Lorenzo Malerba

Ternary Fe–Cu–Ni many-body potential to model reactor pressure vessel steels: First validation by simulated thermal annealing

In recent years, the development of atomistic models dealing with microstructure evolution and subsequent mechanical property change in reactor pressure vessel steels has been recognised as an important complement to experiments. In this framework, a literature study has shown the necessity of many-body interatomic potentials for multi-component alloys. In this paper, we develop a ternary many-body Fe–Cu–Ni potential for this purpose. As a first validation, we used it to perform a simulated thermal annealing study of the Fe–Cu and Fe–Cu–Ni alloys. Good qualitative agreement with experiments is found, although fully quantitative comparison proved impossible, due to limitations in the used simulation techniques. These limitations are also briefly discussed.

Fe?Ni many-body potential for metallurgical applications

A many-body interatomic potential for the Fe–Ni system is fitted, capable of describing both the ferritic and austenitic phase. The Fe–Ni system exhibits two stable ordered intermetallic phases, namely, L10 FeNi and L12 FeNi3, that are key issues to be tackled when creating a Fe–Ni potential consistent with thermodynamics. A procedure, based on a rigid lattice Ising model and the theory of correlation functions space, is developed to address all the intermetallics that are possible ground states of the system. While controlling the ground states of the system, the mixing enthalpy and defect properties were fitted. Both bcc and fcc defect properties are compared with density functional theory calculations and other potentials found in the literature. Finally, the potential is thermodynamically validated by constructing the alloy phase diagram. It is shown that the experimental phase diagram is reproduced reasonably well and that our potential gives a globally improved description of the Fe–Ni system in the whole concentration range with respect to the potentials found in the literature.

Simulation of the nanostructure evolution under irradiation in Fe–C alloys

Abstract Neutron irradiation induces in steels nanostructural changes, which are at the origin of the mechanical degradation that these materials experience during operation in nuclear power plants. Some of these effects can be studied by using as model alloy the iron–carbon system. The Object Kinetic Monte Carlo technique has proven capable of simulating in a realistic and quantitatively reliable way a whole irradiation process. We have developed a model for simulating Fe–C systems using a physical description of the properties of vacancy and self-interstitial atom (SIA) clusters, based on a selection of the latest data from atomistic studies and other available experimental and theoretical work from the literature. Based on these data, the effect of carbon on radiation defect evolution has been largely understood in terms of formation of immobile complexes with vacancies that in turn act as traps for SIA clusters. It is found that this effect can be introduced using generic traps for SIA and vacancy clusters, with a binding energy that depends on the size of the clusters, also chosen on the basis on previously performed atomistic studies. The model proved suitable to reproduce the results of low (

Iron chromium potential to model high-chromium ferritic alloys

We present an Fe–Cr interatomic potential to model high-Cr ferritic alloys. The potential is fitted to thermodynamic and point-defect properties obtained from density functional theory (DFT) calculations and experiments. The developed potential is also benchmarked against other potentials available in literature. It shows particularly good agreement with the DFT obtained mixing enthalpy of the random alloy, the formation energy of intermetallics and experimental excess vibrational entropy and phase diagram. In addition, DFT calculated point-defect properties, both interstitial and substitutional, are well reproduced, as is the screw dislocation core structure. As a first validation of the potential, we study the precipitation hardening of Fe–Cr alloys via static simulations of the interaction between Cr precipitates and screw dislocations. It is concluded that the description of the dislocation core modification near a precipitate might have a significant influence on the interaction mechanisms observed in dynamic simulations.

Modelling the diffusion of self-interstitial atom clusters in Fe-Cr alloys

The results of molecular dynamics simulations of the diffusion of self-interstitial atom clusters in Fe–Cr alloys of different Cr content are presented. It is shown that, with increasing Cr concentration, the cluster diffusivity first decreases and then increases, in accordance with the predictions of a model developed recently and based on molecular static calculations. The minimum diffusivity is found at about 10 at% Cr for small clusters and it shifts towards lower concentration with increasing cluster size. The migration energy of SIA clusters is found to lie in between the binding energy of a Cr atom with a crowdion and half of it. This indicates that the mechanism of cluster migration is via the movement of individual crowdions from one Cr atom to another. The values obtained statically are much higher and are argued to be more reliable due to better sampling of different configurations in a bigger simulation box.

Calculation of proper energy barriers for atomistic kinetic Monte Carlo simulations on rigid lattice with chemical and strain field long-range effects using artificial neural networks.

