A major challenge
in the modeling of ionically conducting glasses
is to understand how the large variety of possible chemical compositions
and specific features of their structure influence ionic transport
quantities. Here we revisit and extend a theoretical approach for
alkali borophosphate glasses, where changes of conductivity activation
energies with the borate to phosphate mixing ratio are related to
modifications of the ionic site energy landscape. The landscape modifications
are caused by varying amounts of different units forming the glassy
network, which lead to spatial redistributions of the counter-charges
of the mobile alkali ions. Theoretical approaches are presented to
calculate variations of both network former unit concentrations and
activation energies with the glass composition. Applications to several
alkali borophosphate glasses show good agreement with experimental
data.
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 0.33Li2O–0.67[xB2O3–(1 − x)P2O5], 0.35Na2O–0.65[xB2O3–(1 − x)P2O5] and 0.4Na2O–0.6[xB2O3–(1 − x)P2O5] shows good agreement with experimental data.
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