![]() ![]() Nonetheless, the spreading of the signal in \(\eta \) and \(\omega \) still remains linked to the evolution of lattice defects in the material, regardless of whether the diffraction signal has distinct (but evolving) peaks associated with individual grains or represents the overlap of many grains having significant gradients in orientation. Under these conditions a peak center-of-mass becomes increasingly difficult to even define and thus decreasingly relevant. As a material plastically deforms and its crystals become misoriented, the morphology of a diffracted intensity signal transitions from individual diffraction peaks to something resembling a uniform powder (as in the data of Fig. In a polycrystalline sample with relatively few lattice defects, an experiment may be designed to follow separable intensity peaks, resolving grain-averaged lattice orientation and strain. ![]() Therefore changes in the heterogeneity of lattice spacing and misorientation can be captured by tracking the width of diffraction peaks in the Bragg angle coordinate \((2\theta \) or r) and orientation coordinates ( \(\eta \) and \(\omega \)), respectively .įull size image Significance of Signal Spread Rotation in \(\omega \) can be used to change the set of crystals satisfying the diffraction condition in order to sample more of orientation space. In the HEXD setting, a beam incident on a crystalline solid diffracts at an angle \(2\theta \) determined by the lattice spacing and at an orientation \(\eta \) determined by the crystal orientation as shown in Fig. Diffraction peaks produced by individual grains of a polycrystal can provide valuable information about the intermittent motion of dislocations that occurs when a metal plastically deforms . High-energy X-ray diffraction (HEXD) is an invaluable tool for studying the phenomena that underpin the macroscopic behaviors and properties of structural materials. Our work draws on ideas from convolutional sparse coding and requires solving a coupled convex optimization problem based on the alternating direction method of multipliers. Our method for characterizing the temporal evolution of signal spread is shown to provide an informative means of data analysis that adds to the capabilities of existing methods. We demonstrate our approach in simulations and on experimental HEXD measurements captured using the MM-PAD. We build on our previous work modeling data using an overcomplete dictionary by treating temporal measurements jointly to improve signal spread recovery. ![]() A distinguishing characteristic of the analysis is the capability to describe the evolution from the distinct diffraction peaks of an undeformed alloy sample through to the non-uniform Debye–Scherrer rings developed upon significant plastic deformation. In this paper, we define and demonstrate a feature computed directly from such diffraction time series data quantifying signal spread in a manner that is correlated with plastic deformation of the sample. High temporal resolution of such dynamics can now be experimentally observed using technologies such as the mixed-mode pixel array detector (MM-PAD) which facilitates in situ dynamic HEXD experiments to study plasticity and its underlying mechanisms. The location of intensity on an areal detector is determined by the lattice spacing and orientation of crystals so that changes in the heterogeneity of these quantities are reflected in the spreading of diffraction peaks over time. Measured intensity in high-energy monochromatic X-ray diffraction (HEXD) experiments provides information regarding the microstructure of the crystalline material under study. ![]()
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