On the Electronic Structure and Thermodynamics of Alloys

A free energy formalism is developed in order to describe phase equilibria in binary alloys. The proposed phenomenological approach uses a limited number of experimental data to provide a global thermodynamic description of a system including its equilibrium and metastable phase diagrams. Emphasis is placed on the description of short range order by means of the cluster variation method. A microscopic theory is also developed in order to predict the enthalpies of formation of transition metal alloys as well as the short range order dependence of these enthalpies. The theory uses a tight-binding Hamiltonian together with the generalized perturbation method. 0ff~diagonal disorder is taken into account, and charge transfer is treated self consistently in the random alloy. All input parameters to the theory are obtained from ab-initio calculations for the pure elements. In this regard, the model can be considered parameter free. The phenomenological approach has been used to analyzed the Al-Ni, Ni~Cr, and Al~Li systems. It is found that the vibrational entropy of‘ formation plays an important role in the thermodynamics of the Al-Li and Ni-Cr alloys. The approach allows an accurate description of stable and metastable order-disorder or order-order equilibria existing in the Ni-Al or AL~Li systems. The model is used to predict a metastable clustering tendency in Al-Li alloys which appears to have been recently confirmed by experiment. The microscopic theory has been applied to the VB-VIE and IVB-VIIIB (Ni, Pt, Pd) alloys. The calculations are in good agreement with the available experimental data and phase diagram information. It is shown that off-diagonal disorder and electronic self-consistency play a crucial role in the accuracy of the results

On the Electronic Structure and Thermodynamics of Alloys

A free energy formalism is developed in order to describe phase equilibria in binary alloys. The proposed phenomenological approach uses a limited number of experimental data to provide a global thermodynamic description of a system including its equilibrium and metastable phase diagrams. Emphasis is placed on the description of short range order by means of the cluster variation method. A microscopic theory is also developed in order to predict the enthalpies of formation of transition metal alloys as well as the short range order dependence of these enthalpies. The theory uses a tight-binding Hamiltonian together with the generalized perturbation method. 0ff~diagonal disorder is taken into account, and charge transfer is treated self consistently in the random alloy. All input parameters to the theory are obtained from ab-initio calculations for the pure elements. In this regard, the model can be considered parameter free. The phenomenological approach has been used to analyzed the Al-Ni, Ni~Cr, and Al~Li systems. It is found that the vibrational entropy of‘ formation plays an important role in the thermodynamics of the Al-Li and Ni-Cr alloys. The approach allows an accurate description of stable and metastable order-disorder or order-order equilibria existing in the Ni-Al or AL~Li systems. The model is used to predict a metastable clustering tendency in Al-Li alloys which appears to have been recently confirmed by experiment. The microscopic theory has been applied to the VB-VIE and IVB-VIIIB (Ni, Pt, Pd) alloys. The calculations are in good agreement with the available experimental data and phase diagram information. It is shown that off-diagonal disorder and electronic self-consistency play a crucial role in the accuracy of the results

Precipitation in Al-Zr-Sc alloys: a comparison between kinetic Monte Carlo, cluster dynamics and classical nucleation theory

Zr and Sc precipitate in aluminum alloys to form the Al\_3Zr\_xSc\_{1-x} compound which, for low supersaturations of the solid solution, exhibits the L1\_2 structure. The aim of the present study is to model at an atomic scale the kinetics of precipitation and to build mesoscopic models so as to extend the range of supersaturations and annealing times that can be simulated up to values of practical interest. In this purpose, we use some ab initio calculations and experimental data to fit an Ising type model describing thermodynamics of the Al-Zr-Sc system. Kinetics of precipitation are studied with a kinetic Monte Carlo algorithm based on an atom-vacancy exchange mechanism. Cluster dynamics is then used to model at a mesoscopic scale all the different stages of homogeneous precipitation in the two binary Al-Zr and Al-Sc alloys. This technique correctly manages to reproduce both the kinetics of precipitation simulated with kinetic Monte Carlo as well as experimental observations. Focusing on the nucleation stage, it is shown that classical theory well applies as long as the short range order tendency of the system is considered. This allows us to propose an extension of classical nucleation theory for the ternary Al-Zr-Sc alloy.Comment: submitted for publication in "Solid-Solid Phase Transformations in Inorganic Materials", edited by TMS, 200

Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

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 di erent 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.Comment: submitted to Physical Review B (2004

Compréhension de la stabilité thermique des alliages d'aluminium Al-Cu-Mg

Les alliages d'aluminium 2xxx (Al-Cu-Mg) sont connus pour être performants à chaud et sont par exemple utilisés pour certaines pièces de structure des avions. L'effet de la composition en Cu et Mg sur leur stabilité thermique, ainsi que celui de la précipitation durcissante associée ont été étudiés. Des comportements différents sont observés et trois zones de composition (en poids %) identifiées: 3,1–3,7Cu et 1,6–2,0Mg : durcissement par la phase S' (Al2CuMg), limite d'élasticité ∼ 465 MPa à l'état T8 et bonne stabilité thermique jusqu'à 200 ∘C

First principles study of the solubility of Zr in Al

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 Mu n 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. Di erent 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 di erent 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

Influence of Mg, Ag and Zn minor solute additions on the precipitation kinetics and strengthening of an Al-Cu-Li alloy

International audienc