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‎images/MaParentGrainReconstruction_15.png

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‎images/SelectingGrains_16.png

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‎index.md

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### News
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* MTEX Online Workshop 2021: ・ [Announcement](https://github.com/mtex-toolbox/mtex/discussions/519#discussioncomment-139964) ・ [Homepage](http://www-user.tu-chemnitz.de/~rahi/mtexWorkshop21) ・
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* MTEX 5.5.1 released: ・ [Download](https://github.com/mtex-toolbox/mtex/releases/download/mtex-5.5.1/mtex-5.5.1.zip) ・ [Release Notes](changelog.html) ・ [Installation](download) ・
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* MTEX 5.5.2 released: ・ [Download](https://github.com/mtex-toolbox/mtex/releases/download/mtex-5.5.2/mtex-5.5.2.zip) ・ [Release Notes](changelog.html) ・ [Installation](download) ・
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* MTEX GUI 2.4 by J. Hiscocks released: ・ [Download](https://www.researchgate.net/profile/Jessica_Hiscocks/publication/341722714_MTEX_GUI_3pt4-_An_updated_graphical_interface_for_MTEX/data/5ed1b00e299bf1c67d274ede/MTEX-GUI-3pt4.zip) ・ [Announcment](https://www.researchgate.net/publication/341722714_MTEX_GUI_3pt4-_An_updated_graphical_interface_for_MTEX) ・
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* New paper: [Gazing at crystal balls - electron backscatter diffraction indexing and cross correlation on the sphere](https://www-user.tu-chemnitz.de/~rahi/paper/gazingAtCrystalBalls.pdf)
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* New paper: [Denoising of Crystal Orientation Maps](https://www-user.tu-chemnitz.de/~rahi/paper/denoising.pdf)

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‎pages/documentation_matlab/ClusterDemo.html

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---
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title: Cluster demo
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last_updated: 11-Dec-2020
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sidebar: documentation_sidebar
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permalink: ClusterDemo.html
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folder: documentation
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toc: false
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---
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<html><head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
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<!--
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This HTML was auto-generated from MATLAB code.
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To make changes, update the MATLAB code and republish this document.
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--><title>Cluster demo</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-11"><meta name="DC.source" content="script_ClusterDemo.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/GeneralConcepts/ClusterDemo.m">
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edit page</a></font><div><!--introduction--><!--/introduction-->
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{% highlight matlab %}
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cs = crystalSymmetry('432');
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odf = unimodalODF(orientation.rand(2,cs),'halfwidth',5*degree)
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ori = odf.discreteSample(10000)
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r = ori * Miller(1,0,0,odf.CS)
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%scatter(r)
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{% endhighlight %}
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{% highlight plaintext %}
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odf = ODF
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crystal symmetry : 432
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Radially symmetric portion:
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kernel: de la Vallee Poussin, halfwidth 5°
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center: Rotations: 2 x 1
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weight: 1
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ori = orientation
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size: 10000 x 1
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crystal symmetry : 432
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r = vector3d
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size: 10000 x 1
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{% endhighlight %}
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{% highlight matlab %}
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[cId,center] = calcCluster(r,'numCluster',12);
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plotCluster(r,cId)
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annotate(center,'add2all')
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{% endhighlight %}
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<center>
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{% include inline_image.html file="ClusterDemo_01.png" %}
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</center>
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{% highlight matlab %}
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r.antipodal = true
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[cId,center] = calcCluster(r,'numCluster',6);
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plotCluster(r,cId)
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annotate(center,'add2all')
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{% endhighlight %}
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{% highlight plaintext %}
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r = vector3d
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size: 10000 x 1
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antipodal: true
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{% endhighlight %}
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<center>
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{% include inline_image.html file="ClusterDemo_02.png" %}
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</center>
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{% highlight matlab %}
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h = ori \ vector3d(1,2,0);
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[cId,center] = calcCluster(h,'numCluster',2);
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plotCluster(h.project2FundamentalRegion,cId,'fundamentalSector')
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annotate(center,'add2all')
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{% endhighlight %}
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<center>
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{% include inline_image.html file="ClusterDemo_03.png" %}
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</center>
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{% highlight matlab %}
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[cId,center] = calcCluster(ori,'numCluster',2,'method','hierarchical');
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plotCluster(r,cId)
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annotate(center * Miller(1,0,0,ori.CS),'add2all')
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{% endhighlight %}
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<center>
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{% include inline_image.html file="ClusterDemo_04.png" %}
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</center>
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{% highlight matlab %}
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[cId,center] = calcCluster(ori,'numCluster',2,'method','odf');
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plotCluster(r,cId)
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annotate(center * Miller(1,0,0,ori.CS),'add2all')
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{% endhighlight %}
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{% highlight plaintext %}
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...
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{% endhighlight %}
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<center>
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{% include inline_image.html file="ClusterDemo_05.png" %}
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</center>
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{% highlight matlab %}
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% compute the full distance matrix
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d = angle_outer(r,r);
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d(d<0.01) = 0;
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%d = d(triu(true(size(d)),1));
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d = squareform(d);
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% use the statistic toolbox
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z = linkage(d,'single');
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%cId = cluster(z,'cutoff',30*degree);
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cId = cluster(z,'maxclust',12);
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plotCluster(r,cId)
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{% endhighlight %}
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{% highlight matlab %}
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function plotCluster(r,cId,varargin)
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scatter(r(cId==1),'MarkerFaceColor',ind2color(1),varargin{:})
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hold on
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for i = 2:max(cId)
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scatter(r(cId==i),'add2all','MarkerFaceColor',ind2color(i),varargin{:})
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end
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hold off
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end
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{% endhighlight %}
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</div></body></html>

