Energy separation of neutrons scattered at small angles from silicon using time-of-flight techniques

The time-of-flight technique is used on a small-angle neutron scattering instrument to separate the energies of the scattered neutrons, in order to determine the origin of the temperature-dependent scattering observed from silicon at Q > similar to 0.1 angstrom(-1). A quantitative analysis of the results in comparison with the phonon dispersion curves, determined by Dolling using a triple-axis neutron spectrometer, shows that the temperature-dependent scattering can be understood in terms of Umklapp processes whereby neutrons gain energy from phonons.