Lattice dynamics and negative thermal expansion in the framework compound ZnNi (CN) 4 with two-dimensional and three-dimensional local environments

ZnNi (CN_{) 4} is a three-dimensional (3D) framework material consisting of two interpenetrating PtS-type networks in which tetrahedral [Zn N₄ ] units are linked by square-planar [Ni C₄ ] units. Both the parent compounds, cubic Zn (CN_{) 2} and layered Ni (CN_{) 2} , are known to exhibit 3D and 2D negative thermal expansion (NTE), respectively. Temperature-dependent inelastic neutron scattering measurements were performed on a powdered sample of ZnNi (CN_{) 4} to probe phonon dynamics. The measurements were underpinned by ab initio lattice dynamical calculations. Good agreement was found between the measured and calculated generalized phonon density-of-states, validating our theoretical model and indicating that it is a good representation of the dynamics of the structural units. The calculated linear thermal expansion coefficients are α_a=-21.2 ×10^-6K^-1 and α_c=+14.6 ×10^-6K^-1 , leading to an overall volume expansion coefficient, α_V of -26.95 ×10^-6K^-1 , pointing towards pronounced NTE behavior. Analysis of the derived mode-Grüneisen parameters shows that the optic modes around 12 and 40 meV make a significant contribution to the NTE. These modes involve localized rotational motions of the [Ni C₄ ] and/or [Zn N₄ ] rigid units, echoing what has previously been observed in Zn (CN_{) 2} and Ni (CN_{) 2} . However, in ZnNi (CN_{) 4} , modes below 10 meV have the most negative Grüneisen parameters. Analysis of their eigenvectors reveals that a large transverse motion of the Ni atom in the direction perpendicular to its square-planar environment induces a distortion of the units. This mode is a consequence of the Ni atom being constrained only in two dimensions within a 3D framework. Hence, although rigid-unit modes account for some of the NTE-driving phonons, the added degree of freedom compared with Zn (CN_{) 2} results in modes with twisting motions, capable of inducing greater NTE.