On the properties of piezoelectric materials based upon orthonormal representations

Abstract

For piezoelectric tensor, the decomposition method based upon irreducible orthogonal representation is overviewed. Besides, orthonormal tensor basis method is improved to express any third rank tensors such as piezoelectric tensor showing the piezoelectric effect of the material properties on the structures. Numerical examples for materials from different crystal symmetry classes serve to illustrate and verify the orthonormal tensor basis method. The differences and similarities are stated by comparing the methods presented in this work and the others in literature. It is also demonstrated that for hexagonal symmetry, each decomposed parts obtained from orthonormal tensor basis method has physical meaning. Furthermore, the norm based upon orthonormal tensor basis representation of piezoelectric tensor is obtained explicitly for each crystal symmetry classes and those results are used to study the piezoelectric effect of different materials. It is also shown that one can determine in which material the piezoelectric effect is stronger by using the norm concept for any material from various crystal symmetry classes.