B. Results
2. Range I: Structural Unit
Mean pair lengths are compared between host, stuffed, and CEAM configurations, for structural pairs and modifying pairs in Table III and Table IV,
respectively. The mean was established by first taking the mean within each timestep examined, then taking the mean across the timestep means. The error represents one standard deviation of the mean across the timesteps.
Pair lengths for network forming pairs are nearly identical among host, stuffed, and CEAM simulations (Table III). The similarly of pair lengths between host and CEAM configurations suggests there is little dependence of this feature on alkali identity.
Further, observation of nearly identical values for the stuffed simulation implies the structural component pair lengths are largely unchanged upon stuffing alkali accommodation (SAA).
Alkali-containing pair lengths show differences between host and CEAM configurations, where the CEAM simulation generally displays longer lengths (Table IV).
Stuffed simulations for the NS series have similar pair lengths to the CEAM simulation for K-containing pairs, demonstrating the ability for these pair lengths to largely be satisfied after SAA. The SLS simulation, on the other hand, shows intermediate pair lengths for the same pairs, although the differences are largely within the standard deviations for the values. For the stuffed SMAS simulation, M-BO and M-M pairs have lengths that are near the CEAM simulation. For SLS and SMAS simulations, alkaline- earth containing pairs have few differences between host and CEAM simulations, and the stuffed pair lengths are nearly equivalent. Overall, the pair lengths showing the largest differences due to SAA are those of alkali-containing pairs and these pair lengths largely achieve a value quite near that of the CEAM glass, i.e. the local environments of the stuffed glasses have pair distances that are not unlike that of their CEAM counterparts.
Table III. Pair Lengths with Network Formers Table IV. Pair Lengths with Network Modifiers
Mean coordination numbers (CN) are compared between host, stuffed, and CEAM configurations, for structural pairs and modifying pairs in Table V and Table VI, respectively. The central element is represented in parentheses.
The (Si)BO and (Si)NBO CN are well defined, showing narrower distributions than other structural pairs (Table V). For the NS series, differences between host and CEAM values are quite small, with the stuffed system taking an intermediate value to the end members for 16NS. For 9NS and 23NS, the stuffed value is lower for (Si)BO and higher for (Si)NBO. The SLS and SMAS series show slightly larger CN differences between host and CEAM configurations, with the stuffed configuration retaining CN near the host value. The (Si)Si CN is nearly identical between host, CEAM, and stuffed configurations for all simulation series.
The (BO)BO and (BO)NBO CN are similar for host and CEAM configurations for all series. The stuffed simulations generally show slightly lower (BO)BO CN and unchanged or very slight increases for (BO)NBO CN. These changes are small relative to their standard deviations and may not be noteworthy. For the SMAS series, the (Al)BO CN is lower for the CEAM glass than the host, and the stuffed value remains near the host. The (Al)NBO CN is quite low, indicating that nearly all of the NBO is preferentially associated with Si, as has been noted in literature.22,23 The (Al)Al CN is lower for the CEAM glass than the host, and the stuffed glass takes an intermediate value, showing greater flexibility than that observed for (Si)Si.
The (M)O CN, where M represents Na or K, was examined previously for the NS series.12 Here, (M)O is deconvoluted into (M)BO and (M)NBO contributions (Table VI).
For (M)BO, all compositions display a larger CN for the CEAM (M=K) simulation than the host (M=Na) simulation. Relative to their CEAM simulations, the stuffed simulations have K over-coordinated by approximately 0.6 BO for the NS series, under-coordinated by about 0.6 BO for SLS, and attain similar coordination for SMAS. (M)NBO is at least marginally different between the host and CEAM simulations for all glasses examined.
The (M)NBO CN of the stuffed simulations is consistently very near that of their CEAM end-members, demonstrating the preference for proper coordination by alkali-bonded oxygen (NBO) over the network bridging oxygen (BO). Decreasing percent change in
(M)BO between host and stuffed configurations trends with increasing system LNDC, whereas the same is not evident for (M)NBO (Figure 7).
The (M)M CN is consistently higher for the CEAM simulation than the host simulation for the NS series glasses and the stuffed simulations have values very near the CEAM simulation (Table VI). The SLS simulation series shows little difference between the host and CEAM (M)M CN, but the stuffed simulation has a value slightly under that of the host simulation. For the SMAS series, the host and CEAM (M)M CN differ by about one and the stuffed (M)M CN remains near the host. For SLS, the (Ca)BO CN is different between the host and CEAM configurations. The stuffed simulation has (Ca)BO CN equivalent to the CEAM simulation. (Ca)NBO for the same series is slightly lower for the CEAM simulation than the host, with the stuffed simulation showing slightly lower value than both end-members. For the SMAS series, (Mg)BO CN is slightly lower for the stuffed and CEAM configurations than the host. The same series has no discernible difference between (Mg)NBO CN between host, stuffed, and CEAM simulations.
Network modifying pairs show larger variation between host and CEAM glasses than the network forming pairs. Network modifying pairs also have larger distribution widths as indicated by their larger standard deviations relative to the network forming pairs, indicating a greater variety of site configurations for the network modifying pairs.
Note, while the majority of the CN alteration is most apparent about the alkali site, if weighted by the number of species in the system, then the minor CN differences between network forming pairs may bear additional significance, although the alkali- related changes remain dominant.
Table V. Coordination Number for Network Formers Table VI. Coordination Number for Network Modifiers
Figure 7. System LNDC versus percent change in alkali-oxygen coordination number between stuffed and host glasses.
The fraction of NBO relative to total oxygen has a maximum difference of 0.4%
between the host, stuffed, and CEAM simulations for each series. Thus NBO populations are not observed to significantly change with SAA for the compositions, temperatures, and timescales studied here.
Intratetrahedral bond angles with Si and Al as the central cations, and all BO and NBO considered collectively, show very minor differences between host, stuffed, and CEAM simulations for all series (Table VII). Intratetrahedral bond angles with Si have a slight broadening of the distribution width after SAA for most series. For SMAS, intratetrahedral bond angles with Al have a slight narrowing of the distribution width after SAA. On the whole, these changes are slight and do not allow a conclusion to be confidently drawn.
Table VII. Intratetrahedral Bond Angles