Archive of Issues
Russia Izhevsk
Section  Mathematics 
Title  Determination of the texture of polycrystalline materials using an algorithm of objectvector representation of reflection planes and visualization of the results in Rodrigues space 
Author(s)  Mokrova S.M.^{a}, Petrov R.P.^{a}, Milich V.N.^{a} 
Affiliations  Physical Technical Institute, Ural Branch of the Russian Academy of Sciences^{a} 
Abstract  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 nonzero 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. 
Keywords  texture, direct pole figure, crystal orientation, textural components, Rodrigues space, textural transformations 
UDC  5172 
MSC  65Z05 
DOI  10.20537/vm160304 
Received  23 May 2016 
Language  Russian 
Citation  Mokrova S.M., Petrov R.P., Milich V.N. Determination of the texture of polycrystalline materials using an algorithm of objectvector 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. 336344. 
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