Net-shape ceramic processing as a route to ultrafine scale 1-3 connectivity piezoelectric...

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1–3 connectivity piezoelectric ceramic–polymer composite transducers made with viscous polymer processing for high frequency ultrasound A. Abrar b , D. Zhang a , B. Su a , T.W. Button a , K.J. Kirk b , S. Cochran b, * a Functional Materials Group, IRC in Materials Processing, School of Engineering, University of Birmingham, Birmingham B15 2TT, UK b Microscale Sensors, School of ICT (EEP), Division of Electronic Engineering and Physics, University of Paisley, Paisley PA1 2BE, UK Abstract Potential applications of high frequency ultrasound exist because of the high spatial resolution consequent upon short wave- length. The frequencies of interest, typically from 25 MHz upwards, are easily supported by modern instrumentation but the capabilities of ultrasonic transducers have not kept pace and the transducers in high frequency commercial ultrasonic systems are still made with single-phase crystal, ceramic or piezopolymer materials. Despite potential performance advantages, the 1–3 con- nectivity piezoelectric ceramic–polymer composite materials now widely used at lower ultrasonic frequencies have not been adopted because of manufacturing difficulties. These difficulties are centred on fabrication of the 1–3 piezoceramic bristle-block comprising tall, thin pillars upstanding from a supporting stock. Fabrication techniques which have been explored already include injection moulding, mechanical dicing, and laser machining. Here, we describe an alternative technique based on viscous polymer processing (VPP) to produce net shape ceramic bristle-blocks. VPP produces green-state ceramic with rheological properties suitable for embossing. We outline how this can be created then report on our work to fabricate PZT bristle-blocks with lateral pillar dimensions of the order of 50 lm and height-to-width ratios of the order of 10. These have been backfilled with low pre-cure viscosity polymer and made into complete 1–3 piezocomposite transducer elements. We outline the performance of the transducers in terms of electrical impedance and pulse-echo behaviour and show that it corresponds well with computer modelling. We conclude that VPP is a promising technique to allow the established advantages of piezocomposite material to be exploited at higher frequencies than have been possible so far. Ó 2004 Elsevier B.V. All rights reserved. Keywords: Viscous polymer processing; Piezoelectric composites; High-frequency ultrasound 1. Introduction The functional advantages of 1–3 connectivity pie- zoelectric ceramic–polymer composite material are now widely recognised [1] and use of this type of material is growing in underwater sonar, biomedical imaging and therapy, and non-destructive testing, with manufactur- ing taking place in many commercial organisations. At present, the predominant fabrication route is based on the dice-and-fill method whereby a ceramic slab is diced in one or two directions to create a Ôbristle-block’ of planks or pillars attached to the remaining stock. The bristle-block is then back-filled with polymer, the stock and excess polymer are removed, and electrodes are applied. Unfortunately, the dice-and-fill concept is difficult to apply to high frequency composites because of the ultrafine lateral scales required for efficient operation. First, the height-to-width (aspect) ratio of the ceramic should be greater than approximately 2 to keep the ideal shape of the pulse response, and much higher, typically around 5, to maximise electromechanical transduction. Second, the inter-pillar polymer must be narrow enough to prevent the frequency of inter-pillar modes coinciding with the operating frequency. This means that a 1–3 piezocomposite operating at 50 MHz must be of the order of 30 lm thick, requiring ceramic pillars less than * Corresponding author. Tel.: +44-141-848-3436; fax: +44-141-848- 3616. E-mail address: [email protected] (S. Cochran). 0041-624X/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.ultras.2004.02.008 Ultrasonics 42 (2004) 479–484 www.elsevier.com/locate/ultras

Transcript of Net-shape ceramic processing as a route to ultrafine scale 1-3 connectivity piezoelectric...

