# MTEX

# MTEX

MTEX is a free Matlab toolbox for analyzing and modeling crystallographic textures by means of EBSD or pole figure data ^{[1]}.

Getting Started

### Installation Guide

How to install MTEX on you computer.

#### Download

- The MTEX toolbox is available for Windows, Linux, and MAC-OSX at [3]

- Since MTEX is a MATLAB toolbox MATLAB
^{[2]}has to be installed in order to use MTEX. It works fine with the student version and does not require any additional toolboxes, addons or packages. Check the table below to see whether MTEX will run on your Matlab version.

#### Installation

In order to install, MTEX proceeds as follows

1. extract MTEX to an arbitrary folder

2. start MATLAB

3. type into the Matlab command window

- addpath your_MTEX_path
- startup_mtex
- addpath your_MTEX_path
- startup_mtex

Configuration and Troubleshooting [4]

Compiling MTEX Compiling MTEX is only necessary if the provided binaries do not run on your system or if you want to optimize them for your specific system. Compiling instructions can be found [5].

### Users Guide

#### Crystal Geometry

Introduces key concepts about the MTEX representation of specimen directions, crystal directions, crystal symmetries, rotations and orientations.

##### Specimen Directions

How to represent directions with respect to the sample or specimen reference system [6].

##### Rotations

Rotations are the basic concept to understand crystal orientations and crystal symmetries. Rotations are represented in MTEX by the class rotation [7] which is inherited from the class quaternion [8] and allow to work with rotations as with matrixes in MTEX.

##### Crystal Symmetries

This section covers the unit cell of a crystal, its space, point and Laue groups as well as alignments of the crystal coordinate system [9].

##### Crystal Directions

Crystal directions are directions relative to a crystal reference frame and are usually defined in terms of Miller indices. This sections explains how to calculate with crystal directions in MTEX [10].

##### Crystal Orientations

Explains how to define crystal orientations, how to switch between different convention and how to compute crystallographic equivalent orientations [11].

##### Misorientations

Misorientation describes the relative orientation of two grains with respect to each other. Important concepts are twinnings and CSL (coincidence site lattice) [12].

##### Fibres

This sections describes the class fibre and gives an overview how to work with fibres in MTEX [13].

##### Antipodal Symmetry

MTEX allows to identify antipodal directions to model axes and to identify misorientations with opposite rotational angle. The later is required when working with misorientations between grains of the same phase and the order of the grains is arbitrary [14].

##### Fundamental Regions

Thanks to crystal symmetry the orientation space can be reduced to the so called fundamental or asymmetric region. Those regions play an important role for the computation of axis and angle distributions of misorientations [15].

#### Pole Figures

Explains how to import pole figure data, how to correct them, and how to recover an ODF.

##### First Steps

Get in touch with PoleFigure Data in MTEX [16].

##### Importing Pole Figure Data

How to import Pole Figure Data [17].

##### Modify Pole Figure Data

Explains how to manipulate pole figure data in MTEX [18].

##### ODF Estimation from Pole Figure Data

This page describes how to use MTEX to estimate an ODF from pole figure data [19].

##### Ambiguity of the Pole Figure to ODF Reconstruction Problem

demonstrates different sources of ambiguity when reconstructing an ODF from pole figure diffraction data [20].

##### Ghost Effect Analysis

Explains the ghost effect to ODF reconstruction and the MTEX option ghostcorrection [21].

##### Simulating Pole Figure data

Simulate arbitrary pole figure data [22].

##### Plotting of Pole Figures

Describes various possibilities to visualize pole figure data [23].

#### ODFs

ODF stands for orientation distribution functions. This section explains how to import and export ODFs, how to define model ODFs and how to analyze ODFs, e.g., with respect to modalorientations, textureindex, volumeportions. Pole figure simulation and single orientation simulation is explained as well.

##### The SantaFe example

Simulate a set of pole figures for the SantaFe standard ODF, estimate an ODF and compare it to the inital SantaFe ODF [24].

##### Model ODFs

Describes how to define model ODFs in MTEX, i.e., uniform ODFs, unimodal ODFs, fibre ODFs, Bingham ODFs and ODFs defined by its Fourier coefficients [25].

##### Importing and Exporting ODF Data

Explains how to read and write ODFs to a data file [26].

##### Simulating Pole Figure data

Simulate arbitrary pole figure data [27].

##### Simulating EBSD data

How to simulate an arbitrary number of individual orientations data from any ODF [28].

##### Characterizing ODFs

Explains how to analyze ODFs, i.e. how to compute modal orientations, texture index, volume portions, Fourier coefficients and pole figures [29].

##### Visualizing ODFs

Explains all possibilities to visualize ODfs, i.e. pole figure plots, inverse pole figure plots, ODF sections, fibre sections [30].

##### Detecting sample symmetry

Explains how to detect orthotropic symmetry in an ODF [31].

##### Misorientation Distribution Function

Explains how to compute and analyze misorientation distribution functions [32].

#### Tensors

Explains how to work with material tensors in MTEX, i.e. how to compute mean material tensors according to an ODF or to EBSD data, how to compute rotate and visualize tensors and how to calculate with elasticity tensors.

