Encyclopedia of Glass Science, Technology, History, and Culture. Группа авторов
rel="nofollow" href="#ulink_53f9dbf2-3bdc-55f6-aeb3-4d958632b535">5 for MD‐simulated B2O3 glass [6]. Once the total correlation and interference functions have been validated, more detailed analysis based on PDF functions can be performed, as shown in Figure 6, and important insight into structural order be obtained. Although the experimental peak positions are reproduced reasonably well by the calculated T(r) and Q I(Q), there are some discrepancies for the peak values. The position and width of the first peak represent the average length and the length distribution of B─O bonds, respectively. The second peak position and peak curve are mostly affected bond angles of O─B─O and B─O─B and size distributions. As indicated by a detailed analysis of the data, most of the discrepancy is due to a simulated fraction of only 30–50% for the so‐called boroxol B3O6 rings (cf. Chapter 7.6) compared to the 60–80% range of the experimental values [13].
Figure 4 Comparisons between the experimental [13] and simulated [6] X‐ray (a) and neutron (b) total correlation functions of B2O3 glass.
5.2 Short‐range Order
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 “Qn 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 Qn 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 Qn is also important for phosphate glasses, because Qn 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 Qn [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