Thermodynamic description of the Nb-Ni-Si phase diagram using ab initio data and experimental information

Full text: Refractory metal-based composite materials show a great potential as the next generation for ultrahigh temperature applications, above the usual range of application of Ni-based superalloys (1200°C). Niobium is added to these materials in order to form niobium carbide precipitates. In most cases, however, there is more Nb than the stoichiometrically required, and the Nb atoms may form other phases such as complex silicides, e.g., the so-called G phase (Ni16Nb6Si7). Despite of its importance, the Nb-Ni-Si phase diagram is almost completely unknown. We therefore performed a thermodynamic assessment of the system. In order to provide experimental data for the verification of the thermodynamic models, we used X-Ray Diffraction (XRD) and Scanning Electron Microscopy (SEM) results from several alloys heat treated at 1100°C for 500 hours. The experimental results were critically coupled with ab-initio electronic structure calculations using the Full Potential - (Linearized) Augmented Plane Wave + local orbitals (FP-(L)APW+lo) method within the Density Functional Theory (DFT), as implemented in the Wien2k code. The calculations provided energies of formation at 0 K for all expected ternary phases in the system. The ab-initio calculations were also extremely important for the creation of sublattice models and attribution of site occupancies for the Compound Energy Formalism (CEF). For the thermodynamic modeling, we used the most recent descriptions of the three binary subsystems from the literature using the CALPHAD (CALculation of PHAse Diagrams) method. The high precision provided by the ab-initio calculations assure that we need no fit to experimental data. Instead, we need only to adjust the calculated parameters to take the temperature effect into account, guided by a simple Debye extrapolation of the calculated 0 K elastic constants. The agreement with the experimental results and the only available experimental Nb-Ni-Si isothermal section is very good. (author)