  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.
