### Electrical Measurement of Ferroelectric Properties

### Piezoelectric Resonance

### Direct Piezoelectric Measurement – The Berlincourt Method

_{33}using the direct method (often called the Berlincourt method). This chapter examines the advantages and disadvantages of the method in detail and with some experimental validation using typical PZT ceramics examine the validity of using the data from this method to predict the displacement of materials in real conditions. The piezoelectric charge coefficient, d

_{33}is one of the fundamental parameters defining the piezoelectric activity of a material, basically the higher the d

_{33}the more active the material is. Consequently, manufacturers, designers, and users want to know the d

_{33}coefficient for the material. Measurement of the d

_{33}coefficient can be realised in several ways varying in accuracy and simplicity. The most reliable method of determining the d

_{33}coefficient is to electrically excite a resonance in a sample, and from the resonance response – given the dimensions of the sample and the density – a d

_{33}coefficient can be calculated. One problem with this method is that the geometry of the sample must be such that only a pure fundamental resonance mode is produced, and the calculated d

_{33}parameter relates to this resonance mode. This leaves the problem how to determine the d

_{33}parameter for shapes that don’t have an ideal resonance geometry, or where the resonance mode is not the mode that will be used. For instance, for thin discs poled in the thickness direction it is easy to excite a resonance in the radial direction, and determine the relevant d

_{ij}parameter, but to obtain the d

_{ij}coefficient for motion in the thickness direction then longer cylinders are needed.The d

_{ij}coefficient is defined as the charge produced for an applied stress, or the strain for an applied voltage, and these are theoretically equivalent. The latter measurement is more difficult to achieve because of the small strains involved, so measurement techniques have concentrated on the former. In this work, initially, the charge was measured in response to an applied static load, but difficulties with thermal drift led to the measurements being performed quasi statically, at a few hundred hertz.The quasi static method is straightforward; a small oscillating force is applied to the sample and the charge output is measured and divided by the applied force amplitude. The simplicity of the technique has been its downfall, in that anyone can easily build up their own system, and there are a growing number of commercial systems. There are currently no standards for this measurement method, and consequently each system performs the measurement slightly differently. This means that, although the results from these systems are good for measuring within a batch or batch to batch variability, external comparisons usually produce a large variability.

### Pyroelectric Materials

### Interferometry for piezoelectric materials and films

_{33}is no more than 3000 pC/N or 3000pm/V. If 1000 volts are applied on a 1 mm PMN-PT, the resulted displacement is only 3 nm. Other piezoelectric materials, such as PZT, the most widely used material, have a d

_{33}nearly one order of magnitude smaller. Optical interferometry has long been established as one of the most promising techniques for small displacement measurements, due to its capability of very high resolution and advantages such as no mechanical contact and no need for calibration on the length scale. The development of lasers in the last a few decades has almost eliminated the problems associated with the optical path length coherence and beam density, and many techniques based on laser interferometry have been developed for the characterisation of piezoelectric materials. This chapter will review the applications of laser interferometry to the characterisation of the piezoelectric bulk and thin film materials and discuss possible problematic issues associated with these techniques.

### Temperature dependence of piezoelectrics

### Measurement and Modelling of Self-Heating in Piezoelectric Materials and Devices

- Ultrasonic Cleaning
- Ultrasonic Welding
- Sonar Transducers
- Diesel Injectors
- Ultrasonic Sewage Treatment

all use piezoelectric materials operated at high drive levels, where thermal loading on the device becomes an issue, and where potentially expensive cooling is needed to maintain device performance. When piezoelectric materials are used as actuators they make use of the indirect piezoelectric effect, where the application of an electric field gives rise to an internal strain. In this solid-state energy transformation there will always be a balance between electrical energy input and work done by the device. The coupling coefficient, k, is used to describe this efficiency for an ideal case where there are no losses. Here, k is essentially the ratio of the open circuit compliance to the short circuit compliance. For most real piezoelectric materials this conversion process is also associated with losses – both mechanical and dielectric. These losses manifest themselves in the form of heat, causing a temperature rise in the device, which, depending on the thermal boundary conditions can be detrimental to device performance. This self-heating effect is most often encountered in resistive components and is termed ‘Joule Heating’. However, it is also seen in non-ideal dielectric materials where the dielectric loss gives rise to internal heat generation. To a first approximation, piezoelectric actuators can be thought of as a non-ideal or lossy dielectric but, because the material is moving, additional mechanical terms are needed to model this behaviour. If the energy loss to the surroundings is greater than the internal power generation, then the sample will eventually reach an equilibrium temperature. If the sample losses are greater than those to the environment, or if the losses increase with increasing temperature, then the sample will heat up until some catastrophic event is reached – such as the soldered connections failing, softening of adhesives, or depolarisation of the material.

### Piezoresponse Force Micropscopy – PFM

### Indentation Stiffness Analysis of Ferroelectric Thin Films

It is now relevant to discuss losses prevalent in piezoelectric ceramic compositions since these values are often as important as the functional, dielectric and elastic constants that resonance analysis yields. In reality, a piezoelectric material comprises losses originating from its dielectric response to an electrical field, mechanical response to applied stress or following piezoelectric motion and its piezoelectric (strain) response to an electric field. The impact of these losses on a resonance sweep is a reactive and resistive part to the measured impedance. A material with zero losses would exhibit zero impedance at resonance. The significance of loss results in sample heating or noise production and this is why for many applications an understanding of loss mechanisms and absolute values becomes important. Normally, the mechanical loss at resonance is calculated from the width of the resonant peak and is labelled the mechanical Q or Quality factor. The narrower the resonant peak, the higher its Q. Dielectric losses are normally calculated from the phase angle between observed capacitance and applied field, labelled tan(delta). Piezoelectric loss may not normally be calculated from resonance data but may be assessed through strain – electric field response whereby any hysteresis present may be tentatively ascribed to this loss alone – of course, if strain is produced then mechanical loss may also have an additive effect. This issue is contentious and discussed in this chapter.