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In order to index the electron backscattered diffraction patterns obtained on the SEM in a reasonable time (sorry, but only for the cubic system right now), I have written a Matlab application (ebsp.m) which also determines the euler angles and the normals of the individual grains. Those data are then used in two other Matlab programs, called eulnorm.m and eulsig.m. eulnorm.m and eulsig.m calculate the grain boundary misorientations and sigmas from the output files of the ebsp.m application, and plot the results into histograms and stereographic projections.

The advantage of using Matlab is that the same input text files can be used on unix, windows or Macintosh platforms. Also, the user can easily change the input or output files, as well as the figures and graphs, if she or he desires. You do not need to know the Matlab programing language to use the Matlab applications contain in the EBSP package files, but that would definitely be usefull if you run into problems in running them. The graphics generated by eulnorm.m or eulsig.m can be saved, copied and used in other documents. On Macintoshes one can just copy and paste the windows containing the graphics. In unix, the operation is a little bit more tricky and you should check the "print" Matlab function in the Matlab user's guide.

In order to use the information that the EBSP package applications provide, it is recomended first to have some understanding of the crystallography of cubic systems and of the formalism and jargon used to described grain orientation and grain misorientation. How a grain orientation is described by its euler angles, definition of grain boundary misorientation and sigmas can be found in books such as *The measurement of grain boundary geometry* by V. Randle, or in *Materials interfaces. Atomic-level structure and properties* by D. Wolf and S. Yip

All the files needed for the indexation of the patterns and their analysis are contained in the EBSP package directory/folder. You should put all those files, as well as the pattern image files, in the same directory/folder from which you can start Matlab. This keeps you from having to redefine the path for Matlab. The pattern image files obtained on the SEM must be saved in raw binary format (.RAW), using for example NIH or graphic converter on a Mac, or using X.V. on unix . In addition to the .m files described earlier, the EBSP package contains other .m and .mat files which are just subroutines. The .mat files are binary files generated the first time you run the calibration and set-up routines such as calibnew.m and vect_type_ebsp.m. The pattern center position is in the text file patcenter.m.

The ebsp.m routine indexes the electron backscattered patterns by comparing the angles between four poles in the pattern, with the ones found in a table containing all the possible angles between pre-defines poles. The angles between poles in the patterns are calculated using their projections on the phosphorus screen and the position of the *Pattern Center*. The *Pattern Center* is the point on the phosphorus screen where the normal of the screen intersects the specimen and the beam (see Figure 1 below). The higher the number of pre-defined pole types in the table, i.e (100), (111) etc ...., the larger is the angle table and the longer it takes to index a pattern. The pole types can be chosen in the text file vect_type_ebsp.m and this procedure is explained in detail in the section : Pole Definition. By running vect_type_ebsp.m, all the vectors and angles are calculated and saved in .mat type files.

**Schematic of the diffraction cone and pattern formation**

The position of the *Pattern Center* will be different for each working distance that you will use on the SEM. The procedure to calibrate its position is described in the calibration section of this manual. The position of the *Pattern Center* has to be entered in the patcenter.m file, which is an editable text file. In patcenter.m, the vector *up* is the coordinate of the *Pattern Center* in pixels for a 640x480 image with the origin at the lower left corner. Z is the distance between the screen and the sample (see Figure 1). The value of tetay in the patcenter.m file is the angle in degrees between the horizontal and the normal of the specimen. In order to obtain a pattern with a uniform contrast, it is recommended to have tetay=20?.