Introduction to Measurement Methods
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.