Phonons in an Inhomogeneous Continuum: Vibrations of an Embedded Nanoparticle

TL;DR

This paper analyzes the vibrational modes of an inhomogeneous elastic continuum, focusing on a nanoparticle embedded in glass, and compares these to free sphere modes and complex frequency calculations.

Contribution

It provides a detailed analysis of vibrational modes in inhomogeneous continua and relates them to free sphere spectra and damping models.

Findings

Vibrational modes of embedded nanoparticles differ from free spheres.

Mode frequencies and damping are characterized using complex frequency methods.

Comparison shows how embedding affects vibrational spectra.

Abstract

The spectrum of acoustic vibrational modes of an inhomogeneous elastic continuum are analyzed with application to a spherical nanoparticle embedded in an infinite glass block. The relationship of these modes to the discrete vibrational spectrum of a free sphere is studied. The vibrational modes of a sphere with a fixed surface are relevant in some situations. Comparisons are also made to calculations of mode frequency and damping based on complex valued frequency.