Pär Olsson

This work presents a full object kinetic Monte Carlo framework for the simulation of the microstructure evolution of reactor pressure vessel (RPV) steels. The model pursues a " grey-alloy " approach, where the effect of solute atoms is seen exclusively as a reduction of the mobility of defect clusters. The same set of parameters yields a satisfactory evolution for two different types of alloys, in very different irradiation conditions: an Fe-C-MnNi model alloy (high flux) and a high-Mn, high-Ni RPV steel (low flux). A satisfactory match with the experimental characterizations is obtained only if assuming a substantial immo-bilization of vacancy clusters due to solute atoms, which is here verified by means of independent atomistic kinetic Monte Carlo simulations. The microstructure evolution of the two alloys is strongly affected by the dose rate: a predominance of single defects and small defect clusters is observed at low dose rates, whereas larger defect clusters appear at high dose rates. In both cases, the predicted density of interstitial loops matches the experimental solute–cluster density, suggesting that the MnNi-rich nanofeatures might form as a consequence of solute enrichment on immobilized small interstitial loops, which are invisible to the electron microscope.

Three semi-empirical force field FeCr potentials, two within the formalism of the two-band model and one within the formalism of the concentration dependent model, have been benchmarked against a wide variety of density functional theory (DFT) structures. The benchmarking allows an assessment of how reliable empirical potential results are in different areas relevant to radiation damage modelling. The DFT data consist of defect-free structures, structures with single interstitials and structures with small di- and tri-interstitial clusters. All three potentials reproduce the general trend of the heat of formation (h.o.f.) quite well. The most important shortcomings of the original two-band model potential are the low or even negative h.o.f. for Cr-rich structures and the lack of a strong repulsion when moving two solute Cr atoms from being second-nearest neighbours to nearest neighbours. The newer two-band model potential partly solves the first problem. The most important shortcoming in the concentration dependent model potential is the magnitude of the Cr-Cr repulsion, being too strong at short distances and mostly absent at longer distances. Both two-band model potentials do reproduce long-range Cr-Cr repulsion. For interstitials the two-band model potentials reproduce a number of Cr-interstitial binding energies surprisingly well, in contrast to the concentration dependent model potential. For Cr interacting with clusters, the result can sometimes be directly extrapolated from Cr interacting with single interstitials, both according to DFT and the three empirical potentials.

The influence of the local environment on vacancy and self-interstitial formation energies has been investigated in a face-centered-cubic (fcc) Fe-10Ni-20Cr model alloy by analyzing an extensive set of first-principle calculations based on density functional theory. Chemical disorder has been considered by designing special quasirandom structures and four different collinear magnetic structures have been investigated in order to determine a relevant reference state to perform point defect calculations at 0 K. Two different convergence methods have also been used to characterize the importance of the method on the results. Although our fcc Fe-10Ni-20Cr would be better represented in terms of applications by the paramagnetic state, we found that the antiferromagnetic single-layer magnetic structure was the most stable at 0 K and we chose it as a reference state to determine the point defect properties. Point defects have been introduced in this reference state, i.e., vacancies and Fe-Fe, Fe-Ni, Fe-Cr, Cr-Cr, Ni-Ni, and Ni-Cr dumbbell interstitials oriented either parallel or perpendicular to the single layer antiferromagnetic planes. Each point defect studied was introduced at different lattice sites to consider a sufficient variety of local environments and analyze its influence on the formation energy values. We have estimated the point defect formation energies with linear regressions using variables which describe the local environment surrounding the point defects. The number and the position of Ni and Cr first nearest neighbors to the point defects were found to drive the evolution of the formation energies. In particular, Ni is found to decrease and Cr to increase the vacancy formation energy of the model alloy, while the opposite trends are found for the dumbbell interstitials. This study suggested that, to a first approximation, the first nearest atoms to point defects can provide reliable estimates of point defect formation energies.

Small interstitial-type defects in iron with complex structures and very low mobilities are revealed by molecular dynamics simulations. The stability of these defect clusters formed by nonparallel 110 dumbbells is confirmed by density functional theory calculations, and it is shown to increase with increasing temperature due to large vibrational formation entropies. This new family of defects provides an explanation for the low mobility of clusters needed to account for experimental observations of
microstructure evolution under irradiation at variance with the fast migration obtained from previous atomistic simulations for conventional self-interstitial clusters.

Density functional theory calculations have been used to study relaxed interstitial configurations in FeCr alloys. The ionic and electronic ground states of 69 interstitial structures have been determined. Interstitials were placed in alloys with up to 14at.% Cr. Cr atoms were either monatomically dispersed or clustered together within a periodically repeated supercell consisting of 4×4×4 cubes of bcc unit cells. The distance between the interstitials and Cr atoms was varied within the supercells. It is shown that Cr atoms beyond third-nearest-neighbor distance from the interstitial can still have an interaction with it of up to 0.9eV . The multibody nature of the Cr-Cr interactions causes the Cr-interstitial interaction to be strongly concentration dependent. The Cr-Cr interaction in defect-free alloys is also dependent on the overall Cr concentration. The effective Cr-Cr repulsion is weaker in alloys than in an environment of pure Fe. Apart from the Cr concentration, the Cr-interstitial interaction also depends on the dispersion level of Cr atoms beyond third-nearest-neighbor distance from the interstitial. The formation energy differences between dumbbell interstitials with different orientations are independent of the Cr concentration. We show that the long-range influence of Cr atoms on the interstitial is not due to the interstitial strain field protruding into Cr-rich parts of the supercells. The Fermi-level and band energies were found not to be the sole governing parameter in determining the formation energies. Implications for the construction of empirical potentials are discussed.

