I'm trying to make a diagram of the Pncn space group.
Firstly, I know that this space group belongs to the orthorhombic system and derives from the point group (2/m 2/m 2/m).
Therefore, although the abbreviated notation does not appear, this spatial group also has binary axes (which may be normal or helical).
We also know that the multiplicity of the space group is 8. That is, there are 8 positions equivalent to (x,y,z). Next, we try to determine them:
- By the translation of the primitive lattice: (x,y,z)
- As the point group 2/m 2/m 2/m/m is centrosymmetric: (-x,-y,-z)
- For the plane type "n" perpendicular to the axis "a": (-x, 1/2+y, 1/2+z)
- By the plane type "c" perpendicular to the axis "b": (x, -y, 1/2+z)
- By the plane type "n" perpendicular to the "c" axis: (1/2+x, 1/2+y, -z)
If they were correct, I'd still be missing three positions. These three positions are given by the binary axes. Here I have a serious problem because I don't know if this binary axis is normal ($2$) or helical ($2_1$).
After that, I realise that some of the equivalent positions do not coincide with those I have deduced. For example, the two of the sliding planes of type "n".
I also have mistakes that I can't explain or understand. These are the following:
a) Why is one of the binaries at 1/4? I've searched the Internet and I can't find any explanation that helps me much.
b) Why is the plane type "n" displaced? I would have placed it on the line of axis "b".