The structural dynamics of a 1D mixed-metal cyanide, Cu$_{1/3}$Ag$_{1/3}$Au$_{1/3}$CN, with intriguing thermal properties is explored. All the current known related compounds with straight-chain structures, such as CuCN, AgCN, AuCN and M$_x$M$_{1-x}$CN (M, M = Cu, Ag, Au), exhibit 1D negative thermal expansion (NTE) along the chains and positive thermal expansion (PTE) perpendicular to them. Cu$_{1/3}$Ag$_{1/3}$Au$_{1/3}$CN 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 DFT calculations. Synchrotron-based PDF analysis and 13C 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. For this system, DFT-based phonon calculations predict small PTE along the chain due to low-energy chain-slipping modes induced by a bond-rotation 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 to accommodate truly co-planar metals 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.
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