Application of Wavelet Transform to the study of Lattice Dynamics of two-dimensional Nanostructures

Abstract

Abstract Theory of vibration of atoms that is the theory of lattice dynamics now forms an important part of study in Nanotechnology as these vibrations determine thermal and mechanical characteristics of a material and also govern phenomena like diffuse scattering of X-rays, neutron scattering, spin-lattice relaxation, etc. Lattice Dynamical analysis is helpful in the design and engineering of Nanomaterial and nanostructures for phononic and acoustic applications. Unlike current techniques that are based on Fourier analysis that gives results for frequency distribution along the wave vector, the wavelet transform can be used to determine how the energy of a simulated system is distributed in time, space, and among wave numbers, simultaneously. This is important in the study of interfacial phonon (quanta of crystal vibration) conductance, where the time the phonon packet interacts with the interface is preserved in the transformation. Wavelet transform is a unique tool for probing localized phonon physics at Nano scales. Two- dimensional Nanostructures like Graphene and hexagonal Boron Nitride has unique thermal properties which make them suited for a variety of applications. Wavelet Transform is applied to the lattice dynamics of a two- dimensional lattice and phonon transport is studied for industrially important materials like Graphene and its variations.