Element Shape

As shown by the frequency constant a piezo element’s frequency is dependent on its thickness.

The relationship between frequency and thickness for thin disc oscillating and polarised axially and made of a common Piezoceramic (PZT-5A1) is shown in Figure 5.5.

Figure 5.5: Frequency Vs. Thickness Relationship for PZT-5A1, Nρ = 2000Hz∙m.

Figure 5.5 is based upon a thin disc whose diameter is much greater than its thickness. This assumes a single mode of resonance within the piezo element. However, depending upon the elements shape, it is possible for more than one mode to be excited.

The responses from two shear sensors with different aspect ratios are shown in Figure 5.6 and Figure 5.7. One sensor was a flat plate (0.2 x 2 mm) while the other was square in cross section (1 x 1mm). The sensors were bonded on steel blocks and the response shows two reflections from the far side of each block. The reflections for the plate sensor are clear, with sharp responses, and only one apparent mode of resonance which equates to the frequency that would be expected given the piezo thickness. The response for the square cross section sensor looks significantly different. The response consists of a package of distinct sharp peaks rather than the smoother joined peaks seen in the flat plate response.

For clarity a single reflection for the square cross section sensor has been plotted in Figure 5.8.

The plot shows that the reflection is built up of multiple higher frequency pulses with consistent spacing. This implies that there are in fact two modes of resonance. When the cross sectional dimensions of the piezo are considered the two modes of resonance can be explained. The time period between the high frequency pulses is approximately 0.45us, this is a frequency of 2.22 MHz. As we can see from Figure 5.5 this equates to a thickness of 0.9mm, and so would correspond to the thickness resonance of the element. The results of a Fast Fourier Transform performed on the window shown in Figure 5.8 is plotted in Figure 5.9 along with the frequency spectrum for a reflection from the flat plate element. The square section element shows multiple resonant harmonics in comparison to the single peak seen in the flat plate sensor. This clearly demonstrates the importance of considering not just the thickness, but also the lateral dimensions of the element used in a transducer.

Figure 5.6: Shear Sensor Response with an Aspect Ratio of ~10:1.

Figure 5.7: Shear Sensor Response with and Aspect Ratio of ~1:1.

Figure 5.8: Single Shear Wave Reflection from Square Cross Section Sensor.

Figure 5.9: Shear Sensors Frequency Response.

5.4.5 Electrodes

In order to induce and measure electrical fields in a piezo element, electrodes must be mounted on either side. These electrodes come in a variety of forms, materials and manufacturing techniques (Morgan Technical Ceramics, n.d.). Key design considerations are electrode bond strength, thickness and solderability. When soldering to the electrodes it is essential that the

piezo does not exceed it’s Curie temperature. As well as the piezoelectric effect, piezoceramics also have a pyroelectric effect. Heating of the piezo during the soldering process can therefore cause a significant build-up of charge, the piezo should be soldered in short-circuit conditions.

Where an electrode is unsuited to soldering the electrical connections can be made either via a conductive adhesive or mechanical clamping. The electrode material and thickness will define the deposition methods that can be used. Electrode deposition techniques are typically split into two types, thin and thick film.

Thick-Film Electrodes

These are in the region of 3 to 10 µm and are applied to the piezo ceramic by screen printing.

After careful cleaning, the components are applied with a conductive electrode paste, typically a noble metal such as silver. Silver and palladium alloys are also commonly used. The electrode paste is fired at a temperature between 600-800 °C depending on the material. This then forms a conductive layer with a good adhesion to the ceramic and results in relatively robust electrodes to which wires can directly be soldered. This method can leave small air pockets between the piezo material and electrode, reducing the ultrasonic transmission. Silver dissolves in standard solders, therefore high silver content solder is normally used to reduce absorption of the electrodes when soldering. In order to create separate ground and positive electrodes an electrode pattern is created by laser cutting the coating.

Thin-Film Electrodes

Physical vapour deposition (sputtering) can be used to create much thinner electrodes. This results in electrode thicknesses in the range of 1 µm down to a few 100 nm, with less air gaps in comparison to the screen printing method. Sputtering can be used with a range of electrode materials including Gold-Nichrome, Nichrome, Silver and Aluminium. The technique involves creating positive ions in an inert gas. The material to be used for the electrode is struck by these ions and broken up into a fine spray that covers the piezo. The electrode shape is defined by masking of the defined area. Shear elements must be metalised in the polarized state and are generally manufactured with thin-film electrodes. Nickel electrodes can be chemically plated or evaporated. Due to the thinness of this electrode type, and the materials involved, wicking of the electrode during soldering is an issue. Therefore, for evaporated electrodes conductive epoxies are typically used.