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Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations
Nuclear Instruments and Methods in Physics Research B xxx (2016) xxx–xxx
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations Petr Grigorev a,b,c,⇑, Alexander Bakaev a, Dmitry Terentyev a, Guido Van Oost b, Jean-Marie Noterdaeme b, Evgeny E. Zhurkin c a
SCKCEN, Nuclear Materials Science Institute, Boeretang 200, Mol 2400, Belgium Ghent University, Applied Physics EA17 FUSION-DC, St. Pietersnieuwstraat, 41 B4, B-9000 Gent, Belgium Department of Experimental Nuclear Physics K-89, Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, 29 Polytekhnicheskaya str., 195251 St. Petersburg, Russia b c
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 24 October 2016 Accepted 25 October 2016 Available online xxxx Keywords: Hydrogen retention Helium Tungsten Dislocation loops Molecular Dynamics
a b s t r a c t The interaction of H and He interstitial atoms with ½h1 1 1i and h1 0 0i loops in tungsten (W) was studied by means of Molecular Static and Molecular Dynamics simulations. A recently developed interatomic potential was benchmarked using data for dislocation loops obtained earlier with two other W potentials available in literature. Molecular Static calculations demonstrated that ½h1 1 1i loops feature a wide spectrum of the binding energy with a maximum value of 1.1 eV for H and 1.93 eV for He as compared to 0.89 eV and 1.56 eV for a straight ½h1 1 1i{1 1 0} edge dislocation. For h1 0 0i loops, the values of the binding energy were found to be 1.63 eV and 2.87 eV for H and He, respectively. These results help to better understand the role played by dislocation loops in H/He retention in tungsten. Based on the obtained results, a contribution of the considered dislocation loops to the trapping and retention under plasma exposure is discussed. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Tungsten (W) is the material to be used for ITER plasma-facing components (PFCs) [1], selected due to its low sputtering yield, high melting point and high thermal conductivity. However, the impact of neutron irradiation in synergy with high heat flux plasma exposure is still to be assessed with respect to the structural integrity [2] and hydrogen isotope retention [3]. In the ITER divertor, the plasma-facing materials will be exposed to a very high plasma flux (1024 D/m2s) [4] with the ion energies lower than 100 eV, i.e., well below the atom displacement threshold (the energy needed to generate a stable Frenkel pair), and the implantation range will be limited to several nanometers. Subsequently, trapping of hydrogen (H) isotopes and helium (He) will be defined by the natural structural defects and neutron-induced defects. By now, many experimental and computational works have been dedicated to the assessment of trapping due to natural defects, such as vacancies, grain boundaries and dislocations (see e.g. [5–9]). Under neutron irradiation, besides the conventionally accepted traps, dislocations loops (DL) are to be accounted for because these ⇑ Corresponding author at: SCKCEN, Nuclear Materials Science Institute, Boeretang 200, Mol 2400, Belgium.
defects are the primary microstructural features observed directly by transmission electron microscopy (TEM) under in-situ irradiation of W in the ITER-relevant temperature range [10]. Dislocation loops of both types ½h1 1 1i and h1 0 0i are formed and their relative fraction depends on irradiation temperature as well as on tungsten purity. In addition to the cascade-producing damage, the dislocation loops have been regularly observed in tungsten under high flux plasma exposure [11] by TEM as well. Presumably, the DLs are formed either as a result of the loop-punching mechanism of H bubble growth or due to sub-surface plastic deformation induced by thermal shock. DLs should exhibit stronger binding as compared to straight screw dislocations, moreover h1 0 0i loops are expected to be stronger traps then ½h1 1 1i types. The purpose of this work is to clarify the strength of ½h1 1 1i and h1 0 0i dislocation loops as traps for H/He interstitial atoms as well as to investigate possible pipe-type diffusion mechanisms of H/He in the core of the loops.
