IEEE TRANSACTIONSULTRASONICS,ON SONICS VOL. SU-32, NO. 4. JULY 1985AND 481

Piezoelectric Composite Materials for Ultrasonic Transducer Applications. Part I: Resonant

Modes of Vibration of PZT Rod-Polymer Composites

T. R.GURURAJA, WALTER A. SCHULZE, MEMBER, IEEE, LESLIE E. CROSS, FELLOW, IEEE, ROBERT E. NEWNHAM,BERTRAMA.AULD, AND YUZHONG J. WANG

Abstmcr-Theobjective of the presentworkwastogainadeeper understanding of the behaviorof lead zirconate titanate (PZT) polymer composites for applications such as ultrasonic medical diagnosis in the megahertzfrequencyrange.Thesecompositeswereoriginally devel-oped for low-frequency hydrophone applications. The PZT rod-poly-mer composites have been prepared withfive to 30 volume percent PZT using 0.28 mm and 0.45 mm rods. In a disc of PZT rod-polymer com-posite material, there are three principal typesof resonance: the planar mode, the thickness mode, and various lateral modes causedby the reg-ular periodicity of the PZT rod in the composite. These resonance modes have been studied with the following techniques:1) electrical impedance measurement as a function of frequency and2) laser probe dilatometry of the dynamic displacementas a function of frequency and position in the composite lattice. The observed resonance behavior is found to be a result of lateral interactions in the composite through the epoxy me- dium. The effect of temperature on the electromechanical properties of the composite has also been investigated. Implicationsof these results for optimizing the design of ultrasonic transducers are discussed.

I. INTRODUCTION

THE DESIGN and fabrication of composite materials optimized for a special application has been the sub-

ject of extensive research recently. The applications range frommechanicalstructures to electronic devices.In de-signing composite materials, primary importance is given to the proper choice of component phases and the way in which they are interconnected to maximize a predefined figure of merit for the application envisaged. An important class of these new materials is the family of piezoelectric ceramic-polymer composite transducers. To date, most of the work on piezoelectric ceramic-polymer composite ma-

mensions of the transducerare muchsmallerthanthe acoustic wavelength [l]-[8]. Until now there have been no studies investigating the usefulness of these composites at higher frequencies(1-10 MHz) for medical diagnostic and nondestructive testing applications. At these frequencies, the acoustic wavelength is comparable to the scale of the composite microstructure. The acoustic impedance, band-width, and radiation patterns of the composite transducer can be controlled in a manner so sophisticated that it is impossible in single phase materials. The results of a sys- tematicinvestigation of the compositematerialsmade from’piezoelectric lead zirconate titanate (PZT) ceramics and piezoelectrically inactive polymer are reported here. Thisstudyfocusesontheunderstanding of electrome-chanical properties of the composite materials in resonant configurations. The knowledge of the high-frequency dy-namic behavior of the composite was then used to evaluate thecompositematerialsforultrasonictransducerappli-cations with an emphasisonmedicaldiagnosticapplica-tions. These results are discussed in an accompanying pa-per (Part 11).

In Section I1 the requirements of a piezoelectric trans- ducer for ultrasonic imaging applications and the limita-tions of the existing single phase transducer materials are described. In Section111a brief review of the earlier works on piezoelectric ceramic-polymer composites of relevance tothepresent work is given.Advantages of the use of composites for ultrasonic applications are pointed out. The criteria used to select an appropriate composite structure for a detailed investigation for high frequency transducer

terials has been focused on hydrophone applications in theapplications are also described. Bulk mechanical proper- low-frequency(lessthan 40 KHz) range,where the di-

ManuscriptreceivedNovember 26, 1984. This work was supported in part by North American Phillips Laboratories.

T. R. Gururaja, L. E. Cross, and R.E. Newnham are with the Materials Research Laboratory, The Pennsylvania State University, University Park, PA 16802, USA.

B. A. Auld and Y.J . Wang, are with the Edward L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA.

W. A. Schulze was with the Materials Research Laboratory, The Penn-sylvaniaStateUniversity. He is now with the New York StateCollege of Ceramics, Alfred University, Alfred, NY 14802, USA.

ties of the polymer phase that strongly influence ultrasonic properties of the composite are summarized in Section IV. The characterization of all the different resonance modes in the composite are discussed in Section V. Laser probe measurements are presented in Section VI. The effect of temperature on the resonance modes in the composite are dealt with in Section VII. Finally, the implication of the resultson thehigh-frequencyvibrationbehavior of the composites in air for the ultrasonic imaging applications are summarized in Section VIII.

482 IEEE ON SONICS AND ULTRASONICS, VOL. SU-32, NO. 4, JULYTRANSACTIONS 1985

11. PIEZOELECTRICTRANSDUCER Desilets er al. [121 and Go11 [151 have further improved MATERIALPARAMETERS the andsensitivity disc transducersbandwidththe of their

usingmultiplelayerimpedancematching schemes. Al- The basic requirements of a piezoelectric transducer for though two layer matching schemes work very well with

ultrasonicdiagnostic imagingare an ability to generate readily available materials, the transducerfabrication is , short acoustic pulses and receive them with high sensitiv- quite involved. As the frequency of operationis increased,

ity in the frequency range Of '-lo MHz. The transducer the thickness ofthe matching layer decreases, which makes should also exhibit good axial and lateral resolution to vis- the fabrication difficult.ualize structures with dimensions of the order of a milli- The recent development of piezoelectric polymer ma-meter or less L91. In terms Of the parameters,terialssuch aspolyvinylidenefluoride(PVF2)hasopenedthese requirements can be summarized as follows: 1) The up new possibilities for transducers operating with mediapiezoelectric material should have a high electromechan- of low acoustic impedance I161. PVF2 has a low acousticical coupling coefficient for highsensitivityand 2) The impedance, reasonable piezoelectric coupling, high 933acousticimpedance of thetransducershouldbe well coefficient, and wide-bandwidth frequency response,matched to that of the load to minimize reflection losses which are excellent properties for acoustic imaging with aat the interface. The acoustic impedance matching at the low-impedance load. Several intrinsic limitations of PVF2 interface determines the quality factor ( Q broadband na- transducers, as discussed in detail by Collerame et al. [171 ture) of the transducer. and Hunt er al. [181, restrain their extensive use in ultra-

It is well known that the piezoelectric ceramic materials sonic imaging applications. Major limitations are men-such as PZTwithhighelectromechanicalcouplingsuffer tioned below. First of all, it is very difficult to produce from a Severe disadvantage when Operated with a low- sampleswithresonancenearthetypicaloperating fie-impedance load such as that Of the human body. The quency in medicalultrasound;although recently somere-acoustic impedance Of PZT i' around 30 x lo6 searchers have been successful in producing 1-2 mm thick whilethetissues have acoustic impedancenearthat of polarized PVF2,films[191,The d33coefficientof PVF2is water, 1.5 kg/m2-s. ~ e n c e f o r t hall acoustic impedances only l op C/N, and hence pVF, is a poor ultrasonic trans-

begiven in units Of IO6 kg/m2-s, As mitter. In addition PVF2 hasdielectric of only a constant a result of the aco.ustic impedance mismatch,thecoupling at KHz whichdecreases at higher frequencies. Thus, of the acoustic energy at the transducer-load interface is the electrical impedance of PVF2transducers is high and

Poor. The resonance behavior is thus high Q (narrow is in general more difficult to match than the piezoelectricbandwidth). The consequence of a high Q in a transducer ceramics. The dielectric loss tangent in P V F ~is 0.25 at

a 'low Pulse-rise time and a Prolonged ring down with 2.5 MHz and acts as a major Source of absorption of elec-a detrimental effect on range resolution. tricalenergyappliedto the transducer. Inthereceiver