Ultrasonics 42 (2004) 479–484

www.elsevier.com/locate/ultras

1–3 connectivity piezoelectric ceramic–polymercomposite transducers made with viscous polymer processing

for high frequency ultrasound

A. Abrar b, D. Zhang a, B. Su a, T.W. Button a, K.J. Kirk b, S. Cochran b,*

a Functional Materials Group, IRC in Materials Processing, School of Engineering, University of Birmingham, Birmingham B15 2TT, UKb Microscale Sensors, School of ICT (EEP), Division of Electronic Engineering and Physics, University of Paisley, Paisley PA1 2BE, UK

Abstract

Potential applications of high frequency ultrasound exist because of the high spatial resolution consequent upon short wave-

length. The frequencies of interest, typically from 25 MHz upwards, are easily supported by modern instrumentation but the

capabilities of ultrasonic transducers have not kept pace and the transducers in high frequency commercial ultrasonic systems are

still made with single-phase crystal, ceramic or piezopolymer materials. Despite potential performance advantages, the 1–3 con-

nectivity piezoelectric ceramic–polymer composite materials now widely used at lower ultrasonic frequencies have not been adopted

because of manufacturing difficulties. These difficulties are centred on fabrication of the 1–3 piezoceramic bristle-block comprising

tall, thin pillars upstanding from a supporting stock. Fabrication techniques which have been explored already include injection

moulding, mechanical dicing, and laser machining. Here, we describe an alternative technique based on viscous polymer processing

(VPP) to produce net shape ceramic bristle-blocks. VPP produces green-state ceramic with rheological properties suitable for

embossing. We outline how this can be created then report on our work to fabricate PZT bristle-blocks with lateral pillar dimensions

of the order of 50 lm and height-to-width ratios of the order of 10. These have been backfilled with low pre-cure viscosity polymer

and made into complete 1–3 piezocomposite transducer elements. We outline the performance of the transducers in terms of

electrical impedance and pulse-echo behaviour and show that it corresponds well with computer modelling. We conclude that VPP is

a promising technique to allow the established advantages of piezocomposite material to be exploited at higher frequencies than

have been possible so far.

2004 Elsevier B.V. All rights reserved.

Keywords: Viscous polymer processing; Piezoelectric composites; High-frequency ultrasound

1. Introduction

The functional advantages of 1–3 connectivity pie-

zoelectric ceramic–polymer composite material are now

widely recognised [1] and use of this type of material is

growing in underwater sonar, biomedical imaging and

therapy, and non-destructive testing, with manufactur-

ing taking place in many commercial organisations. At

present, the predominant fabrication route is based on

the dice-and-fill method whereby a ceramic slab is dicedin one or two directions to create a bristle-block’ of

*Corresponding author. Tel.: +44-141-848-3436; fax: +44-141-848-

3616.

E-mail address: [email protected] (S. Cochran).

0041-624X/$ - see front matter 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.ultras.2004.02.008

planks or pillars attached to the remaining stock. The

bristle-block is then back-filled with polymer, the stockand excess polymer are removed, and electrodes are

applied.

Unfortunately, the dice-and-fill concept is difficult to

apply to high frequency composites because of the

ultrafine lateral scales required for efficient operation.

First, the height-to-width (aspect) ratio of the ceramic

should be greater than approximately 2 to keep the ideal

shape of the pulse response, and much higher, typicallyaround 5, to maximise electromechanical transduction.

Second, the inter-pillar polymer must be narrow enough

to prevent the frequency of inter-pillar modes coinciding

with the operating frequency. This means that a 1–3

piezocomposite operating at 50 MHz must be of the

order of 30 lm thick, requiring ceramic pillars less than

Fig. 1. A scanning electron micrograph of a single piezoceramic pillar

made with VPP.

480 A. Abrar et al. / Ultrasonics 42 (2004) 479–484

20 lm wide with an inter-pillar spacing, filled with

polymer, of less than 10 lm. Dice-and-fill cannot be

used to make such a structure because saw blades are

limited to around 15 lm minimum thickness. However,

relaxing the design constraints removes the biggestadvantages of the composite material. The capabilities

and limitations of the dice-and-fill technique are illus-

trated in a recent paper [2] which makes it clear that

other fabrication methods must be sought.

Two well-known, general purpose alternatives to

dice-and-fill are injection moulding [3] and laser mi-

cromachining [4]. Injection moulding, however, brings

with it high tooling costs and, for high frequency de-vices, pillars at pitches less than 50 lm are easily de-

stroyed during demoulding, whilst laser micromachining

has to be carried out at low power to avoid degrading

the ceramic, which leads to long machining times. Cross-

sectional tapering and material re-deposition are also

problems in this case.

Numerous more specialised methods have also been

investigated. Early work showed that circular pillarscould be fabricated by burnout of sacrificial polymer

moulds [5]. However, pillars narrower than 100 lmcould not survive the thermal stresses during burnout.

