- Email: [email protected]
Atomistic studies of nucleation of He clusters and bubbles in bcc iron
Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Atomistic studies of nucleation of He clusters and bubbles in bcc iron L. Yang a,b, H.Q. Deng c, F. Gao a,⇑, H.L. Heinisch a, R.J. Kurtz a, S.Y. Hu a, Y.L. Li a, X.T. Zu b a
Pacific Northwest National Laboratory, MS K8-93, P.O. Box 999, Richland, WA 99352, USA Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, China c Department of Applied Physics, Hunan University, Changsha 410082, China b
a r t i c l e
i n f o
Article history: Received 13 July 2012 Received in revised form 29 October 2012 Accepted 26 November 2012 Available online 28 December 2012 Keywords: Molecular dynamics He bubble Self-interstitial loop Bcc iron
a b s t r a c t Atomistic simulations of the nucleation of He clusters and bubbles in bcc iron at 800 K have been carried out using the newly developed Fe–Fe interatomic potential, along with Ackland potential for the Fe–Fe interactions. Microstructure changes were analyzed in detail. We found that a He cluster with four He atoms is able to push out an iron interstitial from the cluster, creating a Frenkel pair. Small He clusters and self-interstitial atom (SIA) can migrate in the matrix, but He-vacancy (He-V) clusters are immobile. Most SIAs form <111> clusters, and only the dislocation loops with a Burgers vector of b = 1/2 <111> appear in the simulations. SIA clusters (or loops) are attached to He-V clusters for He implantation up to 1372 appm, while the He-V cluster–loop complexes with more than one He-V cluster are formed at the He concentration of 2057 appm and larger. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction In a fusion reactor environment helium (He) is produced at high rates in steels by nuclear (n, a) transmutation reactions. Because of the extremely low solubility of He in metals, He atoms tend to be deeply trapped in small vacancy clusters and microstructural features, leading to the creation of He-stabilized bubbles, which can significantly degrade the mechanical properties of materials. Therefore, understanding of the nucleation of He bubbles in steels, both in the bulk and within microstructural features, is of fundamental importance to the development of fusion reactors. Multiscale modeling, especially including the atomic scale, provides a basis to obtain insight into and general understanding of the complex radiation damage process. Particularly, molecular dynamics (MD) methods have been widely employed to study the atomic-level processes of defects controlling microstructural evolution in advanced ferritic steels. The behavior of He in Fe has been widely investigated [1–15]. MD simulations have been employed to yield important understanding of the behavior of He defects in bcc Fe using different interatomic potentials [2–4]. Recently, Stewart et al. investigated the formation and diffusion of He clusters and bubbles in bcc iron using a three-body Fe-He interatomic potential [2]. Gao et al. [14] developed a new interatomic potential for Fe–He interactions, which is based on the electronic hybridization between Fe d-electrons and He s-electrons. The diffusion properties of He interstitials
⇑ Corresponding author. Tel.: +1 509 371 6490; fax: +1 509 371 6242. E-mail addresses: [email protected], [email protected] (F. Gao). 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.11.025
and interstitial He clusters in the bulk of bcc Fe have been studied using MD with this newly developed Fe–He potential [15]. The low migration energy barrier for a single He interstitial in the bulk is consistent with that obtained using ab initio methods. It was also found that small He clusters can migrate at low temperatures, but at higher temperatures they can kick out a SIA and become trapped by the resulting vacancy, forming He-vacancy clusters. Also, the binding energies of small He-V and He–He clusters are in good agreement with those obtained by ab initio and other potential calculations. In the present study we investigate the nucleation of He clusters and bubbles, the emission of SIAs from the He clusters, and the formation of dislocation loops in the bulk of bcc Fe, as well as the effects of these phenomena on the microstructural changes.
