Solving the “Coloring Problem” in InPd_3–xAg_x(x = 0–0.7) by Phase Diagrams Modeling and Diffraction Experiments

A series of InPd_3–xAg_x(x = 0–1) compositions were synthesized by conventional high-temperature synthesis, and as-synthesized samples were characterized by powder X-ray diffraction experiments. Up to x = 0.7, InPd_3–xAg_xadopts the ternary substitutional variant of the InPd₃structure (TiAl₃-type), when x > 0.7, elemental Ag starts to segregate along with the main phase. Accurate structural characterization in InPd_3–xAg_xfaces a critical challenge due to the narrow X-ray scattering contrast among constituents In, Pd, and Ag and nearly identical neutron scattering lengths of Pd and Ag. To overcome this “coloring problem”, a combination of calculation of phase diagrams modeling (CALPHAD) and diffraction techniques (X-ray and neutron) was employed. In the compositional range 0 ≤ x ≤ 0.7, InPd_3–xAg_xpresents a ternary variant of the TiAl₃-type structure, where Ag atoms selectively substitute one (the 2b Wyckoff site) of the two Pd sites in InPd₃. Notably, in contrast to the isologous InPd_3–xCu_x(x = 0–1) system, Ag substitution does not form an ordered VRh₂Sn-type structure at the limiting composition. The distinct site preference in InPd_3–xAg_xis elucidated by charge population analysis, electronic structure calculations, and orbital-resolved chemical bonding investigations, and the extent of substitution is supported by formation free energy calculations.