First-principles study of the solubility of Zr in Al

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.

Nucleation ofAl3ZrandAl3Clouet1, Nastar2, Sigli3 2004Phys. Rev. BSelf Cite1335930View full textAdd to dashboardCite

“…One should notice that these solubility limits have been found to be consistent with ab-initio calculations 25,30 and thus with the formation energies we used for Al 3 Zr and and Al 3 Sc.…”

“…until Al melting temperature (T mel = 934K). For Al-Zr interactions, as we want to model precipitation of the metastable L1 2 structure of Al 3 Zr compound, we use the metastable solubility limit that we previously obtained from ab-initio calculations 25 , whereas for Al 3 Sc the L1 2 structure is stable and we use the solubility limit arising from a thermodynamic modelling of experimental data 32 :…”

Final Report for Department of Energy Grant No. DE-FG02-02ER45997, "Alloy Design of Nanoscale Precipitation Strengthened Alloys: Design of a Heat Treatable Aluminum Alloy Useful to 400C"

“…Therefore, we have recalculated these quantities using his C ij values, and the method described in section 2.4. Similarly, we have calculated the polycrystalline elastic moduli of L1 2 -Al 3 Zr using the C ij values of Clouet et al [57]. From these quantities, the polycrystalline elastic moduli of the multicomponent L1 2 phase can be calculated with the assumption of linear superposition effect, which has been demonstrated to be a good approximation [59].…”

Grain Refinement during Rapid Solidification of Aluminum–Zirconium Alloys Using Electrospark Deposition

“…With respect to the formation of the sub-stochiometric phase in the ¢A free region, we believe that the cooling rate has reduced to a point too low to form a supersaturated solid solution and that the solute concentration is too low to form the ¢A phase, favoring the formation of these precipitates. 12) In the case of the AlZr system, Clouet et al 32) have modeled the formation energy of several sub-stoichiometric Al-rich phases and found that the following compounds can be present: Al 4 Zr, Al 7 Zr, Al 8 Zr, Al 15 Zr and Al 31 Zr. It is worth mentioning that no experimental evidence was provided.…”