Bernoulli and self-destructive percolation on non-amenable graphs

In this note we study some properties of infinite percolation clusters on non-amenable graphs. In particular, we study the percolative properties of the complement of infinite percolation clusters. An approach based on mass-transport is adapted to show that for a large class of non-amenable graphs, the graph obtained by removing each site contained in an infinite percolation cluster has critical percolation threshold which can be arbitrarily close to the critical threshold for the original graph, almost surely, as p approaches p_c. Closely related is the self-destructive percolation process, introduced by J. van den Berg and R. Brouwer, for which we prove that an infinite cluster emerges for any small reinforcement.Comment: 7 page

Influence of inversion on Mg mobility and electrochemistry in spinels

Magnesium oxide and sulfide spinels have recently attracted interest as cathode and electrolyte materials for energy-dense Mg batteries, but their observed electrochemical performance depends strongly on synthesis conditions. Using first principles calculations and percolation theory, we explore the extent to which spinel inversion influences Mg$^{2+}$ ionic mobility in MgMn$_2$O$_4$ as a prototypical cathode, and MgIn$_2$S$_4$ as a potential solid electrolyte. We find that spinel inversion and the resulting changes of the local cation ordering give rise to both increased and decreased Mg$^{2+}$ migration barriers, along specific migration pathways, in the oxide as well as the sulfide. To quantify the impact of spinel inversion on macroscopic Mg$^{2+}$ transport, we determine the percolation thresholds in both MgMn$_2$O$_4$ and MgIn$_2$S$_4$. Furthermore, we analyze the impact of inversion on the electrochemical properties of the MgMn$_2$O$_4$ cathode via changes in the phase behavior, average Mg insertion voltages and extractable capacities, at varying degrees of inversion. Our results confirm that inversion is a major performance limiting factor of Mg spinels and that synthesis techniques or compositions that stabilize the well-ordered spinel structure are crucial for the success of Mg spinels in multivalent batteries