Phonon spectroscopy with sub-meV resolution by femtosecond x-ray diffuse scattering

We present a reconstruction of the transverse acoustic phonon dispersion of germanium from femtosecond time-resolved x-ray diffuse scattering measurements at the Linac Coherent Light Source. We demonstrate an energy resolution of 0.3 meV with a momentum resolution of 0.010.28em0exnm^-1 using 10-keV x rays with a bandwidth of ~10.28em0exeV. This high resolution was achieved simultaneously for a large section of reciprocal space including regions closely following three of the principal symmetry directions. The phonon dispersion was reconstructed with less than 3 h of measurement time, during which neither the x-ray energy, the sample orientation, nor the detector position were scanned. These results demonstrate how time-domain measurements can complement conventional frequency domain inelastic-scattering techniques.