Randomly distributed orientation data should follow the Mackenzie distribution, see https://en.wikipedia.org/wiki/Misorientation#Misorientation_Distribution

Try to obtain misorientation angle distribution in the light of considering correlated and uncorrelated situations. In both cases you should find Mackenzie distribution. If you use OIM software for processing EBSD's raw files, you can simply compare your results with Mackenzie distribution. It is worth mentioning that in some specific cases higher fraction of specific HAGB does not mean random distribution ( such as 86.5 misorientated boundaries in Mg base alloys ). please find following article for more detail.

Article The generalized Mackenzie distribution: Disorientation angle...

The Mackenzie distribution is the theoretical misorientation distribution for a perfectly random polycrystal. Random here means that all crystals are randomly oriented, as opposed to crystals being preferentially oriented in some direction (in this case, the polycrystal is textured).

Comparing an actual misorientation distribution of a polycrystal with the Mackenzie distribution allows one to determine if the polycrystal is textured or randomly oriented.

If (at any misorientation angle) the frequency of the actual distribution is higher than the corresponding frequency in the Mackenzie distribution, it means that the polycrystal is textured (with a preference for that particular misorientation angle).

Thank you all for sharing the answers and materials. These would help.

The Mackenzie plot shown at Wiki is the one for the highest enantiomorphic group 432. In other words: for lower symmetries the Mackenzie plot looks different, see e.g. the attached distribution for point group 32 and corundum sample (R -3c).

A short comment regarding correlated and non-correlated setting. The first has not been developed to show the Mackenzie plot. Correlated means, that one of the nearest neighbors are used for comparison. This means there is a high probability that the correlation shows intragranular misorientations comparable to a KAM histogram. If you have many small grains with only a few pixels size both become more and more comparable, however at small angles they highly differ. In case of coarser grains both MO angle distributions look totally different. The frequency of low angles becomes bigger than for higher angles which enables the characterization of the misorientations within grains or the orientation precision .

Dear Girish,

the colleagues explained everything. I only give you my real example of using misorientations. I analysed the initial misorientation distribution angles of mechanically treated material Zirconium alloy and pure Zr and after annealing. Sometimes in hydrogen atmosphere. Always after annealing randomly distributed misorientation became some distinguishable characteristic spectrum of misorientations. I had some special peaks on the misorientation angles, whereas on the mechanically treated material it was very hard to distinguish them. It seems to be that the random distribution is close to highly deformed structure with destruction of a coarse grained structure into fine grained with lots of different misorientation angles obtained during accommodation of applied stress.

Thanks for the question and good luck in your research,

Anton