Giant uniaxial negative thermal expansion in FeZr2 alloy over a wide temperature range

Abstract

Negative thermal expansion (NTE) alloys possess great practical merit as thermal offsets for positive thermal expansion due to its metallic properties. However, achieving a large NTE with a wide temperature range remains a great challenge. Herein, a metallic framework-like material FeZr₂ is found to exhibit a giant uniaxial (1D) NTE with a wide temperature range (93-1078 K, [Formula: see text]). Such uniaxial NTE is the strongest in all metal-based NTE materials. The direct experimental evidence and DFT calculations reveal that the origin of giant NTE is the couple with phonons, flexible framework-like structure, and soft bonds. Interestingly, the present metallic FeZr₂ excites giant 1D NTE mainly driven by high-frequency optical branches. It is unlike the NTE in traditional framework materials, which are generally dominated by low energy acoustic branches. In the present study, a giant uniaxial NTE alloy is reported, and the complex mechanism has been revealed. It is of great significance for understanding the nature of thermal expansion and guiding the regulation of thermal expansion.

Fig. 1. Crystal structure and giant 1D NTE.

a Crystal structure of FeZr₂. b XRD pattern of the bulk sample FeZr₂ measured inside the RD–RD (RD: radial direction) plane. c Rietveld refinements of SXRD patterns for FeZr₂. d Linear thermal expansion measured by a thermo-dilatometer along the vertical direction on heating (93 to 423 K, 300 to 1078 K). e Temperature dependence of the lattice parameter c extracted from NPD, and the change of lattice constant c, △c, extracted by nPDF and SXRD.

Fig. 2. Anisotropic thermal vibration.

a, b Anisotropic displacement parameters (ADPs) of the Zr and M (M = Fe, Ni) atoms in FeZr₂ (a), and NiZr₂ (b) extracted by nPDF. c, d Thermal ellipsoids along different observation directions for FeZr₂ (c) and NiZr₂ (d), respectively.

Fig. 3. Phonon dispersion curves and the schematics of vibrational modes.

a, b Phonon dispersion curves for FeZr₂ (a) and NiZr₂ (b), with the size of the dots corresponding to the magnitude of γ_c; the blue indicates negative γ_c and the red indicates positive γ_c. c Representative phonon modes contribute to the four most negative γ_c at each high-symmetry point (the green dot in (a)) for FeZr₂.

Fig. 4. Electron density of states and -COHP.

a, b The DOS/IDOS (a) of Mdz² (M = Fe, Ni) and -pCOHP/-IpCOHP (b) for the most significant change in isostructure of MZr₂ (M = Fe, Ni). c, d Charge distributions of M₂Zr₄ octahedra in the M–Zr–M–Zr planes with the same isosurfaces at 0.0375 e/r₀³.

Fig. 5. The schematic diagram of the giant 1D NTE.

a, b Zr–M (M = Fe, Ni) bonds expansion: true bond expansion extracted by EXAFS (gray line+symbols) and apparent bond expansion measured by SXRD (orange line+symbols). The bars represent calculated error values. c, d 2D simplified geometry, and evolutions for the schematic diagram of giant 1D NTE FeZr₂ (c) and PTE NiZr₂ (d).