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The image in this question turned out to probably be wrong, but it still makes me wonder. Are there examples of crystals where the atoms within a unit cell can have two (or more) different configurations or orientations who's energies are so close that a sample crystal at room temperature could have a random but static mixture of the two?

With sufficiently large organic molecules (e.g. proteins) this could be true and possibly even common, but I'd like to know about a simple example with a small number of atoms in the unit cell. It might be produced by rapid cooling or crystallization from solution in unusual conditions, and it might be detectable (at least in some cases) by a slight broadening in high resolution X-ray diffraction peaks. (sort of a solid-state version of Raleigh scattering perhaps?)

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    $\begingroup$ Exact position of each and every atom in different unit cell would slightly deviate from each other due to thermal motion — that's why ORTEP diagrams are preferred by crystallographers. Also, there are modulated crystal structures. $\endgroup$
    – andselisk ♦
    Jul 23, 2019 at 7:05
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    $\begingroup$ @andselisk the modulated crystal structures seems along the line of what I was thinking of; I've updated to "random but static" to exclude thermal broadening. Thanks for these! $\endgroup$
    – uhoh
    Jul 23, 2019 at 7:07
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    $\begingroup$ @uhoh Do you refer to something like in the «answer»? $\endgroup$
    – Buttonwood
    Jul 23, 2019 at 13:40
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    $\begingroup$ Partial disorder is a pretty common thing both in organics and inorganics. $\endgroup$
    – Ivan Neretin
    Jul 23, 2019 at 13:42
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    $\begingroup$ @IvanNeretin While I agree with you the question of «randomness» was not clear for me. If random in space but fixed, or mobile (pedal motions), both may of course contribute to diffuse scattering. At least on first look neither of the two picks revealed such. Their site occupations was refined in the models. $\endgroup$
    – Buttonwood
    Jul 23, 2019 at 14:19

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Possibly retracted soon, because I'm not aware how to include a picture in a comment to clarity your question. Do you mean instances like the following, where sites seemingly are occupied by two atoms simultanously -- as in analogues of Prussian blue -- just because the model deposit in the .cif is the average of the unit cells' content?

enter image description here

(Chen et al. in Angewandte Chemie, 129, June 2017, 9151-9156, doi 10.1002/ange.201702955)

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  • $\begingroup$ No problem as far as I'm concerned; if done with care, answer posts like this can evolve quickly into the correct answer. I don't think I mean this. I am asking about a real crystal fixed rather than software artifact. One hypothetical example would be a unit cell which is almost but not quite symmetric under a 180 degree rotation. So it can fit on the lattice in two ways; right-side-up and up-side-down, with only a tiny difference in energy, say of order $k_B T$. This way maybe 1/3 of them are up-side-down, randomly. But once the crystal is built, they are stable ("static") and won't flip. $\endgroup$
    – uhoh
    Jul 23, 2019 at 15:14
  • $\begingroup$ That's not the only way it could happen, it's just meant as an illustrative example. btw it's late where I am, so I might be off line for 6-8 hours... $\endgroup$
    – uhoh
    Jul 23, 2019 at 15:15

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