Longitudinal versus transverse spheroidal vibrational modes of an elastic sphere

TL;DR

This paper distinguishes between longitudinal and transverse spheroidal vibrational modes in elastic spheres, highlighting their qualitative differences and implications for analyzing nanoparticle phonons, while correcting common misconceptions.

Contribution

It provides a detailed analysis of spheroidal modes, clarifies their qualitative grouping, and corrects misconceptions, aiding in the interpretation of inelastic light scattering data.

Findings

Transverse modes have small divergence and are nearly independent of longitudinal sound speed.

A qualitative distinction exists between longitudinal and transverse spheroidal modes.

The analysis improves understanding of nanoparticle phonon scattering experiments.

Abstract

Analysis of the spheroidal modes of vibration of a free elastic sphere show that they can be qualitatively grouped into two categories: primarily longitudinal and primarily transverse. This is not a sharp distinction. However, there is a relatively stark contrast between the two kinds of modes. Primarily transverse modes have a small divergence and have frequencies that are almost functionally independent of the longitudinal speed of sound. Analysis of inelastic light scattering intensity from confined acoustic phonons in nanoparticles requires an understanding of this qualitative distinction between different spheroidal modes. In addition, some common misconceptions about spheroidal modes are corrected.