The properties of 3d, 4d, and 5d transition-metal elements in
-Fe have been studied using ab initio density-functional theory. The intrinsic properties of the solutes have been characterized as well as their interaction with point defects. Vacancies and interstitials of 110 and 111 orientations have been considered in order to discern trends that may explain experimental evidence of solute influences on radiation response and possibly aid future material design regarding the choice of alloy composition. Depending on the solute element, the different interactions are governed by the chemical interactions and the solute size factor. It is shown that magnetic interactions play an important role for the properties of the center series 3d elements, especially so for the antiferromagnetically coupling V, Cr, and Mn. For the 4d, 5d, and remaining 3d elements the interaction with point defects is mainly governed by the solute size factor. The solute-solute interaction is mostly repulsive with a few exceptions. The interactions with vacancies are in most cases binding; but the second nearest neighbor configurations exhibit strong repulsion for the early transition metals. Cr and Mn interact strongly binding with interstitial defects. The trends of the solute defect interactions have been determined to depend on the characteristic local deformation. Early transition metals interact stronger with defects
than late ones of equal size factor.

Basic properties of minor alloying elements, namely Mo, W, Nb, Ta, V, Mn, Si entering the conventional and reduced-activation structural Fe–(9–12)Cr steels have been analyzed using ab initio calculations. The electronic structure calculations were applied to study the interaction of minor alloying elements with a number of important and well defined lattice structures, such as point defects, the 1/2[111] screw dislocation core, high angle symmetric grain boundaries and free surfaces. The studied elements were classified according to their similarities and discrepancies regarding the interaction with the above
mentioned defects. The refractory alloying elements are found to follow the same trend whereas Mn and Si exhibit peculiar behavior with respect to the interaction with both point and extended lattice defects. The obtained results are discussed and compared with previously published ab initio and available experimental data.

The diffusion properties of a wide range of impurities (transition metals and Al, Si, and P) in ferritic alloys are here investigated by means of a combined ab initio–atomic diffusion theory approach. The flux-coupling mechanisms and the solute diffusion coefficients are inferred from electronic-structure calculations of solute-defect interactions and microscopic jump frequencies. All properties except the second nearest-neighbor binding energy are found to have a characteristic bell shape as a function of the d-band filling for the 4d and 5d series, and an M-shape for the 3d row because of the out-of-trend behavior of Mn. The solute jump frequencies are governed by compress-ibility, which makes diffusion of large solutes faster, although this effect is partially compensated for by lower attempt frequencies and larger correlations with the vacancy. Diffusion coefficients are predicted in a wide temperature range, far below the experimentally-accessible temperatures. In accordance with experiments, Co is found to be a slow diffuser in iron, and the same behavior is predicted for Re, Os, and Ir impurities. Finally, flux–coupling phenomena depend on the iron jump frequencies next to a solute atom, which are mainly controlled by similar electronic interactions to those determining the binding energies. Vacancy drag and solute enrichment at sinks systematically arise below a solute-dependent temperature threshold, directly correlated with the electronic-level interactions at the equilibrium and the saddle-point states. Early transition metals with repulsive second nearest-neighbor interactions also diffuse via vacancy drag, although they show a lower temperature threshold than the late metals. This confirms that drag is the most common solute-vacancy coupling mechanism in iron at low temperatures, and this is likely to be confirmed as well for impurity diffusion in other transition metals.

ABSTRACT We applied atomistic kinetic Monte Carlo techniques, together with recently fitted Two Band many body potential to study the precipitation process by simulating thermal aging. The tendency to clustering is observed by inspection of the SRO parameter. The Cr-rich precipitates are coherent with the matrix structure. For their identification a Local Concentration Approximation (LCA) is proposed.

Basic properties of minor alloying elements, namely Mo, W, Nb, Ta, V, Mn, Si entering the conventional and reduced-activation structural Fe–(9–12)Cr steels have been analyzed using ab initio calculations. The electronic structure calculations were applied to study the interaction of minor alloying elements with a number of important and well defined lattice structures, such as point defects, the 1/2[111] screw dislocation core, high angle symmetric grain boundaries and free surfaces. The studied elements were classified according to their similarities and discrepancies regarding the interaction with the above mentioned defects. The refractory alloying elements are found to follow the same trend whereas Mn and Si exhibit peculiar behavior with respect to the interaction with both point and extended lattice defects. The obtained results are discussed and compared with previously published ab initio and available experimental data.