Approximate Elastic Spectrum of β-Brass from X-Ray Scattering

The temperature diffuse scattering of x-rays from a single crystal of β-brass has been measured at room temperature using a Geiger counter spectrometer and crystal monochromated CuKα radiation. Measurements were made throughout a large region in reciprocal space, with special attention given to the hko plane. The results were in excellent qualitative agreement with the theory developed by Laval and James in which temperature vibrations are expressed in terms of elastic waves. From the measurements, dispersion curves are obtained giving the velocity and frequency of the elastic waves, in the [100], [110], and [111] directions, as a function of their wavelengths. An approximate frequency spectrum is then calculated on the basis of these dispersion curves. The velocities at infinite wavelength are shown to agree with those given by elastic theory using the static elastic constants.