Fabric analysis by orientation distribution functions

doi:10.1016/0040-1951(81)90003-2

Tectonophysics

Volume 78, Issues 1–4, 1 October 1981, Pages 1-21

https://doi.org/10.1016/0040-1951(81)90003-2 Get rights and content

Abstract

Crystalline materials (natural or artificial) may consist of several phases (minerals) the crystal structures and relative amounts of which will generally be known. In order to fully characterize such a material, also the form and spatial distribution of the phases, the grain structure, and lattice defects and their distribution must be specified by appropriate distribution functions. Among these, the Orientation Distribution Function (texture, fabric structure) plays an important role. It can be deduced from experimental pole figures by series expansion methods. In textured materials two different symmetries can be distinguished, the crystal symmetry and the statistical sample symmetry. Special consideration must be given to the inversion centre as an element of either of these symmetries and in Friedels' law. A complete description of all possible sample symmetries can be given in terms of black—white symmetry groups. The determination of the odd part of the texture function is strongly related to these groups and the various kinds of the inversion centre. Each combination of a certain crystal symmetry group with a certain sample symmetry group induces a certain space group in the orientation space, the proper consideration of which minimizes the required amount of numerical calculations. The texture function (ODF) is the most important factor in the relation between anisotropic properties of single crystals and the polycrystalline material. Changes of the ODF can be used as a sensitive indicator for solid state processes having occurred in the material.

