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HAL Id: hal-00608032 https://hal.archives-ouvertes.fr/hal-00608032 Submitted on 12 Jul 2011 HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. Simulation of cascades in W-He Niklas Juslin, Ville Bernt Christian Jansson, Kai Nordlund To cite this version: Niklas Juslin, Ville Bernt Christian Jansson, Kai Nordlund. Simulation of cascades in W-He. Philo- sophical Magazine, Taylor & Francis, 2010, 90 (26), pp.3581-3589. 10.1080/14786435.2010.492248. hal-00608032

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HAL Id: hal-00608032https://hal.archives-ouvertes.fr/hal-00608032

Submitted on 12 Jul 2011

HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.

Simulation of cascades in W-HeNiklas Juslin, Ville Bernt Christian Jansson, Kai Nordlund

To cite this version:Niklas Juslin, Ville Bernt Christian Jansson, Kai Nordlund. Simulation of cascades in W-He. Philo-sophical Magazine, Taylor & Francis, 2010, 90 (26), pp.3581-3589. �10.1080/14786435.2010.492248�.�hal-00608032�

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Simulation of cascades in W-He

Journal: Philosophical Magazine & Philosophical Magazine Letters

Manuscript ID: TPHM-09-Aug-0380.R1

Journal Selection: Philosophical Magazine

Date Submitted by the Author:

08-Mar-2010

Complete List of Authors: Juslin, Niklas; University of Helsinki, Department of Physics Jansson, Ville; University of Helsinki, Department of Physics Nordlund, Kai; University of Helsinki, Department of Physics

Keywords: tungsten, radiation damage, simulation

Keywords (user supplied): helium, displacement cascade

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Philosophical MagazineVol. 00, No. 00, 00 Month 200x, 1�9

RESEARCH ARTICLE

Simulation of cascades in W�He

N. Juslina,∗, V. Janssona and K. Nordlunda

aHelsinki Institute of Physics and Department of Physics, P.O. Box 43,FIN-00014

University of Helsinki, Finland

(Received 00 Month 200x; �nal version received 00 Month 200x)

∗Corresponding author. Email: niklas.juslin@helsinki.�

ISSN: 1478-6435 print/ISSN 1478-6443 onlinec© 200x Taylor & FrancisDOI: 10.1080/1478643YYxxxxxxxxhttp://www.informaworld.com

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He will be present in fusion reactor wall materials, and its e�ect on radiation damage must betaken into account. The e�ect of helium on displacement cascades in tungsten has been studiedusing molecular dynamics simulations. Three di�erent W�W potentials were compared andfound to di�er especially for the clustering of the vacancies formed in the cascades. Whilethere are di�erences in the amounts of damage depending on the potential, the overall e�ectof He in interstitial positions was to increase the amount of damage, while He in substitutionalpositions reduce it, due to the e�ect He has on the recombination of tungsten interstititals.

Keywords: Tungsten, helium, radiation damage, displacement cascade

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1. Introduction

Tungsten (W) is considered as a prime candidate for the divertor material in futurefusion reactors, such as the ITER test reactor [1, 2], due to its suitable mechanicaland thermal properties and a low sputtering yield. Due to deposition of He from thefusion plasma, as well as energetic neutron radiation induced (n,α)�transmutationreactions [3], tungsten in fusion reactors will contain small amounts of He [4]. Thee�ect of He on material properties, He retention and di�usion [5�7], trapping [8],bubble formation [9, 10], blistering [11], etc. has been studied previously, however,the e�ect on the primary damage formation due to displacement cascades is notknown.Molecular dynamics (MD) simulation is a valuable tool for studying the onset of

primary damage due to displacement cascades. The length and time scales are inthe range of tens of nm and tens of ps, respectively, which is well within reach ofMD calculations, while not easily observed experimentally. Displacement cascadedamage in pure W has been studied previously [12�14]. Several di�erent interatomicpotentials have been used to investigate cascade damage in W [15�18], but theamount and clustering of the formed defects is similar.The e�ect of helium on displacement cascades in iron [19] and iron-chromium [20]

