Influence of Nanoparticles Size on XRD Patterns for Small Monodisperse Nanoparticles of Cu⁰ and TiO₂ Anatase

The effect of nanoparticle size and structure on XRD and SAXS patterns was investigated using modeling with the Debye scattering equation for a series of nanoparticles (NP) with the positions of atoms kept according to the bulk lattice and after structure relaxation. The purpose of research was to determine if the changes in XRD peak positions for NP are entirely due to the well-known effects of lattice parameter change or if additional effects can arise from the size itself. It was found that for very small NPs with sizes below 5 nm, the size itself influences the XRD patterns. This effect can be caused by interference fringes and is not taken into account when considering XRD patterns in standard software. The research demonstrates that new methods for XRD pattern treatment of very small nanoparticles should be developed.