5.4.6 Measurement of Piezoelectric Properties
Piezoelectric measurements are usually made to measure the displacement of the material when an electric field is applied. These techniques are resonance or subresonance techniques.
In the resonance methods, one conducts the measurement of the characteristic frequencies of the materials upon the application of alternating electric field and is widely used for bulk samples. To a first approximation, the electromechanical response of a piezoelectric material close to the characteristics frequency can represented by the electrical equivalent circuit as shown in the figure 5.24. Simplest measurements are conducted by poling a piezoelectric long rod of length ~6 inch and diameter ~¼ inch along its length.
| Figure 5.24 Schematic representation of (a) equivalent electrical circuit of a piezoelectric sample close to its characteristic frequency (b) Plot of electrical reactance of the sample a function of frequency |
The coupling coefficient, k33, is expressed in terms of series and parallel resonance frequencies (fs and fp respectively) as
Using this relation along with elastic compliance and low frequency dielectric constant , the piezoelectric coefficient, d33, can be calculated by using the following relation:
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Measurements are limited to the specific frequencies determined by the fundamental vibration modes of the sample. In the case of piezoelectric thin films, the thickness resonance occurs in the GHz range in which the measurements involve considerable difficulties. In such cases, the resonance in the substrate driven by a thin film could be used to determine the piezoelectric coefficient of a thin film. The disadvantage of this method is that measurements are limited by the number of characteristics frequencies determined by the electromechanical response of a material.
One can use subresonance techniques for the measurement of piezoelectric properties at the frequencies which are much below the characteristics fundamental resonance frequencies. This includes measurement of direct effect i.e. charge developed on a piezoelectric material under application of an external mechanical stress and measurement of converse effect i.e. measurement of electric field induced displacements. Although displacements can be rather small to measure accurately, technological advances have allowed accurate measurements using techniques like strain gauges or linear variable differential transformers (LVDTs) or optical interferometers or atomic force microscopes. Appropriate electrical circuits needs to drawn and modeled to clearly elucidate the material properties.
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