= Solution
<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.
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