1. L. Messina1,2, P. Olsson2, M.-C. Marinica1, M. Nastar1
N-FAME Workshop
Bruxelles
June 13-14th, 2016
Solute transport by point defects and defect clusters in ferritic alloys
L. Messina1,2, P. Olsson2, M.-C. Marinica1, M. Nastar1
1 Service de Recherche de Métallurgie Physique, CEA Saclay, Université Paris-Sud
2 Reactor Physics Division, KTH Royal Institute of Technology
In collaboration with
L. Malerba, M. Chiapetto, N. Castin (SCK-CEN)
N. Sandberg (KTH, SSM), P. Efsing (KTH, Vattenfall)
C. Domain (EDF)
C. S. Becquart (Université de Lille)
PhD thesis available at:
L. Messina, IGRDM-18

2. Outline Flux coupling and solute diffusion via vacancies/dumbbells
Systematic analysis of vacancy drag
Mobility & Stability of solute-vacancy pairs
Effect of two solutes 2
L. Messina, IGRDM-18

3. Ringhals RPV Embrittlement
[1] P. Efsing et al., J. ASTM Int. 4 (2004).
[2] Miller et al., Journal of Nuclear Materials 437 (2013).
[3] US-NRC, Regulatory Guide 1.99 (1975).
Weld metal composition
R3 – R4 (wt.%) [1] Cu
0.08
0.05 Ni
1.58
1.66 Mn
1.46
1.35 Si
0.21
0.14 P
0.009
0.0015 Cr
0.07
0.04 Mo
0.54
0.50 C
0.052
0.068 Al
0.027
0.024 Co
0.015
0.010 V
0.002
0.00
Balance: Fe
APT maps
[2]
[1]
[1] Cu Si Ni Mn P Mo
25 years
50 years
RPV is made of ferritic steel. It contains mainly Fe with a certain impurity content. Swedish steels are particularly rich in Mn and Ni, more than any other pressure vessel worldwide. This has a strong impact on the structural properties.
Neutron irradiation leads to a chemical redistribution of these impurities, causing the vessel to become harder and more brittle. The embrittlement is seen as a large increase of the ductile-to-brittle transition temperature, far above the values predicted by the regulatory body (surveillance results). Such unexpected shifts must be investigated because they bring the DBTT too close to the operation temperature.
By atom probe we see the formation of small solute clusters containing mainly Mn, Ni, Si with traces of Cu and P. We also observe heavy P segregation on dislocations. These two phenomena are responsible for the observed macroscopic change of mechanical properties.
Mn-Ni-(Si)-(Cu) nanocluster [2]
(≈ 2nm diameter)
P segregation
on dislocations [2]
L. Messina, IGRDM-18

4. Cluster Formation and Growth
Mn-Ni-Si clusters
Hypothesis: radiation-induced precipitation
Exclusively kinetic reason (no TD driving force?)
Would not occur without point defects and clusters
No saturation?
Now, I said that these impurities cluster because of the diffusion of the crystal defects. If we want to know how they form and how to predict the evolution of these steels, we nned to analyze in details the diffusion mechanisms. We have to distinguish between radiation-enhanced and radiation-induced precipitation.
In case of Cu, precipitation is TDlly favorable because the solubility limit of Cu in Fe is very low. (Cu diffuses with vacancies and it is energetically favorable for Cu atoms to cluster together, so eventually they will form.) Since under irradiation the concentration of defects is much higher than in thermal equilibrium, the precipitation process is strongly enhanced by irradiation.
On the other hand, the formation mechanisms of Mn-Ni-Si precipitates are largely unknown. We don’t know much about the phase diagram of the complex multicomponent alloy, so we don’t know if these precipitates are stable, and this is object of debate in the research community. Anyway, it has been suggested that these precipitates form because of kinetic coupling with point defects, as is shown in this animation. Blabla..
In this way, this would be a phenomenon that occurs only under irradiation. But this transport mechanisms that I’ve just shown they were assumed but they needed to be verified, This is why we decided to dedicate part of the project to the analysis of impurity transport.
NEED TO STUDY SOLUTE-DEFECT FLUX COUPLING!
L. Messina, IGRDM-18

5. Outline Flux coupling and solute diffusion via vacancies/dumbbells
Systematic analysis of vacancy drag
Mobility & Stability of solute-vacancy pairs
Effect of two solutes 5
L. Messina, IGRDM-18