‎pages/documentation_matlab/CrystalDirections.html

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---
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title: Miller Indices
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last_updated: 08-Dec-2020
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last_updated: 11-Dec-2020
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sidebar: documentation_sidebar
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permalink: CrystalDirections.html
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<!--
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--><title>Miller Indices</title><meta name="generator" content="MATLAB 9.9"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-08"><meta name="DC.source" content="script_CrystalDirections.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/CrystalGeometry/CrystalDirections.m">
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--><title>Miller Indices</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-11"><meta name="DC.source" content="script_CrystalDirections.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/CrystalGeometry/CrystalDirections.m">
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edit page</a></font><div><!--introduction--><p>Miller indices are used to describe directions with respect to the crystal reference system.</p><!--/introduction--><h2 id="1">Crystal Lattice Directions</h2><p>Since lattice directions are always subject to a certain crystal reference frame, the starting point for any crystal direction is the definition of a variable of type <a href="crystalSymmetry.crystalSymmetry.html">crystalSymmetry</a>.</p>
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{% highlight matlab %}
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cs = crystalSymmetry('triclinic',[5.29,9.18,9.42],[90.4,98.9,90.1]*degree,...

‎pages/documentation_matlab/EBSDReferenceFrame.html

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title: Reference Frame Alignment
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last_updated: 08-Dec-2020
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last_updated: 11-Dec-2020
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sidebar: documentation_sidebar
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permalink: EBSDReferenceFrame.html
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<!--
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--><title>Reference Frame Alignment</title><meta name="generator" content="MATLAB 9.9"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-08"><meta name="DC.source" content="script_EBSDReferenceFrame.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/EBSDAnalysis/EBSDReferenceFrame.m">
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--><title>Reference Frame Alignment</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-11"><meta name="DC.source" content="script_EBSDReferenceFrame.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/EBSDAnalysis/EBSDReferenceFrame.m">
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edit page</a></font><div><!--introduction--><!--/introduction--><p>The most important difference between MTEX and many other EBSD software is that in MTEX the Euler angle reference is always the map reference frame. This mean the \(x\) and \(z\) axes of the map are exactly the rotation axes of the Euler angles.</p><p>In case the map coordinates and the Euler angles in your data are with respect to different reference frames it is highly recommendet to correct for this while importing the data into MTEX. This section explains in detail how to do this.</p><h2 id="2">On Sreen Orientation of the EBSD Map</h2><p>Many peoply are concerned when the images produced by MTEX are not aligned exactly as they are in their commercial software. It is indeed very important to understand exactly the alignment of you data. However, the important point is not whether a map is upside down on you screen or not. The important point is how your map alignes with the specimen, as we want to use the map to describe properties of the specimen.</p><p>There are basicaly two components in an EBSD data set that refers to the specimen reference frame: the spatial coordinates \(x\), \(y\) and the Euler angles \(\phi_1\), \(\Phi\), \(\phi_2\). To explain the difference have a look at the EDAX export dialog</p><p><center>
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{% include inline_image.html file="edax_coordinate_systems.png" %}
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</center></p><p>Here we have the axes \(x\) and \(y\) which describe how the map coordinates needs to be interpreted and the axes \(A_1\), \(A_2\), \(A_3\) which describe how the Euler angles, and in consequence, the pole figures needs to be interpreted. We see that in non of these settings the map reference system coincides with the Euler angle reference frame.</p><p>This situation is not specific to EDAX but occurs as well with EBSD data from Oxford or Bruker, all of them using different reference system alignments. For that reason MTEX stronly recommends to transform the data such that both map coordinates and Euler angles refer to the same coordinate system.</p><p>Doing this we have two choices:</p><div><ol><li>transfrom everything to the reference system \(x\), \(y\) using the option <code class="language-plaintext highlighter-rouge">'convertEuler2SpatialReferenceFrame'</code>. This will keep the map coordinates while changing the Euler angles</li><li>transfrom everything to the reference system \(A_1\), \(A_2\), \(A_3\) using the option <code class="language-plaintext highlighter-rouge">'convertSpatial2EulerReferenceFrame'</code>. This will keep the Euler angles while changing the map coordinates.</li></ol></div><p>In the case of EDAX data imported from an <code class="language-plaintext highlighter-rouge">*.ang</code> file we still need to specify the export option used by the EDAX software. This is done by the options <code class="language-plaintext highlighter-rouge">'setting 1'</code>, <code class="language-plaintext highlighter-rouge">'setting 2'</code>, <code class="language-plaintext highlighter-rouge">'setting 3'</code> or <code class="language-plaintext highlighter-rouge">'setting 4'</code>.</p><p>Since setting 2 is default for most EDAX exports a typical command for importing data from an ang file would look like this</p>

