Molecular dynamics simulations of collision cascades in FeCrHe

Nuclear Instruments and Methods in Physics Research B 267 (2009) 3420–3423

Contents lists available at ScienceDirect

Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb

Molecular dynamics simulations of collision cascades in FeCrHe N. Juslin *, K. Nordlund Department of Physics, University of Helsinki, P.O. Box 43, FI-00014 Helsinki, Finland

a r t i c l e

i n f o

Article history: Received 10 June 2009 Received in revised form 14 July 2009 Available online 21 July 2009 PACS: 61.72.J 61.80Hg 61.82.Bg

a b s t r a c t Radiation damage due to 1 and 5 keV collision cascades in Fe90Cr10 in the presence of 0.1%, 0.5% and 1.0% He defects, relevant for fusion reactor steels, has been studied using molecular dynamics simulations. We show that with 0.1% interstitial He the effect on the damage production in the FeCr matrix is minor, while with 1.0% He, the number of Frenkel pairs is significantly increased in comparison to pure FeCr. The positions of the He interstitials and clusters depend on the Cr atoms and the amount of He inside the cascade region is increased by about 30% due to the cascade. With substitutional He less damage is formed in the FeCr matrix due to cascades. Ó 2009 Elsevier B.V. All rights reserved.

Keywords: Radiation damage Iron–chromium Helium Simulation

1. Introduction Ferritic/martensitic steels are considered candidate structural materials for fusion reactors, as they are known to be resistant to swelling and defect accumulation due to irradiation compared to other steels [1–5]. These steels will contain small amounts of helium, due to neutron irradiation, as 14 MeV neutrons produce He through (n,a) transmutation reactions [6]. He is known to degrade the mechanical properties of steels [5,7] due to e.g. bubble formation, blistering and loss of fracture toughness. Helium in fusion reactor steels is discussed in the review article by Schäublin et al. [5]. The amount of He produced in fusion reactor steels will be around 10–15 appm/dpa, or up to about 0.05–0.1% during the lifetime of the material. While much is still unclear about the effect of He on the micro structure, Helium is known to cluster together and bind to vacancies and cavities, forming bubbles [5,6]. There is an ongoing international effort to understand and predict radiation damage in steels with a multi-scale approach, including density functional theory, molecular dynamics (MD) and Monte Carlo simulations [8]. MD simulations are well suited for the length and time scales of primary damage formation due to collision cascades. Modeling real steel with up to dozens of different elements is still out of reach for MD simulations, but good models exist for FeCr [9,10] which can be used as an approximation for ferritic steels. * Corresponding author. Tel.: +358 9 19150003. E-mail address: niklas.juslin@helsinki.fi (N. Juslin). 0168-583X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.nimb.2009.07.012

Cascades in Fe and Fe–Cr have been studied extensively [11– 14]. Generally the effect of 5–15% of Cr on the total damage is minor. Cascades in Fe with small amounts of He have recently been studied using different potentials [15–18]. Using the most recent potentials, which are also used in this work, Lucas and Schäublin [18] show that 0.1% interstitial He has minor effect on the cascades, but 1% He significantly increases the total damage in the Fe matrix. Substitutional He decreases the cascade damage. Until recently no inter-atomic potential for Cr–He existed [19]. As has been shown in [19], the average behavior of small He defects in Fe90Cr10 is close to that in pure Fe, but can vary with local configuration. For instance, the formation energy of a substitutional He can vary between 3.6 and 4.4 eV. The complex behavior during the cooling down of a heat spike and recombination of defects can be affected by the Cr and He amounts and lead to different damage production. We have studied 1 keV and 5 keV recoils in Fe90Cr10 with 0.1%, 0.5% and 1.0% He. We have chosen to study two cases, starting with all He as interstitial or as substitutional defects and then equilibrating for 25 ps to allow some clustering before starting the cascade. While studying the effect of micro structure complexity such as He bubble size, Cr precipitates and grain boundaries would be interesting, they should first be studied and understood in the simpler binary element cases. At the higher concentrations we see a significant increase in damage compared to pure FeCr and an effect on the He due to the Cr. The simulation and analysis methods are described in the following section and the results are presented and discussed in Section 3.