6. Diffusion mechanisms INVERSE KIRKENDALL VACANCY SINK
vacancy flux
VACANCY SINK
DUMBBELL MECHANISM
VACANCY DRAG
vacancy flux
VACANCY SINK
Solute-defect flux coupling:
Solute diffusion due to defect flux
Effect of solutes on defect flux (correlations, trapping)
L. Messina, IGRDM-18

7. Transport Coefficients
Aim: Analysis of the intrinsic interaction between solute atoms and point defects in dilute binary model alloys Fe-X, to possibly support suspected MnNiSi cluster formation mechanisms.
Model alloys: Fe-X ( X = Al, P, Si and transition metals)
DFT jump frequencies
Mean field transport coefficients (SCMF[5])
Transport properties
Vacancy drag
Interstitial transport
Diffusion coefficients
Correlation effects
Radiation-induced segregation
FICK’S LAW
ONSAGER’S FORMULATION [4]
Flux-coupling phenomena
Formation of pecipitates and solute segregation in RPV steels
Low T diffusion coefficinets
Aim is to compute transport coefficients in dilute Fe-X alloys to determine the transport mechanisms of each impurity.
- TC are like DC, but with them we can express atomic fluxes by separating the TD forces from the kinetic mechanism thhrough which the atomic diffusion actually occurs, with both types of defects. In a binary alloy we have a 2x2 matrix of coefficients, were the off-diagonal terms represent the flux coupling. For instance, in case of vacancy diffusion, with these terms we can determine if the fluxes of vacancies and solutes are in the same direction, or in the opposite direction. When they are In the same direction, we talk about “vacancy drag” because the vacancy is actually carrying a solute atom along its way.
- This is achieved by combining first principle calculations (DFT) with a mean field model called SCMF theory.
- In particular, we use DFT methods to calculate defect jump frequencies expressed here, which are thermally-activated events depending on the migration energy and an attempt frequency.
JUMP FREQUENCY
Flux coupling in off-diagonal coefficients.
Clear separation between thermodynamic and kinetic properties.
Functions of the defect migration frequencies ωij.
Thermally-activated transitions
from transition-state theory.
[4] A.R. Allnatt and A.B. Lidiard, Atomic Transport in Solids, Cambridge University Press (2003).
[5] M. Nastar, Philos. Mag. 85, (2005).
L. Messina, IGRDM-18

8. Solute-defect flux coupling
VACANCY DRAG
DUMBBELL TRANSPORT
Vacancy can carry solute atoms along.
Occurring for Mn, Ni, Cu, P, Si.
Arising systematically with binding solute-vacancy interaction.
Interstitals can couple with solute atoms and move together.
Occurring for Mn, P, Cr.
We move to the results. Here we show the diffusion mechanisms due to coupling with vacancies (on the left) and dumbbells (on the right).
Vacancies: we found that most of the impurities in RPV steels diffuse with a vacancy drag mechanism, which means that the vacancies are actually capable of carring the impurities along. This is due to the attractive interaction between vacancies and such impurities, with the exception of Chromium. There is also for most of them a transition temperature, above which this phenomenon disappears because of the binding energy attenuation.
- Dumbbells: we found that a subgroup of these impurities (namely P, Mn, Cr) can be transported by dumbbells, whereas for the other impurities this mechanism cannot take place. This is mainly related to the stability of the mixed dumbbell Fe-X.
- So, we have found the intrinsic mechanisms guiding the diffusion of each impurity type, as functions of temperature. This mechanisms are surely related to the binding energies, but not in a trivial way. This is why a full kinetic study is needed, and this was among the first ones of this kind.
- These results confirm the capability of point defects to carry solute atoms, and confirm therefore that the cluster formation mechanism can indeed take place.
Not trivially inferrable from solute-defect binding energies.
Speculated cluster formation mechanism is confirmed.
L. Messina, IGRDM-18

