I am looking at the difference between the Miller indices and Laue indices in crystal structures. I will denote the former by $hkl$ and the latter by $HKL$.
I understand that $hkl$ must be coprime integers, however, I have also heard that $hkl$ represent families of lattice planes. For the case of e.g. the bcc lattice these seem contradictory since $(200)$ rather then $(100)$ forms faimiles of lattice planes.
For $HKL$ it appears that they to must be integers (but not necessarily coprime). These are the indices used to determine if we have a systematic absence or not. But this seems to be assuming we only get diffraction peaks from families of planes which are families of lattice planes - yet as far as I can tell you will get a diffraction peak from the planes $(0.5 \ \ 0.5\ \ 0.5)$ .
Please can someone therefore explain to me the difference, what values they can take and how they can be defined?