In practice, two methods are used to increase the trans- mode, the dielectric loss is found to diminish the signal toducer bandwidth. In the first method, the resonanceof the noise ratio.piezoelectric element is mechanically damped with a well As discussed previously, single-phase piezoelectric ma-matched backing medium [l0]. As a a large POrtion terials(ceramic or polymer) arefarfrombeingoptimizedof the available energy is transmitted into the backing ma- for ultrasonicimaging applications. Thus, a compositeterialresultingin a lower sensitivity. In the second material combining the desirable properties of differ-method, the frequency bandwidth Of a transducer is in- ent phases might be superior. This concept has proven to creased the use Of an impedancematching layer Of behighlysuccessful in designing compositematerialsquarter wavelength in thickness and characteristic imped- consisting of PZT and piezoelectrically inactive polymer.ante to the geometric Of those Of the trans- The hydrostatic piezoelectric coefficients of these corn-ducer load [l0]. Nore ["I,and and positeswere two to three orders higher than thatof theDesilets er 1121, andSouquet et al. [l3] havemade piezoelectricphaseused in the composite. Although thecomplete theoretical and experimental analyses for obtain- design and fabrication of different types of piezoelectric jng Optimum acoustic matching.Depending On the 'pe- compositematerialsforhydrophoneapplications at low cific requirementsofsensitivity,bandwidth,andimpulse frequencies (lessthan 40 KHz) hasbeen in several response,the Optimum acoustic impedance of the papers [1]-[8], forcompletenessabriefsummary is pre-inglayer for a PZT ceramic disc operating into a water sented here in the next section. equivalent load varies from four to seven. Since no readily availablematerial has its acoustic impedancenearthis 111. COMPOSITEPIEZOELECTRICTRANSDUCERSvalue, a matching layer must bepreparedsynthetically, which is not always easy. However, in practice,such ma- PZTceramic, which is commonly usedasapiezoelec-terial is prepared by mixing suitablemetallicpowdersuchtric transducer material, suffersfromseveraldisadvan-as aluminum with some epoxy resin [lo], 1131, [141. The tages when used as a hydrostatic pressure sensor. The hy- composite matching layer configurations have relatively drostatic piezoelectric coefficient dh( =d33+ 2d3,)of PZT large attenuation coefficient andadd to further loss of is low due to opposite signs of piezoelectric strain coeffi- acoustic cients d33and d 3 , ,theeven of both d33energy. thoughmagnitudes

483 GURURAJA el ai. : PIEZOELECTRIC COMPOSITE MATERIALS-PART I

TABLE I DIELECTRIC COMPOSITESAND PIEZOELECTRICPROPERTIES OF PZT-POLYMER

Dielectric Description Density Constant

of Composite (gm/cc) K g, V m N - ' ) dh@CP.-') dhgh( 1 0 - % * ~ - ' ) Reference

Single Phase PZT 7.6 1800

3-3 Coral replamine-PZT

PZT-Spurns epoxy (BURPS) PZT-silicone rubber (BURPS)

composite 3.3 4.5 4.0

50 620 450

1-3 PZT rods-Spurns epoxy PZT rods-polyurethane

1.4 1.4

54 40

1-3-0 PZT rods-Spurns epoxy-glass spheres

PZT rods-foamed polyurethane

1.3

0.9

78

41

0-3 PbTi0,-chloroprene rubber Bi,03 modified PbTi03- chloroprenerubber

-

-

40

40

3-1 Perfodted 3-1 composite 2.6 650

3-2 Perforated 3-2 composite 2.5 375

and d 3 , are large. The hydrostaticvoltagecoefficient gh (dhle&) is also small because of its high relative permit-tivity k . ea is the permittivity of free space.

To improve themagnitude of dh and gh, anumber of different diphasic composites using PZT and passive poly- mers have been fabricated. Itwasshownthatthephase connectivity, defined as the manner in which the individ-ual phases areinterconnected, is the key feature in de- signing the compositematerials.Theelectrical flux pat-tern and mechanical stress distribution together with the resulting physical and piezoelectricpropertiesdepend strongly on the phase connectivity. In a diphasic compos-ite, there are ten possible connectivity patterns designated as 0-0, 1-0, 2-0, 3-0, 1-1, 2-1, 3-1,2-2,3-2,and 3-3. A 1-3 connectivity pattern, for example, consists of parallel PZT rods embedded in a three-dimension continuous poly- mer matrix [3]. In the notation used here, the piezoelec-tric phase appears first.

Dielectric and piezoelectric properties of different types of PZT-polymer composite materials designed for the hy- drophone applications are summarized in Table I . Hydro-static d and g coefficients were measured by a substitution method [7]. As listed in the table, a 3-3 composite com-prised of PZT and polymer phases continuously self-con-nected in three dimensions to give two interlocking skel-etons in intimate contact with one another [1, 61. A 1-3-0 compositeisa 1-3 PZT rod-polymercomposite with a thirdphasesuch as hollow glass spheres or pores not in contact with each other [20]. In composite with 0-3 con-nectivity, piezoelectric ceramic particles (PZT, pure, and modified lead titanate) 1-10 p in size are loaded in a poly- mer matrix [g]. Composites of PZT and polymer with 3-1 and 3-2 connectivity patterns have been fabricated by drilling holes in sintered PZT blocks and filling the holes with epoxy [7]. Indesigningallthesecompositemate-

2.5 40 100

140 20 45

56 56

36 110 180

27 20

5040 ,2200 8100

1536 1100

60 41 2460

210

100

73

35

14600

3500

28

30

60

10

170

200

280

5100

12000

rials, the primary goal was to decouple the transverse d3, coefficient and lower the dielectric permittivity to augment the hydrostatic d and g coefficients. The product of dh and g h listed in Table I was used as the figure of merit for the hydrophone applications.

From Table I, it is evident that the hydrostatic pressure sensitivity of some of the composites was orders of mag- nitude larger than the corresponding values of the piezo-electric phase used in the composites. The density of the composite could be adjusted between the densities of the component phases. Composites with porous polyurethane phase were prepared to have positive buoyancy in water. By choosing softpolymerssuchassiliconerubberand polyurethane, composites were made flexible.

PZT polymer composites have several advantages over conventional piezoceramic materials for ultrasonic appli-cations. In composites most of the PZT (70-90 percent) is replaced by a low-density polymer, and hence results in a better acoustic impedance matching to the human body. Thecompositesalso have a relatively low mechanical Q (3-10) [21]. These properties of the compositesappear well suited for the broadbandwidthapplications. Al-though PZT has a high d33coefficient, the voltage coeffi- cient g33is low because of the high dielectric constant. Thus, PZT is a poor receiver of ultrasound. The concept of composite transducerallowsdesigningacomposite structure to enhance the g33 coefficient and improve the sensitivity in the receiving mode. If the receiving voltage sensitivity of the transducer is enhanced, the human body can be interrogated at lower ultrasonic energy andthe bi- ological effects of ultrasound, if any, can be minimized.

The following criteria were used hereto select compos-ite material of an appropriate connectivity for a systematic investigation intendedtowards ultrasonic transducers. Transducers for ultrasonic imaging applications are oper-

484 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-32,NO. 4, JULY 1985

TABLE I1 PHYSICAL, DIELECTRIC, OF PZT ROD-POLYMER A N D PIEZOELECTRIC PROPERTIES

COMPOSITES

Rod Volume percent Diameter

PZT (mm) Periodicity

d (mm) Density

p(gm/cc) Dielectric

Permittivity K d~ Coefficient

( p U N ) ~~ ~

5 0.45 1.78 1.41 19 155 10 0.45 1.26 1.64 I09 I94 20 0.45 0.90 320 2.29

7 . 6400

238 30 0.45 0.73 3 .OS 803 375 10 0.28 0.78 1.62 94 183

0.55 339 2.36 217 20 0.28

Single Phase 1400 -PZT -

ated in a half-wavelengththicknessmodeformaximum sensitivity. Thus, themajor requirement of a composite was to have a well defined thickness resonance with a rea- sonably good piezoelectric coupling coefficient and a low Q. Pulse-echoamplitudeandbandwidthofair-backed compositetransducersoperating with water load in the low megahertz frequency range determined by the tone-burst pulse-echo method [22] were used as additional pa-rameters.

