Trans-interface-diffusion-controlled coarsening of γ' precipitates in ternary Ni-Al-Cr alloys

摘要

Published data on the coarsening behavior of γ' precipitates in three ternary Ni-Al-Cr alloys are examined in light of the theory of trans-interface-diffusion-controlled (TIDC) coarsening, in which the kinetics is controlled by diffusion through the coherent precipitate-matrix interface. The experimental data are independent of the equilibrium γ' volume fraction, as expected for TIDC coarsening. Kinetics of the type (r)~n ∝ t for the growth of precipitates of average radius (r), and X_(∞Al) and X_(∞Cr) ∝ t~(-1/n) for the variations of the far-field matrix solute concentrations, X_(∞Al,Cr) with aging time, t, are characteristic of TIDC coarsening. The temporal exponent n ≈ 2.4 was obtained from the fitting of published particle size distributions. Based on correlation coefficients, the dependencies of (r)~n on t and X_(∞Al,Cr) on t~(-1/n) were comparable for n = 2.4 and n = 3 (the temporal exponent for matrix-diffusion-controlled coarsening). The dependencies of volume fraction, f, and number density, N_v, on t are also compared with theoretical predictions. Using a thermodynamic model of the Ni-Al-Cr phase diagram, the interfacial free energy, σ, was estimated from analysis of the data; σ varies from ~14.5 to 19 mJ m~(-2) in the three alloys. Interfacial diffusion coefficients, also obtained from analysis of the data, are greater than those in the γ' phase but smaller than those in the y phase, which is consistent with the demands of the TIDC theory. Comparisons with the results from previously published work are noted and all discrepancies are discussed.