Quantitative predictions of the trans-interface diffusion-controlled theory of particle coarsening

Abstract

Data on the coarsening of γ′ (Ni 3Al) precipitates in binary Ni–Al alloys are re-examined quantitatively in light of the theory of trans-interface diffusion-controlled (TIDC) coarsening, which predicts time-dependent behavior of the type 〈 r〉 n ≈ k Tt for the growth of precipitates of average radius 〈 r〉 and X ≈ κ Tt –1/ n for the depletion of solute concentration in the matrix, X. The exponent n is intimately related to the width of the precipitate–matrix interface, δ, which depends on r as δ ∝ r m ( m = n − 2). The scaled distribution of particle sizes (PSD) also depends on n, while the rate constants k T and κ T depend on the thermophysical constants of the alloy system. In Ni–Al alloys n = 2.4, determined from analyzing three different sets of PSDs. Quantitative analysis yields interfacial free energies and chemical diffusion coefficients that agree exceptionally well with extant data. The TIDC theory is the only theory that is consistent, both qualitatively and quantitatively, with the entirety of the data.