ANHARMONIC GAP MODE IN A ONE-DIMENSIONAL DIATOMIC LATTICE WITH NEAREST-NEIGHBOR BORN-MAYER-COULOMB POTENTIALS AND ITS INTERACTION WITH A MASS-DEFECT IMPURITY

Both stationary and moving intrinsic anharmonic gap modes are generated in a perfect one-dimensional diatomic chain. Within the rotating-wave approximation, the eigenfrequency, eigenvector, and energy of such a localized packet can be found from differential-difference equations. A connection between the anharmonic system treated here and the harmonic one is that since the effective force constants are determined by the eigenvector of the particular localized mode, they can be viewed as renormalized force constants in a harmonic lattice. For the diatomic chain the even-parity anharmonic mode is unstable against conversion to an odd-parity mode while the odd-parity mode shows long term stability, in contrast with the result found earlier for a monatomic chain. Part of the mean energy of the odd-parity gap mode is associated with kinetic and potential terms of the ac vibration while the rest resides in a localized dc distortion of the lattice. Strongly localized gap modes can be approximated by the dynamics of a triatomic molecule. For larger vibrational amplitudes and associated dc distortions, the potential for the gap mode becomes double valued and the rotating-wave approximation fails. When the interaction of intrinsic gap modes with stationary anharmonic mass defect impurity modes is examined in numerical simulation studies, a variety of scattering results are found depending on the mass defect magnitude and the site in the diatomic chain. Two important features of the trajectories are that the gap mode is trapped at the mass defect when the vibrational frequencies of the moving mode and the anharmonic defect mode are near resonance and that the scattering is elastic when the frequencies are far apart.