Determination of the Thermal Diffuse Scattering at the Bragg Reflections of Si and Al by Means of the Mössbauer Effect

The 14.4-keV $\gamma$ rays from ${\mathrm{Co}}^{57}$ sources were scattered on different crystallographic planes of various Si and Al Crystals. By using nuclear resonance absorption it was possible to separate the elastic and inelastic components of the scattered beams. An analysis of the nuclear resonance absorption peak on the beam diffracted by the {555} planes of Si and a double Braggscattering experiment support the expectation that the elastic component of the scattered beam is due to Bragg diffraction. The angle dependence of the relative intensities of the inelastic parts at various Bragg peaks of Si and Al crystals, corrected for the contributions of Compton scattering, were in satisfactory agreement with the angle dependence calculated on the basis of the lattice wave theory of thermal diffuse scattering. These calculations were simplified by assuming that the crystals were elastically isotropic and that the reciprocal lattice volume, over which the thermal scattering was integrated, had either a spherical or cylindrical shape. Good agreement between theory and experiment was found for the temperature dependence of the thermal scattering intensity at the {444} and {555} diffraction peaks of silicon, between 80 and 600 °K.