1. N. Castin, M. Chiapetto, C. Domain, C. Becquart
OKMC model for FeNiMn with solute transport: first results and importance of method of analysis
N. Castin, M. Chiapetto, C. Domain, C. Becquart
and L. Malerba

2. Synopsis What did we do? How was the solute transport modelled?
We introduced explicit solute transport in an object kinetic Monte Carlo model
We applied it to study an FeMnNi alloy
How was the solute transport modelled?
Ni and Mn dragged by single point-defects, as according to the latest DFT studies
What did we obtain?
Spontaneous formation of solute clusters around point-defect clusters.
Analyse the results with the eyes of APT
Comparison with experimental measurement shows encouraging signs

3. Grey alloy OKMC approach : solute clusters are associated with point-defect clusters
SIA clusters
Number density of Mn-Ni precipitates according to APT is of the order of the density of TEM-invisible SIA clusters
 Assumed to be solute clusters!
Atomistic simulations reveal that loops make Mn-Ni ppts stable
NUMBER DENSITY (m-3)
TEM-visible SIA clusters
(>90 SIA, 1.3 nm)
G. Bonny et al., Journal of Nuclear Materials 452 (2014) 486
How to introduce solute transport in an OKMC model where solutes are not present?

4. Key atomistic mechanism: solute dragging by point defects
In general, one may expect that a solute atom will move via vacancy in the opposite direction to the vacancy A V
Instead, Mn and Ni, but also Cu, Si, and P, follow the vacancy during its migration B Fe V Fe
Mn / P Fe
Finally, any solute forming a mixed dumbbell wil be dragged by it Fe

5. DFT-based models reveal that all solutes found in clusters in RPV steels are dragged by point defects
VACANCY DRAG
INTERSTITIAL TRANSPORT
Vacancy can carry solute atoms along.
Occurring for manganese, nickel, copper, phosphorus, silicon.
Interstital atoms can couple with solute atoms and move together.
Occurring for manganese, phosphorus, chromium.
Flux-coupling phenomena
Formation of pecipitates and solute segregation in RPV steels
Low T diffusion coefficinets
L. Messina, P. Olsson, M. Nastar, T. Garnier, C. Domain, PRB 90, (2014)
L. Messina, IGRDM-18

6. Atomistic KMC provides DFT-based parameters to describe Ni & Mn transport when dragged by point-defects
The fastest and most stable diffuser is the Mn via dumbbell
Single-vacancies drag both Mn & Ni
Mn slightly more efficiently dragged because of lower migration energy
Small point-defect clusters will also contribute to solute transport but this is neglected in first approximation

7. New MATEO software developed @ SCK•CEN
Hybrid A/OKMC model
New MATEO software SCK•CEN
OKMC for microstructure, AKMC for solute transport
Only single point-defects transport solutes
Solute transport by mobile clusters is disregarded
Each time a point-defect finds a solute, a new object (solute-Va pair, mixed dumbbell, …) is created
The binding energy defines for how long the point-defect drags the solute, i.e. until dissociation
Correlation effects with surrounding solutes are disregarded
C atoms are simulated as traps and most parameters are the same as in the grey alloys model
Alternative: remove traps and consider that the defect falls randomly in a “trapped status”
Here the slide is unchanged compared to last conference.
Message is slightly changed:
1°) The hybrid OKMC – AKMC model is inherently going to predict lots of clusters of solute atoms, around nearly all fixed trap. Presented like this, it looks like the model fails because the density of solute clusters is 1 or 1.5 orders of magnitude too high compared to APT measurements.
2°) There are improvable aspects of the model from a physical point of view, as will be shown in the next slides
2.1 – Fixed traps could be avoided by introducing explicit C, even though this is far easier to say than to do.
2.2 – More mechanisms of solute transport, so far neglected for simplicity, could be added with the desired effect to dilute some clusters
3°) Last but not least, the results of our simulation are not 1-to-1 comparable to APT. This is important because some solute clusters might be invisible by APT.
REMARK: I hope the circles supposed to represent SIA’s will remain grey on your computer, because otherwise it becomes confusing. They appeared white on my computer, i.e. identical to vacancies.

8. Problem: excess of clusters produced around Va-traps
Possible reasons
Overestimation of solute transport
– unlikely because of DFT based parameter and neglect of clusters …
No mechanism for solute-vacancy cluster dissolution
NEW: analysis does not take into account APT features!
New MATEO software SCK•CEN

9. Introduction of mechanisms of dissolution
Mechanism of dissolution introduced as limiting case: all emitted vacancies carry a solute out
Solute-vacancy complex
Solutes -
Vac
Solute +
Vac
Solute +
SIA
Surviving Vac cluster
Accumulating solutes
Releasing few of them.
Annihilated Vac cluster leaving solutes behind
New MATEO software SCK•CEN

10. Introduction of mechanisms of dissolution
Dissolution of SIA-solute complexes forbidden because of high thermal stability
Solute-SIA complex
Solute -
SIA
Solute +
Vac
Solute +
SIA
Surviving SIA cluster Accumulating solutes
Releasing none of them.
Annihilated SIA cluster with solutes left behind
New MATEO software SCK•CEN

11. Model improved but still no good agreement

12. Looking at our result from the simulation with the eyes of the APT
Emulating the effects of APT measurements
Apply detection probability
Apply random perturbations of atomic coordinates
Search for clusters using defendable algorithm in alignment with what APT people do.
Most impacting effect
The smallest clusters are “dissolved”,
i.e. not anymore identifiable as cluster.
XY-plane
Large perturbation !
(up to 1nm)
40% of atoms detected in while sample
Z-axis
Small perturbation

13. Our results after the APT treatment
Results are in excellent agreement with experiment!
Our overall model for the formation of solute clusters is consistent with experimental evidence, provided that the analysis is performed with the “eyes” of the experimental technique!

14. Summary & Outlook
Dragging of solutes by point-defects leading to segregation of solutes on point-defect clusters has been identified as the key mechanism leading to formation of solute clusters in iron alloys and specifically RPV steels
A hybrid Object/Atomistic KMC model (new code Mateo) has been developed to include explicitly the transport of solutes
Its use with a "not-too-unrealistic“ set of parameters leads to the formation of solute clusters in the correct amount and of the correct size
Outlook: verify the model in all its parts (visible loops, …) and develop the parameterisation further, to have a single all-including model
L. Messina, IGRDM-18 15