# Elastic scattering of x rays in 3D: the principle for XRD analysis

I have some trouble visualising scattering of x-rays in 3D, since all textbooks and examples present it in 2D. Under I will share some reflections (no pun intended) about the elastic scattering of x rays, and the diffraction effects observed, which is the basis of XRD analysis. Here you see a figure of two crystal planes, separated by the distance d. Two parallel and in-phase x-rays hit an atom in the planes. The scattering cones are drawn. The darker area represents those scattering directions going into the crystal itself, and thus not detectable and uninteresting for XRD analysis. The light area are those scattered rays exiting the crystal.

Thinking in three dimensions is different from thinking in one dimension. To achieve constructive interference, the rays must travel in the same direction and also be superimposed on each other. Even though the scattered rays ' angle is, say, 45 degrees, they may not travel in the same direction.

However, if Bragg's law is valid for 45 degrees, all rays of 45 degrees scattering angle will interfere constructively. So we would get a diffraction cone of increased intensity. However, we cannot detect the whole diffraction cone, partly because some of the rays travel into the crystal, and partly because the detector surface area only covers parts of the diffraction cone; we would measure a curved segment of the diffraction cone. This is called the Debye-Scherrer ring, yes?

Though we get constructive interference in all directions of 45 degrees scattering angle, the scattering angle itself is random. This means there are scattered rays which do not undergo constructive interference in all directions, regardless of angle (though smaller angles are more probable). So, in an ocean of random scattering, we have diffraction cones of much greater intensity, since Bragg's law is fulfilled.

Is this a correct assessment of the XRD situation?