‎pages/documentation_matlab/EBSDSelect.html

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---
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title: Select EBSD data
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last_updated: 20-Nov-2020
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last_updated: 15-Dec-2020
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sidebar: documentation_sidebar
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permalink: EBSDSelect.html
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<!--
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--><title>Select EBSD data</title><meta name="generator" content="MATLAB 9.9"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-11-20"><meta name="DC.source" content="script_EBSDSelect.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/EBSDAnalysis/EBSDSelect.m">
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edit page</a></font><div><!--introduction--><!--/introduction--><p>In this section we discuss how to select specific EBSD data by certain properties. Let us first import some example <a href="mtexdata.html">EBSD data</a>. and plot the raw data</p>
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--><title>Select EBSD data</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-15"><meta name="DC.source" content="script_EBSDSelect.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/EBSDAnalysis/EBSDSelect.m">
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edit page</a></font><div><!--introduction--><!--/introduction--><p>In this section we discuss how to select specific EBSD data by certain properties. Let us first import some example EBSD data using the command <a href="mtexdata.html"><code class="language-plaintext highlighter-rouge">mtexdata</code></a>.</p>
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{% highlight matlab %}
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mtexdata forsterite
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{% endhighlight %}

‎pages/documentation_matlab/GrainSmoothing.html

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title: Grain Boundary Smoothing
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last_updated: 08-Dec-2020
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last_updated: 11-Dec-2020
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sidebar: documentation_sidebar
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<!--
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--><title>Grain Boundary Smoothing</title><meta name="generator" content="MATLAB 9.9"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-08"><meta name="DC.source" content="script_GrainSmoothing.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/GrainBoundaries/GrainSmoothing.m">
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--><title>Grain Boundary Smoothing</title><meta name="generator" content="MATLAB 9.10"><link rel="schema.DC" href="http://purl.org/dc/elements/1.1/"><meta name="DC.date" content="2020-12-11"><meta name="DC.source" content="script_GrainSmoothing.m"></head><body><font size="2"><a href="https://github.com/mtex-toolbox/mtex/blob/develop/doc/GrainBoundaries/GrainSmoothing.m">
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edit page</a></font><div><!--introduction--><!--/introduction--><p>EBSD data is usually acquired on a regular grid. Hence, even over a finite number of grid points, all possible grain boundary directions can not be uniquely represented. One way of overcoming this problem - and also allowing to compute grid-independent curvatures and grain boundary directions - is the interpolation of grain boundary coordinates using <a href="grain2d.smooth.html"><code class="language-plaintext highlighter-rouge">grains.smooth</code></a>.</p><p>Proper smoothing has an influence on measures such as total grain boundary length, grain boundary curvature, triple point angles or grain boundary directions among others.</p><p>While we used <a href="grain2d.smooth.html"><code class="language-plaintext highlighter-rouge">grains.smooth</code></a> before, here we will illustrate the different options.</p>
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{% highlight matlab %}
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mtexdata csl

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