Trans-interface-diffusion-controlled coarsening in ternary alloys

Abstract 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 ≈ κ T 2,3 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 κ T 2,3 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 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.