Negative thermal expansion and low-frequency modes in cyanide-bridged framework materials

We analyze the intrinsic geometric flexibility of framework structures incorporating linear metal-cyanide-metal (M-CN-M^') linkages using a reciprocal-space dynamical matrix approach. We find that this structural motif is capable of imparting a significant negative thermal expansion (NTE) effect upon such materials. In particular, we show that the topologies of a number of simple cyanide-containing framework materials support a very large number of low-energy rigid-unit phonon modes, all of which give rise to NTE behavior. We support our analysis by presenting experimental verification of this behavior in the family of compounds Zn_xCd_1-x(CN)₂ , which we show to exhibit a NTE effect over the temperature range 25-375K more than double that of materials such as ZrW₂O₈ .