3421

N. Juslin, K. Nordlund / Nuclear Instruments and Methods in Physics Research B 267 (2009) 3420–3423

The interatomic potentials used were the PAW version (based on projector augmented wave density functional theory results) of the Fe–Cr potential by Olsson et al. [9] which was developed to be used together with the Olsson Cr–Cr potential [9] and the Ackland–Mendelev 2004 Fe–Fe potential [20]. We have recently developed potentials for Fe–He [21] and Cr–He [19]. This set of potentials was chosen, out of a few possible Fe–Cr [10] and Fe–He [22,23] potentials, as the potentials have been developed for simulation of radiation damage, and to be used with each others. The simulations were carried out using the MD code PARCAS [24]. First a FeCr simulation cell with 10% Cr in random body-center cubic (bcc) lattice positions was created. The cell size was chosen large enough that the cascade would not overlap with itself over the periodic cell borders, which was checked during the simulations by monitoring the kinetic energy of border atoms. For 1 keV cascades the box size was 25  a0 and for 5 keV 42  a0 , or 31,250 and 148,176 atoms, respectively. Then 0.1%, 0.5% or 1% He was inserted in random tetrahedral interstitial positions. These cells were first equilibrated at 300 K and zero pressure using the Berendsen pressure and temperature control [25]. During equilibration at room temperature, interstitial He atoms migrate rapidly and form clusters. Most of the substitutional He stay bound to the vacancies, but some small clusters are formed. The amount of clustering depends on the equilibration time and He concentration. The simulation time was 25 ps. This equilibration time was chosen in order to have similar equilibration effects in the cascade region before and after the cascade, as an equilibration time of 20– 25 ps after the cascade has proven enough to assess the primary damage in FeCr [11]. Equilibration on a longer time scale would create a micro structure with larger helium bubbles and regions with low He concentration, thus making the cascades dependent on where they are located. The cascades were then started by choosing a Fe atom as the primary knock-on atom and giving it a recoil energy of 1 or 5 keV. The atom and direction was chosen at random, however, such that the cascade would not be too close to the cell border, and directed towards the center. This was repeated 20 times for 1 keV and 10 times for 5 keV in order to get sufficient statistics. The simulation time was 25 ps. The volume was kept constant, and the temperature was scaled at the borders to remove heat from the system. The simulations were repeated without introducing a recoil to assess the amount and nature of the damage coming from the cascade, as compared to the clusters formed during equilibration. The damage was analyzed using the occupancy of Wigner–Seitz (WS) cells. An empty WS cell means a vacancy and a multiply occupied cell means one or more interstitials. While a lot of He defects are present, as we have inserted 0.1–1% interstitial He, the primary damage formed in the cascade is mainly seen as Frenkel pairs (FP) in the FeCr matrix. The clustering of metal interstitials and vacancies was analyzed by assigning a cut-off radius of 3rd nearest neighbor (nn) and 2nd nearest neighbor, respectively. If a defect is within this distance of at least one other defect in the cluster, it belongs to the same cluster. In order to discern the differences between the main region affected by the cascade and the surrounding region we labeled the atoms as being part of the cascade region (CR) or the surrounding region (SR). The exact border where atoms are not significantly affected by the cascade is not well defined. We chose to label an atom as being in the CR if it was in the vicinity of several atoms that were liquid, based on kinetic energy, during the peak of the heat spike. Thus the CR is the region that was molten during the cascade, as well as atoms within about one lattice constant around

it, and an atom that has migrated in to or out from the region is labeled as CR or SR, respectively.

