Crystallographic approach to obtain intensive elastic parameters of k₃₃ mode piezoelectric ceramics

This paper presents an advanced piezo-material characterization method to obtain intensive elastic parameters of the k₃₃ vibration mode from the k₃₁ geometry through crystallographic approach with canted polarization. Three effective k₃₁ bars with 0, γ, and π/2-γ degree angled polarization is needed where 0 < γ < π/4. Eliminating s₁₃^E,* and s₅₅^E,* components from the effective elastic parameters, the k₃₃ mode elastic parameters could be derived. Pb{(Zr_0.56Ti_0.44)_0.99Nb_0.01}O₃ with 0, 15, 30, 45, 60, 75 ° angled polarization were prepared and characterized under constant vibration velocity to obtain the effective elastic parameters for the k₃₁ mode. The intensive elastic compliance s₃₃^E and elastic loss tanϕ′₃₃ are derived and compared to the measured value from the conventional methods Due to the low structural impedance of the measured geometry (i.e., large sample capacitance), the reliability on the proposed method is extraordinary, and the implicit relative error in the conventional methods could be avoided.