Microscopic spherical variational models of AgI (Cu halide)-based solid electrolytes

A new microscopic description of the ${\mathrm{Ag}}^{+}$ electrolyte in AgI-based superionic conductors is presented. It is argued that the energy differences between available ${\mathrm{Ag}}^{+}$ sites are dominated by screened Coulomb ${\mathrm{Ag}}^{+}$-${\mathrm{Ag}}^{+}$ repulsion. Site-free energies are obtained by varying a trial function for the distribution of ${\mathrm{Ag}}^{+}$ ions amongst the available sites of a sphere centered at a given probe site. We demonstrate the superiority of our lattice-liquid picture over previous lattice-gas models for the ${\mathrm{Ag}}^{+}$ electrolyte. For $\alpha -\mathrm{A}\mathrm{g}\mathrm{I}$, we obtain very good agreement with experimental data for activation energy and disorder entropy, and with molecular-dynamics calculations of the Ag-Ag pair distribution. Our method is applied to $\alpha -\mathrm{R}\mathrm{b}{\mathrm{Ag}}_4{\mathrm{I}}_5$, and it appears sensitive enough to distinguish between two existing conflicting crystallographic determinations.