3. Results and discussion Starting from random interstitial positions, 0.1% He does not lead to large He defect clusters during a 25 ps equilibration run at 300 K. Most helium atoms remain as single interstitials and no metal Frenkel pairs are formed. At 0.5% and 1.0% larger clusters with sizes ranging from a few He to He-vacancy clusters with tens of He atoms are formed, and some Fe and Cr atoms are displaced to form damage in the FeCr matrix. The lattice constant of Fe90Cr10 with 0.1–1.0% He at 300 K is about 2.87 Å. The total number of Frenkel pairs formed in the FeCr matrix during the cascade is shown in Fig. 1 and Table 1, together with the the results for pure Fe90Cr10 [11]. The damage in the FeCr matrix due to the clusters from the equilibration is not included in these results. The damage increase with higher concentration and higher recoil energy. For 0.1% He the results are statistically the same as for pure FeCr, while for 1% we note a clear increase compared to pure FeCr for both 1 and 5 keV. At 5 keV as much as about 60 Frenkel pairs are produced, compared to 15 for pure FeCr. The explanation for this increase in damage is that interstitial He and vacancies form substitutional He during the cascade, thus decreasing the amount of vacancies the interstitial metal atoms can recombine with. The amount of substitutional He after the cascade is given in Fig. 2 and the amount Hen V1 clusters, with the majority having 1–3 He atoms, in Fig. 3. The nature of the damage in the FeCr matrix is not greatly affected by the addition of He. As can be seen in Table 1, at 1.0% He the vacancies are less clustered and the interstitials more than for pure FeCr. The fraction of interstitials with Cr is unchanged by the addition of He, while the fraction of Cr among interstitial atoms appears to be slightly reduced for 1.0% He, indicating less Cr–Cr interstitials. For low He concentrations the clustering statistics is rather poor, as the amount of FP produced is low. As the statistics for all other results is good and the clustering amount can be expected to be between the results for 0.0% and 1.0%, increasing the number of simulations tenfold to reach an error of about 2 is unnecessary.

100

0.0% He 0.1% He

50

Frenkel pairs

2. Methods

0.5% He a

20

10

5

1

Energy(keV)

5

Fig. 1. The total number of Frenkel pairs produced by the cascades. The error bars, given in Table 1, are of the scale of the markers and have been left out for clarity. The data for pure FeCr is from [11].

3422

N. Juslin, K. Nordlund / Nuclear Instruments and Methods in Physics Research B 267 (2009) 3420–3423

Table 1 Damage in the FeCr matrix due to 5 keV cascades with 0–1.0% He. The data for pure FeCr is from [11]. Amount of He

0.0%

0.1%

0.5%

1.0%

Frenkel pairs Vacancy clustered fraction (%) Interstitial clustered fraction (%) Frac. of Cr among interstitial atoms (%) Frac. of interstitials with Cr (%)

15.3 ± 0.6 43 ± 2 34 ± 2 13 ± 1 27 ± 2

14.4 ± 1.2 29 ± 10 36 ± 4 15 ± 3 30 ± 6

19.9 ± 2.9 32  3 40  4 13 ± 1 28  3

59.4 ± 2.3 37 ± 2 44 ± 2 10 ± 1 27 ± 3

0.1% He 0.5% He

20

SubstitutionalHe

1.0% He 15

10

5

1

Energy(keV)

5

Fig. 2. The amount of substitutional He formed in the cascade.

60

0.1% He 0.5% He

50

Hen-V1 clusters

can be seen in Table 2. The variation from case to case is quite high, but on average there are about 25–40% more He atoms. The reason for the high percentage for 1 keV, 0.1% is that there are about 1–3 He atoms in the region before the cascade which increase by 1–2 He during the cascade. A likely cause for the increase is that the substitutional He defects formed during the cascade, which are less mobile than interstitial He, stay within the region and bind other He atoms to form He clusters. Thus there would be a lower fraction of mobile He in the cascade region than outside it, leading to more migration into than out of it. This is, however, a very complicated process, due to the liquid–solid interface during the cascade, the damage in the Fe–Cr matrix, the He defect clusters and the stochastic nature of He migration. During equilibration, the helium interstitials and clusters tend to migrate away from Cr atoms. The reason for this is that the pair potential describing Cr–He is a bit more repulsive than for Fe–He. One or more He very rarely, about 0.1–0.2% of the He atoms, occupy the same WS cell as a Cr. In the cascade region, the Cr concentration within the nearest 0.5–1.5  a0 around a He atom increases slightly compared to the surrounding region, though it remains well below the 10% in a random solution, as can be seen in Fig. 4. This can be explained by the formation of less mobile substiTable 2 The fraction of interstitials in clusters due to 5 keV cascades with 0–1.0% He, including He interstitials. At higher He concentration a majority of the interstitials are close to other interstitials. The data for pure FeCr is from [11]. Also shown is the He increase inside the cascade region (CR) due to the cascade.