9. Dominant diffusion mechanism
Ratio of interstitial- vs vacancy partial diffusion coefficient
Finally, we can also analyze radiation induced segregation thanks to the transport coefficients.
If you remember, in the RPV steels we observed also segregation of P on dislocations.
This can be explained in terms of solute-defect flux coupling, as is shown in this figure. Since we have a constant flux of defects towards sinks, which can be GB or dislocations, it is clear that if these defects are coupled to impurities, this can lead to the accumulation of solutes on the sink.
Depending on the flux coupling regime, we have the contribution from both vac. And int. diffusion, and we can either have enrichment or depletion.
- The group of impurities that we have investigated fully is split into three types of behavior. Ni, Si, and Cu are predominantly driven by vacancies, so we have enrichment because of the vacancy drag mechanism, which disappears above a certain T. On the other hand, we have P and Mn which are instead dominated by dumbbell transport, and since this occurs at all temperatures we have a consistent temp-independent heavy enrichement, which is confirmed by these exp. observations. Finally, the case of Cr is interesting because we have a balance of two opposite tendencies: vacancies tend to depletion, and dumbbells to enrichment. The outcome is therefore a switchover between enrichment and depletion at a rather low temperature, which is also consistent with experiments.
L. Messina, IGRDM-18

10. Dominant diffusion mechanism
Ratio of interstitial- vs vacancy partial diffusion coefficient
Finally, we can also analyze radiation induced segregation thanks to the transport coefficients.
If you remember, in the RPV steels we observed also segregation of P on dislocations.
This can be explained in terms of solute-defect flux coupling, as is shown in this figure. Since we have a constant flux of defects towards sinks, which can be GB or dislocations, it is clear that if these defects are coupled to impurities, this can lead to the accumulation of solutes on the sink.
Depending on the flux coupling regime, we have the contribution from both vac. And int. diffusion, and we can either have enrichment or depletion.
- The group of impurities that we have investigated fully is split into three types of behavior. Ni, Si, and Cu are predominantly driven by vacancies, so we have enrichment because of the vacancy drag mechanism, which disappears above a certain T. On the other hand, we have P and Mn which are instead dominated by dumbbell transport, and since this occurs at all temperatures we have a consistent temp-independent heavy enrichement, which is confirmed by these exp. observations. Finally, the case of Cr is interesting because we have a balance of two opposite tendencies: vacancies tend to depletion, and dumbbells to enrichment. The outcome is therefore a switchover between enrichment and depletion at a rather low temperature, which is also consistent with experiments.
L. Messina, IGRDM-18

11. Radiation Induced Segregation
Solute enrinchment on defect sinks (dislocation, grain boundaries, precipitates) due to solute-defect flux coupling.
enrichment
Enrichment if slower solute diffusion
depletion
Miller et al., JNM 437 (2013).
Finally, we can also analyze radiation induced segregation thanks to the transport coefficients.
If you remember, in the RPV steels we observed also segregation of P on dislocations.
This can be explained in terms of solute-defect flux coupling, as is shown in this figure. Since we have a constant flux of defects towards sinks, which can be GB or dislocations, it is clear that if these defects are coupled to impurities, this can lead to the accumulation of solutes on the sink.
Depending on the flux coupling regime, we have the contribution from both vac. And int. diffusion, and we can either have enrichment or depletion.
- The group of impurities that we have investigated fully is split into three types of behavior. Ni, Si, and Cu are predominantly driven by vacancies, so we have enrichment because of the vacancy drag mechanism, which disappears above a certain T. On the other hand, we have P and Mn which are instead dominated by dumbbell transport, and since this occurs at all temperatures we have a consistent temp-independent heavy enrichement, which is confirmed by these exp. observations. Finally, the case of Cr is interesting because we have a balance of two opposite tendencies: vacancies tend to depletion, and dumbbells to enrichment. The outcome is therefore a switchover between enrichment and depletion at a rather low temperature, which is also consistent with experiments. Mn P
C. Pareige et al., JNM 456 (2015).
L. Messina, IGRDM-18

12. Outline Flux coupling and solute diffusion via vacancies/dumbbells
Systematic analysis of vacancy drag
Mobility & Stability of solute-vacancy pairs
Effect of two solutes 12
L. Messina, IGRDM-18