has been studied recently. At the relatively high concentrations of 1 atomic percent(at.�%) interstitial He, a signi�cant increase in damage formation is seen, while adecrease is observed for substitutional He. At 0.1 at.�% He, the e�ect is not sta-tistically signi�cant. As these are body-centered cubic metals like tungsten, similarresults can be expected. There are, however, large di�erences in He, vacancy andself interstitial defect properties and thermal properties between iron and tungsten,which can a�ect primary damage formation.Most of the cascade studies in pure W have been done in the low keV range. As

the e�ect of He can be expected to be more pronounced at higher energies, due tomore total damage, we have compared how He a�ects cascades in tungsten for threeW potentials for 2 keV recoils, which is the highest energy studied in the literaturefor pure W for these potentials. For the potential by Derlet et al.[18], for whichhigher energy recoils have been studied, we also studied 5 keV and 20 keV recoils.Many di�erent interesting initial He positions could be considered, and in a fusion

reactor many factors will determine the He content and micro�structure. In additionone would always �nd deuterium and other defects in a real divertor. While He willbe found in both interstitial or substitutional positions and in particular He bubbleformation is an issue in a real material, in this paper, we focus on all He eitherin interstitial or all He in substitutional positions initially, with a relatively shortequilibriation time, in order to study the basic e�ect of He. The He concentrationsused were 0.1 at.�% and 1.0 at.�%.

2. Methodology

Three W�W interatomic potentials were compared in this work. The Ackland�Thetford (AT) [16], the Juslin et al. (J) [17] and the Derlet et al. (D) [18]. TheAT potential is the improved version of the Finnis�Sinclair potential [15]. For Dthe repulsive part is by Björkas et al. [12]. The AT and D potentials are Finnis-Sinclair type potentials, which are similar to the embedded atom method, and theJ potential is a bond order potential of Terso� type. The potentials have all beendeveloped with di�erent applications in mind, yet perform relatively similarly forlow keV cascades in pure W (see Tables 3 and 5).For W�He, the potential developed by Henriksson [11] was used. It was devel-

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oped to describe He interstitials and bubbles in W for the AT potential, but canbe expected to perform similarly for other potentials that describe W well. Sinceits development, recent ab initio results [8, 21] indicate that it overestimates theformation energy of interstitials and the ground state position depends on the Wpotential used, (see Table 2). There is also an old W�He potential from 1972 byWilson [22] which underestimates the formation energy and gives a ground stateposition that does not agree with density functional theory (DFT) calculations. ForHe�He, the Beck potential [23] was used.The simulations were performed with the MD code PARCAS [24]. The simulation

cells were constructed as a BCC lattice of W atoms with He atoms randomlydistributed in either octahedral interstitial or substitutional positions. Cells with0.1 at.�% or 1.0 at.�% He were used. The simulation cells were at �rst relaxed for25 ps at zero pressure and 300 K, after which an atom near the center was givena recoil energy of 2 keV, 5 keV or 20 keV in a random direction. The temperaturedependence was not investigated in this work, but can be expected to be similarto that found in iron�helium by Lucas and Schäublin [19], where the e�ect of Heis more pronounced with increasing temperature. The temperature was controlledusing the Berendsen method [25]. A variable time step, periodic boundaries in allthree dimensions and electronic stopping were used. Temperature scaling with aconstant of 100 fs was applied in the cell's border regions, which have a thickness ofone lattice parameter. The simulation was stopped if the kinetic energy of a borderatom was larger than 10 eV and restarted with the recoil atom placed farther awayfrom the border. In the simulation of a 2 keV recoil in a cell with 0.1 % He, aborder energy threshold of 15 eV was used , as energies around 10 eV were observedat the beginning of the initial equilibration. While only an issue for the �rst fewtimesteps, the threshold was unchanged when the recoil was introduced. During therecoil and cooling down of the cascade, the energies of border atoms were below the10 eV threshold as in the other cases. Information about the amount of He in thesimulation cells, the simulation time and the size for the simulation cells for eachrecoil energy and potential, is given in Table 1.The simulations were analyzed using Wigner�Seitz cells in order to �nd defects

