Study of High-Frequency Vibrational Modes for Nonlinear Diatomic Chains

Abstract

The model of a one-dimensional diatomic chain with two different types of nonlinearity (quartic nearest-neighbor interparticle interaction potential and substrate potential, respectively) is studied. The nonlinear partial differential-difference equations in the two parallel cases for the model are transformed into nonlinear ordinary differential equations by the approach of decoupling ansatz plus continuum approximation. Through the qualitative analysis the nonlinear vibrational modes with various frequencies above the cut-off frequency of the linear spectrum are obtained for the systems. The difference of the modes for the two types of nonlinearity almost disappears as the mass of heavy atoms is three times greater than that of light ones. This similarity of interparticle interaction nonlinearity to substrate nonlinearity for the nonlinear diatomic chain is in agreement with the origin of the nonlinear substrate potential.