Negative thermal expansion in the Prussian Blue analog Zn3[Fe(CN)6]2: X-ray diffraction and neutron vibrational studies

Negative thermal expansion of cubic silicon dicarbodiimide, Si(NCN)2, studied byab initiolattice dynamics

We report anab initiocalculation of crystal structure and lattice dynamics of cubic silicon dicarbodiimide, Si(NCN)2, using density functional theory methods. The calculations reveal a low-energy spectrum of rigid unit modes that are shown to be associated with negative thermal expansion. Comparisons are drawn with the closely-related materials Zn(CN)2and the cubic-cristobalite phase of SiO2. Instabilities in the spectrum of rigid unit modes point to the existence of disorder of the positions and orientations of the dicarbodiimide molecular anions.

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.

Negative thermal expansion and associated anomalous physical properties: review of the lattice dynamics theoretical foundation

Negative thermal expansion (NTE) is the phenomenon in which materials shrink rather than expand on heating. Although NTE had been previously observed in a few simple materials at low temperature, it was the realisation in 1996 that some materials have NTE over very wide ranges of temperature that kick-started current interest in this phenomenon. Now, nearly two decades later, a number of families of ceramic NTE materials have been identified. Increasingly quantitative studies focus on the mechanism of NTE, through techniques such as high-pressure diffraction, local structure probes, inelastic neutron scattering and atomistic simulation. In this paper we review our understanding of vibrational mechanisms of NTE for a range of materials. We identify a number of different cases, some of which involve a small number of phonons that can be described as involving rotations of rigid polyhedral groups of atoms, others where there are large bands of phonons involved, and some where the transverse acoustic modes provide the main contribution to NTE. In a few cases the elasticity of NTE materials has been studied under pressure, identifying an elastic softening under pressure. We propose that this property, called pressure-induced softening, is closely linked to NTE, which we can demonstrate using a simple model to describe NTE materials. There has also been recent interest in the role of intrinsic anharmonic interactions on NTE, particularly guided by calculations of the potential energy wells for relevant phonons. We review these effects, and show how anhamonicity affects the response of the properties of NTE materials to pressure.