Piezooptic Effect and Electrostriction

Matrix notation allows to represent them in the form of 6 by 6 matrices which, in general, are not symmetric abont the leading diagonal. In the triclinic crystal no coefficients vanish for symmetiy reasons and all 36 of them are independent. 

The ambiguity of their interpretation has already been pointed out in Sect. 6.3 They could be seen to represent the dependence either of a dielectric coefficient on a mechanical variable (and in this way related to the piezooptic effect) or of a piezoelectric coefficient on an electric variable (and associated with electrostriction). 

Electrostriction, in the original sense, means a mechanical deformation caused by an electric field, in general proportional to the square of the field strength. Such an effect is, in principle, quite common and can exist in solid, liquid, and even gaseous substances. It does not require aity special symmetiy properties. Yet, the deformations are exceedingly small and very difficult to measure. In defect-free ciystals electrostriction is caused by the direct action of the electric field on the atoms forming the crystal lattice and by the Maxwell stress (Becker and Sauter (1973), Grindlay (1970)). Displacements and reorientation of defects may contribute to the electrostrictive effect in doped crystals. 

The most direct experimental access to this effect is the direct measurement of deformation (changes of specimen thickness, e.g.) under the action of an electric field. In piezoelectric ciystals, however, this effect is masked to a large extent by the superimposed converse piezoelectric effect, hnear in the electric field. Nevertheless, Uchino etal (1982) andLnymes (1983) have constmcted measuring apparatus based on an interferometric techniqne. By compensating the linear piezoelectric response Luymes (1983) measured an electrostriction constant of a-quartz. 

Much of what has been said above concerning the electrooptic effect also applies mutatis mutandis to the piezooptic effect (variation of refractive index by external mechanical stress). Due to unavoidable dispersion piezooptic coefficients measured by optical techniques can hardly be related to the low-frequency regime for which the definitions of Sect. 6.3 are intended. Determining these constants quasistatically or at sufficiently low frequencies would involve the measurement of permittivity under mechanical stress. Investigations of this type have been made by the group around Newnham and Cross (Uchino et al. (1980), Rittenmyer et al. (1983), Meng and Cross (1985)). 

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