Monte Carlo Study of the Precipitation Kinetics of Al3zr in Al-Zr (original) (raw)
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Zr and Sc precipitate in aluminum alloys to form the Al 3 Zr x Sc 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.
Physical Review B, 2004
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.
Complex precipitation pathways in multicomponent alloys
Nature Materials, 2006
One usual way to strengthen a metal is to add alloying elements and to control the size and the density of the precipitates obtained. However, precipitation in multicomponent alloys can take complex pathways depending on the relative diffusivity of solute atoms and on the relative driving forces involved. In Al-Zr-Sc alloys, atomic simulations based on first-principle calculations combined with various complementary experimental approaches working at different scales reveal a strongly inhomogeneous structure of the precipitates: owing to the much faster diffusivity of Sc compared with Zr in the solid solution, and to the absence of Zr and Sc diffusion inside the precipitates, the precipitate core is mostly Sc-rich, whereas the external shell is Zr-rich. This explains previous observations of an enhanced nucleation rate in Al-Zr-Sc alloys compared with binary Al-Sc alloys, along with much higher resistance to Ostwald ripening, two features of the utmost importance in the field of light high-strength materials.
Precipitation behavior of L12 Al3Zr phase in Al-Mg-Zr alloy
Materials Characterization, 2018
Increasing the recrystallization resistance and the mechanical properties of aluminum-based alloys is possible due to the formation of a nanoscale L1 2-structured Al 3 Zr phase. Treatment conditions and alloys composition affect the size and density of dispersoids and their final properties. In this work we analyze the decomposition of the supersaturated solid solution in the as-cast Al-3%Mg-0.25%Zr alloy for different annealing modes to understand the precipitation kinetics of the Al 3 Zr phase in the presence of Mg. We found that both discontinuous and continuous precipitation mechanisms of the Al 3 Zr phase are possible in the studied low-alloyed material. One-step annealing leads to the formation of coarse (17 nm) spherical precipitates of a coherent L1 2-structured Al 3 Zr phase and discontinuously formed fan-shaped aggregations of the same phase. Two-step annealing provided for the maximum precipitation hardening with the formation of high-density nanoscale (7 nm) dispersoids of the Al 3 Zr phase. This study highlights the importance of the annealing mode of the as-cast material for achieving a high density of the fine L1 2 structured Al 3 Zr phase and the maximum hardening effect.
Precipitation kinetics of AlZr and AlSc in aluminum alloys modeled with cluster dynamics
Acta Materialia, 2005
Precipitation kinetics of Al 3 Zr and Al 3 Sc in aluminum supersaturated solid solutions is studied using cluster dynamics, a mesoscopic modeling technique which describes the various stages of homogeneous precipitation by a single set of rate equations. The only parameters needed are the interface free energy and the diffusion coefficient which are deduced from an atomic model previously developed to study the same alloys. A comparison with kinetic Monte Carlo simulations based on the vacancy diffusion mechanism shows that cluster dynamics correctly predicts the precipitation kinetics provided a size dependent interface free energy is used. It also manages to reproduce reasonably well existing experimental data.
Molecular dynamics analysis of the lattice expansion of Al induced by solid solution of Zr
MATHEMATICS EDUCATION AND LEARNING
Severe plastic deformation is known for its potential to obtain non-equilibrium solid solutions of metals, which under normal conditions are immiscible or have limited solubility. An important role in this process is played by the increased density of defects, which facilitates diffusion in the material during deformation. In particular, recently it was found that the application of ultra-severe plastic deformation can lead to dissolution of Zr atoms in aluminum, while the equilibrium phase diagram of these two metals shows that solid solution of Zr in Al is impossible. In the present work, we use molecular dynamics simulation to calculate the dependence of the lattice parameter of the Al-Zr solid solution as a function of the Zr concentration in the range from one to four atomic percent. It is found that our simulation results are in a reasonably good agreement with the experimental measurements of lattice parameter of Al-Zr solid solution obtained by ultra-severe plastic deformation.
First-principles study of the solubility of Zr in Al
Physical Review B, 2002
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.
Kinetic Monte Carlo Simulations of Precipitation
Advanced Engineering Materials, 2006
We present some recent applications of the atomistic diffusion model and of the kinetic Monte Carlo (KMC) algorithm to systems of industrial interest, i.e. Al-Zr-Sc and Fe-Nb-C alloys, or to model systems. These applications include study of homogeneous and heterogeneous precipitation as well as of phase transformation under irradiation. The KMC simulations are also used to test the main assumptions and limitations of more simple models and classical theories used in the industry, e.g. the classical nucleation theory. Fig. 5. Variation with the nominal concentration and the temperature of the steadystate nucleation rate J st for Al 3 Zr precipitation. Symbols correspond to KMC simulations and lines to CNT.