Low-Frequency Phonon Driven Negative Thermal Expansion in Cubic GaFe(CN)₆ Prussian Blue Analogues

The understanding of the negative thermal expansion (NTE) mechanism is vital not only for the development of new NTE compounds but also for effectively controlling thermal expansion. Here, we report an interesting isotropic NTE property in cubic GaFe(CN)₆ Prussian blue analogues (α_l = -3.95 × 10^-6 K^-1, 100-475 K), which is a new example to understand the complex NTE mechanism. A combined study of synchrotron X-ray diffraction, X-ray total scattering, X-ray absorption fine structure, neutron powder diffraction, and density functional theory calculations shows that the NTE of GaFe(CN)₆ originates from the low-frequency phonons (< ∼100 cm^-1), which are directly related to the transverse vibrations of the atomic -Ga-N ≡C-Fe- chains. Both the Ga-N and Fe-C chemical bonds are much softer to bend than to stretch. The direct evidence that transverse vibrational contribution to the NTE of GaFe(CN)₆ is dominated by N, instead of C atoms, is illustrated. It is interesting to find that the polyhedra of GaFe(CN)₆ are not rigid, which is a starting assumption in some models describing the NTE properties of other systems. The NTE mechanism can be vividly described by the "guitar-string" effect, which would be the common feature for the NTE property of many open-framework functional materials, such as Prussian blue analogues, oxides, cyanides, metal-organic frameworks, and zeolites.