Approximate Elastic Spectrum of Acoustic Waves in AgCl from X-Ray Scattering

The temperature diffuse scattering of x-rays from a large single crystal of AgCl has been measured at room temperature using a Geiger counter spectrometer and crystal monochromated CuK-α radiation. Measurements were made throughout the hk0 plane in reciprocal space, and in certain other regions. The data are analyzed on the basis of the theory developed by Laval and James, in which temperature vibrations are expressed in terms of traveling elastic waves. An assumed set of vibrational frequencies is used for the optical branch. Dispersion curves for waves in the acoustical branch traveling in the [100], [110], and [111] directions are obtained. The velocities at infinite wavelength are shown to agree fairly well with those given by the static elastic constants. An approximate frequency spectrum is then calculated, and suggestions are made as to how the effects of the optical and acoustical branches may be separated.