A correlative four-dimensional study of phase-separation at the subnanoscale to nanoscale of a NiAl alloy

The temporal evolution of ordered γ′(L1₂)-precipitates precipitating in a disordered γ(f.c.c.) matrix is studied in extensive detail for a Ni-12.5 Al at.% alloy aged at 823 K (550 °C), for times ranging from 0.08 to 4096 h. Three-dimensional atom-probe tomography (3-D APT) results are compared to monovacancy-mediated lattice-kinetic Monte Carlo (LKMC₁) simulations on a rigid lattice, which include monovacancy-solute binding energies through 4th nearest-neighbor distances, for the same mean composition and aging temperature. The temporal evolution of the measured values of the mean radius, $〈R\left(t\right)〉$, number density, aluminum supersaturations, and volume fraction of the γ′(L1₂)-precipitates are compared to the predictions of a modified version of the Lifshitz-Slyozov diffusion-limited coarsening model due to Calderon, Voorhees et al. The resulting experimental rate constants are used to calculate the Gibbs interfacial free-energy between the γ(f.c.c.)- and γ′(L1₂)-phases, which enter the model, using data from two thermodynamic databases, and its value is compared to all exiting values. The diffusion coefficient for coarsening is calculated utilizing the same rate-constants and compared to all archival diffusivities, not determined from coarsening experiments, and it is demonstrated to be the inter-diffusivity, $\tilde{D}$, of Ni and Al. The monovacancy-mediated LKMC₁ simulation results are in good agreement with our 3-D APT data. The compositional interfacial width, for the {100}-interface, between the γ(f.c.c.)- and γ'(L1₂)-phases, decreases continuously with increasing aging time and $〈R\left(t\right)〉$, both for the 3-D APT results and the monovacancy-mediated LKMC₁ simulations, in disagreement with an ansatz intrinsic to the trans-interface diffusion-controlled coarsening model, which assumes the exact opposite trend for binary alloys.