Forward modeling method for microstructure reconstruction using x-ray diffraction microscopy: Single-crystal verification

Abstract

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 comprise charge-coupled device 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 50 keV x rays. Our sample is a thin silicon wafer. By choosing the appropriate threshold fraction and convergence criteria, we are able to reconstruct to ≤10 μm errors the subregion 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°. 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.