Lattice and basis vectors for a NaCl structure I am supposed to obtain the selection rules of a NaCl lattice considering a rhombohedral set of lattice vectors but I am not getting any valid results. My guess is that I am not choosing the basis correctly.
I define my FCC lattice vectors as
$a_1=\frac{a}{2}(1,0,1)$, $a_2=\frac{a}{2}(-1,0,1)$ and $a_3=\frac{a}{2}(0,1,1)$ 
and my basis as
Na$(0,0,0)$ Cl$(\frac{1}{2},\frac{1}{2},\frac{1}{2})$ 
which results in no extinctions since
$f_{Na}+f_{Cl}e^{i\pi(h+k)}\neq0$
Is my choice of basis wrong and/or is it there something else I am not taking into account?
 A: You should ask this on chemistry forum.
If I remember it correctly, I think NaCl is a cubic lattice where each chlorine atom is surrounded by 6 sodium atoms at equal distance and vice versa. So with this information, we can start like:
The Na basis atom is at (0,0,0) and Cl basis atom is at (0.5,0.5,0.5) or vice versa. While you can reproduce the lattice with Cl at (0.5,0,0), that would mess up the primitive cell. The second basis point has to be inside the FCC unit. Of the 4 octahedral sides that can be the second basis point (3 of the edge half sites and the body center site), only the body center lies within the primitive unit FCC cell. Hope this helps.
A: I didn't realise that using a non-cubic set of vectors implies the interplanar distances $d_{hkl}$ are obviously given by a different expression. 
Since my vectors define a primitive cell, they won't result in any selection rules; in addition, NaCl doesn't have any new selection rules either due to the different form factors. However, the interplanar distances which relate to the Bragg reflexions are not given by
$d_{hkl}=\frac{a}{\sqrt{h^2+k^2+l^2}}$
but by another equation with a more complicated dependency on the Miller indices so that in the end the same values of $d_{hkl}$ are obtained.
The derivation of the needed $d_{hkl}$ is rather simple.
Thank you all for your help!
