Physical properties of {Ti,Zr,Hf}₂Ni₂Sn compounds

Physical properties, i.e. electrical resistivity (4.2-800 K), Seebeck coefficient (300-800 K), specific heat (2-110 K), Vickers hardness and elastic moduli (RT), have been defined for single-phase compounds with slightly nonstoichiometric compositions: Ti_2.13Ni₂Sn_0.87, Zr_2.025Ni₂Sn_0.975, and Hf_2.055Ni₂Sn_0.945. From X-ray single crystal and TEM analyses, Ti₂₊Ni₂Sn_1-, x ∼ 0.13(1), is isotypic with the U₂Pt₂Sn-type (space group P4₂/mnm, ternary ordered version of the Zr₃Al₂-type), also adopted by the homologous compounds with Zr and Hf. For all three polycrystalline compounds (relative densities >95%) the electrical resistivity of the samples is metallic-like with dominant scattering from static defects mainly conditioned by off-stoichiometry. Analyses of the specific heat curves C_pvs. T and C_p/T vs. T² reveal Sommerfeld coefficients of γ_Ti = 14.3(3) mJ mol^-1 K^-2, γ_Zr = 10(1) mJ mol^-1 K^-2, γ_Hf = 9.1(5) mJ mol^-1 K^-2 and low-temperature Debye-temperatures: θLTD = 373(7)K, 357(14)K and 318(10)K. Einstein temperatures were in the range of 130-155 K. Rather low Seebeck coefficients (<15 μV K^-1), power factors (pf < 0.07 mW mK^-2) and an estimated thermal conductivity of λ < 148 mW cm^-1 K^-1 yield thermoelectric figures of merit ZT < 0.007 at ∼800 K. Whereas for polycrystalline Zr₂Ni₂Sn elastic properties were determined by resonant ultrasound spectroscopy (RUS): E = 171 GPa, ν = 0.31, G = 65.5 GPa, and B = 147 GPa, the accelerated mechanical property mapping (XPM) mode was used to map the hardness and elastic moduli of T₂Ni₂Sn. Above 180 K, Zr₂Ni₂Sn reveals a quasi-linear expansion with CTE = 15.4 × 10^-6 K^-1. The calculated density of states is similar for all three compounds and confirms a metallic type of conductivity. The isosurface of elf shows a spherical shape for Ti/Zr/Hf atoms and indicates their ionic character, while the [Ni₂Sn] sublattice reflects localizations around the Ni and Sn atoms with a large somewhat diffuse charge density between the closest Ni atoms.