2. Computational details Given the need to consider nano-metric sized dislocation loops, as experimentally observed, the work was carried out using classical Molecular Dynamics (MD). Simulations were performed using
http://dx.doi.org/10.1016/j.nimb.2016.10.036 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: P. Grigorev et al., Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.10.036
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LAMMPS [12]. The embedded atom method (EAM) (‘‘EAM2” version as stated in the original paper) interatomic potential for WH-He system from [13] was used. This potential uses the second version of the EAM potential for W-W interaction from [14]. Previously, the pure W potential was validated with respect to different properties including the dislocation relevant features (see [15] for a review) as well as the H/He-vacancy interaction has been fitted in the original work [13]. As of now, we are not aware of another WHe-H interatomic model for large-scale calculations wherein both dislocation and He/H features are incorporated and validated using ab initio data. Molecular Static (MS) calculations were performed by means of conjugate gradient algorithm implemented in LAMMPS with relative (DEtot/Etot) energy change between relaxation steps of 1010 as a stopping criterion. The size and the crystallographic orientation of the principal axes of the model crystal depended on the type of the loop considered. For the loops with Burgers vector h1 0 0i, cubic boxes with the axes orientation of x: h1 0 0i, y: h0 1 0i, z: h0 0 1i were used. The dislocation loop was created by replacing two atomic planes of atoms along x direction with h1 0 0i dumbbells within the required dislocation loop radius in the y-z plane. For the loops with Burgers vector ½h1 1 1i the model boxes with the axes orientation of x: h1 1 1i, y: h 1 1 2i, z: h1 1 0i were used. The dislocation loop was created by replacing three planes of atoms along x direction with h1 1 1i dumbbells within a required radius in y-z plane. The size of the box was varied from 104 to 1.5 106 atoms depending on the loop size. The lattice constant a0 was equal to 0.314 nm. The formation energy of the loop was calculated as the difference between the total energy of the system containing the loop and the total energy of the perfect crystal containing the same amount of atoms with the following formula:
Eform ¼ Eloop Nat Eat
ð1Þ
where Eloop is the total energy of the system containing the loop, Nat is the number of atoms in the system, Eat is the energy per atom in ideal bulk material predicted by the potential. The binding energy of H and He atoms with the loops was calculated by placing the He/H atom in a tetrahedral position close to the loop and relaxing the system. The region around the loop was scanned in this way in order to investigate all possible attractive positions. The value of the binding energy was calculated using the following expression:
EB ¼ EGA þ Eloop EGAloop N at Eat
ð2Þ
where EGAloop is the total energy of the system when a He/H atom is attached to the dislocation loop, Eloop and EGA the total energy of the system containing only a He/H atom in a tetrahedral position or only a dislocation loop, respectively. NatEat (same as above) is introduced to respect the particle number balance and to compensate for the different number of matrix W atoms present in the configurations corresponding to EGAloop, Eloop and EGA energies.
3. Results and discussion 3.1. Benchmark calculations In order to calculate the dislocation loop formation energy as well as the He/H atom binding energy it is important to eliminate any artefacts of the calculations related to the limited size of the model system. We tested different box sizes for each of the considered loops. The results are shown in Fig. 1(a). The box size is reported in lattice units. It can be seen that the formation energy decreases with the box size dimension reaching a plateau beyond a certain box size. This behavior is explained by elastic interaction of the loop with its image via periodic boundaries. From these calculations, we chose the box size to minimize the self-interaction and ensure constant formation energy of the loop vs. box size. Typically, it is enough that the loop is surrounded by 10 a0 of ideal atomic structure in all directions to accommodate the elastic stress. This is also confirmed by calculating the pressure distribution across the loop habit plane as shown in Fig. 1(b) for the ½h1 1 1i loop done by means of the virial calculation procedure embedded in LAMMPS [16]. As can be seen 80% (higher than 0.06 Mbar) of negative pressure is localized within 1 nm (~3a0)distance from the loop and within 2 nm (~6a0) within the positive pressure part, which substantiates our choice for the dimensions of the MD boxes. The pressure distribution for the h1 0 0i{1 0 0} loop is not shown here but remains qualitatively the same as for the ½h1 1 1i{1 1 1} loop. The stability of the nanometric dislocation loops was studied in [17] using the EAM potentials by Ackland [18] and by Derlet [19]. The Authors considered the loops with the Burgers vector h1 0 0i and the habit plane {100}, and the Burgers vector ½h1 1 1i with the habit plane {1 1 1} and {1 1 0}. In Fig. 2, we present the formation energy of the DLs calculated here and add data from [17] for comparison. We did not find any significant difference in the formation energy for the ½h1 1 1i{1 1 1} and the ½h1 1 1i{1 0 0} loops and thus we report only the formation energy for the ½h1 1 1i
Fig. 1. (a) Loop formation energy per atom depending on the size of the model box given in lattice units (L.U.) (b) pressure distribution around a ½h1 1 1i dislocation loop with 5 nm radius along the Burgers vector. The limits of dislocation loop are marked by the \ and > symbols. The red area of the colorcode corresponds to compressive and the blue area corresponds to tensile pressure. The contour plot is added for convenience and for the black and white version of the article.
