90 research outputs found

    The vacancy - edge dislocation interaction in fcc metals: a comparison between atomic simulations and elasticity theory

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    The interaction between vacancies and edge dislocations in face centered cubic metals (Al, Au, Cu, Ni) is studied at different length scales. Using empirical potentials and static relaxation, atomic simulations give us a precise description of this interaction, mostly in the case when the separation distance between both defects is small. At larger distances, elasticity theory can be used to predict this interaction. From the comparison between both approaches we obtain the minimal separation distance where elasticity applies and we estimate the degree of refinement required in the calculation. In this purpose, isotropic and anisotropic elasticity is used assuming a perfect or a dissociated edge dislocation and considering the size effect as well as the inhomogeneity interaction

    Monte Carlo Study of the Precipitation Kinetics of Al3zr in Al-Zr

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    Zr precipitates in Al to form the phase Al3Zr. For a low supersaturation in Zr of the fcc solid solution, it has been observed that during the precipitation first steps the Al3Zr precipitates have the metastable L12 structure and that they transform themselves to the stable DO23 structure for long enough annealing time. The aim of this study is to model the kinetics of precipitation during this nucleation stage. We use FP-LMTO (Full-Potential Linear-Mu n-Tin-Orbitals) calculations to fit a generalized Ising model describing thermodynamics of the Al-Zr system. As we are interested in the nucleation stage, the structures considered to obtain the interactions of the Ising model are lying on a perfect fcc lattice having the lattice parameter of Al. This allows us to stabilize the L12 structure with respect to the DO23. In order to be able to take into account the influence of local environment on kinetics, interactions for the tetrahedron of first nearest-neighbors are considered, and for the pair of second nearest neighbours so as to stabilize the L12 structure. We then generalize our description of the configurational energy of the binary Al-Zr to the one of the ternary Al-Zr-Vacancy system by including interactions with vacancies. Saddle point energies for the migration of the vacancy are fitted using experimental di usion coe cients. This model is then employed in a kinetic Monte Carlo simulation which considers the di usion through the jumps of a vacancy. Thus we are able to study the Al3Zr kinetics of nucleation.Comment: Proceeding of the Third International Alloy Conference, Lisbon 2002. Published in P.E.A. Turchi, A. Gonis, K. Rajan and A. Meike (Eds.), Complex Inorganic Solids - Structural, Stability, and Magnetic Properties of Alloys, (Springer Verlag, New York, 2005), pp. 215-24

    Classical nucleation theory in ordering alloys precipitating with L12 structure

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    By means of low-temperature expansions (LTEs), the nucleation free energy and the precipitate interface free energy are expressed as functions of the solubility limit for alloys which lead to the precipitation of a stoichiometric L12 compound such as Al-Sc or Al-Zr alloys. Classical nucleation theory is then used to obtain a simple expression of the nucleation rate whose validity is demonstrated by a comparison with atomic simulations. LTEs also explain why simple mean-field approximation like the Bragg-Williams approximation fails to predict correct nucleation rates in such an ordering alloy

    Elastic energy of a straight dislocation and contribution from core tractions

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    International audienceWe derive an expression of the core traction contribution to the dislocation elastic energy within linear anisotropic elasticity theory using the sextic formalism. With this contribution, the elastic energy is a state variable consistent with the work of the Peach-Koehler forces. This contribution needs also to be considered when extracting from atomic simulations core energies. The core energies thus obtained are real intrinsic dislocation properties: they do not depend on the presence and position of other defects. This is illustrated by calculating core energies of edge dislocation in bcc iron, where we show that dislocations gliding in {110} planes are more stable than the ones gliding in {112} planes

    Precipitation kinetics of Al3Zr and Al3Sc in aluminum alloys modeled with cluster dynamics

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    Precipitation kinetics of Al3Zr and Al3Sc 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.Comment: Acta Mater. (2005), in pres

    Hydrogen and vacancy clustering in zirconium

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    The effect of solute hydrogen on the stability of vacancy clusters in hexagonal closed packed zirconium is investigated with an ab initio approach, including contributions of H vibrations. Atomistic simulations within the density functional theory evidence a strong binding of H to small vacancy clusters. The hydrogen effect on large vacancy loops is modeled through its interaction with the stacking faults. A thermodynamic modeling of H segregation on the various faults, relying on ab initio binding energies, shows that these faults are enriched in H, leading to a decrease of the stacking fault energies. This is consistent with the trapping of H by vacancy loops observed experimentally. The stronger trapping, and thus the stronger stabilization, is obtained for vacancy loops lying in the basal planes, i.e. the loops responsible for the breakaway growth observed under high irradiation dose.Comment: submitte

    Dislocation dynamics simulations with climb: kinetics of dislocation loop coarsening controlled by bulk diffusion

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    Dislocation climb mobilities, assuming vacancy bulk diffusion, are derived and implemented in dislocation dynamics simulations to study the coarsening of vacancy prismatic loops in fcc metals. When loops cannot glide, the comparison of the simulations with a coarsening model based on the line tension approximation shows a good agreement. Dislocation dynamics simulations with both glide and climb are then performed. Allowing for glide of the loops along their prismatic cylinders leads to faster coarsening kinetics, as direct coalescence of the loops is now possible

    Cluster Dynamics Modeling of Materials: Advantages and Limitations

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    The aim of this paper is to give a short review on cluster dynamics modeling in the field of atoms and point defects clustering in materials. It is shown that this method, due to its low computer cost, can handle long term evolution that cannot, in many cases, be obtained by Lattice Kinetic Monte Carlo methods. Indeed, such a possibility is achieved thanks to an important drawback that is the loss of space correlations of the elements of the microstructures. Some examples, in the field of precipitation and irradiation of metallic materials are given. The limitations and difficulties of this method are also discussed. Unsurprisingly, it is shown that it goes in a very satisfactory way when the objects are distributed homogeneously. Conversely, the source term describing the primary damage under irradiation, by nature heterogeneous in space and time, is tricky to introduce especially when displacement cascades are produced

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

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    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
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