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Note
1 Reviewers:Steve Feller, Physics Department, Coe College, Cedar Rapids, IA, USADiane Holland, Physics Department, Warwick University, Coventry, UK
2.2 Structural Probes of Glass
Grant S. Henderson
Department of Earth Sciences, University of Toronto, Toronto, Ontario, Canada
1 Introduction
The atomic arrangements that make up the structure of a condensed phase can be probed only with particles or electromagnetic radiation that penetrate into the material and interact with its atoms in such a way that analysis of the changes they undergo yield the specific information sought after. Probably the most basic information is relative atomic positions, which can be derived from X‐ray and neutron diffraction experiments because groups of atoms may act as gratings with respect to radiation whose wavelengths are in the Ångström‐range of interatomic distances. Alternatively, all other structural probes rely on the exchange of electromagnetic energy in certain frequency ranges to yield information not on the bulk structure of the material, but on individual types of atoms or groups of atoms. As a first example, absorption of X‐rays by electrons at eV‐energies probes the effects of interatomic bonding on the electronic levels of a given atom and, thus, the environment of this atom and even its redox state. As a second example, similar information may be derived for appropriate transition metal elements with Mössbauer spectroscopy from interactions at higher energies of gamma rays with atomic nuclei. A summary of the methods presented in this chapter along these lines is given in Table 1.
Regardless of the method used, probing atomic structure is much easier for crystals than for amorphous materials. To “solve” the structure, one only requires knowledge of the unit cell as defined by the crystallographic axes (a, b, c) and angles (α, β, γ), the lattice type (P, F, I, A, B, C, H, R), the symmetry associated with both the unit cell (point group) and the lattice (space group), and the positions of the atoms relative to the origin of the unit cell. One does not need to determine the position of all the atoms in the structure, but only the minimum number required by the point group symmetry.
Solving the structure of an amorphous material such as glass, on the other hand, currently is not possible and is unlikely in the foreseeable future because of the lack of long‐distance atomic periodicity. Hence, one cannot define a unit cell, a lattice, or their associated symmetry that would enable reproduction of the positions of atoms without having to determine the explicit location of all the atoms in three‐dimensional space. In essence, glasses have an infinite unit cell so that “solving” the structure would require knowledge of the position of every atom, an impossible task.
Nevertheless, it is possible to probe a great many structural features if one keeps in mind that the discrete values of interatomic angles and distances existing in crystals give way in glasses to continuous distributions that can be characterized by their shapes, widths, and maximum or averaged values. In addition to these parameters that characterize the bulk structure of the glass, information pertaining to specific atoms can also be gathered, such as the coordination polyhedra of the various constituents of the material.
Because the structure of a glass represents that of the solid “frozen‐in” at the glass transition, it is also important to investigate the marked temperature‐induced structural changes that take place in melts at higher temperatures. In this regard, two cases should be distinguished depending on the differences between the experimental timescale of the method and the rate of structural change of the melt. If the former is very short with respect to the latter, then the result will be a snapshot of a solid‐like structure; if it is long, the result will represent a time‐averaged structure that brings little information on the individual features that are averaged (see Section 4).
Table 1 Summary of techniques used to determine various features of glass structure.
| Technique | Energy (eV) | Frequency (Hz) | Wavelength (nm) | Process | Information obtained |
|---|---|---|---|---|---|
| X‐ray diffraction | 0.1–100 keV | 3 × 1016–3 × 1019 | 0.01–10 nm | Scattering/diffraction from electrons | ~0–15 Å, quantitative bond lengths and angles over short‐ and intermediate‐range length scales |
| Neutron diffraction | 0.1–500 meV | 0.04–120 THz | 0.04–3 nm | Scattering/diffraction from neutrons | ~0–15 Å, quantitative bond lengths and angles over short‐ and intermediate‐range length scales, dynamics |
| EXAFS | 0.1–100 keV | 3 × 1016–3 × 1019 | 0.01–10 nm | Atom‐specific absorption of X‐rays, multiple scattering | ~5–6 Å, quantitative atom‐specific bond lengths and coordination |
| XANES | 0.1–100 keV | 3 × 1016–3 × 1019 | 0.01–10 nm | Atom‐specific electronic transitions to unoccupied orbitals, multiple scattering |
|
