Material nonlinearities and the extensional mode of quartz rods

The DC-field induced change in frequency of the extensional mode of rods is related to the third-order elasticity and the third-order piezoelectricity (electroelasticity). Five combinations of the corresponding material constants of quartz are determined by least-squares fit to data obtained from 50 different rods. The results are notable for their small standard errors of less than 2% on average. They also agree very well with the values obtained independently by the transit-time method. The resonator method of determination of the above nonlinearities of quartz using the rods vibrating in length is attractive not only for its accuracy but also for its experimental simplicity; it is also free of interference from electrostriction and third-order permittivity