Electrical properties of the $\alpha $-pyrochlore Bi$_{2-y}$Sr$_{y}$Ir$_{2}O_{7}$ solid solution

To study the electrical properties of the \textit{Bi}$_{2-y}$\textit{Sr}$_{y}$\textit{Ir}$_{2}O_{7}$ (\textit{\textbraceleft Ir}$_{2}$\textit{O1}$_{6}$\textit{\textbraceright \textbraceleft Bi}$_{2-y}$\textit{Sr}$_{y}$\textit{O2\textbraceright }) solid solution \textit{ab-initio DFT} (\textit{WIEN2k}) calculations were done. In this compound, when \textit{Sr} is introduced the resistivity increases and the $\rho /T$ slope also increases. In this system the \textit{Bi}$_{2-y}$\textit{Sr}$_{y}$\textit{O2} substructure has little contribution to the conductivity, even so, it is indirectly responsible to the conductivity modifications, since it affects the other substructure; \textit{Ir}$_{2}$\textit{O1}$_{6}$, which is conducting. When \textit{Bi} is substituted by \textit{Sr}, it pushes \textit{O1}, shortening the \textit{Ir-O1} bond and the resistivity is supposed to decrease; instead a small increment is found. What is found is that this increment is due to the relaxation time, $\tau $. There are two contributions to $\tau $; a) static; the random replacement of \textit{Bi} by \textit{Sr} introduces `impurities', shortening $\tau $, therefore increasing the resistivity, b) dynamic; due to the thermal oscillations of the atoms. What is found is that the effect of the oscillations in the compound with \textit{Sr} has a larger impact on the electronic structure, thus increasing the $\rho /T$ slope.