an accurate impedance analyzer is a crucial requirement as use for the testing of the resonant frequencies fs and antiresonant frequencies fa as well as the free capacitance CT at 1 kHz. The commercially available lineups of impedance analyzers differ in terms of frequency range and sensitivity. The most regularly used one are, for example, Agilent E4294A and Wayne Kerr 65120B, produced by Agilent and Wayne Kerr, respectively. The other thing to notice is that a set of samples in the forms of a disk, a plate, and a cylinder, which have different vibration modes, should be prepared before the measurements are carried out. Obtaining all the needed sample items from a single bulk material of appropriate size is preferred. The sample dimensions should conform to the world standard CEI/IEC 60483:1976.
Material constants such as piezoelectric coefficient d, dielectric coefficient ε, and elastic coefficient s are anisotropic in general. They are usually described by tensor components written in a simplified matrix form according to the point‐group symmetry of the materials. For piezoelectric ceramics, the complete matrix of the coefficients of electromechanical properties can be written as follows:
(1.21)
Based on the IEEE standards [22], the requirement of the sample dimensions and the complete matrix of piezoelectric constants can be established as illustrated in Figure 1.7 [37].
After acquiring the entry parameters, namely, resonant frequencies, antiresonant frequencies, capacitance, density, and sample dimensions, we can calculate the electromechanical coupling coefficients, according to which elastic coefficients
Figure 1.7 Establishing the complete set of material coefficients defined by IEEE standards [37].
Source: Reprinted with permission from Fialka and Benes [37]. Copyright 2013, IEEE.
(1.22)
(1.23)
(1.24)