2. Simulation procedure In the present simulations a modified version of the MOLDY computer code [16] is used. The interatomic potentials of Ackland [17] and Beck [18] are used to describe the Fe–Fe and He–He interactions respectively, while the Fe He interaction is described by the newly developed Fe He potential [14]. The NVT ensemble [15] is used in the simulations, and periodic boundary conditions are applied along all three axes to avoid the influence of free surfaces. A MD box of 45a0 45a0 45a0 with 182,250 Fe atoms is used, where a0 is the lattice constant of perfect bcc iron (2.8553 Å). Initially 125 He atoms are randomly distributed in the box, which corresponds to a mean He concentration of 685 appm. Then, the box is quenched to 0 K for 10,000 time
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
steps, followed by a temperature rescaling to 800 K and annealing at 800 K for 1.2 ns, where there is no significant migrations or jumps of atoms that affect the size and distribution of He clusters. After the equilibrium state has been achieved, an additional125 He atoms are randomly inserted into the system, which gives a total of 250 He atoms. The same quenching and annealing approach is used, but the annealing time is about 0.6 ns, which is long enough for the system to reach its equilibrium state (i.e. the defect configurations remain without obvious changes). The same approach is repeated until a total of 500 He atoms have been added, i.e. the mean He concentration is 2743 appm, which is lower than the maximum He concentration of 3000 appm used in experiments [19]. It should be noted that helium atoms are gradually added from low to high concentrations, and thus, the nucleation mechanism and growth of helium clusters (bubbles) can be explored, at least at the early stage of nucleation. The highest concentration mimics the experimental condition, which will allow us to study up-limit effects on the nucleation of He clusters. After annealing at 800 K, the system is then quenched to 0 K for further analysis in terms of defect configurations, He bubble distributions and dislocation loop orientation. 3. Results and discussion 3.1. 125 He atoms (685 appm He) The initial 125 He atoms are randomly distributed in the simulation box as single interstitials, either in tetrahedral or octahedral positions. These single He interstitials can easily migrate at 800 K because of their low migration energy barrier of 0.058 eV [14]. It is of interest to note that two He atoms can join together, forming a He dimer (He2), but it sometimes dissociates into two single He interstitials because of its small binding energy (0.3 eV with the present potential). Also, a He2 cluster migrates easily in the Fe matrix because of its low migration energy of 0.09 eV and the emission of a self-interstitial from the He2 cluster is not observed. Once a He atom migrates into a He2 cluster, a He3 cluster is formed. Similarly, the He3 cluster can easily migrate with the migration energy of 0.097 eV [15], but He dissociation from the He3 cluster does not occur due to its slightly higher binding energy [14]. Although a Fe atom can be displaced from its site, temporarily forming a He3VFe complex, the emission of a self-interstitial does not occur, as shown in Fig. 1. The structure of the He3VFe complex appears at 0.27 ns, but during the annealing process, this complex structure transfers to a He3 cluster because of the recombining of the Fe
69
atom and the vacancy. It is also noted that the He3 cluster can fast migrate, which is clearly shown in Fig. 1, where interstitials and vacancies were identified and counted using a displacement analysis method [20]. When the He cluster reaches four He atoms, an Fe atom can be kicked out, forming a He-vacancy (He4V) cluster and a SIA, as shown in Fig. 2. It is of interest to find that the He atoms in the cluster rotate quickly around the vacancy, but the centre of mass of the He4V cluster does not change with time. This suggests that the helium atoms in the cluster still strongly bond with the vacancy, forming a stable configuration at 800 K. The emitted SIA forms a dumbbell with another Fe atom, and attaches to the He4V cluster. With increasing simulation time, some of the SIAs are able to escape from their original He-vacancy clusters, and join with other SIAs, forming SIA clusters attached to He-vacancy clusters. A few He4 clusters are observed to share one lattice vacancy with an attached Fe atom, forming He4VFe at 800 K, which is similar to the configuration of He3VFe. Thus, a cluster of four or more He atoms can emit a SIA, forming a Frenkel pair at 800 K. This is different from Stewart’s results [2] in which it is demonstrated that Frenkel pair creation happens in clusters with six or more He at 800 K. After annealing 1.2 ns, most He atoms become part of He-V defects. The He and defect distributions at 1.2 ns for the case of 125 He atoms are shown in Fig. 3, from which it is clearly shown that almost all the SIA clusters are attached to He clusters, and most SIA clusters are made up of <111> crowdions and split dumbbells. Some SIA clusters consist of <111> crowdions and <110> split dumbbells, while some form the mixture configurations of many Fe3V, one of which is shown in the inset in Fig. 3(a). The formation of the mixture configurations of many Fe3V may be due to the fact that the pressure of its nearest He cluster is not enough to push SIAs away to form <111> crowdions. The size distribution of He and SIA clusters is shown in Fig. 3(b). The largest He cluster includes 12 He atoms, while the largest SIA cluster contains only 7 SIAs. Both the size distributions of He and SIA clusters exhibit almost uniform distributions. 3.2. 250 He atoms (1372 appm He) After randomly inserting the second 125 He atoms in the simulation box, corresponding to the mean He concentration of 1372 appm, the system is quenched to 0 K and annealed at 800 K. The distributions and configurations of the He-V and SIA clusters, as well as point defects, after 0.2 ns and 0.6 ns are shown in Figs. 4(a) and (b), respectively. It is found that the centers of the He-V clusters remain the same, while single He atoms and SIAs can migrate in the matrix. Since some He clusters already existed in the simulation box, the inserted He atoms can join the existing He-V
0.33 ns
0.27 ns
Fig. 1. Structure change of the He3VFe complex, where the red circle indicates the He3VFe complex at 0.27 ns. This configuration transfers to a He3 cluster by the recombination of the SIA and the vacancy at 0.33 ns, indicated in the black circle. Green, black and magenta spheres represent vacancies, SIAs and He atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Structure of a He4V cluster and a SIA, where the representations of spheres are the same as those in Fig. 1.