13. Systematic analysis of vacancy drag
L. Messina, M. Nastar, N. Sandberg, P. Olsson, Phys. Rev. B 93, (2016)
Objectives:
Provide wide database of low-temperature impurity diffusion coefficients and flux coupling in Fe dilute alloys.
Investigate conditions under which vacancy drag can arise (binding/repulsion?)
Four interaction types:
Binding at 1nn, repulsive at 2nn.
Weak interactions.
Binding at 1nn and 2nn.
Anomalous strong 2nn binding. Al Si P
In Paper II we extended the study of vacancy drag to all transition-metal impurities in Fe.
- We found common trends for a wide range of properties, going from the solute-vacancy B.E. to migration energies and the drag transition temperature.
- Surely, the most important outcome is the finding that vacancy drag occurs systematically for all of these impurities in the low-temperature side (although low is not really low for many of them), which was surely unexpected. We found also that it can occur in presence of repulsive SOL-VAC interactions. And thanks to these common trends we were able to show that this diffusion behavior takes orgin from the electronic interactions occurring between iron atoms, impurities and vacancies. Ti V Cr Mn Fe Co Ni Cu Zr Nb Mo Tc Ru Rh Pd Ag Hf Ta W Re Os Ir Pt Au
L. Messina, IGRDM-18

14. Systematic analysis of vacancy drag
Extension to all transition-metal impurities.
Identified common trends for wide range of properties.
Impurity diffusion and flux coupling linked to electronic interactions between iron, impurities, and vacancies.
Drag for all impurities! Even with repulsive solute-vacancy interactions.
Electronic origin might suggest similar trends in other metals.
In Paper II we extended the study of vacancy drag to all transition-metal impurities in Fe.
- We found common trends for a wide range of properties, going from the solute-vacancy B.E. to migration energies and the drag transition temperature.
- Surely, the most important outcome is the finding that vacancy drag occurs systematically for all of these impurities in the low-temperature side (although low is not really low for many of them), which was surely unexpected. We found also that it can occur in presence of repulsive SOL-VAC interactions. And thanks to these common trends we were able to show that this diffusion behavior takes orgin from the electronic interactions occurring between iron atoms, impurities and vacancies.
(open symbols: experimental values)
L. Messina, IGRDM-18

15. Solute diffusion coefficients
Solute diffusion coefficients at low temperature!
Remarkable agreement with experiments (except Mn).
Valuable information for modeling many types of alloys.
Difffusion coefficient prediction for non-measured impurities.
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
L. Messina, IGRDM-18

16. Slow diffusers
Slow diffusers: impurity diffusion coefficient lower than self-diffusion coefficient
Co, Re, Os, Ir
High solute migration barrier is not sufficient!
Condition for slow diffusion is
Attractive (negative) binding energy counteracts higher migration barrier (increased pair probability).
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
L. Messina, IGRDM-18

17. Thermodynamics-kinetics decoupling
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
L. Messina, IGRDM-18

18. Thermodynamics-kinetics decoupling
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
L. Messina, IGRDM-18

19. Outline Flux coupling and solute diffusion via vacancies/dumbbells
Systematic analysis of vacancy drag
Mobility & Stability of solute-vacancy pairs
Effect of two solutes 19
L. Messina, IGRDM-18

20. Mob/Stab of solute-vacancy pairs
MEAN FREE PATH BEFORE DISSOCIATION (550 K)
V-Cr
0.24 nm
V-Cu
0.86 nm
V-Mn
0.68 nm
V-Ni
0.42 nm
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
V-P
3.51 nm
V-Si
1.00 nm
FROM AB INITIO DATA!!
L. Messina, IGRDM-18

21. Mob/Stab of solute-vacancy pairs
SELF-CONSISTENT MEAN FIELD THEORY (T. Schuler, M. Nastar, PRB 93, (2016))
Decomposing the Onsager matrix in cluster contributions (MOBILITY + ASSOC/DISSOC)
ASSOCIATION/
DISSOCIATION
MOBILITY
ATOMISTIC KMC
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
1. Follow cluster evolution until dissociation.
2. Register cluster lifetime and trajectory.
3. Repeat many times (collection of statistics).
4. Calculate average life time and diff. coeff.
5. Linear regression on Arrhenius domain.
L. Messina, IGRDM-18

22. Mob/Stab of solute-vacancy pairs
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
L. Messina, IGRDM-18

23. Outline Flux coupling and solute diffusion via vacancies/dumbbells
Systematic analysis of vacancy drag
Mobility & Stability of solute-vacancy pairs
Effect of two solutes 23
L. Messina, IGRDM-18

