Ion conductivity relaxation and specific heat close to the first-order phase transition of $\gamma -$RbAg$_{4}$I$_{5}$

We report on simultaneous measurements of specific heat at normal pressure and ac conductivity in single-crystalline $\gamma $-RbAg$_{4}$I$_{5}$ close to and below its $\gamma $-to-$\beta $ first order phase transition at 121 K. We found an accurate proportionality between the specific heat, \textbf{\textit{c}}$_{P}$, and the temperature derivative of the product \textbf{\textit{nE}}$_{\sigma }$, where \textbf{\textit{$\beta $ =1- n}}, is the Kohlrausch stretching exponent for the conductivity relaxation and \textbf{\textit{E}}$_{\sigma }$\textbf{\textit{ = d(ln$\sigma )$/d(T}}$^{-1}$\textbf{\textit{)}} is the dc conductivity activation energy, which is non-Arrhenius. Thus, our results show that the dc conductivity activation energy \textbf{\textit{E}}$_{\sigma }$\textbf{\textit{(T)}} includes, besides the true microscopic energy ``barrier'' for independent ionic motion, \textbf{\textit{(1-n) E}}$_{\sigma}$ (according the coupling model), an additional contribution from the enthalpy of the mobile Ag-ions defects, \textbf{\textit{h}}.