Lattice modes in molecular crystals measured with nuclear inelastic scattering

Abstract

We reveal an important property of nuclear inelastic scattering in a molecular crystal with well-separated lattice and molecular modes: The presence of the molecular modes does not change the shape but merely rescales the lattice part of the energy dependence of nuclear inelastic scattering. Therefore, the density of states (DOS) of the lattice vibrations can be properly derived even from the lattice part of nuclear inelastic scattering alone. In this case, one has to substitute the mean recoil energy of a nucleus by the effective recoil energy of the molecule. In first approximation, the ratio of the recoil energies is close to the ratio of the nuclear and molecular masses. More precisely, it is given by the relative area of the lattice part in the entire DOS. The theoretical analysis is verified with numerical calculations for a model DOS and with the experimental data for the decamethyl ferrocene molecular crystal. More generally, the analysis is valid for any region of nuclear inelastic scattering around the central elastic peak with sufficiently narrow lines beyond it. Therefore, the demonstrated property of nuclear inelastic scattering allows for a much shorter measuring time in studies of lattice modes in molecular crystals, low-energy molecular modesmore » in proteins, and in investigations of glass dynamics with molecular probes.« less