Approximate analytical method and its use for calculation of phase velocities of acoustic plane waves in crystals for example LiNbO3

TL;DR

This paper introduces an analytical method to calculate phase velocities of elastic waves in crystals, specifically applied to LiNbO3, providing graphical tools for easy determination of wave velocities in any direction.

Contribution

The paper presents a new analytical approach to determine phase velocities of elastic waves in piezoelectric crystals, demonstrated on LiNbO3, with graphical representations for practical use.

Findings

Calculated phase velocities for three elastic waves in LiNbO3

Graphical phase velocity cards for arbitrary directions

Analytical determinant relation for elastic wave velocities

Abstract

By means of the offered analytical method the determinant relation for a phase velocities of elastic waves for an arbitrary propagation directions in a piezoelectric crystal are received. The phase velocities of three normal elastic waves for the crystal of LiNbO3 are calculated. Results of this calculation for each of waves are presented graphically in the form of the cards allowing easily to define phase velocities in any given direction in crystal.