Different crystals have different symmetries and these can be read off from the structure factor. For example, a perfect single crystal with the symmetry called body-centred cubic (bcc) shows, when viewed from one angle, a structure factor with a set of sharp points including six arranged at the corner of a hexagon.
The structure factor above is of what some people call a nanocrystalline system, a set of small, ‘nano’ crystals — not one big one. One of these has bcc symmetry and it is mainly responsible, I think, for the kind of hexagonal arrangement of dark spots just about visible in the innermost ring.
There are two distinct rings in the image, and clearly two dark spots pretty much opposite each other in the innermost and darkest ring. But if you look a bit more closely in the first ring you can see four more kind-of double spots in a roughly symmetrical arrangement. I think these are partly from the hexagon of spots that bcc gives you and partly from another different crystal with a different symmetry that is also present.
Roughly speaking, we are about halfway between a single crystal that gives a set of symmetrically distributed points, and a very large number of randomly oriented crystals that gives you a set of concentric rings. Basically, if you have many many hexagons of points and all the hexagons are the same size but rotated, and then you superimpose them the points all blur into a ring. We have not one, not many, but a few crystals and so have a mixture of spots and rings.
This is not just pretty. It may well be that we can make cheap solar panels from systems with little crystals like the system shown above in reciprocal space.
Chance & Necessity 