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Multiscale modeling of atomic transport phenomena in ferritic steels
KTH, School of Engineering Sciences (SCI), Physics, Reactor Physics.ORCID iD: 0000-0003-0562-9070
2015 (English)Doctoral 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.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2015. , xvii, 90 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2015:80
Keyword [en]
diffusion, impurities, iron, metals, kinetic Monte Carlo, ab initio, mean field, defects, embrittlement, reactor pressure vessel, neural networks
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-177525ISBN: 978-91-7595-764-7 (print)OAI: oai:DiVA.org:kth-177525DiVA: diva2:873176
Public defence
2015-12-11, Svedberg Hall, Room FD5, Albanova Universtitetscentrum, Roslagstullsbacken 21, Stockholm, 13:00 (English)
Opponent
Supervisors
Funder
Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyVattenfall ABEU, FP7, Seventh Framework Programme
Note

QC 20151123

Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2015-11-24Bibliographically approved
List of papers
1. Exact ab initio transport coefficients in bcc Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys
Open this publication in new window or tab >>Exact ab initio transport coefficients in bcc Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys
Show others...
2014 (English)In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 90, no 10, 104203- p.Article in journal (Refereed) Published
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.

Keyword
Radiation-Induced Segregation, Pressure-Vessel Steels, Augmented-Wave Method, Monte-Carlo Approach, Alpha-Iron, Phenomenological Coefficients, Positron-Annihilation, Ultrasoft Pseudopotentials, Atomistic Simulations, Multicomponent Alloy
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-157221 (URN)10.1103/PhysRevB.90.104203 (DOI)000344014700002 ()2-s2.0-84907478712 (Scopus ID)
Note

QC 20141209

Available from: 2014-12-09 Created: 2014-12-08 Last updated: 2017-12-05Bibliographically approved
2. Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron
Open this publication in new window or tab >>Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron
(English)Manuscript (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. 

Keyword
diffusion, impurities, ab initio, metals
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-177519 (URN)
Funder
Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyVattenfall ABEU, FP7, Seventh Framework Programme
Note

QS 2015

Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2015-11-23Bibliographically approved
3. Ab initio-based investigation of solute-dumbbell transport and radiation induced segregation in Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys
Open this publication in new window or tab >>Ab initio-based investigation of solute-dumbbell transport and radiation induced segregation in Fe-X (X=Cr, Cu, Mn, Ni, P, Si) dilute alloys
(English)Manuscript (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. 

Keyword
diffusion, impurities, defects, metals, ab initio
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-177522 (URN)
Funder
Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyVattenfall ABEU, FP7, Seventh Framework Programme
Note

QS 2015

Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2015-11-23Bibliographically approved
4. Stability and mobility of small vacancy-solute complexes in Fe-MnNi and dilute Fe-X alloys: A kinetic Monte Carlo study
Open this publication in new window or tab >>Stability and mobility of small vacancy-solute complexes in Fe-MnNi and dilute Fe-X alloys: A kinetic Monte Carlo study
2015 (English)In: Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, ISSN 0168-583X, E-ISSN 1872-9584, Vol. 352, 61-66 p.Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Elsevier, 2015
Keyword
Ferritic alloys, AKMC, Vacancy diffusion, Solute clusters
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-163932 (URN)10.1016/j.nimb.2014.12.032 (DOI)000355053200015 ()
Funder
EU, FP7, Seventh Framework ProgrammeGöran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Note

QC 201550420

Available from: 2015-04-13 Created: 2015-04-13 Last updated: 2017-12-04Bibliographically approved
5. Introducing ab initio-based neural networks for transition-rate prediction in kinetic Monte Carlo simulations
Open this publication in new window or tab >>Introducing ab initio-based neural networks for transition-rate prediction in kinetic Monte Carlo simulations
(English)Manuscript (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.

Keyword
thermal aging, computer simulations, ab initio, kinetic Monte Carlo, neural networks
National Category
Condensed Matter Physics
Research subject
Physics
Identifiers
urn:nbn:se:kth:diva-177523 (URN)
Funder
Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of TechnologyVattenfall ABEU, FP7, Seventh Framework Programme
Note

QS 2015

Available from: 2015-11-23 Created: 2015-11-23 Last updated: 2015-11-23Bibliographically approved

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