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  • 1.
    Castin, N.
    et al.
    Studie Ctr Kerneenergie, Ctr Etud Energie Nucl SCK CEN, NMS Unit, Boeretang 200, B-2400 Mol, Belgium..
    Pascuet, M. I.
    Consejo Nacl Invest Cient & Tecn CONICET, Godoy Cruz 2290 C1425FQB CABA, Buenos Aires, DF, Argentina..
    Messina, Luca
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Domain, C.
    EDF R&D, Dept Mat & Mecan Composants, F-77250 Moret Sur Loing, France..
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Pasianot, R. C.
    Consejo Nacl Invest Cient & Tecn CONICET, Godoy Cruz 2290 C1425FQB CABA, Buenos Aires, DF, Argentina.;Comis Nacl Energia Atom CNEA, Gcia Mat, Av Gral Paz 1499, RA-1650 San Martin, Argentina..
    Malerba, L.
    Studie Ctr Kerneenergie, Ctr Etud Energie Nucl SCK CEN, NMS Unit, Boeretang 200, B-2400 Mol, Belgium..
    Advanced atomistic models for radiation damage in Fe-based alloys: Contributions and future perspectives from artificial neural networks2018In: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 148, p. 116-130Article in journal (Refereed)
    Abstract [en]

    Machine learning, and more specifically artificial neural networks (ANN), are powerful and flexible numerical tools that can lead to significant improvements in many materials modelling techniques. This paper provides a review of the efforts made so far to describe the effects of irradiation in Fe-based and W-based alloys, in a multiscale modelling framework. ANN were successfully used as innovative parametrization tools in these models, thereby greatly enhancing their physical accuracy and capability to accomplish increasingly challenging goals. In the provided examples, the main goal of ANN is to predict how the chemical complexity of local atomic configurations, and/or specific strain fields, influence the activation energy of selected thermally-activated events. This is most often a more efficient approach with respect to previous computationally heavy methods. In a future perspective, similar schemes can be potentially used to calculate other quantities than activation energies. They can thus transfer atomic-scale properties to higher-scale simulations, providing a proper bridging across scales, and hence contributing to the achievement of accurate and reliable multiscale models.

  • 2.
    Chang, Zhongwen
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Messina, Luca
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Sandberg, Nils
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Yousfi, Amine
    Toijer, Elin
    Thuvander, Mattias
    Boizot, Bruno
    Brysbaert, Gauthier
    Metayer, Vincent
    Gorse-Pomonti, Dominique
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Electron irradiation accelerated Cu precipitation in cast iron and an FeCu model alloyManuscript (preprint) (Other academic)
  • 3. Chiapetto, Monica
    et al.
    Messina, Luca
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics. Université Paris-Saclay, Gif-sur-Yvette, France.
    Becquart, Charlotte S.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Malerba, Lorenzo
    Nanostructure evolution of neutron-irradiated reactor pressure vessel steels: Revised Object kinetic Monte Carlo model2017In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, ISSN 0168-583X, E-ISSN 1872-9584, Vol. 393, p. 105-109Article in journal (Refereed)
    Abstract [en]

    This work presents a revised set of parameters to be used in an Object kinetic Monte Carlo model to simulate the microstructure evolution under neutron irradiation of reactor pressure vessel steels at the operational temperature of light water reactors (∼300 °C). Within a “grey-alloy” approach, a more physical description than in a previous work is used to translate the effect of Mn and Ni solute atoms on the defect cluster diffusivity reduction. The slowing down of self-interstitial clusters, due to the interaction between solutes and crowdions in Fe is now parameterized using binding energies from the latest DFT calculations and the solute concentration in the matrix from atom-probe experiments. The mobility of vacancy clusters in the presence of Mn and Ni solute atoms was also modified on the basis of recent DFT results, thereby removing some previous approximations. The same set of parameters was seen to predict the correct microstructure evolution for two different types of alloys, under very different irradiation conditions: an Fe-C-MnNi model alloy, neutron irradiated at a relatively high flux, and a high-Mn, high-Ni RPV steel from the Swedish Ringhals reactor surveillance program. In both cases, the predicted self-interstitial loop density matches the experimental solute cluster density, further corroborating the surmise that the MnNi-rich nanofeatures form by solute enrichment of immobilized small interstitial loops, which are invisible to the electron microscope.

