Lattice dynamics and negative thermal expansion in the framework compound ZnNi(CN)4 with two-dimensional and three-dimensional local environments
Abstract
ZnNi(CN)4 is a 3D framework material consisting of two interpenetrating PtS-type networks in which tetrahedral [ZnN4] units are linked by square-planar [NiC4] 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 αa=-21.2 × 10-6 K-1 and αc=+14.6×10-6K-1, leading to an overall volume expansion coefficient αV of -26.95×10-6K-1, pointing towards pronounced NTE behavior. Analysis of the derived mode-Gr\"uneisen parameters shows that optic modes around 12 and 40 meV make a significant contribution to NTE. These modes involve localized rotational motions of the [NiC4] and/or [ZnN4] 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 Gr\"uneisen 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 2D within a 3D framework. Hence, although rigid-unit modes account for some of the NTE-driving phonons, the added d-o-f compared with Zn(CN)2 results in modes with twisting motions, capable of inducing greater NTE.
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