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{1 1 1} loops. It can be seen from Fig. 2 that for the majority of the considered loops, the Ackland potential (green curves) predicts the lowest values of the formation energy, while the Derlet potential (red curves) predicts the middle value and presently used potential derived by Marinica et al. (blue curves) gives the highest values. This trend is consistent with the values for the formation energies reported in [20]: 8.87, 9.48, 10.46 eV for the h1 1 1i SIA dumbbell and 9.8, 11.34, 12.83 eV for the h1 1 0i SIA dumbbell as predicted, respectively, by the Ackland, Derlet and Marinica potentials. It is important to note that none of the considered potentials predict the stability of ½h1 1 1i (squares and triangles on Fig. 2) loops over h1 0 0i (circles on Fig. 2) loops as can be expected from the linear isotropic elasticity theory [21]. This important feature of the potentials should be kept in mind for the interpretation of MD simulations at finite temperatures.
shown in Fig. 3(a), where the binding energy map in the {1 0 0} plane around the h1 0 0i{1 0 0} loop with a radius of 2.5 nm is shown. It can be seen that H is attracted to the loop core in the tensile region (see Fig. 1(b)) while there is a repulsive interaction in the compression zone. The binding energy distribution of scanned positions is shown in Fig. 3(b, upper bar). It demonstrates that there is a wide range of the binding energies with a maximum value of 1.64 eV. Upon the relaxation of H attached next to the ½h1 1 1i{1 1 1} loop, the loop was seen to transform into the ½h1 1 1i{1 1 0} configuration so that the orientation of the habit plane normal was tilted at 35o from the Burgers vector orientation. The visualization of the dislocation loop core and the rotation of the habit plane in the as-relaxed crystal is shown in Fig. 4. The dislocation loop is represented by a green line, obtained with the dislocation identification algorithm [23] implemented in the OVITO tool [24], and H positions are shown by red spheres. No such rotation was seen for the h1 0 0i loops. In Fig. 3(b, lower bar) we present the binding energy distribution for H - ½h1 1 1i loop (with a radius of 5 nm) and compare it with the results for a straight ½h1 1 1i{1 1 0} edge dislocation already reported in [22]. In the case of the edge dislocation, the distribution has a higher number of counts near the two energy channels: 0.8 and 0.55 eV. This means that the majority of the scanned H positions relaxed into two types of stable positions. At the same time the distribution for the loop is more uniform, reflecting less rigorous structure of the loop core and availability of the trapping sites with the binding energy exceeding the maximum binding energy with the straight dislocation line. The maximum binding energy for the loop reaches 1.1 eV. These high binding energy positions correspond to the groups of positions shown in Fig. 4. The same MS calculations for He showed similar trends as for H. The maximum binding energy with the ½h1 1 1i and h1 0 0i dislocation loop was determined to be, respectively, 1.93 eV and 2.87 eV. The latter values are significantly higher as compared to the binding energy with the straight ½h1 1 1i{1 1 0} edge dislocation being 1.56 eV.
3.2. Interaction of H and He atoms with dislocation loops
3.3. Finite temperature dynamic calculations
The binding energy of H and He atoms to the DLs was calculated using the methodology described above. The results for H are
MD simulations at finite temperature were performed to study the interaction of H and He interstitials with the core of dislocation
Fig. 2. Comparison of the loops formation energies predicted by different potentials. The h1 0 0i{1 0 0} loops are shown with circles, the ½h1 1 1i{1 1 1} loops are shown with squares and the ½h1 1 1i{1 1 0} loops are shown with triangles. The results for the Ackland potential are shown in green, for the Derlet potential in red and the present study results are shown in blue.
Fig. 3. (a) The binding energy map around the h1 0 0i{100} loop with radius 2.5 nm, positive values of binding energies are shown in red and represent attraction positions, negative values are shown in blue and represent repulsion positions. (b) the H and h1 0 0i{111} loop binding energy distribution (top x axis), H binding energy distribution for a ½h1 1 1i dislocation loop and a ½h1 1 1i edge dislocation are reported in [22] (bottom x axis). The distributions were normalized to 1.
