Euler angles and the orientation matrix 

Hi! Thanks for the questions. Let's go through them one by one. 1: When you create the pole figure for example, the texture component of each grain (or point) becomes significant. There are different "predefined" texture components, such as cube, brass, Goss...etc. You can see how a point's texture component compares to these. 2: I said in the video that you have to round the numbers to the closest integer. So, I just simply rounded the 0.88 and 0.79 up and they became 1. 3: They are very important when you want to distinguish the slip systems. Let's consider a FCC crystal. The (111)[101] is _one specific_ slip system where the (111) is the slip plane and [101] is the slip direction. On the other hand, {111} describes all possible (111) planes and [101] directions. So, the parentheses () and square brackets [] denote one single case, the curly {} brackets and angle brackets denote a set of planes and directions. Usually, we say, FCC has 12 slip systems and they are {111}-type. And when we define a certain system among these 12, we can say, that now we work with the (111)[10-1] slip system which is one particular case out of the 12 cases. I hope this makes sense.

@@CuriousScientist I appreciate your reply. It looks like my point of confusion is that the title and first part of the video is about Euler angle and orientation matrix (easy to follow, but just plain trigonometry), but then suddenly veers into material specialized to crystalography assuming we viewers know the motivation behind (h,k,l) and (u,v,w), and of rounding perfectly good vectors to closest integers. No doubt with more background this all would make sense, and presumably it wasn't your intent to get into that. It just didn't make sense relative to the title and hence expectations.

@@Graham_Wideman Yes, I totally agree with you, the second part might be a bit too specific to crystallography and materials science. I just wanted to show an application of the orientation matrix, so the viewer can be motivated about the usefulness of the meticulous matrix operations and similar things. My plan is to create a whole bunch of videos in this subject, so after a while, all key topics mentioned in the videos will be found in other videos within the same playlist. The final goal with this specific series is that you will be able to understand most of the calculations behind the different colorful maps generated in commercial EBSD software.

Hi! I got 10, 3, 5. And u, v, w: -2, 5, 1.

Thanks for the sub, it means a lot. I also use Aztec, so I can explain. Before you acquire a map, you have to define the sample geometry this is very important, since this will determine the relationship between the specimen and the crystal coordinate system. But once you set up properly and acquire the map according to it, then there's no problem. You always get phi1, PHI, and phi2. The orientation matrix method I showed so far works with cubic systems only as far as I know. I will have to double check this. The Miller indices perhaps can be obtained with the demonstrated method but the misorientation is pretty sure different because you will need different symmetry operators. If you have any further questions, let me know, however I am a bit busy in the next three weeks, so I cannot answer promptly.

@@CuriousScientist Hey CS, I tried to confirm the demonstrated method to get the miller indices with an aligned orientation of Mg single crystal. The surface of the crystal is aligned to the prismatic plane I (100). On the screen, everything shows up pretty nicely, all blue. However, the calculated values are (0.5 0.5 0.13), which can only be rounded to (441). Which seems really wired to me. Does it mean the method is not suitable for hcp? Do you have any thoughts on this?

Sorry for the late reply. The texture components (hkil)[uvtw] can be determined for HCP, but in a different way. The reason behind the difference and the solution is described in the following work: Y.N. Wang, J.C. Huang / Materials Chemistry and Physics 81 (2003) 11-26. Please take a look a see if it solves your issue.

@@CuriousScientist Hey, no need to apologize dude! I know you said you'll be busy. I will check out the paper you listed. Thanks so much for your help!

Thank you! For your g(), I get (-0.0096, 0.0036, -0.9999)[0.8804,-0.4742,-0.0103] or something like this. If we simplify it, then we get (001)[2-10]. Another example I found in my notes is the following: (0.662,0.684,0.306)[0.095,-0.482,-0.871] which was given as (221)[0-1-2]. Let's pick the ABS(max). Put the calculation in an Excel sheet and show two decimals. We get (2.16,2.24,1.00)[0.11,-0.55,-1.00]. Of course, we do not use fraction numbers for lattice planes, so just let's multiply the second part with 2, then after also rounding it we get [0-1-2]. So yes, the best practice is to divide the hkl-uvw elements with abs(max) and then readjust the numbers to integers.

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