Indexing TEM diffraction patterns from single crystals with hexagonal unit cells

In this video (as always, filmed raw, unedited, uncensored, and uncut), I cover indexing TEM (parallel beam) diffraction patterns from single crystals with hexagonal unit cells. For purposes of simplicity, this is limited here to only hexagonal close packed and wurtzite structures with ideal c/a ratios. This is this much requested follow-up to the video I created several weeks ago covering indexing of TEM diffraction patterns from cubic single crystals.
If you did not already see the previous video (or are not already familiar with indexing TEM diffraction patterns), I suggest you watch that video first:
kzbin.info/www/bejne/bpWzfWpofKyEiM0
Thanks for watching! Please like, subscribe, and share and let me know if you have any questions or comments. Video topic requests are always welcome and appreciated; I enjoy making these videos and wish I could make them more frequently, but the demands of my job make it tough to do so; I’m in charge of 3 S/TEMs, 2 dual FIB/SEM systems, and 1 SEM and this keeps me very busy!
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www.linkedin.com/in/nicholas-rudawski-30414528/
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[@NicholasRudawski]

Hi everyone: at 13:00 when I discuss the polarity of the Wurtzite unit cell using GaN as an example (Ga = green, N = blue), I incorrectly described the as-shown structure as N-face, when it is actually Ga-face. The N-face version would be if the unit cell was flipped upside-down. My apologies for any confusion.

[@deepak.dinkar]

Wonderful New Year gift! Thank you very much Dr. Nick for accepting my request. It’s very helpful!

[@NicholasRudawski]

You're welcome; glad you found it helpful.

[@DW-iq8lt]

Great video! High quality as always. Hopefully to see more about TEM-related theories like this one in the future!

[@NicholasRudawski]

Thank you! Yes, there are thankfully no shortage of topics like this that I could turn into videos; one I've had on my mind for a while now is about interpreting STEM-EDS maps, so I hope to do that one soon.

[@DW-iq8lt]

@@NicholasRudawski Thanks! Could you also consider to do a 4D STEM theory and application video in the future?

[@NicholasRudawski]

@@DW-iq8lt Yes, a 4D-STEM video would definitely be useful; in the meantime, there are already some great videos about 4D-STEM here on YT (particularly on the Gatan channel). Just do a basic YT search for "4D-STEM".

[@AmaniElFathan]

Thank you for the lecture Professor

[@NicholasRudawski]

You're welcome; while I do hold a faculty position at a university I'm not actually a professor (ha ha). This actually gives me an idea to do an "about me" video talking about my position and where I work, so thank you for the inspiration!

[@AmaniElFathan]

@@NicholasRudawski oh I am so sorry Dr. Rudawski

[@NicholasRudawski]

@@AmaniElFathan ha ha, no worries and no need to apologize; it happens all the time.

[@angelinabraham68]

Hi Dr. Nicolas! this video was highly helpful. I have a doubt while calculating the table of distance ratios (g1/g2) should we use the hkl values given in the jcpds/icdd file of our sample.

[@NicholasRudawski]

Hi Angelina: glad the video was helpful. Unless your sample is HCP or wurtzite (which usually conform fairly close to the idea c/a ratio) I would use the experimental d spacing information. That being said, if you have access to simulation software, you can generate the d spacing list for any structure even if JCPDS/ICDD data doesn't exist (or is not easily obtained). This is helpful for something like sapphire, which has a very complicated unit cell.

[@mostafaeid9955]

Thanks for your videos. I have some questions that I hope to find answer 1. If I work on material that I already know the values of a and c parameters. so I shouldn't put the ideal ratio (c/a) in the g1.g2 calculation, right? 2. I have CBED, not SAD so can I take the distances of g1 and g2 from the CBED pattern? 3. How can I get the g1/g2 table for HCP material? 4. I am not familiar with Matlab, so what do you recommend after getting g1/g2 ratio? can I get the code from your side that calculates the possibilities of g1 and g2 vectors? If not what should I do in this case 5. Why do you only focus on the non-zero value for l and ignore h and k values (when you exclude the possibilities) I understand g1.g2=0 when h1.h2+k1.k2+l1.l2=0 6. what is the important of n1 and n2 ( n1=6 and n2=4) in the ex2 . Is this something regarding the code? I understand when you put n1=6 and n2=4 we will get 6 columns and 4 rows of possibilities but this doesn't happen in your code output results ( I find 12 rows and 4 columns) 7. I collected the CBED pattern from material that has space group p63/mmc. However, the symmetry was 1m. But I couldn't find any zone axis that gives 1m symmetry (from the Zone axis symmetries table) in this structure and that is why I tried to index this pattern manually so do you think I got this pattern from the defect area for example? Thanks again

[@NicholasRudawski]

Hi @mostfafeid9955: this is a bit too detailed to address via YT comment; please email me directly so we can discuss this further. That being said, you can't index a CBED pattern from a polar crystal exactly like a SAED pattern because the polarity will show up in the appearance of the DP spots (discs). You would need some simulations to help you figure out which face is which.

[@sindhug7130]

How are you getting those g vectors ? like the hkl list ?

[@NicholasRudawski]

@sindhug7130 the list of allowable g vectors (or as you correctly alternatively describe as the allowable hkl list) is determined by calculating the structure factor for all unique hkl and determining which are non-zero. The unique hkl with non-zero structure factors make up the list. Unique simply means that hkl is not crystallographically equivalent to another hkl; e.g., 010 is not unique because is crystallographically equivalent to 100, but 001 would be unique (assuming HCP unit cell). It actually would be a good idea to do a separate video covering the structure factor in depth since I basically just sort of hand-waived over this in the two indexing videos. Thank you for the inspiration!