Ensemble modeling of very small ZnO nanoparticles.

The detailed structural characterization of nanoparticles is a very important issue since it enables a precise understanding of their electronic, optical and magnetic properties. Here we introduce a new method for modeling the structure of very small particles by means of powder X-ray diffraction. Using thioglycerol-capped ZnO nanoparticles with a diameter of less than 3 nm as an example we demonstrate that our ensemble modeling method is superior to standard XRD methods like, e.g., Rietveld refinement. Besides fundamental properties (size, anisotropic shape and atomic structure) more sophisticated properties like imperfections in the lattice, a size distribution as well as strain and relaxation effects in the particles and-in particular-at their surface (surface relaxation effects) can be obtained. Ensemble properties, i.e., distributions of the particle size and other properties, can also be investigated which makes this method superior to imaging techniques like (high resolution) transmission electron microscopy or atomic force microscopy, in particular for very small nanoparticles. For the particles under study an excellent agreement of calculated and experimental X-ray diffraction patterns could be obtained with an ensemble of anisotropic polyhedral particles of three dominant sizes, wurtzite structure and a significant relaxation of Zn atoms close to the surface.