Knowledge Bank

Calculations of the vibration spectrum, atomic amplitudes, and infrared absorption have been carried out for a chain consisting of forty atoms in an array of the form ABABABACACAB\ldots\ldots in which the composition varies from pure AB to pure AC. Nearest neighbor interactions and clamped end boundary conditions are assumed. The arrangement of the mixed atoms is chosen to be random. This provides a simple model for which calculations can be readily carried out and which might be of some value in explaining the experimental results reported by others for mixed crystal systems. The experimental results fall into two categories. In one case, the strongest modes appear to be at the frequencies of the pure compounds with the intensities varying with composition. In the other case, the frequency of the strongest absorption appears to vary continuously and approximately linearly with concentration. The calculations reported here for a simple model give different types of behavior for different mass ratios in qualitative agreement with experiment. In the one-dimensional model, ``two mode'' behavior occurs when the optical branches of the pure compounds do not overlap. When the optical branches overlap, the situation is more complicated.