Aspects of the modelling of the radial distribution function for small nanoparticles

An approach to modelling radial distribution functions (RDFs) of nanoparticle samples over a wide range of interatomic distances is presented. Two different types of contribution to the model RDF are calculated. The first explicitly reflects the structure of the nanoparticle parts with more or less crystalline atomic structure. It can be calculated precisely and contains comparatively sharp peaks, which are produced by the set of discrete interatomic distances. The second includes RDF contributions from distances between weakly correlated atoms positioned within different nanoparticles or within different parts of a nanoparticle model. The calculation is performed using the approximation of a uniform distribution of atoms and utilizes the ideas of the characteristic functions of the particle shape known in small-angle scattering theory. This second RDF contribution is represented by slowly varying functions of interatomic distance r. The relative magnitude of this essential part of the model RDF increases with increasing r compared with the part that represents the ordered structure. The method is applied to test several spherical and core/shell models of semiconductor nanoparticles stabilized with organic ligands. The experimental RDFs of ZnSe and CdSe/ZnS nanoparticle samples were obtained by high-energy X-ray diffraction at beamline BW5, HASYLAB, DESY. The ZnSe nanoparticles have a spherical core with approximately 26 Å diameter and zincblende structure. The RDF of the CdSe/ZnS nanoparticle sample shows resolved peaks of the first- and the second-neighbour distances characteristic for CdSe (2.62 and 4.27 Å) and for ZnS (2.33 and 3.86 Å) and for the first time clearly confirms the presence of CdSe and ZnS nanophases in such objects. The diameters of the CdSe and ZnS spherical cores are estimated as 27 and 15 Å. CdSe and ZnS are present in the sample for the most part as independent nanoparticles. A smaller amount of ZnS forms an irregularly shaped shell around the CdSe cores, which consists of small independently oriented ZnS particles.