  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.
