Pairing Effects in Impure Lattice Dynamics

Abstract

<p> A study is made of the effects of pairing of defects on the dynamics of impure lattices, with the prospect of calculating the properties of crystals with a reasonably high concentration of impurities. A harmonic theory is used, with a mass-defect model, i.e. mass differences only are considered.</p> <p> Various parameters of lattice dynamics are studied, such as the atomic mean square displacement, by use of the Green's functions of Zubarev (1960), as evaluated by Bruno (1971).</p> <p> Finally, a calculation is made of the shifts and widths in the phonon spectrum of Copper due to the addition of 20% Gold impurities. The theory of Aiyer et al. (1969) is used, as corrected by Nickel and Krumhansl (1971), with a derivation along the lines of Langer (1961).</p> <p> It is shown that pairing effects are small and that the high-concentration calculation does not reproduce the experimental results of Svensson and Kamitakahara (1972) so that a more detailed model must be employed, in particular the inclusion of force constant changes and volume effects appears to be necessary.</p>