Simulation of vibrational properties of nanostructures

Abstract

In this thesis we study the vibrational properties of different nanostructures by using the continuum and the discrete models. The continuum method is based on the elasticity theory while the discrete method employs the molecular dynamics. With the continuum method we obtain the dispersion curves and the displacement patterns of the vibrational modes. We also calculate the radial acoustic modes of cylinders, cylindrical shells, "core-shell" and composite cylinders of general anisotropy. We finally use the Surface Green Function Matching method to obtain the acoustic waves dispersion curves in superlattices formed by anisotropic hexagonal crystallographic materials. With the discrete method, we develop a technique for the calculation of the density of states and the Raman spectra from the data obtained by the molecular dynamics approach.