Diffraction by small crystals with incomplete unit cells

X-ray crystallography is a method for determining three-dimensional images of materials arranged in regular arrays through the phenomenon of diffraction. These periodic arrays exist within structures of crystals and each period of this array is termed the unit cell. The recent invention of a new x-ray source offer novel ways of doing x-ray crystallography where very small crystals, only a few unit cells across, can be used. As a result of their larger surface-to-volume ratio, disorder on the surface of small crystals will have a larger impact on their diffraction than for large crystals. This edge-effect of crystals being terminated with partial segments of the whole unit cell, which we refer to as “partial unit cells,” are investigated via simulation and we propose a simple way to “grow” crystals in the computer based on a random-walk type construction. Diffraction patterns from an ensemble of crystals grown in this way with different unit cell contents and different partial unit cells on their surface is studied and the characteristics of the diffraction is discussed.