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

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 a second order ordinary differential equation and two interrelated second order differential equations for 3 polarizations according to 3 dimensions. Although first equation can easily be solved, the next two interrelated equations cannot be solved by usual numerical methods. Based on discretization, a new technique is proposed for studying the motion equations. The results are presented by dispersion curves for shear, dilatational, and flexural modes of phonons.