Ionic conductivity of mixed glass former 0.35Na(2)O + 0.65[xB(2)O(3) + (1 - x)P(2)O(5)] glasses

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, 0.35Na2O + 0.65[xB2O3 + (1 - x)P2O5], 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.