Measurement of Piezoelectric Phase Angles in a Ferroelectric Ceramic

A method is described for measuring the phase angle of the piezoelectric coefficient d
₃₁
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 d
₃₁
of the ferroelectric ceramic [Pb
_0.99
Nb
_0.02
(Zr
_0.65
T
_0.35
)
_0.98
O
₃
].