Diffusion effects

The aim of this section is to explain how it is possible to determine the diffusion model from a set of different time spectra accumulated at different temperatures and sample orientations. The usual procedure is schematically sketched in figure and will be discussed in more details in this section. From the knowledge of the structure of the investigated sample a jump model for the diffusion is created. This model can be written using the self-correlation function formalism derived for thermal neutrons [37] and later modified for absorption processes [38] as a set of differential equations for the self-correlation function G$_{s}$(r,t). The self-correlation function describes the probability for a jump of an atom at the time $t$ and position $r$ if the same atom was at the time $t=0$ at the position $r=0$. A detailed description of the formalism can be found in [39]. A Fourier transform of the self-correlation function leads to the intermediate-scattering function I(t,k$_{R}$) which is the function measured during an NRS experiment. The parameters of the model or the model itself have to be modified until the best possible match with the experimental spectra is reached. In principle it should be possible to recalculate the self-correlation function from the measured spectrum. In reality it is not possible. The reason is the convolution of the intermediate-scattering function with the experimental resolution.

Figure 3.8: Fit procedure to determine the jump-diffusion model from NRS measurements.