Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 245

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.