Mixed-mode growth of a multicomponent precipitate in the quasi-steady state regime

Abstract

An exact analytical solution of the Fick's second law was developed and applied to the mixed-mode growth of a multicomponent ellipsoidal precipitate growing with constant eccentricities in the quasi-stationary regime. The solution is exact if the nominal composition, equilibrium concentrations and material properties are assumed constant, and can be applied to compounds having no limitations in the number of components. The solution was compared to the solution calculated by a diffusion-controlled application software and it was found that the solute concentrations at the interface can be determined knowing only the nominal composition, the full equilibrium concentrations and the coefficients of diffusion. The thermodynamic calculations owing to find alternative tie-lines are proven to be useless in the mixed-mode model. From this, it appears that the search of alternative tie-lines is computationally counterproductive, even when the interface has a very high mobility. A more efficient computational scheme is possible by considering that a moving interface is not at equilibrium.

Multiphase modelling of the growth kinetics of precipitates in Al-Cu alloys during artificial aging

“…That model provided a quasi-stationary solution for a precipitate in an infinite binary matrix [16]. This approach was extended for the growth of multicomponent precipitates [17], and a time-discretization technique was introduced to upgrade the analysis capability of the model for finite systems, including the dissolution of the unstable phases [18]. Nevertheless, the application of all these contributions [16][17][18] was limited so far to the isothermal evolution of only one type of precipitate.…”

Analytical Modeling of the Mixed-Mode Growth and Dissolution of Precipitates in a Finite System

“…Larouche [9] provided an exact analytical solution for the quasi-stationary mixed-mode growth of an ellipsoidal precipitate in a binary system. Naseri et al [10] later extended the mixed-mode solution to calculate the growth of a precipitate containing more than one specie diffusing in the matrix. These authors showed that the search for alternative tie-lines is useless for the calculation of interfacial compositions, since the interface is not at equilibrium during growth.…”