Measurement of Piezoelectric Phase Angles in a Ferroelectric Ceramic

A method is described for measuring the phase angle of the piezoelectric coefficient d₃₁ in 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 d₃₁ of the ferroelectric ceramic [Pb_0.99 Nb_0.02 (Zr_0.65 T_0.35) _0.98 O₃].