ZnNi(CN)4 is a three-dimensional (3D) framework material consisting of two interpenetrating PtStype 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 (INS) 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 -6 K -1 , leading to an overall volume expansion coefficient, αV of -26.95 × 10 -6 K -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 [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 Grüneisen parameters. Analysis of their eigenvectors reveals that a large transverse motion of the Ni atom in the direction perpendicular to its squareplanar 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.

The structural dynamics of a quasi-one-dimensional (1D) mixed-metal cyanide, Cu1/3Ag1/3Au1/3CN, with intriguing thermal properties is explored. All the current known related compounds with straight-chain structures, such as group 11 cyanides CuCN, AgCN, AuCN and bimetallic cyanides MxM'1-xCN (M, M' = Cu, Ag, Au), exhibit 1D negative thermal expansion (NTE) along the chains and positive thermal expansion (PTE) perpendicular to them. Cu1/3Ag1/3Au1/3CN exhibits similar PTE perpendicular to the chains, however PTE, rather than NTE, is also observed along the chains. In order to understand the origin of this unexpected behavior, inelastic neutron scattering (INS) measurements were carried out, underpinned by lattice-dynamical density-functional-theory (DFT) calculations. Synchrotron-based pairdistribution-function (PDF) analysis and 13 C solid-state nuclear-magnetic-resonance (SSNMR) measurements were also performed to build an input structural model for the lattice dynamical study. The results indicate that transverse motions of the metal ions are responsible for the PTE perpendicular to the chains, as is the case for the related group 11 cyanides. However NTE along the chain due to the tension effect of these transverse motions is not observed. As there are different metal-to-cyanide bond lengths in Cu1/3Ag1/3Au1/3CN, the metals in neighboring chains cannot all be truly co-planar in a straight-chain model. For this system, DFT-based phonon calculations predict small PTE along the chain due to low-energy chain-slipping modes induced by a bondrotation effect on the weak metallophilic bonds. However the observed PTE is greater than that predicted with the straight-chain model. Small bends in the chain provide an alternative explanation for thermal behavior. These would mitigate the tension effect induced by the transverse motions of the metals and, as temperature increases and the chains move further apart, a straightening could occur resulting in the observed PTE. This hypothesis is further supported by unusual evolution in the phonon spectra, which suggest small changes in local symmetry with temperature.

This study explores the relationship between phonon dynamics and negative thermal expansion (NTE) in CuxNi2-x(CN)4. The partial replacement of nickel (II) by copper (II) in Ni(CN)2 leads to a line phase, CuNi(CN)4 (x = 1), and a solid solution, CuxNi2-x(CN)4 (0 ≤ x ≤ 0.5). CuNi(CN)4 adopts a layered structure related to that of Ni(CN)2 (x = 0), and interestingly exhibits 2D NTE which is ~ 1.5 times larger. Inelastic neutron scattering (INS) measurements combined with first principles lattice dynamical calculations provide insights into the effect of Cu 2+ on the underlying mechanisms behind the anomalous thermal behavior in all the CuxNi2-x(CN)4 compounds. The solid solutions are presently reported to also show 2D NTE. The INS results highlight that as the Cu 2+ content increases in CuxNi2-x(CN)4, large shifts to lower energies are observed in modes consisting of localized in-and out-of-plane librational motions of the CN ligand, which contribute to the NTE in CuNi(CN)4. Mode Grüneisen parameters calculated for CuNi(CN)4 show that acoustic and low-energy optic modes contribute the most to the NTE, as previously shown in Ni(CN)2. However, mode eigenvectors reveal a large deformation of the [CuN4] units compared to the [NiC4] units, resulting in phonon modes not found in Ni(CN)2, whose NTE-driving phonons consist predominately of rigid-unit modes. The deformations in CuNi(CN)4 arise because the d 9 square-planar center is easier to deform than the d 8 one, resulting in a greater range of out-of-plane motions for the adjoining ligands.

Mixed-metal cyanides (Cu 1/2 Au 1/2 )CN, (Ag 1/2 Au 1/2 )CN, and (Cu 1/3 Ag 1/3 Au 1/3 )CN adopt an AuCN-type structure in which metal-cyanide chains pack on a hexagonal lattice with metal atoms arranged in sheets. The interactions between and within the metal-cyanide chains are investigated using density functional theory (DFT) calculations, 13 C solid-state NMR (SSNMR), and X-ray pair distribution function (PDF) measurements. Long-range metal and cyanide order is found within the chains: (−Cu–NC–Au–CN−) ∞ , (−Ag–NC–Au–CN−) ∞ , and (−Cu–NC–Ag–NC–Au–CN−) ∞ . Although Bragg diffraction studies establish that there is no long-range order between chains, X-ray PDF results show that there is local order between chains. In (Cu 1/2 Au 1/2 )CN and (Ag 1/2 Au 1/2 )CN, there is a preference for unlike metal atoms occurring as nearest neighbors within the metal sheets. A general mathematical proof shows that the maximum average number of heterometallic nearest-neighbor interactions on a hexagonal lattice with two types of metal atoms is four. Calculated energies of periodic structural models show that those with four unlike nearest neighbors are most favorable. Of these, models in space group Immm give the best fits to the X-ray PDF data out to 8 Å, providing good descriptions of the short- and medium-range structures. This result shows that interactions beyond those of nearest neighbors must be considered when determining the structures of these materials. Such interactions are also important in (Cu 1/3 Ag 1/3 Au 1/3 )CN, leading to the adoption of a structure in Pmm 2 containing mixed Cu–Au and Ag-only sheets arranged to maximize the numbers of Cu···Au nearest- and next-nearest-neighbor interactions.