In this paper we take a few steps further in the development of an approach based on the use of an artificial neural network (ANN) to introduce long-range chemical effects and zero temperature relaxation (elastic strain) effects in a rigid lattice atomistic kinetic Monte Carlo (AKMC) model. The ANN is trained to predict the vacancy migration energies as calculated given an interatomic potential with the nudged elastic band method, as functions of the local atomic environment. The kinetics of a single-vacancy migration is thus predicted as accurately as possible, within the limits of the given interatomic potential. The detailed procedure to apply this method is described and analyzed in detail. A novel ANN training algorithm is proposed to deal with the necessarily large number of input variables to be taken into account in the mathematical regression of the migration energies. The application of the ANN-based AKMC method to the simulation of a thermal annealing experiment in Fe-20%Cr alloy is reported. The results obtained are found to be in better agreement with experiments, as compared to already published simulations, where no atomic relaxation was taken into account and chemical effects were only heuristically allowed for.

The effect of prolonged irradiation on defect production and ordering in Fe–Cr and Fe–Ni alloys

The understanding of the primary radiation damage in Fe-based alloys is of interest for the use of advanced steels in future fusion and fission reactors. In this work Fe-Cr alloys (with 5, 6.25, 10 and 15% Cr content) and Fe-Ni alloys (with 10, 40, 50 and 75% Ni content) were used as model materials for studying the features of steels from a radiation damage perspective. The effect of prolonged irradiation (neglecting diffusion), i.e. the overlapping of single 5 keV displacement cascade events, was studied by molecular dynamics simulation. Up to 200 single cascades were simulated, randomly induced in sequence in one simulation cell, to study the difference between fcc and bcc lattices, as well as initially ordered and random crystals. With increasing numbers of cascades we observed a saturation of Frenkel pairs in the bcc alloys. In fcc Fe-Ni, in contrast, we saw a continuous accumulation of defects: the growth of stacking-fault tetrahedra and a larger number of self-interstitial atom clusters were seen in contrast to bcc alloys. For all simulations the defect clusters and the short range order parameter were analysed in detail depending on the number of cascades in the crystal. We also report the modification of the repulsive part of the Fe-Ni interaction potential, which was needed to study the non-equilibrium processes.

Modelling of Radiation Damage in Fe-Cr Alloys

High-Cr ferritic/martensitic steels are being considered as structural materials for a large number of future nuclear applications, from fusion to accelerator-driven systems and GenIV reactors. Fe-Cr alloys can be used as model materials to investigate some of the mechanisms governing their microstructure evolution under irradiation and its correlation to changes in their macroscopic properties. Focusing on these alloys, we show an example of how the integration of computer simulation and theoretical models can provide keys for the interpretation of a host of relevant experimental observations. In particular we show that proper accounting for two basic features of these alloys, namely, the existence of a fairly strong attractive interaction between self-interstitials and Cr atoms and of a mixing enthalpy that changes sign from negative to positive around 8 to 10 % Cr, is a necessary and, to a certain extent, sufficient condition to rationalize and understand their behavior under irradiation. These features have been revealed by ab initio calculations, are supported by experimental evidence, and have been adequately transferred into advanced empirical interatomic potentials, which have been and are being used for the simulation of damage production, defect behavior, and phase transformation in these alloys. The results of the simulations have been and are being used to parameterize models capable of extending the description of radiation effects to scales beyond the reach of molecular dynamics. The present paper intends to highlight the most important achievements and results of this research activity.

Modeling the first stages of Cu precipitation in α-Fe using a hybrid atomistic kinetic Monte Carlo approach

We simulate the coherent stage of Cu precipitation in α-Fe with an atomistic kinetic Monte Carlo (AKMC) model. The vacancy migration energy as a function of the local chemical environment is provided on-the-fly by a neural network, trained with high precision on values calculated with the nudged elastic band method, using a suitable interatomic potential. To speed up the simulation, however, we modify the standard AKMC algorithm by treating large Cu clusters as objects, similarly to object kinetic Monte Carlo approaches. Seamless matching between the fully atomistic and the coarse-grained approach is achieved again by using a neural network, that provides all stability and mobility parameters for large Cu clusters, after training on atomistically informed results. The resulting hybrid algorithm allows long thermal annealing experiments to be simulated, within a reasonable CPU time. The results obtained are in very good agreement with several series of experimental data available from the literature, spanning over different conditions of temperature and alloy composition. We deduce from these results and relevant parametric studies that the mobility of Cu clusters containing one vacancy plays a central role in the precipitation mechanism.

Interatomic potentials for alloys: Fitting concentration dependent properties

A detailed analysis of the embedded atom method and Finnis–Sinclair formalisms is performed, showing their limitations to fit concentration dependent properties of alloys. Two empirical extensions of the former methods, so-called two-band model and concentration dependent model, are analysed in depth, and their heuristic equivalence is shown. An algorithm is proposed for the two-band model, capable of fitting concentration dependent properties of the alloy, such as mixing enthalpy and bulk modulus. The algorithm is then applied to the Fe-Cr system, deriving two interatomic potentials that closely reproduce Fe-Crs complex mixing enthalpy.