MTEX - free crystallographic texture analysis software

The variant graph is a new, hybrid algorithm that combines the strengths of established global grain graph and local neighbor level voting approaches, while alleviating their shortcomings, to reconstruct parent grains from orientation maps of partially or fully phase-transformed microstructures. The variant graph algorithm is versatile and is capable of reconstructing transformation microstructures from any parent-child combination by clustering together child grains based on a common parent orientation variant. The main advantage of the variant graph over the grain graph is its inherent ability to more accurately detect prior austenite grain boundaries. A critical examination of Markovian clustering and neighbor level voting as methods to reconstruct prior austenite orientations is first conducted. Following this, the performance of the variant graph algorithm is showcased by reconstructing the prior austenite grains and boundaries from an example low-carbon lath martensite steel microstructure. Programmatic extensions to the variant graph algorithm for specific morphological conditions and the merging of variants with small mutual disorientation angles are also proposed. The accuracy of the reconstruction and the computational performance of the variant graph algorithm is either on-par or outperforms alternate methods for parent grain reconstruction. The variant graph algorithm is implemented as a new addition to the functionalities for phase transformation analysis in MTEX 5.8 and is freely available for download by the community.

This manual is aimed at quickly teaching new MTEX users how to correctly do EBSD texture analysis to produce EBSD maps and pole figures. It will also provide a reference for intermediate users, and advice on verifying the accuracy of your EBSD maps. It is intended to be simple, direct, and accessible to users of all backgrounds with many examples and images.

A versatile generic framework for parent grain reconstruction from fully or partially transformed child microstructures was integrated into the open-source crystallographic toolbox MTEX. The framework extends traditional parent grain reconstruction, phase transformation and variant analysis to all parent-child crystal symmetry combinations. The inherent versatility of the universally applicable parent grain reconstruction methods, and the ability to conduct in-depth variant analysis are showcased via example workflows that can be programmatically modified by users to suit their specific applications. This is highlighted by three applications namely, $\alpha$-to-$\gamma$ reconstruction in a lath martensitic steel, $\alpha$-to-$\beta$ reconstruction in a Ti alloy, and a two-step reconstruction from $\alpha$-to-$\varepsilon$-to-$\gamma$ in a twinning and transformation -induced plasticity steel. Advanced orientation relationship discovery and analysis options, including variant analysis, is demonstrated via the add-on function library, ORTools.

The analysis of manifold valued data using embedding based methods is linked to the problem of finding suitable embeddings. In this paper we are interested in embeddings of quotient manifolds SO(3)/S of the rotation group modulo finite symmetry groups. Data on such quotient manifolds naturally occur in crystallography, material science and biochemistry. We provide a generic framework for the construction of such embeddings which generalizes the embeddings constructed in arXiv:1701.01579. The central advantage of our larger class of embeddings is that it comprises isometric embeddings for all crystallographic symmetry groups.

This paper compares several well known sliding-window methods for denoising crystal orientation data with variational methods adapted from mathematical image analysis. The variational methods turn out to be much more powerful in terms of preserving low-angle grain boundaries and filling holes of non-indexed orientations. The effect of denoising on the determination of the kernel average misorientation and the geometrically necessary dislocation density is also discussed. Synthetic as well as experimental data are considered for this comparison. The examples demonstrate that variational denoising techniques are capable of significantly improving the accuracy of properties derived from electron backscatter diffraction maps.

We present spherical analysis of electron backscatter diffraction (EBSD) patterns with two new algorithms: (1) band localisation and band profile analysis using the spherical Radon transform; (2) orientation determination using spherical cross correlation. These new approaches are formally introduced and their accuracies are determined using dynamically simulated patterns. We demonstrate their utility with an experimental dataset obtained from ferritic iron. Our results indicate that the analysis of EBSD patterns on the sphere provides an elegant method of revealing information from these rich sources of crystallographic data.

