Kinetic pathways for phase separation: An atomic-scale study in Ni–Al–Cr alloys

The kinetic pathways involved in the formation of γ′(L12 structure)-precipitates during aging of concentrated Ni–Al–Cr alloys at 873 K, for three distinct alloy compositions, are studied experimentally by atom probe tomography, and computationally with lattice kinetic Monte Carlo (LKMC) simulations using parameters deduced from first-principles calculations of cohesive energies, and from experimental diffusion data. It is found that the compositional evolution of the γ′-precipitate phase does not follow the predictions of a classical mean-field model for coarsening of precipitates in ternary alloys. LKMC simulations reveal that long-range vacancy–solute binding plays a key role during the early stages of γ′-precipitation. With the aid of Monte Carlo techniques using the parameters employed in the LKMC simulations, we compute the diffusion matrix in the terminal solid-solutions and demonstrate that key features of the observed kinetic pathways are the result of kinetic couplings among the diffusional fluxes. The latter are controlled by the long-range vacancy–solute binding energies. It is concluded that, because it neglects flux couplings, the classical mean-field approach to phase separation for a ternary alloy, despite its many qualitatively correct predictions, fails to describe quantitatively the true kinetic pathways that lead to phase separation in concentrated metallic alloys.