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Physics-Based Image Reconstruction of SiC Grain Boundaries

Amirkoushyar Ziabari, Charles A. Bouman, Jeffrey M. Rickman, Jeff. P. Simmons

2017
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Microscopy and Microanalysis
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The continuing progress in transmission electron microscopy along with image reconstruction algorithms have led to significant advancement in micro to nanoscale material characterization. As a powerful alternative to conventional techniques such as Filtered Back Projection (FPB), or algebraic SIRT and DART algorithms [1, 2] , Model Based Image Reconstruction (MBIR) have demonstrated superior performance for 2D/3D image reconstruction of material [3] . While MBIR and other image reconstruction
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... ge reconstruction techniques provide high quality reconstructed images, they mainly rely on bizarrely simplistic regularization parameter estimation in their prior model. This prevents the reconstruction techniques from extracting rigorous quantitative information such as actual interfacial properties in grain boundaries from the projection data. In fact, interactions in material follow certain known physical laws and equations, and can be modelled using modern physic-based approaches. These equations can be used as an input to the prior model, and the physic-based models can be leveraged to estimate corresponding parameters. Therefore, by introducing physics of the problem to the prior model and integrating modern physics modelling in the analysis of microscope image data, one can extract quantitative meaningful properties along with high quality 2D/3D images from the projected data. The goal of this work is to perform reconstruction of polycrystalline microstructures from their electron microscopy data, using the physical models of internal interfaces (i.e., grain boundaries) as prior model into the MBIR framework. We employ atomistic simulation to calculate the excess interfacial energy per unit area and the width for grain boundaries in a model of silicon carbide (SiC). These parameters serve as input to a phase-field model of a microstructure, and the resulting model constitute a prior in the maximum-a-posteriori (MAP) estimate cost function for image reconstruction. Atomistic simulations of grain-boundaries in SiC using a modified Tersoff potential were performed [4, 5] . For concreteness, we focused on twist boundaries at zero temperature and calculated the associated excess grain-boundary energies per unit area, σ. Figure 1a shows a schematic of the atomic positions above and below the twist boundary. For three (100) twist boundaries of Σ13, Σ5, and Σ9, the corresponding interfacial energy densities were calculated to be 4.76 J/m 2 , 5.63 J/m 2 and 5.79 J/m 2 , respectively. In addition, for these boundaries, we also determined the effective boundary width, w, by calculating the planar structure factor, ( ⃗ ), for a selected Bragg peak, ⃗ . The diminution in peak heights that attends boundary disorder is shown in Figure 1b . From the shape of these curves one can infer w by assuming that an interface is well-described by a hyperbolic tangent profile. We calculated the interface width to be 4Å for interfacial energy density of 5 J/m 2 . We next established a connection between these atomistic results and a phase-field model of a grain boundary [6, 7] . A simulated phantom of grain boundaries with Poisson noise is shown in Figure 1c . The extracted w and σ from atomistic simulations are used to obtain coefficients for the phase field model. 188

doi:10.1017/s1431927617001623
fatcat:j7cxyncyofajnoafepk2egsfxm