A new method of calculating the piezo-electric constants of α-quartz

Abstract

A method of calculating the piezo-electric constants of α-quartz is described which consists in determining the electric moment developed by changes of bond-lengths and bond-angles on strain. Considering three atoms P, Q, R, of which P and R are silicon atoms and Q an oxygen atom orvice-versa, the electric moment developed on strain may be resolved into moments in the plane PQR and moments perpendicular to this plane. Resolving these moments along the axes of the crystal and summing up for all the forty-two planes in the unit cell, we get the piezoelectric equations and constants of the crystal. The electric moment in the plane is equivalent to the moment produced by the change of bondlength along the direction of the bonds before strain, while for the moment normal to the plane we take the average value,i.e., half the value of the moment normal to the plane when the displacements of the atoms are wholly normal to the plane. The method gives good agreement with the observed values.