1.0% He

40 30

Amount of He

0.0%

0.1%

0.5%

1.0%

Interstitial clustered fraction (%) He increase in CR (%), 1 keV He increase in CR (%), 5 keV

34 ± 2 – –

30 ± 1 71 ± 11 25 ± 5

69  0.4 30 ± 7 28 ± 3

86 ± 0.4 38  4 23  2

20 10 0.1

Energy (keV)

5

Fig. 3. The amount of vacancies in the FeCr matrix filled with one or more He atoms due to the cascade.

Comparing with He in Fe by Lucas and Schäublin [18], we note a higher amount of damage, at 5 keV and 1% about a twofold number of Frenkel pairs. While we find that the behavior of helium depends on the chromium, as described below, the difference is surprisingly large. Lucas and Schäublin used a much shorter equilibration time (2 ps) before the recoil, and thus observed less clustering of He. While the clusters in the cascade region break up during the heat spike, the amount of clustering combined with the addition of Cr could explain the higher number of Frenkel pairs in our simulations. The amount of He in the core region of the cascade, which was molten during the heat spike, here called cascade region (CR), is increased by the cascade for all energies and He concentrations as

n Cr /(nFe+nCr)

1

0.08

5 keV0.1%CR 5 keV0.1%SR 5 keV0.5%CR

0.06

5 keV0.5%SR 5 keV1.0%CR 5 keV1.0%SR 1

2

r (a0)

3

Fig. 4. The Cr concentration among metal atoms within distance r of He atoms. CR stands for cascade region and SR for the surrounding region, as defined in the text. The Cr concentration close to He atoms is increased by the cascade.

N. Juslin, K. Nordlund / Nuclear Instruments and Methods in Physics Research B 267 (2009) 3420–3423

0.8

5 keV 0.1% CR 5 keV 0.1% SR

0.7

5 keV 0.5% CR

nHe/(nFe+nCr)

0.6

5 keV 0.5% SR 5 keV 1.0% CR

0.5

5 keV 1.0% SR

3423

ence between FeHe and FeCrHe. For substitutional He the damage production in a cascade decreases. During equilibration at room temperature, the He interstitials cluster together. The interstitials and defect clusters tend to migrate away from Cr atoms. Due to the cascade, the He concentration in the cascade region increases by about 30%, and the Cr concentration in the vicinity of He atoms increases, though remain at about half that of a random solution.

0.4 Acknowledgement

0.3 This work, supported by the European Communities under the contract of Association between Euratom/Tekes, was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

0.2 0.1

1

2

3

r (a0) Fig. 5. The He concentration among metal atoms within distance r of He atoms. CR stands for cascade region and SR for the surrounding region, as defined in the text.

tutional He, and a higher concentration of He, in the cascade region. In Fig. 5, the He atoms per metal atoms fraction around a He atom is shown. Due to the clustering of He, the concentration within the first 1–1.5  a0 is on average almost two orders of magnitude larger than a random solution. For 1.0% He the amount of He close to a He atom in the cascade region is significantly increased compared to the surrounding region, while this effect is not seen at lower He concentrations, mainly due to fewer He-vacancy clusters as there is less damage in the FeCr matrix. Starting with substitutional instead of interstitial He in FeCr reduces the amount of damage caused by the cascade. For 5 keV cascades the Frenkel pairs are 11.6 ± 1.3 for 0.1% He and 2.1 ± 0.4 for 1.0%, significantly lower than 15.3 ± 0.6 for pure FeCr. This is easily understood, as some of the substitutional He will become interstitial during the cascade, leading to a higher concentration of vacancies for the Fe and Cr interstitials to recombine with. As interstitial He leads to an increase of cascade damage and formation of substitutional He in the cascade region, and on the other hand substitutional He reduces the damage, cumulative cascades can be expected to reach an equilibrium. 4. Conclusions We have studied the effect of He defects in Fe90 Cr10 on the damage formed due to collision cascades. For up to 5 keV cascades, less than about 0.5% He has little impact on the damage production, while a higher concentration significantly increases the total number of Frenkel pairs. This is increase is about fourfold for 1% He in a 5 keV cascade. This is explained by formation of substitutional He reducing the recombination. In comparison with cascade damage in Fe with He defects [18], we see an even higher increase in FeCr. The methods used, however, are not identical and further studies will be needed to determine the exact nature of the differ-

