MTEX A MATLAB Toolbox Tutorial Texture Analysis

Transcription

1 MTEX A MATLAB Toolbox Tutorial Texture Analysis Ana María Fernández Blanco IMDEA Materials, Madrid 1. INTRODUCTION The MATLAB toolbox MTEX provides a unique way to represent, analyze and interpret crystallographic preferred orientation, i.e. texture, based on integral ( pole figure ) or individual orientation ( EBSD ) measurements. In particular, MTEX comprises functions to import, analyze and visualize diffraction pole figure data as well as EBSD data, to estimate an orientation density function from either kind of data, to compute texture characteristics, to model orientation density functions in terms of model functions or Fourier coefficients, to simulate pole figure or EBSD data, to create publication ready plots, to write scripts for multiple use, and others. Thus MTEX is a versatile free and open-source software toolbox for texture analysis and modeling. [1] 2. REQUIREMENTS 1. MTEX requires MATLAB version 7.1 or higher. It should also work fine on student versions. 2. Download the archive file mtex-3.1.zip from the web page The MTEX toolbox is available for Windows, Linux and MAC-OSX 3. Installation: you should proceed as follows: a. extract MTEX to an arbitrary folder b. start MATLAB c. navigate to the MTEX folder d. type startup_mtex 1

2 3. PROCEDURE Texture measurement in the X-ray laboratory Files data (Incomplete Pole Figures) from the laboratory of X-Ray MTEX Calculation of the ODF (complete information) Calculation of the Final Pole Figures 3.1. Import measured pole figures MTEX allows to create a Pole Figure object from data files containing diffraction data (note these files are the corrected data exported from the X-Ray diffractometer machine). Some formats are currently supported by MTEX, but.txt obtained from Philips difractometer (used at the Facultad de Químicas at the Universidad Complutense de Madrid ) is the most common interface (file type). The main steps in order to represent the Pole Figures are as follows: NOTE: In this tutorial, we will be using the Magnesium alloy AZ31 (Hexagonal Closed Packed metal) 2

3 1. The main way of getting any kind of experimental data into MTEX is the import wizard. 2. You can see the following window when you click the option import pole figure data in the Command Window of MATLAB. 3

4 3. Click the option add data files and you select your pole figure data (files.txt). 4. Click Open. 5. Click next. 4

5 6. Now, you should define the Crystal Geometry depending of your samples. MTEX has some data of the most common metals and defines automatically the crystal geometry (this is with the option Load Cif File ). However, if the parameters are different, you should insert them. Let s load the Magnesium material file and press Open button Click next. 8. In this step you should define the Specimen Geometry, mainly the Symmetry of the specimen. The rest of the options you can play with them (they are plotting conventions). 5

6 9. Click next. 10. Here, you can see the corresponding pole figure data and MTEX normally gives the Miller Indices. 11. Click next. 6

7 12. This window is the last! It is a summary of Pole Figure data has been imported. Choose the option script (m-file) and default in order to analyze the data according to the needs of each one. 13. Click finish. 14. The script is automatically generated. Now, we will work with that. 15. The screen should appear as follows: 7

8 3.2. Pole Figure representation In this section we will work with the script (m-file) generated in order to visualize and to represent the pole figures. As soon as you press the run button, if all is ok, a computation will start and the progressive output will be visible in the new window. Click run 8

9 The script contains different parts: Specify Crystal and Specimen Symetries, Specify File Names, etc. In the section Plot Calculated Pole Figures is where the command line necessary to execute the plot of the pole figures plotpdf (odf, h) is written. When you press the run button, a window will appear showing the result of the computation. As the computation is finished we will see the corresponding plots (pole figures). Note that you can modify the representation of the texture. Next, we will explain some plotting options in order to obtain the representation according to the needs of each one. 9

10 Plotting options: Notice that all modifications listed here must be made in the section of the script Plot Calculated Pole Figure. 1. Antipodal option The pole figures are a superposition of the northern and the southern hemisphere (since antipodal directions are associated). In order to plot pole figures as a superposition of the northern and southern hemisphere one has to enforce antipodal symmetry. This is done by the option antipodal. plotpdf(odf, h, antipodal ) ; 2. Remove min & max If you do not want to appear the minimum and maximum in the figures you should write the following line: plotpdf(odf, h, antipodal, minmax, off ) ; 10

11 3. Set plotting scale This option allows plotting all the pole figures with the same intensity scale (setcolorrange) and you can add the colorbar. You should write two lines in the following order: plotpdf(odf, h, antipodal, minmax, off ) ; setcolorrange( equal, all ) ; colorbar 11