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Characterization of crystal orientation and grain boundaries is of great interest in the understanding of the mechanisms taking place during the degradation process originated by the exposure of materials to erosive media. In the present study, an austenitic stainless steel previously analyzed by electron backscatter diffraction was exposed to ultrasonic cavitation erosion. Several parameters such as crystal orientation, misorientation, coincidence site lattice, Schmid factor and twin orientation were examined in order to determine their influence on the local susceptibility to early damage induced by cavitation. Crystallographic orientation was found to play a significant role in the deformation mechanisms occurring inside grains. Furthermore, high misorientation between adjacent grains was recognized as a determining factor leading to early damage observed at random grain boundaries, while the difference in Schmid factor was identified to have a significant effect on the cavitation resistance of twin boundaries. Moreover, the effect of the deviation from the ideal orientation predicted for coherent twins was analyzed in connection with cavitation resistance.
Development of crystallographic preferred orientation during cataclasis in low-temperature carbonate fault gouge
2019, Journal of Structural Geology
Citation Excerpt :
To avoid artefact grains in the analysis, grains that were made of < 10 pixels (i.e., with an equivalent diameter of c. ≤ 3.5 μm) were deleted. Orientation data were plotted both as stereonets and contoured using the Orientation Density Function (ODF, after Bunge, 1982; Bachmann et al., 2010). The ODF was calculated using a de la Vallee Poussin kernel, a half width of 10°, and accounting for one point per grain.
Grain size reduction due to cataclasis is a key process controlling fault frictional properties during the seismic cycle. We investigated the role of cleavage planes on fracturing and microstructural evolution during cataclasis in wet and dry carbonate fault gouges (50 wt% calcite, 50 wt% dolomite) deformed in a rotary-shear apparatus over a wide range of slip rates (30 μms⁻¹ to 1 ms⁻¹) and displacements (0.05–0.4 m). During shearing, progressive strain localization forms a narrow slip zone that undergoes significant frictional heating (at high slip rates), but the bulk gouge always accommodates low finite shear strains and deforms at low temperatures. Microstructural analysis of the bulk gouges indicates that deformation occurred by brittle fracturing and twinning. Microfractures in calcite are closely spaced, often exploit ${10 \bar{1} 4}$ cleavage r-rhomb planes, and occur mainly subparallel to the expected principal stress orientation (σ₁). Instead, twin planes typically occur sub-perpendicular to σ₁. Electron backscatter diffraction analysis of the bulk gouges shows that calcite develops a well-defined crystallographic preferred orientation (CPO) at all investigated deformation conditions. The CPO is defined by a clustering of the calcite c-axes around an orientation sub-parallel to σ₁. The calcite CPO is interpreted to result from grain rotation during granular flow, followed by brittle fracturing that occurred preferentially along calcite cleavage planes. This interpretation is supported by measurements of calcite grain shape-preferred orientations that show a population of elongate calcite grains oriented with their long axes sub-parallel to σ₁. Our experimental results indicate that well-defined CPOs can form at low temperature in cataclastic fault rocks, and that mineral cleavage can strongly influence the evolution of grain sizes and shapes during comminution.
Coseismic ultramylonites: An investigation of nanoscale viscous flow and fault weakening during seismic slip
2019, Earth and Planetary Science Letters
Faults weaken during the propagation of earthquakes due to the onset of thermally-activated mechanisms, which vary depending on the rock type. Recent experimental work suggests that carbonate-hosted faults are lubricated by viscous flow in nano-granular aggregates having ultramylonitic textures. However, their frail nature has often hindered unbiased characterisation of the textures and deformation mechanisms operating at such extreme conditions (strain rates as high as 10⁴), which remain so far poorly investigated and understood.
We explore the formation, evolution and deformation mechanisms of coseismic ultramylonites in carbonate-hosted faults generated during high velocity (1.4 m s⁻¹), displacement-controlled shear experiments in a rotary apparatus. Microstructures were analysed using integrated SEM and TEM imaging while detailed crystallographic fabrics were investigated using the electron back-scattered diffraction (EBSD) technique.
Mechanical data show that the strength of the experimental fault decays dynamically with slip, according to a characteristic four stage evolution; each stage is associated with characteristic textures. Microstructural observations show that brittle processes dominate when the fault is strong (friction coefficients >0.6). Cataclasis, aided by twinning and crystal plasticity, operates forming an extremely comminuted shear band (mean grain size ∼200 nm). As the fault starts weakening, shear localises within a well-defined principal slip zone. Here, thermally-activated grain size sensitive (GSS) and insensitive (GSI) creep mechanisms compete with brittle processes in controlling fault strength. GSI mechanisms produce strong monoclinic crystallographic preferred orientations in the slip zone, while textures and crystallographic orientations in adjacent locations do not evolve from the previous deformation stage. By the end of the transient weakening stage, the slip zone has reached a steady state thickness (30 μm) and shows a nanogranular ultramylonitic texture. The intensity of the crystallographic preferred orientation in the coseismic ultramylonite is reduced compared to the previous stage, due to grainsize sensitive creep mechanisms becoming gradually more dominant. As the experimental fault re-strengthens, upon deceleration to arrest, the ultramylonite may be partially reworked by brittle deformation.
Our findings show that the crystallographic orientations of transient microstructures are preserved in the slip zone of coseismic ultramylonites and in narrow, adjacent deactivated layers, where mirror-like surfaces are located. This shows that EBSD techniques can usefully be employed to determine the deformation mechanisms of coseismic ultramylonites and their evolution during earthquake slip in both experimental and, potentially, natural faults.
