# x-ray diffraction of crystals

In explaining x-ray diffraction of crystals, usually the approach is to consider the atoms absorb radiation and scatter it, at some angles constructive interference occur and bright spots can be observed. It seems that it is different from the diffraction of slits or gratings because in these cases light or radiation go through a small space or aperture but in crystal it seems it is an absorption-->scatter (or reflection) --> interference process. Therefore I wonder whether there is actually some differences in their nature.

Also I wonder whether all the reflection, refraction and diffraction process can be explained in terms of scattering and interference?

## 2 Answers

x-ray diffraction is not caused by atoms absorbing radiation.

x-ray diffraction and diffraction by gratings do have an underlying mechanism in common.

In both cases, when two incoming rays of waves (x-rays or light waves, in the case of optical diffraction grating) both rays bounce of the crystal or grating, they have travelled a different distance, say $\Delta L$. If that difference is a whole number of wave lengths $\lambda$ then these waves will show positive reinforcing interference. So for $\Delta L=n\lambda$ (with $n$ an integer) we get ‘bright’ areas on our detector. For other values of $\Delta L$ we get negative, reducing interference and thus ‘dark’ areas on our detector.

In the case of x-ray diffraction, both rays (1 and 2, see schematic) bounce of different crystal planes and the distance between two crystal planes $D$, as well as the angle of incidence $\alpha$ will determine $\Delta L$.

In the case of optical reflective diffraction by a grating, both rays (1 and 2, see schematic) bounce of different reflective areas of the grating and the distance between the reflective areas $D$, as well as the angles of incidence $\alpha$ and reflection $\beta$ will determine $\Delta L$.

So both types of diffraction have similar causes but the overall phenomena are not the same either.

• thanks for answering. In the two figures you have shown it seems that they are actually reflection and interference. Whay they are termed as "diffraction"? – Kelvin S Aug 27 '15 at 5:20
• In a nutshell: because reflection followed by interference of the reflected waves is what diffraction is. Not all forms of diffraction require reflection though and not all forms of reflection lead to interference (diffraction). But you asked about x-ray diffraction and there reflection plays a part in the phenomenon. – Gert Aug 27 '15 at 13:17

A crystalline solid is more than a bunch of atoms arranged nicely, because the atoms are "feeling" each other.

I don't see scattering at crystals as the interference of absorption/emission of each atom separately (and I don't think that's the usual approach either), but rather as reflection at planes determined by the crystal structure as a whole.

So, Yes, it is different from a grating.

To fully characterize the processes you mentioned, you also need to know the energy band structure.