none 10.1144/SP409.8 Geological Society of London Geological Society of London 1881 70173529 65091 2024072310094800715 10.1144 2025-05-03T21:47:23Z 2014-08-02T00:34:10Z 273 Geological Society, London, Special Publications SP 0305-8719 2041-4927 10 02 2015 01 2015 409 1 David Mainprice Geosciences Montpellier UMR CNRS 5243, Université Montpellier 2, 34095 Montpellier Cedex 05, France Florian Bachmann Mathematische Geologie und Geoinformatik, Institut für Geophysik und Geoinformatik, Technische Universität Freiberg, 09596 Freiberg, Germany Ralf Hielscher Fakultät für Mathematik, Technische Universität Chemnitz, 09126 Chemnitz, Germany Helmut Schaeben Mathematische Geologie und Geoinformatik, Institut für Geophysik und Geoinformatik, Technische Universität Freiberg, 09596 Freiberg, Germany Abstract This paper presents the background for the calculation of various numbers that can be used to characterize crystal-preferred orientation (CPO), also known as texture in materials science, for large datasets using the combined scripting possibilities of MTEX and MatLab®. The paper is focused on three aspects in particular: the strength of CPO represented by orientation and misorientation distribution functions (ODFs, MDFs) or pole figures (PFs); symmetry of PFs and components of ODFs; and elastic tensors. The traditional measurements of texture strength of ODFs, MDFs and PFs are integral measurements of the distribution squared. The M-index is a partial measure of the MDF as the difference between uniform and measured misorientation angles. In addition there other parameters based on eigen analysis, but there are restrictions on their use. Eigen analysis does provide some shape factors for the distributions. The maxima of an ODF provides information on the modes. MTEX provides an estimate of the lower bound uniform fraction of an ODF. Finally, we illustrate the decomposition of arbitrary elastic tensor into symmetry components as an example of components in anisotropic physical properties. Ten examples scripts and their output are provided in the appendix. 08 2014 01 2015 251 271 10.1144/SP409.8 https://doi.org/10.15223/policy-002 10.1144/SP409.8 https://www.lyellcollection.org/doi/10.1144/SP409.8 https://www.lyellcollection.org/doi/pdf/10.1144/SP409.8 https://pubs.geoscienceworld.org/UrlRedirectHandler.ashx?routename=books&chapterdoi=10.1144/SP409.8&request=chapter 10.1016/S0191-8141(97)00001-1 10.1190/1.1888997 10.1107/S002188981003027X 10.1016/j.ultramic.2011.08.002 10.1029/RG008i003p00633 10.1016/S0191-8141(01)00137-7 10.1016/S0040-1951(98)00141-3 Bingham C.An antipodally symmetric distribution on the sphere. Annals of Statistics1974212011225 10.1111/j.1365-246X.2004.02415.x Mathematische Methoden der Texturanalyse Bunge H. J. 1969 Bunge H. J.Mathematische Methoden der Texturanalyse1969BerlinAkademie-Verlag Texture Analysis in Materials Science: Mathematical Models Bunge H. J. 1982 Bunge H. J.Texture Analysis in Materials Science: Mathematical Models1982LondonButterworths 10.1107/S0108767385000101 10.1155/TSM.29.127 10.1126/science.290.5496.1564 10.1051/jphystap:018940030039300 10.1086/628192 Introduction to Texture Analysis: Macrotexture, Microtexture, and Orientation Mapping Engler O. 2010 Engler O., Randle V.Introduction to Texture Analysis: Macrotexture, Microtexture, and Orientation Mapping2010Boca Raton, USACRC Press, Taylor and Francis Group 10.1098/rspa.1953.0064 10.1016/0036-9748(79)90058-9 10.1111/j.1365-246X.1988.tb02269.x 10.1107/S0021889808030112 10.1107/S0021889806055476 10.1016/j.epsl.2012.10.003 Philosophical Transactions of the Royal Society Kelvin L. 481 1666 1856 Elements of a mathematical theory of elasticity, Part I, On stresses and strains Kelvin L.Elements of a mathematical theory of elasticity, Part I, On stresses and strainsPhilosophical Transactions of the Royal Society18561666481498(William Thomson) 10.1023/B:MATG.0000048799.56445.59 10.1016/0956-7151(93)90130-K 10.1016/0191-8141(85)90119-1 10.1016/0031-9201(93)90160-B 10.1144/SP360.10 Statistics of Directional Data Mardia K. V. 1972 Mardia K. V.Statistics of Directional Data1972New YorkAcademic Press Directional Statistics Mardia K. V. 2000 Mardia K. V., Jupp P. E.Directional Statistics2000Chichester, UKJohn Wiley and Sons Standard Distributions in Texture Analysis Volume 1 Matthies S. 1987 10.1515/9783112736173 Matthies S., Vinel G. W., Helming K.Standard Distributions in Texture Analysis Volume 11987BerlinAkademie-Verlag 10.1016/S0040-1951(01)00157-3 10.1002/mma.560 10.1007/s10659-006-9082-0 10.1007/978-3-662-09156-2 Forma Nakamura N. 87 15 2000 Curie symmetry principle: does it constrain the analysis of structural geology? Nakamura N., Nagahama H.Curie symmetry principle: does it constrain the analysis of structural geology?Forma2000158794 10.2475/ajs.273.10.853 10.1130/0016-7606(1961)72[841:SCITSA]2.0.CO;2 10.1007/978-3-7091-9809-4 10.1063/1.341694 10.1107/S0021889896002804 10.1016/j.tecto.2005.08.023 10.1139/e66-035 10.1029/1999JB900411 10.1016/j.jsg.2004.11.003 10.1130/0016-7606(1990)102<0786:AAOEMT>2.3.CO;2 Statistics on Spheres Watson G. S. 1983 Watson G. S.Statistics on Spheres1983New YorkJ. Wiley and Sons 10.1086/627211 10.1016/B978-0-12-744020-0.50008-0 10.1130/0016-7606(1977)88<1231:SOFSUA>2.0.CO;2