):328–333, Apr. 2004.

[9] E. Fukada, M. Date, H. Kodama, and Y. Oikawa. Elasticity control of curved piezoelectricpolymer films. Ferroelectrics, 320(1):471–481, 2005.

[10] E. Fukada, M. Tamura, and I. Yamamoto. Polypeptides piezoelectric transducers. In Pro-ceedings of the International Congress on Acoustics, pages D–31, Tokyo, Japan, 1968.

[11] N. W. Hagood and A. A. Bent. Development of piezoelectric fiber composites for struc-tural actuation. In AIAA/ASME/ASCE/AHS/ASC 34th Structures, Structural Dynamics, andMaterials Conference, volume -1, pages 3625–3638, Apr. 1993.

[12] N. W. Hagood, R. Kindel, K. Ghandi, and P. Gaudenzi. Improving transverse actuation ofpiezoceramics using interdigitated surface electrodes. In Proc. SPIE 1917, Smart Struc-tures and Materials 1993: Smart Structures and Intelligent Systems, pages 341–352, 1993.

[13] H. Kawai. The Piezoelectricity of Poly (vinylidene Fluoride). Japanese Journal of AppliedPhysics, 8(7):975–976, July 1969.

[14] P. Mokrý, P. Psota, K. Steiger, J. Václavík, R. Dolecek, V. Lédl, and M. Šulc. Noisesuppression in curved glass shells using macro-fiber-composite actuators studied by themeans of digital holography and acoustic measurements. AIP Advances, 5(2):027132, Feb.2015.

[15] P. Mokry, E. Fukada, and K. Yamamoto. Sound absorbing system as an application ofthe active elasticity control technique. Journal of Applied Physics, 94(11):7356–7362, Dec.2003.

[16] B.-I. Popa, L. Zigoneanu, and S. A. Cummer. Tunable active acoustic metamaterials. Phys-ical Review B, 88(2):024303, July 2013. WOS:000321856400002.

[17] H. A. Sodano, G. Park, and D. J. Inman. An investigation into the performance of macro-fiber composites for sensing and structural vibration applications. Mechanical Systems andSignal Processing, 18:683–697, 2004.

[18] M. Tamura, T. Yamaguchi, T. Oyaba, and T. Yoshimi. Electroacoustic transducers withpiezoelectric high polymer films. J. Audio Eng. Soc, 23(1):21–26, 1975.

[19] W. Voigt. Lehrbuch der Kristallphysik: mit Ausschluß der Kristalloptik. Leipzig, 1910. OCLC:913701611.

10