in the atom lattices. Thus, a cell without a W atom corresponded to a vacancy,while cells with more than one W atom were de�ned as self interstitials. A vacancyand self interstitial clustered fraction were calculated. The vacancy cluster analysisused the second nearest neighbor distance as cuto� radius, while the third nearestneighbor distance was used for interstitials, in order to be comparable with earlierwork on pure W [12, 13].

3. Results and Discussion

During the 25 ps equilibration before the recoil is introduced, the He atoms migrateand some cluster together. The amount of clustering is, however, limited, as the Heatoms cannot easily displace a W atom from its lattice point due to the high for-mation energy of a W Frenkel pair, creating space for He bubbles (as opposed to Feand FeCr where this occurs [20]). For 1% He inititially in interstitial positions, 1�3He generally occupy the same Wigner�Seitz cell as a W atom. Clusters spread overseveral Wigner�Seitz cells also form, but the sizes are still limited to less than 10He atoms. For substitutional He, some of the He migrated from the vacancy theyinitially occupied, and ended up as interstitial He or often getting trapped by othersubstitutional He, forming He�vacancy clusters containing a small number of Heatoms. The amount of He clustering is, however, much smaller starting from substi-tutional He than from interstitial He, as the subsitutional He atoms are relatively

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stable on this time scale.We compared the formation energies of an interstitial and a substitutional He

with the di�erent potentials (Table 2). The ground state formation energy of theHe interstitial is relatively high compared to density functional theory (DFT) re-sults, and within 1 eV for all potentials. The di�erence in formation energy betweenthe octahedral and the tetrahedral interstitial is small, except for the AT potentialwhere the tetrahedral position is unstable. Only the D potential gives the groundstate position as tetrahedral as predicted by DFT, though signi�cantly more un-stable. The formation energy of the substitutional position is about 6.2 eV for ATand D and 4.2 eV for the J potential, which is due to the low formation energy ofthe vacancy for that potential [17]. Compared to DFT results, the formation energyof the substitutional interstitial is closest for the J potential results, the di�erencein energy between interstitial and substitutional is best with the AT potential andthe ground state position of the interstitial is correct only for the D potential. Thusthe basic defect properties do not show that one potential would be superior to theothers for studying He in W.The three di�erent W�W potentials were compared for 2 keV cascades with 1%

He. This energy was chosen, as it is the highest energy for which results for pure Wexist for all the potentials [12, 13]. A higher energy means more damage and thusa more discernable di�erence between the potentials due to the e�ect of He on thedamage.As can be seen in Table 3, in the case of 1.0% He initially in interstitial positions,

all three potentials agree that there is more total damage in the W matrix, givenby the number of Frenkel pairs formed due to the cascade. This can be understoodby the binding of He to vacancies and W interstitials, reducing the mobility of theinterstitials and making it less energetically favorable for W interstitials to recom-bine with the vacancies, as He atoms go into vacancies and a kick�out mechansimis needed to recombine. From the time the heat spike recrystallizes, almost all re-maining vacancies are �lled with one or more He. Lucas and Schäublin explain thesimilar e�ect seen in Fe by He strongly binding to and stabilizing intersterstitialclusters [19], but as discussed in the following paragraph, in tungsten�helium theclustering of self interstitial atoms (SIA) is close to that in pure W. In FeCr, wherethe clustering of self interstitial atoms is increased as in Fe, a fast binding of Heto vacancies formed in the cascade was also observed [20]. In all these materialsthe e�ect of He on the recombination mechanism seems to be governed by bind-ing of He to all defects in the metal matrix, though the binding to and stablizingof SIA clusters is di�erent in Fe and W. It should, however, be noted that thecooling down and recombination of a heat spike is a complicated combination ofseveral processes over a large temperature scale. With the J potential, the e�ect isconsiderably higher than for the others potentials. This is due to the stability ofthe substitutional, which means that the He atoms are more prone to bind to thevacancies.An interesting di�erence between the potentials appears in the clustering of va-

