Phonon dynamics in the layered negative thermal expansion compounds C uxN i2 -x(CN) 4

This study explores the relationship between phonon dynamics and negative thermal expansion (NTE) in C u_xN i_{2 -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, C u_xN i_{2 -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 two-dimensional (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 C u^{2 +} on the underlying mechanisms behind the anomalous thermal behavior in all the C u_xN i_{2 -x}(CN_{) 4} compounds. The solid solutions are presently reported to also show 2D NTE. The INS results highlight that as the C u^{2 +} content increases in C u_xN i_{2 -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 [Cu N₄ ] units compared to the [Ni C₄ ] 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 d⁹ square-planar center is easier to deform than the d⁸ one, resulting in a greater range of out-of-plane motions for the adjoining ligands.