Vacancy-Mediated NiAs–Ni ₂ In-Type Intermetallic Phases: Ni 1+δ (In/Sb)

Ni1+δSn (δ = 0.2, 0.4) and Ni1+δ(In/Sb) (δ = 0.1-0.5) (NiAs/Ni₂In type) were synthesized, and their crystal structures were studied in this report. In Ni1+δ(In/Sb), the excess nickel atoms (δ = 0.1-0.5) occupy the vacant trigonal bipyramidal interstitial sites in the NiAs-type structural arrangement, leading to the evolution of a fully disordered to ordered superstructure through a series of incommensurately ordered structures within the B8 phase field. In the phase field, Ni1+δ(In/Sb) (δ = 0.15) that crystallize in the space group P6₃/mmc adopt structure having an intermediate atomic arrangement between NiAs- and Ni₂In-type structures. Phases with δ = 0.2-0.4, adopt incommensurate modulation, and the structure was modeled using (3 + 1)D superspace formalism. The structures of Ni1+δSn (δ = 0.2, 0.4) and Ni1+δ(In/Sb) (δ = 0.2-0.4) crystallize in the orthorhombic superspace group Cmcm(α00)0s0 (a ≈ 4.05 Å, b ≈ 7 Å, and c ≈ 5.15 Å) with a modulation vector q ≈ αa* (where α = 0.42-0.48). Ni1+δ(In/Sb) (δ = 0.45, 0.5) that adopts the ternary variant of Ni₃Sn₂ type (Pnma with a = 7.111(3) Å, b = 5.193(3) Å, and c = 8.2113(2) Å) can alternatively be represented as a commensurately modulated structure (lock-in phase, Cmcm(α00)0s0, α = 0.5). The structural outcome in the phase field is primarily governed by the partial Ni occupancy, and the vacancy disorder in the Ni1+δ(In/Sb) (δ = 0.15) was rationalized by density functional theory (DFT) calculations.