First and Second Order Equations for Piezoelectric Crystals Expressed in Tensor Form

Abstract

Aeolotropic substances have been used for a wide variety of elastic piezoelectric, dielectric, pyroelectric, temperature expansive, piezo-optic and electro-optic effects. While most of these effects may be found treated in various publications <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> there does not appear to be any integrated treatment of them by the tensor method which greatly simplifies the method of writing and manipulating the relations between fundamental quantities, Other short hand methods such as the matrix method <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> can also be used for all the linear effects, but for second order effects involving tensors higher than rank four, tensor methods are essential. Accordingly, it is the purpose of this paper to present such a derivation. The notation used is that agreed upon by a committee of piezoelectric experts under the auspices of the Institute of Radio Engineers.