No abstract

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 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 Al3Zr and Al3Sc. 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) 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 L12 clusters.

No abstract

The experimental solubility limit of Zr in Al is well-known. Al3Zr has a stable structure DO23 and a metastable one L12. Consequently there is a metastable solubility limit for which only few experimental data are available. The purpose of this study is to obtain by ab-initio calculations the solubility limit of Zr in Al for the stable as well as the metastable phase diagrams. The formation energies of several ordered compounds AlxZr (1−x) , all based on an fcc underlying lattice, were calculated using the FP-LMTO (Full Potential Linear Muffin Tin Orbital) method. Taking into account all the relaxations allowed by the symmetry, we found the DO23 structure to be the stable one for Al3Zr. This set of results was then used with the cluster expansion in order to fit a generalized Ising model through the inverse method of Connolly-Williams. Different ways to consider volume relaxations were examined. This allowed us to calculate in the Bragg-Williams approximation the configurational free energy at finite temperature. According to the previous FP-LMTO calculations the free energy due to electronic excitations can be neglected. For the vibrational free energy of ordered structures we compared results obtained from a calculation of the elastic constants used with the Debye model and results obtained from a calculation of the phonon spectrum. All these different steps lead to a calculation of the solubility limit of Zr in Al which is found to be lower than the experimental one. The solubility limit in the metastable phase diagram is calculated in the same way and can thus be compared to the stable one.

No abstract