Fourier Transforms and the Phase Problem
At the end of my inorganic course, I teach several "cool" spectroscopic techniques that inorganic chemists use. These techniques are discussed within the context of bioinorganic chemistry, and I typically cover EXAFS/XANES, X-ray crystallography, EPR and Mössbauer.
This website introduces (or reviews) Fourier Transforms in a neat graphical way, but most importantly, illustrates the phase problem. Given the intensities from your crystal and the phases from your model, the phases are more important! Which is too bad, as we don't have ready access to that information.