Amongallthedifferentcomposites,onlythose with PZT rods embedded in Spurrs epoxy' matrix with regular periodicity (1-3 connectivity) appeared to be very prom-

Fig. 1. Typical 1-3 composites with PZT rods embedded in Spurrs epoxy.isingfor the ultrasonic transducer application [21]. The thicknesscouplingcoefficientfor thesecomposites was ers [3]. In brief, PZT-501A2 rods were extruded using an

organic binder and then fired at 1285°C for one half hour. Fired rodswerealignedusinganarray of appropriately spaced holes drilled in a pair of brass discs bolted parallel to each other. The array of PZT rods wasthencastin Spurrs epoxy matrix. The resultingcomposite was cut perpendicular to the length of the rod and lapped to the requiredthickness.Thecomposite wasthenelectroded with silver paint on the major surfaces and poled conven- tionally by applying an electric field of 20 kV/cm for five minutes in a heated oil bath at 80°C. Different composites werepreparedwithapproximatelyfive, ten,20, and30 volume percent PZT using 0.45 mm rods and with ten and

determined to beabout 60-70 percent. This value com- pares favorably with the thickness coupling coefficient of 49 percent for the PZT-5 disc which is usedin commercial transducers. Mechanical Q of the composites was low (3- 10) compared to that of PZT-5 (80). The pulse-echo am-plitude of these composite transducers was large (from 2-3 V to 10 V input signal) and comparable to those of com- merciallyavailable transducers.The 1-3 composites had additional advantages. There are many variables including PZT rod diameter andvolumepercent of the PZT and polymer phases, which can be vaned relatively easily to optimizetheproperties for particular application. The continuous poling technique [23] can be used to polarize long PZT rods, which can then be arranged in a polymer matrix in such a way to obtain a desired radiation pattern. Since the composite structure resembles a transducer ar-

20 volume percent PZT using 0.28 mm rods.Table I1 gives the periodicity (distance between the centers of neighbor- ing PZT rods) of PZT rods in each of these composites. Thecomposite sampleswereshapedascirculardiscs ofray, the knowledge of the high-frequency dynamic behav-diameter 19 mm and varying thickness from 0.5 mm to 5ior of these composites might be helpful in resolving some

of the problems encountered in array applications, such as minimizing the acoustic cross talk between the adjacent elements.Because of these advantages, 1-3 composites were chosen for an extensive investigation aimed at high frequency transducer applications.

A detailed procedure for fabricatingcomposites with 1-3 connectivity has been reported by Klicker and co-work-

'Trademark of Polysciences, Warrington, PA.

mm. A picture of typical compositesamplesisgivenin Fig.1.

Results on the average properties including density, pi-ezoelectric d33coefficient,anddielectricpermittivity of PZT rod-polymer composites have been reported earlier by Klicker et al. [3]. Data for the composite samples used in this work are listed in Table I1 along with the properties of single phase PZT-5O1A for comparison.

'Trademark of Ultrasonic Powders, Inc., South Plainfield, NJ

485 GURURAJA er al.: PIEZOELECTRICCOMPOSITEMATERIALS-PART I

IV. BULKMECHANICALPROPERTIESOF

SPURRSEPOXY Spurrs epoxy is the piezoelectricallyinactivephase in

thecompositematerialconsideredhere. However, its function in the compositetransducer is quite critical. When the composite is used as an ultrasonic transmitter, the epoxy has to effectively couple the ultrasonic energy fromahigh-acoustic-impedance PZT to a low-acoustic- impedance load. Similarly, in the receiving mode, the ul-trasonic energy incident on the composite should be trans- ferred effectively to the piezoelectrically active PZT. The importantparameters of the polymerthatinfluencethe performance of the composite as an ultrasonic transducer are its acoustic impedance, longitudinal and shear wave velocities,and attenuation coefficients and their depen- dence on frequency. These properties of the polymer de-termine the interaction among the neighboring PZT rods andhencethehigh-frequencydynamicbehavior of the composite.Measurementtechniques used to determine these parameters in Spurrs epoxy are described elsewhere [24]. Only the results which are useful for analysis of the vibration behavior of the composites are presented here.

The longitudinal andtransverse wave velocities in Spurrs epoxy were determined to be 2060 m/s and 1150 m/s, respectively. The acoustic impedance of the Spurrs epoxy was calculated to be 2.27 X lo6 kg/m2-s. The at-tenuation of the transverse wave in Spurrs epoxy was mea- sured to be 6 dB/cm at 0.5 MHz. The attenuation coeffi- cient wasfound to increase with thesquare of the frequency. The glass transition temperature Tg is another characteristic parameter for polymeric material. Theglass transition temperature is defined as the temperaturebelow which the material behaves like a glass and above which thematerial is rubberlike and soft [25]. In the present work Tgand its dependence on frequency was determined by measuring the dielectric loss tangent of Spurrs epoxy as a function of temperature and frequency. At the glass transition temperature, the loss tangentgoesthrougha peakandcanbeeasilyidentified.ForSpurrsepoxy, TR was found tobe a function of frequency varying from 70°C at 1 0 0 Hz to 121°C at 1 MHz with a shift of 12-15°C per decade of frequency.

_--. Radial Mode P

(b) Fig. 2. Resonance modes in a disc-shapedpiezoelectricmaterial.(a) Ra-

dial mode. (b) Thickness mode.

A . Planar-ModeResonance The planar mode (alsocalledradial)vibrationinthin

disc, as illustrated in Figure 2(a), involves simultaneous mechanical motion in the 1 and 2 directions driven by the electric field in the 3 direction direction).(poling Since the diameter was the largest dimension (19 mm) in all the composite samples, the planar mode was thelowest frequency resonance mode.

TheIRE(nowIEEE)standardon piezoelectricmea-surements [26] was used to determine the electromechan-ical coefficients and elastic constants. The most important parameters for calculating these constants are the series and parallel resonance frequenciesf, and&, the geometric capacitance C,, and the impedance minimum lZ,l at res- onance. A spectrumanalyzer(HP 3585A), which pro- vides a circuit similar to the transmissionnetworkrec-ommended by the IRE standard, was used in measuring frequenciesfm and f, corresponding to minimum and max-imumimpedance. In the presence of high mechanical losses, fm andf, are quite different fromfs and&. TheIRE Standard recommends the following approximation to cal-culate Af = f p - fs from the measured value off, and f, L261

where the figure of merit M is given by

V. RESONANCEMODES 1 M = 1

2rfJ1Co 2nfm(Co + CI)lzml.Resonancemodes in composite materials, as in single phase materials, are defined by the geometry and dimen-

I (2)

sion of the specimen. In a circularly shaped 1-3 composite The C,, C , are the capacitance of the parallel and series branch, and R , is the resistance of the series branch of the

material,theresonancemodesobservedare theplanar mode, the thickness mode, and a number of lateral modes related to the regular periodicity of the PZT rods in the composite.Characterization of the differentresonance modes in 1-3 PZT rod-polymer compositewillbede-scribed in the followingsubsections.Knowledge of the resonant vibration behavior of the composites in air is im-portant and helpful in the evaluation of the composites as anultrasonic transduceroperating intowaterequivalent load.

equivalent circuit of the piezoelectric material near reso- nance. The sum (C, + C , ) is the static capacitance, which was measured at a frequency well below fundamental res-onance, for instance at 1 KHz. These approximations are valid for resonances with M > 3.

