at low temperatures above the Debye threshold – typically around 10 K. Using either INS or excess Cp 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 IBP are correlated, with the peak frequency νBP 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 Å3). (b) Hybrid glass ZIF‐8 (Zn(C4H5N2)2) (73.4 Å3).
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 Cp experiments, then the enthalpy captured at supercooled temperatures can also be recorded. A direct link exists between IBP and the glass enthalpy, which can be reduced by annealing Figure 5f [20]. As annealing increases, the glass density, νBP, also increases while IBP 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 Tg.
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).
3 Structural Order over Different Length Scales
3.1 Network Glasses
Network‐oxide glass formers like SiO2, GeO2, P2O5, and B2O3 [1] are defined by three‐ or fourfold directionally bonded polyhedra comprising hybridized units measuring ~2.5 Å, similar to nearest‐neighbor arrangements in crystalline polymorphs [1]. For low‐density hybrid glasses like a‐ZIF‐4 and a‐ZIF‐8, tetrahedral units are much larger, measuring about 9.5 Å [14]. Generally, SRO polyhedra are comparatively rigid, with variations in bond angle of less than 10%. The IRO is located between 3 and 4 Å for oxides increasing to 13 Å for hybrid glasses, covering correlation distances between SRO polyhedra (Figure 2 [1, 7, 14]). In oxide glasses the interpolyhedral distance is defined by the BO that is also hybridized, with interpolyhedral angles ranging from around 145° for SiO2, 130° for GeO2, and P2O5 to 120° for B2O3 (Figures 1 and 4 [1]). The imidazolate bridge between metal nodes in a‐ZIFs is ~145° [14]. On average, the rigidity of tetrahedral and bridging angles is similar.
Figure 5 The collective atomic vibrations involved in the boson peak observed either dynamically in the reduced density of states g(E)/E2 (a, b) or thermodynamically in the non‐Debye excess low‐temperature specific heat Cp/T3 (c, d) for silica (left) and densified silica (right). Similar features occur in crystalline SiO2 isomorphs of similar density [18]. (e) INS spectra of the collapse of zeolite Y [16], the cage subunits merging into a single peak of lower intensity IBP as a glass is formed while νBP increases – dashed arrow. (f) Boson peak in the metallic glass Zr50Cu40Al10[20] where annealing increases the density, but decreases the trapped enthalpy and the Cp/T3 intensity IBP falls as νBP increases – dashed arrow.
Source: (a–d) Reproduced from [18] © (2014) APS; (e) reproduced from [16] © (2005) AAAS; (f) reproduced from [20] © AIP.
In network glasses LRO begins at around 6 Å – the width of a typical sixfold ring (Figures 1 and 4) – and continues as far as out as features in the RDF can be discerned (Figure 2). Providing a direct link with a multiplicity of rings of corner‐sharing polyhedra with different sizes, LRO is perpetuated
