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Materials Data on NbNi by Materials Project

NiNb is Frank-Kasper $\mu$ Phase-like structured and crystallizes in the trigonal R-3m space group. The structure is three-dimensional. there are seven inequivalent Nb sites. In the first Nb site, Nb is bonded in a 8-coordinate geometry to eight Nb and six equivalent Ni atoms. There are a spread of Nb–Nb bond distances ranging from 2.61–3.11 Å. All Nb–Ni bond lengths are 2.69 Å. In the second Nb site, Nb is bonded in a 8-coordinate geometry to eight Nb and six equivalent Ni atoms. There are a spread of Nb–Nb bond distances ranging from 2.83–3.13 Å. All Nb–Ni bond lengths are 2.67 Å. In the third Nb site, Nb is bonded in a 6-coordinate geometry to nine Nb and six Ni atoms. All Nb–Nb bond lengths are 2.83 Å. All Nb–Ni bond lengths are 2.77 Å. In the fourth Nb site, Nb is bonded in a 6-coordinate geometry to nine Nb and six Ni atoms. All Nb–Ni bond lengths are 2.78 Å. In the fifth Nb site, Nb is bonded in a 6-coordinate geometry to four Nb and twelve Ni atoms. All Nb–Nb bond lengths are 2.91 Å. There are a spread of Nb–Ni bond distances ranging from 2.73–2.96 Å. In the sixth Nb site, Nb is bonded in a 9-coordinate geometry to seven Nb and nine equivalent Ni atoms. There are three shorter (2.85 Å) and three longer (2.92 Å) Nb–Nb bond lengths. There are three shorter (2.85 Å) and six longer (3.02 Å) Nb–Ni bond lengths. In the seventh Nb site, Nb is bonded to six equivalent Nb and six equivalent Ni atoms to form distorted NbNb6Ni6 cuboctahedra that share corners with twelve equivalent NiNb8Ni4 cuboctahedra, edges with six equivalent NbNb6Ni6 cuboctahedra, and faces with eighteen equivalent NiNb8Ni4 cuboctahedra. All Nb–Ni bond lengths are 2.56 Å. There are three inequivalent Ni sites. In the first Ni site, Ni is bonded to eight Nb and four equivalent Ni atoms to form distorted NiNb8Ni4 cuboctahedra that share corners with two equivalent NbNb6Ni6 cuboctahedra, corners with thirteen NiNb8Ni4 cuboctahedra, edges with five NiNb7Ni5 cuboctahedra, faces with three equivalent NbNb6Ni6 cuboctahedra, and faces with ten equivalent NiNb8Ni4 cuboctahedra. There are two shorter (2.42 Å) and two longer (2.48 Å) Ni–Ni bond lengths. In the second Ni site, Ni is bonded to seven Nb and five Ni atoms to form NiNb7Ni5 cuboctahedra that share corners with fifteen NiNb8Ni4 cuboctahedra, edges with five NiNb7Ni5 cuboctahedra, and faces with thirteen NiNb7Ni5 cuboctahedra. There are one shorter (2.44 Å) and four longer (2.45 Å) Ni–Ni bond lengths. In the third Ni site, Ni is bonded to six equivalent Nb and six equivalent Ni atoms to form NiNb6Ni6 cuboctahedra that share corners with twelve equivalent NiNb7Ni5 cuboctahedra, edges with six equivalent NiNb6Ni6 cuboctahedra, and faces with eighteen equivalent NiNb7Ni5 cuboctahedra.

36 MATERIALS SCIENCE↗

Thermodynamic modeling of the Nb-Ni system with uncertainty quantification using PyCalphad and ESPEI

Here, the Nb–Ni system is remodeled with uncertainty quantification (UQ) using software tools of PyCalphad and ESPEI (the Extensible, Self-optimizing Phase Equilibria Infrastructure) with the presently implemented capability of modeling site fraction based on Wyckoff positions. The five- and three-sublattice models are used to model the topologically close pack (TCP) μ-Nb 7 Ni 6 and δ-NbNi 3 phases according to their Wyckoff positions. The inputs for CALPHAD-based thermodynamic modeling include the thermochemical data as a function of temperature predicted by first-principles and phonon calculations based on density functional theory (DFT), ab initio molecular dynamics (AIMD) simulations, together with phase equilibrium and site fraction data in the literature. In addition to phase diagram and thermodynamic properties, the CALPHAD-based predictions of site fractions of Nb in μ-Nb 7 Ni 6 agree well with experimental data. Furthermore, the UQ estimation using the Markov Chain Monte Carlo (MCMC) method as implemented in ESPEI is applied to study the uncertainty of site fraction in μ-Nb 7 Ni 6 and enthalpy of mixing (ΔH mix ) in liquid.

36 MATERIALS SCIENCE↗