A method is described for measuring the phase angle of the piezoelectric coefficient d31in a ferroelectric ceramic. This method requires only data on the complex electrical admittance of a length-extensional bar resonator. Measurements based on this procedure gave a phase angle on the order of 3° for the piezoelectric constant d31of the ferroelectric ceramic [Pb0.99Nb0.02(Zr0.65T0.35)0.98O3].
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Richard Holland (1970) studied this question.