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I'm writing a program and need a way to identify and enumerate the number of possible distinct crystallographic domains when depositing one 2D lattice on top of another.

I've posed this as a question in Math SE: Number of possible rotational domains of one 2D lattice on top of another? but possibly because I lack the proper "math words" it might not be receiving views by the users who can answer it.

I'm sure that this is a solved problem for mathematicians, and for crystallographers!

Questions:

  1. Would this question be on-topic here if suitably rewritten for this site?
  2. If so, might it be likely to receive an answer?

Snippet from the linked question:

Square and hexagonal lattices shown at 0, 30 and 60 degrees:

square and hexagonal lattices shown at 0, 30 and 60 degrees

Square and hexagonal lattices shown at +/-10 degrees:

square and hexagonal lattices shown at +/-10 degrees

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    $\begingroup$ I suspect your lattices question is better on Mathematics.SE, but I appreciate it may not be easy to attract answerers without the right keywords. Have you looked at en.wikipedia.org/wiki/Wallpaper_group ? $\endgroup$
    – PM 2Ring
    Mar 3 '20 at 11:48
  • $\begingroup$ @PM2Ring Thanks! Those are mentioned there in the question, and at the end I also link to my previous question about them. Any surface scientist who looks at how adatoms on crystal surfaces form lattices of their own will understand this problem, and some of them will have seen the answer at some point in their career. However, 1) whether we call that Physics or Chemistry is a tossup, and 2) whether people active in those fields also bother to read SE questions regularly is also in question. $\endgroup$
    – uhoh
    Mar 3 '20 at 12:07
  • $\begingroup$ @PM2Ring just fyi what I'm after is in Chapter 6 of Crystallography and Surface Structure by Klaus Hermann, 2nd edition. It's too much for me to digest all at once and I want to start with only the simplest symmetry groups rather than do everything at once. If only I could be a planarian and just eat chapter 6 to learn it. $\endgroup$
    – uhoh
    Mar 4 '20 at 10:30
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To answer this I would look at the core of your question:

Question: For pairs of 2D lattices each with either a 2, 3, 4 or 6-fold rotational symmetry (ten possible pairs in total), how can I calculate the number of possible ways I can uniquely configure them with a given angle who's absolute value is $\theta$.

OK, this is a perfectly good premise for a question. In order to turn it into a good question for this site, I think you'd need to describe what you've tried so far, otherwise it would trigger my mental "insufficient effort" warning. For example, let us know about any literature searches or web searches you've done, whether you consulted any relevant textbooks, or if you tried any calculations. The partial summary table you presented is a start but I'd rather see something going a little further than that - I mean, evidently you didn't have any trouble filling out part of the table, so what stops you from going all the way and filling out the remaining cells?

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  • $\begingroup$ It's hard for me to defend a question I haven't written yet, but I appreciate the advice. To my question "Would this question be on-topic here if suitably rewritten for this site?" is a boolean response possible? $\endgroup$
    – uhoh
    Mar 3 '20 at 8:43
  • $\begingroup$ As far as the table in the other question, those are kinda self-evident to me, which is a fancy way to say "I think so". I worked one example graphically to make it clearer. What I've tried is brute force guessing because I can't think of a way to systematize this and I'm not 100% sure the ones I've entered are right because I don't know how to exhaustively test them. I'll have to figure out how to say that "I just guessed" in such a way that it sounds like I've tried hard enough. This site has a stronger presumption of laziness than most other SE sites, but that's probably for cause. $\endgroup$
    – uhoh
    Mar 3 '20 at 8:49
  • $\begingroup$ just fyi what I'm after is in Chapter 6 of Crystallography and Surface Structure by Klaus Hermann, 2nd edition. It's too much for me to digest all at once and I want to start with only the simplest symmetry groups rather than do everything at once. $\endgroup$
    – uhoh
    Mar 4 '20 at 10:30
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    $\begingroup$ I don't think you need to get too fancy about showing your effort. If you mention what you guessed and found not to work, and mention the books or resources you checked without finding anything helpful, that might be good enough. $\endgroup$
    – David Z
    Mar 4 '20 at 10:49
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In my (not very strong) opinion, the question as it stands reads like a homework-and-exercise question of "how do I calculate this?", but at a much higher level than most questions like that on PSE. I also think it was smart to post on MathSE, as the heart of your question really is more mathematical than physical. So my first instinct is that I would VTC for one of those two reasons (probably the math reason).

However, you seem to think that this question might have an answer in the crystallography literature. At that point you might be able to frame your question as more of a reference request, which is on topic here. If you were to post on PSE, then that might be the way to go. Especially given that (hopefully) the math will be covered on MathSE already.

Of course, I'm not a crystallographer, and I'm sure others would disagree with my categorization of your question. I think I tend to be more strict about these things than other users are. But we have the discussion tag here, so let's have a discussion :) I certainly don't think my opinion is the only one that matters, or that it is even a "correct opinion". But if you do decide to post, the worst that can happen is that the question gets migrated or closed. It looks like you know how to write coherent posts, so I doubt you would get down voted even if the question did get closed.

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  • $\begingroup$ I definitely need to know how to calculate this, and I definitely don't know how. I've been struggling for days to figure out a way to do it correctly and systematically and I can't think of one. That seems like an excellent SE question if it can be worded so as not to look like a "homework-and-exercise question". If it ends up being moved here then I'll have to work hard to figure out how to do that. Thanks! $\endgroup$
    – uhoh
    Mar 3 '20 at 8:53

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