The planar coupling coefficient kp was calculated from the expression given by [27]

l + a 1

486 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS. VOL. SU-32. NO. 4. JULY 1985

TABLE 111 ELECTROMECHANICALPROPERTIES OF COMPOSITES FROM THE RADIALMODERESONANCE

c* N(Hzm) Longitudinal

Volume percent PZT (Frequency Velocity (Rod Diameter) Thickness’ M k, Q Constants) (mis)

5 Thin 17.0 1064 14830.97 40 21.7

l 0 Thin 16.6 1011 1409 (0.45 mm) Thick - 1.4 36 1120 1561

1 . 1 42 (0.45 mm) Thick 1.5 to 2.023.0 34 l080 1506

20 Thin 21.0 955 l33 11.2 23 (0.45 mm) Thick 1.5 to 2.326.534 1043 1454

30 Thin 1 . 1 20 .0 32 950 1324 (0.45 mm) Thick 2.026.736 1046 1458

10 Thin 1 . 1 18.8 36 1032 1439 (0.28 mm) Thick 1.523.1 35 1097 1529

20 Thin 1 . 1 (0.28 mm) Thick 1.7

‘Thick = 0 . 6 mm, and thin > 3 mm.

where U is the Poisson’s ratio of the material. Since the Poisson’s ratio of both PZT and epoxy are approximately 0.3, the Poisson’s ratio of the composite was assumed to be 0.3. The value of R1 = 2.05 for U = 0.3. The f, was approximated tofm.

The mechanical quality factor Q can be evaluated from the relation [26]

For M > 3, (4) was simplified to

The calculated values of kp and Q from (3) and ( 5 ) for several composites are summarized in Table 111. The fre-quency constant Np for the planar mode (product of reso- nancefrequencyandthediameter)isalsolisted in the table. The data are divided into two groups depending on the thickness of the sample. The first group investigated consisted of thinsampleswithathickness of about 0.6 mm.Thesecondgroup was comprised of all samples thicker than 3 mm and was classified as thick samples. The properties remained virtually constant in the two extreme limits. The data listed in the table are an average of the measurements of at least five samples.

As it emerges from Table 111, the figure of merit M for the radial-mode resonance of all the composites was be- tween one and two. As mentioned before, (3) and ( 5 ) used for calculating kp and Q are not fully valid for values of M < 3. Subsequently, the valuesof kpand Q listed in Table 111are far from being exact. However, since the value of M is approximately the same for all the samples, the un-certainty in assessing k,,, and Q is of the same order. Hence the results can be used for a relative comparison of sam- ples having different volume fraction PZT.

Table I11 indicates that the planar couplingcoefficient k,, of the composites increases with increase in the volume

22.0 32 970 1352 25.5 35 1057 1474

fraction of PZT. Thick composites have a higher kp com-paredto thincomposites of thesame volume fraction. Lower values of kp in thin samples indicate that the me-chanicalenergy is not efficiently coupledfromthe PZT rods to the polymer and from the polymer backto the PZT rods. Thecouplingbecomesmore efficientforthicker samplesindicating a greater homogeneity. A similarex-planation can be given for the difference in the frequency constant between the thick and thin samples.

In the last column of Table 111, the longitudinal velocity C, perpendiculartothelength of the rodislisted. The value of C,was calculated using the relation [27]

2.05fs =-27ra

[(E,lp(l - C?)]”*

where fs is the series resonance frequency of the planar resonance. The modulus E, is the elastic modulus of the composite perpendicular to the PZT rod axis, p is the den- sity, and a is the radius. In (6 )(E,lp)”* corresponds to the longitudinal velocity C, perpendicular to the rod axis. In calculating C, from (6), fs was measured and D was as- sumed to be 0.3 as already mentioned.

An attempt was made to theoretically estimate the lon- gitudinal velocity C, by obtaining anexpression for the elastic modulus E, perpendicular to the rod axis as a func- tion of volume fraction of PZT. Knowing E,. and the den- sity p of the composite (Table 11), C, was calculated from the expression C, = (E,/fi)”2.

The effective modulus E, in the transverse direction can becalculated by the Reussconstantstressmodel [14], which assumes that the two phases experience equal stress. This assumption seems appropriate for a combination of hard filler in a soft matrix, because the matrix should de-formmorethanthefillerandthestressinsuchasolid shouldbefairlyconstant.Theeffectivemodulus by the Reuss model is given by

1 U1 “2_ - _ + -- (7)Et E, E2

487 GURURAJA er al. : PIEZOELECTRIC COMPOSITE MATERIALS-PART I

2300- I I l 1

----

l300 I I I l0 IO 20 30 40 50

Volume Percent PZT

Fig. 3. Longitudinal velocity perpendicular to the PZT rod axis as a func-tion of volume percent PZT In composites.

nessdecreases,approachingthe Q of single-phase PZT 501A (80) [28].

The planar-mode resonance was studied as a function of temperature up to 100°C. It was observed that the planar couplingcoefficientremainedvirtuallyconstant with in- crease in temperature. However, the amplitude of the res-onancespectrumdecreasedgradually with temperature andwassuppressed below 0.1 dB at 100°C. Measure-mentscould not be made on the radial-moderesonance above 100°C. It is interesting to note thatthis temperature corresponds to the glass transition temperature of Spurrs epoxy (Section IV) at the resonance frequencyf, (50 KHz). It is conceivable that the suppression of the radial mode above 100°C is due to the very lossy nature of the Spurrs

488 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS. VOL. SU-32, NO. 4, JULY 1985

TABLE IV COMPARISON A N D VECTOR IMPEDANCE METHODOF IRE STANDARD METHOD FOR CALCULATING

ELECTROMECHANICAL COUPLING COEFFICIENTS'

Vector Impedance Standard IRE Method Method

Thickness fm - f, Af=fp - L Sample in mm (KHz) M (KHz) Kp (%) Q fp -fs kp (%) Q

12.9 72 20.3 48

200 0.66 2.320 1.0 1 . 0 4 1 22.6 24 0.350 201 2.54 1.820 1.7 1.168 22.8 390.929 202 3.05 1.998 1.9 1.364 24.7 37 1.184 22.9 43

351.48026.4 204 4.60 2.386 2.2 1.760 21.8 35 1.711 27 .1 37

25.6 39203 3.95 2.225 2 . 0 1.585

301.79230.8

'In a 20-percent PZT composite, with rod diameter = 0.45 mm.

27.8 37205 5.15 2.842 2.4 2.172

5 0 0 0 " " " " " " " '50 l00 I 5 0

Temperature, ' C

Fig. 4. Effectof temperature on the Frequency constant of radial mode res- onance of 1-3 composites.

and

Np =fpt (10)

where r is the thickness, andthemeaning of theother terms in (8)-(IO) is given in Section V-A. The IRE Stan-dard method was used to calculate these propertiesof the compositecorrespondingtothethickness-mode reso-nance.

Theexperimentalresultsaresummarizedin Table V. The data are again divided into two groups: thin samples withthickness around 0.6 mmandthicksampleswith thickness above 3 mm. As it can be seen in the table, with the exception of the five percent PZT composites, the fig- ure of merit M for the thicknessmoderesonance of all othersampleswasabovethree.Hence,theapproxima-tionsrecommended by the IREStandard to calculate k, and Q are valid. Indeed the values of the kt and Q deter-mined by the vector impedance methodon a selected num-ber of samples were within two percent of the values cal-culated by the IRE standard method.

