When a compound is maintained in far for equilibrium configurations by nuclear collisionsunder irradiation, the steady-state properties of the system can no longer be predicted from equilibrium thermodynamics. Here we propose Monte Carlo simulations for addressing the question of phase stability under irradiation. They are based on a kinetic model with two dynamics acting in parallel: thermally activated jumps of vacancies and ballistic events induced by nuclear collisions. Two transformations are studied: the A2-B2 order-disorder transition and the precipitation of copper in iron. In the former case a shift from second to first order of the A2-B2 transition, predicted by the model, has been experimentally checked by I MeV electron irradiations of a FeA1 alloy. In the latter case, the precipitation kinetics are determined by Monte Carlo simulations and are found to be in very good agreement with available experimental data.

Cascade size may affect phase stability under irradiation because of two distinct contributions: the replacement to displacement cross section ratio depends on the deposited energy density; ballistic jumps which tend to disorder ordered compounds occur by bursts (of size b), while thermal jumps which restore long range order occur one by one. The latter effect cannot be handled by standard rate theory. A stochastic treatment of the problem, based on a Fokker Planck approximation of the relevant master equation is summarized. It is shown that the possible values of the long range order parameter under irradiation are not affected by the size b of the bursts, but that the respective stability of the former is b dependent. As a consequence, the stability diagram of phases under irradiation varies with b. Such a diagram is computed for the Ni4Mo system where three structures are competing: the disordered solid solution, Dia and D023. A broadening by 100K of the stability domain of the short range ordered structure to the expense of the long range ordered one is predicted when increasing b from 1 to 100. The stochastic potentials introduced in the present treatment are by no means free energies of some constrained state. They can however be computed in a mean field type approximation.

Based on atomic-scale simulation techniques, we study the dislocation pinning mechanism in a dilute Ni(Al) model solid solution. For a solute concentration between 1 and 10 at.%, we found that the pinning of the dislocation on obstacles made of Al pairs is an interaction that operates significantly. The statistics of the dislocation motion is then modified accordingly to the nature of the obstacles and follows modified Mott-Nabarro statistics. Finally, a method to address thermal activation is proposed and exemplified on a periodic row of solute pairs.

The concept of forced alloys is explained and application examples are described. Systematic experiments with natural test pieces and by computer simulations show that, under the working conditions studied (irradiation, crushing, cyclic loading), the alloy may reach a stationnary configuration. Among the parameters controlling this process, the working intensity is of particular importance. The introduced concepts are applied to the study of the wear behaviour of fast train wheels (TGV). Wear rates and out-of-roundness are found to be proportional to this intensity.

The rolling strip of swift train wheels undergoes cyclic loading, which triggers phase transformations in the steel. We define an intensity of forcing, comparable to the milling intensity of the high energy ball milling process, which accounts for the observed evolution of the wear process with distance.

We present molecular dynamics simulations of the interactions between glissile interstitial loops and an edge dislocation in a fcc nickel crystal. This study shows atomic-scale reactions leading to a pinning of the dislocation by the loops which are dragged along when the dislocation unpinns. This atomic-scale information is incorporated in a micromechanical model. Predictions of the model at the micron scale are compared to the initial hardening and subsequent softening of irradiated specimens observed experimentally in traction tests.

Using a vacancy diffusion mechanism for substitutional elements and an interstitial mechanism for carbon atoms, we propose a Monte Carlo method for simulating the coherent precipitation of niobium carbide in alpha -iron. Iron, niobiurn, and carbon atoms are distributed on a rigid, simple cubic lattice which describes both the bcc ferrite structure and the fec NaCl-type structure of NbC. The Monte-Carlo parameters have been fitted with good accuracy to the experimental diffusion and equilibrium data. A residence time algorithm has been adapted in order to handle both the fast interstitial C diffusion and the slow substitutional Nb and Fe diffusion. Depending on the concentration and temperature, the simulations exhibit two kinds of kinetic paths: formation of transient iron carbides at high supersaturation, and nucleation of NbC precipitates at low supersaturation. Not only can the resulting kinetics of nucleation be compared with the classical theory but the simulations also provide information on cluster size, shape and density on the atomic scale which can then be directly compared with tomographic atom probe (TAP) results.

