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

Abstract

The temporal evolution of ordered γ'(L12)-precipitates precipitating in a disordered γ(f.c.c.) matrix is studied in extensive detail for a Al at.% alloy aged at 823 K (550 o 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 4 th nearest-neighbor distances, for the same mean composition and aging temperature. The temporal evolution of the measured values of the mean radius, <R(t)>, 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-Wagner 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 extant values dating from 1966. The diffusion coefficient for coarsening is calculated utilizing the same rate constants and compared to all archival diffusivities, not determined from coarsening experiments, and is demonstrated to be the inter-diffusivity, , of Ni and Al. The monovacancy-mediated LKMC1 simulation results are in good agreement with our 3-D APT data. It is demonstrated that 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(t)>, both for the 3-D APT results and monovacancy-mediated LKMC1 simulations, in disagreement with an ansatz intrinsic to the so-called trans-interface diffusion-controlled coarsening model, which assumes the exact opposite trend for binary alloys. | P a g e

Temperature Dependence of the γ/γ′ Interfacial Energy in Binary Ni–Al Alloys

“…and the value reported by Wendt and Haasen (0.005) is quite inconsistent with the solubility limit at 823 K (X ce = 0.1074). The investigation of Plotnikov et al [22] bears some similarities to that of Wendt and Haasen in that the aging temperature, 823 K, was the same and ATP figured prominently in the research. The main differences were the smaller alloy concentration, 12.50 at.…”

“…Using their data to calculateD c andD c 0 at the equilibrium compositions of both phases (see Appendix A), and substituting the results into Eq. [18], leads to the temperature dependence of D c =D I displayed in Figure 1 The interface width, d, was estimated from the limited sources of available experimental data, i.e., the composition profiles across c/c¢ interfaces published by Plotnikov et al [21,22] and a value of d reported by Forghani et al [23] Details of the analyses used to extract the data from figures published by Plotnikov et al are provided in Appendix B; the analyses assume that the concentration profile across an interface is best described by a sigmoid function. [24] The results, based on limited data, indicate that d increases with increasing temperature.…”

“…[27] In all the others the largest values of hri were smaller than r trans , satisfying the condition required for TIDC coarsening. [20] the details of which are described in Appendix A; (b) The temperature dependence of the interface width, d, obtained from analyses of sigmoid fits to the concentration profiles of Plotnikov et al [21,22] and Forghani et al [23] (see Appendix B). Also shown are theoretically calculated results of Woodward et al [25] for the widths of the (100) and (110) c/c¢ interfaces.…”

“…There are four contributions in this area. In chronological order they include the author's data, [11] the data of Chellman and Ardell, [27] the data of Wendt and Haasen [28] , and the data of Plotnikov et al [22] In the first of these investigations X c was measured using the aforementioned magnetic analysis, while the kinetics of particle growth was measured using dark-field TEM. The author's data and the data of Plotnikov et al were previously analyzed using different values of n = 2.432 [7] and 2.2, [2] respectively, and for that reason are re-evaluated here using n = 2.4.…”

“…Fig. 5-The data of Plotnikov et al [22] : (a) the kinetics of particle growth plotted as hri 2.4 vs t; (b) the kinetics of solute depletion plotted as X c vs t -1/2.4 .…”