Phonon-driven phase changes inCs2LiCr(CN)6

Dicesium lithium chromicyanide ${\mathrm{Cs}}_2$LiCr${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_6$ undergoes first- and second-order phase changes at 348 and 310°K, respectively. The room-temperature structure is only slightly distorted from the high-temperature $\mathrm{Fm}3m$ phase. While it was not possible to solve the room-temperature structure using diffraction methods alone, owing to complex multiple twinning, a suitable model could be found with the aid of light-scattering experiments and group theory. The first-order phase transformation at 348°K involves an antiferrodistortive rotation of the rigid Cr${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_6^{3-}$ octahedron about the $z$ axis of the cubic cell ${\nu }_{14}\left(X^{2+}\right)$. The second-order instability at $T_c=310\mathrm{}$°K can be modeled as a soft cesium displacive mode at the $X$ point ${\nu }_{16}\left(X^{5+}\right)$. The room-temperature structure ($\frac{P{2}_1}{n}$) shows the largest distortions from the parent high-symmetry form only along these two phonon directions (6.2° rotation of the complex ion and a 0.09-Å translation of the Cs atom). The lattice instability in the ${\mathrm{Cs}}_2$LiCr${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_6$ crystal is attributable to a thermally excited Cs atom which occupies a site which is too large. Those ${\mathrm{Cs}}_2\mathrm{Li}M{\left(\mathrm{CN}\right)}_6$ salts with smaller Cs holes ($M={\mathrm{Mn}}^{+3\mathrm{}},{\mathrm{Fe}}^{+3\mathrm{}},\mathrm{and} {\mathrm{Co}}^{+3\mathrm{}}$) exhibit $\mathrm{Fm}3m$ cells at room temperature, supporting the suggestion that the size of the Cs environment determines the stability with respect to distortion along the ${\nu }_{14}\left(X^{2+}\right)$ and ${\nu }_{16}\left(X^{5+}\right)$ phonon directions.