Formfactors of Hollow and Massive Rectangular Parallelepipeds at Variable Degree of Anisometry

The present work is a comparative study on the scattering behaviour of hollow and filled rectangular parallelepipeds. Comparison is based on the model formfactors of rectangular parallelepipeds, which cover the entire regime of variable wall thickness. The entire regime of wall thicknesses has been made available by the present work, which completed the set of formulas by calculating the formfactor for the limit of hollow parallelepipeds with infinitely thin walls, which was still lacking. The formfactors are expressed as a function of the momentum transfer q. Discrimination between massive and hollow structures by means of the q-dependent scattering data SF(q) gets possible once the Guinier radius and the particle volume can be established at the lower limit of q or a power law of SF(q) similar to q(alpha) can be extracted towards large q. Whereas the former requires extrapolation of the scattering data to q = 0 with high accuracy, the latter needs experiments over a very broad q-regime. If experimental data is restricted to a q-regime which includes only the first peak in a KratIcy representation of q(2)SF(q) vs. q without giving way to an accurate extrapolation to q = 0 nor to a clear power law in q, discrimination between a hollow and a massive structure gets extremely difficult. Yet, the effect of anisometry is striking and enables extraction of a crude guess of the degree of anisometry already from the first Kratky peak. This could be achieved by introducing a dimensionless parameter established from the width and location of the first Kratky peak.