The motion of interstitial clusters in nickel is investigated by Molecular Dynamics, using embedded-atom-method potentials. The observed configuration of clusters consists of dumbbells oriented along a < 110 > direction and centered on one or several adjacent {111} planes. At the simulation temperatures from 450 to 1400 K, these small "loops" with their < 110 > vector were found to be very mobile along their glide cylinder. At least for clusters up to six dumbbells, thermally activated flip of the Burgers vectors is observed and results in a three-dimensional migration path made of several long segments of one-dimensional random walk. We report the calculated one- and three-dimensional diffusion coefficients of clusters up to twelve dumbbells at different temperatures up to 1400K. A diffusion model is presented to take into account the net effect of this mixed 1d-3d migration path.

We present a new microscopic kinetic theory for the calculation of the phenomenological coefficients for matter transport in alloys. The theory is based on the master equation which gives the evolution with time of the distribution function of the system. While at equilibrium the distribution function depends on the configurational Hamiltonian, in the general case it is expressed by a time-dependent effective Hamiltonian. The zero-order self consistent approximation consists in considering only the effective pairwise interactions. Kinetic equations are written to zero order for a stationary state close to equilibrium, from which we infer the analytical expression of the transport coefficients (both diagonal and off-diagonal) in a homogeneous binary solid solution with a vacancy diffusion mechanism. These expressions depend on the configurational Hamiltonian pairwise interactions, the attempt jump frequencies, the alloy composition and the correlation factor for selfdiffusion which reflects the crystallographic structure. They are then compared with Monte Carlo values, obtained from the fluctuation—dissipation theorem. The agreement for the bcc structure is better than 20% over the whole composition range, for a positive as well as a negative heat of mixing. In the pure material, the theory yields the exact value of the correlation factor. Comparisons with the Manning relations and the other microscopic approaches are discussed.

We present a study on the kinetics of coherent precipitation in weakly super-saturated substitutional solid solutions by the Monte Carlo method. Our simulations are based on a simple atomistic model of diffusion by vacancy jumps. The whole precipitation process (from early stages to late stage coarsening) is followed for various supersaturations and temperatures, and typical behaviors observed in the simulations are compared to those predicted by the classical theories. Special emphasis is placed on the first stages of the decomposition (incubation and nucleation) and on the effects of the vacancy diffusion mechanism. Finally we consider the addition of a third (impurity) element, which can be used to control the kinetic pathway: such effects are quantitatively explored with the Monte Carlo method.

Optimal properties of modern interstitial-free ferritic steels are achieved by appropriate additions of certain elements such as Ti. The latter triggers the precipitation of carbides, sulphides and nitrides. The precipitation of FeTiP is sometimes observed but cannot be understood because of the lack of any thermochemical data. This raises the question of the unexpected stability of FeTiP relative to the other phosphides. We have performed ab initio electronic structure calculations to elucidate the origin of this stability. Our calculations show that the position of the Fermi level in the d bands of the various phosphides plays a crucial role in determining their relative stability. In the case of FeTiP, the Fermi level is situated in a region where the bonding states of the intermetallic compound are nearly filled while the antibonding states remain empty. This is quite similar to the case of the pure intermetallic compound FeTi where also the bonding states are filled while the antibonding states remain empty and the Fermi level falls in a pseudogap in the densities of states. This results in a maximum in the cohesion for this compound. Thus the increased stability of the ternary phosphide relative to those of the binary phosphides can, in part, be attributed to the formation of strong metallic bonds, and this increase in cohesion can be qualitatively explained in terms of a simple Friedel-type tight-binding model. The increased metal-P interactions also play a role owing to reduced metal-P distances in the ternary phosphide.

Molecular-dynamics simulations show that, in an embedded-atom method nickel crystal, interstitial loops made of (110) dumbbells may be absorbed by an edge dislocation in two different ways, either being attached to one of the Shockley partials by means of a dislocation junction or being transformed into a double superjog on the dislocation. In both cases, the absorption is assisted by a flip of the loop Burgers vector. The simulations also show that double superjogs lock the dislocation but are only weak obstacles. In all cases, the loops may be dragged by the dislocation and induce on the latter an additional friction which is evaluated from the simulations.

