Lattice dynamics and negative thermal expansion in the framework compound ZnNi(CN)$_4$ with two-dimensional and three-dimensional local environments

TL;DR

This study combines neutron scattering and ab initio calculations to analyze phonon dynamics in ZnNi(CN)$_4$, revealing significant negative thermal expansion driven by localized rotational and transverse modes involving its 2D and 3D structural units.

Contribution

It provides the first detailed phonon analysis of ZnNi(CN)$_4$, demonstrating how mixed dimensional local environments influence NTE through specific vibrational modes.

Findings

ZnNi(CN)$_4$ exhibits pronounced NTE with a volume expansion coefficient of -26.95×10$^{-6}$K$^{-1}$.

Optic modes around 12 and 40 meV significantly contribute to NTE, involving rigid unit rotations.

Modes below 10 meV involving transverse Ni motions induce greater NTE due to 2D constraints.

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}$, pointing towards pronounced NTE behavior. Analysis of the derived mode-Gr\"uneisen parameters shows that optic modes around 12 and 40 meV make a significant contribution to NTE. These modes involve localized rotational motions of the [NiC$_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 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.