As we saw before, neutron or x-ray quanta can interact with the sample in several ways. Alternatively, they may also not be scattered at all and go straight through the sample unperturbed. When quanta are scattered incoherently or inelastically or are captured by the sample, they can no longer contribute to the diffraction signal. Diffraction intensities are computed ignoring this effect, but when samples have high probabilities for neutron or x-ray absorption or non-diffraction scattering, the fraction of lost quanta will depend on the scattering geometry, the wavelength and the diffraction angle. If a significant fraction of the quanta are absorbed or are otherwise scattered by non-diffraction events, a correction factor may be needed to accurately match the idealized diffraction intensities to what is actually observed. This is known as an absorption correction, but it should be noted that non-diffraction scattering as well as actual absorption is corrected for in this factor. To evaluate the effects of absorption, GSAS-II includes a program (also in the Calculate menu) called Absorb where a chemical formula is supplied along with a sample size and density or packing fraction (since powder samples usually are not fully dense) and the value of \(\mu r\) is computed as function of wavelength. Absorption corrections are discussed in more depth in §13.1.7.
Another assumption that is made when computing diffraction intensities is that the probe quanta are only scattered once and only a small fraction are scattered. In an effect called multiple scattering, it is possible for a scattered quantum to be scattered again before it leaves the sample. This occurs most significantly for intense reflections in large single crystals and this effect is called primary extinction. This effect is greatest when crystals have very large domains, without defects to disrupt ordering. To compute primary extinction quantitatively, one must use a higher level of scattering theory than will be discussed here, called dynamical diffraction. Note that primary extinction can be quite significant in electron diffraction because with the high electron energies used, only small domains within a sample are probed and are much more likely to have “perfect” ordering on these distance scales.
Another effect can occur, similar to absorption, if significant fraction of the incident quanta are diffracted before many of the particles penetrate into the sample. The result of this is that fewer quanta are available to be scattered than will be expected. This is known as secondary extinction.
Both primary and secondary extinction are most likely to be observed with large and highly perfect crystals. More commonly, so-called single crystals are actually constructed of relatively small domains due to defects and these domains have small misalignments with each other. Such a crystal is known as ideally mosaic. The small domain sizes disrupt the dynamical scattering needed to cause primary extinction and the small misalignments between domains prevent secondary extinction. Single-crystal experiments will sometimes benefit if a crystal is thermally shocked to induce mosaicity. However, extinction is quite rare in powder diffraction because when crystallite sizes are larger than a few microns, sample grinding should be used. GSAS-II does provide correction terms for extinction that can be used for both single-crystal and powder diffraction and with both x-rays and neutron. While rarely needed, these do work well for materials with very large crystallite sizes. Note that laboratory powder diffraction experiments with such large-grain materials are likely to be inaccurate, due to poor particle counting statistics, but this is less likely to be a problem with high-energy x-rays and neutrons.