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 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.

Quantitative X-ray tomography

“…The irradiated sample plane is meshed with equilateral triangles and, in each triangle, a fundamental zone of crystal orientations is 'searched' so as to generate Bragg scattering that optimally overlaps that seen in the measurement. This procedure is computer intensive but gives robust results including in the case of deformed grains, [140][141][142][143][144] for studying lattice rotation during plastic deformation 118,119 and for mapping local strains.…”

Three-dimensional grain mapping by x-ray diffraction contrast tomography and the use of Friedel pairs in diffraction data analysis

“…In this case one seeks ͑by assigning orientations to voxels in sample space͒ the configuration that minimizes the difference between experimentally observed and simulated diffraction patterns. 15,16 Such algorithms can account for local variations in orientation inside grains and may overcome the current restriction to low levels of orientation spread. Some encouraging results have been obtained for 2D ͑line focus illumination of one sample cross section͒ simulated data of deformed specimen 16 and first 3D maps for an undeformed specimen have been obtained from stacking of 2D data.…”

A rotational and axial motion system load frame insert for in situ high energy x-ray studies

“…28 This required the development of sample grips with minimal radial dimensions. The grip design chosen is shown in Figure 3, where the near field detector is also shown for reference.…”

“…To date, this collection of methods have largely been thought of as individual techniques, including far field HEDM (ff-HEDM) to measure the average elastic strain tensor of individual grains (stress tensor with known elastic stiffness matrix) [24][25][26][27] and near field HEDM (nf-HEDM) to map the structure and local crystallographic orientation within and between grains. 21,28,29 While the individual techniques are valuable on their own, the concurrent application of nf-HEDM, ff-HEDM, and others such as absorption micro-computed tomography (µ-CT) for mapping the structure of voids, cracks, and/or inclusions which may be present, 30 can provide incredibly rich datasets from which to develop and validate microstructure sensitive materials models.…”