  • 4.
    Messina, Luca
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Multiscale modeling of atomic transport phenomena in ferritic steels2015Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Defect-driven transport of impurities plays a key role in the microstructure evolution of alloys, and has a great impact on the mechanical properties at the macroscopic scale. This phenomenon is greatly enhanced in irradiated materials because of the large amount of radiation-induced crystal defects (vacancies and interstitials). For instance, the formation of nanosized solute clusters in neutron-irradiated reactor pressure vessel (RPV) ferritic steels has been shown to hinder dislocation motion and induce hardening and embrittlement. In Swedish RPV steels, this mechanical-property degradation is enhanced by the high content of manganese and nickel impurities. It has been suggested that the formation of Mn-Ni-rich clusters (which contain also Cu, Si, and P) might be the outcome of a dynamic process, where crystal defects act both as nucleation sites and solute carriers. Solute transport by point defects is therefore a crucial mechanism to understand the origin and the dynamics of the clustering process.

    The first part of this work aims at modeling solute transport by point defects in dilute iron alloys, to identify the intrinsic diffusion mechanisms for a wide range of impurities. Transport and diffusion coefficients are obtained by combining accurate ab initio calculations of defect transition rates with an exact mean-field model. The results show that solute drag by single vacancies is a common phenomenon occurring at RPV temperature (about 300 °C) for all impurities found in the solute clusters, and that transport of phosphorus and manganese atoms is dominated by interstitial-type defects. These transport tendencies confirm that point defects can indeed carry impurities towards nucleated solute clusters. Moreover, the obtained flux-coupling tendencies can also explain the observed radiation-induced solute enrichment on grain boundaries and dislocations.

    In the second part of this work, the acquired knowledge about solute-transport mechanisms is transferred to kinetic Monte Carlo (KMC) models, with the aim of simulating the RPV microstructure evolution. Firstly, the needed parameters in terms of solute-defect cluster stability and mobility are calculated by means of dedicated KMC simulations. Secondly, an innovative approach to the prediction of transition rates in complex multicomponent alloys is introduced. This approach relies on a neural network based on ab initio-computed migration barriers. Finally, the evolution of the Swedish RPV steels is simulated in a "gray-alloy" fashion, where impurities are introduced indirectly as a modification of the defect-cluster mobilities. The latter simulations are compared to the experimental characterization of the Swedish RPV surveillance samples, and confirm the possibility that solute clusters might form on small interstitial clusters.

    In conclusion, this work identifies from a solid theoretical perspective the atomic-transport phenomena underlying the formation of embrittling nanofeatures in RPV steels. In addition, it prepares the ground for the development of predictive KMC tools that can simulate the microstructure evolution of a wide variety of irradiated alloys. This is of great interest not only for reactor pressure vessels, but also for many other materials in extreme environments.

  • 5.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Castin, N.
    Domain, C.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Introducing ab initio based neural networks for transition-rate prediction in kinetic Monte Carlo simulations2017In: Physical Review B, ISSN 2469-9950, E-ISSN 2469-9969, Vol. 95, no 6, article id 064112Article in journal (Refereed)
    Abstract [en]

    The quality of kinetic Monte Carlo (KMC) simulations of microstructure evolution in alloys relies on the parametrization of point-defect migration rates, which are complex functions of the local chemical composition and can be calculated accurately with ab initio methods. However, constructing reliable models that ensure the best possible transfer of physical information from ab initio to KMC is a challenging task. This work presents an innovative approach, where the transition rates are predicted by artificial neural networks trained on a database of 2000 migration barriers, obtained with density functional theory (DFT) in place of interatomic potentials. The method is tested on copper precipitation in thermally aged iron alloys, by means of a hybrid atomistic-object KMC model. For the object part of the model, the stability and mobility properties of copper-vacancy clusters are analyzed by means of independent atomistic KMC simulations, driven by the same neural networks. The cluster diffusion coefficients and mean free paths are found to increase with size, confirming the dominant role of coarsening of medium- and large-sized clusters in the precipitation kinetics. The evolution under thermal aging is in better agreement with experiments with respect to a previous interatomic-potential model, especially concerning the experiment time scales. However, the model underestimates the solubility of copper in iron due to the excessively high solution energy predicted by the chosen DFT method. Nevertheless, this work proves the capability of neural networks to transfer complex ab initio physical properties to higher-scale models, and facilitates the extension to systems with increasing chemical complexity, setting the ground for reliable microstructure evolution simulations in a wide range of alloys and applications.

