Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
where the phonon mean free path equates with its wavelength [19]. At this point vibrations no longer propagate, which suggests that LRO vibrations are localized. Demonstrated by computer simulation of Lennard‐Jones glass models, collective vibrations in these close‐packed structures replicate the scaling down of IBP with density referred to earlier and the increase in νBP.
4 Structural Aspects of Density Fluctuations
4.1 Non‐ergodicity and Elastic Moduli
Beyond the length scales of LRO and MRO are the DFs characteristic of the liquid state. They originate from the dynamics of the liquid state in thermodynamic response to temperature and pressure. Whereas liquids are in equilibrium and ergodic above the melting point, supercooled liquids are non‐ergodic at Tg, which is reflected in the size of the non‐ergodicity factor f(Q,T) (Section 2). In particular f(Q → 0,T) is related to the magnitude of DFs, and as T → Tg, a dynamic crossover occurs to non‐ergodicity – typically ~1.2Tg. On vitrification DFs increase in amplitude and eventually become frozen in.
In glasses the spatial extent and amplitude of DFs can be determined from IXS and S(0) [1]. In glass formers DFs are typically ≥20 Å in scale, their amplitude being proportional to the melt compressibility κ, which is greater for network glasses than metallic glasses, for example, reflecting the considerable differences in atomic packing (Figure 7). In network glasses like silica, light scattering from DFs limits losses in fiber‐optic applications [7]. Interestingly the amplitude of DFs is inversely related to Poisson's ratio, which is smaller for oxide glasses, which are usually brittle, than for many metallic glasses, which are tough [17].
4.2 Polyamorphism and Phase Separation
At high degrees of supercooling, liquid–liquid phase transitions have been observed, a phenomenon now commonly referred to as polyamorphism ([26], Chapter 3.9). These phase transitions have been observed in water, supercooled oxides, semiconductors, and metallic alloys, leading to new types of glass, such as low‐ and high‐density amorphous phases – LDA and HDA respectively – each differing in density and entropy but sharing the same composition [1, 14, 21, 26].
In some multicomponent supercooled oxide liquids, on the other hand, atomic diffusion can result in the coexistence of liquids with different compositions, the analogue of multiple phases in crystalline systems. On cooling these lead to phase‐separated glasses (PSG) – the best‐known being borosilicates [7]. Pyrex, for example, combines low thermal expansion with high mechanical strength, whereas Vycor glass owes its special open microporous structure to the continuous silicate phase that is left when the borate phase has been leached out.
In summary, the extended structure of glass connects all of the various ordered regions present on different length scales and underpins the diverse global properties of the glassy state.
5 Models of Glass Structure
5.1 Conceptual Models
Two conceptual models have proved very influential over the years in picturing the overarching aperiodic structure of glass. Zachariasen's continuous random network (CRN), devised for oxide glasses, dates from 1932 [13]. In 1960 Bernal introduced the dense random packing of hard spheres (DRPHS) to describe the structure of liquid metals [25], which has been applied widely to glassy metals once these had been discovered. Both constructs of glass structure, for insulators and metals, respectively, came in advance of experimental techniques that have since illuminated their strengths as well as their shortcomings. The two models are illustrated in Figure 7, reduced to 2‐D arrangements. Presented in this way, they reveal a common basis for constructing aperiodic arrays from contiguous spheres. They markedly differ, however, because each sphere touches just three neighbors in the CRN, resulting in a more open network structure than with the DRPHS where the number of neighboring spheres lies between five and seven. Taken together, though, both the CRN and DRPHS noncrystalline schemes yield a lower density than for their crystalline counterparts, and voids are seen to align mimicking the quasiperiodicity attributed to the FSDP (dashed curves in Figure 7). The increased free volume derives from variations in packing. As such, both CRN and DRPHS offer respective snapshots of the glassy state without informing on the quenching process during which the configurational entropy is generated. With the CRN each sphere embodies the SRO surrounding individual atoms: MO3 units, for example, mimic SiO4 tetrahedra in silica glass or BO3 and BO4 polyhedra in borate glasses (Figure 7).
The SRO units are interconnected to create corner‐sharing networks of directionally bonded atoms perpetuating indefinitely, which in addition provides a conceptual representation of the extended structures of network glass formers. Although amorphous semiconductors were not yet discovered in 1932, the CRN is equally applicable to chalcogenide glasses like As2S3 and also to elemental semiconductors like amorphous As and Ge [7]. In all cases fixed CNs and bond lengths are prescribed by the tenets of the CRN. Usually these parameters are informed from crystalline structures even though space group symmetry is broken by variations in bond angles. Distortions between SRO units lead to rings of atoms of different sizes (Figure 7), including odd‐membered rings seldom found in the crystalline state. Because of the bond angle flexibility of the CRN, point defects, like vacancies and interstitials, can formally be avoided, which is consistent with the observation that optical‐quality glass is almost free of point defects.
By contrast Bernal's DRPHS structure is the geometric outcome of the random packing of spheres, originally ball bearings in a can [25], each representing a metal atom (Figure 7). Designed to model elemental liquid metals, the DRPHS became an approximate structure for glassy metallic alloys where components have similar atomic radii, such as Pd80Si20. Nearest‐neighbor distances in densely packed structures scale with metallic radii, but the packing scheme in three dimensions incorporates icosahedral units avoiding dense‐packed crystalline arrangements. By analogy with the CRN, Bernal's model is free from dislocations that render crystalline metals prone to mechanical damage, which qualitatively explains the exceptional toughness of metallic glasses. Moreover, as the main contribution to metallic electrical resistivity at ambient temperature is governed by the scattering of electrons by irregularities in the positions of core ions, the DRPHS supports the greater electrical resistivity of glassy metals compared to than crystalline metals, enabling the low‐loss of metglas magnetic transformer cores.
The major success of the Zachariasen and Bernal models has been in reconciling SRO with the extended structure of the glassy state. These model structures are isotropic and homogeneous by definition, however, and as such they fail to account for DFs observed almost universally in network as well as in metallic glasses. The solution to this drawback can only be solved through the computer modeling of large 3‐D melt‐quenched structures.
5.2 Computational Modeling of Extended Structure
Atomistic modeling of liquids and solids goes back over 50 years. Over the interim period three main approaches have been developed in relation to glass‐forming materials (Chapters