Negative thermal expansion in NbF₃ and NbOF₂: A comparative theoretical study*

Abstract

Thermal expansion control is always an obstructive factor and challenging in high precision engineering field. Here, the negative thermal expansion of NbF3 and NbOF2 was predicted by first-principles calculation with density functional theory and the quasi-harmonic approximation (QHA). We studied the total charge density, thermal vibration, and lattice dynamic to investigate the thermal expansion mechanism. We found that the presence of O induced the w bond in NbOF2, thus weakening the transverse vibration of F and O in NbOF2, compared with the case of NbF3. In this study, we proposed a way to tailor negative thermal expansion of metal fluorides by introducing the oxygen atoms. The present work not only predicts two NTE compounds, but also provides an insight on thermal expansion control by designing chemical bond type.

Theoretical prediction of negative thermal expansion in cubic VF3

“…Compound Lattice parameters a (Å) Atom (site) Wyckoff position VF 3 3.875 V (1a) (0, 0, 0) F (3d) (0.5, 0, 0) metal fluorides with NTE, such as NbF 3 and ScF 3 . 33,46 As per previous reports, phonons in the low-frequency regions have a significant impact on thermal expansion at low temperatures. 47 The thermal expansion of VF 3 might be mainly determined by the F atoms.…”

“…On the other hand, the temperature dependence of a V follows the same trend with the variation in unit cell volume. The minimum of a V is À6.4 Â 10 À6 K À1 at around 80 K. This value is smaller than that reported for NbF 3 , which also undergoes NTE, and the minimum a V is À31 Â 10 À6 K À1 at around 100 K. 33 We also compare our results with other metal fluorides with cubic symmetry. Most of them exhibit negative expansion properties, and some of them have positive thermal expansion coefficients (Fig.…”

“…Similar to most metal fluorides, the NTE of VF 3 originates from the bridging atom with lateral thermal vibration. 33,49 R point refers to the vibration of the V-F chemical bond in the ab-plane. Interestingly, the F atoms in the ab-plane exhibit mutually perpendicular vibration, along the a and b directions, respectively, while the metal V atoms remain motionless.…”

“…32 Gao firstly predicted that the maximum NTE coefficient of NbF 3 is À31 Â 10 À6 K À1 at 100 K and found that the O-doped NbF 2 O has weaker NTE owing to the smaller transverse vibration amplitude of the O atom. 33 The NTE difference between cubic ScF 3 and NbF 3 may be related to their different chemical bond strength and electrical conductivity. This provides a foundation for modulating ScF 3 -based thermal expansion materials by doping Nb.…”

Isotropic negative thermal expansion and its mechanism in tetracyanidoborate salt CuB(CN)4

“…After the discovery that ZrW 2 O 8 displays strong negative thermal expansion (NTE) over a wide temperature range, [1,2] the interest in NTE has increased considerably due to its promising applications in different engineering fields from fiber optics coatings, high performance fuel cell cathodes to tooth fillings. [3,4] Since then different NTE materials were found out [5][6][7][8] and classified into two classes according to the NTE mechanism: [9][10][11][12][13] phonons driven open-framework materials, such as oxides, [1,3,14,15] fluorides, [16,17] cyanides/Prussian blue analogues (PBAs) [18][19][20][21] and MOFs; [22,23] electronic-related driven materials, such as magnetovolume effect in manganese nitrides [24,25] and Invar alloys, [26,27] ferroelectrovolume effect in PbTiO 3 , [28] charge transfer in BiNiO 3 , [29] metal-insulating transition in Ca 2 RuO 4 . [30] Other examples can be found in the review papers.…”