Determination of Phonon Dispersions from X-Ray Transmission Scattering: The Example of Silicon

A beam of monochromatic synchrotron x-ray incident on a silicon wafer creates a rich intensity pattern behind the wafer that reflects the cross section of scattering by thermally populated phonons. A least-squares fit of the patterns based on a lattice dynamics calculation yields the phonon dispersion relations over the entire reciprocal space. This simple and efficient method is suitable for phonon studies in essentially all materials, and complements the traditional neutron scattering technique.