Experimental and computational diffusion analysis in Ni-X binary and Ni-Al-X (X = Cr, Mo, Ta, W, Re) ternary systems

Abstract

An extensive diffusion analysis is presented for binary Ni-X and ternary Ni-Al-X (X = Cr, Mo, Ta, W, Re) systems, which play a crucial role in microstructural evolution and phase stability in Ni-Al-based superalloys. Specifically, we highlight changes in the diffusion coefficients of X in the presence of Al and compare diffusional interactions across systems considered. First-principles calculations, combined with activation energies derived from temperature-dependent experiments, reveal consistent trends in Ni-X systems, with variations in activation energies largely attributed to differences in migration energies. In ternary systems, diffusion coefficients estimated from intersecting diffusion profiles show that the main interdiffusion coefficient of X is comparable to its binary counterpart, with similar activation energies. However, cross-diffusion coefficients are shown to significantly influence fluxes, either enhancing or reducing diffusion lengths depending on the relative directions of diffusing elements. For Ni-Al-Re, a single-profile method is employed to overcome uncertainties in estimating composition gradients at the near-end-member intersecting composition. The diffusion coefficients obtained correlate well with the nature of diffusion paths when represented on Gibbs triangles. To extend these findings, a physics-informed neural network (PINN) optimization method is applied to extract composition-dependent diffusion coefficients across the full composition range. The analysis demonstrates the necessity of incorporating experimentally estimated diffusion coefficients as equality constraints, without which optimization reliability is compromised. Overall, the results establish a robust framework for diffusion studies in Ni-Al-X systems, highlighting the critical role of cross-diffusion effects and constraint-enhanced numerical methods.