Dynamical Theory: A Tool for Analyzing Scattering From Periodic Nano-confinements
The behavior of matter in nano-confinements is being investigated as a means for obtaining controlled highly-ordered nanomaterials. To facilitate improved materials design, knowledge of the three-dimensional structure is needed. Non-destructive probing of such samples challenges conventional microscopy techniques. On the other hand, the submicron size of a single confinement is impractical for neutron and x-ray scattering experiments because the scattering is so weak.
This dilemma can be overcome by using a confining matrix made up of an array of identical confinements, e.g. the grooves of a diffraction grating. The caveat is that the periodicity of the sample amplifies dynamical scattering effects that are not accounted for in approximate scattering theories and a full dynamical theory calculation becomes unavoidable. Dynamical theory calculations, applied to spin-echo measurements on nanostructured gratings, give a good account of all the data sets we have collected so far in reflection and transmission scattering geometries. Calculations on recent measurements performed on a silica suspension in contact with the grooves of a diffraction grating show colloidal jamming in the grooves.