Nonlinear material properties of quartz determined by the resonator method

Attempts to provide least-squares estimates of all 31 independent thrid-order nonlinear electromechanical constants of alpha quartz using the resonator method produce parameters containing third-order elastic constants linearly combined with the remaining three types of electromechanical nonlinearities: electroelastic, electrostrictive and dielectric. To maximize the yield of the resonator method in terms of these latter three types of nonlinear constants, the third-order elastic constants must be "imported" from an external source. They can be introduced, with the same effect, before or after the least-squares process is executed. Their reliability is crucial for the quality of the electroelastic constants and apparently (considering the size of their respective standard errors) less important for the electrostrictive and third-order dielectric constants. A comparison with the results of others, yielding in most cases an excellent agreement, is facilitated by introducing uniformity into the values of the linear constants used for their determination. This produces changes in the calculated nonlinear parameters but does not remove the few differences which were noted.