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

First-principles study of the solubility of Zr in Al