Acoustic modes in metallic nanoparticles: Atomistic versus elasticity modeling

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 1.5-4 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 in 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.