Abstract
Propagation of the mean waves in a simple cubic crystal with small, random mass defects is studied using the results of a previous paper. The dispersion equations for two- and three-dimensional crystals are analyzed. For uncorrelated mass defects, the effective propagation constants are obtained explicitly in the limits of low frequency and near cut-off frequency. The mean reflection and transmission coefficients are determined for a plane wave incident in a crystal formed by joining a semi-infinite perfect crystal to a semi-infinite defective crystal or by connecting two semi-infinite perfect crystals to a finite imperfect crystal. We also construct the mean Green's functions for an infinite crystal lattice containing defective masses distributed throughout it or confined to a half-space.
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