MTEX is a free Matlab toolbox for analyzing and modeling crystallographic textures by means of EBSD or pole figure data. It runs inside matlab and it is very useful to work and plot grain orientations. The homepage for MTeX is at http://mtex-toolbox.github.io/ with an extensive user manual at http://mtex-toolbox.github.io/documentation.html.

These pages do not intend to provide a full MTeX manual. We will just show tips and tricks which are useful to the community.

Depending on what you have as input data, the procedure might change.

Once you ran an indexing, you can plot the grain orientations in MTeX.

First, you should extract a list of Euler angles for the indexed grains, which can be done using timelessExtractEulerAngles.py, which is part of the TIMEleSS tools. You will have a list of Bunge Euler angles (using a Bunge convention) such as

-31.88 273.49 206.05
-55.09 133.91 157.65
83.39 235.30 204.46
-47.58 78.99 149.71
-60.87 17.28 33.07

For this option you need to have a text file with a list of Euler angles in the following format. There is also a TIMEleSS tool to create such a list from a Grainspotter .log file. But be aware that there are lots of different ways to arrange a set of Euler angles!

 70.469029217	237.905359456	160.103826456
 65.061195645	232.020366708	153.370063692
 -83.53256124	160.47139216	52.262899769
 81.812326561	201.132499009	220.391622469
 ...            ...             ...

Furthermore, have the correct .cif file ready. Now, go on with the following procedure:

1. Load MTeX into MatLab and make sure that your workspace to the right is empty.
2. Click on Import ODF data. A new window should open.
3. In the new window, click on the + symbol to the right and choose the text file with the Euler angles. A window with a short example of your data is popping up. Below, assign each column to the correct Euler angle (usually phi1, Phi, phi2). If the convention of your Euler angles is not listed, you have to convert it to another format before.
4. Click Finish. The window will close and a short calculation is running. After that, the file name should be visible in the list. Click Next».
5. Now, load the .cif file of your phase.
6. Click Next» until the end or Finish immediately.
7. The import wizard created a script in your editor with four sections. Execute all sections starting from top by clicking Run and advance several times.
8. In the workspace to the right, some parameters should have appeared. They need to be there to continue. To avoid the importing procedure next time, save the current script.

• a) For plotting each and every point in a pole figure: Define a new variable: ori = calcOrientations(odf,100), then plot by typing plotPDF(ori,Miller({1,0,0},{0,1,0},{0,0,1},CS),'antipodal','MarkerSize',4) to the command line. Depending on crystal symmetry other pole figures might be of interest.
• b) For plotting a smoothened pole figure, type plotPDF(odf,Miller({1,0,0},{0,1,0},{0,0,1},CS)) to the command line. To see the intensity, click Insert Colorbar (a button in the figure window). Depending on crystal symmetry other pole figures might be of interest.
• c) For plotting orientation spot colored depending on the density of points, one need to use the fonction 'eval' as in plotPDF(o,eval(odf,o),Miller(1,0,0,CS)) where o is a set of orientations simulated from the odf (you can obtain it by o = discreteSample(odf,100)). The colorbar (if it's not showing automatically you can add mtexColorbar in the command line) is in multiple of a uniform distribution. By default it is from blue to yellow. To have it from blue to red you can use : mtexColorMap blue2red.

Another way to do it : define euler angles list as an EBSD object

First, import your list of Euler angles by : Euler = txt2mat('grainsAll_euler.txt'); then define the property of the EBSD object to be created, one by one :

• [X,Y] = meshgrid(1:100,1:100) this is to create spatial information. I guess, it's needed for EBSD object.
• opt.x = reshape(X,1,[]);
• opt.y = reshape(Y,1,[]);
• cs = crystalSymmetry('mmm',[5.680337,11.363549,7.9293904],'mineral','Wadsleyite','color','blue');
• ss = specimenSymmetry('cubic');
• phase = 1 It's also needed. Here I study only one phase so it's easy but be careful with multiple phases..
• phi1 = Euler(:,1)
• phi = Euler(:,2)
• phi2 = Euler(:,3)

Finaly you can create an EBSD object :

ebsd = EBSD(orientation('Euler',phi1*degree,phi*degree,phi2*degree,'ZXZ'),phase,cs,ss,'options',opt)

From here you can use tis new object as a regular EBSD object.

Sometimes it's easier to deal with quaternions because you don't spend hours figuring out which convention was used for making them (there is only one convention for quaternions). MTeX can also read quaternions so there shouldn't be a problem. The data should be a list like this one:

0.18819093551927868 -0.011978786894112407 0.5338129942637391 -0.8243084177709855
0.9558327208154278   0.1455093219888857  -0.1091295638562596 -0.23087136099017058
0.42400840011908053 -0.2054132067385653   0.25008006803551774 0.8458618390122514
0.557578365011369   -0.6042298517163799  -0.5577004881010722 -0.11394217278021418
 ...            ...             ...           ...