  • 6.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Castin, Nicolas
    Domain, Christophe
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Introducing ab initio-based neural networks for transition-rate prediction in kinetic Monte Carlo simulationsManuscript (preprint) (Other academic)
    Abstract [en]

    This work presents an innovative approach to kinetic Monte Carlo (KMC) simulations, in which atomic transition rates are predicted by an artificial neural network trained on ab initio migration barriers. The method is applied to the parameterization of a hybrid atomistic-object KMC model to simulate copper precipitation during thermal aging in iron. The stability and mobility of copper clusters containing one vacancy is analyzed by means of independent atomistic KMC simulations driven by the same neural network, with the aim of parameterizing the object KMC part of the model. Copper clusters are found to be more stable and mobile with respect to previous studies, and can cover longer diffusion paths, reaching up to a few lattice units. The mean free path increases with cluster size up to around 100 copper atoms. In addition, the emission of the vacancy often occurs concurrently with the emission of one or more copper atoms, because of strong vacancy-copper correlations and kinetic coupling. In the hybrid KMC simulations, the density of copper clusters is overestimated because of the excessively high solution energy predicted by the ab initio method. Nevertheless, this work proves the capability of neural networks to transfer detailed ab initio thermodynamic and kinetic properties to the KMC model, and sets the ground for reliable microstructure evolution simulations in a wide range of alloys.

  • 7.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Chang, Zhongwen
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Ab initio modelling of vacancy-solute dragging in dilute irradiated iron-based alloys2013In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, ISSN 0168-583X, E-ISSN 1872-9584, Vol. 303, p. 28-32Article in journal (Refereed)
    Abstract [en]

    The formation of solute-defect nanoclusters in RPV steels is the main cause of radiation induced embrittlement. Solute atoms may diffuse in the alloy by a vacancy drag mechanism, depending on the strength of interaction with point defects. A multifrequency model based on ab initio computed migration barriers was applied in order to investigate the possibility of solute drag in iron-based bcc binary alloys containing Ni, Cr, Cu or Mn, and the obtained solute diffusion coefficients were compared with previous experiments. The results show that Ni is expected to be dragged at temperatures below approximately 900 K, while Cr and Mn are not involved in the dragging mechanism. As for Cu, the results are controversial because the computed migration barriers are strongly affected by the particular choice of the ab initio method.

  • 8.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Chiapetto, Monica
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Becquart, Charlotte S.
    Malerba, Lorenzo
    An object kinetic Monte Carlo model for the microstructure evolution of neutron-irradiated reactor pressure vessel steels2016In: Physica Status Solidi (a) applications and materials science, ISSN 1862-6300, E-ISSN 1862-6319, Vol. 213, no 11, p. 2974-2980Article in journal (Refereed)
    Abstract [en]

    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 "gray-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 immobilization 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.

  • 9.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Malerba, Lorenzo
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Stability and mobility of small vacancy-solute complexes in Fe-MnNi and dilute Fe-X alloys: A kinetic Monte Carlo study2015In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, ISSN 0168-583X, E-ISSN 1872-9584, Vol. 352, p. 61-66Article in journal (Refereed)
    Abstract [en]

    Manganese and nickel solute atoms in irradiated ferritic steels play a major role in the nanostructural evolution of reactor pressure vessels (RPV), as they are responsible for the formation of embrittling nanofeatures even in the absence of copper. The stability and mobility of small vacancy solute clusters is here studied with an atomistic kinetic Monte Carlo approach based on ab initio calculations, in order to investigate the influence of Mn and Ni on the early life of small radiation-induced vacancy clusters, and to provide the necessary parameters for advanced object kinetic Monte Carlo simulations of the RPV long-term nanostructural evolution. Migration barriers are obtained by direct ab initio calculations or through a binding energy model based on ab initio data. Our results show a clear immobilizing and stabilizing effect on vacancy clusters as the solute content is increased, whereas the only evident difference between the two solute species is a somewhat longer elongation of the cluster mean free path in the presence of a few Mn atoms.

