Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
(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.
There is now much support for the idea of reconciling structural heterogeneity with transport properties [28]. For example, the mixed alkali effect, where the mixing of different mobile alkalis in the same glass drastically affects the mobility of both, can be understood in terms of the segregation of alkalis packing within channels, diluting the diffusivity of each ([2], Chapter 4.6). The huge fall in the average ionic mobility with alkali mixing reduces the ionic conductivity of glass and increases its corrosion resistance and other related transport properties [28].
Fast‐ion conducting glasses based on silver salts, like AgI dissolved in oxide and sulfide matrices, have unusually high ionic conductivities at ambient temperature, exceeding those of binary alkali silicates and borosilicates by three or four decades, making them attractive as possible electrolytes for solid‐state batteries. For these systems RMC modeling has been interpreted in terms of the MRN and the high diffusivity of Ag+1 along percolating channels that are approximately one‐dimensional (Figure 8). Like for conventional modified oxide glasses, the FSDP is often structured for fast‐ion conducting glasses with Ag–Ag and anion–anion components, the former with a quasiperiodicity approaching 10 Å. This is illustrated for (AgI)0.6–(Ag2O–2B2O3)0.4 glass in Figure 8 where the topology of ion transport channels can be clearly seen. As the AgI content increases,