Displacement Correlations and Frequency Spectra for Mass-Disordered Lattices. II

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Abstract
The full cluster expansion for the phonon Green's function of a binary isotopic disordered alloy is derived for the case of a reference lattice of atomic mass intermediate between that of the two constituents. This result is extended to an alloy which is disordered except for specified atoms which occupy a small number of distinguished lattice sites. The latter Green's functions determine the displacement correlations of atoms in or near a small cluster of impurities in an alloy. The one- and two-vertex self-energies are calculated formally to all orders in the concentration, and it is shown that the disease of spurious poles, reported earlier, persists to the two-vertex self-energy and is a general feature of infinite partial summations when the cumulants of the full cluster expansion are used. The approximation of Elliott and Taylor, which does not have spurious poles, is discussed in this context and is used to evaluate the one-vertex self-energy for a reference lattice of intermediate atomic mass.

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