The calculation of multiphonon X-ray scattering

The coherent scattering of X-rays by phonons is considered in the harmonic approximation for processes involving any number of phonons. The total scattering cross section is evaluated using the best eigendata and up to 24000 sample frequencies in the Brillouin zone. Intensities are presented for NaF, NaCl, NaBr and Al, and it is found that the results converge rapidly with increasing sample size. A comparison with independent calculations of the one-phonon and two-phonon cross sections shows that the higher order processes are important for moderate values of K. The contribution from the very small wave vector phonons is treated separately, and this enables the integrated diffuse scatter to be calculated near a Bragg peak.