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

Abstract

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) Prussian blue analogues (α = -3.95 × 10 K, 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) originates from the low-frequency phonons (< ∼100 cm), 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) is dominated by N, instead of C atoms, is illustrated. It is interesting to find that the polyhedra of GaFe(CN) 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.

Effect of H2O Molecules on Thermal Expansion of TiCo(CN)6

“…The sample was held at 475 K for 1 h to ensure an anhydrous state, and then the SXRD data of TiCo­(CN) 6 were collected during the cooling process. TiCo­(CN) 6 displays a linear NTE relationship from 475 to 100 K with a linear CTE (α l ) of −4.05 × 10 –6 K –1 (Figure ), which is similar to that of GaFe­(CN) 6 (α l = −3.95 × 10 –6 K –1 , 100–475 K) but smaller than those of ScCo­(CN) 6 (α l = −6.6 × 10 –6 K –1 , 25–600 K) and CdPt­(CN) 6 (α l = −6.65 × 10 –6 K –1 , 375–25 K) . Gao et al proposed the concept of average atomic volume (AAV), i.e., the average volume of atoms occupying a unit cell [AAV = V / ZN , where V = unit cell volume, Z = cell formula units, and N = number of atoms in the chemical formula], aiming to evaluate, explore, and design NTE compounds with open-framework structure.…”

Discovering Large Isotropic Negative Thermal Expansion in Framework Compound AgB(CN)4 via the Concept of Average Atomic Volume

“…As shown in Figure 2b, it is interesting to observe that the present AgB(CN) 4 exhibits a large isotropic NTE behavior in a wide temperature range (α v = −40 × 10 −6 K −1 , 100−600 K). The NTE behavior of AgB(CN) 4 is stronger than the most popular NTE materials ZrW 2 O 8 7 and ScF 3 8 and stronger than most PBAs, such as GaFe(CN) 6 , 22 but smaller than (Zn,Cd)(CN) 2 . 11 Furthermore, the present AgB(CN) 4 shows a wide NTE range, which can be comparable to those in the electronic-driven functional 13 and M(CN) 2 (M = Zn or Cd).…”

EXAFS spectroscopy: a powerful tool for the study of local vibrational dynamics

“…It was found that NTE is induced by the transverse vibrations of the atomic -M-N≡C-M'-linkages through a tension mechanism, since both M-N and M'-C bonds are much softer to bend than to stretch. However, the main vibrational contribution to the NTE comes from the N atoms, since the relative transverse vibrations of the M-N bonds are much larger than that of the M'-C bonds [Figure 17] [113][114][115] . shows the resulting anisotropy of the relative thermal vibrations.…”

“…However, it can be observed that the main contribution comes from the Ga-N thermal vibrations. Figure taken from Ref [113]. .…”