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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?

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  • $\begingroup$ You compare a model to reality. Apart from some possible degeneracies, if it fits, you got it. $\endgroup$ – mikuszefski Apr 15 '15 at 12:13
  • $\begingroup$ 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). $\endgroup$ – Jon Custer Apr 15 '15 at 15:36
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With the x-ray diffraction and the Bragg's equation '2dsint=n^ you can get the inter planer spacing 'd' which can also lead you to get the lattice constant which is a vital property of a crystal structure.

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