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 2.7 and 2.8): (i) MD, where empirical potentials describing the repulsive and attractive interactions between atoms are used in conjunction with classical dynamics to explore P–T phase space; (ii) RMC, in which sequential adjustments in atomic positions are made to improve agreement with the experimental structure factor S(Q); and (iii) density functional theory (DFT) based on all‐electron quantum mechanical methods that replace the empirical potential in MD. At the present time ensembles 300 Å in size are feasible with MD and RMC, whereas ab initio DFT MD, which is computationally more demanding, is currently limited to systems of about 15 Å. Empirical 2‐ and 3‐body potentials are formally ionic but have been successful for predicting the structure and dynamics of liquids and glasses where chemical bonding is predominantly directional in character such as in feldspar compositions ([27], Figure 8). Interestingly, RMC and latterly DFT have been used for metallically bonded systems as well ([4] Figure 1).
Neutron S(Q) data from single experiments were originally used with RMC, together with simple constraints, such as nearest interatomic approach, CN, etc., to avoid unphysical SRO [10]. Now other sources of data are used in conjunction, the most common being high‐energy X‐ray diffraction [8], but these have been augmented by other sources of data – notably EXAFS and MAS NMR spectra [10]. From large models, LRO effects such as clustering, channels, and other sources of heterogeneity can be examined.
In simulating glass structure with MD and DFT, crystalline ensembles are typically “melted” at, say, 5000 K over 10's of ps until thermodynamic equilibrium is reached, after which they are cooled at ~1 K/ps, through the supercooled regime and glass transition, to a glass at ambient temperature. At each stage the SRO of bond lengths and bond angles of polyhedra in directionally bonded systems, and bond lengths and icosahedral geometry in metallic systems, can be catalogued and compared with experiment. Likewise, one can examine directly IRO and LRO such as ring statistics in covalent structures and MRO, for example, the icosahedral variety, in metallic alloyed structures. Moreover, dynamic properties like ion diffusivities can be predicted as a function of temperature and pressure, the same applying to vibrational modes that determine the VDOS – not least the many‐atom cooperative motion responsible for the boson peak.
6 Structural Heterogeneity in Glasses
The conceptual CRN and DRPHS models for glass structure [15, 16] are based on single‐type polyhedra or atoms, respectively, and predict extended range order to be homogeneous everywhere. Because these models are constructed statically, not dynamically, DFs are also excluded. A geometric consequence of introducing more than one size of polyhedron or atom type is microsegregation in the packing of the minority component, first as clusters, which then coalesce into channels above the percolation limit (~20%). This evolution was originally predicted from the 2‐D modified random network (MRN) model [9] and later from 3‐D MD simulated structures [2].
Interestingly, a similar clustering is also evident in computer‐simulated metallic glass structures, such as the metalloid P in the RMC model for Ni0.8P0.2 metallic glass, where this microsegregation can be seen threading through the close‐packed Ni structure ([12] Figure 1).
For MRN structures (Figure 8), channels are defined by nonbridging oxygens (NBOs) resulting in silicons, for example, being surrounding by mixtures of BOs and NBOs, which can be readily identified by 29Si MAS NMR [1, 28]. In aluminosilicate glasses, aluminums occupy tetrahedral sites AlO4 −1 [1] where the extra charge is compensated for by adjacent modifier cations like alkalis or alkaline earths. For fully compensated compositions, like those of feldspars, glasses, silicon, and aluminum tetrahedra are corner‐shared via BOs, adopting a CRN‐like geometry that is categorized as a compensated continuous random network (CCRN) [28]. Alkali channels have also been predicted in aluminosilicate melts and glasses, like the nepheline family (NaxK1−xAlSiO4) (Figure 8), confirmed by MD modeling, which also reproduces the way the viscosity changes with composition [27].
Figure 8 Microsegregation in network glasses. (a) Modified random network (MRN) used to model oxide glasses [9]. Cation modifier channels clearly seen percolating through the two‐dimensional network, 3‐D microsegregation later confirmed with MD methods [2]. (b) Isosurfaces delineating K+ conducting pathways in MD simulated K2Si2O5 disilicate glass, with cutaway showing adjacent interweaving modified silicate network. (c) Alkali channels in MD simulated aluminosilicate Na0.25K0.75AlSiO4[27]. (d) Ag+1 channels in the superionic glass (AgI)0.6–(Ag2O–2B2O3)0.4 separated from anion borohalide pockets.
Source: (a) Reproduced from [9] © (1985) Elsevier; (b) image courtesy Z. Zhou; (c) reproduced from [27] © (2017) Nature Publications; (d) reproduced from [10] © 2001 Institute of Physics.
Modifier channels were envisaged from the start as supporting ionic diffusion, such as that of alkali ions migrating through oxide glasses [28]. The use of isosurfaces to delineate channels (Figure 8) helps visualize the separation of mobile ions from the surrounding network. The presence of well‐defined channels explains the additional FSDP observed, for example, in modified silicate glasses around 0.8 Å−1, which can be attributed to correlations between alkalis with a quasiperiodicity of about 8 Å [1]. Other evidence comes from EXAFS and MAS NMR experiments.
