Simple model for the vibrations of embedded elastically cubic nanocrystals

TL;DR

This paper introduces a simplified model to calculate vibrational modes of elastically anisotropic nanocrystals embedded in isotropic matrices, aiding interpretation of low-frequency Raman spectra.

Contribution

It develops an isotropic approximation for vibrational modes of cubically elastic spheres embedded in matrices, improving spectral analysis of nanocrystals.

Findings

Nearly independent vibrational modes of free cubically elastic spheres identified

The model accurately explains Raman spectra of gold and copper nanocrystals in glass

Provides a practical approach for analyzing vibrational spectra of embedded nanocrystals

Abstract

The purpose of this work is to calculate the vibrational modes of an elastically anisotropic sphere embedded in an isotropic matrix. This has important application to understanding the spectra of low-frequency Raman scattering from nanoparticles embedded in a glass matrix. First some low frequency vibrational modes of a free cubically elastic sphere are found to be nearly independent of one combination of elastic constants. This is then exploited to obtain an isotropic approximation for these modes which enables to take into account the surrounding isotropic matrix. This method is then used to quantatively explain recent spectra of gold and copper nanocrystals in glasses.