Dear James Foadi ,

Concerning your question, I'll answer it from a general space group perspective, not strictly associated with one of them.

For a most general P2 (monoclinic), there are three space group sub-settings. The standard settings for the P2 space group, used by default are the B-unique axis (P 1 2 1), primitively centered (0,0,0). Also, there is the A-Unique (P 2 1 2) and the C-Unique (P 1 1 2) space group's long name. The fundamental differences are in the crystallographic operators:

Standard B-Unique: x,y,z, and -x, y,-z

A-Unique: x,y,z and x,-y,-z and so on..

It is even more complex for a more symmetric monoclinic space group as C2, the A, B, and C-Unique axis are associated with Cells 1,2, and 3.

I don't remember any manuscript concerning the detailed discussion. Nevertheless, it is full of details in the Table of Crystallography Vol. A.

Best regards,

WNM

I do not know which specific problem you want to solve. But there is some detail also available in https://scripts.iucr.org/cgi-bin/paper?sc5097.

Dear James Foadi ,

Here are some examples of crystal structures in A2/a and B2/b from the ICSD database.

A 1 2/a 1 -- CaAlSiO4F -- https://doi.org/10.1007/s00710-015-0393-3

A 1 1 2/a -- Li2CrCl4 -- https://doi.org/10.1016/0022-4596(88)90301-5

B 1 1 2/b -- SrNa2B5O8(OH)2(CO3)0.8 -- https://doi.org/10.1134/S1063774509010027

B 1 1 2/b -- YbTaO4 -- https://doi.org/10.1016/S0925-8388(02)00504-2

Best wishes

Most of the specific examples you'll find are inorganics. Here's an example of a molecular crystal in which an unconventional setting was used in order to make the twinning easier to comprehend and deal with:

Article Zero-obliquity twin lattice quasi-symmetry threefold twinnin...