In generating these microstructures

In generating these microstructures, the volume fraction of the smaller BF12 is crucial since they surround the larger LMO grains and relatively few are needed to create a conductive network. The BF12 grains effectively by-pass the resistive LMO grains, as shown in Figs. 9(b) and 8(c) for 20 vol% BF12. At lower values of x, these paths become discontinuous with gaps forming, Figs. 9(d) and 8(e) for 5 vol%. This percolation threshold is observed directly in the measured s. Fig. 10 highlights the extracted s and εr arising from the FEM simulations. For 5 vol% BF12, s rises but at 10 vol% there is a discontinuous change, attributed to the formation and conducting pathways. For >10 vol% BF12, there is gradual convergence towards s of the BF12 end member. However, for εr no percolation effect is observed and the value tends towards LMO, consistent with a parallel summation, predicted by series mixing rules: