Direct observation of a transverse vibrational mechanism for negative thermal expansion in Zn(CN)₂: An atomic pair distribution function analysis

The instantaneous structure of the cyanide-bridged negative thermal expansion (NTE) material Zn(CN)₂ has been probed using atomic pair distribution function (PDF) analysis of high energy X-ray scattering data (100-400 K). The temperature dependence of the atomic separations extracted from the PDFs indicates an increase of the average transverse displacement of the cyanide bridge from the line connecting the Zn^II centers with increasing temperature. This allows the contraction of non-nearest-neighbor Zn-Zn′ and Zn-C/N distances despite the observed expansion of the individual direct Zn-C/N and C-N bonds. Thus, this analysis provides definitive structural confirmation that an increase in the average displacement of bridging atoms is the origin of the NTE behavior. The lattice parameters reveal a slight reduction in the NTE behavior at high temperature from a minimum coefficient of thermal expansion (α = dl/ldJ) of -19.8 × 10^-6 K ^-1 below 180 K, which is attributed to interaction between the doubly interpenetrated frameworks that comprise the structure.