Thickness Modes Of Plates Research Articles

The electroelastic tensor of quartz determined by the resonator method

The complete electroelastic tensor of quartz has been calculated—for the first time—exclusively using the data obtained by the resonator method. Its eight independent components were obtained by the least-squares fit to 184 observations of the dc-field-induced change in the resonance frequency of the extentional mode of rods and thickness modes of plates. Simultaneously, an attempt has been made to calculate the eight independent components of the electrostrictive tensor and the only independent component of the third-order permittivity tensor of quartz. Only seven values have been obtained here; three of them are linear combinations of these quantities. A comparison made with similar tensors as calculated from the transit-time experiment [Kittinger, Tichy, and Friedel, J. Appl. Phys. 60, 1465 (1986)] yields excellent agreement for the electroelastic tensor. Differences between the corresponding tensor components are comparable with their standard errors. The comparisons available for the electrostrictive tensor are considerably less encouraging. No comparison for the third-order permittivity (disregarded in the analysis of the transit-time experiment) could be made.

Combinations of the electroelastic and electrostrictive constants of quartz determined using the thickness modes of plates

Ten linear combinations of the fundamental material constants of electroelasticity and electrostriction of quartz have been determined. They were obtained by the least-squares fit to 134 observations of the change in the resonance frequency of the thickness modes of quartz plates caused by a dc field. With one exception, there is very good agreement between our results and their counterparts obtained independently by the transit-time method (pulse propagation in bulk quartz). The differences between comparable constants are no longer out of proportion with their standard errors. This work supersedes earlier results [J. Appl. Phys. 65, 715 (1989)].