Analiza legii de dispersie a fononilor în cristalul cvasiunidimensional TTT2I3

Abstract

The paper presents a theoretical study of the crystalline vibration spectrum in the quasi-one-dimensional organic crystal of the Tetratiotetracene-Iodide (TTT2I3). The dynamic matrix and the dispersion equation are obtained for the cases when both the first and second coordination spheres were taken into consideration. For simplicity the plane model of the lattice is used, the Ox axis being directed along the molecular chains. The numerical calculations are carried out with the help of package Mathematica, taking into account the quasi-one-dimensional crystal proprieties. For the second sphere of coordination only the central forces are taken into consideration, being introduced a single additional quasi-elastic coefficient. The numerical data are analyzed and the graphs of the longitudinal and transverse frequency dependence as functions of wave vectors oriented along the directions Ox and Oy are built up. The vibration spectra for fixed values of the wave vector in the direction Oy in the cases of first and second coordination sphere are presented too.