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Section
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Mathematics
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Title
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Determination of the texture of polycrystalline materials using an algorithm of object-vector representation of reflection planes and visualization of the results in Rodrigues space
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Author(-s)
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Mokrova S.M.a,
Petrov R.P.a,
Milich V.N.a
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Affiliations
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Physical Technical Institute, Ural Branch of the Russian Academy of Sciencesa
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Abstract
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The article deals with the method of search and analysis of textural components using direct polar figures with due account for the symmetry of a cubic crystal and a sample. The algorithm is based on the representation of reflection planes by a polar complex of vectors. Search of orientation is made by moving the axis of a polar complex over the unit hemisphere followed by the rotation of a polar complex relative to this axis. Then the position of stereographic projections of the polar complex vectors on a discrete direct pole figure is determined. Orientation is found when the projections of at least three polar complex vectors are located in the area with non-zero intensity. For each orientation a Rodrigues vector is calculated. In addition, Euler angles and Miller indices are determined. Textural components are allocated interactively by clustering the data in Rodrigues space. Using the covariance matrix the eigenvalues and eigenvectors are determined characterizing the spatial dispersion of textural components. Pole figures of an aluminum foil after various textural transformations are investigated in the article. Obtained textural components are displayed in Rodrigues space.
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Keywords
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texture, direct pole figure, crystal orientation, textural components, Rodrigues space, textural transformations
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UDC
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51-72
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MSC
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65Z05
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DOI
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10.20537/vm160304
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Received
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23 May 2016
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Language
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Russian
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Citation
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Mokrova S.M., Petrov R.P., Milich V.N. Determination of the texture of polycrystalline materials using an algorithm of object-vector representation of reflection planes and visualization of the results in Rodrigues space, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2016, vol. 26, issue 3, pp. 336-344.
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References
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- Titorov D.B., Volkov V.A., Lebedev V.P., Mineev F.V., Titorova D.V. Texture transformations upon annealing of aluminum foils: I. Strong texture components, The Physics of Metals and Metallography, 2006, vol. 102, issue 1, pp. 83-89. DOI: 10.1134/S0031918X06070118
- Umanskii Ya.S., Skakov Yu.A., Ivanov A.N., Rastorguev L.N. Kristallografiya, rentgenografiya i elektronnaya mikroskopiya (Crystallography, X-ray and electron microscopy), Moscow: Metallurgiya, 1982, 632 p.
- Neumann P., Heinz A. Representation of orientation and disorientation data for cubic, hexagonal, tetragonal and orthorhombic crystals, Acta Crystallographica Section A, 1991, vol. 47, part 6, pp. 780-789. DOI: 10.1107/S0108767391006864
- Frank F.C. Orientation mapping, Metallurgical Transactions A, 1988, vol. 19, issue 3, pp. 403-408. DOI: 10.1007/BF02649253
- Korn G., Korn T. Spravochnik po matematike dlya nauchnykh rabotnikov i inzhenerov (Mathematical handbook for scientists and engineers), Moscow: Nauka, 1978, 832 p.
- Mokrova S.M., Petrov R.P., Milich V.N., Titorov D.B. Analysis of the texture components of metal using the direct pole figures on the basis of the object-vector representation of the reflection planes, Zavodskaya Laboratoriya. Diagnostika Materialov, 2014, vol. 80, no. 5, pp. 30-34 (in Russian).
- Tou J.T., Gonzalez R.C. Pattern recognition principles, MA: Addison-Wesley, 1974, 377 p. Translated under the title Printsipy raspoznavaniya obrazov, Moscow: Mir, 1978, 412 p.
- Lur’e A.I. Analiticheskaya mekhanika (Analytical mechanics), Moscow: Gos. Izd. Fiz.-Mat. Lit., 1961, 824 p.
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