MTEX is a MATLAB toolbox that allows to solve a wide range of problems in quantitative texture analysis. This includes:

• Crystal Geometry
• ODF Modelling
• Texture Calculations
• Pole Figure Diffraction Data
• Pole Figure to ODF Inversion
• EBSD Data
• Grain Detection
• Orientation Density Estimation from EBSD Data
• Material Tensors
• Elasticity Tensors
• Publication Ready Plots
• Writing Scripts to Process Many Data Sets
• Exhaustive Documentation

Crystal Geometry

MTEX knows all the concepts of symmetry groups, crystal reference systems, Euler angles, crystallographic equivalent orientations, Miller indices, etc. It allows you to calculate with crystallographic directions and orientations is a natural and consistent manner.

As an example we define the crystal coordinate system for Quartz and plot it

cs = symmetry('-3m',[1.4,1.4,1.5],'mineral','Quartz');
plot(cs)

ODF Modelling

MTEX offers a very simple way to define model ODFs. An ODF may be composed of an arbitrary number of the following components

• unimodal components
• fibre components
• uniform components
• Bingham distributed components
• components given by there Fourier coefficients
• components that come from pole figure inversion
• components that come from individual orientation measurements

For instance, the well known Santa Fe model ODF can be defined by

% define crystal and specimen symmetry
CS = symmetry('cubic');
SS = symmetry('222');

% define the shape and the modal orientation of the components
psi = kernel('von Mises Fisher','HALFWIDTH',10*degree);
g0 = orientation('Miller',[1,2,2],[2,2,1],CS,SS);

% set up the ODF
odf =  0.73 * uniformODF(CS,SS) + 0.27 * unimodalODF(g0,CS,SS,psi);

plot(odf)

Texture Calculations

MTEX offers to compute a wide range of texture characteristics from ODFs. This includes, e.g.,

• modal orientation
• volume portions (also along fibres)
• differences between ODFs
• differences between pole figures
• entropy
• texture index
• Fourier coefficients

Pole Figure Diffraction Data

MTEX allows you to import diffraction data from a wide range of pole figure formats. These data may be corrected and analyzed in a consistent manner.

Pole Figure to ODF Inversion

MTEX offers a very flexible and powerful method to compute an ODF from any pole figure measurements. The method used is based on a discretization of the ODF space by radially symmetric function and on the fast spherical Fourier transform. The algorithms has proven to be very stable and adaptive in particular to very sharp textures with low symmetry. It has the following features

automatic zero range detection automatic ghost correction works for any measurement grid works for incomplete and not normalized pole figures works for all crystal and specimen symmetries

The calculation if done by the command

odf = calcODF(pf)

EBSD Data

MTEX allows to import EBSD data from all common data formats. The imported data may then be corrected according to MAD values, grain size or specimen alignment.

Grain Detection

MTEX offers a fully automatic way of grain detection in EBSD data. The approach is based on the Voronoi decomposition and automatically fills missing measurements in a consistent, i.e. phase and rotational invariant way.

Orientation Density Estimation from EBSD Data

ODF estimation from EBSD data is done by kernel density estimation, i.e. a bell shaped model ODF is placed at every measured individual orientation. Since the halfwidth of the bell shaped model ODF is crucial for the resulting ODF it is very important to choose it carefully. Alternatively, MTEX offers for the first time a statistical founded approach for the automatically estimation of the optimal halfwidth.

Material Tensors

MTEX allows for complex tensor calculations as well as for the calculation of averaged tensors from ODF or EBSD data. Averaging for ODFs may be computed by quadrature rules or in Fourier space.

Elasticity Tensors

MTEX knows everything about elasticity tensors, e.g. it knows the relationships between

• the elastic stiffness tensor
• the elastic compliance tensor
• the Young's modulus,
• the shear modulus,
• the Poisson's ratio,
• the linear compressibility,
• the compressional and shear elastic wave velocities,
• the wavefront velocities,
• the mean sound velocities

All these properties may be computed for single crystals as well as averaged for aggregates.

Publication Ready Plots

Founded on the state of the art MATLAB plotting routines MTEX allows you to create professional plots of pole figures, inverse pole figures, ODF sections and many more. There are many plotting options that allow to addapt the plots to the specific standards of your journal. Plots may be saved in various image formats, e.g. as pdf, jpg, png, eps, tiff, bmp.

The next plot shows recalculated pole figures overlaid with two different EBSD data sets.

Writing Scripts to Process Many Data Sets

Using the MTEX toolbox it is easy to write scripts that import pole figure data, automatically corrects them, recalculate an ODF, postprocess it, store it to a given location and finally create several plots. Such scripts can be used to batch process many pole figure data sets. Examples of those scripts are included in the help.

Exhaustive Documentation

MTEX comes with over 500 html-help pages explaining the mathematical concepts, the philisophy behing MTEX and the syntax and usage of all 300 functions available in MTEX. Furthermore, you find numerous examples and tutorials on ODF estimation, data import, calculation of texture characteristics, ODF and pole figure plotting, etc.