form factor
/ FORM FAK-ter /
An atom is not a hard pinpoint; its electrons form a soft, fuzzy cloud around the nucleus. When a wave scatters off that cloud, the different parts of the cloud send out wavelets that are slightly out of step with one another. The form factor captures how this fuzziness shapes a single atom's scattering — how strongly one atom deflects a wave, and how that strength changes with the scattering angle.
Precisely, the form factor is the scattering power of one atom as a function of scattering angle. For X-rays, which bounce off the electron cloud, it equals the total number of electrons when the wave is barely deflected (forward scattering), then falls off smoothly at larger angles because wavelets from opposite sides of the cloud begin to interfere destructively. A spread-out cloud falls off fast; a compact one falls off slowly. The form factor is, in essence, the cloud's shape translated into reciprocal space.
This matters because the form factor is the per-atom ingredient that, summed with phases across a repeat unit, builds the structure factor and hence the spot brightnesses. It explains why diffraction spots fade at high angles. An honest distinction: for X-rays the form factor mirrors the electron cloud and shrinks with angle, whereas neutrons scatter off the pinpoint nucleus, so their atomic form factor stays essentially flat with angle — a key reason the two probes complement each other.
Compare a heavy lead atom with a light carbon atom. Lead has dozens more electrons, so its form factor is much larger and its diffraction contribution far brighter — which is exactly why a few heavy atoms sprinkled into a protein crystal can be used as bright landmarks to help solve the whole structure.
Heavier atoms have larger form factors and scatter X-rays more strongly.
Do not confuse the single-atom form factor with the whole-cell structure factor. The form factor describes one atom's scattering; the structure factor adds up many atoms' form factors, each carrying the phase set by its position.