Monte Carlo Study of the Precipitation Kinetics of Al3zr in Al-Zr
  Zr precipitates in Al to form the phase Al3Zr. For a low supersaturation in Zr of the fcc solid solution, it has been observed that during the precipitation first steps the Al3Zr precipitates have the metastable L12 structure and that they transform themselves to the stable DO23 structure for long enough annealing time. The aim of this study is to model the kinetics of precipitation during this nucleation stage. We use FP-LMTO (Full-Potential Linear-Mu n-Tin-Orbitals) calculations to fit a generalized Ising model describing thermodynamics of the Al-Zr system. As we are interested in the nucleation stage, the structures considered to obtain the interactions of the Ising model are lying on a perfect fcc lattice having the lattice parameter of Al. This allows us to stabilize the L12 structure with respect to the DO23. In order to be able to take into account the influence of local environment on kinetics, interactions for the tetrahedron of first nearest-neighbors are considered, and for the pair of second nearest neighbours so as to stabilize the L12 structure. We then generalize our description of the configurational energy of the binary Al-Zr to the one of the ternary Al-Zr-Vacancy system by including interactions with vacancies. Saddle point energies for the migration of the vacancy are fitted using experimental di usion coe cients. This model is then employed in a kinetic Monte Carlo simulation which considers the di usion through the jumps of a vacancy. Thus we are able to study the Al3Zr kinetics of nucleation. 
Emmanuel Clouet, Maylise Nastar