Hierarchical percolation and electrical conduction of glasses in the 50WO3-(50 − x)P2O5-xNa2O system

The validity of the proposed concept of hierarchical percolation is demonstrated using glasses in the WO3-P2O5-Na2O system as an example. The dependence of the electrical conductivity σ = σ0(ξ − ξcrit)μ (where ξ is the percolation parameter) with an exponent μ ≃ 1.4 close to the exponent theoretically predicted for two-dimensional percolation is obtained for the first time. This confirms our hypotheses regarding the two-dimensional percolation nature of electrical conduction over the surface of a phosphate cluster after the percolation threshold is overcome.