On the evaluation of neutron scattering elastic scan data

Neutron scattering elastic scans are a common technique to obtain an overview of the microscopic dynamics over a wide range of a control parameter, in most cases the temperature. The data evaluation usually aims at calculating the mean-square displacement 〈 r 2 〉 of the scatterers. Unless there is a clear separation of fast and slow dynamics, this mean-square displacement has to be treated as a time-dependent quantity 〈 r 2 〉 ( t ) . In this paper a definition of the timescale t res of an elastic scan from the energy resolution of the instrument is proposed. A common assumption in the evaluation of elastic scans is that the Q-dependence of the elastic scattering decays like a Debye–Waller factor. Here, it is shown that this can only be expected under certain conditions. In general there will be a non-linearity in plots ln I el ( Q ) vs. Q 2 because 〈 r 2 〉 ( t ) is not constant close to t res , and I el ( Q = 0 ) ≠ 1 due to multiple scattering. Finally, a procedure is suggested to calculate 〈 r 2 〉 taking these facts into account.