Negative thermal expansion of cubic silicon dicarbodiimide, Si(NCN)₂, studied by ab initio lattice dynamics

Abstract

We report an ab initio calculation 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) 2 and the cubic-cristobalite phase of SiO 2 . Instabilities in the spectrum of rigid unit modes point to the existence of disorder of the positions and orientations of the dicarbodiimide molecular anions.

The contribution of phonons to the thermal expansion of some simple cubic hexaboride structures: SmB6, CaB6, SrB6 and BaB6

“…This is in contrast to the analogous material Si(NCN) 2 , which we have recently studied using an approach similar to the one here. 41 In that case, the Si–N–C linkage is much more flexible, and the RUMs are well separated from the frequencies of all other phonons and are clearly identified as such.…”

“…In the case of oxides with corner-sharing polyhedra, the RUMs typically propagate with low frequency. The concept of RUMs can be extended to systems composed of structural polyhedra connected via a shared molecular ligand, as in the related materials Zn(CN) 2 3,40 and Si(NCN) 2 , 41 or analogues of Prussian Blue, Fe 4 III [Fe II (CN) 6 ] 3 . 40 However, as was found in the case of Zn(CN) 2 , the RUMs that involve bending of the linear Zn-CN-Zn linkage have relatively high frequency, so one should not assume that in these extended network systems the RUMs will have low frequencies, 3 which is the pertinent issue for the cubic metal hexaborides.…”

Atomic structure of the continuous random network of amorphous C[(C6H4)2]2, PAF-1

“…It is not surprising that the PAF-1 network shows NTE, because in its idealised form it is fully expanded, so fluctuations in local structure involving rotations and displacements of the biphenyl moieties will necessarily give rise to NTE through the tension mechanism. This has been discussed in several places [63][64][65][66], and particularly pertinent is the discussion of networks where the linkers are rod-like molecular ions, such as Zn(CN) 2 [16,67] or Cd(CN) 2 [68], and Si(NCN) 2 [19].…”

“…Elemental carbon and silicon form stable crystalline and amorphous tetrahedral networks, and similar crystalline and amorphous tetrahedral networks are found in silica (including the diamond-like β-cristobalite form [14,15]). Other tetrahedral crystalline networks include the negative thermal expansion materials zinc cyanide [16], Cu 2 O [17,18] and silicon dicarbodiimide [19], and the zeolitic imidazolate frameworks (ZIFs) [20].…”

Insight into the Relationship between Negative Thermal Expansion and Structure Flexibility: The Case of Zn(CN)2-Type Compounds

“…In the past three decades, NTE materials have attracted considerable attention, and a large number of experimental and theoretical studies have been conducted in this topic. − To date, it is well-known that NTE behavior can be driven by low-frequency (phonon) vibrations in framework materials such as oxides, − ,, fluorides, , and cyanides, ,,− but NTE can also be due to magnetovolume effects, ferroelectricity, and charge transfer phenomena. NTE materials can have practical applications, − especially in the control of thermal expansion coefficients and in the design of zero expansion materials. − Therefore, the discovery of new NTE compounds is of great interest.…”