Wang et al. [6] reported a lost silicon mould method to

fabricate features with dimensions around 50 lm but

chemical reaction between the PZT and the mould

during hot isostatic pressing was a problem. Hirata et al.

[7] achieved pillar diameters of 25 lm and aspect ratiosof 3 to 9 using synchrotron radiation lithography to

make a polymer mould for PZT slurry. The drawback

was that the polymer had to be removed by a slow

plasma etching process. Starke and his co-authors [8]

used a reusable soft mould method but the pillar size (85

lm), kerf (45 lm) and aspect ratios (less than 4) were

limited. Finally, Meyer et al. reported using bundles of

15–50 lm diameter PZT fibres [9]. However, the fibredistribution was random, making it unsuitable for small

transducers such as ultrasonic array elements, and the

maximum ceramic volume fraction was 45%, at the

lower end of the typical 40–70% range.

In this paper, we report on work emerging from

demonstration of a series of net shape fabrication routes

for fine scale ceramic structures and thick films based on

viscous polymer processing (VPP) [10], a techniquedeveloped originally to make macro-defect-free struc-

tural ceramics. One advantage of VPP over conventional

slurry casting is the increase in the strength of the

ceramic green bodies by at least an order of magnitude

because of the high molecular weight polymer binder

system and high shear stress used during processing. A

second advantage is the highly plastic nature of the

ceramic paste or dough which is thus amenable to var-ious forming methods. Section 2 of the paper describes

in more detail the manufacturing process developed for

1–3 piezocomposites. We then outline the material

structures we have made and how we have incorporated

these into transducers for practical evaluation. Experi-

mental results are reported and compared with simula-

tion. We conclude that VPP is a promising technique to

allow the established advantages of piezocompositematerial to be exploited at higher frequencies than have

been possible so far, and outline the further work nee-

ded to realise this.

2. VPP-based fabrication of 1–3 piezocomposites

VPP-based fabrication is a three stage process firstinvolving high shear twin-roll milling of a combination

of ceramic powder, solvent and binder/plasticiser to

generate a ceramic paste suitable for moulding. For

small feature sizes, such as the single pillar shown in the

scanning electron micrograph in Fig. 1, a fine ceramic

powder is required with particle size around 1 lm and

the present work was based on PZT 5A powder (Mor-

gan Electroceramics, Wrexham, UK). The VPP pastematerial is then calendared to form a tape sufficiently

thick to manufacture the bristle-block, comprising pil-

lars upstanding from a stock. For the devices discussed

here, the tape thickness is typically of the order of 1 mm.

A section of tape is then embossed into a solid mould.

For the preliminary devices, polymer moulds made by

direct synchrotron radiation were used. Alternative

mould fabrication techniques are currently underdevelopment whereby, for example, low-cost hot

embossing methods can be used to fabricate the polymer

moulds from LIGA nickel master moulds. Such devel-

opments would be a necessary step for volume manu-

facture [11]. After embossing, a demoulding process is

required. One approach that has been proven successful

is to dissolve the polymer mould in a solvent.

As the design of the 1–3 piezocomposite has veryparticular requirements in terms of pillar dimensions

and pillar array structures, VPP shows undoubted suit-

ability in three aspects. First, the very high green

strength of the VPP pillars after drying maintains the

designed shape and avoids the damage from the mould

A. Abrar et al. / Ultrasonics 42 (2004) 479–484 481

dissolving process. Second, the flexibility to choose the

binder system for the VPP process offers the opportunity

to dissolve the mould without damaging the binder

system of the green pillars. Third, the homogeneity of

the VPP paste system enables accurate prediction of thedrying and sintering shrinkages so that the required net-

shape pillar structure is formed after sintering.

After demoulding, the bristle-block is sintered at 1200

C for 2 h in a closed crucible. The components are

placed on a bed of zirconia sand to which PbO powder

has been added in order to maintain a lead-rich atmo-

sphere within the crucible and reduce Pb loss during

sintering. Fig. 2(a) shows an array of high aspect ratiofine-scale pillars with a circular cross section. The pillars

are approximately 80 lm in diameter with an aspect

ratio of 10. Fig. 2(b) shows an array of low aspect ratio

fine-scale hexagonal pillars. The feature sizes are around

20 lm with an aspect ratio of 2. Notably, the array in

Fig. 2(b) has higher volume fraction, approximately

60%. Thus the capability to manufacture very fine scale

structures with high volume fraction and good micro-structural and geometrical quality has been demon-

strated.

