Past exam of the frontiers of experimental condensed matter physics course of the University of Cambridge / 2013 / Paper 1 / 1 / a

X-ray diffraction arises predominantly from electromagnetic scattering by the electronic charge distribution. For elastic scattering, contributions from different unit cells interfere constructively at a reciprocal lattice vector, while the unit-cell structure factor weights the different atoms and their positions. The atomic X-ray scattering factor generally decreases with increasing momentum transfer because an extended electron cloud scatters out of phase with itself. Heavy atoms often scatter more strongly, making a light atom difficult to locate beside a heavy one; near an absorption edge, anomalous dispersion changes the contrast and can provide additional chemical sensitivity.

In neutron diffraction, the strong interaction with atomic nuclei supplies a short-range nuclear scattering amplitude. Its coherent scattering length depends on isotope and does not vary monotonically with atomic number; isotope substitution can therefore give useful contrast, and some light elements can be prominent. A neutron's magnetic moment also couples to magnetic moments in a specimen, so magnetic diffraction measures ordered spin structures. Absorption and incoherent scattering depend strongly on isotope as well. The nuclear scattering length is approximately independent of momentum transfer in the usual thermal-neutron regime, whereas magnetic scattering has a form factor reflecting the electronic magnetization distribution.

Electron diffraction probes the electrostatic potential of both nuclei and electrons. The electron's charge makes scattering strong, allowing thin specimens or surfaces to be studied with intense signals. Strong interaction also makes multiple, dynamical scattering more important, so electron diffraction intensities often cannot be interpreted as a simple single-scattering structure factor squared. Transmission geometry needs electron-transparent material; reflected low-energy electrons provide a surface-sensitive geometry. All three methods use phase-sensitive interference to reveal periodic structure, but their scattering interactions, penetration, sample requirements and contrast differ.