References [1] L. Malerba, D. Terentyev, G. Bonny, A.V. Barashev, C. Björkas, N. Juslin, K. Nordlund, C. Domain, P. Olsson, R. Chakarova, N. Sandberg, J. Wallenius, J. ASTM Int. 4 (6) (2007) 1. [2] L. Malerba, A. Caro, J. Wallenius, J. Nucl. Mater. 382 (2008) 112. [3] R. Klueh, K. Ehrlich, F. Abe, J. Nucl. Mater. 191–194 (2002) 116. [4] B. van der Schaaf, D. Gelles, S. Jitsukawa, A. Kimura, R.L. Klueh, A. Möslang, G.R. Odette, J. Nucl. Mater. 283–287 (2000) 52. [5] R. Schäublin, J. Henry, Y. Dai, C.R. Physique 9 (2008) 389. [6] H. Ullmaier, Atomic Defects in Metals, Landolt-Börnstein, New Series III, Vol. 25, Springer, 1991. [7] T. Yamamoto, G.R. Odette, H. Kishimoto, J.-W. Rensman, P. Miao, J. Nucl. Mater. 256 (2006) 27. [8] S. Dudarev, J.-L. Boutard, R. Lässer, M. Caturla, P.M. Derlet, M. Fivel, C.-C. Fu, M. Lavrentiev, L. Malerba, M. Mrovec, D. Nguyen-Manh, K. Nordlund, M. Perlado, R. Schäublin, H.V. Swygenhoven, D. Terentyev, J. Wallenius, D. Weygand, F. Willaime, J. Nucl. Mater. 386–388 (2009) 1. [9] P. Olsson, J. Wallenius, C. Domain, K. Nordlund, L. Malerba, Phys. Rev. B 72 (2005) 214119. [10] A. Caro, D.A. Crowson, M. Caro, Phys. Rev. Lett. 95 (2005) 075702. [11] C. Björkas, K. Nordlund, L. Malerba, D. Terentyev, P. Olsson, J. Nucl. Mater. 372 (2008) 312. [12] C. Björkas, K. Nordlund, Nucl. Instr. Meth. Phys. Res. B 259 (2007) 853. [13] K. Vörtler, C. Björkas, D. Terentyev, L. Malerba, K. Nordlund, J. Nucl. Mater. 382 (2008) 24. [14] C. Björkas, K. Nordlund, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 1830. [15] L. Yang, X.T. Zu, H.Y. Xiao, F. Gao, K.Z. Liu, H.L. Heinisch, R.J. Kurtz, S.Z. Yang, Mater. Sci. Eng. A 427 (2006) 343. [16] R. Schäublin, Y.L. Chiu, J. Nucl. Mater 362 (2007) 152. [17] J. Yu, G. Yu, Z. Yao, R. Schäublin, J. Nucl. Mater. 366–370 (2007) 462. [18] G. Lucas, R. Schäublin, J. Phys.: Condens. Matter 20 (2008) 415206. [19] D. Terentyev, N. Juslin, K. Nordlund, N. Sandberg, J. Appl. Phys. 105 (2009) 103509. [20] G.J. Ackland, M.I. Mendelev, D.J. Srolovitz, S. Han, A.V. Barashev, J. Phys.: Condens. Matter 16 (27) (2004) S2629. [21] N. Juslin, K. Nordlund, J. Nucl. Mater. 382 (2–3) (2008) 143. [22] W.D. Wilson, Conference on Fundamental Aspects of Radiation Damage in Metals, USERDA-CONF-751006-P2, Vol. 1025, 1975. [23] T. Seletskaia, Y.N. Osetsky, R.E. Stoller, G.M. Stocks, J. Nucl. Mater. 351 (2006) 109. [24] K. Nordlund, PARCAS computer code, private communication. The main principles of the molecular dynamics algorithms are presented in [26,27]. The adaptive time step and electronic stopping algorithms are the same as in [28]. [25] H.J.C. Berendsen, J.P.M. Postma, W.F. Gunsteren, A.D. Nola, J.R. Haak, J. Chem. Phys. 81 (1984) 3684. [26] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia, J. Tarus, Phys. Rev. B 57 (13) (1998) 7556. [27] M. Ghaly, K. Nordlund, R.S. Averback, Phil. Mag. A 79 (4) (1999) 795. [28] K. Nordlund, Comput. Mater. Sci. 3 (1995) 448.