ABSTRACT
This chapter presents numerical methods that can be used to track the vibrational properties of atomistic systems. Vibrational response of materials has important applications not only in terms of acoustic damping and acoustic resonance but also in terms of thermal capacity, thermal conductivity and structural analysis. The chapter summarizes different techniques that can be used to infer numerically the vibrational properties of materials: calculation of normal modes and eigenfrequencies, calculation of the vibrational density of states (VDOS), calculation of the dynamical structure factor (DSF) for transverse as well as longitudinal waves, and propagation of a wave packet. It focuses on the case of crystalline inclusions in an amorphous matrix. The chapter reviews briefly different numerical techniques that can be used to infer the vibrational properties, and compare with experimental measurements. Different experiments can be used to probe the vibrational frequencies of nanoparticles embedded in a matrix, such as low- frequency resonant Raman spectroscopy, or time- resolved optical pump-probe experiments.
