NUMERICAL SOLUTION OF THE INTERRELATED DIFFERENTIAL EQUATION OF MOTION IN PHONON ENGINEERING

Abstract

In this work, we study numeric calculations of phonon modes in nanostructures. The motion equation of atoms in a crystal with some simplification, results in asecond order ordinary differential equation and two interrelated second order differentialequations for 3 polarizations according to 3 dimensions. Although first equation caneasily be solved, the next two interrelated equations cannot be solved by usual numericalmethods. Based on discretization, a new technique is proposed for studying the motionequations. The results are presented by dispersion curves for shear, dilatational, andflexural modes of phonons.