X-Ray Diffraction in Crystals: Exploring Scattering & Interference

[kelvin490]

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?

 

[sophiecentaur]

to consider the atoms absorb radiation and scatter it

You are not quite putting that in the right way. If a photon were 'absorbed' by an atom, it would be re-emitted at some random time later. It could not then be part of a coherent beam of Xrays and would not therefore produce a maximum in a particular direction. Atoms in a lattice behave in a unified way and affect incoming X rays as a group, arranged in a structure The alternative model is the classical wave interference / diffraction model. There will be a 'photon explanation' but it would not be straightforward and would have to involve loads of atoms and not just one. (The standing up in a hammock explanation.)

 

[kelvin490]

If a photon were 'absorbed' by an atom, it would be re-emitted at some random time later. It could not then be part of a coherent beam of Xrays and would not therefore produce a maximum in a particular direction.

Is scattering a process of absorption and re-emission of radiation? If not what is the difference? In some books they tend to explain the fact that incident angle equals to reflected angle by considering the re-emission of light from atom and considering the interference, only when reflected angle equals incident angle constructive interference occurs. This makes me confused about scattering and reflection (and other processes).

 

[sophiecentaur]

Is scattering a process of absorption and re-emission of radiation? If not what is the difference? In some books they tend to explain the fact that incident angle equals to reflected angle by considering the re-emission of light from atom and considering the interference, only when reflected angle equals incident angle constructive interference occurs. This makes me confused about scattering and reflection (and other processes).

Yes, that is confusing when you consider the energy transition in one atom would need to be hf per photon and it would have to be on a photon by photon - atom by atom basis. That would produce a diffraction pattern with no form because of the random element in the phases of all the re radiated waves. To produce specular reflection (or refraction) requires that all the scattering centres interact synchronously with the incident wave. So, if you want to talk 'photons' the reaction between a photon and a structure has to be with the structure as a whole and the structure won't actually absorb any energy - the photon energy is just stored temporarily as in a capacitor (reactive) rather than as in a battery (resistive). Absorption and re-emission would, imo, be terms used for what happens when em passes through a diffuse gas where all the atoms behave independently and where the re-emitted energy radiates in all directions and incoherently.
If you stick to the wave model then you have an incident wave that interacts with the whole lattice (/mirror / glass/ whatever) and will produce a diffraction pattern according to the geometry of the situation. For reflection by a plane in a crystal, the phases have to be right, both for the incident and for the reflected wave (The Bragg formula). When the angles are wrong, the wave power must still survive (conservation) but the resulting wavefront would have no identifiable peaks.