Direct mapping of phonon dispersion relations in copper by momentum-resolved x-ray calorimetry

We have developed a new method of mapping phonon dispersion relations based on momentum-resolved x-ray calorimetry. X-ray scattering intensities are measured at selected points in reciprocal space with suitably chosen polarization configurations; the thermal part of the scattering intensity is extracted by scanning the temperature of the sample. The intensity variations, governed by the phonon populations, are analyzed to yield the energies of the phonons. This method is applied to copper. With high-order effects under control, the results are in excellent agreement with the known phonon dispersion relations.