Structure uncovering from fluctuation x-ray scattering of randomly oriented nanoparticles*

We have carried out a fluctuation x-ray scattering experiment on platinum coated gold nanoparticles randomly oriented on a substrate. A complete algorithm for determining the electron density of an individual particle from diffraction patterns of many particles, randomly oriented about a single axis is demonstrated. This algorithm operates on angular correlations among the measured intensity distributions and recovers the angular correlation functions of a single particle from measured diffraction patterns. Taking advantage of the cylindrical symmetry of the nanoparticles, we proposed a cylindrical model to reconstruct the structure of the nanoparticle by fitting both the experimental ring angular auto-correlation and the small angle scattering data. The physical meaning of the resulted structure is discussed in terms of their statistical distributions of the shape and electron density profile.