Nucleation ofAl3ZrandAl3Scin aluminum alloys: From kinetic Monte Carlo simulations to classical theory

Abstract

Zr and Sc precipitate in aluminum alloys to form the compounds ${\mathrm{Al}}_3\mathrm{Zr}$ and ${\mathrm{Al}}_3\mathrm{Sc}$ which for low supersaturations of the solid solution have the ${L1\mathrm{}}_2$ structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of ${\mathrm{Al}}_3\mathrm{Zr}$ and ${\mathrm{Al}}_3\mathrm{Sc}.$ These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test different mean-field approximations [Bragg-Williams approximation as well as cluster variation method (CVM)] for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small ${L1\mathrm{}}_2$ clusters.