The mixed alkali effect as a consequence of network density and site energy distribution

By reviewing experimental findings on ion diffusion and electrical conductance in binary and ternary glasses it will be shown that three effects determine ion mobility. These are (i) the direct Coulomb interaction between alkali cations and non-bridging oxygen anions, (ii) a broad distribution of cation site energies arising from structural and/or Coulomb disorder and (iii) the network packing density as expressed by the molar volume per mole of oxygen. In ternary glasses with two network modifying oxides the site energy distribution leads to a competition for the low energy sites. By assuming that smaller cations succeed because they come closest to anions, their activation energies for diffusion have to be larger on the average. Thus substituting cations by bigger cations reduces the mobility of the smaller ones. The diffusivity of bigger cations is reduced as well, because they have to move through a network with a mesh size being reduced by the presence of the smaller cations. Describing these counteracting effects with two reasonable parameters allows one to explain the mixed alkali effect quantitatively for a variety of glasses. From a simple estimation of elastic energies one of the parameters can be calculated from the bulk modulus and, therefore, only one parameter which is the width of an energy distribution is left as a free fitting parameter to explain a large body of experimental results.