Читать книгу Encyclopedia of Glass Science, Technology, History, and Culture - Группа авторов - Страница 315

Of particular interest for characterizing short‐range order are CN. In atomistic simulation, this parameter is well defined as the number of atoms falling within a given distance from an arbitrary atom. For each atomic pair this cutoff radius is typically estimated either from the corresponding bond lengths in crystal structures or from the position of minimum between the first and second peaks of the pair‐distribution function. Alternatively, the CN can be estimated experimentally from the height of the first peak observed in the X‐ray diffraction or neutron diffraction spectra or from the chemical and isomer shifts in NMR or Mössbauer spectra, respectively. In MD studies the oxygen CN of network‐forming cations (Si, B, P, Ge, etc.) are generally calculated to be within 5% of the experimental data even for the changes with varying pressure or concentration of network‐modifier alkali or alkaline earth cations. Such coordination changes from 3 to 4 for B atoms in borate glasses and from 4 to 6 for Si and Ge in silicate and germanate glasses have been well documented in this way (e.g. [12]).

Figure 5 Comparisons between the experimental [13] and simulated [6] X‐ray (a) and neutron (b) interference functions of B₂O₃ glass.

On the other hand, the oxygen CN is not well defined for intermediate network‐forming cation (Al, Fe, Zr, etc.) or network‐modifier cations when the distance distribution between cation and oxygen atom is broad. A slight change in the definition of cutoff radius then translates in a large change in CN. In MD simulations on sodium aluminosilicate glasses, the switch of Al from a network‐forming to a network‐modifying role has nonetheless been evidenced by a CN increase from six in crystal to four and five in glass (e.g. [14]) whereas the existence of fivefold coordinated aluminum and threefold coordinated oxygens has also been evidenced [15].

In silicate glasses another fundamental feature to describe variations of structure and properties is the “Q_n distribution,” where the subscript n indicates the number of bridging oxygen (BO) in an SiO₄ tetrahedra (Chapter 2.3). In MD simulations it is easy to identify nonbridging oxygens (NBO) on the basis of the cutoff radius. The calculated Q_n distributions for sodium‐silicate glasses have been compared with that determined by MAS‐NMR experiments [16]. The MD calculations reproduce the experiments reasonably, although the extremely rapid quenching rates prevailing in the MD simulation may broaden the distribution, which does depend on actual T,P conditions. The analysis of Q_n is also important for phosphate glasses, because Q_n distribution reflects their polymer‐like structure that results from the existence of doubly bonded oxygen atoms. In the case of phosphate glass not many MD studies have been published and more validated potential models need to be developed. Recent MD calculations on iron phosphate glasses have demonstrated that the network connectivity is indeed dominated by the expected Q_n [11].

Figure 6 PDF functions in simulated B₂O₃ glass and their structural assignments [6]. The peaks labeled in (a) refer to the specific distances indicated in the elementary structural units (b).

The third useful information on short‐range order is the “bond angle distribution” (BAD), because the nature of the existing polyhedral units can be ascertained from oxygen–cation–oxygen angles. For SiO₂ and silicate glass, the simulated peak position is, for instance, found near 109.47° in O─Si─O angle distributions, which of course reflects the presence of Si within SiO₄ tetrahedra. Likewise, the peak of O─B─O angles in B₂O₃ lies around 120°, in harmony with the formation of BO₃ triangles (Figure 7). As for the B─O─B distribution, a significant amount of angles with 120° reveals the presence of boroxol rings (Figure 7) because, without boroxol rings, the B─O─B distribution should be around 129° as observed in B₂O₃ crystal [6]. In this respect, the interest of MD simulations stems from the fact that there is no direct method for determining the BAD experimentally – just a possibility to estimate roughly average values from X‐ray or neutron diffraction data. These simulated cation–oxygen–cation BADs are specially valuable to probe local structural changes with either temperature or pressure in single‐component glasses such as SiO₂, B₂O₃, P₂O₅, or GeO₂.

Figure 7 Bond angle distribution in simulated B₂O₃ glass.

The fourth information of interest is the “torsion angle distribution” (TAD), to which particular attention is paid for polymers whose structure and properties are significantly affected by the twisted arrangement of side chains. Again, B₂O₃ glass illustrates the relevance of this distribution to inorganic glasses because of the steric problem raised by the interconnection of BO₃ units and boroxol B₃O₆ rings (Figure 8). In this case, the calculated TAD suggests different connecting geometries between BO₃–BO₃ linkages and B₃O₆–B₃O₆ units: the former are preferentially oriented in a perpendicular direction, which means that connected BO₃ units do not lie in the same plane, whereas the latter are oriented in the same direction, which means that B₃O₆ units do lie in the same plane [6]. For SiO₂ glass, no such distinction is of course found, but MD simulations do suggest that a torsional transformation takes place between neighboring SiO₄ tetrahedra at elevated temperature, in analogy with the structural changes associated with the α–β transition in cristobalite [17]. In addition, it has been suggested that the abrupt rotation of Si─O─Si equivalent to torsion movement between two SiO₄ tetrahedra is the cause of anomalous thermomechanical properties in silica glass [17].