Finite size effects of nanoparticles on the atomic pair distribution functions

The finite size effects of nanoparticles on the atomic pair distribution functions (PDF) are discussed by calculating the radial distribution functions (RDF) on nanoparticles with various shapes, such as sheet, belt, rod, tube and sphere, assuming continua. Their characteristics are shown depending on the shapes and the sizes of the nanoparticles. The formulas of a PDF analysis which take account of such effects are presented and are found to reproduce the experimental data.