We describe and illustrate a forward modeling method for quantitatively reconstructing the geometry and orientation of microstructural features inside of bulk samples from high energy x-ray diffraction microscopy data. Data sets are comprised of CCD images of Bragg diffracted beams originating from individual grains in a thin planar section of sample. Our analysis approach first reduces the raw images to a binary data set in which peaks have been thresholded at a fraction of their height after noise reduction processing. We then use a computer simulation of the measurement and the sample microstructure to generate calculated diffraction patterns over the same range of sample orientations used in the experiment. The crystallographic orientation at each of an array of area elements in the sample space is adjusted to optimize overlap between experimental and simulated scattering. In the present verification exercise, data are collected at the Advanced Photon Source beamline 1-ID using microfocused 50keV x-rays. Our sample is a thin silicon wafer. By choosing the appropriate threshold fraction and convergence criteria, we are able to reconstruct to ≤ 10µm errors the sub-region of the silicon wafer that remains in the incident beam throughout the rotation range of the measurement. The standard deviation of area element orientations is ≈ 0.3 degrees. Our forward modeling approach offers a degree of noise immunity, is applicable to polycrystals and composite materials, and can be extended to include scattering rules appropriate for defected materials.

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We produced millions of morphologically identical platinum catalyst nanoparticles in the form of ordered arrays epitaxially grown on (111), (100), and (110) strontium titanate substrates using electron beam lithography. The ability to design, produce, and characterize the catalyst nanoparticles allowed us to relate microscopic morphologies with macroscopic catalytic reactivities. We evaluated the activity of three different arrays containing different ratios of (111) and (100) facets for an oxygen-reduction reaction, the most important reaction for fuel cells. Increased catalytic activity of the arrays points to a possible cooperative interplay between facets with different affinities to oxygen. We suggest that the surface area of (100) facets is one of the key factors governing catalyst performance in the electrochemical reduction of oxygen molecules.