Trans-interface-diffusion-controlled coarsening in ternary alloys

摘要

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 ≈ k_(T~t) for the growth of precipitates of average radius (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) ≈ K_(T2,3~(t~(-1/n)) The dependencies of the volume fraction, f, and number density, N_v, on t are also predicted. Equations for the rate constants k_T and K_(T2,3) are derived. These constants depend on the thermophysical parameters of the system, including the trans-interfacial intrinsic diffusion coefficients, D_(I2) and D_(I3), interfacial energy, σ and curvatures of the Gibbs free energies of mixing. Equations are derived that enable σ and D_(I2,3) 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.