# How to identify a crystal structure by its x-ray reflection bragg angles?

How to identify a crystal structure by its x-ray reflection bragg angles?

Suppose we have a crystal sample to examine its crystal structure (e.g. SC, BCC, FCC, etc). What we can get from an X-ray diffraction experiment is the incidence beam wave vector $\vec{k}$, reflected wave vector $\vec{k}'$, and the bragg angles $\theta$.

I know what primitive cell is, what Wigner-Seitz cell is, reciprocal lattice, and how to derive scattering amplitude, and the diffraction condition $\Delta\vec{k}=\vec{G}$, structure form factor. But how can you determine the structure of the sample by x-ray diffraction experiment?

• You compare a model to reality. Apart from some possible degeneracies, if it fits, you got it. – mikuszefski Apr 15 '15 at 12:13
• Each crystal structure has different symmetries, a combination of the Bravais lattice and the unit cell, resulting in the 270 different point groups. These symmetries are then exhibited in the diffraction pattern in a deterministic way through the scattering amplitude and conditions. It is 'easy' for an experienced x-ray diffraction expert to determine the Bravais lattice symmetry. Complex unit cells make life harder, but it all follows from symmetry (which Wigner was really good at). – Jon Custer Apr 15 '15 at 15:36