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Fig. 4. Visualization of initial configuration (most left picture) and final configurations demonstrating the transformation of ½h1 1 1i{1 1 1} loops to ½h1 1 1i{1 1 0} loops when H is in the vicinity if the loop.
loops in dynamics, in particular to clarify whether pipe diffusion occurs and how the association of H/He with a loop affects its mobility (if any). Due to the high mobility of h1 1 1i crowdions, the ½h1 1 1i DLs are seen to move already at the relatively low temperature of 600 K in a short MD run for 1 ns. H and He atoms also have low migration barriers in W [25]. However, the relatively strong loop-H/He binding energy implies suppression of the loop diffusion, unless pipe diffusion of H/He enables the movement of the loopH/He complex (see example studied in iron [26]). MD simulations involving both ½h1 1 1i and h1 0 0i loops with H/He attached were performed at 600, 1200 and 1800 K for 10 ns. In all the cases, the H/He-loop complex remained immobile within the whole timespan. Diffusion of H/He was also not detected. Increasing the simulation temperature did not activate pipe diffusion and detachment events were observed instead. As of now, there is no evidence for pipe diffusion of H and He in the core of either ½h1 1 1i or h1 0 0i dislocation loops. On the contrary, MD simulations performed in [22] for a H atom attached to a straight ½h1 1 1i{1 1 0} dislocation core demonstrated one dimensional diffusion along the core with the migration barrier calculated to be 0.17 eV. 3.4. Hierarchy of defects trapping H To structure the obtained results and to assess the role of the dislocation loops in the trapping and release of H isotopes, we con-
structed a plot where the binding energy of H to different microstructural defects such as straight dislocation lines, vacancy, vacancy-HN clusters, voids and dislocation loops is presented. In addition, in Fig. 5, the right hand Y axis corresponds to the temperature at which detrapping is expected to occur given the heating ramp of 0.5 K/s (which was typically used in many works to measure the thermal desorption spectra). It was estimated by integrating the release equation:
dCðtÞ Eb þ Em ¼ CðtÞm exp dt kT
ð3Þ
where Eb is the binding energy, Em is the H bulk migration energy, k is the Boltzmann factor, m is the Debye frequency, T is temperature. In this estimation temperature varied in time as T(t)=T0 + 0.5t to mimic TDS measurements. The detrapping activation temperature was estimated as a temperature at which the release rate from the trap has a maximum. One can see that the binding energy to the ½h1 1 1i loop lays in the range of binding energies calculated for the vacancy-HN clusters [27–29], which therefore contribute to the detrapping stage occurring around 450–550 K and in fact is seen to magnify in the plastically-deformed samples [30,31]. The binding energy for the h1 0 0i loops is placed in between vacancy-H pair and void, and therefore the detrapping temperature is around 700 K, clearly above the stage typically attributed to the trapping from the dislocations and vacancies [32]. Notably, the first results for
Fig. 5. The binding energy of H to different microstructural defects such as straight dislocation lines, vacancy, vacancy-HN clusters, voids and dislocation loops. The right hand side Y axis corresponds to the temperature at which detrapping is expected to occur given the heating ramp of 0.5 K/s.
