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In this work, all the independent elastic coefficients, piezoelectriccoefficients, and internal frictions of a single alpha-quartz crystal aredetermined using our recently proposed partial-electrode electromechanicalimpedance spectroscopy (PE-EMIS) at 25 centigrade. In PE-EMIS, the rectangularparallelepiped quartz sample with two small partial electrodes fabricated on acorner is self-excited/sensed. The conductance spectrum (equivalent to theresonance spectrum) measured by an impedance analyzer under a true freeboundary condition is noiseless, allowing the first 100 eigenmodes ranging from50 to 310kHz to be accurately fitted. To avoid mode misidentification, theoff-plane displacement distributions of the quartz sample under differenteigenmodes are determined using a scanned-laser vibrometer. The resonancespectrum measured using a commercial sandwich-like RUS apparatus is alsopresented for comparison, and the results show that the clamping force insandwich-like RUS shifts the sample's resonance frequencies, causing 13% and75% overestimations for the piezoelectric coefficients e11 and e14,respectively. In comparison to the RUS, our proposed PE-EMIS is more effectiveand convenient, and will be widely used for characterization of piezoelectriccrystals.

Elastic, piezoelectric coefficients, and internal frictions of a single  alpha-quartz crystal determined by partial-electrode electromechanical  impedance spectroscopy