NDTnet - September 1996, Vol.1 No.09

## PVDF and Array Transducers

#### Author: Robert A. Day

We express our gratitude to the author for
contribution most of the HTML formating work.

Transducer Workshop

#### Abstract

PVDF has become popular in recent years because of it's unique advantages. It is not a panacea however and I will discuss it's advantages and disadvantages relative to other popular materials. Because the PVDF family of materials offers advantages for arrays of transducers, especially large arrays, I will describe the various types of arrays and how they may be used in NDE.

I will also provide a tutorial for the advanced technologist who wishes to make his own transducers from PVDF and describe the advantages and difficulties in doing so.

My objective is to allow a more optimum selection of transducers based on the users needs and requirements. Each application is different, as is each material, and I hope to show how the properties of transducers effect NDE performance.

### Introduction

Transduction, conversion from one form of energy to another, is a complex process. Ultrasonic transducers for out purposes will be limited to piezoelectric and ferroelectric (giant electrostriction) types. The piezoelectric effect is well known to most of us and is based on the relationships:

• dta=d33*Vt, Eq. (1)
• Where Vt is an applied voltage
• dta is a resultant change in thickness
• d33 is the piezoelectric moduli appropriate for the crystal in question. (this is of course a simplification but I will ignore that in the interest of clarity).
• Vtau=g33*P, Eq. (2)
• Vtau=h33*dtb, Eq. (3)
• Where Vtau is the voltage produced
• P is the applied pressure amplitude
• dtb is the applied change in thickness
• g33 is the piezoelectric pressure constant, and
• h33 is the piezoelectric deformation constant.
Equation 1 tells us what happens when we apply a voltage, equation 2 when we apply a pressure, and equation 3 what happens when we change the thickness. It should be noted that these processes are not reversible, that is applying a voltage changes the thickness but the same change in thickness doesn't produce the same voltage.
Imagine we place two identical piezoelectric material between immovable plate, yes I know this is impossible. This is what physicists call a thought experiment. What we are really doing is making dta=dtb. The reason this is of interest is because the ratio of Vtau/Vt is a direct measure of how much displacement we would expect for a given voltage. Solving the above for dta=dtb we get

• Vtau/Vt=h33*d33 or
• k^2=h33*d33

where k is often called the electromechanical coupling efficiency. Because much energy actually gets put into competing modes a correct factor usually called effective coupling efficiency is often used (ke). For quartz this number is about 1%. Lithium niobate and lithium sulfate are several percent while some ceramic materials are much higher. Ceramics of course are ferroelectric.

What is a ferroelectric? Most dielectric material are electrostrictive. This means they shrink when a voltage is applied. What's more the amount of shrinkage is proportional to the voltage squared. This means it doesn't matter what polarity of voltage is applied. If that was all there was to it then electrostrive materials wouldn't be of interest. The interest is generated because some materials have a giant electrostriction. This is usually called ferroelectric, analogous to ferromagnetism. These materials, PZT and lead metaniobate are the most common, can be tricked into being piezoelectric by polling.

Polling has nothing to do with the electoral process but has to do with imposing a very large voltage on the crystal while it is held at a high temperature, above the Curie temperature. The crystal is cooled and now has a large "preshrink" on it since the voltage has left a large dipole on the crystal. Under these conditions the ferroelectric now acts like a piezoelectric. Voltage opposite to the imposed dipole lets the crystal grow while voltage in the same sense makes it shrink. Many ferroelectrics are also piezoelectrics. Lithium niobate is one such, so that lithium niobate crystals are usually poled to increase the effective k. Lithium niobate is also not a ceramic so the terminology surrounding this field must be treated with caution.

So far I have not really dealt with transmission and reception but they are clearly separate functions and our previous discussion of k as a figure of merit leaves something to be desired. We can use k to derive an approximate but serviceable figure of merit for transmission and reception:

• Yt = (kt/(1-kt^2))*(e33^s/c33^D) = (kt/1-kt^2)*(1/h33) and for reception
• Yr = (kt/(c33^D*e33^s)^0.5 = h33*t/c33^D

Where c33 is the sound speed, D is the probe diameter, e33 is the dialetric constant , kt and h33 are as defined previously, while Yt is the transmitter efficiency parameter and Yr is the receiver efficiency parameter. For a pulse-echo system Yt*Yr is the system performance. This also works if you have pitch-catch but in this case you can choose to use a different material to receive than to transmit. To compare different piezoelectric materials it is popular to compare everything to quartz. Table 1 is such a comparison. There is a basic conflict here because to maximize Yt we want c33 large while to maximize Yr we need e33 small. It is very difficult to make a material that is both a good transmitter and a good receiver.

