Quasielastic Scattering of Synchrotron Radiation by Time Domain Interferometry

We use synchrotron radiation and time resolved x-ray detection to measure structural relaxations of glycerol [${\mathrm{C}}_3$ ${\mathrm{H}}_5$(OH${)}_3$] having time scales of 30 to 200 ns at $1.5{Å}^{-1\mathrm{}}$ momentum transfer. Foils containing ${}^{57}$Fe (14.4 keV nuclear resonance, 141 ns lifetime) are placed before and after the nonresonant sample, and a small difference $\left(\sim 70\mathrm{MHz}\right)$ is established in their nuclear response frequencies. Quasielastic scattering from the sample perturbs the 70 MHz quantum beat pattern of the nuclear scattering. A simple model relates the perturbation to the dynamic structure factor of the sample.