Datalisted inTable Vindicate thatforthethickness mode resonance of thin samples (r = 0.6 mm), kt was 60-70 percent,and Q was three to ten.For thicksamples ( t > 3 mm), k, was approximately 50 percent,and Q

thick samples while the mechanical Q showed the reverse trend. The coupling coefficient and the frequency constant of thin sampleswereclosetothat of single phase PZT 501A (k33 = 70 percent,and = 3700 Hz m for PZT 501A) and were independentof the volume percentof PZT. In thick thick samples bothk, and NP were proportional to the volume percent of PZT.

The observed behavior of the composites in thickness-mode resonance can be explained as follows. At the res- onance frequency, PZT rods vibrate with a large ampli-tude. The vibrating rods act as a source of complex trans-verse waves intheepoxypropagatingin adirection perpendicular to the axis of PZT rods. These transverse waves generated in theepoxy interact with the array of PZT rods. In the first approximation the interaction is as- sumed to involve only nearest neighbors. Effectiveness of the interaction depends on the amplitude and phase of the transverse wave relative to that of the PZT rods. For thin samples resonating around 2.25 MHz, the wavelength of the transverse wave is approximately 0.5 mm (taking the transverse wave velocity to be 1150 m/s from Section IV). It is also known that the Spurrs epoxy is extremely lossy for transverse waves at this frequency. This results in only a weak interaction between the vibration of neighboring PZT rods. The relatively low Q of thin samples indicates that the rod vibrations are partly damped by the surround-ing polymer.

The thick sampleresonatearound 0.5 MHz and the wavelength of transverse waves in theepoxy is approxi- mately 2.3 mm. The wavelength is 1.5to three times larger than the separation distance between the PZT rods in the composites of different volume percent PZT. Since the at- tenuation of the transverse waves in the epoxy is relatively low at 0.5 MHz ( - 6 dB/cm), the amplitude of the trans-verse wave must be significant to cause a strong interac-tion between the rods through the epoxy medium. Thelow coupling coefficient in thick samples is probably a result of the phase cancellation effect between the vibrating rods (due to the electrical excitation) and the mechanical inter-action between the rods through the epoxy. The low me-

was 20 to 30. In general, thin composites had higher coupl-chanical loss in the epoxy is reflected in the high Q of the ing coefficient k, and frequency constant ecompared to composite.

489 GURURAJA er al.: PIEZOELECTRIC COMPOSITE MATERIALS-PART I

TABLE V THICKNESS-MODE RESONANCEIN COMPOSITES

Longitudinal FrequencyVelocity

Volume Percent PZT Thickness Figure of k, Constant (mis) (Rod Diameter in mm) (mm) Merit M percent Q Nf (Hz m) c, 2NP

5 0.6 2.2 (0.45) 4 to 6 2.4

57.1 5 1834 3668 27.5 31 1327 2654

10 (0.45)

0.6 3.6

4-6 4-6

68.0 7 1820 40.0 23 1492

3640 2984

20 (0.45)

0.6 3 to 5

5-7 5-7

68.9 9 1853 3706 55.11603 18 3203

30 - - - - - -(0.45) 2.4 12 61.1 26 1687 3374

10 (0.28)

0.6 1.9

3-5 3.6

62.6 4 1956 40.6 22 1403

2912 2806

20 (0.28)

0.6 2.9 to 3.4

5-7 5-7

72.0 8 1874 50.0 25 1555

3748 3110

C. Lateral-ModeResonances In addition totheradial-andthickness-modereso-

wa

d by calcestimate

velength is

u I and u2 a

ulatingtheelastic

much

(11)

rethe

nancesandtheirovertones,otherresonanceswereob-served in the frequency range 0-2 MHz. The frequencies of these resonances were independentof sample thickness, but were related to the lateral periodicity of the PZT rods in the composite. Absolute value of electrical admittance was measured on samples as a functionof frequency in the ambience of air and water using a spectrum analyzer (HP 3585A). Here samples of different thickness and volume fractionwereexaminedtoidentifythedifferentreso-nances observed in the 0 to 2 MHz frequency range. Three major resonances of interest are designated as fi, A I , and A2 as categorized in Table VI.

Theresonancecorresponding to fi was inversely pro- portional to the thickness of the sample. This resonance was heavily damped when the resonator was immersed in water. Such behavior suggests that resonance at fi is the longitudinal thickness vibration. The longitudinal velocity of sound, calculated usingtheformula Cl = 2tf , agrees very well with thetheoreticallyestimatedvalueforthe composites of different volume fractions, as discussed in detail in the previous section.

The resonances at&, and&? werevery similar in nature. For a certain volume fraction, these resonancesalways oc- curred at specified frequencies regardless of the thickness of the sample. As can be seen in Table VI, increase in the

40001 I 1 I I 1

2000 0 IO 20 30 40 50

Volume Percent PZT

Fig. 5. Longitudinal velocity along the PZT rod axis as a function of vol- ume percent PZT in composites.

The longitudinal velocity Cl along the length of the rod canbetheoretically modulus EI of the composite parallel to the PZT rods. At frequencieswherethetransverse larger than the separation distance between the rods, the Voigt constant strain model [l41 can be applied. The com-posite modulus using the Voigt average is written as

El = u , E ~+ u ? E ~

where El and E2 arethemoduli,and volume fractions of the two phases (PZT and epoxy). For PZT rods witha diameter that is small compared to length,volume fraction results in closer spacings of rods (reduc-themodulusalongthelength is given by E = l/$: = 10.5 x 10" N/m2(the Young's modulus of the rod at con-stant electric displacement). The longitudinal velocity Cl was calculated from the relation Cl = (El/p)"2.

The experimentally determined longitudinal velocity Cl, expressed as twice the frequency constant @, is given in the last column of Table V. This velocity is compared with the calculated values in Fig. 5. The excellent agreement betweentheexperimentalandtheoreticalvaluesfurther supports the equal strain model for calculating the effec-tivemodulusofthecompositealongtherodaxis.propagation

tion of the unit cell) and the resonances and A2 move to higher frequencies.

The behavior of the composites could be explained by simpleaveragingschemessuchastheconstantstrain model and the constant stress model for wavelengths large or small compared to the lattice periodicity (Section V-A and V-B). In the vicinity of the resonances of A, and A2, the wavelength of the transverse shear wave is comparable to the unit cell dimensions of the array and the analysis is morecomplicated. A Brillouin theory of elastic wave

in a two dimensionallyperiodiclatticecor-

- -

- -

490 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-32, NO. 4. JULY 1985

TABLE V I R E S O N , ~ N T IK COMPOSITE MATERIALS MODES

Resonance Frequency. . i n (1KHz c = -r hPercentVolume Rod Thickness I Periodicity c, = 2tfi c, = dfil

3 v2

5 51 0.45 2330 604 878 1.58 52 0.45 4.00 1.76 3 I 2 483 691 2496 853 859 53 0.45 4.80 1.76 262 449 25 l4 790

2.59 450 786 954

261 8 908 4371.76

10 101 0.45 1.93 I .27 604 804 1096 2294 1021 984 I02 0.45 3.64 1.27 410 662 1006 2984 840 903 103 0.45 5. 15 1.27 262 644 2698 72 1

54 0 .45 5 .90 222 730 769

20 20

30 30

-I 0.45 2.54 0 .90 540 894 - 2742 804 -202 0.45 3 .OS 0.90 455 830 - 2774 747 -203 0.45 3.95 0.90 348 828 - 2748 745 -204 0.45 4 .60 0.90 296 886 - 2722 792 -205 0.45 5.15 0.90 270 825 - 2780 742

-I 0 45 2.44 0.73 569.5 1125 - 2778 82 1 -302 0.45 5.15 0.73 276.5 1188 - 2848 867

When the rod spacingd is one'shear wavelength, a com-Scanned obng rods -

(a) (b)

Fig. 6. Unit cell geometriesandlaserscanpaths. (a) Standing waves at the second stopband, along thc unit cell edge. (b) Standing haves at the sec- ond stopband.alonr the unit cell diagonals.