Table 1: Efficiencies Of Various Transducer Materials
 Material Relative Trans. Eff. (Yt) Relative Rec. Eff. (Yr) Pulse-Echo Eff. (Yt*Yr) Quartz 1.0 1.0 1.0 Lithium Niobate 2.8 0.54 1.51 Lithium Sulfate 6.9 - - PZT-4 65 0.235 15.3 PZT-5A 70 0.21 14.7 Cadnium Sulfite 2.3 - - Zinc Oxide 3.3 1.42 4.7 Barium Titanate 8.4 - - Lead metaniobate 32 - - PVDF 6.9 1.35 9.3

These numbers are from Reference 1 and are only approximate.

If we choose PZT-5 as the transmitter Yt is 70 but using it to receive lowers the product to 14.7. But using PVDF we get 94.5. This is not the optimum choice in all circumstances but it is close if what we want is signal-to-noise ratio. If we want better damping we can pick lead metaniobate and PVDF and get the product up to 43.2. Although the power is down by a factor of two we have improved the resolution at least that much.

Table 2: Comparison Of Various Transducer Materials for NDE
 Material Immersion Use (Yt) Contact Use(Yr) Dissadvanteges Advanteges Quartz Poor Poor Week Trans & Rec. not much used Inexpensive and rugged Lithium Niobate Good Excellent Expensive Good to excellent bandwidth, rugged and can operate to very high temp Lithium Sulfate Excellent - Dissolves in Water None PZT-4 Excellent Good Narrow Band Good penetration & inexpensive PZT-5A Excellent Excellent Narrow Band Good penetration & inexpensive Zinc Oxide Excellent - Above 20 MHz Only & expensive Good bandwidth & operable to GHz frequencies Barium Titanate Excellent Excellent Very Narrow Bandwith Excellent penetration & inexpensive Lead metaniobate Excellent Excellent Expensive Good bandwidth & sensitivity PVDF Excellent Good Poor Trans. Excellent bandwidth & inexpensive

This table is the opinion of the author only and is approximate. The best evalutation is to try transducers in your application using your own instrumentation.

### PVDF and It's Properties

I have already alluded to one of PVDF's properties but first I going to have to clarify just what I mean by PVDF. Poly(vinylidene flouride) the base chemical used in most polymer piezoelectric materials is ferroelectric and pyroelectric and can be polled as I described for ceramic and crystalline ferroelectrics to make it piezoelectric. It is usually stretched 4 to 5 times in size and then polled. The stretching increases the area and decreases the thickness proportionally. Just to confuse everything the PVDF is often mixed with other polymers to change and improve it's properties.

We can see that from Table I PVDF doesn't look all that great. YtYr is only 4.7 while PZT-4 is 15.4 and PZT-5A is 14.7. So why bother with PVDF? Well I have neglected to mention one other factor and that is the acoustic impedance of the load. Since we often have water as a load, immersion testing, or we use plastic delay line and wedges we have to consider the acoustic mismatch between the crystal and these loads. For water the transmission is 78% and for plastic 98% while PZT-5 would be 17% and 31% respectively. You can see the another article in this workshop on composite material made from PVDF and conventional ceramics which have advantages for some applications by taking advantage of both materials in one "crystal."

Figure 1 shows the construction of a standard immersion transducer. The basic construction doesn't vary much but the materials used does change. The primary function changed by the choice of materials is the bandwidth of the transducer. As the acoustic impedance (density*sound speed) of the backing material increases the bandwidth. The acoustic impedance of the backing member must be adjusted for each type of crystal and to produce the desired bandwidth. Gaining bandwidth is not without a price, however, since the amplitude of the crystal is greatest with zero acoustic impedance, air is a good approximation. More amplitude means a better signal-to-noise ratio (electronic only the acoustic "noise" may actually be worse). Resolution however declines. Balancing between acoustic power (and better penetration) and resolution is always tricky since improvements in resolution will not get you anything if you can't penetrate.

