Mixed Alkali Effect in Glasses

We have applied the bond-valence technique to reverse Monte Carlo produced structural models of mixed alkali phosphate glasses in order to elucidate the mixed alkali effect (MAE) in glasses. For the first time, the MAE is reproduced and understood directly from structural models in quantitative agreement with available experimental results. The two types of alkali ions are randomly mixed and have distinctly different conduction pathways of low dimensionality. This implies that $A$ ions tend to block the pathways for the $B$ ions and vice versa, and this is the main reason for the MAE.

Figure 1

Activation energy $E_{\sigma }$ and dc conductivity ${\sigma }_{\mathrm{d}\mathrm{c}}$ versus composition for the glass system ${\mathrm{L}\mathrm{i}}_x{\mathrm{R}\mathrm{b}}_{1-x}{\mathrm{P}\mathrm{O}}_3$ at 300 K. Open squares are experimental data points, taken from Ref. 29, and filled squares correspond to the values predicted from the pathway volume fractions $F$ of the structural models. The solid lines are a guide to the eye.

Figure 2

A $12\AA$ thick slice of the RMC produced structural model of the ${\mathrm{L}\mathrm{i}}_{0.5}{\mathrm{R}\mathrm{b}}_{0.5}{\mathrm{P}\mathrm{O}}_3$ glass, respectively. Small blue spheres refer to Li, large red ones to Rb, and the ${\mathrm{P}\mathrm{O}}_4$ groups are shown as orange tetrahedra.

Figure 3

$7\AA$ thick slices through the conduction pathways $\Delta V<0.2$) for Li and Rb ions in the glasses ${\mathrm{L}\mathrm{i}}_x{\mathrm{R}\mathrm{b}}_{1-x}{\mathrm{P}\mathrm{O}}_3$: (a) $x=0$; (b) $x=0.25$; (c) $x=0.5$; (d) $x=0.75$; (e) $x=1$. The pathways for the Li and Rb ions are shown as blue and red isosurfaces, respectively. (f) Li pathways in ${\mathrm{L}\mathrm{i}}_{0.5}{\mathrm{R}\mathrm{b}}_{0.5}{\mathrm{P}\mathrm{O}}_3$ (blue) and those regions that are blocked by Rb ions but otherwise would have a matching bond valence and therefore been conduction pathways for the Li ions (pink).

Figure 4

Number of sites at a distance up to $r$ from a site in the infinite pathway cluster that are also part of the same cluster, shown for the ${\mathrm{L}\mathrm{i}\mathrm{P}\mathrm{O}}_3$ glass for the valence mismatch threshold values $\Delta V=0.025$ (open squares), $\Delta V=0.1$ (filled squares), $\Delta V=0.2$ (open triangles), and $\Delta V=0.35$ (filled triangles). The slope of the log-log representation represents the fractal dimension of the infinite pathway cluster, and is shown in the figure inset as a function of the chosen $\Delta V$.