Predicting conductivities of alkali borophosphate glasses based on site energy distributions derived from network former unit concentrations

For ion transport in network glasses, it is a great challenge to predict conductivities specifically based on structural properties. To this end it is necessary to gain an understanding of the energy landscape where the thermally activated hopping motion of the ions takes place. For alkali borophosphate glasses, a statistical mechanical approach was suggested to predict essential characteristics of the distribution of energies at the residence sites of the mobile alkali ions. The corresponding distribution of site energies was derived from the chemical units forming the glassy network. A hopping model based on the site energy landscape allowed to model the change of conductivity activation energies with the borate to phosphate mixing ratio. Here we refine and extend this general approach to cope with minimal local activation barriers and to calculate dc-conductivities without the need of performing extensive Monte-Carlo simulations. This calculation relies on the mapping of the many-body ion dynamics onto a network of local conductances derived from the elementary jump rates of the mobile ions. Application of the theoretical modelling to three series of alkali borophosphate glasses with the compositions $0.33$Li$_2$O$-0.67$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$], $0.35$Na$_2$O$-0.65$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] and $0.4$Na$_2$O$-0.6$[$x$B$_2$O$_3$-$(1\!-\!x)$P$_2$O$_5$] shows good agreement with experimental data.