The figures remind me on Y. He et al :-) collected at the Gibeon meteorite. As far as I know he generated these pole figures by himself. At least for the pole figures you can do this even with Excel, but if you have Channel5 or MTEX it is very easy to do it. Please consider, that the data have been rotated additionally in order to express the three-fold symmetry of the austenite. In fact, this is not required, but since the transformation is often explained as parallelity between (111) planes of austenite it might be beneficial to look perpendicular to one of these planes. But it is absolutely not necessary. The R-F presentations are perhaps also available in MTEX but then as intersections and not as 3D presentation. R-F is also quite unusual. I don't want say "not necessary" But I do not know many people who are able to read them properly. If you can read them, you should be also able to generate them by yourself. Therefore my question: do you really need them or do you simply like this kind of presentation because it looks somehow special? My recommendation: only use tools you are familiar with. Everything else does not help you.

The determination or visualization of OR between fcc and bcc phases is an old story and therefore not simple. On this topic already people are working for decades and there is still no final tool which explains all. Nevertheless, for a representation pole figures are usually not sufficient.

I've only added a few links to some of my own papers which are related to this topic, but thee are tens of them from other scientists, e.g. Cyril Cayron. The OR is typically also not the solution of the problem since usually you want to find out which variant belong to a single grain. This is a typical task for grain reconstruction. Also for this specific task a few groups around the world already developed software packages which are, however, not free available. First address is again Cyril Cayron, but also a group in Metz (France), Japan, UK etc. developed code. As far as I've heard most stable are probably the both french packages. But usually all different software packages have specific advantages.

Could you post an image of your measurements? The here presented pole figures only make sense since they are data collected in only one single parent grain. For a martensitic structure this is usually not the case, but - more problematic - in technical products the data are not that idea as shown for the Gibeon meteorite, where also date are removed which do not match that nicely. Usually I would expect much more scattered data (cf. the content of the linked papers).  

Article A new method for the investigation of orientation relationsh...

Article Investigation of orientation relationships by EBSD and EDS o...

Article Irrational orientation relationship derived from rational or...

 Dr. Gert Nolze,

Sorry for my late reply.

Thank you very much for your answer. Yes. These two figures were from Dr. Youliang He’s papers.

Recently, I am trying to determine the orientation relationship (OR) of the austenite and the martensite. I have downloaded the papers which you gave the links in your answer. You did a lot work on this subject.

As far as I know, pole figure is a good way to do determine the OR. I have obtained the orientation date (Ouler angles) of the austenite (single grain) and the martensite (in the same austenite grain) by EBSD. And, I understand that I need to rotate the orientations of martensite to the austenite reference frame before generating the pole figure (as shown in your papers). But, I don’t know how to rotate these Ouler angles to the austenite reference frame. Besides, I don’t know how to generate the pole figures using the rotated angles with Channel 5.

I am looking forward to learning from you. Thank you.

If you have Channel5 you have there a virtual chamber which enables you to apply a pre-rotation on the data set. To see the effect you need to change the reference co-ordinate system from C0 to C1 (I do not remember the correct terms at the moment but they are given in virtual chamber and need to be changed in Mambo as well as Tango in the settings of the respective presentation). You can e.g. generate two pole figure presentations, one with X0, Y0 and Z0 and the other with X1, Y1 and Z1. The same is possible with Tango. In MTEX it is certainly also possible using a simple command.

Dear Gert,

   Since Song has the orientation data for both austenite and martensite, he can directly calculate the average orientation relationship between these two phases, right?

To Song:

  As Gert mentioned it is not necessary to rotate the data to let the three fold axis along the projection direction in pole figure. As you have the orientation relationship of austenite, you can plot the pole figure directly by using the tools suggested by Gert. Alternatively, you can use PTCLab (see attached figure), which is available on https://sourceforge.net/projects/tclab/

BTW, PTCLab will have a free and general solution to reconstruct the orientation of parent phase based on the crystallography from daughter phases. Now, the function is under test and will be available soon. 

Dear GuXinfu,

if he has the orientation data of the parent phase he can determine the mean orientation using quaternions only. All software packages using quaternions as only efficient way although the export is still done by Euler angles.

A bit more complicated is the "averaging" of variants. He needs to apply the symmetry to transfer all variants onto one. Because of data scattering it might become difficult to realize which one is the "initial" variant. This is the major challenge....

Since when do you work on PTCLab?

Best greetings

Gert 

Thank you Gert. I got the point. I started to write PTCLab at 2014 to summary the crystallographic models used in Prof. Zhang's group.