Substitutional Defects and Resonant Modes in Solids

Abstract

We examine in some detail the reasons for the observed discrepancy between, on the one hand, the neutron-scattering experiments on crystals of chromium containing tungsten impurities and of copper containing Gold, and, on the other hand, Elliott and Maradudin's calculations on low-concentration isotope defects. A more careful analysis and a self-consistent calculation of the Brueckner type gives results which are in good agreement with experiment in the very low frequency region, but the resonance frequency is shifted to the lower frequency side. It is further established by diagram techniques that a higher concentration of defects also lowers the resonance frequency. The effect of changes in force constants are treated exactly in the low-concentration limit. It is then possible to reproduce the value of the resonance frequency correctly, but the magnitudes of frequency shifts are much smaller than the experimental results.