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

Abstract

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, Nv, 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 19mJm–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 γ 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.