Negative Thermal Expansion inZrW2O8: Mechanisms, Rigid Unit Modes, and Neutron Total Scattering

Abstract

The local structure of the low-temperature ordered phase of the negative thermal expansion (NTE) material has been investigated by reverse Monte Carlo (RMC) modeling of neutron total scattering data. We obtain, for the first time, quantitative measurements of the extent to which the and polyhedra move as rigid units, and we show that these values are consistent with the predictions of rigid unit mode theory. We suggest that rigid unit modes are associated with the NTE. Our results do not support a recent interpretation of x-ray-absorption fine structure spectroscopy data in terms of a larger rigid structural component involving the Zr-O-W linkage.

GASP: software for geometric simulations of flexibility in polyhedral and molecular framework structures

“…Geometric analysis of structural models confirms the significance of collective polyhedral rotations in generating NTE. [26] Subsequent materials were developed to maximise the scope for such motion and display NTE on a colossal scale. [27] …”

Soft modes and negative thermal expansion inZn(CN)2from Raman spectroscopy and first-principles calculations

“…As mentioned earlier, using a topological model the network structure of Zn(CN) 2 has been argued to have a large number of low-frequency rigid units modes of (Fig.9 of Ref. [14]) suggesting inconsistency between the Rietweld refined structure and that obtained from PDF analysis.…”

“…Based on structural analysis transverse displacements of the shared oxygen atoms and consequent rotation of polyhedra [1] was suggested as the cause of NTE in Zr(WO 4 ) 2 . In the context of corner linked structures, Zn(CN) 2 is remarkable, as it has C≡N as the linking species between tetrahedral units instead of a single atom and exhibits twice as much coefficient of NTE (-17x10 -6 K -1 ) [10] as that of Zr(WO 4 ) 2 . The structure of Zn(CN) 2 consists of three-dimensional, inter-penetrating, tetrahedral frameworks of Zn-CN-Zn chains [11].…”

“…In the context of corner linked structures, Zn(CN) 2 is remarkable, as it has C≡N as the linking species between tetrahedral units instead of a single atom and exhibits twice as much coefficient of NTE (-17x10 -6 K -1 ) [10] as that of Zr(WO 4 ) 2 . The structure of Zn(CN) 2 consists of three-dimensional, inter-penetrating, tetrahedral frameworks of Zn-CN-Zn chains [11]. Two different cubic structures, m P 3 4 From a topological model treating ZnN 4 /ZnC 4 as rigid units the structure was argued to support a large number of low frequency rigid unit phonon modes (ω ph < 2 THz, ≈70 cm -1 ) that contribute to NTE [13].…”

“…Interest in materials that exhibit negative thermal expansion (NTE) was renewed after the report [1] of high and isotropic NTE in Zr(WO 4 ) 2 over a wide temperature range, leading to extensive work and several reviews on the subject [2][3][4][5]. The structure of Zr(WO 4 ) 2 and several other NTE materials consist of corner sharing tetrahedral and octahedral units.…”