Acoustic modes in metallic nanoparticles: atomistic versus elasticity modeling

TL;DR

This study compares atomistic and elasticity models to examine vibrational properties of metallic nanoparticles at nanometer scales, revealing the importance of anisotropy, size effects, and surface phenomena.

Contribution

It demonstrates the necessity of including elastic anisotropy and surface effects for accurate vibrational modeling of nanoparticles at very small sizes.

Findings

Elastic anisotropy is crucial for model agreement.

Number of vibrational modes decreases with size.

Frequency scaling breaks down due to surface effects.

Abstract

The validity of the linear elasticity theory is examined at the nanometer scale by investigating the vibrational properties of silver and gold nanoparticles whose diameters range from about 1.5 to 4 nm. Comparing the vibration modes calculated by elasticity theory and atomistic simulation based on the Embedded Atom Method, we first show that the anisotropy of the stiffness tensor in elastic calculation is essential to ensure a good agreement between elastic and atomistic models. Second, we illustrate the reduction of the number of vibration modes due to the diminution of the number of atoms when reducing the nanoparticles size. Finally, we exhibit a breakdown of the frequency-spectra scaling of the vibration modes and attribute it to surface effects. Some critical sizes under which such effects are expected, depending on the material and the considered vibration modes are given.