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The four pillars of material science and engineering namely structure, processing, properties and performance form the so-called material paradigm. At the heart of the material paradigm is materials characterization, which is used to measure and identify the relationships. Materials Characterization typically reconstructing the conditions giving rise to a measurement, a classic inverse problem. The solutions of these inverse problems are under or over determined and not unique. The solutions of these inverse problems can be greatly improved if accurate forward models exist for these characterization experiments. In this thesis, we will be focusing of developing forward models for electron diffraction modalities. Specifically, four different forward models for electron diffraction, namely the Electron Backscatter Diffraction, Electron Channeling Patterns, Precession Electron Diffraction and Transmission kikuchi Diffraction modalities are presented. Further, these forward models are applied to important materials characterization problems, including diffraction pattern indexing using the dictionary approach and forward model based orientation refinement. Finally, a novel pole figure inversion algorithm using the cubochoric representation and model based iterative reconstruction is also presented.

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