##### Tensor Arithmetics

how to calculate with tensors in MTEX MTEX offers some basic functionality to calculate with tensors as they occur in material sciense. It allows defining tensors of arbitrary rank, e.g., stress, strain, elasticity or piezoelectric tensors, to visualize them and to perform various transformations [33].

##### Average Material Tensors

how to calculate average material tensors from ODF and EBSD data [34] MTEX offers several ways to compute average material tensors from ODFs or EBSD data [35].

##### The Elasticity Tensor

how to calculate and plot the elasticity properties MTEX offers a very simple way to compute elasticity properties of materials. This includes Young's modulus, linear compressibility, Christoffel tensor, and elastic wave velocities [36].

##### Schmid Factor Analysis

This script describes how to analyze Schmid factors [37].

##### The Piezoelectricity Tensor

how to work with piezoelectricity This m-file mainly demonstrates how to illustrate the directional magnitude of a tensor with mtex [38].

##### Seismic velocities and anisotropy

Calculating and plotting elastic velocities from elastic stiffness Cijkl tensor and density (by David Mainprice) [39].

##### Slip Systems

How to analyze slip transmission at grain boundaries [40].

##### Slip Transmission

How to analyze slip transmission at grain boundaries [41].

##### Slip Transmition

How to analyse slip transmission at grain boundaries [42].

##### Taylor Model

[43].

#### EBSD

Data Import of Electron Backscatter Diffraction Data, Correct Data, Estimate Orientation Density Functions out of EBSD Data, Model Grains and Misorientation Density Functions.

##### Short EBSD Analysis Tutorial

How to detect grains in EBSD data and estimate an ODF [44].

##### Importing EBSD Data

How to import EBSD Data [45].

##### Modify EBSD Data

How to correct EBSD data for measurement errors [46].

##### Smoothing of EBSD Data

Discusses how to smooth and to fill missing values in EBSD data [47].

##### Analyze EBSD Data

Here we discuss tools for the analysis of EBSD data which are independent of its spatial coordinates. For spatial analysis, we refer to this page [48].

##### Plotting Individual Orientations

Basics of the plot types for individual orientations data This section gives an overview over the possibilities that MTEX offers to visualize orientation data [49].

##### ODF Estimation from EBSD data

How to estimate an ODF from single orientation measurements [50].

##### Bingham distribution and EBSD data

testing rotational symmetry of individual orientations [51].

##### Plotting spatially indexed EBSD data

How to visualize EBSD data This section gives you an overview of the functionality MTEX offers to visualize spatial orientation data [52].

##### Visualizing EBSD data with sharp textures

How visualize texture gradients within grains [53].

##### Simulating EBSD data

How to simulate an arbitrary number of individual orientations data from any ODF [54].

#### Grains

Explains how to reconstruct grains form EBSD data, visualize Grains and EBSD, analyzing misorientations.

##### First Steps and Function Overview

Get in touch with grains [55].

##### Grain Reconstruction

Grain Reconstruction from EBSD data [56].

##### Working with Grains

How to index grains and access shape properties [57].

##### Plotting grains

Overview about colorizing grains and (special) grain boundaries [58].

##### Analyzing Individual Grains

Explanation how to extract and work with single grains from EBSD data [59].

##### Misorientation Analysis

How to analyze misorientations [60].

#### Grain Boundaries

MTEX provides several functionalities to analyze grain boundaries with respect to twinning, CSL boundaries, etc.

##### Grain Boundaries

Overview about colorizing grain boundaries [61].

##### Misorientations at grain boundaries

Analyse misorientations along grain boundaries [62].

##### Twinning Analysis

Explains how to detect and quantify twin boundaries [63].

##### CSL Boundaries

Explains how to analyze CSL grain boundaries [64].

##### Triple points

how to detect triple points [65].

#### Plotting

Explains different plot types and how to customize them, inlcuding annotations, spherical projections, color coding.

##### Plotting Overview

Overview over the plotting facilities of MTEX, including annotations, plot types, color coding, combined plots and export of plots [66].

##### Annotations

Explains how to add annotations to plots. This includes colorbars, legends, specimen directions and crystal directions [67].

##### Combined Plots

Explains how to combine several plots, e.g. plotting on the top of an inverse pole figure some important crystal directions [68].

##### Plot Types

Explains the different plot types, i.e., scatter plots, contour plots, and line plots [69].

##### Spherical Projections

Explains the spherical projections MTEX offers for plotting crystal and specimen directions, pole figures and ODF [70].

##### Pole Figure Color Coding

Explains how to control color coding across multiple plots. A central issue when interpreting plots is to have a consistent color coding among all plots. In MTEX this can be achieved in two ways. If the minimum and maximum values are known then one can specify the color range directly using the options colorrange or contourf, or the command setcolorrange is used which allows setting the color range afterward [71].

##### EBSD Color Coding

Explains EBSD color coding [72].

## Video tutorial

Using MATLAB for Advanced Materials Design: Describing the Grain Orientation in Metals [[73]].

View slides [[74]].