Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
orderMASmagic angle spinningMDmolecular dynamicsMQmultiple quantumNBOnon‐bridging oxygenNMRnuclear magnetic resonanceNRIXSnon‐resonant inelastic X‐ray scatteringPDFpair distribution functionPSFpartial structure factorQSquadrupole splittingRDFradial distribution functionRFradio frequencyRMCreverse Monte CarloSROshort‐range orderTOtransverse opticTSFtotal structure factorUVultra violetVisvisibleXANESX‐ray absorption near‐edge structureXASX‐ray absorption spectroscopyXPSX‐ray photoelectron spectroscopyXRSX‐ray Raman spectroscopy
2 Diffraction (Scattering)
2.1 X‐ray and Neutron
Neutron and X‐ray diffraction are two of the principal techniques used to probe the bulk structure of glasses through determination of average bond lengths, coordination numbers (CN), and angles over both the short (nearest neighbors) and intermediate (next‐nearest neighbors) length scales. Data analysis and interpretation are comparable for X‐ray and neutron diffraction so that I will differentiate between the two methods only when needed. In passing, note that in earlier studies the interaction between the X‐rays and the sample was termed scattering, and not diffraction as made now.
For X‐rays, diffraction experiments are readily made but they are not well suited to discriminate between neighbor atoms in the periodic table, such as silicon and aluminum, because of the similar electronic clouds with which X‐rays interact in these cases. Thanks to their lack of electrical charge, neutrons are (with neutrinos) the only particles that can penetrate a condensed phase. They do not interact with electronic clouds, but are diffracted by atomic nuclei because they are strongly sensitive to nuclear forces. If both methods are available, the choice of X‐ray or neutron diffraction depends to some extent on the chemical composition of the glass. Neutrons are, for instance, better suited than X‐rays for investigating light elements such as H and they have the advantage of providing better spatial resolution and allowing more detailed information to be obtained through isotope substitution methods, which rely on the fact that neutron diffraction is sensitive to the neutron content of a nuclei. Practical factors have also to be taken into account: intense sources are much more widely available for X‐rays than for neutrons, whereas the required sample sizes are of the order of 1 mg and 50 g, respectively. The samples themselves may be in the form of powders, glass chips, or shaped glass chips.
The “diffraction pattern” of a glass is very different from that of a crystal (cf. [3]). A crystal will produce a series of “spots” or “reflections” on a two‐dimensional diffraction image or sharp diffraction lines on a powder diffraction trace. These cannot be seen in the diffraction image of a glass. This contrast is illustrated by the area electron‐diffraction images of a crystalline material (Ba2TiGe2O8, Ge‐substituted fresnoite) and of an amorphous material (Ba2TiSi2O8, fresnoite glass) shown in Figure 1a, b. Clearly, no “reflections” are observed in the glass image. A similar contrast is seen between an X‐ray powder diffraction trace of quartz (crystalline SiO2) and that of the glass plate on which the quartz sample was mounted (Figure 1c, d). Note the very weak intensity, lack of diffraction peaks (reflections), and low signal‐to‐noise ratio of the glass trace. Where there is a “diffraction peak,” it has weak intensity and is extremely broad and diffuse, which is characteristic of a material lacking periodic structure.
Figure 1 Structural differences between crystals and glasses revealed by diffraction images and patterns. (a) Selected area electron diffraction image of crystalline Ba2TiGe2O8 (fresnoite). (b) Similar image for Ba2TiSi2O8 glass. (c, d) Powder diffraction traces for crystalline SiO2 (quartz) and the glass slide on which the sample was mounted. Glass diffraction trace included in (c) to give an indication of the difference in intensity between a glass and a crystalline sample.
Each reflection in a crystal image represents coherent diffraction from a plane of atoms whose intensity depends on the nature of these atoms. The “diffraction pattern” of a homogeneous glass will exhibit no such reflections but simply a series of diffuse rings or peaks reflecting those interatomic distances that prevail throughout the glass structure (Figure 1b, d). One does need to be aware that if the material is polycrystalline, it will also exhibit a series of rings but they will be better defined than those characteristic of glasses. Nevertheless, this type of diffraction image can be analyzed and interpreted to obtain average interatomic bond distances and angles, characteristic of the short‐range order (SRO, nearest‐neighbor distances), and to a lesser extent, the intermediate‐range order (IRO). An example of SRO (typically up to ~3 Å) would be around a Si atom with the four oxygens of its SiO4 tetrahedron, whereas IRO (typically up to ~3–5 Å) would be the linkage of this tetrahedron with others to form groups such as rings.
Figure 2 Information drawn for GeO2 glass from diffraction data. (a) Measured total structure factor. (b) Total correlation function. (c) Pair‐correlation functions showing the contribution from the individual atom pairs. Comparison with the earlier data of [4] is also shown.
(Source: After [5].) Results corrected for a number of instrumental effects before derivation of pair distributions serving to identify the individual atomic pairs contributing to the bulk diffraction pattern of the sample.
The most common information derived for glasses from the diffraction peaks shown in Figure 2 are radial distribution functions (RDF), which represent the probability of finding a given atom at any distance r from some atom considered to be at the center of the system. A RDF thus is a one‐dimensional representation of the three‐dimensional structure of a glass that is averaged over the entire system. Because these functions represent the sum of individual pair distributions for every atom of the material, they are widely used for comparisons with theoretical results to check the accuracy of the simulated glass structure.
If two theta (2θ) is the angle between incident and scattered beams and λ the X‐ray or neutron wavelength, the wave or scattering vector is 4π sin θ/λ. It is denoted as Q in neutron scattering, and as s or k in X‐ray diffraction. In the latter case, it is common to extract the X‐ray weighted Faber‐Ziman or total structure factor (TSF),