Electronic structure, bonding and phonon modes in the negative thermal expansion materials of Cd(CN)₂and Zn(CN)₂

Abstract

The disordered configuration, band structures, density of states, Mulliken population, elastic constants, zone center optic phonon modes and their Grüneisen parameters of M(CN)(2) (M = Cd, Zn) have been studied for possible cyanide-ordering patterns by the first-principles plane-wave pseudopotential method based on density functional theory. Total energy calculations predict that MC(2)N(2)-MC(2)N(2) is the most favorable configuration for Cd(CN)(2) whereas all three possible configurations are near equally favorable for Zn(CN)(2). Effective charges and bond order analyses reveal that the M(CN)(2) (M = Cd, Zn) frameworks include much stiffer [Formula: see text] and weaker M-C/N bonds, which account for the flexing of the M-CN-M linkage during the transverse motion of the cyanide-bridge. The transverse translational and the librational modes give rise to negative Grüneisen parameters and therefore contribute to the negative thermal expansion. Transverse vibrations of the C and N atoms in the same (transverse translational modes) or opposite (librational modes) directions have the same effect of drawing the anchoring metal atoms closer. Among all the optical phonon modes, the lowest-energy transverse translational optical modes which are neither Raman nor infrared active in Cd(CN)(2) and Zn(CN)(2) give rise to the largest contribution to the negative thermal expansion.

Relationship between phonons and thermal expansion in Zn(CN)2and Ni(CN)2from inelastic neutron scattering andab initiocalculations

“…Further, investigation using ab-initio calculations [8] of the geometry and electronic structure of Zn(CN) 2 shows that the naturally stiff C≡N bond is paired with weak Zn-C/N bonds. This type of bonding allows large transverse thermally excited motions of the bridging C/N atoms to occur in (M-CN-M) bridges within metal-cyanide frameworks.…”

Mechanism of negative thermal expansion in LaC2 from first-principles prediction

“…Due to numerical errors, slightly imaginary of acoustic phonon modes (∼0.006 THz) was found in the vicinity of point. According to previous calculations [23][24][25], the tiny effects of these imaginary are found to be negligible.…”

“…Within QHA, it is given by (2) ω and g(ω) are the harmonic phonon frequency and the phonon density of states (PhDOS), respectively. In our previous works [23][24][25], this method gained intriguing success. Phonon dispersions and PhDOS are calculated using the supercell method implemented in PHONOPY package [26].…”

Near-Zero Thermal Expansion and Phase Transitions in HfMg1−xZnxMo3O12

“…The low wavenumber modes arise from the external librational and translational vibrations of the connected octahedra–tetrahedra, or the librational and translational motions of metal ions in the Hf(Mg/Zn)–O–Mo linkages, which can also be regarded as the transverse vibrations of the bridging oxygen from the point of view of relative movement. Such an harmonic vibrations along with the distortion of the polyhedra are believed to be the origin of the NTE in the open frame work structure since they bring the two end atoms closer upon heating (Evans, 1999; Ding et al, 2008; Marinkovic et al, 2009; Wang et al, 2013). …”