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Far-Field High-Energy Diffraction Microscopy


Figure 5 : (a) Macroscopic stress-strain curve of the copper alloy investigated in [ 23 ]. (b) View of the virtual polycrystal created using the orientations of the constituent grains obtained from FF-HEDM measurements. Colors denote grains of different orientations. Figures replicated from [ 23 ] with permission of Cambridge University Press.


to the incoming X-rays. When a particular crystallographic plane satisfi es the Bragg diff raction condition, the diff racted X-ray is recorded on an area detector. Currently, three fl avors of high-energy diff raction microscopy techniques exist. Table 1 summarizes the HEDM techniques available to the general users at the APS 1-ID-E beamline. Similar capabilities also exist at the other synchrotron facilities around the world, with various spatial and angular resolution capabilities. As indicated in Table 1 , the FF-HEDM technique is insensitive to the shape of the grain illuminated by X-rays. It is only sensitive to the crystallographic orientation and spatial location of the grain. Additionally, it is sensitive to the elastic strain of the grain. T e ability to measure elastic strain, albeit grain averaged, is useful by itself and when combined with other HEDM techniques and tomography techniques. Our setup at the APS is capable of conducting in situ multimodal experiments to obtain information about the evolution of the microstructure and micromechanical state of polycrystals.


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Figure 1a shows a schematic of the key components for the FF-HEDM technique, and Figure 1b shows a panoramic view of the ex situ setup in the 1-ID-E hutch of the APS. High-energy monochromatic X-rays illuminate a volume of polycrystalline sample, which is placed on top of rotation and translation stages. T e width of the beam is typically larger than the maximum width of the sample, while the height of the beam is adjusted to be as large as possible without allowing diff raction spots from the constituent grains to overlap. T e beam size is defi ned either by slits or refraction-based high-energy X-ray focusing optics that allow a 1 μ m beam size in the Y L direction [ 13 – 14 ]. For most samples, a double-Laue monochromator is used (energy range: 40–130 keV; energy bandwidth ( dE/E ) ≈ 10 −3 ), but for samples requiring increased reciprocal-space resolution (for example, aſt er large plastic deformation where the diff raction spots are smeared signifi cantly or substructures have formed in the grains), a secondary high-resolution monochromator can be used ( dE/E ≈ 10 −4 ) [ 20 – 21 ]. Rotation is performed about the Y L axis (ω rotation). A set of translation and rotation stages are used to align the ω rotation axis to be perpendicular to the incident X-ray beam propagating on the X L -Z L plane. Oſt en, the sample has its own natural coordinate system (for example, a sample extracted from a rolled plate), and rotation and translation stages are used to align the sample with respect to the beam. Both ex situ and in situ experiments are possible; for the latter, thermo-mechanical loading may be used to follow the evolution of microstructure and micromechanical state on a grain-by-grain basis. Diff raction patterns and analysis . Diff raction patterns are typically taken at 0.25  intervals as the sample is rotated between -180 and +180  in ω . When a crystallographic plane from a constituent grain in the illuminated volume satisfi es the diff raction condition, the corresponding diff raction spot is recorded on the area detector. A GE Revolution 41RT detector [ 22 ], with 409.6 mm × 409.6 mm active area and 0.2 mm × 0.2 mm pixel pitch, is typically used for the measurements, with the detector placed ~1 m downstream of the sample. In some cases, four detectors are arranged in a diamond pattern for enhanced resolution and coverage [ 23 ]. At these detector distances, information related to the detailed shapes of the diff racting grains is lost, but their centers of mass (COM), crystallographic orientations, and lattice strain tensors can be obtained. Figure 2a shows an example of an FF-HEDM diff raction pattern, where distinct diff raction spots can be seen. Diff raction patterns like the one shown in Figure 2b are used to determine the COM, orientation, and lattice strain of the constituent grains through a processing called indexing. T e indexing methods are described extensively in various references [ 4 , 24 – 25 ]. In general, the following steps are taken and iterated: (1) Identify and isolate all the diff raction spots from the raw diff raction pattern. Each spot can be parame- terized by X L , Y L , and ω . (2) Search in orientation space for crystallographic orientations that yield the observed diff raction spots. (3) For a particular crystallographic orientation found in the previous step and associated spots, search in physical space (X S -Y S -Z S ) and strain space to obtain the COM and strain tensor associated with the orientation. T ere are several analysis tools available to the general public [ 24 – 26 ]. T e APS staff , in collaboration with the


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