standing results,illus-pletely different wave pattern as trated in Fig. 6(a). In this case a z-polarized, x-propagat-ing wave is again Bragg-scattered with a phase shiftof 27r from one vertical plane of rods toan adjacent plane. How- ever, it is easily verified that the wave is also Bragg-scat-tered at the same frequency by the 45" planes of rods, so that resonant scattering of the x-propagating wave into a y-propagating wave occurs. Thesey-propagating waves

respondingtothe PZT rod-polymercomposite was de- veloped by Auld er ul. in 1311. Forlaterallypropagating shear waves with polarizationalongtherods, the lowest stopbandfrequencieswerecalculated.Theexistence of stopbands was related to Bragg-scattering from planes of rods having various orientations in the square lattice. The essential phenomena can be explainedby reference to Fig. 6.Suppose in Fig. 6(a) that az-polarized,x-propagating shear wave is incidect on the grating. At a frequency for which the rod spacing d is one-half the shear wavelength (X,), constructive reflection (Bragg-scattering)occurs fromverticalplanes of rods, andresonanceoccursbe-tween adjacent vertical planes. The x-propagating wave is also scattered from planes of rods at 4.5" to the x and y axes; but in this case, Bragg conditionsare not satisfied andresonancedoesnotoccur. A stopbandexistsat d = h,/2 for an x-propagating wave, but there is no resonant scattering into y-propagating waves.At the stopband edge, the solution is a standing wave along x. From the square symmetry of the lattice, a similar standing wave solution along y also exists. This behavior corresponds to the first stopband of the lattice.

also experience resonance scattering of the same type. As a result, the solution is a two dimensional resonant stand-ing wave pattern as shown in Fig. 6(a). Here the rods all

vibrate in phase correspond second ofand to the stopbandthe square lattice.

For-a z-polarized z-propagating wave incident on the lat-tice, no Bragg scattering can occur because the structure is uniform along z . However, a spatial modulation of the phase fronts is produced by the difference in the properties of the rods andmatrix.Consequently,spaceharmonics are generated but none are resonant. Similar conclusions areobtained forz-propagating wavesof otherpolariza-tions.

In the following section, detailed laser probe measure-ments of the actual displacement on the composite to ana-lyzethenatureofvibration atthesefrequenciesarere-ported.

VI. LASERPROBEMEASUREMENTS

The measurements of actual displacement on the com-posite samples were performed using the laser heterodyne technique [31]. The samples were fine polished (+ 1 pm) andelectroded with highly reflecting gold electrodes for the laser probemeasurements. Relativeamplitudeand phase of the ultrasonic displacement was measured along two scan paths: along a row of PZT rods and on the epoxy surface in between twoadjacentrows of PZT rods as

GURURAJA er al.: PIEZOELECTRIC ICOMPOSITEM.4TERIALS-PART

- 40

400 IO00 I600 Frequency (KHz)

Fig. 7. Measuredelectricalinputimpedance of compositetransducer #l01 (tenpercentPZT in Spurrs epoxy,PZT rod diameters = 0.45 mm. period = 1.27 mm, thickness = 1.93mm).Transducerdiameter = 19.0 mm.

shown in Fig. 6. Fig. 7 giveselectricalinputimpedanceory data taken On One Of these lol in

showing the existence Of three strongresonances. Figs' show laser Scan plots Of vibration amp1itude and phase taken at frequencies f t l , andfi, respec-tively, for this sample.

A . Vibration Pattern at Frequency f,, The plot in Fig. 8 shows the complex vibration pattern

atfrequency 5, correspondingtothesecondstopband along the unit cell, (Fig. 6(a)), where the rods all vibrate in phase. (Vibrations at the first stopband discussed earliertheperiodicity of the lattice. As the wavelength of the have a 180" phase shift from one plane of the rods to the next and cannot be excited electrically in a uniformly elec-trodedsample.)Superposition of the x and y standing waves illustrated shows that the z-displacement has a pos-itive maximum at a , negative maximum at b, and zero at c . Because of symmetry, thesestatements applyatall equivalent points in the lattice. In the scans of Fig. 8, the maxima of the standing wave pattern at a and b arel80" out of phase, as predicted. The predicted zerosat c in Fig. 8(a) and at the equivalent point in Fig. 8(b) are lesssat-isfactorilyreproduced, possibly due toimperfections in the lattice and inaccuracy in alignment of the scan. The velocity of the transverse waves, c, = dfil is tabulated in Table VI.

B. VibrationPatternatFrequencyft2 The plot in Fig. 9 shows the complex vibration pattern

at frequencyj? corresponding to the stopband in Fig. 6(b). This is another of the higher stopbands for which the rods vibrate in phase and can be excited by uniform electrodes. Atf2, standing transverse waves along the unit cell diag-onals are superposed to give maximum displacements180" out of phase at a and c , and maximum in phase displace-ments at a and b. These features are clearly observable in the scans of Fig. 9, except that the maximum ata is smaller than that predicted from the assumed standing wave pat- tern.This is attributed tothepresence of higher space harmonicssuchthatthestanding wave patterns are not simplesinusoids. It canalsobeseenfromFig.6(b) that the displacement at point d, midway between a and b, is

491

predictedtobezero;andthishasbeen verified experi- mentally. The velocity C,, of transverse waves, as tabu- lated in the last two columns of Table VI is lower than the measured velocity of 1150 m/s (Section V). Thisispos-sibly due to the mass loading by the PZT rods.

C . Vibration Pattern at Frequency f(

Fig. 10 shows plots of complex vibration pattern at the frequency fr, which corresponds the to simple longitudinal thickness of the plate z. Itresonance homogeneousalong was noted earlier that no resonant space harmonic exist in this case, so thatweaker standing-wavepatternsare tobe expected in the plane. is clearly visible in the fig-ure. The small phase variations are attributedto the damp-ing in the composite which was not considered in the the-

outlined above ,311.

As is clearly Seen in Fig. 10, the amplitude of vibration on the epoxy at f i is about 5 to 8 dB larger than on the PZT rods indicating an effective couplingof the ultrasonic energy from PZT to epoxy. The PZT rods vibrating due to electrical excitation act as the source of transverse waves in the epoxy travelling in a direction perpendicular to the axis of the PZT rods. The transverse waves produced in-teract with neighboring rods to produce the resultant vi-bration pattern. The vibration pattern depends very much on the wavelengthof the transverse waves in relation to

transverse waves becomes larger compared to the lattice periodicity,ultrasonicdisplacementonthecomposite is expected to be more uniform.

Fig. 10-12 compare the ultrasonic displacements on the surface of composites 101, 102, and 103(Table VI) reso-nating in the longitudinal thickness vibration at frequen-cies 620, 414, and 270 KHz, respectively. All the samples have ten-volume-percent PZT with a periodicity of the lat-ticeequal to 1.27 mm. The only variable in the samples are the wavelengthsof transverse wave at thethickness resonance frequency, which are respectively 1.9, 2.7, and 4.3 mm for the above three samples (calculated using the transverse wave velocity in Spurrs epoxy of 1150 m/s). The difference in amplitude of vibration between the PZT andepoxyobserved in sample 101 is greatly reduced in sample 102. This is directly attributed to the longer wave- length of transverse waves in sample 102. For sample 103 the transverse wavelength is more than three times the pe-riodicity,and there isno noticeabledifference in ampli- tude between the PZT and epoxy. The composite vibrates uniformly across the surface with almost equal strain on thePZTandepoxy.Smallphasevariationsseenacross sampe 101 are not measurable forsample 103. This is probably because of the reduced attenuation in the epoxy atlowerfrequencies(SectionIV).Thevibrationpattern observed in sample 103 is in accordance with the assump-tion in Section V-B of the constant strain model used to calculate the effective modulus along the fiber axis, when transverse wavelengths are large compared to periodicity. This uniform ultrasonic displacement observed on the sur-

492 IEEE TRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-32,NO. 4, JULY 1985

D e

I (mm) -Position (mm) -60- - Position

face of the composite is a clear indication of efficient cou-pling of the mechanical energy from PZT to the epoxy. Sincethe acousticimpedance of the epoxy is relatively close to that of the human body, an effective coupling of acoustic energy from the composite transducer to the hu-man body is ensured.

