Characterization of all the elastic, piezoelectric, and dielectric constants of tetragonal Pb(Mg_1/3Nb_2/3)O ₃-PbTiO₃ single crystals

Pb(Mg_1/3Nb_2/3)O₃-PbTiO₃ (PMN-PT) single crystals have a tetragonal 4 mm symmetry. In this paper, the elastic, piezoelectric, and dielectric constants of PMN-PT single crystals were measured by the resonance method. A total of eleven independent material constants were measured including six elastic compliance constants at a constant electric field, two dielectric constants at constant stress, and three piezoelectric constants d. Four crystal sample sets of different geometries were prepared in order to measure the length-thickness extensional, thickness extensional, length extensional and thickness shear modes of vibrations, respectively. The experimental impedance spectrum of the PMN-PT crystals was compared with a numerical impedance spectrum calculated with the measured material constants. Good agreement between the two spectra confirmed the validity of the characterization method. In addition, the piezoelectric constant d₃₃, which was determined by the resonance method, was also compared with that measured by a commercial d₃₃ meter. This further confirmed the validity of the resonance measurements.