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<p>Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the <em>thickness function</em> of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the <em>shape amplitude</em>, the Fourier transform of the <em>shape function</em> defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L₃ edge of the three Fe atoms in its basis.</p>

Two new methods for calculating the double differential scattering cross-section (DDSCS) in electron energy loss spectroscopy (EELS) have been developed, allowing for simulations of sample geometries which have been unavailable to earlier methods of calculation. The new methods concerns the calculations of the thickness function of the DDSCS. Earlier programs have used an analytic approximation of a sum over the lattice vectors of the sample that is valid for samples with parallel entrance and exit surfaces.The first of the new methods carries out the sum explicitly, first identifying the unit cells illuminated by the electron beam, which are the ones needed to be summed over. The second uses an approach with Fourier transforms, yielding a final expression containing the shape amplitude, the Fourier transform of the shape function defining the shape of the electron beam inside the sample. Approximating the shape with a polyhedron, one can quickly calculate the shape amplitude as sums over it’s faces and edges. The first method gives fast calculations for small samples or beams, when the number of illuminated unit cells is small. The second is more efficient in the case of large beams or samples, as the number of faces and edges of the polyhedron used in the calculation of the shape amplitude does not need to be increased much for large beams. A simulation of the DDSCS for magnetite has been performed, yielding diffraction patterns for the L3 edge of the three Fe atoms in its basis.

No description available.

No description available.

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.