Characterization of piezoceramic rectangular parallelepipeds by means of a two-dimensional model

The characterization of piezoelectric resonators is a field of intense scientific work; moreover, clear and accepted IEEE and IEC Standards have been published, showing the concepts and routes to perform the complete characterization of piezoelectric resonators. All of the accepted procedures define some resonator geometries, each of them related with a set of parameters, that can be obtained following resonance measurements at the corresponding resonance frequencies. The basis of the standards is the existence, for each geometry, of well-defined modes that have been analytically solved. The development of multi-dimensional models of the waves' propagation in piezoceramic materials opens the possibility of characterizing piezoelectric resonators with geometries different from those recommended in the standards. In this paper, a two-dimensional model, which takes into account the mechanical and dielectric losses, has been used to characterize piezoceramics with the shape of a regular parallelepiped. A set of elastic, dielectric, and piezoelectric parameters, which are useful for piezoelectric transducer design, can be obtained. For a given sample, the measured input electrical impedance is used to obtain the parameters by means of a fitting process with the corresponding model output. The results obtained with low and high loss materials show that the parameters found have values similar to those obtained following the procedures and geometries recommended by the standards. This procedure permits the characterization of materials when the manufacturing procedure does not allow the fabrication of the shapes recommended by the standards, making it a useful tool for transducer manufacturers and material scientists.