Ripening of L1 ₂ Ni ₃Ti precipitates in the framework of the trans-interface diffusion-controlled theory of particle coarsening

Abstract

Data are presented on the kinetics of coarsening of γ′-type Ni ₃Ti precipitates (L1 ₂ crystal structure) in three binary Ni–Ti alloys containing 10.31, 11.84, and 13.72at.% Ti aged at 720°C for times up to 64 h. Data on the distributions of particle sizes (PSDs) are also presented. These data, as well as previously published data, are analyzed in light of a new theory of coarsening in which diffusion is controlled by transport through the non-sharp interface between the matrix and precipitate phases. The new theory, called the trans-interface diffusion-controlled (TIDC) theory of coarsening, predicts time (t)-dependent behavior of the type 〈r〉 ⁿ ∝ t for the growth of precipitates of average radius 〈r〉 and X _Ti ∝ t ^−1/n for the depletion of the solute concentration of the matrix, X _Ti. The exponent n is intimately related to the width of the interface between the precipitate and matrix phases, δ, which is assumed to depend on the particle radius as δ ∝ ^m, where n = m + 2. The shape of the scaled distribution of particle sizes (PSD) depends on n and the thermo-physical kinetic constants are independent of volume fraction. The data on kinetics are evaluated and compared for n=2.375, determined from analyses of the PSDs, and for n=3, which is the traditionally accepted value. The agreement between the data on kinetics and predictions of the TIDC theory is acceptable, and the TIDC theory is the only one capable of explaining the experimentally observed absence of an effect of volume fraction on the kinetics at larger volume fractions, and the shapes of the PSDs.