VII. EFFECTOF TEMPERATUREON THE RESONANCEMODES

In this section the effect of temperature on the electro-mechanical properties of the composite is discussed. It is clear from the preceding sections that the high-frequency

493 GURURAJA et a l . : PIEZOELECTRICCOMPOSITEMATERIALS-PART I

'"c 'Or 15

-S i

Fig. IO. Laser scan measurements of relativeamplitudeandphase of the acoustic vibration atfr = 620.7 KHz (sample # 101). (a) Scan along rods. (h) Scan between rods.

l .I

dynamic behavior of 1-3 composite is strongly dependent on the mechanical properties such as the velocity and at-tenuation of ultrasonic waves in the Spurrs epoxy. These properties of Spurrs epoxy are very sensitive to tempera- ture. The Spurrs epoxy is glassy at room temperature and goes through the glass transition temperature to a rubber likematerial in a temperatureinterval ofonly about 100°C.Intheglassystate, it was also shown (Section V-A) that thecompliance of the epoxy increased by ap- proximately 65 percent in the temperature range of 0 to 100°C. Thus, a study of the temperature dependence of the resonance modes will help in understanding the elec-

tromechanical properties of composites with differentpoly-mer matrices, having a wide range of elastic properties.

In the experiment, the resonance behavior of compos-ites freely suspended in air was studied as a function of temperature from 0 to 150°C. The thickness-mode cou-pling coefficient k, , mechanical Q, and the frequency con-stant N f of the composite were determined at 2°C inter-vals both in heating and cooling cycles. The heating and cooling rates were maintained at approximately 2"C/min.

Fig. 13 shows plots of absolute value of admittance as a function of frequency from 0.1 to 1.1 MHz forsample 103 (ten-percent PZT compositewith 0.45-mm rods,

494 IEEETRANSACTIONS ON SONICS AND ULTRASONICS, VOL. SU-32. NO. 4, JULY 1985

Fig. 12. Laser-probemeasurements of relativeamplitudeandphase of the acoustic vibration at pi = 270 KHz of sample #103. (a) Scan on rods. (b) Scan in between rods:

thickness 5.15 mm) at different temperatures up to 170°C. while to note that above 130"C, the amplitudeof thickness Thebehavioris typical of all thick(thickness > 3 mm) mode was increased (Fig. 13(e)-(h)). The secondary low- composites.Accordingtotheanalyses given in thepre- frequencyresonancesclearlyseenat25°Cdisappearat vious section, the three major resonances observed at roomapproximately100°C.Thisdisappearance is again as-temperature (Fig. 13(a)) were identified as follows.

1) Resonance at0.262 MHz was identified as ahalf wave resonance along the thickness of the composite and is denoted byf,.

2) Resonance at 0.644 MHz was identified as the stand-ing wave pattern in the epoxy arising from lateral peri-odicity of the PZT rods. This resonance is denoted byf,,.

3) Resonance at 1.030 MHz was identified as the third overtone of the thickness mode.

Weak secondary resonances below the frequency of thickness-mode resonance were ascribed to the overtones of the planar-mode resonance of the composite disc.

cribed to the lossy nature of the epoxy around the glass transition temperature.

The coupling coefficient k, and Q of the thickness-mode resonance for sample 130 are plotted as a function of tem- perature in Figs. 14 and 15, respectively. The value of k, (0.48)determined at room temperature(25°C)did not changesubstantiallyuptoapproximately110°C. In the temperature range from 100 to 130"C, k, exhibited a min-imum. Above 130"C, after the transverse mode had dis- appeared, k, increasedsignificantly to about 60 percent. As shown in Fig. 15, the mechanical Q at 25°C was about 20. The Q remained constant to approximately 100°C and

The effect of temperature on the above resonance modesdecreased to a value of five at temperatures above 130°C. (Fig. 13.) is explained by the following. As the temperature was increased from 25"C, the epoxy is expected to me- chanically soften at a faster rate than PZT. Therefore, the resonancefrequency A I , which is mainly determined by the elastic modulus of the polymer, decreased at a faster rate than the resonance frequency fi, which is defined by thecompositemodulus E,. As seen in Fig. 13(b)-(d), at higher temperaturesf,, gradually approachesf, and finally merges withf, at approximately 110°C. In the temperature range 11O-13O0C, the two modes interfere with each other. At temperatures above130"C, f r l passesthrough h and eventually disappears at a temperature around135"C. This disappearance can be attributed to the fact that above the glass transition temperature the epoxy is less viscous and cannot support a standing wave pattern of the transverse wave (glasstransitiontemperature of Spurrs epoxy is around 110°C at 200 KHz, from Section IV). It is worth-

The observed coupling coefficient k, and Q in a thick sample at room temperature were attributed to the strong mechanical interaction among PZT rods through the epoxy matrix. At temperatures abovetheglass transition tem-perature TK= llO"C), the epoxy is rubber like and soft. As a result, the mechanical interaction among PZT rods becomesweaker as also indicated by an increase in the amplitude of the resonance spectrum (Fig. 13(e)-(h)). In effect, k, of the composite approach kS3of afreely sus-pended PZT rod (70 percent) and Q decreases because of the damping provided by the lossy polymer. It may be re- called here that for a thin (thickness = 0.6 mm) composite sample, k,was 60-70 percent, and Q was 3-10 (Table V). These values are very closetothosemeasuredforthick composites above the temperature TR.It appears that the nature of vibration of a thick composite above TK resem-bles that of a thin composite at room temperature.

495 CURURAJA e1 al. : PIEZOELECTRICCOMPOSITEMATERIALS-PAR7 I

(d) (h) Fig. 13. Temperature-dependenc e o f various resonances in a composite

samples (sample # 103). The x axis is the frequency 0.1 t f l 1 . l MHz and the y axis is the relative admit!.ance (50 dB).

496 IEEE TRANSACTIONSON SONICS ANDULTRASONICS. VOL.SU-32, NO. 4, JULY 1985

further supports the proposed model describing the nature of vibration for different resonance modes of 1-3 compos-ites.

VIII.CONCLUSION

The resonance modes in circular shaped 1-3 PZT rod- polymer composites were fully characterized. In general, the planar coupling coefficient increased with increase in volumepercent PZT. For a givenvolumepercentPZT, thick samples had better planar coupling coefficient than the thin samples.

For thickness mode resonance of thin samples, k, = 60-70 percent and Q = 3-10. For thick samples, kt = 50 per-cent and Q = 20-30. The difference in the observed be-haviorwasexplained by considering thestrength of the interaction among the PZT rods through theepoxy. At the thickness-moderesonance,thecoupling of acoustic en-ergy from PZT to epoxy was found to be most efficient, when the transverse wavelength in epoxy at the resonance frequency was much larger than the periodicity of the lat-tice.Whenthisconditionissatisfied,thecompositevi-brates like a homogeneous body and it will be shown in Part I1 of this work that the composite materials exhibit excellentsensitivity operating into water load. From the effect of temperature on resonance behavior, it is clear that theinteractionamongthePZTrodsthroughtheepoxy matrix can either be enhanced or suppressed depending upon the propertiesof the polymer phase. Composites with low transverse coupling could be utilizedforlinearand phased array systems.

