Characterization of medium-range order in disordered materials by fluctuation x-ray microscopy

Measuring medium-range order is a challenging problem in the structural study of disordered materials. We have developed a technique which we call fluctuation x-ray microscopy that offers quantitative insight into medium-range correlations in disordered materials at nanometer- and larger-length scales. The technique examines spatially resolved fluctuations in the intensity of x-ray speckle patterns. To demonstrate this new technique at micron-length scales, we studied a model system comprised of polystyrene latex spheres. Using nanofocusing optics, we have further developed fluctuation x-ray microscopy for the study of nanomaterials. The medium-range order in two hybrids of \textit{PI-b-PEO/ aluminosilicates }was quantitatively examined and compared. by fluctuation x-ray microscopy.