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 [ZnN${}_4$] units are linked by square-planar [NiC${}_4$] 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 ${\alpha }_a$=-21.2 $\times$ 10${}^{-6}$ K${}^{-1}$ and ${\alpha }_c$=+14.6$\times$10${}^{-6}$K${}^{-1}$, leading to an overall volume expansion coefficient ${\alpha }_V$ of -26.95$\times$10${}^{-6}$K${}^{-1}$, pointing towards pronounced NTE behavior. Analysis of the derived mode-Grüneisen parameters shows that optic modes around 12 and 40 meV make a significant contribution to NTE. These modes involve localized rotational motions of the [NiC${}_4$] and/or [ZnN${}_4$] rigid units, echoing what has previously been observed in Zn(CN)${}_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 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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