70
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
Fig. 3. (a) He and defect distributions for the case of 125 He atoms and (b) size distribution of He-V clusters and SIA clusters after annealing for 1.2 ns, where the representations of spheres are the same as those in Fig. 1. The inset in (a) is the detailed arrangements of a He-SIA cluster.
Fig. 4. He and defect distributions after inserting 250 He at 0.2 ns (a) and at 0.6 ns (b), and size distribution of He-V and SIA clusters at 0.6 ns (c). The inset in (b) is the detailed arrangements of a He cluster–SIA loop complex.
cluster, leading to the formation of larger He clusters, and more SIAs are emitted from the clusters. However, all the SIA clusters are also attached to He clusters, but the size of the SIA clusters becomes larger, as compared with the clusters of the He concentration of 685 appm. Most SIA clusters orient along the <111> direction, forming <111> crowdions, and some of the larger SIA clusters can be identified as ½ <111> loops, as shown in the inset in Fig. 4(b). The size distributions of the He-V and SIA clusters after annealing for 0.6 ns are shown in Fig. 4(c). The number of He atoms in the largest He cluster increases up to 20, while the largest SIA cluster contains only 10 SIAs. The size distribution of He clusters is slightly different from that at the He concentration of 685 appm. It is clear that a large number of small He-V clusters are formed at the He concentration of 1372 appm although the size of He-V clusters increases. This may be attributed to the immobility of He-V clusters. Once a He-V cluster is formed, it cannot easily migrate to combine with other He-V clusters, and form a larger cluster. The He-V cluster can grow into a larger cluster only by absorbing single He atoms and small He clusters. 3.3. 375 and 500 He atoms (2058 and 2743 appm He) After annealing 0.6 ns at 1372 appm He concentration, an additional 125 He atoms were randomly inserted into the system, which corresponds to a He concentration of 2058 appm. Some existing He-V clusters grow into larger clusters by absorbing more He atoms and emitting more SIAs, but more small He clusters also appear due to the coalescence of several He atoms. The He and defect distributions at 0.6 ns are shown in Fig. 5(a). Compared to Fig. 4(b), the He and SIA clusters grow into larger clusters, and it is of interest to note that three He-V cluster-SIA loop complexes are formed, which are indicated using the black circles in Fig. 5(a). These complexes with more than one He-V cluster are formed by the evolution of small He clusters and the movement
of the SIAs. He bubble-loop complexes were also found in the experiments by Chen et al. [19], who indicated that most bubbles are attached to dislocations, forming bubble-loop complexes at 673 K in ferritic steel after He implantation. In the present simulations, the structures of the complexes are similar to those found in experiments, even though the size of the complexes is smaller than the experimental results. The size distribution of He-V and SIA clusters after inserting 375 He at 0.6 ns is shown in Fig. 5(b). The size of these He clusters is evidently larger than those formed at the He concentration of 1372 appm. The largest He cluster at 2058 appm includes 30 He atoms, as compared to 20 He atoms at the He concentration of 1372 appm, while the largest SIA cluster contains 15 SIAs. After adding an additional 125 He atoms, the He concentration increases up to 2743 appm. The microstructure is similar to that at the He concentration of 2058 appm, as shown in Fig. 5(c). As compared to Fig. 5(a), it is clear that more He cluster-SIA loop complexes are formed, which are indicated by the black circles in Fig. 5(c). However, it should be noted that these loops are formed by the collection of the SIAs at the peripheries of the He-V clusters, and attached to the He-V clusters. The formation and emission of dislocation loops are in contrast to the traditional theory proposed by Trinkaus and Wolfer [21]. From the size distribution of He-V and SIA clusters at 0.6 ns shown in Fig. 5(d), it can be found that the size and number of He bubbles (the number of He atoms in the bubbles is larger than 20) are generally close to those at the He concentration of 2058 appm. More middle and small He clusters (the number of He atoms is less than 20) are formed with increasing He concentration. However, the emission of dislocation loops is not observed, which may be due to the fact that the size of He clusters is too small and the pressure is not large enough to punch the dislocations out from the clusters. The periodical boundary condition may also have effect on the emission of dislocations.
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
71
Fig. 5. (a) He and defect distributions and (b) size distribution of He-V and SIA clusters after inserting 375 He at 0.6 ns. (c) He and defect distributions and (d) size distribution of He-V and SIA clusters after inserting 500 He at 0.6 ns.