The sintered blocks are back-filled with the passive

phase of the final 1–3 composite. For the work reported

here, CY1301/HY1300 polymer was used (Vantico

Polymer Specialties Division, Basel, Switzerland). This

is a hard-setting potting compound with the particular

advantage of low viscosity prior to curing. The stock

Fig. 2. Fine scale pillar arrays (a) with high aspect ratio pillars and (b)

with low aspect ratio pillars.

and excess polymer are removed by lapping then elec-

trodes are applied, either sputtered gold or conductive

silver paint. For high frequency applications, the gold is

preferred because it is thinner and more uniform. Poling

is carried out as the last stage in the fabrication process.Because the samples are thin, the voltage required is

relatively low, and the relatively low glass transition

temperature of the polymer we used meant that the

poling temperature was also restricted.

3. Practical evaluation and simulation

A small number of samples have been taken through

from initial VPP material preparation to complete 1–3

composite production, constrained mainly by the cost

and availability of suitable mould designs. So far, these

have included samples with round and hexagonal pillars,

ceramic volume fractions of around 10–60%, and aspect

ratios of 2–10, with active areas up to 1 · 1 cm2, and

final pillar heights from 50 to 850 lm. Here we focus onone particular sample. This has slightly elliptical pillars,

with a major axis of approximately 65 lm and a minor

axis approximately 50 lm. The ceramic volume fraction

is approximately 20% and the sample was initially lap-

ped to a thickness of 760 lm, this being the maximum

permitted by the bristle-block. This gives a pillar aspect

ratio of almost 12 and indicates that the same material

could be lapped down to a thickness of around 300 lmwhile still preserving the ideal aspect ratio of 5 men-

tioned in the introduction. The overall area of the

sample was 63 mm2.

Before encapsulating the sample for practical testing,

its electrical impedance was recorded, as shown in Fig.

3. As expected, the impedance plot indicates good

behaviour, with a single, clear fundamental resonance

mode at around 2.4 MHz. Fig. 3 also includes simulatedresults. These were prepared with in-house code for one-

dimensional modelling based on matrix solutions to the

wave equation. The equivalent composite parameters

are calculated within this code using the approach of

Smith and Auld [12] and the validity of the output has

been established by comparison with other experimental

results of our own and in the literature.

A crucial question in work of the type reported here isthe source of the material parameters for the two phases

in the composite. CY1301/HY1300 is a very well known

material and standard parameters have been used. The

ceramic in the sample was produced using commercial

PZT 5A powder and standard PZT 5A parameters were

used initially for the simulation. However, it was ac-

cepted that the VPP-based ceramic preparation method

could result in non-standard parameters. Full charac-terisation has not yet been completed, but a simple

optimisation was carried out by altering e33, the piezo-

electric stress constant of the ceramic, and comparing

10

100

1000

10000

100000

0 1 2 3 4 5 6 7

Frequency (MHz)

Ele

ctri

cal I

mp

edan

ce (

Ω)

-90

-60

-30

0

30

60

90

0 1 2 3 4 5 6 7

Frequency (MHz)

Imp

edan

ce P

has

e (D

eg.)

Fig. 3. Electrical impedance of the practical evaluation sample before

encapsulation, thick lines––experimental, thin lines––predicted.

Fig. 4. Composite encapsulation for underwater testing.

482 A. Abrar et al. / Ultrasonics 42 (2004) 479–484

simulated results with the measurement. This showed

that the best fit was obtained with a reduction from the

standard value by a factor of 12.5%, indicating that the

performance of the ceramic phase is slightly poorer than

in commercial ceramic. The thickness mode coupling

coefficient, kT, calculated from the measured electrical

impedance was 0.52. This compares with a value of 0.55using standard material parameters and 0.53 using the

modified parameters.

