The W divertor will contain He, both due to He bombardment from the plasma, and transmutation reactions. Most of the ions from the plasma have very low energy, but the divertor will be subject to some ions energetic enough to cause cascade damage, as well as the high energy neutron irradiation all reactor materials suffer from. Thus it is of interest to study how He affects displacement cascades in W. As W, Fe and FeCr are BCC metals, the effect can be expected to be similar to that in Fe and FeCr. There are, however, large differences in material properties, and in the pure materials, the amount of damage is much smaller in W. A comparison of different W–W potentials, the Ackland-Thetford (AT), Derlet et al. (D) and Juslin (J) potentials described in Sect. 4.1.2 and the effect of He on cascades was performed in paper VI.
First the basic interstitial and substitutional He formation energies were compared between the
poten-Table 2: The fraction of vacancies (V) and self-interstitials (SI) that are in clusters, as described in the text, for 2 keV cascades. The He atoms were initially in interstitial positions. The results for pure W are, for the Derlet et al. (D) potential from Ref. [61] and for the Ackland-Thetford (AT) and Juslin (J) potentials from Ref. [72].
AT D J
Pure 1.0% He Pure 1.0% He Pure 1.0% He
V 0.28±0.04 0.04±0.01 0.24±0.08 0.23±0.02 0.22±0.04 0.07±0.01 SI 0.24±0.04 0.20±0.03 0.31±0.07 0.29±0.02 0.24±0.04 0.20±0.01
tials, and the most recent DFT results. The formation energy is overestimated in all cases compared to DFT [16], except for the substitutional He for the J potential, due to the low vacancy formation energy with this potential. The formation energy of the interstitital is relatively high both in the MD simu-lations and in DFT, 7.8–9 eV and 6.2–6.5 eV respectively. This discrepancy can affect the cascade damage, and development of a new W–He potential should be considered for future studies.
7.3.1 Damage production
As can be expected, the same mechanics that govern the effects of interstitial and substitutional He described in Sect. 7.2.1 for FeCr, are found for tungsten. The total damage, and the increase in damage due to interstitial He, is less than in FeCr, though the smaller effect of He can partially be attributed to the difference in micro-structure. Studying the effect of the micro-structure is certainly of interest for future studies.
A recoil energy of 2 keV is the highest energy, for which pure W has been studied for all the potentials.
As the effect of He can be expected to be more pronounced at higher energies, the potentials were compared for this recoil energy. Both the amount of damage and the clustering of vacancies and interstitials, are relatively similar, with the amount of Frenkel pairs and interstitial clustering slightly higher for the potential by Derlet et al. than for the others as can be seen in Fig. 11(a) and Table 2.
For substitutional He, the amount of damage compared with pure W is reduced for 1% He, while it is unchanged for 0.1%, except for the W–W potential from Sect. 5.1, for which it is a bit higher. While there are apparent differences between the potentials, the qualitative features of the damage are the same.
For the D potential, higher energy recoils have been simulated. As can be seen in Fig. 11(b), the damage production increases exponentially with recoil energy, as it does for pure W. The slope of the fitted curve in a log-plot remains the same with 1% interstitial He as for pure W. The damage production with 5 keV recoil with 0.1% He is surprisingly very similar to that with 1% He. Even for
2 4 6 8 10
Frenkelpairs
AT D J
Potential 1.0% He subs.
0.1% He subs.
0% He 0.1% He int.
1.0% He int.
(a)
1 2 5 10 20 50
Frenkelpairs
0 5 10 15 20
Energy (keV)
0.0% He 0.1% int. He 1.0% int. He 0.1% subs. He 1.0% subs. He
(b)
Figure 11: The damage produced by cascades in W with different He concentrations and recoil energies for both interstitial (int.) and substitutional (subs.) He. In (a) the number of Frenkel pairs are compared for the Ackland-Thetford (AT), Derlet et al. (D) and Juslin (J) W–W potentials. In (b) the number of Frenkel pairs for 2, 5 and 20 keV recoils for the D potential. The results for 0% He are from Ref. [61] for the D potential and from Ref. [72] for the AT and J potentials.
pure tungsten, the 5 keV recoil produces a high amount of damage compared to other energies. With substitutional He, the amount of damage is reduced for 1% He, especially in the 5 keV case, where the number of Frenkel pairs is reduced to about a quarter of that in pure W. For 0.1% the damage is unchanged.
