Trans-interface-diffusion-controlled coarsening in ternary alloys

A theory of trans-interface-diffusion-controlled (TIDC) coarsening of coherent precipitates in ternary alloys is developed, building largely on prior theories of matrix-diffusion-controlled (MDC) coarsening previously published by Morral and Purdy (Scripta Metall Mater, 30 (1994) 905) and Kuehmann and Voorhees (Metall Mater Trans A, 27A (1996) 937). It predicts time-dependent behavior of the type 〈r〉n ≈ kTt   for the growth of precipitates of average radius 〈r〉〈r〉 on aging time, t, where the temporal exponent n (2 ⩽ n ⩽ 3) is intimately connected to the scaled distribution of particle sizes. The theory also predicts the dependencies on t of the far-field matrix solute concentrations of minority components 2 and 3, X∞2,3, specifically X∞2,3 ≈ κT2,3t−1/n. The dependencies of the volume fraction, f, and number density, Nv, on t are also predicted. Equations for the rate constants kT and κT2,3 are derived. These constants depend on the thermophysical parameters of the system, including the trans-interfacial intrinsic diffusion coefficients, DI2 and DI3, interfacial energy, σ and curvatures of the Gibbs free energies of mixing. Equations are derived that enable σ and DI2,3 to be obtained independently of each other from analyses of the data on coarsening. The equations of the TIDC theory are compared with those of the MDC theories (n = 3); all agreements are noted and discrepancies discussed.