cancies and self interstitials in the W matrix for 2 keV cascades. For pure W, theclustering is similar for the potentials, 20�30% for all cases as shown in Table 5.With 1.0% He, the amount of vacancy clustering for the AT and the J potentialsis reduced to about 4% and 7% respectively, while it remains the same for D. Theinterstitial clustering is almost the same as for pure W, though slightly reduced.This di�erence in vacancy clustering between the potentials is not easily explainedby the W�W potentials or the behavior of single He defects, and analyzing howthe He atoms a�ect the clustering during the cooling down of the heat spike is nottrivial. Thus it is di�cult to estimate which potential describes the clustering best.

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For substitutional He, the number of Frenkel pairs decreases for 1% He (Table4). As the heat spike cools down, all the He atoms will not recombine with avacancy to form substitutional He and thus there are more vacancies for the Watoms to recombine with. This reduces the overall amount of Frenkel pairs formedin the cascade. For the AT potential almost all damage recombines. For 0.1% He,the e�ect is much smaller. For the D potential the results are within the statisticalerror of pure W and for the J potential the number of Frenkel pairs is even increasedto a similar value as that for 0.1% interstitial He, though in this case the result forpure W appears to be quite low.For the D potential, the behavior at higher recoil energies was studied. As ex-

pected, the number of Frenkel pairs increases with the recoil energy for 1% intersti-tial He initially. The slope in a log plot remains almost the same as for pure W (Fig.1) and the number of Frenkel pairs is signi�cantly higher than in pure W, especiallyat higher energies. The clustering of vacancies (Fig. 2) and self interstitials (Fig. 3)is close to that in pure W for the recoil energies studied. For 1% substitutional He,we note that the number of Frenkel pairs for 5 keV cascades is reduced to almostthe same amount as for 2 keV cascades, 2.0 and 1.5 respectively.Generally the e�ect of He concentration is that the more He in the system, the

larger the di�erence compared to pure W is. Both for interstitial and substitutionalHe, the results are close to those in pure W for 0.1% He and signi�cantly di�erentfor 1.0% He. There is a rather surprising exception to this. The number of Frenkelpairs for the 5 keV cascade with 0.1% interstitial He is the same as with 1% Hedown to two decimals of accuracy. The interstitial clustering, on the other hand, ismuch lower in this case than for both 1% and 0% He. The recombination results in amore spread out interstitial con�guration for the 0.1% case, though the mechanismbehind this is unclear. It can be noted that for pure W [12] the amount of Frenkelpairs is also quite high for 5 keV cascades, almost as high as for 10 keV, with anapparent change in the recoil energy dependance between a low and a high energyregion. This indicates that there could be a change in the recombination mechanismsat about 5 keV for the D potential. This is an interesting venue for future studies,both for the pure material and for the e�ect of He concentration.While the composition and structure of a real divertor material is more compli-

cated, with He bubbles, other impurity atoms, surfaces and grain boundaries, themechanisms of how He a�ects the recombination in W for this simplistic view ofinitially interstitial or substitutional He can be expected to exist in a real material.As the He concentrations approach 1 at.�%, the e�ect on cascades in a real materialis likely to be appreciable, as the e�ect is dramatic for both cases studied here, Heinitially in interstitial and in substitutional positions.