In addition to these two modesof resonances, additional modes were observed because of the regular lateral peri-odicity in the structure. The results showed that these res-onances arose from the superposition of the standingwave pattern of the transverse waves in the epoxy. The experi-mental results were in excellent agreement with the theory of wave propagation in two dimensionally periodic solids.

ACKNOWLEDGMENT The authors are grateful to Dr. W. A. Smith and Dr. A.

Shaulov of North American Philips Laboratories and Dr. P. A. Lewin of Drexel University (Dept. of Electrical and Computer Engineering and Biomedical Engineering andScienceInstitute) for their commentsanddiscussions, Mrs. Linda Websterforpreparingsamples,andMr. P. Moses for writing software for computer interfacing.

00 I O 0 200

Temperature, ‘C

Fig. 14. Typical effect of temperature on the thicknecs coupling coefficient of a thick composite sample (sample # 103).

1

o Cooling Run

Hemnq Run

c-70.60 50 l00 I50

Temperature, “C Fig. 16. Typicaleffect of temperature on thethicknesscoupling coeffi-

cient of a thin composite sample ( I ) .

cIn thin samples, since the coupling among the PZT rods

is very weak at room temperature, the increase of tem- perature above TR is unlikely to affect theresonancebe-havior. This seems to be confirmedby the plot of k, versus temperature for a typical thin compositesamplewith thickness mode frequency at 2.25 MHz (Fig. 16). No sig-nificant variation of k, was seen over the entire tempera-ture range of 0 to 150°C. Thus, the temperature depen-dence of the electromechanical properties of composites

[ I ]

I?]

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[ S ] R. E. Newnham, L. J . Bowen. K . A. Klicker. and L. E. Cross, “Com-positepiezoelectrictransducers,” Mater. Eng . , vol. 2, pp. 93-106, 1980.

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[20] S. Y. Lynn, R. E. Newnham, K. A. Klicker, K. Rlttenmyer, A . Safari, and W. A . Schulze, “Ferroelectric composites for hydrophones,” Fer-roelecrrics, vol.38, pp. 955-958, 1981.

[21] T. R. Gururaja, W. A.Schulze. T. R. Shrout.A.Safari, L. Webster, and L. E. Cross, “High-frequency applications of PZT-polymer com-positematerials,” Ferroelecfrics, vol. 39, pp. 1245-1248, 1981.

[22] K. R . Erikson,“Tone-burst testing of pulse-echo transducer,” /EEE Trans. Sonics Ultrason., vol.SU-26,pp. 7-14, 1979.

[23] T. R. Gururaja, D. Christopher, R . E. Newnham, and W. A . Schulze. “Continuous poling of PZT fibers and ribbons and its application to new devices,” Ferroelectrics, vol. 47,pp.193-200. 1983.

[24] T. R.Guraraja, W. A. Schulze.andL.E.Cross.“Bulkmechanical properties of the Spurrs epoxy and eccogel polymers,” submitted to IEEE Trans. Sonics Ultrasonics.

[25] J. D.Ferry, ViscoelasticProperties of Polymers. New York: John Wiley. 1980.

[26] “IRE standards on piezoelectric crystals: Measurements of Piezoelec-tricceramics,” Proc. IRE, vol.49,pp. 1161-1169. 1961.

1271W.P. Mason,“Electrostrictive effect in bariumtitanateceramics,” Phys. Rev., vol. 74, pp. 1134-1147, 1948.

[28] D. A. Berlincourt, D. R. Curran. and H. Jaffe, “Piezoelectric and pi-ezomagnetic materials and their function in transducers,” in Physrcal Acoustics, vol. I , W.P. Mason,Ed. New York: Academic, 1964, part A, Chap. 3.

[29]C.A.Ross,“Stress wave propagation in compositematerials,’’ D?-namic Response of Composite Materials, (Fall meeting of the Society for Experimental Stress Analysis), pp. 1-19, 1980.

[30] R . Holland, E. P. EerNisse, “Accuratemeasurement of coefficients in a ferroelectricceramic,” IEEE Trans. Sonics Ultruson., vol. SU-16, pp. 173-181, 1969.

[31]B.A.Auld,H.A.Kunkel, Y. A. Shui,and Y. Wang,“Dynamicbe-havior of periodic piezoelectric composites,” in Proc. 1983 /€E€ Ul-frason. Symp., 1984, pp. 554-558.

T. R. Gururaja was born on September 24, 1954, in Bangalore, India.HereceivedtheB.Sc.and M.Sc. in physics from the University of Mysore, India. in 1974 and 1976, respectively. He received the M.Tech. degree in materials science from the

I IndianInstitute of Technology, Kanpur in 1978 and the Ph.D. degree in solid state science from The PennsylvaniaStateUniversity, University Park in 1984.

m”: currently Associate_- isHeResearch with the Materials Research Laboratory, The Pennsylvania

State University. His researchinterests are in the field of dielectricand piezoelectriccrystals,ceramics,andcomposites. He is also working on ultralow permittivity materials for packaging Ga:As integrated circuits.

> . ”‘g,

Walter A. Schulze, Jr. (“84) was born on De- cember 8, 1943. He obtainedtheB.S.degree in 1965 and theM.S.andPh.D.degrees in solid- statescience in 1968 and1973, respectively,from The Pennsylvania State University.

He is currently AssociateProfessorwiththe Ceramic Science department at Alfred University. He worked as Senior Research Associate at The

’ PennsylvaniaStateUniversityfrom 1974 to 1983. Dr. Schulze hasbeenworking in theareas of

ferroelectric,piezoelectric,andpyroelectricma-terialsandcomposites.thick-filmmaterialsforcircuitryanddielectrics, ceramicpreparation,secondharmonicgeneration,andelectricalproperty measurements.

Leslie E. Cross (SM’79-F’84) was born on Au-gust 14, 1923, in Leeds, England. He received the B.Sc.andPh.D.degrees in physics from Leeds University in 1948 and1952,respectively.

Currently, he is Professor of Electrical Engi-neeringandAssociateDirector of the Materials ResearchLaboratoryatThePennsylvaniaState University. Prior to joining The Pennsylvania State University, in 1961, he held positions with Leeds University as Lecturer (1948-1951) and as a re- search associate (1954-1961).

Hisresearchinterestsincludeferroelectricmaterialsandferroic phe-nomena;dielectric,piezoelectricandpyroelectriccrystals,ceramicsand composites; electronic ceramics and their applications, electrostriction and phase transitions.

Dr. Cross is a member of the National Academy of Engineering and a Fellow of the American Institute of Physics and the American Ceramic So-ciety.

Robert E. Newnham was born on March 28, 1929 in Amsterdam, NY. He received the B.S. degree from Hartwick College, Oneonta, NY, in 1950 and theM.S.degree from Colorado State University, Fort Collins, in 1952. He received his Ph.D. de-gree in physics from The Pennsylvania State Uni-versity, University Park, i n 1956 and subsequently he received the Ph.D.degree in crystallography from Cambridge University, England, in 1960.

CurrentlyDr.Newnham is Professor of solid state science and ceramic science at The Pennsyl-

vania State University. He is also the chairman of the solidstatescience program. Before he joined The Pennsylvania State University, he worked as Research Associate and Assistant Professor i n the Massachusetts Insti-tute of Technology, Cambridge, MA, from 1958-1966.

His research interests include crystal physics and structure-property re-lationships, phase transitions in ferroic materials, piezoelectric, pyroelec-tricandelectrostrictivephenomena,andcompositematerialsfortrans-ducerapplications. He is author of a bookentitled StructureProperty Relations.

Dr.Newnhamisa Fellow of the MineralogicalSociety of America.

498 IEEE TRANSACTIONS ON SONICS AND VOL. SU-32, NO. 4, JULYULTRASONICS, 1985