Possible reasons for the discrepancies include the

non-optimised design of the polymer mould and non-

optimised processing conditions. In particular, it should

-1

-0.5

0

0.5

1

47 48 49 Time (µs) 50

Hyd

rop

ho

ne

Sig

nal

(ar

b. u

nit

s)

-1

-0.5

0

0.5

1

47 48 49 Time (µs) 50

Hyd

rop

ho

ne

Sig

nal

(ar

b. u

nit

s)S

imu

late

d

(a) (b

Fig. 5. Transmitted pulse characteristics of the practical evaluation sample op

the frequency domain, experiment––, simulation––.

be noted that the pillar structures produced here have

as-sintered’ surfaces and are thus very susceptible to

loss of Pb during the sintering process with a consequent

reduction in key properties. Although care has been

taken to try to minimize this effect, the process route has

not yet been fully optimised. In contrast, pillar struc-

tures produced via a conventional fabrication routewould be expected to have properties similar to bulk

material as all the active surfaces have been machined or

cut thus removing any poor quality surface material.

After impedance measurement, the sample was

encapsulated by attaching it to a plastic housing with a

membrane of CY1301/HY1300 polymer as indicated in

Fig. 4. As the material performance was under review,

neither acoustic matching nor protective layers wereapplied to the front, and the sample was air-backed. One

meter of RG174A/U cable was used to connect the de-

vice to a commercial pulser-receiver (JSR Ultrasonics,

Pittsford, NY, USA) and underwater testing was per-

formed. The excitation from the pulser-receiver was a

)50 V edge with a fall time of 20 ns.

The transmitted pulse shape and frequency response

recorded with a needle hydrophone (Precision Acous-tics, Dorchester, Dorset, UK) are shown in Fig. 5, along

0

5

10

15

20

0 2 4 6 8 10

Frequency (MHz)

Pre

ssu

re (

Pa)

)

erating in water (a) in the time domain, with simulation inset, and (b) in

-1

-0 .5

0

0. 5

1

100 101 102 103 104 105 106

Time(µs)

Pu

lse-

ech

o S

ign

al (

arb

. un

its)

-1

0

1

100 101 102 103 104 105 106

Time(µs)

Pu

lse-

ech

o S

ign

al(a

rb. u

nit

s)S

imu

late

d

0

5

10

15

20

25

0 2 4 6 8 1 0

Frequency (MHz)

Pu

lse-

Ech

o S

ign

al M

agn

itu

de

(arb

.un

its)

(a) (b)

Fig. 6. Pulse-echo characteristics of the practical evaluation sample operating in water (a) in the time domain, with simulation inset, and (b) in the

frequency domain, experiment––, simulation––.

A. Abrar et al. / Ultrasonics 42 (2004) 479–484 483

with the simulated equivalents. For these simulations,

the reduced value of e33 was used. The results indicate afrequency of peak output of 2.5 MHz and )3 dB

bandwidth of 0.67 MHz. The signal in Fig. 5 is not

sinusoidal because the broad bandwidth of the pulser-

receiver and the hydrophone allow observation of the

reverberation of the individual wavefronts generated at

the front and back faces of the composite when the very

short excitation pulse is applied [13]; this effect is exac-

erbated by the lack of mechanical damping as thecomposite is air-backed. Pulse-echo testing was also

carried out, with the results shown in Fig. 6. As ex-

pected, the time domain pulse is longer, with a peak

output frequency of 2.4 MHz and a )6 dB bandwidth of

0.47 MHz. Correspondence with simulation in Figs. 5

and 6 is reasonable, with discrepancies attributed to

aspects of the instrumentation, such as the cabling, not

included in the simulation. Most importantly, all theunderwater results indicate that the VPP-based com-

posite is behaving as expected.

4. Conclusions and further work

We have outlined a new manufacturing process for 1–

3 piezoelectric–polymer composites which has charac-teristics which make it suitable for high frequency device

fabrication. In particular, in using very precise mould

manufacture and embossing techniques developed for

other applications, it avoids the difficulty of further saw

blade thickness reduction [2] that would be required to

make high frequency devices with a conventional dice

and fill process. To accommodate the requirement for

high aspect ratio pillars with small absolute dimensionsand close spacing, a VPP route has been explored and

optimised to produces high strength green state ceramic

able to withstand the embossing and demoulding pro-

cedures. Using this process, bristle-blocks were made

with commercial PZT 5A powder and fabrication wastaken through to final 1–3 composites. We have re-

ported on the characteristics of one sample here, which

we have compared with simulation. This showed that

the behaviour was within expectations, though the pie-

zoelectric stress constant of the material requires

improvement to match standard figures. The sample was

encapsulated and tested underwater and it behaved well.

