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

Abstract

This is a study of the vibrational properties of random substitutional impurities and their nearest neighbors in cubic monatomic harmonic crystals in the low-impurity-concentration limit. Mass changes, as well as force-constant changes between the impurity and its nearest and, in some cases, next-nearest neighbors, are taken into account. The problem is formulated in terms of an incoherent-neutron-scattering experiment, although the results are useful for other experiments as well. Analytic expressions are given for the resonance frequencies for all the normal modes of the defect cage in fcc and bcc lattices. Expressions for the mean-square displacement of the impurity and its nearest neighbors at all frequencies are given for the fcc case. Results are 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.