Fig. 1: A cross-sectional view of the mechanical assembly of a typical transducer showing the basic components. The lens can often be deleted when using PVDF. Backing members are also often deleted (air backed) but the transducer is then more delicate.

The main differences between PVDF and other materials that I haven't discussed are it's inherent bandwidth (resolution) and the fact that it is flexible and can be formed into a variety of shapes to suit special applications.

The bandwidth of PVDF is actually the best of any material so far discovered and routinely produces transducers with 0.5 to 1 cycle transmitted and received pulses. The usual practice of measuring the transducer's bandwidth in pulse-echo actually produces the bandwidth squared since the transmission bandwidth equals the receive and you have done both. Measuring the bandwidth directly can be done with optical methods which can out perform PVDF in bandwidth but who's transmitted power is much lower than any of the materials discussed so far. I also have to point out that the bandwidth of the material is also involved since water and most other materials have a frequency dependent attenuation. For water this becomes important at frequencies above 20 MHz.

The fact that PVDF can be bent and formed into complex shapes, it is a plastic so it can be formed to some very complex shapes, allows some previously very costly transducers to be made inexpensively. A typical application is to make aspherical transducers to focus angle beams or to focus in complex geometries. The advantage is that the aberration caused by Snell's law can be eliminated as well as the part geometry. This is valuable for the detection of small flaws and to allow better flaw sizing. Figure 2 shows one such application schematically. The crystal must be shaped in a sphere in one plane but involuted in the other.

Fig. 2: An example use of aspheric transducer to correct for aberrations caused by off axis entry (angle beam) ultrasonic inspection. The lens has two curves, a spherical focus in the plane out of the screen, and aspheric as shown. The involute form allows correction for the nonlinear refraction caused by Snell's law.

The PVDF foils are actually easy enough to work with that for some types of applications the average user can make a transducer himself. I will provide some tips on doing so in a subsequent section.

### Phased Arrays

Now to phased arrays. Phased arrays have been around for a long time and are used in some types of medical imagers. Many have probably seen ultrasonic images of unborn babies obtained with this technology. The cost of phased array systems is dominated by the cost of the electronics and for many NDT applications by the design of the array. A little background is required. Be patient it isn't as complex as it first sounds.

A phased array is basically a way of forming a sound beam electronically. The way this is done is with an array of little transducers that are very close together (on the order of a wavelength of sound). Figure 3 shows a linear array which is the type used for some medical scanners. Each little sliver or element of the array has it's own pulser and amplifier. For a typical application there might be anywhere from 8 to 128 elements. This can get expensive but some types cost little more than a typical conventional ultrasonic transceiver that we have all used.

Fig. 3: A linear array can steer the beam by pulsing the individual elements of the array at different times. The individual "wavelets" combine to form a straight or curved beam. By controlling the phase during reception of each element you reverse the process and produce a electronically stearable and focusable beam.

The phase of the pulses driving each element can be controlled. This is equivalent to controlling the time delay between each pulse and all the others. The sound waves combine (add) according to these delays or phases and can be focused and steered electronically. This can be done very fast so real time images can be formed that can be in focus everywhere. Because the linear array is only phased in one plane the electronic focus is a line focus, very much like a cylindrical transducer with an electronically controlled focus and direction! So why aren't these things being used in NDE?

Actually they are on a very limited scale but there is a problem. The medical users have only one subject, people, and we are mostly water. The medical imagers therefore only deal with very slight changes in acoustic velocity and can ignore refraction. Things like steel and aluminum most definitely refract and this cannot be ignored. Medical scanners have been used and some companies are now offering phased arrays better suited to NDE applications.

The fact that the linear array is a line focus is a disadvantage in many industrial applications and limits the value of this type of array to NDE applications. There is another type of array (Fig. 4) that solves this problem called a 2D array or a "filled" array. This is a straight forward extension of the linear array where instead of slivers we have little squares. Now controlling phase in two dimensions is possible and we can focus and steer the beam where we will. This very cool but there is still a problem. A 16x16 filled array needs 256 independent pulsers and amplifiers able to control phase. If you have to ask the price you can't afford it!

