I am trying to understand the crystal structure of Molybdenum Disulfide (MoS2). In most of papers, people have used the term "Broken Inversion Symmetry" which I could not understand yet. It would be very helpful for me if someone explain this term as well as some basics about the crystal structure of MoS2 or share some relevant literature.
Thanks
The most stable form of MoS2 stacks layers such that there is an inversion center (space group: P 6₃/mmc), but it lies between the layers. That is, the inversion operation carries one layer into another, and vice-versa. However, there is no inversion center within the MoS2 layers (Mo has trigonal prismatic coordination, not octahedral, and there's no inversion center in a trigonal prism). you can get crystalographic data at the Inorganic Structural database (in Karlsruhe) - the free version of the interface will be sufficient to get a .cif file. A graphics program like "Crystalmaker" or "Diamond" will allow easy import of the .cif file. Anyway, there is no inversion center in trigonal prismatic single layers.
Dear Prof. T. Hughbanks,
Thanks for your nice answer and recommendation regarding crystallographic database.
Just an addition to Prof. Hughbanks,
you analyse the symmetry of a given layer by the concept of the layer group
https://en.wikipedia.org/wiki/Layer_group .
The layer group of the layers contained in the MoS2 polytypes is p(-6)m2 (where the brackets indicate the symmetry element given with respect to the non-periodic direction. This layer group lacks of a center of inversion. However, the space group of polytypes can contain a center of inversion: in between two pairs, which you can see if you look at a pair of layers stacked appropriately.
The layer group of CdCl2/CdI2 is p(-3)m1, and contains an inversion center. However, you can have polytypes in which the center of inversion within the layer gets lost due to the specific stacking.
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