Thermal responses of Prussian blue lattice, that is, a rocksalt-type network of metal ions bridged by cyano group, are systematically investigated for ${\left(\text{Cs},\text{Rb}\right)}_x{M}^{\text{II}}{\left[{\text{Fe}}^{\text{III}}{\left(\text{CN}\right)}_6\right]}_{y}z{\text{H}}_2\text{O}$ ($M=\text{Ni}$, Cu, Zn, and Cd) and ${\left(\text{Cs},\text{Rb}\right)}_x{M}^{\text{III}}{\left[{\text{Fe}}^{\text{II}}{\left(\text{CN}\right)}_6\right]}_{y}z{\text{H}}_2\text{O}$ ($M=\text{Fe}$ and Co) by means of the synchrotron-radiation x-ray powder diffraction. We found a universal relation between the coefficient ($\beta \equiv d\text{ln}a/dT$; $a$ is lattice constant) of the thermal expansion and magnitude of $a$: $\beta$ changes the sign from positive to negative with increase in $a$. We ascribed the negative thermal expansion observed in the large-$a$ region to intrinsic rotational instability of the $\left[\text{Fe}{\left(\text{CN}\right)}_6\right]$ unit.

• Received 29 March 2009

DOI:https://doi.org/10.1103/PhysRevB.79.172302