of glasses, a wide portfolio of techniques has developed [1, 3, 5]. For many years the principal experimental method has been X‐ray and neutron scattering [6], initially concentrating on the radial distribution function (RDF) from which the radially averaged local structure T(r) can be determined, as illustrated in Figure 2 for silica glass and the metallic glass Ca60Mg25Cu15. The maxima identify interatomic correlations, first between nearest neighbors (SRO) defining the polyhedral or icosahedral building units and then between adjacent units (MRO or IRO), as spelt out in the cartoons. The SRO and IRO in glasses are often similar to their crystalline cousins. On the other hand, topology influences LRO – ring statistics for network glasses [1] and icosahedral packing for metallic glasses ([3], Chapter 7.10) – where mismatching frustrates crystallization.
Attention has subsequently shifted to the measured scattered intensity i(Q) from which the static structure factor S(Q) is obtained, which leads to T(r) via Fourier transform [1]. The scattering vector Q is defined by Q = 4πsinθ/λ , where θ is the scattering angle and λ the wavelength of the scattering particles. The i(Q) for the two exemplar glasses are plotted in Figure 3. Two important features are located early on for Q < 5 Å−1: the first sharp diffraction peak (FSDP), for which the spacing 2π/QFSDP is a metric for IRO, and the principal peak (PP), which is directly related to the average nearest‐neighbor distance 2π/QPP [6, 7]. Both the FSDP and the PP are features common to network glasses as well as metallic glasses (Figure 3). With high‐intensity spallation neutron sources, the Q‐range reliably reaches 50 Å−1, enabling the T(r) to be confidently measured to 20 Å, embracing SRO with LRO.
Figure 2 Contrast between the radially averaged local structure T(r) of directionally and metallically bonded structures as exemplified by the network glass SiO2 (a) and the bulk metallic glass Ca60Mg25Cu15 (b). The short (SRO), intermediate (IRO), long (LRO), and medium (MRO) range orders are identified alongside 2‐D schematics of local atomic arrangements. Note the difference in the widths of atomic shells reflecting the bonding strength of covalent networks compared to the dense metallic random packings.
Source: Courtesy of A. Hannon (http://alexhannon.co.uk/DBindex.htm).
Compared with diffraction techniques used for crystalline materials, diffuse scattering methods seriously underdetermine the extended structure of glass, even for monatomic systems. Other independent structural measurements are needed in order to increase the credibility of atomistic models. Although X‐ray and neutron S(Q)′s are independent measures of the same radially averaged structure, until recently X‐ray measurements lacked the extensive Q‐range of neutron instruments. However, with the arrival of high‐energy X‐ray scattering [8], both methods are now compatible and are generally applied sequentially to the same material.
Most glasses, though, are multicomponent, which adds chemical complexity to the radial averaging of three‐dimensional (3‐D) arrays. More chemically selective techniques are thus generally required, even though isotopic neutron scattering can assist when different isotopes of an element are available [6]. Accordingly, neutron and X‐ray scattering are now increasingly complemented by spectroscopies, like magic- and dynamic-angle spinning nuclear magnetic resonance (MAS NMR and DAS NMR), and extended X‐ray absorption fine structure (EXAFS) [1, 5, 9]. As these are element specific and increase the mix of independent measurements of the same structure, they add rigor to models of extended glass structure derived from computational methods such as reverse Monte Carlo (RMC) and molecular dynamics (MD) [1, 10–12]. Moreover, expressed as S(Q), the credibility of predictions of atomic arrangements in glasses can be judged against experimental data quality.
Figure 3 Contrast between the network structure of SiO2 (a) and the metallic structure of Ca60Mg25Cu15 (b) manifest in the scattered intensities i(Q), from which the T(r)'s of Figure 2 were obtained. The SRO as defined by the principal peak (PP) and IRO defined by the first sharp diffraction peak (FSDP) are labeled alongside LRO and MRO for each glass.
Source: Data courtesy of A. Hannon (http://alexhannon.co.uk/DBindex.htm).
Compared to the direct analysis of experimental RDFs, which dates back to the 1930s, these new combinations of experiment and computational modeling now offer impressive insight into the nature of the extended structure glasses, on the scale of 30 Å or more (Figure 1). Often glasses with equivalent local structure lead to images that at first glance appear to be quite dissimilar (Figure 4). The tetrahedral glass network of silica may thus be contrasted with that of amorphous ZIF‐8 – one of a newly discovered family of hybrid glasses derived from organic–inorganic materials [14, 15]. The extended structure of silica is perpetuated through corner‐sharing SiO4 tetrahedra (SRO) via bridging oxygens (BOs), IRO ultimately extending to LRO comprising rings of different size (Figure 4). The geometry of amorphous ZIF‐8 [Zn(C4H5N2)2] develops in a similar way, with Zn atoms tetrahedrally coordinated to 2‐methylimidazolate bridges that form into silica-like rings, despite the atomic volume being hugely different, viz. the 11.1 Å3 of SiO2 compared with the 73.4 Å3 of amorphous Zn(C4H5N2)2.
In adding further confidence to modeling extended glass structure, studies of dynamic properties, using inelastic spectroscopies like inelastic neutron scattering (INS) and Raman spectroscopy, have played an important part [1, 5, 16] – principally in highlighting stretching and bending optic mode vibrations between the atom pairs in network glasses and providing fingerprints of the polyhedra and small molecular groups that constitute SRO and aspects of IRO.
At lower frequencies, inelastic spectroscopies like INS access acoustic modes that are generically subsumed into the boson peak, ubiquitous in the glassy state [1, 5, 17–19]. Derived from the localized collective vibrations of groups of atoms, the boson peak relates to the dynamics of MRO and LRO considered to be the source of fast β relaxation [1, 7]. Located at the bottom of the vibrational density of states (VDOS) in the THz region (1 THz = 4.1 meV), the boson peak is generally accepted as comprising quasi‐localized transverse vibrational modes (Chapter
