Fluctuation X-ray Microscopy for Measuring Medium-Range Order

Abstract

ABSTRACTMany x-ray techniques exist to probe long- and short-range order in matter, in real space by imaging and in reciprocal space by diffraction and scattering. However, measuring mediumrange order (MRO) in disordered materials is a long-standing problem. Based on fluctuation electron microscopy, which was applied successfully to the understanding of MRO in amorphous materials, we have developed fluctuation x-ray microscopy (FXM). This novel approach offers quantitative insight into medium-range correlations in materials at nanometer and larger length scales. It examines spatially resolved fluctuations in the intensity of a series of x-ray speckle patterns. The speckle variance depends on higher order correlations that are more sensitive to MRO. Systematically measuring the speckle variance as function of the momentum transfer and x-ray illumination size produces a fluctuation map that contains information about the degree of MRO and the correlation length. This approach can be used for the exploration of MRO and subtle spatial structural changes in a wide range of disordered materials from soft condensed matter to nanowire arrays, semiconductor quantum dot arrays and magnetic materials. It will also help us to understand the mechanisms of order-disorder transitions and may lead to control of ordering, which is important in developing ordered structures tailored for particular applications. A theory for FXM and preliminary experimental results from polystyrene latex spheres are discussed in this paper.