Classical nucleation theory in ordering alloys precipitating with L12 structure

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

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

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

Phenomenological coefficients in a concentrated alloy for the dumbbell mechanism

International audienceWe present an adaptation of the self-consistent mean field (SCMF) theory to calculate the transport coefficients in a concentrated alloy for diffusion by the dumbbell mechanism. In this theory, kinetic correlations are accounted for through a set of effective interactions within a non-equilibrium distribution function of the system. Transport coefficients are calculated for the FCC and BCC multicomponent concentrated alloys for simple sets of jump frequencies, including different stabilities of the different defects. A first approximation leads to an analytical expression of the Onsager coefficients in a binary alloy, and a second approximation provides with a more accurate prediction. The results of the SCMF theory are compared with existing models and available Monte Carlo simulations, and an interpretation of the set of effective interactions in terms of a competition between jump frequencies is proposed

A mean field theory for diffusion in a dilute multi-component alloy: a new model for the effect of solutes on self-diffusion

International audienceA new extension of the self-consistent mean field (SCMF) theory is developed to describe diffusion in dilute alloys, special attention being paid to the problem of self-diffusion in presence of solute atoms. We start from a microscopic model of the atom-vacancy exchange frequency including nearest neighbour interactions and derive kinetic equations from a Master equation. The non-equilibrium distribution function is expressed trough time dependent effective interactions. Their range of interaction is controlling the level of description of the paths of a vacancy after a first exchange. In contrast to the previous diffusion models devoted to concentrated alloys, the present formulation makes appear into the final result several exchange frequencies associated to a given atom depending on the chemical species of the atoms nearby. A first approximation restricted to nearest neighbour effective interactions yields analytical expressions of the transport coefficients of a face centered cubic dilute binary alloy. The phenomenological coefficients are equivalent to the ones obtained using the five frequency model within the first shell approximation. A new expression of the self-diffusion coefficient is proposed and compared to Monte carlo (MC) simulations using the same atomic diffusion model. The SCMF theory reproduces the main tendencies of the MC simulations, in particular within the random alloy region where the recent five-frequency model was mistaken. The limitations and future improvements of the SCMF approach are easily related to the range of the effective interactions considered

Atomic scale modeling of the thermodynamic and kinetic properties of dilute alloys driven by forced atomic relocations

Sustained external forces acting on a material provide additional mechanisms to evolve the state of the system, and these mechanisms do not necessarily obey the microscopic detailed balance. Therefore, standard methods to compute the thermodynamic and kinetic properties do not apply in such driven systems. The competition between these mechanisms and the standard thermally activated jumps leads to non-equilibrium steady states. We extend the Self-Consistent Mean Field theory to take into account forced atomic relocations (FARs) as a model of these additional kinetic mechanisms. The theory is applied to the atomic-scale modelling of radiation damage. Using a first-shell approximation of the theory, we highlight the violation of Onsager reciprocal relations in driven systems. An implementation of the extended theory into the KineCluE code yields calculations of the effective Onsager coefficients in agreement with Monte Carlo simulations. A systematic parametric study is performed to emphasize the effect of FAR distances and the solute-defect interaction on the diffusion properties. The effect of FAR on the vacancy-solute flux coupling and the solute tracer diffusivity is non-negligible when: (i) the solute-vacancy thermodynamic attraction is large, (ii) the magnitude of the thermal jump frequencies is lower or comparable to the frequencies of FAR, and (iii) the range of interactions between vacancies and solute atoms is close to FAR distances.Comment: typos corrected, references added, revised arguments in Introduction and Modeling section

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

Chemical Evolution in the Substrate due to oxidation: A Numerical Model with Explicit Treatment of Vacancy Fluxes

To get a better understanding of oxidation behavior of Ni-base alloys in PWR primary water, a numerical model for oxide scale growth has been developed. The final aim of the model is to estimate the effects of possible changes of experimental conditions. Hence, our model has not been restricted by the classical hypothesis of quasi-steady state and can consider transient stages. The model calculates the chemical species concentration profiles, but also the vacancy concentration profiles evolution in the oxide and in the metal as a function of time. It treats the elimination of the possible supersaturated vacancies formed at the metal/oxide interface by introducing a dislocation density at the interface and in the metal bulk. This latter density can be related to the cold-working state. Its effect on the vacancy profile evolution is studied in the case of a pure metal. Eventually an extension of the present model to the oxidation of Ni-base alloys is discussed regarding a recent vacancy diffusion model adjusted on Ni-base alloys

Effect of cationic chemical disorder on defect formation energies in uranium-plutonium mixed oxides

At the atomic scale, uranium-plutonium mixed oxides (U,Pu)O_2 are characterized by cationic chemical disorder, which entails that U and Pu cations are randomly distributed on the cation sublattice. In the present work, we study the impact of disorder on point-defect formation energies in (U,Pu)O_2 using interatomic-potential and Density Functional Theory (DFT+U) calculations. We focus on bound Schottky defects (BSD) that are among the most stable defects in these oxides. As a first step, we estimate the distance R_D around the BSD up to which the local chemical environment significantly affects their formation energy. To this end, we propose an original procedure in which the formation energy is computed for several supercells at varying levels of disorder. We conclude that the first three cation shells around the BSD have a non-negligible influence on their formation energy (R_{D} = 7.0 \{AA}). We apply then a systematic approach to compute the BSD formation energies for all the possible cation configurations on the first and second nearest neighbor shells around the BSD. We show that the formation energy can range in an interval of 0.97 eV, depending on the relative amount of U and Pu neighboring cations. Based on these results, we propose an interaction model that describes the effect of nominal and local composition on the BSD formation energy. Finally, the DFT+U benchmark calculations show a satisfactory agreement for configurations characterized by a U-rich local environment, and a larger mismatch in the case of a Pu-rich one. In summary, this work provides valuable insights on the properties of BSD defects in (U,Pu)O_2, and can represent a valid strategy to study point defect properties in disordered compounds.Comment: 33 pages, 20 figure