Ultrasonic pulse-echo technique for the characterization of elastic constants of single domain Pb(Zn_1/3Nb_2/3)O₃–5.5%PbTiO₃ single crystals with 3m symmetry

The ultrasonic pulse-echo (UPE) technique is a classical method to characterize the elastic constants of solid materials. However, no detailed analysis exists in the literature regarding the application of this technique on the characterization of relaxor–PbTiO₃ single crystals with 3m symmetry. This study systematically investigated the UPE technique for the characterization of elastic constants of [111]_c poled Pb(Zn_1/3Nb_2/3)O₃–5.5%PbTiO₃ single domain single crystals with 3m symmetry. Longitudinal and transversal wave echoes in a rectangular parallelepiped sample were identified based on the theory of wave propagation in piezoelectric materials. Experimental results showed that c11E and c33D can be directly and precisely determined by UPE, but c44E cannot be determined by UPE neither directly nor indirectly. The elastic constants c14D, c44D, and c66D cannot be directly determined by UPE but they can be calculated from directly measured c_i (i = 1, 2, 3, 4). Experimental results also showed that c₄ cannot be precisely determined by UPE. Based on error analysis, the uncertainty of c₄ will strongly influence the precision of measured c44D and c66D but only weakly influence the accuracy of c14D.