Éditeur(s) : HAL CCSD Geological Society of London
Résumé : International audience
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.
Geological Society Special Publication

hal-01277689
https://hal.archives-ouvertes.fr/hal-01277689
DOI : 10.1144/SP409.8

Éditeur(s) : HAL CCSD
Résumé : International audience
This paper presents the background for the calculation of anisotropic piezoelectric properties of single crystals and the graphical display of the results in two or three dimensions, and the calculation of the aggregate properties from constituent crystals and the texture of the aggregate in a coherent manner. The texture data can be obtained from a wide range of sources, including pole figure diffraction and single orientation measurements (electron backscattered diffraction, electron channelling pattern, Laue Pattern, optical microscope universal-stage). We consider the elastic wave propagation in piezoelectric crystals as an example of the interaction of electrical (2nd rank tensor), piezoelectric (3rd rank tensor) and elastic properties (4th rank tensor). In particular, we give explicit formulae for the calculation of the Voigt averaged tensor from individual orientations or from an orientation distribution function. For the latter we consider numerical integration and an approach based on the expansion into spherical harmonics. We illustrate the methods using single crystals, polycrystalline quartz measured using electron channelling patterns and ideal Curie limiting groups applied to quartz aggregates. This paper also serves as a reference paper for the mathematical tensor capabilities of the texture analysis software MTEX
Geological Society Special Publication, 409

hal-01277789
https://hal.archives-ouvertes.fr/hal-01277789
DOI : 10.1144/SP409.2

Éditeur(s) : HAL CCSD Springer
Résumé : International audience
This contribution is an attempt to present a self-contained and comprehensive survey of the mathematics and physics of material behavior of rocks in terms of texture and anisotropy. Being generally multi-phase and poly-crystalline, where each single crystallite is anisotropic with respect to its physical properties, texture, i.e., the statistical and spatial distribution of crystallographic orientations becomes a constitutive characteristic and determines the material behavior except for grain boundary effects, i.e., in first order approximation. This chapter is in particular an account of modern mathematical texture analysis, explicitly clarifying terms, providing definitions and justifying their application, and emphasizing its major insights. Thus, mathematical texture analysis is brought back to the realm of spherical Radon and Fourier transforms, spherical approximation, spherical probability, i.e., to themathematics of spherical tomography
Handbook of Geomathematics

hal-00564939
https://hal.archives-ouvertes.fr/hal-00564939

Éditeur(s) : HAL CCSD Geological Society of London
Résumé : This paper presents the background for the calculation of physical properties of an aggregate from constituent crystal properties and the texture of the aggregate in a coherent manner. Emphasis is placed on the important tensor properties of 2nd and 4th rank with applications in rock deformation, structural geology, geodynamics and geophysics. We cover texture information that comes from pole figure diffraction and single orientation measurements (electron backscattered diffraction or EBSD, electron channelling pattern, Laue pattern, optical microscope universal-stage). In particular, we provide explicit formulae for the calculation of the averaged tensor from individual orientations or from an orientation distribution function (ODF). For the latter we consider numerical integration and an approach based on the expansion into spherical harmonics. This paper also serves as a reference paper for the mathematical tensor capabilities of the texture analysis software MTEX, which is a comprehensive, freely available MatLab toolbox that covers a wide range of problems in quantitative texture analysis, for example, ODF modelling, pole figure to ODF inversion, EBSD data analysis and grain detection. MTEX offers a programming interface which allows the processing of involved research problems as well as highly customizable visualization capabilities; MTEX is therefore ideal for presentations, publications and teaching demonstrations.
Deformation Mechanisms, Rheology and Tectonics: Microstructures, Mechanics and Anisotropy

hal-00688833
https://hal.archives-ouvertes.fr/hal-00688833