Note: Version 3.3 replaced due to waitbar bug. MTEX lets you do EBSD data analysis in MATLAB. This app is a GUI to make it easier. This app was designed to provide the most common EBSD map utilities (and a few for pole figures) to help a new user quickly plot maps, annotate them for presentation, and investigate their data. While you do this, you can also generate the corresponding command line instructions for these actions, allowing you to learn, save a copy, and expand on them This app does not have anywhere near the functionality of MTEX- it's much more basic. Some MTEX functions not included in this app are IPF maps, ODF maps, Twin calculations, data smoothing, and rotation operations. For more information about MTEX capabilities, take a look at http://mtex-toolbox.github.io/documentation.html

This is a revision of the algorithm for prior austenite reconstruction written for Matlab R2017X and MTEX 5.1.1. It allows the calculation of prior austenite orientation for individual misorientations and triple points.

Progressive deformation of upper mantle rocks via dislocation creep causes their constituent crystals to take on a non-random orientation distribution (crystal preferred orientation or CPO). The resulting anisotropy of the rock’s elastic properties can be observed by seismic techniques, and provides a means to constrain mantle convective flow patterns. Existing methods for calculating the evolution of CPO in deforming olivine-dominated rocks rely on unwieldy discrete representations of the crystal orientation distribution in terms of a large number (10^3–10^4) of individual grains. Here we propose a more efficient method in which CPO is represented using three continuous analytical functions (structured basis functions or SBFs), each of which represents a virtual CPO produced by the action of just one of the three dominant slip systems of olivine. The SBFs are then combined using an appropriate weighting scheme to represent a realistic CPO that results from the simultaneous activity of all three slip systems. We assume that olivine CPO is a unique function of the finite strain experienced by the aggregate, which implies that the weights of the SBFs depend only on the two ratios of the lengths of the axes of the finite strain ellipsoid (FSE) and the two ratios of the strengths (critical resolved shear stresses) of the slip systems. Our preferred set of weighting coefficients is obtained by least-squares fitting of the SBF expansion to the predictions of a kinematic model (solved by the method of characteristics) in which the amplitudes of the crystallographic spins do not increase with strain. Calculation of CPO using this model is ≈107 times faster than full homogenization approaches such as the second-order self-consistent model, and the result fits the characteristics-based solution with a variance reduction ≥88.6 percent ≥88.6 percent for equivalent strains up to 0.9. Finally, we propose a simple modification of the FSE that prevents the CPO from becoming singular at large strains.

We present spherical analysis of electron backscatter diffraction (EBSD) patterns with two new algorithms: (1) pattern indexing utilising a spherical Radon transform and band localisation; (2) pattern indexing with direct spherical cross correlation on the surface of the sphere, with refinement. These new approaches are formally introduced and their accuracies are determined using dynamically simulated patterns. We demonstrate their utility with an experimental dataset obtained from ferritic iron. Our results indicate that analysis of EBSD patterns on the surface of a sphere provides a valuable method of unlocking information from these rich sources of crystallographic data. Highlights 1. We present a method to approximate Kikuchi patterns on the surface of a sphere. 2. Our approximations enable spherical Radon transformations for pattern indexing. 3. Cross correlation is performed on the sphere for precise orientation determination. 4. All methods are speed optimized using fast Fourier algorithms on the sphere and the orientation space.

MTEX is a free command-line driven crystallographic software developed by Ralf Hielscher to run on Matlab. This GUI was written by Jessica Hiscocks to simplify use of MTEX for casual users, and make free crystallographic analysis more accessible to everyone. If you would like individual help, I offer personal tutoring sessions and can write custom scripts to automate your data analysis. Email me at grandriverjh@gmail.com for further details. This version of the app (2.4) requires MTEX version 5 or later, and was written for Matlab 2016b. In Version 2.4, a script recording button has been added, allowing you to see the MTEX code for yourself, generate a personalised script, adapt it, and learn how to write it. Several bugfixes have also been made, most notably to the histogram export function and annotation of cubic and HCP shapes. To install: download the .zip file and extract it. Take the GUI (extension .mlapp), and put it in your matlab working directory (where your EBSD data is located). Rename it to AnnotateR2p4.mlapp if necessary. You should see it listed the 'current folder' area of matlab at the left. Double click on it to run. When the app opens, click the 'getting started' button for more help. If you get stuck, just send me a message.

