Thermal Expansion in 3$d$-Metal Prussian Blue Analogs -- A Survey Study

We present a comprehensive study of the structural properties and the thermal expansion behavior of 17 different Prussian Blue Analogs (PBAs) with compositions $M^{II}_{3}[(M')^{III}$\textit{(CN)}$_{6}]_{2}$\textit{.nH}$_{2}O$ and $M^{II}_{2}$\textit{[Fe}$^{II}$\textit{(CN)}$_{6}$\textit{].nH}$_{2}O$, where $M^{II}$\textit{ = Mn, Fe, Co, Ni, Cu} and \textit{Zn}, $(M')^{III}$\textit{ = Co, Fe} and $n$ = 5 to 18. Temperature-dependent X-ray diffraction studies were performed in the temperature range between -150$^{o}$C (123 K) and room temperature. The vast majority of the studied PBAs were found to crystallize in cubic structures of space groups$Fm\overline 3 m$, $F\overline 4 3m$ and$Pm\overline 3 m$. The temperature dependence of the lattice parameters was taken to compute an average coefficient of linear thermal expansion in the studied temperature range. Of the 17 compounds, 9 display negative values for the average coefficient of linear thermal expansion, which can be as large as 39.7 x 10$^{-6}$ K$^{-1}$ for \textit{Co}$_{3}$\textit{[Co(CN)}$_{6}]_{2.}12H_{2}O$. All of the $M^{II}_{3}$\textit{[Co}$^{III}$\textit{(CN)}$_{6}]_{2}$\textit{.nH}$_{2}O $compounds show negative thermal expansion behavior, which correlates with the Irving-Williams series for metal complex stability. The thermal expansion behavior for the PBAs of the $M^{II}_{3}$\textit{[Fe}$^{III}$\textit{(CN)}$_{6}]_{2}$\textit{.nH}$_{2}O$ family are found to switch between positive (for \textit{M = Mn, Co, Ni}) and negative (\textit{M = Cu, Zn}) behavior, depending on the choice of the metal cation ($M)$. On the other hand, all of the $M^{II}_{2}$\textit{[Fe}$^{II}$\textit{(CN)}$_{6}$\textit{].nH}$_{2}O$ compounds show positive thermal expansion behavior.