4. Conclusion The nucleation and growth of He clusters and bubbles in bcc Fe have been investigated using MD simulations with our newly developed Fe-He interatomic potential. Groups of 125 He atoms are additively inserted into the simulation system in four cycles, and the simulations are carried out at 800 K. The high mobility of He atoms leads to the formation of interstitial He clusters. A He cluster containing four or more He atoms is large enough to emit an Fe interstitial, creating a Frenkel pair. The emitted SIA can easily migrate away from the He-V cluster, while the He-V cluster becomes immobile. As He atoms continue to be inserted, more He atoms join the He-V cluster, and more SIAs can be created, leading to the formation of large SIA clusters or dislocation loops. Most SIAs in the clusters form <111> crowdions, and larger SIA clusters have been identified to be dislocation loops with a Burgers vector of b = 1/2 <111>. It is of interest to note that SIA clusters or loops are attached to the He clusters at the He concentration up to 1372 appm, while some He-V cluster–loop complexes are formed at the higher He concentration. These results are in good agreement with experimental observations. The formation mechanism of the He clusters (or bubbles), SIA clusters (or loops) and the He cluster-loop complexes are investigated in detail. Acknowledgements F. Gao, S.Y. Hu, Y.L. Li, R.J. Kurtz and H.L. Heinisch are grateful for support by the US Department of Energy/Office of Fusion Energy Science under Contract DE-AC06-76RLO 1830. L.Yang and
X.T. Zu are grateful for the support by the National Natural Science Foundation of China – NSAF (Grant no.: 10976007). References [1] G. Ackland, Science 327 (1587) (2010) 1587. [2] D. Stewart, Y. Osetskiy, R. Stoller, J. Nucl. Mater. 417 (2011) 1110. [3] N. Gao, H. Van Swygenhoven, M. Victorian, J. Chen, J. Phys. Condens. Matter 23 (2011) 442201. [4] Z.F. Di, X.M. Bai, Q.M. Wei, J.H. Won, R.G. Hoagland, Y.Q. Wang, A. Misra, B.P. Uberuaga, M. Nastasi, Phys. Rev. B 84 (2011) 052101. [5] G. Lucas, R. Schaublin, J. Nucl. Mater. 386–388 (2009) 360. [6] T. Seletskaia, Y. Osetsky, R.E. Stoller, G.M. Stocks, Phys. Rev. Lett. 94 (2005) 046403. [7] C.C. Fu, F. Willaime, Phys. Rev. B 72 (2005) 064117. [8] L. Yang, X.T. Zu, H.Y. Xiao, F. Gao, H.L. Heinisch, R.J. Kurtz, K.Z. Liu, Appl. Phys. Lett. 88 (2006) 091915. [9] Steven J. Zinkle, Phys. Plasmas 12 (2005) 058101. [10] A. Van Veen, R.J.M. Konings, A.V. Fedorov, J. Nucl. Mater. 320 (2003) 77. [11] E.H. Lee, J.D. Hunn, T.S. Byun, L.K. Mansur, J. Nucl. Mater. 280 (2000) 18. [12] J.D. Hunn, E.H. Lee, T.S. Byun, L.K. Mansur, J. Nucl. Mater. 282 (2000) 131. [13] J. Henry, M.H. Mathon, P. Jung, J. Nucl. Mater. 318 (2003) 249. [14] F. Gao, H.Q. Deng, H.L. Heinisch, R.J. Kurtz, J. Nucl. Mater. 418 (2011) 115. [15] H.Q. Deng, W.Y. Hu, F. Gao, H.L. Heinisch, S.Y. Hu, Y.L. Li, R.J. Kurtz, to be published in J. Nucl. Mater. [16] F. Gao, D.J. Bacon, P.E.J. Flewitt, T.A. Lewis, J. Nucl. Mater. 249 (1997) 77. [17] G.J. Ackland, M.I. Mendelev, D.J. Srlolovitz, S. Han, A.V. Barashev, J. Phys. Condens. Matter 16 (2004) s2629. [18] R.A. Aziz, A.R. Janzen, M.R. Moldover, Phys. Rev. Lett. 74 (1995) 1586. [19] J. Chen, P. Jung, W. Hoffelner, H. Ullmaier, Acta Mater. 56 (2008) 250. [20] L. Yang, X.T. Zu, Z.G. Wang, H.T. Yang, F. Gao, H.L. Heinisch, R.J. Kurtz, J. Appl. Phys. 103 (2008) 063528. [21] H. Trinkaus, W.G. Wolfer, J. Nucl. Mater. 552 (1984) 122–123.