  • 10.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Nastar, Maylise
    Garnier, Thomas
    Domain, Christophe
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Exact ab initio transport coefficients in bcc Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys2014In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 90, no 10, p. 104203-Article in journal (Refereed)
    Abstract [en]

    Defect-driven diffusion of impurities is the major phenomenon leading to formation of embrittling nanoscopic precipitates in irradiated reactor pressure vessel (RPV) steels. Diffusion depends strongly on the kinetic correlations that may lead to flux coupling between solute atoms and point defects. In this work, flux coupling phenomena such as solute drag by vacancies and radiation-induced segregation at defect sinks are systematically investigated for six bcc iron-based dilute binary alloys, containing Cr, Cu, Mn, Ni, P, and Si impurities, respectively. First, solute-vacancy interactions and migration energies are obtained by means of ab initio calculations; subsequently, self-consistent mean field theory is employed in order to determine the exact Onsager matrix of the alloys. This innovative multiscale approach provides a more complete treatment of the solute-defect interaction than previous multifrequency models. Solute drag is found to be a widespread phenomenon that occurs systematically in ferritic alloys and is enhanced at low temperatures (as for instance RPV operational temperature), as long as an attractive solute-vacancy interaction is present, and that the kinetic modeling of bcc alloys requires the extension of the interaction shell to the second-nearest neighbors. Drag occurs in all alloys except Fe(Cr); the transition from dragging to nondragging regime takes place for the other alloys around (Cu, Mn, Ni) or above (P, Si) the Curie temperature. As far as only the vacancy-mediated solute migration is concerned, Cr depletion at sinks is foreseen by the model, as opposed to the other impurities which are expected to enrich up to no less than 1000 K. The results of this study confirm the current interpretation of the hardening processes in ferritic-martensitic steels under irradiation.

  • 11.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Nastar, Maylise
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Ab initio-based investigation of solute-dumbbell transport and radiation induced segregation in Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloysManuscript (preprint) (Other academic)
    Abstract [en]

    In this work are analyzed the solute-transport mechanisms due to coupling with dumbbell-type defects in iron alloys, for selected impurities, by combining ab initio calculations of defect transition rates with a mean-field treatment yielding the transport coefficients of the alloy. Average radiation-induced segregation tendencies are determined based on these results and the vacancy-diffusion tendencies derived in a previous study. A new mathematical framework allows for such tendencies to be expressed in terms of vacancy-solute and dumbbell-solute flux-coupling, as well as the relative efficiency of the two mechanisms. The results show that P, Mn, and Cr to a lesser extent are transported by dumbbells thanks to the combination of high mixed-dumbbell stability and mobility, whereas Cu, Ni, and Si impurities are not. For the latter impurities the vacancy mechanism is dominant, which entails solute enrichment at low temperature and depletion above the drag transition temperature. For P and Mn, the mixed-dumbbell mechanism is dominant and leads to consistent enrichment at defect sinks, independently of temperature. Finally, the RIS tendency for Cr is the outcome of a balance between enrichment due to dumbbells and depletion due to vacancies, leading to a switchover between enrichment and depletion at 460 K. The results are in qualitative agreement with resistivity-recovery experiments and experimental RIS observations in ferritic alloys. 

  • 12.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Nastar, Maylise
    Sandberg, Nils
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics. Swedish Radiation Safety Authority, Sweden.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron2016In: Physical Review B, ISSN 2469-9950, Vol. 93, no 18, article id 184302Article in journal (Refereed)
    Abstract [en]

    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 compressibility, 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.

  • 13.
    Messina, Luca
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Nastar, Maylise
    Sandberg, Nils
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc ironManuscript (preprint) (Other academic)
    Abstract [en]

    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 compressibility, 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. 

  • 14.
    Sandberg, Nils
    et al.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics. Swedish Radiat Safety Author, Sweden.
    Chang, Z.
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Messina, Luca
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Olsson, Pär
    KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.
    Korzhavyi, Pavel
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering.
    Modeling of the magnetic free energy of self-diffusion in bcc Fe2015In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 92, no 18, article id 184102Article in journal (Refereed)
    Abstract [en]

    A first-principles based approach to calculating self-diffusion rates in bcc Fe is discussed with particular focus on the magnetic free energy associated with diffusion activation. First, the enthalpies and entropies of vacancy formation and migration in ferromagnetic bcc Fe are calculated from standard density functional theory methods in combination with transition state theory. Next, the shift in diffusion activation energy when going from the ferromagnetic to the paramagnetic state is estimated by averaging over random spin states. Classical and quantum mechanical Monte Carlo simulations within the Heisenberg model are used to study the effect of spin disordering on the vacancy formation and migration free energy. Finally, a quasiempirical model of the magnetic contribution to the diffusion activation free energy is applied in order to connect the current first-principles results to experimental data. The importance of the zero-point magnon energy in modeling of diffusion in bcc Fe is stressed.

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