Fig. 4: A filled array can steer the beam by pulsing the individual elements of the array at different times. The beam can also focus but both can be done in two dimensions. This allows focus at any depth allowed by diffraction and at angle allowed by refraction.

If linear arrays are limited and filled arrays are two expensive why get excited about phased arrays? Well there are annular arrays (Fig. 5). An annular array has elements (slivers) that are annuli. Such an array is able to focus by controlling the phase of each element. Eight to twelve annuli will allow focusing at frequencies less than 5 MHz. This essentially gets us infinite (not quite but really large) depth of field. Our ultrasonic image or scan can be in focus through several inches of steel or aluminum with no penalty in scanning speed!

Fig. 5: An annular array consists of rings, I have drawn a zone plate like array but equal width annuli have also been used. Each element in the array can be set to a different phase which corresponds to a different focus. We now have electronic focus, sometimes called dynamic focus, but have lost the ability to steer the beam.

Are we happy yet? This is cool but we had to give up the ability to steer the beam. We can fix this using the segmented annular array (Fig. 6). We can chop up the annuli into segments and get steering back. In addition we know something about diffraction and we don't need as many segments in the center as in the edge of the beam. This means we can build an segmented annular array with somewhere between 32 and 64 elements. This is a lot but much more economical than 256 and we get steering, although not over as many degrees as a linear or filled array. The amount of steering we need is less because we have refraction which magnifies the angle as well. This arrangement also lets us do aspherical focus much like the aspherical transducer I described earlier. By doing this electronically we can do longitudinal and shear wave inspection with the same transducer and they can be focused at different depths and we can do it very fast.

Fig. 6: An segmented annular array consists of rings that have been chopped into segments, I have show quarters here but the number of segments can vary. We now have electronic focus we can steer the beam.

Although phased array NDE oriented equipment has only recently become available I expect it to become an important element in the toolkits of ultrasonic inspectors. It's advantages in flaw detection and in flaw characterization are compelling. Phased arrays are the only method that allows this type of operation in production since if you are going to use enough conventional transducers to do the same thing by brut force you are already going to have 32 to 64 transducers and you might as well have the advantage of the phased array which need not be changed for the next application.

#### Making Arrays from PVDF?

So how does all this relate to PVDF? Well phased arrays have traditionally been made by dicing large conventional crystals with diamond saws. This is slow and expensive so the arrays are expensive. Dicing PVDF can be done with a razor blade which is cheaper but there is an even better way. You can use the printed circuit board techniques to place electrodes anywhere and any size on the PVDF sheet and then use the razor blade to remove the spaces between. You need to remove the regions between to run wires and to prevent cross talk between each element of the array. Cross talk between elements reduces the capabilities of the array.

### Making Your Own Transducers from PVDF

I mentioned that users can make there own transducers using PVDF foils and that this has advantages. One of them is that the transducer can be glued to a part to monitor it's condition. This only works at ordinary temperatures since PVDF has a Curie temperature of 100C. I had mentioned before about polling above this temperature but I didn't mention that the poling vanishes if you go above this temperature. In fact if the temperature gets close to the Curie temperature PVDF will eventually depole. How long this will take depends on the temperature but the foil will not last long at 90C and most experience would indicate that use about 60C is unwise.

How to glue the foil on is somewhat tricky. It is critical the bondline be very thin. Studies have shown bondline thickness much greater than 1/100 of an acoustic wavelength will degrade performance. That's about 1/50 of the thickness of the foil. I have had good luck with "crazy glue" or cynoacrylic type adhesives, epoxies, and acrylic glue (from a plastics firm that sells acrylic plastic). Some kind of clamp or dead weight fixture to hold the foil in place is needed. With cynoacrylic glues I have used my thumb but the results depend on the "operator."

Making electrical connection is the next problem. This can be done mechanically using spring clip or screws but conductive epoxies also work well. Basically use the conductive epoxy as a solder. You will need a way to hold the wires in place while the epoxy sets up. You have to use room temperature epoxy and one that doesn't contain acids. Soldering PVDF foils is possible but not for the faint of heart. Soldering requires special preparation that is usually done by the manufacturer so it's out for most do it your self types.