Contents lists available at SciVerse ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Atomistic studies of nucleation of He clusters and bubbles in bcc iron L. Yang a,b, H.Q. Deng c, F. Gao a,⇑, H.L. Heinisch a, R.J. Kurtz a, S.Y. Hu a, Y.L. Li a, X.T. Zu b a
Pacific Northwest National Laboratory, MS K8-93, P.O. Box 999, Richland, WA 99352, USA Department of Applied Physics, University of Electronic Science and Technology of China, Chengdu 610054, China c Department of Applied Physics, Hunan University, Changsha 410082, China b
a r t i c l e
i n f o
Article history: Received 13 July 2012 Received in revised form 29 October 2012 Accepted 26 November 2012 Available online 28 December 2012 Keywords: Molecular dynamics He bubble Self-interstitial loop Bcc iron
a b s t r a c t Atomistic simulations of the nucleation of He clusters and bubbles in bcc iron at 800 K have been carried out using the newly developed Fe–Fe interatomic potential, along with Ackland potential for the Fe–Fe interactions. Microstructure changes were analyzed in detail. We found that a He cluster with four He atoms is able to push out an iron interstitial from the cluster, creating a Frenkel pair. Small He clusters and self-interstitial atom (SIA) can migrate in the matrix, but He-vacancy (He-V) clusters are immobile. Most SIAs form <111> clusters, and only the dislocation loops with a Burgers vector of b = 1/2 <111> appear in the simulations. SIA clusters (or loops) are attached to He-V clusters for He implantation up to 1372 appm, while the He-V cluster–loop complexes with more than one He-V cluster are formed at the He concentration of 2057 appm and larger. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction In a fusion reactor environment helium (He) is produced at high rates in steels by nuclear (n, a) transmutation reactions. Because of the extremely low solubility of He in metals, He atoms tend to be deeply trapped in small vacancy clusters and microstructural features, leading to the creation of He-stabilized bubbles, which can significantly degrade the mechanical properties of materials. Therefore, understanding of the nucleation of He bubbles in steels, both in the bulk and within microstructural features, is of fundamental importance to the development of fusion reactors. Multiscale modeling, especially including the atomic scale, provides a basis to obtain insight into and general understanding of the complex radiation damage process. Particularly, molecular dynamics (MD) methods have been widely employed to study the atomic-level processes of defects controlling microstructural evolution in advanced ferritic steels. The behavior of He in Fe has been widely investigated [1–15]. MD simulations have been employed to yield important understanding of the behavior of He defects in bcc Fe using different interatomic potentials [2–4]. Recently, Stewart et al. investigated the formation and diffusion of He clusters and bubbles in bcc iron using a three-body Fe-He interatomic potential [2]. Gao et al. [14] developed a new interatomic potential for Fe–He interactions, which is based on the electronic hybridization between Fe d-electrons and He s-electrons. The diffusion properties of He interstitials
⇑ Corresponding author. Tel.: +1 509 371 6490; fax: +1 509 371 6242. E-mail addresses: [email protected], [email protected] (F. Gao). 0168-583X/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nimb.2012.11.025
and interstitial He clusters in the bulk of bcc Fe have been studied using MD with this newly developed Fe–He potential [15]. The low migration energy barrier for a single He interstitial in the bulk is consistent with that obtained using ab initio methods. It was also found that small He clusters can migrate at low temperatures, but at higher temperatures they can kick out a SIA and become trapped by the resulting vacancy, forming He-vacancy clusters. Also, the binding energies of small He-V and He–He clusters are in good agreement with those obtained by ab initio and other potential calculations. In the present study we investigate the nucleation of He clusters and bubbles, the emission of SIAs from the He clusters, and the formation of dislocation loops in the bulk of bcc Fe, as well as the effects of these phenomena on the microstructural changes.
