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.

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.

 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). 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».
4. Now, load the .cif file of your phase.
5. Click Next» until the end or Finish immediately.
6. In the workspace to the right, some parameters should have appeared. They need to be there to continue. If the workspace is empty, execute the whole script by clicking in each of the four sections (yellow background), followed by Ctrl+Enter. To avoid the importing procedure next time, save the current script.
7. Type to the command line: plotPDF(odf,Miller({1,0,0},{0,1,0},{0,0,1},CS)) and press Enter. Depending on crystal symmetry other pole figures might be of interest.
8. The pole figures should pop up. To see the intensity, click Insert Colorbar (a button in the figure window).

…

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

• 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. You can do it either by typing them in by hand and pressing Return afterwards, like so:

>> MQuartz =....
  [[86.74  6.99  11.91 -17.91  0.0    0.0];...
  [  6.99 86.74  11.91  17.91  0.0    0.0];...
  [ 11.91 11.91 107.2    0.0   0.0    0.0];...
  [-17.91 17.91   0.0   57.94  0.0    0.0];...
  [  0.0  0.0     0.0    0.0  57.94 -17.91];...
  [  0.0  0.0     0.0    0.0 -17.91  39.88]];

or you use the import the data (more info on this later …).

Now, you have to tell Matlab that the variable MQuartz is not just any tensor but the stiffness tensor. We do this by typing CQuartz = stiffnessTensor(MQuartz,CS) to the command line. You will get a list of According to the symmetry, some of the constants might have changed to zero.

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

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