Diffusion in solids at moderate temperatures is a well-known phenomenon. However, direct experimental evidence about the responsible atomic-scale mechanisms has been scarce, due to difficulties in probing the relevant length- and time-scales. The present thesis deals with the application of X-ray Photon Correlation Spectroscopy (XPCS) for answering such questions. This is an established method for the study of slow dynamics on length-scales of a few nanometres. The scattered intensity in the diffuse regime, i.e. corresponding to atomic distances, is very low, however, and so it has so far...