Modeling and Numerical Simulations of Microdiffraction from Deformed Crystals
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Modeling and Numerical Simulations of Microdiffraction from Deformed Crystals
R.I. Barabash, G.E. Ice, F.J. Walker Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge TN 37831-6118 ABSTRACT Brilliant synchrotron microprobes offer new opportunities for the analysis of stress/strain and deformation distributions in crystalline materials. Polychromatic x-ray microdiffraction is emerging as a particularly important tool because it allows for local crystal-structure measurements in highly deformed or polycrystalline materials where sample rotations complicate alternative methods; a complete Laue pattern is generated in each volume element intercepted by the probe beam. Although a straightforward approach to the measurement of stress/strain fields through white-beam Laue microdiffraction has been demonstrated, a comparable method for determining the plastic-deformation tensor has not been established. Here we report on modeling efforts that can guide automated fitting of plastic-deformation-tensor distributions in three dimensions. INTRODUCTION White x-ray microdiffraction makes it possible to distinguish the intensity distributions related to different grains (or subgrains) within a size ∼ 1-100 µm. This scale corresponds to the so-called “mesoscopic” level of dislocation structure which can not be probed by classic x-ray methods. For example, typical rocking curves provide averaging over much larger regions while TEM gives very local information. The observed local lattice rotations at high deformation result from the dislocation structure within the above “mesoscopic ” level. For the first time these local material properties can be quantitatively characterized using broad-bandpass x-ray microbeams. A general kinematic treatment of x-ray scattering by crystals with dislocations was developed by Darwin [1], Krivoglaz et al. [2], Warren [3], and Wilkens [4]. This approach is widely used for the analysis of dislocation substructure and local rotations in single crystals measured by means of rocking curves [5-11]. The main disadvantage of the rocking curve technique is the need to rotate the sample; rotations introduce uncertainties in the real space coordinates of the scattering volume [12]. Laue white beam measurements however are performed at a fixed orientation of the sample. Special instrumentation [13] makes it possible to correlate different points of the Laue intensity with diffraction from regions within the crystal. Here, we apply the general kinematic treatment of x-ray scattering from dislocations to determine the dislocation structure of crystals from white beam microdiffraction Laue measurements. Although whitebeam Laue diffraction is a classic method widely used to determine crystal symmetry and orientation, unit cell volumes cannot be determined with standard Laue measurements, and the typical precision is not high enough for measurement of strain or dislocation structure. The development of ultra-brilliant third-generation synchrotron x-ray sources [14,15] and recent progress in x-ray o
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