The effects of diffusional couplings on compositional trajectories and interfacial free energies during phase separation in a quaternary Ni-Al-Cr-Re model superalloy

Abstract

The temporal evolution of ordered γ′(L12)-precipitates and the compositional trajectories during phase-separation of the γ(face-centered-cubic (f.c.c.))- and γ′(L12)-phases are studied in a Ni–0.10Al-0.085Cr-0.02Re (mole-fraction) superalloy, utilizing atom-probe tomography, transmission electron microscopy, and the Philippe-Voorhees (PV) coarsening model. As the γ′(L12)-precipitates grow, the excesses of Ni, Cr and Re, and depletion of Al in the γ(f.c.c.)-matrix develop because of diffusional fluxes crossing the γ(f.c.c.)/γ′(L12) heterophase interfaces. The coupling effects on diffusional fluxes are introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, G″, obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, σγ/γ′, are (6.9 ± 1.4) mJ/m2 with all terms in D and G″, which changes to (18.9 ± 2.1) mJ/m2, (37.7 ± 3.3) mJ/m2, and (-7.5 ± 1.2) mJ/m2 when not including the off-diagonal terms in D, G″, and both D and G″, respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a partial tetrahedron. The compositional trajectories measured by APT exhibit curvilinear behavior in the nucleation and growth regimes, t < 16 h, which become vectors, moving simultaneously toward the γ(f.c.c.) and γ′(L12) conjugate solvus-surfaces, for the quasi-stationary coarsening regime, t ≥ 16 h. The compositional trajectories for t ≥ 16 h are compared to the PV model with and without the off-diagonal terms in D and G″. The directions, including the off-diagonal terms in the D and G″tensors, are consistent with the APT experimental data.