Explicit secular equations for piezoacoustic surface waves: Rayleigh modes

TL;DR

This paper derives explicit secular equations for Rayleigh surface waves in 2mm piezoelectric crystals, providing analytical solutions for wave speeds and fields, especially in the case of Potassium niobate.

Contribution

It offers a complete analytical solution for Rayleigh wave propagation in specific piezoelectric crystals, including explicit polynomial secular equations for different boundary conditions.

Findings

Derived polynomial secular equations of degree 10 and 48.

Identified relevant wave speed roots analytically.

Calculated piezoelectric coupling coefficient for Potassium niobate.

Abstract

The existence of a two-partial Rayleigh wave coupled to an electrical field in 2mm piezoelectric crystals is known but has rarely been investigated analytically. It turns out that the Z-cut, X-propagation problem can be fully solved, up to the derivation of the secular equation as a polynomial in the squared wave speed. For the metallized (unmetallized) boundary condition, the polynomial is of degree 10 (48). The relevant root is readily identified and the full description of the mechanical and electrical fields follows. The results are illustrated in the case of the superstrong piezoelectric crystal, Potassium niobate, for which the effective piezoelectric coupling coefficient is calculated to be about 0.1