This paper compares several well-known methods for denoising orientation data with methods adapted from mathematical image analysis. The latter ones turn out to be much more powerful in terms of preserving low angle grain boundaries and filling holes of non-indexed orientations. We also discuss the effect of denoising to the determination of the kernel average misorientation and the geometrically necessary dislocation density. Synthetic as well as experimental data are considered for this comparison. The examples demonstrate that variational denoising techniques are capable of significantly improving the accuracy of properties derived from EBSD maps.

The crystallography and morphology of the intercritical austenite phase in two high-aluminum steels annealed at 850 °C were examined on the basis of electron backscattered diffraction analysis, in concert with a novel orientation relationship determination and prior austenite reconstruction algorithm. The formed intercritical austenite predominantly shared a Kurdjumov–Sachs-type semicoherent boundary with at least one of the neighboring intercritical ferrite grains. If the austenite had nucleated at high-energy sites (such as a grain corner or edge), no orientation relationship was usually observed. The growth rate of the austenite grains was observed to be slow, causing phase inequilibrium even after extended annealing times. The small austenite grain size and phase fraction were consequently shown to affect martensite start temperature. Both steels had distinct variant pairing tendencies under the intercritically annealed condition.

MTEX is a free command-line driven crystallographic software developed by Ralf Hielscher to run on Matlab. This GUI was written by Jessica Hiscocks to simplify use of MTEX for casual users, and make free crystallographic analysis more accessible to everyone. If you would like individual help, I offer personal tutoring sessions and can write custom scripts to automate your data analysis. Email me at grandriverjh@gmail.com for further details. This version of the app (2.2) requires MTEX version 5 or later, and was written for Matlab 2016b.

Major improvments in MTEX 5.1. are GND computation and Birefringence

computing geometrically necessary dislocations with MTEX, the geometry of misorientations, clustering algorithms

Comparison of EBSD denoising techniques, computation of geometrically necessary dislocations using MTEX

An updated version of the previous GUI, this app for Matlab allows you to plot EBSD Maps, calculate grains, and add annotations. The current version allows for plotting of pole figures, includes test data, and adds new misorientation colouring options to EBSD maps. Requires Mtex and Matlab.

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 MatLabw. 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.

1 This paper presents the theoretical background for the calculation of physical 2 properties of an aggregate from constituent crystal properties and the texture of the 3 aggregate in a coherent manner. Emphasis is placed on the important tensor proper-4 ties of 2 nd and 4 th rank with applications in rock deformation, structural geology, geo-5 dynamics and geophysics. We cover texture information that comes from pole figure 6 diffraction and single orientation measurements (Electron Backscattered Diffraction, 7 Electron Channeling Pattern, Laue Pattern, Optical microscope universal-stage). In 8 particular, we give explicit formulas for the calculation of the averaged tensor from 9 individual orientations or from an ODF. For the latter we consider numerical integra-10 tion and an approach based on the expansion into spherical harmonics. This paper 11 also serves as a reference paper for the tensor mathematic capabilities of the texture 12 analysis software MTEX, which is a comprehensive, freely available MATLAB toolbox 13 that covers a wide range of problems in quantitative texture analysis, e.g. orienta-14 tion distribution function (ODF) modeling, pole figure to ODF inversion, EBSD data 15 analysis, and grain detection. MTEX offers a programming interface, which allows the 16 processing of involved research problems, as well as highly customizable visualiza-17 tion capabilities, which makes it perfect for scientific presentations, publications and 18 teaching demonstrations.

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.