Low-temperature phases of the solid electrolyte RbAg 4 I 5

Important structural features of the two low-temperature phases of ${\mathrm{RbAg}}_{4}$${\mathrm{I}}_{5}$, designated $\ensuremath{\beta}$,$\ensuremath{\gamma}$ in order of decreasing temperature, have been determined, even though the precise structure of the $\ensuremath{\gamma}$ phase is unattainable because of the large number of structural parameters and the limitations on available data. At 130 K, the $\ensuremath{\beta}$ phase is rhombohedral, space group $R32({D}_{3}^{7})$, with $a=11.17\ifmmode\pm\else\textpm\fi{}0.01$ \AA{}, $\ensuremath{\alpha}=90.1\ifmmode^\circ\else\textdegree\fi{}\ifmmode\pm\else\textpm\fi{}0.05\ifmmode^\circ\else\textdegree\fi{}$. Most of the displacements of ions and equilibrium ${\mathrm{Ag}}^{+}$ ion sites, relative to the $\ensuremath{\alpha}$ phase, are small, the largest, 0.3 \AA{}, being those for two ${\mathrm{Ag}}^{+}$ ion sites. The largest displacement of an ${\mathrm{I}}^{\ensuremath{-}}$ ion is 0.1 \AA{}. The most significant difference between the $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases is the preferential distribution of ${\mathrm{Ag}}^{+}$ ions, in the latter, over sets of sites formerly crystallographically equivalent. However, the distribution does not change very much over analogous sites: In $\ensuremath{\alpha}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ the distribution is 0.9, 9.4, and 5.5 ${\mathrm{Ag}}^{+}$ ions in the $\mathrm{Ag}\ensuremath{-}c$, Ag-II, and Ag-III sites, respectively, while the analogous values in $\ensuremath{\beta}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ are 1.3, 10.5, and 4.2. (The limits of error are probably about the same as in the $\ensuremath{\alpha}$ phase.) Neither $\ensuremath{\alpha}$- nor $\ensuremath{\beta}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ can be ordered and therefore the 209-K transition is a "disorder-disorder" transition. The $\ensuremath{\gamma}\ensuremath{-}\mathrm{Rb}{\mathrm{Ag}}_{4}{\mathrm{I}}_{5}$ is trigonal, most probable space group $P321 ({D}_{3}^{2})$, with $a=15.776\ifmmode\pm\else\textpm\fi{}0.005$ \AA{} and $c=19.320\ifmmode\pm\else\textpm\fi{}0.005$ \AA{} at 90 K. The unit cell has three times the volume of the rhombohedral cell and therefore contains 12 ${\mathrm{RbAg}}_{4}$${\mathrm{I}}_{5}$. The structure of the $\ensuremath{\gamma}$ phase is closely related to that of the $\ensuremath{\beta}$ phase and can be derived from it by first transforming the rhombohedral structure to a triply primitive hexagonal cell and then permitting further displacement of ions and ${\mathrm{Ag}}^{+}$ ion sites with respect to their positions in the $\ensuremath{\beta}$ phase, thus resulting in a primitive cell. It is shown that there are 146 possible ordering schemes (under the assumption that 30 ${\mathrm{Ag}}^{+}$ ions fill Ag-II type sites) and that a study of these leads to the probable ${\mathrm{Ag}}^{+}$ ion distribution schemes in the $\ensuremath{\beta}$ phase. This was actually instrumental in attaining the distributions in the $\ensuremath{\beta}$ phase. The $\ensuremath{\gamma}$ phase does not appear to be ordered at 90 K, but the single most probable arrangement for an ordered $\ensuremath{\gamma}$ phase is deduced from the ${\mathrm{Ag}}^{+}$ ion distribution in the $\ensuremath{\beta}$ phase.