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 as a result of diffusional fluxes crossing γ(f.c.c.)/γ′(L12) heterophase interfaces. The coupling effects on diffusional fluxes was introduced (PV coarsening model) in terms of the diffusion tensor, D, and the second-derivative tensor of the molar Gibbs free energies, , obtained employing Thermo-Calc and DICTRA calculations. The Gibbs interfacial free energies, , are (16.9±3.4) mJ/m2 with all terms in D and , which changes to (46.3±5.1) mJ/m2, (92.3±7.9) mJ/m2, and (-18.5±2.6) mJ/m2 without including the off-diagonal terms in D, , and both D and , respectively. The experimental APT compositional trajectories are displayed and compared with the PV model in a partial quaternary phase-diagram, employing a 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 . The directions including the off-diagonal terms in D and tensors are consistent with the APT experimental data.
Walter P. Murphy is Prof. of Materials Science and Engineering, Northwestern University, 1996 to present, Founding Director, August 2004, Northwestern University Center for Atom-Probe Tomography (NUCAPT), Member of the National Science Foundation Funded Materials Research Science and Engineering Center, Member of the Department of Energy Funded Superconducting Quantum Materials and System Center, Member of the International Institute for Nanotechnoloygy (IIN) at Northwestern University, Co-Founder and Co-Chief Scientific Officer of NanoAl LLC.