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Section II. Structure

Figure 1 The atomic disorder of the glass structure (left) giving way to crystalline order (right): the boundary between a Zr‐bearing magnesium aluminosilicate glass and a ZrO₂ crystal that precipitated in it. Bar scale: 5 nm. Abberation‐corrected, high‐resolution transmission‐electron micrograph courtesy Christian Patzig and Thomas Höche.

It is usually stated that the various properties of glasses and melts are determined by the structures of these phases. This statement is thermodynamically incorrect: a melt has a structure that is fixed instead by the minimum of its Gibbs free energy and, thus, by the temperature‐dependent balance between enthalpy and entropy factors that are themselves determined by the existing atomic interactions. This is the manner in which the structures of melts predicted in theoretical calculations are assumed to be those of glasses quenched from some pressure and high temperature.

Structural studies are nonetheless useful either at a small scale, for example, to figure out how the local environment of an ion determines its optical properties (Section VI), or at a larger scale to gain insights on property–composition relationships when the specific influence of chemical entities on the properties of interest can be evaluated in terms of well‐defined structural elements such as rings or coordination polyhedra. The method was pioneered in Antiquity by Plato (‐428–347): to each of the four elements then acknowledged, he assigned geometrical shapes accounting for their properties, namely the tetrahedron for fire, octahedron for air, icosahedron for water, and cube for earth. Of course, such assignments are no longer purely intellectual constructs; they have an experimental basis. Interestingly, however, one should realize that the first atomic models of glass were devised shortly before any experimental tool was available to determine their structural components (Chapter 10.11). In other words, glass structure represents a good example of a situation where theory not only preceded experiments but also defined their paradigmatic framework.

To set the frame of this second section of the Encyclopedia, a broad overview of the structure of amorphous materials and of associated theoretical models at different length scales is first given by A.C. Hannon for network oxide and chalcogenide glasses, with particular emphasis on the random‐network model (Chapter 2.1). Recently, progress in the analytical techniques used in structural studies has been enhanced by the availability of intense sources of electromagnetic radiation, namely lasers and synchrotron facilities. From X‐ray diffraction and absorption to vibrational and Mössbauer spectroscopies, these various methods and the information they yield are reviewed by G. Henderson (Chapter 2.2). Whether purposely produced in glass ceramics or formed spontaneously in industrial or natural processes, inhomogeneous glasses are also given increased attention (Figure 1). To determine their microstructure and analyze their constituents at a scale down to the nm range, C. Patzig and T. Höche then present scanning and transmission electron microscopy, analytical tools, and the relevant analytical tools and other ancillary techniques available (Chapter 2.3).

From the results obtained with these methods, the next three chapters focus on the glass structure. Short‐range order is dealt with by J.F. Stebbins in a chapter where he defines such concepts as network formers and modifiers, bridging and nonbridging oxygens and their tetrahedral distribution around the network‐forming cations they coordinate, and he also discusses how they change with temperature and composition (Chapter 2.4). From the scale of atoms to that of macroscopic bodies, the increasing complexity found at longer distances is then examined by G.N. Greaves who also points out the basic differences found between oxide and metallic systems (Chapter 2.5). Because glasses have generally complex chemical compositions in both industrial and geological contexts, the relationships between the structures of simple and multicomponent systems are finally described by B.O. Mysen in a perspective aimed at understanding composition–property relationships (Chapter 2.6).

Returning to more theoretical aspects, the next chapter by P.K. Gupta stresses with the constraint theory the importance of simple topological considerations and of temperature‐dependent bond strengths to understand the glass structure and composition–property relationships. To conclude this section, two chapters review the rapid advances made in the growing field of atomistic simulations in two complementary ways. In the Monte‐Carlo and molecular‐dynamics simulations presented by A. Takada (Chapter 2.8), the interatomic potentials used to simulate the structure and properties of glass‐forming systems are determined a priori, with the advantage that up to a few thousand particles can be considered with current computing power. As reviewed by W. Kob and S. Ispas, atomic interactions are determined instead from first principles in the more fundamental and precise ab initio approaches, such as density functional theory; the price is that only relatively small systems can be currently investigated (Chapter 2.9). Ascertaining the energetics of a glass‐forming melt is fraught with considerable difficulties, however, because phase transformations, in which one is interested, are driven by small differences of typically a few kJ between the very large numbers yielded with significant uncertainties by ab initio methods.

Throughout this section the emphasis is generally put on oxide glasses. Metallic glasses are specifically dealt with in Chapter 7.10 and organic polymers in three other contributions (Chapters 8.8–8.10).

Reference

1 Plato, T. 55e–56d, transl. by D.J. Zeyl p. 1224–91 in Plato Complete Works. Indianapolis: Hackett Pub. Co., 1997.