Phase transition and theAg+-ion diffusion in AgI: Effect of homovalentBr−-ion substitution

The incorporation of ${\mathrm{Br}}^{-}$ ions in $\beta -\mathrm{A}\mathrm{g}\mathrm{I}$ leads to an anomalously large increase in the ionic conductivity (${\sigma }_{{\mathrm{Ag}}^{+}}$) and hence in the self-diffusion coefficient of ${\mathrm{Ag}}^{+}$ ions ($D_{{\mathrm{Ag}}^{+}}$) as well as a substantial decrease in the first-order ($\beta -\alpha$) phase-transition temperature ($T_c$). The effect of substitution is found to be qualitatively analogous to that of pressure ($P$), and is attributed to purely elastic displacement (lattice distortion) caused by the "wrong" size of the substituent ($r_{{\mathrm{Br}}^{-}}<r_{{\mathrm{I}}^{-}}$). It is concluded that the order-disorder transition is essentially driven by a critical concentration of Frenkel defects ($n_{\mathrm{ci}}$) beyond which the hexagonal $\beta -\mathrm{A}\mathrm{g}\mathrm{I}$ becomes unstable and transforms to disordered bcc $\alpha -\mathrm{A}\mathrm{g}\mathrm{I}$, a behavior consistent with the theory of Rice, Strassler, and Toombs of phase transitions to superionic conductors.