A new ternary intermetallic compound Hf _<i>x</i> Ti _{1- <i>x</i>} Ni ₂ (0.55 ≤ <i>x</i> ≤ 0.72) in the Hf–Ti–Ni system: crystal and electronic structure

Abstract Microstructural and microprobe analyses of as-cast and annealed alloys (1,000 °C for 61 h) revealed a new congruently melting Hf 0.45 Ti 0.55 Ni 2 compound in the Hf–Ti–Ni system. The compound forms two-phase equilibria with Hf 7 Ni 10 , Hf 3 Ni 7 , αHfNi 3 and TiNi 3 and exhibits a homogeneity range of 18–24 at.% Ti at 65 ± 0.5 at.% Ni. Its crystal structure was determined by single-crystal and powder X-ray diffraction. Hf 0.45 Ti 0.55 Ni 2 crystallizes in a derivative of the Co 1.75 Ge prototype exhibiting statistical mixture of hafnium and titanium atoms on 2 d site and two 2 a , 2 c sites occupied by nickel atoms: PS hP 6, SG P 6 3 / mmc , a = 4.225(2), c = 5.044(4) Å. The Rietveld-refined composition, Hf 0.482(2) Ti 0.518(2) Ni 2 , is in close agreement with both the single-crystal X-ray diffraction data and the energy-dispersive X-ray analysis results. The homogeneity range of the compound Hf x Ti 1- x Ni 2 has been refined from powder X-ray diffraction and energy-dispersive X-ray data: (0.55 ≤ x ≤ 0.72), variation of the lattice parameters is the following: a = 4.2045(3) – 4.185(1), c = 5.0055(4) – 5.000(1) Å. The microstructure shows a characteristic twin morphology. The microhardness of the compound was measured as 1,160 ± 20 and 1,140 ± 60 H μ for single-phase as cast alloys containing 18 and 24 at.% Ti, respectively. Electronic structure calculations based on the LMTO method for the ordered model HfTiNi 4 ( P 6/ mmm ) indicate a metallic behavior with significant Ti–Ni, Hf–Ni, and Ti–Hf bonding interactions. The analysis of DOS and COHP indicates strong covalent contributions alongside Ni–Ni antibonding states, suggesting a complex hybrid metallic–covalent bonding nature that stabilizes the Hf–Ti–Ni three-dimensional network.