On the constitution and thermodynamic modelling of the system Ti–Ni–Sn

Abstract

Phase equilibria of the system Ti–Ni–Sn have been determined for the isothermal section at 950 °C based on X-ray powder diffraction (XPD) and electron probe microanalysis (EPMA) of about 60 ternary alloys in as cast and annealed state. The section is characterized by the formation of four ternary compounds labelled τ₁ to τ₄. Whereas two of the ternary compounds are found without significant homogeneity regions: τ₁-TiNiSn (half Heusler phase, MgAgAs-type), τ₃-Ti₂Ni₂Sn (U₂Pt₂Sn-type), τ₄-(Ti_1−x−ySn_xNi_y)Ni₃ with AuCu₃-type exhibits a solution range (0.22 ≤ x ≤ 0.66 and 0.22 ≥ y ≥ 0.02) and a particularly large homogeneity region is recorded for τ₂-Ti_1+yNi_2−xSn_1−y (Heusler phase, MnCu₂Al-type). Extended solid solutions starting from binary phases at 950 °C have been evaluated for Ti₅Ni_1−xSn₃ (filled Mn₅Si₃ = Ti₅Ga₄-type; 0 ≤ x ≤ 1), Ti_1−xSn_xNi₃ (TiNi₃-type; 0 ≤ x ≤ 0.27) and (Ti_1−xNi_x)_1−ySn_y (CsCl-type) reaching a maximum solubility at x = 0.53, y = 0.06). From differential thermal analysis (DTA) in alumina crucibles under argon a complete liquidus surface has been elucidated revealing congruent melting for τ₂-TiNi₂Sn at 1447 °C, but incongruent melting for τ₁-TiNiSn (pseudobinary peritectic formation: + τ₂ ↔ τ₁ at 1180 °C), τ₃-Ti₂Ni₂Sn (peritectic formation: L + τ₂ + Ti₅NiSn₃ ↔ τ₃ at 1151 °C) and τ₄-Ti_1−xSn_xNi₃ (peritectic formation: L + TiNi₃ + (Ni) ↔ τ₄ at 1157 °C). A Schultz–Scheil diagram for the solidification behavior was constructed for the entire diagram involving 20 isothermal four-phase reactions in the ternary. For a thermodynamic CALPHAD assessment of the ternary diagram we relied on the binary boundary systems as modelled in the literature. As thermodynamic data in the ternary system were only available in the literature for the compounds TiNi₂Sn and TiNiSn, heat of formation data were supplied by our density functional theory (DFT) calculations for Ti₂Ni₂Sn, as well as for the solid solutions, which were modelled for Ti_1−xSn_xNi₃, Ti₅Ni_1−xSn₃ and (Ti_1−xNi_x)_1−ySn_y. Thermodynamic calculation was performed with the Pandat software and finally showed a reasonably good agreement for all the 20 invariant reaction isotherms involving the liquid.