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I'm confused about the crystal system of MoS2.

In the case of the monolayer MoS2, it has 3-fold rotation symmetry when viewed from the top of its unit cell (c-axis). Even in the case of bulk (AB stacking) MoS2, it has only 3-fold rotation symmetry from the same direction. So, I expected that it must be the trigonal system. However, 'Materials Projects' doesn't seem the trigonal system.

Here are some database from 'Material Projects'

List of MoS2

https://materialsproject.org/#search/materials/{%22reduced_cell_formula%22%3A%22MoS2%22}

Bulk MoS2

https://materialsproject.org/materials/mp-2815/

Bilayer MoS2

https://materialsproject.org/materials/mp-1025874/

and so on.

Some of them are the trigonal system, and the others are the hexagonal system. I studied the minimum symmetries determine the crystal system, or that is a misconception. But now, it might be wrong by the web data.

Which one is correct and if both are correct, how can I check the 6-fold rotation symmetry for the hexagonal system?

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enter image description here

This is the figure for the HCP structure. Its symmetry along the c-axis can be called 3/m or bar(6).

enter image description here

This view is the bulk MoS2 along c-axis. In the unit cell, it has two layers of MoS2. However, it has 6/mmm point group. How does this happend?... https://materialsproject.org/materials/mp-1018809/#

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Naturally occurring molybdenum disulfide can occur in either of two crystal systems, hexagonal or "trigonal"; the latter is also known as rhombohedral (see here).

In both cases the coordination geometry around molybdenum has only threefold rotational symmetry, but in the hexagonal form the crystal will add a center of symmetry to become hexagonal. Such a conversion is seen in other cases such as hexagonal close-packed metals like magnesium and zinc, which actually have only threefold symmetry about any axis perpendicular to the basal plane and passing through an atom, yet the Crystal's are hexagonal. In general, when you have a unit cell with $D_{3h}$ symmetry -- a mirror plane perpendicular to the threefold exis -- you will get hexagonal crystals in both molybdenum disulfide and hexagonal close-packed metals.

The rhombohedral crystal, with a different arrangement of mirror planes (the point group symmetry is $D_{3d}$ instead of $D_{3h}$, and $D_{3d}$ has no mirror plane perpendicular to the threefold axis), has the required center of symmetry without going from threefold to sixfold rotational symmetry.

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  • $\begingroup$ More precisely, let's see hcp structure. Its point group is 6/mmm or D_6h. By the way, can you think space or point group as Hermann–Mauguin notation because I prefer this? So, 6/m in hexagonal, it means it has 6/m symmetry along the c-axis. However, when I rotated six times and reflected atoms, I couldn't see the overlappings. Where should I insert the mirror perpendicular to the c-axis? $\endgroup$ – Noki Lee Oct 17 '18 at 12:56
  • $\begingroup$ Any mirror perpendicular to the threefold axis makes the symmetry you need to get a hexagonal crystal. You have to look for it. In the hcp case it would be along the basal plane. In molybdenum disulfide try a plane of molybdenum atoms. $\endgroup$ – Oscar Lanzi Oct 17 '18 at 15:56
  • $\begingroup$ I've found the figure for the symmetry along the c-axis and posted it. I should change the word I mentioned. The symmetry of HCP structure along the c-axis is one mirror after 3-fold rotation or inversion with 6-fold rotation one after another (bar(6)m2). en.wikipedia.org/wiki/Crystallographic_point_group So, bar(6) means anyway it has six-rotation. Andhttps://en.wikipedia.org/wiki/Crystal_system $\endgroup$ – Noki Lee Oct 18 '18 at 1:45
  • $\begingroup$ And, then I can understand. en.wikipedia.org/wiki/Crystal_system But, one case! Can you check this structure? materialsproject.org/materials/mp-1018809/# This is bulk MoS2. And Materials Project noted this has 6/mmm. I posted this too. $\endgroup$ – Noki Lee Oct 18 '18 at 2:06

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