Diffraction is a quantum phenomenon that requires a particle/wave that has a wavelength that is similar in magnitude to the features that one wants to detect. For diffraction from atoms, this means a wavelength similar to the distance between atoms (Ãngstroms) or less. Diffraction measurements are routinely done with x-rays (photons) or neutrons, but not only with these. Increasingly, crystallography is being done with electrons, traditionally with an electron microscope, but some newer instruments are optimized specifically for electron diffraction. Scattering of alpha particles or neutral atoms is sometimes performed – but not for crystallography, e.g. structural information on the arrangement of atoms. Also, though not considered here, muon scattering can be valuable for magnetic studies. I will use the term quantum particles to discuss features that x-rays, neutrons, and electrons all share, but it is worth noting that for diffraction studies, energies needed for neutrons, x-rays and electrons are typically mili-eV, kilo-eV and mega-eV, respectively, to generate wavelengths that are on the order of 1 Å.
One of the most fundamental concepts in scattering is what physicists call momentum transfer: a measure of the deflection of the diffracted quantum particle from that of the impinging beam. This angle is for historical reasons described as \(2\theta \) and is usually measured in degrees. Thus, forward scattering, where the particle does not have its scattering direction changed, will have a \(2\theta \) value of zero. Complete backscattering, where the particle is scattered back towards the source will have \(2\theta =180^\circ \). The \(2\theta \) value itself is not useful without knowing the wavelength used. Further, an important class of diffraction measurements is done with energy-dispersive diffraction, where instead of measuring scattering at a fixed wavelength while varying the angle, the measurements are made at a fixed scattering angle as a function of wavelength. Thus, it is best to get away from angular values and use an absolute term that removes the wavelength dependence. Traditionally, crystallographers have used the quantity \(\sin \theta /\lambda \) for this but that sees little use, Physicists use a related quantity Q, where \(Q = 4 \pi \sin \theta /\lambda \). I am a chemist by training and self-identify as a crystallographer, but I prefer Q over \(\sin \theta /\lambda \) due to its more wide-spread acceptance.