8 CONCLUSIONS
In this thesis, interatomic potentials needed for molecular dynamics simulations of irradiation of materials have been developed and applied. The focus is on the fusion reactor relevant materials tungsten and iron chromium, and the deuterium bombardment of tungsten and effects of helium in both tungsten and iron chromium. While the motivation for the work was to study materials for future fusion reactor applications, the research leans towards study of the basic science behind the phenomena, rather than an engineering approach.
New potentials have been developed for the W–W, W–C and W–H interactions, based on data from both literature and ab initio calculations in this thesis. While the potentials have certain known short-comings, they perform well for their intended use and they are still the only potential set for simulating a WCH system. The W–C and W–H potentials are not used further in this thesis, but have been applied by several groups for a wide range of studies.
Pair potentials able to describe He defect properties in Fe and Cr were developed in order to study the effect of He on irradiation properties in Fe and FeCr, as model materials for fusion reactor steels.
The potentials are able to describe the interstitial and substitutional energies very well, as well as migrational properties adequately. The Fe–He potential has also been widely used and tested by others. For the Cr–He potential, the lack of known experimental or ab initio data limits the testing possibility. There are, however, groups performing ab initio studies of He in Cr and FeCr and it remains to be seen how well the potential can reproduce those results.
The presence of 10% Cr does not greatly affect the formation, mobility and lifetime of He and He–
vacancy clusters. The formation energy can be quite different depending on the local neighborhood, but on average cluster formation, as well as the binding to and dissociation from a cluster, of a He or vacancy, is not significantly affected by Cr. The mobility of pure He clusters is retarded by a small degree due to 10% Cr. The mobility and dissociation frequency of the clusters were shown to be higher than previously assumed, in some cases several orders of magnitude.
The effect of Cr on the displacement threshold energies in FeCr with 10% Cr was shown to be neg-ligible. There is a small difference on whether the displaced atom is Cr or Fe, but even for the Cr atom, the results are close to those for a Fe atom in pure Fe. On the other hand, there are considerable differences between the results for FeCr and pure Cr. Together with the results that Cr hardly affects the total damage in displacement cascades in FeCr, this indicates that the experimentally observed effect that the dependence on Cr on the irradiation response of FeCr most likely comes from long time scale damage evolution and is not due to primary damage formation.
A concentration of 0.5-1% interstitial He significantly increases the displacement cascade damage production, while He in substitutional positions reduces it. This is seen both in FeCr and W. At lower concentrations the primary damage production is not notably different than for the pure materials.
The increase due to interstitials is explained by He atoms combining with vacancies produced during the cascade, thus reducing the recombination of metal atoms and vacancies. The reduction due to substitutional He has the opposite mechanism, as some of the He become interstitial or clusters, leaving more vacancies for the metal interstitials to recombine with.
All of the studies performed on FeCr and FeCrHe in this thesis indicate that 10% randomly distributed Cr influences the primary damage production or He migration and clustering to an insignificant de-gree. Helium,on the other hand, can greatly increase the amount of primary damage, but only for concentrations that approach the limit of what is expected to be produced during the lifetime of a reactor. Also in tungsten a similar effect of He is seen. Local variations in concentration and micro-structure of He could, however, play a significant role in a real material and are certainly of interest for further studies.
ACKNOWLEDGMENTS
I wish to thank the head of the Department of Physics at the University of Helsinki, Professor Juhani Keinonen, as well as the head of the Accelerator Laboratory, Professor Jyrki Räisänen, for providing me with an excellent and exciting place to study and conduct my research, all the way from my first stumbling steps as a physicist to a doctoral degree.
I especially wish to thank my supervisor Professor Kai Nordlund, without whom I would not be here today. You took me into the group with open arms and have provided me with an interesting and encouraging field of research. You have both guided me and allowed me to figure things out on my own, making a materials scientist out of me.
I am grateful to have so many great co-workers and friends at the Accelerator Laboratory. In particu-lar, I wish to thank Toffe, Caro, Tommi, Jani and Eero for being amazing friends.
Several collaborators at other laboratories have made this research possible, as well as being excellent hosts while visiting them. I also wish to thank my co-workers and friends at Lawrence Livermore National Laboratory for giving me a wonderful summer institute filled with experiences.
Many thanks are due to my family and friends, who have always been there to support me. All the wonderful people in Spektrum have made it a second home for me all these years.
Marie, thank you for everything!
Helsinki, October 2, 2009 Niklas Juslin
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