2. Simulation procedure In the present simulations a modified version of the MOLDY computer code [16] is used. The interatomic potentials of Ackland [17] and Beck [18] are used to describe the Fe–Fe and He–He interactions respectively, while the Fe He interaction is described by the newly developed Fe He potential [14]. The NVT ensemble [15] is used in the simulations, and periodic boundary conditions are applied along all three axes to avoid the influence of free surfaces. A MD box of 45a0 45a0 45a0 with 182,250 Fe atoms is used, where a0 is the lattice constant of perfect bcc iron (2.8553 Å). Initially 125 He atoms are randomly distributed in the box, which corresponds to a mean He concentration of 685 appm. Then, the box is quenched to 0 K for 10,000 time
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
steps, followed by a temperature rescaling to 800 K and annealing at 800 K for 1.2 ns, where there is no significant migrations or jumps of atoms that affect the size and distribution of He clusters. After the equilibrium state has been achieved, an additional125 He atoms are randomly inserted into the system, which gives a total of 250 He atoms. The same quenching and annealing approach is used, but the annealing time is about 0.6 ns, which is long enough for the system to reach its equilibrium state (i.e. the defect configurations remain without obvious changes). The same approach is repeated until a total of 500 He atoms have been added, i.e. the mean He concentration is 2743 appm, which is lower than the maximum He concentration of 3000 appm used in experiments [19]. It should be noted that helium atoms are gradually added from low to high concentrations, and thus, the nucleation mechanism and growth of helium clusters (bubbles) can be explored, at least at the early stage of nucleation. The highest concentration mimics the experimental condition, which will allow us to study up-limit effects on the nucleation of He clusters. After annealing at 800 K, the system is then quenched to 0 K for further analysis in terms of defect configurations, He bubble distributions and dislocation loop orientation. 3. Results and discussion 3.1. 125 He atoms (685 appm He) The initial 125 He atoms are randomly distributed in the simulation box as single interstitials, either in tetrahedral or octahedral positions. These single He interstitials can easily migrate at 800 K because of their low migration energy barrier of 0.058 eV [14]. It is of interest to note that two He atoms can join together, forming a He dimer (He2), but it sometimes dissociates into two single He interstitials because of its small binding energy (0.3 eV with the present potential). Also, a He2 cluster migrates easily in the Fe matrix because of its low migration energy of 0.09 eV and the emission of a self-interstitial from the He2 cluster is not observed. Once a He atom migrates into a He2 cluster, a He3 cluster is formed. Similarly, the He3 cluster can easily migrate with the migration energy of 0.097 eV [15], but He dissociation from the He3 cluster does not occur due to its slightly higher binding energy [14]. Although a Fe atom can be displaced from its site, temporarily forming a He3VFe complex, the emission of a self-interstitial does not occur, as shown in Fig. 1. The structure of the He3VFe complex appears at 0.27 ns, but during the annealing process, this complex structure transfers to a He3 cluster because of the recombining of the Fe
69
atom and the vacancy. It is also noted that the He3 cluster can fast migrate, which is clearly shown in Fig. 1, where interstitials and vacancies were identified and counted using a displacement analysis method [20]. When the He cluster reaches four He atoms, an Fe atom can be kicked out, forming a He-vacancy (He4V) cluster and a SIA, as shown in Fig. 2. It is of interest to find that the He atoms in the cluster rotate quickly around the vacancy, but the centre of mass of the He4V cluster does not change with time. This suggests that the helium atoms in the cluster still strongly bond with the vacancy, forming a stable configuration at 800 K. The emitted SIA forms a dumbbell with another Fe atom, and attaches to the He4V cluster. With increasing simulation time, some of the SIAs are able to escape from their original He-vacancy clusters, and join with other SIAs, forming SIA clusters attached to He-vacancy clusters. A few He4 clusters are observed to share one lattice vacancy with an attached Fe atom, forming He4VFe at 800 K, which is similar to the configuration of He3VFe. Thus, a cluster of four or more He atoms can emit a SIA, forming a Frenkel pair at 800 K. This is different from Stewart’s results [2] in which it is demonstrated that Frenkel pair creation happens in clusters with six or more He at 800 K. After annealing 1.2 ns, most He atoms become part of He-V defects. The He and defect distributions at 1.2 ns for the case of 125 He atoms are shown in Fig. 3, from which it is clearly shown that almost all the SIA clusters are attached to He clusters, and most SIA clusters are made up of <111> crowdions and split dumbbells. Some SIA clusters consist of <111> crowdions and <110> split dumbbells, while some form the mixture configurations of many Fe3V, one of which is shown in the inset in Fig. 3(a). The formation of the mixture configurations of many Fe3V may be due to the fact that the pressure of its nearest He cluster is not enough to push SIAs away to form <111> crowdions. The size distribution of He and SIA clusters is shown in Fig. 3(b). The largest He cluster includes 12 He atoms, while the largest SIA cluster contains only 7 SIAs. Both the size distributions of He and SIA clusters exhibit almost uniform distributions. 3.2. 250 He atoms (1372 appm He) After randomly inserting the second 125 He atoms in the simulation box, corresponding to the mean He concentration of 1372 appm, the system is quenched to 0 K and annealed at 800 K. The distributions and configurations of the He-V and SIA clusters, as well as point defects, after 0.2 ns and 0.6 ns are shown in Figs. 4(a) and (b), respectively. It is found that the centers of the He-V clusters remain the same, while single He atoms and SIAs can migrate in the matrix. Since some He clusters already existed in the simulation box, the inserted He atoms can join the existing He-V
0.33 ns
0.27 ns
Fig. 1. Structure change of the He3VFe complex, where the red circle indicates the He3VFe complex at 0.27 ns. This configuration transfers to a He3 cluster by the recombination of the SIA and the vacancy at 0.33 ns, indicated in the black circle. Green, black and magenta spheres represent vacancies, SIAs and He atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 2. Structure of a He4V cluster and a SIA, where the representations of spheres are the same as those in Fig. 1.
