Fluctuation X-ray Microscopy for Measuring Medium-Range Order
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Fluctuation X-ray Microscopy for Measuring Medium-Range Order Lixin Fan1, Ian McNulty1, David Paterson1, Michael M.J.Treacy2 and J. Murray Gibson1 1 Advanced Photon Source, Argonne National Laboratory, 9700 S. Cass Ave, Argonne IL 60439 2 Department of Physics and Astronomy, Arizona State University, Tempe, AZ 85287 ABSTRACT Many 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. INTRODUCTION In recent years, materials research has increasingly focused on developing a better understanding of the disordered state of matter. Most of the effort in understanding amorphous materials has focused on structural models with an atomic pair distribution function (PDF) consistent with diffraction experiments. However, the PDF method has poor sensitivity to medium-range order (MRO, ~5 to ~20 coordination radii). Recently, fluctuation electron microscopy (FEM) was developed and successfully used for probing MRO in amorphous materials [1,2]. This technique examines fluctuations in the coherently scattered (speckle) intensity patterns from very small sample volumes, on a length scale R determined by the illuminated volume or associated image resolution. Measurements of the speckle variance in a particular segment of Q space (usually an annulus) are plotted as a function of Q to give the degree of MRO. Systematically changing R enables variable resolution microscopy, which can be used to directly measure the correlation length. The speckle variance depends on two-, threeand four-body atomic correlation functions, whereas the average, which is just the diffracted intensity, depends only
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