Heterogeneity of strain path, texture and microstructure evolution of AA6063-T6 processed by Equal Channel Angular Sheet Extrusion (ECASE)
2018, Journal of Alloys and Compounds
Citation Excerpt :
The orientation distribution functions (ODFs) were calculated by series expansion method using truncation at L = 22 (L represents the truncation error because the series expansion method has to be truncated to a limited number of terms to keep the computation time to practical limits. In practical terms, a value of Lmax = 22 is generally taken as a limit for cubic materials) [13,14]. The X-ray diffraction measurements of the processed samples were carried out on a Philips X pert Pro MPD diffractometer with Cu-Kα radiation, X-ray lenses, parallel plate collimator and Xe detector.
An Aluminum alloy 6063T6 was processed at room temperature by Equal Channel Angular Sheet Extrusion (ECASE). Microstructure evolution was investigated by Electron Back Scattering Diffraction (EBSD), and X-ray diffraction analysis. The texture evolution was heterogeneous and represented by a mix of rolling and shearing components through the sheet thickness. Ncorr™ calculations showed higher shear strains close to the edges than in the sheet core, in agreement with the through thickness expected variation. The Geometrically Necessary Dislocation (GND) calculations corroborated the existence of a heterogeneous microstructure through the sheet thickness.
Post-deformational annealing at the subgrain scale: Temperature dependent behaviour revealed by in-situ heating experiments on deformed single crystal halite
2010, Journal of Structural Geology
The dynamics of substructures, which encompass all structures present at the subgrain-scale, were investigated by static, in-situ annealing experiments. Deformed, single crystal halite was annealed inside a scanning electron microscope at temperatures between 280 and 470 °C. Electron backscatter diffraction maps provided detailed information about crystallographic orientation changes. Three temperature dependent regimes were distinguished based on boundary misorientation changes. In regime I (280–300 °C) some low angle boundaries (LABs), i.e. with 1°–15° misorientation, increase in misorientation angle, while others decrease. In regime II (∼300 °C) all LABs undergo a decrease in misorientation angle. Regime III (>300 °C) is defined by enhancement of the subgrain structure as remaining LABs increase and some undergo a rotation axis change. Throughout regimes I and II, new LABs develop, subdividing subgrains. LABs could be divided into four categories based on annealing behaviour, orientation and morphology. We suggest that these observations can be directly related to the mobility and activation temperature of climb of two dislocation groups introduced during deformation. Therefore, with in-depth investigation of a substructure with known deformation geometry, we can infer ratios of dislocation types and their post-deformation and post-annealing location. These can potentially be used to estimate the post-deformational annealing temperature in crystalline materials.
Two orogens - One shear belt: 1 Ga of repeated deformation along the Central Tanzanian Shear Belt
2007, Journal of Structural Geology
Citation Excerpt :
Polished rock chips were placed in the X-ray beam of a Bruker AXS texture goniometer (wavelength CuKα = 1.5418, beam current = 40 kV and 40 mA) used in reflection mode. Eight lattice planes (〈100〉, 〈110〉, 〈102〉, 〈200〉, 〈201〉, 〈112〉, 〈211〉, 〈113〉) have been directly measured, lattice planes 〈001〉, 〈101〉 and 〈011〉 were calculated using the orientation density function (ODF) based on the harmonic method of Roe (1965) and Bunge (1981). Quartz c-axes and 〈a〉-axes from which crystal glide plane and glide direction are commonly inferred are displayed on stereo plots.
The Central Tanzanian Shear Belt (CTSB) constitutes a 300-km long W–E trending dextral shear belt that was active during Paleoproterozoic and Neoproterozoic orogenies. It formed along the southern margin of the Archean Tanzania Craton that acted as rigid indenter during both orogenies. Based on structural and microtextural methods several deformational stages have been identified. Paleoproterozoic shear is recorded in the 1.8–2.0 Ga old magmatic Usagaran Belt. This shear was accompanied by vast melt intrusions in a hot and soft crust leading to low strain and coaxial flow. It ceased in an exhumation phase with localized non-coaxial shear followed by the deposition of nonconform sediments dated around 1.9 Ga. In the Neoproterozoic, the CTSB is found as reactivated shear zones in the Usagaran Orogen and as megascale shear zone in the metamorphic Mozambique Belt. It is a release (or counterflow) structure that evolved in the course of crustal thickening in a strong crust around 0.6 Ga. Along the strike of the Neoproterozoic CTSB syntectonic conditions change from localized brittle shear along the Tanzania Craton to distributed high temperature coaxial shear in the eastern section of the orogen's root. This goes along with a significant change in microstructures and LPO patterns.

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Fabric analysis by orientation distribution functions

Abstract

Scr. Metall.

Tectonophysics

On the symmetry of orientation distribution in crystal aggregates

Adv. X-Ray Anal.

Zur Darstellung allgemeiner Texturen

Z. Metallkd.

Mathematische Methoden der Texturanalyse

Texture analysis by orientation distribution functions

Z Metallkd

Textur und Anisotropie

Z. Metallkd.

Determination of the odd part of the texture function

J. Phys. (Paris), Lett.

Neutron-diffraction studies of the recrystallization textures in cold-rolled low-carbon steel

Met. Sci. J.

The role of inversion centre in texture analysis

J. Appl. Crystallogr.

Charts for analysing crystallite distribution function plots for cubic materials

J. Appl. Crystallogr.

Charts for analysing crystallite orientation distribution function plots for hexagonal materials

J. Appl. Crystallogr.

Die röntgenographische und optische Gefügeanalyse von Erzen, insbesondere mit dem Zählrohr-Texturgoniometer

Beitr. Mineral. Petrogr.

A standard System of FORTRAN programmes for three-dimensional texture analysis

Metallurgia (Cracow)

Texture development in calcite and quartz rocks deformed at uniaxial and real triaxial states of strain

Bull. Minéral.