70
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
Fig. 3. (a) He and defect distributions for the case of 125 He atoms and (b) size distribution of He-V clusters and SIA clusters after annealing for 1.2 ns, where the representations of spheres are the same as those in Fig. 1. The inset in (a) is the detailed arrangements of a He-SIA cluster.
Fig. 4. He and defect distributions after inserting 250 He at 0.2 ns (a) and at 0.6 ns (b), and size distribution of He-V and SIA clusters at 0.6 ns (c). The inset in (b) is the detailed arrangements of a He cluster–SIA loop complex.
cluster, leading to the formation of larger He clusters, and more SIAs are emitted from the clusters. However, all the SIA clusters are also attached to He clusters, but the size of the SIA clusters becomes larger, as compared with the clusters of the He concentration of 685 appm. Most SIA clusters orient along the <111> direction, forming <111> crowdions, and some of the larger SIA clusters can be identified as ½ <111> loops, as shown in the inset in Fig. 4(b). The size distributions of the He-V and SIA clusters after annealing for 0.6 ns are shown in Fig. 4(c). The number of He atoms in the largest He cluster increases up to 20, while the largest SIA cluster contains only 10 SIAs. The size distribution of He clusters is slightly different from that at the He concentration of 685 appm. It is clear that a large number of small He-V clusters are formed at the He concentration of 1372 appm although the size of He-V clusters increases. This may be attributed to the immobility of He-V clusters. Once a He-V cluster is formed, it cannot easily migrate to combine with other He-V clusters, and form a larger cluster. The He-V cluster can grow into a larger cluster only by absorbing single He atoms and small He clusters. 3.3. 375 and 500 He atoms (2058 and 2743 appm He) After annealing 0.6 ns at 1372 appm He concentration, an additional 125 He atoms were randomly inserted into the system, which corresponds to a He concentration of 2058 appm. Some existing He-V clusters grow into larger clusters by absorbing more He atoms and emitting more SIAs, but more small He clusters also appear due to the coalescence of several He atoms. The He and defect distributions at 0.6 ns are shown in Fig. 5(a). Compared to Fig. 4(b), the He and SIA clusters grow into larger clusters, and it is of interest to note that three He-V cluster-SIA loop complexes are formed, which are indicated using the black circles in Fig. 5(a). These complexes with more than one He-V cluster are formed by the evolution of small He clusters and the movement
of the SIAs. He bubble-loop complexes were also found in the experiments by Chen et al. [19], who indicated that most bubbles are attached to dislocations, forming bubble-loop complexes at 673 K in ferritic steel after He implantation. In the present simulations, the structures of the complexes are similar to those found in experiments, even though the size of the complexes is smaller than the experimental results. The size distribution of He-V and SIA clusters after inserting 375 He at 0.6 ns is shown in Fig. 5(b). The size of these He clusters is evidently larger than those formed at the He concentration of 1372 appm. The largest He cluster at 2058 appm includes 30 He atoms, as compared to 20 He atoms at the He concentration of 1372 appm, while the largest SIA cluster contains 15 SIAs. After adding an additional 125 He atoms, the He concentration increases up to 2743 appm. The microstructure is similar to that at the He concentration of 2058 appm, as shown in Fig. 5(c). As compared to Fig. 5(a), it is clear that more He cluster-SIA loop complexes are formed, which are indicated by the black circles in Fig. 5(c). However, it should be noted that these loops are formed by the collection of the SIAs at the peripheries of the He-V clusters, and attached to the He-V clusters. The formation and emission of dislocation loops are in contrast to the traditional theory proposed by Trinkaus and Wolfer [21]. From the size distribution of He-V and SIA clusters at 0.6 ns shown in Fig. 5(d), it can be found that the size and number of He bubbles (the number of He atoms in the bubbles is larger than 20) are generally close to those at the He concentration of 2058 appm. More middle and small He clusters (the number of He atoms is less than 20) are formed with increasing He concentration. However, the emission of dislocation loops is not observed, which may be due to the fact that the size of He clusters is too small and the pressure is not large enough to punch the dislocations out from the clusters. The periodical boundary condition may also have effect on the emission of dislocations.
L. Yang et al. / Nuclear Instruments and Methods in Physics Research B 303 (2013) 68–71
71
Fig. 5. (a) He and defect distributions and (b) size distribution of He-V and SIA clusters after inserting 375 He at 0.6 ns. (c) He and defect distributions and (d) size distribution of He-V and SIA clusters after inserting 500 He at 0.6 ns.
