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Shape functions in calculations of differential scattering cross-sections

<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 L<sub>3</sub> edge of the three Fe atoms in its basis.</p>

Identiferoai:union.ndltd.org:UPSALLA/oai:DiVA.org:uu-126674
Date January 2010
CreatorsJohansson, Anders
PublisherUppsala University, Department of Physics and Astronomy
Source SetsDiVA Archive at Upsalla University
LanguageEnglish
Detected LanguageEnglish
TypeStudent thesis, text
RelationFYSAST

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