Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 238

In addressing the extended structure 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/Q_FSDP is a metric for IRO, and the principal peak (PP), which is directly related to the average nearest‐neighbor distance 2π/Q_PP [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 ų of SiO₂ compared with the 73.4 ų 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 3.4 [16, 18]). These vibrations also enhance the specific heat C_p at low temperatures above the Debye threshold – typically around 10 K. Using either INS or excess C_p reveals that the boson peak intensity is directly related to glass density (Figure 5a–d [18, 19]). For zeolites, which share compositions with silicate and aluminosilicates but have characteristically low densities, the different cage‐like units that define their nanoporous structures resonate at different THz frequencies [16]. As the temperature or pressure is increased, these subunits collapse [1] through a process of decelerated melting [21], and a glass, similar in density to a melt‐quenched glass, is formed with a single boson peak (Figure 5e). In particular, atomic volume and peak intensity I_BP are correlated, with the peak frequency ν_BP shifting to higher values as the atomic volume falls.

Figure 4 Visualization of MD simulations of two tetrahedral glasses with vastly different atomic volumes but both conforming to the CRN prescription [13]. (a) SiO₂ glass (11.1 ų). (b) Hybrid glass ZIF‐8 (Zn(C₄H₅N₂)₂) (73.4 ų).

Source: Images courtesy of J. Du (a) and W. Chen (b).

As for metallic glasses (Chapter 7.10), these also exhibit soft collective vibrations whose origins are similar to oxide glasses boson peaks [3, 20]. If these are accessed from low‐temperature C_p experiments, then the enthalpy captured at supercooled temperatures can also be recorded. A direct link exists between I_BP and the glass enthalpy, which can be reduced by annealing Figure 5f [20]. As annealing increases, the glass density, ν_BP, also increases while I_BP decreases (compare Figure 5e and f).

Whereas inelastic scattering S(ω) measures the VDOS integrated over Q, and the structure factor S(Q) time‐averaged atomic distributions, both derive from the dynamic structure factor S(Q,ω), which through comparisons with experiment affords a global view of the structure and dynamics of glassy systems and melts over extended regions of space and time. Related to S(Q,ω) is the intermediate scattering function F(Q,t), which registers structural relaxation from liquid to glass as a function of time [1]. In the limit t → ∞ F(Q,t)/S(Q) yields the non‐ergodicity factor f(Q,T), which is particularly relevant in the present context as it records the degree to which a liquid departs from thermodynamic equilibrium as it is supercooled (Section 4.1). It is readily measured using inelastic X‐ray scattering (IXS). Structural relaxation is dominated by fast β processes at high temperatures, with slow α processes emerging through the supercooled region, only to be frozen out at the glass transition T_g.

Microscopy has always played a part in glass structure determination, albeit as a distant companion to diffraction and spectroscopy techniques. It originally provided qualitative evidence for IRO [7]. But the SRO and LRO of network glasses can now be imaged [1, 22] with the emergence of atomic‐scale resolution by atomic force microscopy (AFM) and high‐resolution transmission electron microscopy (HRTEM). With nanobeam electron diffraction (NBED), images can also be obtained for the variety of icosahedral clusters present in metallic glasses [23] (Figure 6).