Space Group Reflection Conditions
What a space group extinguishes: the integral, zonal and serial reflection conditions of any of the 230 groups, in any of the settings the International Tables list. Ask about one reflection and the page names the symmetry operation that removes it.
- You supply
- A space group number or symbol. Non-standard settings are included, so P21/n, Pbnm and I2/a answer for themselves rather than being redirected to a sibling with different conditions. A reflection is optional.
- Reading it
- Absences narrow the space group and rarely determine it: the 230 groups produce only 80 distinct patterns of absence, and 37 of them extinguish nothing at all. When your conditions fit more than one group, the page names the others.
Worked examples: P21/c – the commonest space group there is · P21/n – the same group, a different setting · P43212 – screw axes and nothing else · R3c – rhombohedral, in hexagonal axes · Fd3m – diamond, and (2 0 0) missing
Input
Conditions belong to a setting, not to a space group number. Pnma, Pbnm and Pmcn are one space group with its axes labelled three ways, and the three tables differ: the mirror that empties hk0 in one of them empties 0kl in another. Every setting in the International Tables is here with its own operations, so P21/n and P21/a answer for themselves.
Reflection conditions
Enter a space group above. There are 230 of them, in 497 settings, and every setting has its own table.
Reading down the table: integral conditions come from the lattice centring and apply to every hkl; zonal conditions come from glide planes and empty one plane of reciprocal space; serial conditions come from screw axes and empty one row. The same three kinds are named under the stick pattern on the HKL page, which applies the integral ones only.