Small-angle scattering from spherical particles on randomly oriented interfaces

Small-angle scattering (SAS) has long been used to study nucleation and growth of particles in solid or liquid matrices. In some special cases, nucleation of particles occurs on interfaces, e. g., grain boundaries in crystalline solids or membranes in a solvent. Clearly, the position of the particles is constrained in this case to a narrow region close to the interface, which leads to correlations between the particles. In the present paper, we derive simple expressions for the analysis of SAS data from particles located on planar interfaces, and compare the analytical approximations with computer simulations.