24. Effect of two solutes P Mn At 300 °C
Eb = eV
0.23 eV
≈ 0.68 eV
≈ 0 eV
0.57 eV
0.11 eV
Eb = eV Mn
Eb(Fe-P) = eV
Eb = eV
0.45 eV
≈ 0.42 eV
0.26 eV
So, in order to solve the issue of the migration barriers we decided to attempt a new approach, where we make use of neural networks. Thanks to neural networks we can build an interpolation scheme that can be trained on a set of known migration barriers, so that it can provide a prediction of any atomic configuration.
This was done in the past by calculating the training set of data with interatomic potentials, but we attempted for the first time to use DFT instead.
The advantages are:
We expect the diffusion mechanisms to be more accurately reproduced.
It is possible to apply it to complicated multicomponent alloys with just a small increase of amount of calculations, but we don’t need to develop an interatomic potential in each case.
We applied this for thermal aging in FeCu as a first test case, and we were able to reproduce the experimental microstructure evolution.
0.21 eV
0.47 eV
Eb = eV
0.78 eV
Eb(Fe-Mn) = eV
At 300 °C
105 more probable for Fe-Mn dumbbell to fall into the trap!
L. Messina, IGRDM-18

25. Planned work
Effect of strain/elastic fields on solute-transport tendencies and radiation-induced segregation profiles, e.g. next to large defect clusters, dislocations, and grain boundaries.
Corrected solute-segregation profiles on defect clusters.
Improved symmetry analysis with point- and space-group theory.
Example: Cr segregation in Fe
2. Calculation of transport coefficients beyond the dilute-alloy limit.
SCREW DISLOCATION
EDGE DISLOCATION
Effect of multiple solutes (e.g. SIA trapping by two solute atoms).
Effect of multiple defects (solute transport by defect clusters).
So, in order to solve the issue of the migration barriers we decided to attempt a new approach, where we make use of neural networks. Thanks to neural networks we can build an interpolation scheme that can be trained on a set of known migration barriers, so that it can provide a prediction of any atomic configuration.
This was done in the past by calculating the training set of data with interatomic potentials, but we attempted for the first time to use DFT instead.
The advantages are:
We expect the diffusion mechanisms to be more accurately reproduced.
It is possible to apply it to complicated multicomponent alloys with just a small increase of amount of calculations, but we don’t need to develop an interatomic potential in each case.
We applied this for thermal aging in FeCu as a first test case, and we were able to reproduce the experimental microstructure evolution.
3. DFT-based investigation of solute interaction with interstitial and C15 clusters.
Segregation energies and analysis of stable configurations.
Solute migration inside the clusters and on its surface.
Effect on solute transport and microstructure evolution (by KMC simulations).
L. Messina, IGRDM-18

26. Conclusions
Investigation of diffusion mechanisms of impurities via interaction with single point defects in Fe alloys.
Solute-transport capabilities by single defects have been proven theoretically. The findings are consistent with the suggested formation mechanism for MnNiSi clusters
Theoretical framework for studying flux-coupling and diffusion phenomena in metals.
Vacancy drag is systematic at low temperature, even in the presence of repulsive vacancy-solute interactions.
Database of DFT migration barriers and low-temperature diffusion coefficients.
The mean field method is now mature to yield mobility and stability parameters for small solute-defect clusters, to be used in OKMC simulations.

28. Self Consistent Mean Field method [*]
CONFIGURATION = ENSEMBLE OF OCCUPATION NUMBERS
configuration n
MASTER EQUATION
EQUILIBRIUM
NON EQUILIBRIUM (QUASI EQUILIBRIUM)
Possible configurations n’
E0(n) : sum of pair interactions
THERMODYNAMIC INTERACTIONS
E(n) : unknown
KINETIC INTERACTIONS
vij are found by writing down kinetic equations --> self-consistent system of equations
FLUX EQUATIONS
(Onsager’s equation)
[*] M. Nastar, Philos. Mag. 85 (2005).
L. Messina, IGRDM-18

29. Vacancy clusters in Fe-MnNi alloys
M. Chiapetto, L. Malerba, C. S. Becquart, J. Nucl. Mater. 462 (2015)
us.arevablog.com
us.arevablog.com ?? ??
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
RINGHALS
RINGHALS
“Arbitrary” reduction of vacancy cluster mobility (and immobilization for n > 10) to match experimental characterization of FeMnNi alloy in OKMC simulations.
Same assumption works also for Ringhals steels.
Possible explanations: effect of Mn/Ni solutes OR vac-Mn-Ni interaction with carbon traps.
corporate.vattenfall.se
corporate.vattenfall.se 29
L. Messina, IGRDM-18

