Diffraction from a Crystal

Diffraction from an entire crystal should now be readily quantified.  Start with the normal scattering diagram using a lattice point as an origin and the tip of an Rmn vector as the scatterer (point A).  The scattered radiation will be observed at P which is located a distance R away from the scattering center so that R>>|Rmn|.

The observed scattering, y, from the origin and point A will be:

This is then the scattering for one atom in the crystal.  But there are m unit cells and n atoms per unit cell to consider.

The scattering for all vectors Rm (all M unit cells) is