Precipitation in Al-Zr-Sc alloys: a comparison between kinetic Monte   Carlo, cluster dynamics and classical nucleation theory
  Zr and Sc precipitate in aluminum alloys to form the Al\_3Zr\_xSc\_{1-x} compound which, for low supersaturations of the solid solution, exhibits the L1\_2 structure. The aim of the present study is to model at an atomic scale the kinetics of precipitation and to build mesoscopic models so as to extend the range of supersaturations and annealing times that can be simulated up to values of practical interest. In this purpose, we use some ab initio calculations and experimental data to fit an Ising type model describing thermodynamics of the Al-Zr-Sc system. Kinetics of precipitation are studied with a kinetic Monte Carlo algorithm based on an atom-vacancy exchange mechanism. Cluster dynamics is then used to model at a mesoscopic scale all the different stages of homogeneous precipitation in the two binary Al-Zr and Al-Sc alloys. This technique correctly manages to reproduce both the kinetics of precipitation simulated with kinetic Monte Carlo as well as experimental observations. Focusing on the nucleation stage, it is shown that classical theory well applies as long as the short range order tendency of the system is considered. This allows us to propose an extension of classical nucleation theory for the ternary Al-Zr-Sc alloy. 
Emmanuel Clouet, Maylise Nastar, Alain Barbu, Christophe Sigli,   Georges Martin