12 Note that if you write in the setcolorrange option ( equal, all ) means that all pole figures have the same intensity scale. However, if you need to have a different range of scale because, for example you should compare different pole figures in other conditions, you should replace equal by [0, to whatever you want ]. plotpdf(odf, h, antipodal, minmax, off ) ; setcolorrange([0, 20], all ) ; colorbar Also, if you prefer to have the colorbar under the plot, you should write: colorbar( south ); 4. Annotations You can include specimen or crystal directions using the command annotate: plotpdf(odf, h, antipodal, minmax, off ) ; annotate([xvector, yvector, zvector], label, { x, y, z }, BackgroundColor, w ) ; setcolorrange( equal, all ) ; colorbar 12

13 5. Plot types Grayscale: plotpdf(odf, h, antipodal, minmax, off, gray ) ; setcolorrange( equal, all ) ; colorbar Contours: plotpdf(odf, h, antipodal, minmax, off, contourf ) ; setcolorrange( equal, all ) ; colorbar 13

14 Other option is: plotpdf(odf, h, antipodal, minmax, off, contour, 0:1:16) ; % the numbers mean that the contours go from 0 to 16 (step = 1). setcolorrange( equal, all ) ; colorbar 14

15 Note that you can change some options of the plot accessing from the plot options menu: 6. Representation the individual pole figures plotpdf(odf, Miller(0,0,0,1,CS), antipodal, minmax, off ) ; 7. Rotation of the pole figures You can represent the pole figures changing their orientation respect to one axis. For instance, you want the Normal Direction (ND) to be perpendicular to the Z axis, that is, that the ND is not in the center of the pole figure but, in the top of the plot. For that, you have to modify some lines in the script as follows: 1.- Rotation of the imported pole figures %% Import the Data % create a Pole Figure variable containing the data pf = loadpolefigure(fname, h, CS, SS, interface, philips ); rot = rotation( axis, yvector, angle, 90*degree); pf_rotated = rotate(pf, rot); % Visualize Data % plot or the raw data plot(pf_rotated) 15

16 2.- Calculation of the ODF %% ODF estimation % estimate some ODF odf = calcodf(pf_rotated); 3.- Plot calculated pole figures %% Plot Calculated Pole Figures plotpdf(odf, h, ) in this section do not change nothing. 16

17 Inverse pole figures: So far we have treated the case for direct pole figures, but it is possible to represent the case for inverse pole figures. For this, we have to write the following lines in the section Plot Calculated Pole Figures : Note: this representation is for FCC metal. %% Plot Calculated Pole Figures plotipdf(odf, [xvector, yvector], antipodal, minmax, off, contour, 0:0.55:33) annotate([miller(1,0,0), Miller(1,1,0), Miller(1,1,1)], all, labeled ) setcolorrange( equal, all ); colorbar 17

18 Representation of the Orientation Distribution Function (ODF): If you want to represent the ODF, you should define the angle convention, for this case it is defined by the three Euler angles. So, you should write the following lines: %% ODF estimation % estimate some ODF odf = calcodf(pf_rotated); plot(odf, Euler 3, sections, 12, projection, plain, gray, contourf ); % section means the number of sections you want to represent and the projection, plain means that the ODF is plotted in a simple rectangular plot. 18

19 Saving files and images: In order to save the images, you click File and then choose Save As and you can select the image file format (.jpg,.png,.tiff, etc): Volume portions: A volume portion describes the relative volume of crystals having a certain orientation. The relative volume of crystals having an orientation close to a given orientation is computed by the command volume. For this, you should write the following lines in the section ODF estimation : %% ODF estimation odf=calcodf(pf) o = orientation( Euler, 90*degree, 90*degree, 0*degree, CS, SS) % it is necessary to define the orientation of the crystal and specimen symmetry, in this case with the Euler convention. volume(odf, o, 60*degree) % 60*degree is an example, it is the spread around the given orientation o. The result from this calculation is a number given in the Command Window of MATLAB: 19

20 4. REFERENCES [1] Texture Analysis with MTEX - Free and Open Source Software Toolbox, F. Bachmann, R. Hielscher, H. Schaeben: Solid State Phenomena (2010), 160, [2] Available from: NOTE: This tutorial should help you become familiar with the basic operational concepts in order to represent and to visualize the texture through easy way. However, this software is a powerful tool, so if you are interested to use more options, use MATLAB s Help and you could explore the all possibilities! 20