4. Conclusions

We have simulated the e�ect of helium on the primary damage formed in displace-ment cascades in tungsten. Three W�W potentials have been compared and whilethere are di�erences, it is not clear which potential describes He in W best. Thepresent He�W potential overestimates the formation energy of He interstitials forall the W�W potentials, in comparison with DFT data from the literature. TheW�W potentials especially di�er when looking at the clustering of vacancies froma cascade with He present, with large di�erences compared to the results for pureW, where it is relatively similar.All potentials predict that the overall e�ect of He is that He in initially interstitial

position increases the number of Frenkel pairs in the W matrix and substitutionalHe reduces it. Especially at higher He concentrations and recoil energies the e�ect

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is signi�cant. The increase due to interstitial He is explained by He entering thevacancies produced as the heat spike cools down, reducing the recombination oftungsten interstitials. For substitutional He, the opposite takes place, as some Hebecome interstitial or cluster with other He, thus leaving more vacancies for the Winterstitials to recombine with.

References

[1] ITER Physics Basis Editors, ITER Physics Expert Group Chairs and Co-Chairs and ITER JointCentral Team and Physics Integration Unit, Nuclear Fusion 39 (1999) p.2137�2638.

[2] Progress in the ITER Physics Basis editors, Nuclear Fusion 47 (2007) p.1�413.[3] C.H.M. Broeders and A.Y. Konobeyev, Nucl. Instr. Meth. Phys. Res. B 234 (2005) p.387.[4] Q. Xu, N. Yoshida and T. Yoshiie, J. Nucl. Mater. 357-370 (2007) p.806.[5] S.B. Gilliam, S.M. Gidcumb, D. Forsythe, N.R. Parikh, J.D. Hunn, L.L. Snead and G.P. Lamaze,

Nucl. Instr. Meth. Phys. Res. B 241 (2005) p.491.[6] A. Wagner and D. Seidman, Phys. Rev. Lett. 42 (1979) p.515.[7] J. Amano and D. Seidman, J. Appl. Phys. 56 (1984) p.983.[8] S.C. Lee, J.H. Choi and J.G. Lee, J. Nucl. Mater. 383 (2009) p.244.[9] K.O.E. Henriksson, K. Nordlund and J. Keinonen, Nucl. Instr. Meth. Phys. Res. B. 244 (2005) p.377�

391.[10] K.O.E. Henriksson, K. Nordlund, A. Krasheninnikov and J. Keinonen, Appl. Phys. Lett. 87 (2005)

p.163113.[11] K.O.E. Henriksson, K. Nordlund, J. Keinonen, D. Sundholm and M. Patzschke, Physica Scripta T108

(2004) p.95.[12] C. Björkas, K. Nordlund and S. Dudarev, Nucl. Instr. Meth. Phys. Res. B 267 (2008) p. 3204.[13] K. Vörtler, private communications. To be published.[14] J. Fikar and R. Schäublin, J. Nucl. Mater. 386-388 (2009) p.97.[15] M.W. Finnis and J.E. Sinclair, Phil. Mag. A 50 (1984) p.45 see also Erratum, ibid. 53 (1986) 161.[16] G.J. Ackland and R. Thetford, Phil. Mag. A 56 (1987) p.15.[17] N. Juslin, P. Erhart, P. Träskelin, J. Nord, K.O.E. Henriksson, K. Nordlund, E. Salonen and K. Albe,

J. Appl. Phys. 98 (2005) p.123520.[18] P.M. Derlet, D. Nguyen-Manh and S.L. Dudarev, Phys. Rev. B 76 (2007) p.054107.[19] G. Lucas and R. Schäublin, J. Phys. Condens. Mat. 20(2008) p. 415206.[20] N. Juslin and K. Nordlund, Nucl. Instr. Meth. Phys. Res. B 267 (2009) p. 3420.[21] C.S. Becquart and C. Domain, Nucl. Instr. Meth. Phys. Res. B 255 (2007) p.23.[22] W.D. Wilson, R.A. Johnson, in: P.C. Gehlen, J.R. Beeler, R.I. Ja�ee (Eds.), Interatomic Potentials

and Simulation of Lattice Defects, Plenum, New York, 1972, p. 375.[23] D.E. Beck, Mol. Phys. 14 (1968) p.311.[24] K. Nordlund parcas computer code. 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. Gunsterenvan , A. DiNola and J.R. Haak, J. Chem. Phys.81 (1984) p.3684.

