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How do I know if the reconstruction in the picture is a 2x2 reconstruction or not?

                                   crystallography

I believe that this corresponds to a 2x2 reconstruction because there's an even horizontal and vertical distance between the half-order and the full-order points in the corners of the pattern but I don't really understand how this is any different from a 4x4 or so.

On the Wikipedia page on LEED the following image is shown, representing the superposition of two different patterns, the 2x1, and the 1x2 patterns. These look identical to me apart from the direction of the drawn rectangle which thus far I have presumed to be a choice of the individual.

                                      enter image description here

Can these projections also indicate if such a surface is faceted? If so, how can this be deduced?

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  • $\begingroup$ I cant help answer, but I can point out your interpretation of the diagram from wikipedia is probably correct. They are the same, but its showing that you may have domains aligned differently, which superimpose to give the pattern in LEED. I think we have a few people that know LEED better than me around here though $\endgroup$
    – Tristan Maxson
    Jan 18, 2021 at 15:54
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    $\begingroup$ Hello Nike, I didn't find an answer to the question, but it is indeed no longer a subject of study of mine. Nonetheless, it has some votes, and I wonder if perhaps that means that it is a broad question that others are keen on knowing and therefore should not just be considered an abandoned question. It is completely up to you of course, I hope this question helps others by being answered of course. $\endgroup$
    – user7077252
    Sep 6, 2021 at 15:38
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    $\begingroup$ @user7077252 I didn't see your reply to my comment! Without pinging me with the @ symbol, I won't get a notification that you replied. I do see the benefits of keeping this open, but also there's benefits of closing it, especially if this is no longer a subject of yours: specifically, the fewer questions we have in our unanswered queue, the more likely people can find questions that they can answer. It looks unlikely that this question will get an answer any time soon, but if someone does come along and wants to write an answer, they can comment and we'll reopen it! $\endgroup$
    – Nike Dattani
    Jan 13 at 0:45
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    $\begingroup$ @Tyberius Can someone please reopen, I'd like to answer the question. The question itself seems alright, it does not lack details or clarity. $\endgroup$
    – PhilipPirrip
    Mar 26 at 13:30
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    $\begingroup$ @PhilipPirrip the question is now reopened. I agree the close reason was a bit misleading in this case. We tend to close questions with this reason when the OP hasn't responded to requests for clarification, but we also occasionally use it to for questions where the OP seems to have disappeared or has stated a lack of further interest. This is so we can more easily track which ones of our unanswered questions seem answerable and have someone actively seeking an answer. This has been a long standing unanswered question, so I think the community will be glad to see an answer. $\endgroup$
    – Tyberius ♦
    Mar 26 at 14:07

1 Answer 1

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Start by constructing 1×1 and 2×2 reciprocal space lattices; the latter case has the real space lattice constant twice as big, so its reciprocal lattice unit cell will be half the size, and square. The 1×2 structure is rectangular with a=1 and b=2, its reciprocal lattice has a* ~ 1 and b* ~ ½. LEED diffraction spots for 1×2 are at the vertices of (a*,b*) rectangles, and nothing in between. It has to be an incoherent sum of the two images from different domains of 1×2 and 2×1 superstructures (green and orange spots in the attached figure) that gives you the pattern in question. Original 1×1 structure, 2x2 structure, and 1×2, 2x1 structures superimposed (incoherently)

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  • $\begingroup$ Welcome to Matter Modeling! There are several reasons that a given set of LEED spots can be invisible in an image There are "missing LEED spots" due to certain symmetries within the unit cell which will be present at all energies, and there are always nulls due to destructive interference at some energies. I think the only way to say it's definitely 1 x 2 and rule out 2 x 2 is to measure a large range of closely spaced energies and show that no (1/2, 1/2) spot ever appears. (e.g. here although zero has been suppressed in this image) $\endgroup$
    – uhoh
    Mar 26 at 21:59
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    $\begingroup$ @uhoh Sure, there are many possibilities that need to be investigated but the 1×2 + 2×1 domain combination is what's most often encountered in practice. If at some electron energy there were (½, ½) points present, I'm sure that image would be shown instead. $\endgroup$
    – PhilipPirrip
    Mar 28 at 8:52

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