Effect of Force-Constant Changes on the Coherent Neutron Scattering from Face-Centered Cubic Crystals with Point Defects

This is a study of the effects of a low concentration of random substitutional impurities on the vibrational properties of fcc monatomic harmonic crystals. Central-force-constant changes between the impurities and their nearest neighbors, as well as mass changes, are taken into account. The problem is formulated in terms of a coherent neutron-scattering experiment, although the results are useful for other experiments as well. Analytic expressions are given for the phonon self-energy function for K along some high-symmetry directions in the lattice, with results expressed in terms of perfect-lattice Green's functions. Numerical computations are performed on Al containing heavy impurities. The Al-impurity force constants are treated as parameters which are varied over a wide range.