[26] K. Nordlund, M. Ghaly, R.S. Averback, M. Caturla, T. Diaz de la Rubia and J. Tarus, Phys. Rev. B57 (1998) p.7556.

[27] M. Ghaly, K. Nordlund and R.S. Averback, Phil. Mag. A 79 (1999) p.795.[28] K. Nordlund, Comput. Mater. Sci. 3 (1995) p.448.

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Table 1. The simulations performed with interstitial He. For substitutional He, the same simulations were per-

formed for 2 and 5 keV, with 59582 and 148176 atoms respectively.

Recoil energy % He Number of events Time Box size No. of atoms[keV] D J AT [ps] ×a0

2 0.1 100 100 100 50 31 596412 1.0 100 100 100 50 31 601835 0.1 100 - - 50 42 1483245 1.0 100 - - 50 42 14967220 1.0 10 - - 50 67 607602

Table 2. The interstitial and substitutional formation energies for He in W for the di�erent potentials and DFT.

Formation energies are given in eV. The tetrahedral interstitial is unstable with the AT potential.

AT D J DFT[8, 21]Tetrahedral - 8.8 8.3 6.2Octahedral 7.8 9.0 8.2 6.4�6.5

Substitutional 6.3 6.2 4.2 4.7�5.0

Table 3. The number of Frenkel pairs with He initially in interstitial positions. The results for pure W are, for

the D potential from Ref. [12] and for the AT and J potentials from Ref. [13].

2 keV Pure 0.1% He 1.0% HeAT 2.6±0.1 3.4±0.1 4.1±0.1D 3.6±0.3 4.2±0.1 6.1±0.2J 2.8±0.1 3.8±0.1 10.3±0.2

5 keVD 7.5±0.7 11.8±0.2 11.8±0.2

20 keVD 17.9±1.1 - 44.7±1.7

Table 4. The number of Frenkel pairs with He initially in substitutional positions. The results for pure W are,

for the D potential from Ref. [12] and for the AT and J potentials from Ref. [13].

2 keV Pure 0.1% He 1.0% HeAT 2.6±0.1 1.8±0.1 0.3±0.05D 3.6±0.3 3.5±0.2 1.5±0.1J 2.8±0.1 3.6±0.1 1.7±0.1

5 keVD 7.5±0.7 7.8±0.2 2.0±0.1

Table 5. The fraction of vacancies (V) and self interstitials (SI) that are in clusters, as described in the text, for

2 keV cascades. The results for pure W are, for the D potential from Ref. [12] and for the AT and J potentials

from Ref. [13].

AT D JPure 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±0.01SI 0.24±0.04 0.21±0.03 0.31±0.07 0.29±0.03 0.24±0.04 0.20±0.01

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Figure captions

Fig. 1: The number of Frenkel pairs formed for di�erent recoil energies andHe contents using the D potential. The results for pure W are from Ref. [12].The error bars for for the results in this work are of the size, or smaller, thanthe markers, and have been left out for clarity. The errors are given in Tables 3 and 4.

Fig. 2: The clustered fraction, in %, of vacancies in the W matrix for the Dpotential. A vacancy belongs to a cluster if it is within second nearest neighbordistance of another vacancy. The results for pure W are from Ref. [12].

Fig. 3: Self interstitial clustered fraction, in %, for the D potential. An in-terstitial belongs to a cluster if it is within third nearest neighbor distance ofanother interstitial. The results for pure W are from Ref. [12].

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