How to measure atomic diffusion processes in the sub-nanometer range

Self-diffusion of the atomic constituents in the solid state is a fundamental transport process that controls various materials properties. With established methods of diffusivity determination it is only possible to measure diffusion processes on a length scale down to 10 nm at corresponding diffusivities of 10−23 m2 s−1. However, for complex materials like amorphous or nano-structured solids the given values are often not sufficient for a proper characterization. Consequently, it is necessary to detect diffusion length well below 1 nm. Here, we present the method of neutron reflectometry on isotope multilayers. For two model systems, an amorphous semiconductor and an amorphous metallic alloy, the efficiency of this method is demonstrated to detect minimum diffusion lengths of only 0.6–0.7 nm. It is further shown that diffusivities can be derived which are more than two orders of magnitude lower than those obtainable with conventional methods. Prospects of this method in order to solve actual kinetic problems in materials science are given.