Finally you can make immersion or wedge transducers using acrylic plastic. The wedge is easy just make a wedge out of UVAII or polycarbonate and glue the foil in the appropriate spot. PVDF doesn't require a backing member. You make electrical connection and start scrubbing.

Immersion transducers can use an acrylic or polycarbonate backing member to glue the foil onto. You don't need a lens because PVDF is a good match to the water. You do have to worry about the length of the backing member because the wave going into it will return and that echo may mask what you want to look at in the part. Calculating the time of travel first is an excellent idea. You can adjust the arrival of this echo to occur at a convenient time by making the backing member longer or shorter.

Home made will not equal those you buy but, they can be a life saver or at least mighty handy from time to time.

### Conclusions

The use of PVDF and it's superior resolution has many advantages in thickness gaging, near surface resolution and bond evaluation applications where maximum resolution is needed and penetration requirements are not severe (moderately lossey materials). It also is lowering the cost of transducers with specialized and unusual shapes making them viable in a wider number of circumstances.

Phased array transducers made with PVDF can be cheaper and more complex in design than conventional materials and will be increasingly in use in the future. Improvements in flaw sizing and flaw detection are likely to result.

The major problems with PVDF and to a lesser extent with conventional materials are:

• Lack of reproducibility so that the amplitude of signal from one transducer does not match that of the next. This is a long standing problem in transducer technology. The only way to address this problem, at the moment, is to buy several transducers and require them to match. Most vendors will furnish matches to 1 or 2% in conventional materials and 5 to 10% in PVDF. Of course when you need a new transducer to match the old that is not possible. Most of this variation is in the manufacture of PVDF, crystals or ceramic materials.

• PVDF is more delicate than conventional materials and can be damaged mechanically. This is more of a problem for immersion transducers where the risk that the transducer will run into something is greater. It is always wise to buy a spare.

• Phased array electronics are not widely available commercially. There is only one manufacturer I am aware of and this limits both the available capability and increases the price. New manufacturers are more likely to become interested in this technology if it is successful, I believe it will be successful but the jury is still out. Better and more versatile software will also be required for general use although this is improving so fast it may already be available.

• A general problem in immersion transducers is alignment of the transducer beam with the case. Current alignment capabilities are plus or minus a couple of degrees. What is needed in many cases is plus or minus 0.1 or 0.2 degrees. PVDF doesn't make this problem better. Ways to fix this problem are being worked on in the industry but the only solution now is to buy sorted transducers. That is ask for a tight alignment and pay a premium. The manufacturer sorts through their inventory and ships only the ones that meet the requirement.

The ultrasonic transducer industry is changing fast and users have more choices in performance and capability than ever before with promise of even more in the immediate future. We live in an exciting time in ultrasonic where change is constant and the need to stay on top of the technology essential to get the most out of our transducers.

### Recommended References

1. M. G. Silk, Ultrasonic Transducers for Nondestructive Testing, 1984, Adem Hilger Ltd., Bristol.
2. W. G. Cady, Piezoelectricity, 1946, McGraw Hill Book Co.
3. W. P. Mason, Piezoelectric Crystals and Their Application to Ultrasonics, 1950, D. Van Nostrand Co.
4. W. P. Mason, Physical Acoustics and the Properties of Solids, 1958, D. Van Nostrand Co.

### Author

Robert A. Day.
Headed NDE Labortory for the GE Fst Breeder Reactor Department. Worked on reactor related NDT applications. Received three patents on transducer manufacturing techniques. Winner of the 1981 Engineering Award for Technical Achievement in Materials, Manufacturing, and Quality Engineering from the Power Systems Sector of General Electric Co.
Today he workes at Lawrence Livermore National Laboratory and developed ultrasonic inspection techniques for the proposed US geological reactor spent fuel repository at Yucca Mountain. Developed a 1 GHz acoustic microscope for use on integrated circuit applications. Invented new acoustic emission transducer which could withstand the intense light pulse associated with Nova laser (biggest laser in the world) to help diagnose lens cracking problem.
Second Sound: Consultancy providing expertise to major and minor organizations on ultrasonics, NDE robotics, and fixturing design service.
Robert A. Day is a registered Professional Engineer in California (QU - 1129).
E-mail: rockyd@netcom.netcom.com