Origin of the colossal positive and negative thermal expansion in Ag$_3$[Co(CN)$_6$]: an {\it ab initio} Density Functional Theory study

TL;DR

This study uses ab initio DFT calculations to uncover the structural origins of the extreme positive and negative thermal expansion in Ag₃[Co(CN)₆], highlighting the role of a shallow energy surface and nearly-rigid bonds.

Contribution

The paper provides a detailed DFT-based analysis explaining the colossal thermal expansion in Ag₃[Co(CN)₆] and predicts similar behavior in related compounds.

Findings

Positive expansion in the basal plane and negative expansion orthogonally are coupled.

The colossal thermal expansion arises from a shallow energy surface allowing structural flexing.

Inclusion of dispersive interactions improves agreement with experimental data.

Abstract

DFT calculations have been used to provide insights into the origin of the colossal positive and negative thermal expansion in Ag$_3$[Co(CN)$_6]$. The results confirm that the positive expansion within the trigonal basal plane and the negative expansion in the orthogonal direction are coupled due to the existence of a network defined by nearly-rigid bonds within the chains of Co--C--N--Ag--N--C--Co linkages. The origin of the colossal values of the coefficients of thermal expansion arise from an extremely shallow energy surface that allows a flexing of the structure with small energy cost. The thermal expansion can be achieved with a modest value of the overall Gr\"{u}neisen parameter. The energy surface is so shallow that we need to incorporate a small empirical dispersive interaction to give ground-state lattice parameters that match experimental values at low temperature. We compare the results with DFT calculations on two isostructural systems: H$_3$[Co(CN)$_6$], which is known to have much smaller values of the coefficients of thermal expansion, and Au$_3$[Co(CN)$_6$], which has not yet been synthesised but which is predicted by our calculations to be another candidate material for showing colossal positive and negative thermal expansion.