After the underwater testing reported here, the pi-ezocomposite element was cut from its casing and fur-

ther lapping was performed in stages to a minimum

thickness of less than 200 lm, corresponding to a pillar

aspect ratio of about 3, very close to the limit required in

composite design. As expected, the frequency of the

device increased to approximately 10 MHz. To take the

work to still higher frequencies, further research is

therefore required in a number of areas. Specialisedmoulds are needed to take advantage of the results of

standard composite design techniques. These will have

combinations of smaller feature sizes and higher ceramic

volume fractions than have so far been investigated.

Additional investigation will be needed to determine the

cause of the difference between standard ceramic

parameters and the parameters of the material as sim-

ulated. If it is successful, this research will allow 1–3piezocomposite material to be manufactured with pre-

viously impossible geometrical characteristics, in turn

bringing the established benefits of 1–3 composites to

high frequency ultrasonic transducers.

Acknowledgements

A. Abrar is supported by a University of Paisley

Ph.D. studentship and S. Cochran by an EPSRC Ad-

vanced Fellowship. D. Zhang acknowledges support of

484 A. Abrar et al. / Ultrasonics 42 (2004) 479–484

a British Council ORS award and a scholarship from the

Department of Metallurgy and Materials at the Uni-

versity of Birmingham. The polymer moulds used in this

study were fabricated at IMM (Mainz, Germany) with

the support of the EU Emerge Project.

References

[1] E.P. Papadakis, Ultrasonic Instruments and Devices, Academic

Press, CA, USA, 1999, pp. 471–562, ISBN 0-125-31951-7.

[2] T. Ritter, T.R. Shrout, R. Tutwiler, K.K. Shung, A 30 MHz

piezo-composite ultrasound array for medical imaging applica-

tions, IEEE Trans. Ultrason. Ferroelec. Freq. Cont. 49 (2) (2002)

217–230.

[3] B.G. Pazol, L.J. Bowen, R.L. Gentilman, H.T. Pham, W.J.

Serwatka, Ultrafine scale piezoelectric composite materials for

high frequency ultrasonic imaging arrays, in: Proc. 1995 IEEE

Ultrason. Symp., 1995, pp. 1263–1268.

[4] R. Farlow, W. Galbraith, M. Knowles, G. Hayward, Microma-

chining of a piezocomposite transducer using a copper vapor laser,

IEEETrans. Ultrason. Ferroelec. Freq. Cont. 48 (3) (2001) 639–640.

[5] V.F. Janas, A. Safari, Overview of fine-scale piezoelectric ceramic/

polymer composite processing, J. Am. Ceram. Soc. 78 (11) (1995)

2945–2955.

[6] S. Wang, J.F. Li, K. Wakabayashi, M. Esashi, R. Watanabe, Lost

silicon mold process for PZT microstructures, Adv. Mater. 11

(1999) 873–876.

[7] Y. Hirata, T. Numazawa, H. Takada, Effects of aspect ratio of

lead zirconate titanate on 1–3 piezoelectric composite properties,

Jpn. J. Appl. Phys. 36 (1997) 6062–6064.

[8] S. Starke, A. Schonecker, W. Gebhardt, Fine scale piezoelectric 1–

3 composites: a new approach of cost effective fabrication, in:

Proc. 11th IEEE Symp. Appl. Ferroelectr., 1998, pp. 393–

396.

[9] R.J. Meyer, S. Yoshikawa, T.R. Shrout, Processing and properties

of 15–70 MHz 1–3 PZT fiber/polymer composites, Mater. Res.

Innov. 3 (6) (2000) 324–331.

[10] B. Su, D.H. Pearce, T.W. Button, Routes to net shape electroce-

ramic devices and thick films, J. Eur. Ceram. Soc. 21 (2001) 2005–

2009.

[11] A. Schneider, B. Su, T.W. Button, L. Singleton, O. Wilhelmi, S.E.

Huq, P.D. Prewett, R.A. Lawes, Comparison of PMMA and SU-

8 resist moulds for embossing of PZT to produce high-aspect-ratio

microstructures using LIGA process, Microsystems 8 (2002) 88–

92.

[12] W.A. Smith, B.A. Auld, Modeling 1–3 composite piezoelectrics

thickness mode oscillations, IEEE Trans. Ultrason. Ferroelec.

Freq. Cont. 38 (1) (1991) 40–47.

[13] J. Krautkramer, H. Krautkramer, Ultrasonic Testing of Materi-

als, Springer Verlag, 1990, ISBN 0-387-51231-4.