4. Conclusion The nucleation and growth of He clusters and bubbles in bcc Fe have been investigated using MD simulations with our newly developed Fe-He interatomic potential. Groups of 125 He atoms are additively inserted into the simulation system in four cycles, and the simulations are carried out at 800 K. The high mobility of He atoms leads to the formation of interstitial He clusters. A He cluster containing four or more He atoms is large enough to emit an Fe interstitial, creating a Frenkel pair. The emitted SIA can easily migrate away from the He-V cluster, while the He-V cluster becomes immobile. As He atoms continue to be inserted, more He atoms join the He-V cluster, and more SIAs can be created, leading to the formation of large SIA clusters or dislocation loops. Most SIAs in the clusters form <111> crowdions, and larger SIA clusters have been identified to be dislocation loops with a Burgers vector of b = 1/2 <111>. It is of interest to note that SIA clusters or loops are attached to the He clusters at the He concentration up to 1372 appm, while some He-V cluster–loop complexes are formed at the higher He concentration. These results are in good agreement with experimental observations. The formation mechanism of the He clusters (or bubbles), SIA clusters (or loops) and the He cluster-loop complexes are investigated in detail. Acknowledgements F. Gao, S.Y. Hu, Y.L. Li, R.J. Kurtz and H.L. Heinisch are grateful for support by the US Department of Energy/Office of Fusion Energy Science under Contract DE-AC06-76RLO 1830. L.Yang and
X.T. Zu are grateful for the support by the National Natural Science Foundation of China – NSAF (Grant no.: 10976007). References [1] G. Ackland, Science 327 (1587) (2010) 1587. [2] D. Stewart, Y. Osetskiy, R. Stoller, J. Nucl. Mater. 417 (2011) 1110. [3] N. Gao, H. Van Swygenhoven, M. Victorian, J. Chen, J. Phys. Condens. Matter 23 (2011) 442201. [4] Z.F. Di, X.M. Bai, Q.M. Wei, J.H. Won, R.G. Hoagland, Y.Q. Wang, A. Misra, B.P. Uberuaga, M. Nastasi, Phys. Rev. B 84 (2011) 052101. [5] G. Lucas, R. Schaublin, J. Nucl. Mater. 386–388 (2009) 360. [6] T. Seletskaia, Y. Osetsky, R.E. Stoller, G.M. Stocks, Phys. Rev. Lett. 94 (2005) 046403. [7] C.C. Fu, F. Willaime, Phys. Rev. B 72 (2005) 064117. [8] L. Yang, X.T. Zu, H.Y. Xiao, F. Gao, H.L. Heinisch, R.J. Kurtz, K.Z. Liu, Appl. Phys. Lett. 88 (2006) 091915. [9] Steven J. Zinkle, Phys. Plasmas 12 (2005) 058101. [10] A. Van Veen, R.J.M. Konings, A.V. Fedorov, J. Nucl. Mater. 320 (2003) 77. [11] E.H. Lee, J.D. Hunn, T.S. Byun, L.K. Mansur, J. Nucl. Mater. 280 (2000) 18. [12] J.D. Hunn, E.H. Lee, T.S. Byun, L.K. Mansur, J. Nucl. Mater. 282 (2000) 131. [13] J. Henry, M.H. Mathon, P. Jung, J. Nucl. Mater. 318 (2003) 249. [14] F. Gao, H.Q. Deng, H.L. Heinisch, R.J. Kurtz, J. Nucl. Mater. 418 (2011) 115. [15] H.Q. Deng, W.Y. Hu, F. Gao, H.L. Heinisch, S.Y. Hu, Y.L. Li, R.J. Kurtz, to be published in J. Nucl. Mater. [16] F. Gao, D.J. Bacon, P.E.J. Flewitt, T.A. Lewis, J. Nucl. Mater. 249 (1997) 77. [17] G.J. Ackland, M.I. Mendelev, D.J. Srlolovitz, S. Han, A.V. Barashev, J. Phys. Condens. Matter 16 (2004) s2629. [18] R.A. Aziz, A.R. Janzen, M.R. Moldover, Phys. Rev. Lett. 74 (1995) 1586. [19] J. Chen, P. Jung, W. Hoffelner, H. Ullmaier, Acta Mater. 56 (2008) 250. [20] L. Yang, X.T. Zu, Z.G. Wang, H.T. Yang, F. Gao, H.L. Heinisch, R.J. Kurtz, J. Appl. Phys. 103 (2008) 063528. [21] H. Trinkaus, W.G. Wolfer, J. Nucl. Mater. 552 (1984) 122–123.