Furthermore, have the correct .cif file ready. Now, go on with the following procedure:

1. Load MTeX into MatLab and make sure that your workspace to the right is empty.
2. Click on Import ODF data. A new window should open.
3. In the new window, click on the + symbol to the right and choose the text file with the list of quaternions. A window with a short example of your data is popping up. Below, assign each column to the correct quaternion (real, i, j, k).
4. Click Finish. The window will close and a short calculation is running. After that, the file name should be visible in the list. Click Next».
5. Now, load the .cif file of your phase.
6. Click Next» until the end or Finish immediately.
7. The import wizard created a script in your editor with four sections. Execute all sections starting from top by clicking Run and advance several times.
8. In the workspace to the right, some parameters should have appeared. They need to be there to continue. To avoid the importing procedure next time, save the current script.

• a) For plotting each and every point in a pole figure: Define a new variable: ori = calcOrientations(odf,100), then plot by typing plotPDF(ori,Miller({1,0,0},{0,1,0},{0,0,1},CS),'antipodal','MarkerSize',4) to the command line. Depending on crystal symmetry other pole figures might be of interest.
• b) For plotting a smoothened pole figure, type plotPDF(odf,Miller({1,0,0},{0,1,0},{0,0,1},CS)) to the command line. To see the intensity, click Insert Colorbar (a button in the figure window). Depending on crystal symmetry other pole figures might be of interest.

For calculating the average elastic tensors from a textured polycrystalline sample, you need several things beforehand:

• Have MTeX ready (either installed or open the “startup.m” file)
• An ODF in Matlab (can be loaded by using the import wizard, see 'How to produce pole figures with MTeX' above for more info)
• The crystal system loaded in Matlab (can be loaded by using the import wizard, see 'How to produce pole figures with MTeX' above for more info)
• The elastic tensor with all independent elastic constants

If you have these things ready, you can start by loading the elastic tensor into Matlab. Let's do it for quartz as an example.

Type it in by hand and press Return afterwards, like so:

>> MQuartz =....
  [[86.74  6.99  11.91 -17.91   0.00   0.00];...
  [  6.99 86.74  11.91  17.91   0.00   0.00];...
  [ 11.91 11.91 107.20   0.00   0.00   0.00];...
  [-17.91 17.91   0.00  57.94   0.00   0.00];...
  [  0.00  0.00   0.00   0.00  57.94 -17.91];...
  [  0.00  0.00   0.00   0.00 -17.91  39.88]];

Please note that the three dots at the end of each row are necessary.

For this, save your matrix as comma-separated values in a text file (.txt). Then, in Matlab go to the Home tab and click Import Data. The import assistant will open. Check if the data is in the way you want to have it and change the Output Type to Numeric Matrix. Finally, click in the Import dropdown menu on the right Generate Script. Change the name of the file in the script to whatever you like (in this example I changed it to MQuartz).

The easiest way if you ask me.

1. In your command line, scroll all the way up until you see the three buttons for importing ODF/EBSD/pole figure data.
2. Click on any of them. A new window opens.
3. Switch to the tab Tensor, then click on + on the right side of the window and open the file where your tensor is stored.
4. Click Next and load the CIF file of your phase. It doesn't matter if you imported it already before when you imported your Euler angles because it should be the same anyway.
5. Click Next and Finish.
6. Run all sections of your script.

Note that the created script has already a line for assigning the matrix to the tensor. The following step is not necessary if you are loading the tensor this way.

Now, you have to tell Matlab that the variable MQuartz is not just any matrix but the stiffness tensor. We do this by typing

CQuartz = stiffnessTensor(MQuartz,CS)

to the command line. You will get a printout like this one:

CQuartz = stiffnessTensor (show methods, plot)
  unit   : GPa                             
  rank   : 4 (3 x 3 x 3 x 3)               
  mineral: Quartz (321, X||a*, Y||b, Z||c*)
 
  tensor in Voigt matrix representation:
 86.74  6.99 11.91     0     0     0
  6.99 86.74 11.91     0     0     0
 11.91 11.91 107.2     0     0     0
     0     0     0 57.94     0     0
     0     0     0     0 57.94     0
     0     0     0     0     0 39.88

As you can see in this example, some of the constants have changed to zero, according to the symmetry.

Now you can finally calculate the weighted tensor of the textured material. But be careful! A lot of memory is necessary for this kind of calculation and your computer might get stuck for a moment!

THill = calcTensor(odf,MQuartz,'Hill')