30. Vacancy-MnNi clusters
us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
STABILITY
IMMOBILITY
RINGHALS
corporate.vattenfall.se
L. Messina, IGRDM-18

31. Vacancy-MnNi clusters
us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
STABILITY
IMMOBILITY
RINGHALS
corporate.vattenfall.se
L. Messina, IGRDM-18

32. Vacancy-MnNi clusters
us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
STABILITY
IMMOBILITY
RINGHALS
corporate.vattenfall.se
L. Messina, IGRDM-18

33. Vacancy-MnNi clusters
us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
STABILITY
IMMOBILITY
RINGHALS
corporate.vattenfall.se
L. Messina, IGRDM-18

34. Vacancy-MnNi clusters
us.arevablog.com
us.arevablog.com
Partial immobilization observed
(Emig < 1.20 eV)
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
STABILITY
IMMOBILITY
+Mn&Ni
+Ni
+Mn
RINGHALS
RINGHALS
corporate.vattenfall.se
corporate.vattenfall.se
L. Messina, IGRDM-18

35. Gray-alloy approach us.arevablog.com us.arevablog.com us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
RINGHALS
RINGHALS
RINGHALS
L. Messina, IGRDM-18

36. Gray-alloy approach
us.arevablog.com
us.arevablog.com
us.arevablog.com
us.arevablog.com
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
declanbutler.info/Fukushima/Fukushima.kmz
Another important outcome of this systematic investigation is the prediction of impurity diffusion coefficients.
Here we show the comparison of our predictions with experimental values in the high-temperature range, and we see in general a remarkable agreement.
- However, the most valuable information concerns the low-temperature end, where we cannot perform diffusion experiments since diffusion becomes really slow.
- So, in general this combined ab initio-mean field method provides not only information about flux coupling, but also the possibility to predict impurity diffusion coefficients that are otherwise unknown.
Estimated slowdown at 573 K is only 1 order of magnitude.
RINGHALS
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The OKMC model has been now re-tuned with a slightly higher mobility for vacancies.
L. Messina, IGRDM-18

37. THANKS FOR YOUR ATTENTION!
Publications
L. Messina, M. Nastar, T. Garnier, C. Domain, P. Olsson, Exact ab initio transport coefficients in bcc Fe-X dilute alloys, Physical Review B 90, (2014).
L. Messina, M. Nastar, N. Sandberg, P. Olsson, Systematic electronic-structure investigation of substitutional impurity diffusion and flux coupling in bcc iron, Physical Review B 93, (2016).
L. Messina, M. Nastar, P. Olsson, Ab initio-based study of solute-dumbbell transport and radiation induced segregation in Fe-X dilute alloys, submitted to Physical Review B.
L. Messina, L. Malerba, P. Olsson, Stability and mobility of small vacancy-solute complexes in Fe-MnNi and dilute Fe-X alloys: A kinetic Monte Carlo study, Nuclear Instruments and Methods in Physics Research B 352, (2015).
L. Messina, N. Castin, C. Domain, P. Olsson, Introducing ab initio-based neural networks for transition-rate prediction in kinetic Monte Carlo simulations, submitted to Journal of Chemical Physics.
L. Messina, Z. Chang, P. Olsson, Ab initio modeling of vacancy-solute dragging in dilute irradiated iron-based alloys, Nuclear Instruments and Methods in Physics Research B 303, (2013).
N. Sandberg, Z. Chang, L. Messina, P. Olsson, P. Korzhavyi, Modeling of the magnetic free energy of self-diffusion in bcc Fe, Physical Review B 92, (2015).
Acknowledgments
Financial support from Vattenfall AB, Göran Gustafsson Stiftelse, MatISSE and SOTERIA FP7 European projects.
Computational power from SNIC, CSCS, EDF.
Host institutions: KTH, CEA, EDF, SCK-CEN.
Collaborators:
M. Nastar, T. Garnier, F. Soisson, T. Schuler (CEA)
C. Domain (EDF)
N. Castin, L. Malerba, M. Chiapetto (SCK-CEN)
C. Becquart (Université de Lille)
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L. Messina, IGRDM-18