Non-equilibrium interfacial segregations have often their origin in the non conservation of point defects at interfaces; under appropriate circumstances, point defect fluxes to or from interfaces can be triggered which, because of inverse Kirkendall effect, induce an alteration of the composition field in the vicinity of the interface. While this effect has long been modelled in a reliable manner in the special case of dilute ideal solid solutions, describing concentrated alloys raises interesting problems, the solution of which is not fully established. We discuss the available models and present advances, based on kinetic mean field approximations (vacancy and interstitial drag).

In order to identify those features of the phase separation kinetic pathway which are influenced by the vacancy diffusion mechanism in crystalline solid solutions, a simple model of vacancy jump on a rigid lattice is treated by a Monte Carlo technique. The activation energy is configuration dependent, in a way to drive the system towards thermodynamic equilibrium, keeping the details of the vacancy diffusion mechanism. The model is used either to reproduce experimental observations (Fe-Cu, Ni-Cr-Al, Fe-Al), or in a heuristic manner. The effect of the difference in cohesive energies of the alloy constituents (the asymmetry energy) is clearly identified. The direct exchange mechanism fails to reproduce such effects, when treated as in the Kinetic Ising Model (which ignores the asymmetry energy); when treated with the present model, the direct exchange reproduces, at least qualitatively, many observed features, but the vacancy diffusion mechanism introduces some unique features which have been observed experimentally.

Les segregations interfaciales de non-equilibre ont souvent leur origine dans le fait que les defauts ponctuels peuvent etre elimines ou crees aux interfaces; dans les conditions appropriees, par exemple sous irradiation par des particules de haute energie, on peut entretenir des flux de defauts vers les interfaces; ces flux entrainent une redistribution des constituants des alliages (effet Kirkendall inverse) au voisinage des interfaces. Cet effet, qui a des consequences importantes en metallurgie nucleaire, est modelise de maniere satisfaisante depuis longtemps dans le cas des alliages dilues. Par contre, les alliages concentres posent d'interessants problemes, dont tous ne sont pas resolus.

We present a study on the kinetics of coherent precipitation in metallic binary alloys by Monte Carlo simulations, based on a simple atomistic model with diffusion by vacancy jumps. The whole precipitation process (from early stages to late stage coarsening) is followed for various supersaturations and temperatures, and typical behaviours observed in the simulations are compared to those predicted by the classical theories. Special emphasis is placed on the first stages of the decomposition (incubation and nucleation).

A comprehensive mean field treatment of the unmixing of driven solid solutions is given. The stability fields of the stationary, non-equilibrium states which define a dynamical phase diagram are investigated by a linear stability analysis with respect to small concentration fluctuations. Their time evolution is determined by the atomic fluxes which are caused by thermodynamical, ballistic and Kirkendall forces which result from the coupling between solute and sustained point defect fluxes. In the case of a spinodally decomposing alloy, the influence of the irradiation is reflected in a modified amplification factor, from which the decomposition behavior and thus the dynamical phase diagram under irradiation is obtained. For a regular solution, a simple expression of an effective free energy of the system is obtained which proves to be very helpful for the discussion of alloy stability under external forcing.

La segregation induite par l'irradiation (SII) dans les aciers austenitiques est due au flux permanent des lacunes et des interstitiels crees par l'irradiation vers les puits de defauts que sont les surfaces et les interfaces. Pour simuler la SII, nous proposons un modele de cinetique chimique configurationelle en champ moyen. Pour l'alliage ternaire Fe-Ni-Cr, nous ajustons les 15 parametres qui definissent les frequences de saut des lacunes sur des proprietes d'equilibre incluant les enthalpies de melange et sur des donnees experimentales de diffusion de traceur. Des mesures de segregation par spectroscopie d'electrons Auger ne sont utilisees que dans la derniere etape d'ajustement: lors du choix du jeu de frequences de saut des interstitiels (au nombre de 27). Cette methode d'ajustement permet de souligner la contribution importante des interstitiels a la SII. Nous modelisons egalement le piegeage des interstitiels par une impurete et reproduisons l'inhibition complete de la segregation deja observee experimentalement [1].