In order to understand diffraction, we need to consider how our probe particle (an x-ray photon, electron, or neutron) interacts with an atom. When this quantum particle encounters an atom, it may or may not scatter from that atom. The probability of scattering depends on the type of particle, the type of atom it scatters from, and the energy (wavelength) of that particle. When a photon, electron, or neutron is scattered, there are a total of four different types of scattering that can occur. First of all, there are two modes for scattering with regard to energy exchange: elastic and inelastic. Secondly, since the scattering particle has a phase, it is possible for the phase of the particle to retain that phase, which is known as coherent scattering. Alternately, the phase can be randomized in the process of scattering, which is incoherent scattering. These are quantum-mechanical properties and don’t have direct analogs in the world we live in, but the best analogy I can make would be to consider scattering of a tennis ball by a tennis racket. Consider the speed of the tennis ball: Does it leave the racket with the same speed it had before? If the speed changes, the scattering is inelastic. From a physics perspective, in elastic scattering, the quantum particle leaves the atom with no interchange of energy and thus, it has exactly the same energy as it started with, though its direction is usually changed through an exchange of momentum. If the scattering is inelastic or quasi-elastic, the scattered particle transfers energy to (or from) the atom it scatters from. In most cases, the scattered particle loses energy and atoms in the sample receive energy from this process, but for scattering of thermal neutrons, which have energies comparable to atomic vibrational modes, for atoms can transfer energy to the scattering particle. In either case, the particle’s energy changes, which results in a wavelength change.
Absorption is the extreme case of inelastic scattering, where all of the probe particle’s energy is lost. Absorption of neutrons leads to neutron activation, where excited nuclear states are created, these may decay immediately or become new elements or isotopes. If the new isotope is radioactive, the half-life can be of any length, from tiny fractions of a second to millennia. With x-rays, photon absorption can be followed by emittance of a lowered energy photon (Compton scattering) or can involve an electronic resonance resulting in fluorescence. When x-ray scattering results in a net transfer of energy to the atom, this energy can cause ejection of an electron (ionization) or can cause localized heating, or both. Either can degrade the material, which is known as beam damage. X-ray and neutron absorption also cause biological damage to living tissue, which is why we must protect ourselves from any appreciable exposure to these phenomena. Note that we will be always exposed to some non-negligible levels of radiation. This is in part from natural sources, but also from very beneficial medical procedures. A less welcome contribution is from radioactive fallout due to past use of nuclear weapons and other forms of nuclear pollution.
To provide an analogy for coherent vs. incoherent scattering, consider the timing for the arrival of our tennis ball. If the ball bounces off the racket instantaneously, this is coherent scattering. The timing is unchanged. However, for incoherent scattering, consider what happens if the tennis ball spends some time on the racket before leaving. (Envision a Velcro wrapping on the racket?) At this point, we have lost track of the timing for our tennis ball. This matters because, considering wave-like interactions, the scattering from this particle will no longer be able to interact with other particles. From a physics perspective, in coherent scattering, the wavefunction of the incident particle is changed in a systematic way by the interaction with the atom. We describe this wavefunction as having a phase. In coherent scattering, the phase may be unchanged by the interaction with the atom, or it may be inverted. In contrast, with incoherent scattering, the phase of the quantum particle is randomized in the scattering event. In fact, the quantum world behaves with very different rules than the macroscopic one we live in, and the phase of a particle is best described as a complex quantity – complex meaning a special type of 2D vector having components in two different directions, where numbers can be written as \(z = x + iy\) where \(i=\sqrt {-1}\). Here \(x\) is called the real component and \(y\) the imaginary component. That the phase is a complex quantity, which will become important as we consider scattering at resonance edges for atoms.
All four combinations of the two types of scattering occur. For diffraction, we only want scattering that is elastic and coherent, but it is worthwhile to understand the other three combinations: the other scattering modes can provide different types of information, and these are utilized via a plethora of non-diffraction techniques such as XAFS, inelastic neutron scattering, EELS, and even prompt-neutron activation analysis, to name just a few from a long list. These other scattering/absorptive processes may degrade the quality of a diffraction experiment, in some cases significantly. As an example, for each element, there are edges where x-ray absorption increases dramatically. Above these edges, many of the incident x-rays are re-emitted at different wavelengths via fluorescence, which thus increases dramatically the background scattering coming from the sample, which reduces our ability to measure the diffraction signal precisely unless our x-ray detection system is able to filter this out. As another example, 1H (hydrogen as opposed to deuterium) scatters neutrons incoherently more than 100 times stronger than most atoms can scatter neutrons coherently. This means if a sample contains just a few atom percent 1H, (which corresponds to an even tinier fraction by weight/mass,) one will see the incoherent scattering as background, which again reduces the measurement signal-to-noise.