The mixed glass former effect (MGFE) is defined as a nonlinear and nonadditive change in the ionic conductivity with changing glass former fraction at constant modifier composition between two binary glass forming compositions. In this study, mixed glass former (MGF) sodium borophosphate glasses, 0.35Na 2 O + 0.65[xB 2 O 3 + (1 -x)P 2 O 5 ], 0 ≤ x ≤ 1, have been prepared, and their sodium ionic conductivity has been studied. The ionic conductivity exhibits a strong, positive MGFE that is caused by a corresponding strongly negative nonlinear, nonadditive change in the conductivity activation energy with changing glass former content, x. We describe a successful model of the MGFE in the conductivity activation energy terms of the underlying short-range order (SRO) phosphate and borate glass former structures present in these glasses. To do this, we have developed a modified Anderson-Stuart (A-S) model to explain the decrease in the activation energy in terms of the atomic level composition dependence (x) of the borate and phosphate SRO structural groups, the Na + ion concentration, and the Na + mobility. In our revision of the A-S model, we carefully improve the treatment of the cation jump distance and incorporate an effective Madelung constant to account for many body coulomb potential effects. Using our model, we are able to accurately reproduce the composition dependence of the activation energy with a single adjustable parameter, the effective Madelung constant, that changes systematically with composition, x, and varies by no more than 10% from values typical of oxide ceramics. Our model suggests that the decreasing columbic binding energies that govern the concentration of the mobile cations are sufficiently strong in these glasses to overcome the increasing volumetric strain energies (mobility) caused by strongly increasing glass-transition temperatures combined with strongly decreasing molar volumes of these glasses. The dependence of the columbic binding energy term on the relative high-frequency dielectric permittivity suggests that the increased polarizability of the bridging oxygens connecting SRO tetrahedral boron units to phosphorus units causes further charge delocalization away from the negatively charged tetrahedral boron units, leading to a lowering of the charge density, and is the underlying cause of the MGFE. Disciplines Materials Science and Engineering CommentsReprinted with permission from Journal of Physical Chemistry B 117 (2013) , 0 ≤ x ≤ 1, have been prepared, and their sodium ionic conductivity has been studied. The ionic conductivity exhibits a strong, positive MGFE that is caused by a corresponding strongly negative nonlinear, nonadditive change in the conductivity activation energy with changing glass former content, x. We describe a successful model of the MGFE in the conductivity activation energy terms of the underlying short-range order (SRO) phosphate and borate glass former structures present in these glasses. To do this, we have developed a modified Anderson-Stuart (...

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The mixed glass former (MGF) effect (MGFE) is defined as a nonlinear and nonadditive change in the ionic conductivity with changing glass former composition at constant modifier composition. In this study, sodium borophosphate 0.35Na2O + 0.65[xB2O3 + (1 -x)P2O5], 0 ≤ x≤ 1, glasses which have been shown to exhibit a positive MGFE have been prepared and examined using Raman and 11B and 31P magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopies. Through examination of the short-range order (SRO) structures found in the ternary glasses, it was determined that the minority glass former, B for 0.1 ≤ x ≤ 0.7 and P for 0.7 ≤ x ≤ 0.9, is "overmodified" and contains more Na+ ions than would be expected from simple linear mixing of the binary sodium borate, x = 1, and sodium phosphate, x = 0, glasses, respectively. Changes in the intermediate range order (IRO) structures were suggested by changes in the NMR spectral chemical shifts and Raman spectra wavenumber shifts over the full composition range x in the Raman and MAS NMR spectra. The changes observed in the chemical shifts of 31P MAS NMR spectra with x are found to be too large to be caused solely by changing sodium modification of the phosphate SRO structural groups, and this indicates that internetwork bonding between phosphorus and boron through bridging oxygens (BOs), P-O-B, must be a major contributor to the IRO structure of these glasses. While not fully developed, a firstorder thermodynamic analysis based upon the Gibbs free energies of formation of the various SRO structural units in this system has been developed and can be used to account for the preferential formation of tetrahedral boron groups, B4, by the reaction of B3 with P2 groups to form B4 and P3 groups, respectively, where the superscript denotes the number of BOs on these units, in these glasses. This preference for B4 units appears to be a predominate cause of the changing modifier to glass former ratio with composition x in these ternary MGF glasses and appears to be associated with the large negative value of the Gibbs free energy of formation of this group. Disciplines Materials Science and Engineering | Physical Chemistry CommentsReprinted with permission from The Journal of Physical Chemistry B 117 (2013) P magic angle spinning nuclear magnetic resonance (MAS NMR) spectroscopies. Through examination of the short-range order (SRO) structures found in the ternary glasses, it was determined that the minority glass former, B for 0.1 ≤ x ≤ 0.7 and P for 0.7 ≤ x ≤ 0.9, is "overmodified" and contains more Na + ions than would be expected from simple linear mixing of the binary sodium borate, x = 1, and sodium phosphate, x = 0, glasses, respectively. Changes in the intermediate range order (IRO) structures were suggested by changes in the NMR spectral chemical shifts and Raman spectra wavenumber shifts over the full composition range x in the Raman and MAS NMR spectra. The changes observed in the chemical shifts of 31 P MAS NMR spectra with x are found to be too large to be ...

We present new results for the Reverse Monte Carlo modeling of 0.35Na2O + 0.65[xB2O3 + (1 -x)P2O5] glasses based on previously reported X-ray diffraction (XRD) data. Structural models have been generated that accurately reproduce the pair correlation functions and structure factors determined by XRD while maintaining nearly perfect charge neutrality between the positively charged cations and the negatively charged phosphate and borate oxyanion groups and while maintaining appropriate bond distances between the various atom pairs. These models, however, are not successful in accounting for the concentrations of network forming units (NFUs), as predicted by recent theoretical modeling and by magic-angle spinning nuclear magnetic resonance (MAS NMR) data for sodium borate glasses with similar stoichiometry. By a further refinement of the modeling, the NFU concentrations can be successfully reproduced as well. For the optimized structures, we investigate the question if the conductivity activation energy correlates with the volume fraction of the sodium long-range diffusion paths, as identified in the RMC modeling.

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