Determination of the third-order material constants of quartz by the transit-time method and its strategy

The values of nonlinear material constants of quartz are generally computed by means of a least-squares fit to overdetermined linear systems. Past experience indicates that any new linear system would be used most productively if all nonlinear constants in it that have been determined earlier are substituted into it and if all nonlinear constants making a negligible contribution there are eliminated from the system prior to executing the least-squares fit. The weaknesses of this approach are explained, and a strategy to be adopted is given. This is applied to the calculation of the nonlinear constants on the basis of the transit-time experiment. The results provide new values for the third-order piezoelectric and electrostrictive constants of quartz and also add to them a value of third-order permittivity