How to call ellipse packing structures?

Question

My research group and I are trying to figure out what is the correct terminology for two different packing structures of 2D ellipses. The two structures are displayed below as Structure A and Structure B. The goal is to be able to distinguish the two cases with meaningful descriptions/names/classifications when referring to them.

If we don't find a precise name for the 2D structures, can we identify two different classes of structures (hexagonal vs. centered rectangular vs. triclinic, etc.)? Or maybe the equivalent 3D nomenclature could work too, though we don't know the arrangements of layers below. Or if we can at least name the planes in analogy to e.g., fcc(111) and bcc(110) planes that could work too. In the literature I only find analogies to liquid crystals, but I find this vague and in my opinion it's more of a crystal than a liquid crystal (at least for Structure B).

If it helps, I notice that when compressed along the x-axis, both packing arrangements result in the same hexagonal packing of circles, just rotated. This makes me think that both structures belong to the same hexagonal-based family of structures, but maybe for ellipses that is not the correct way to think about it and it becomes something entirely different.

Finally, I will mention that we are actually working with colloidal nanocrystals that are more cylindrical in shape, so the cross-section is more like a rectangle. I am choosing to talk about ellipses here because I am guessing it is more general.

Thanks!

Answer 1

I'm not aware of any specific terminology, but it makes sense to me to consider both of these as hexagonal configurations of hard-core ellipses. Reversing your compression operation, they can be characterized by deforming hexagonal lattices of disks as described in a recent paper S. Wagner, G. Kahl, R. Melnyk, A. Baumketner: "On the lattice ground state of densely packed hard ellipses", J. Chem. Phys. 160, 151101 (2024) [arXiv link]. They describe how this allows parametrizing a family of configurations by a rotational angle and a parameter describing the packing.