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Point process microstructural model of metallic thin films with implications for coarsening

npj Computational Materials 2023年第1期9卷 2074-2082页

作者： J.M.Rickman k.barmak Y.Epshteyn C.Liu Department of Materials Science and Engineering Lehigh UniversityBethlehemPA 18015USA Department of Physics Lehigh UniversityBethlehemPA 18015USA Department of Applied Physics and Applied Mathematics Columbia UniversityNew YorkNY 10027USA Department of Mathematics The University of UtahSalt Lake CityUT 84112USA Department of Applied Mathematics Illinois Institute of TechnologyChicagoIL 60616USA

We develop a thin-film microstructural model that represents structural markers(i.e.,triple junctions in the two-dimensional projections of the structure of films with columnar grains)in terms of a stochastic,marked point process and the microstructure itself in terms of a grain-boundary *** advantage of this representation is that it is conveniently applicable to the characterization of microstructures obtained from crystal orientation mapping,leading to a picture of an ensemble of interacting triple junctions,while providing results that inform grain-growth models with experimental *** specifically,calculated quantities such as pair,partial pair and mark correlation functions,along with the microstructural mutual information(entropy),highlight effective triple junction interactions that dictate microstructural *** validate this approach,we characterize microstructures from Al thin films via crystal orientation mapping and formulate an approach,akin to classical density functional theory,to describe grain growth that embodies triple-junction interactions.

关键词： grain microstructure process

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Fourier-Mellin expansion coefficients of scaled pupils

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Chinese Optics Letters 2013年第8期11卷 1-4页

作者： barmak Honarvar Shakibaei Raveendran Paramesran Department of Electrical Engineering University of Malaya

Orthogonal polynomials over the interior of a unit circle are widely used in aberration theory and in describing ocular wavefront in ophthalmic applications. In optics, Zernike polynomials （ZPs） are commonly applied for the same purpose, and scaling their expansion coefficients to arbitrary aperture sizes is a useful technique to analyze systems with different pupil sizes. By employing the orthogonal Fourier-Mellin polynomials and their properties, a new formula is established based on the same techniques used to develop the scaled pupil sizes. The description by the orthogonal Fourier-Mellin polynomials for the aberration functions is better than that by the ZPs in terms of the wavefront reconstruction errors.

关键词： Fourier-Mellin expansion coefficients of scaled pupils

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