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the desorption of deuterium after the high flux plasma exposure in neutron irradiated tungsten, reported by Shimada et al. [33], identified a need to introduce new types of traps (as compared to standard two-trap parameterization sufficient to describe nonirradiated material) with the low energy (<1.1 eV) and high energy (>1.7 eV). Note that the neutron irradiation in those experiments was carried out at 50 °C and up to 0.025 dpa. The presence of voids for such conditions has never been reported, since both irradiation temperature and dose are low enough to induce sufficient vacancy migration to form visible voids. Dislocation loops on the other hand, are formed directly in cascades induced by fast neutrons and therefore might be responsible for the high energy detrapping stages together with vacancy clusters (also formed in cascades and upon annealing induced by thermal desorption experiment). 4. Conclusions The interaction of H and He interstitials with ½h1 1 1i and h1 0 0i dislocation loops of circular shape was studied by means of atomistic simulations. Molecular Static simulations demonstrated that the dislocation loops can act as traps with a wide spectrum of the binding energy. Both DLs are stronger taps for He/H as compared to a straight edge or screw dislocation with Burgers vector ½h1 1 1i. With respect to H trapping, a 5 nm ½h1 1 1i loop binds with H with a maximum energy of 1.1 eV, which is 0.2 eV higher than the binding energy with a straight dislocation line (0.89 eV), while a h1 0 0i loop has a binding energy of 1.64 eV. The computational analysis of the TDS spectra for neutron irradiated samples reported by Shimada et al. [33], demonstrated that multiple lowenergy (<1.1 eV) traps are required to reproduce the structure of the temperature peaks around 300–600 K well, and our results suggest that ½h1 1 1i loops can explain the origin of such traps. Indeed, ½h1 1 1i loops provide a wide spectrum of the binding energy with a maximum value of 1.1 eV and these loops are formed directly in cascades during neutron irradiation at the temperature applied in Shimada’s experiment. The assessment of the H release stages that are affected by the presence of the dislocation loops in the material was made on the basis of the obtained binding energies. It can be concluded that ½h1 1 1i loops might contribute to the desorption stage occurring around 450 K, usually assigned to dislocations, while h1 0 0i loops release H at higher temperatures, in the temperature range attributed to H-vacancy complexes or even higher. Molecular Dynamic simulations at finite temperature did not reveal pipe diffusion of H or He in the core of the dislocation loops (of either type). In all the cases, the H/He-loop complex remained immobile within the whole timespan of the MD run. Increasing the simulation temperature did not activate pipe diffusion and detachment events were observed instead.
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International Doctoral College in Fusion Science and Engineering (FUSION-DC). This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] R.E. Clark, D. Reiter, Nuclear Fusion Research: Understanding Plasma-Surface Interactions, Springer, 2005. [2] A. Hasegawa, M. Fukuda, S. Nogami, K. Yabuuchi, Fusion Eng. Des. 89 (2014) 1568. [3] T. Tanabe, Phys. Scr. T159 (2014). [4] R.A. Pitts, S. Carpentier, F. Escourbiac, T. Hirai, V. Komarov, S. Lisgo, et al., J. Nucl. Mater. 438 (Supplement) (2013) S48. [5] O.V. Ogorodnikova, S. Markelj, U. von Toussaint, J. Appl. Phys. 119 (2016). [6] R.A. Causey, R. Doerner, H. Fraser, R.D. Kolasinski, J. Smugeresky, K. Umstadter, et al., J. Nucl. Mater. 390–391 (2009) 717. [7] A. Manhard, K. Schmid, M. Balden, W. Jacob, J. Nucl. Mater. 415 (2011) S632. [8] D. Terentyev, V. Dubinko, A. Bakaev, Y. Zayachuk, W. Van Renterghem, P. Grigorev, Nucl. Fusion 54 (2014) 042004. [9] V. Dubinko, P. Grigorev, A. Bakaev, D. Terentyev, G. Van Oost, F. Gao, et al., J. Phys.: Condens. Matter 26 (2014) 395001. [10] X.O. Yi, M.L. Jenkins, M.A. Kirk, Z.F. Zhou, S.G. Roberts, Acta Mater. 112 (2016) 105. [11] A. Dubinko, A. Bakaeva, M. Hernandez-Mayoral, D. Terentyev, G. De Temmerman, J.M. Noterdaeme, Phys. Scr. T167 (2015) 014030. [12] S. Plimpton, J. Comput. Phys. 117 (1995) 1. [13] G. Bonny, P. Grigorev, D. Terentyev, J. Phys.: Condens. Matter. 26 (2014) 485001. [14] M.-C. Marinica, L. Ventelon, M.R. Gilbert, L. Proville, S.L. Dudarev, J. Marian, et al., J. Phys.: Condens. Matter. 25 (2013) 395502. [15] G. Bonny, D. Terentyev, A. Bakaev, P. Grigorev, D. Van Neck, Model. Simul. Mater. Sci. 22 (2014). [16] A.P. Thompson, S.J. Plimpton, W. Mattson, J. Chem. Phys. 131 (2009) 154107. [17] J. Fikar, R. Schäublin, Nucl. Instr. Meth. Phys. Res. B 267 (2009) 3218. [18] G.J. Ackland, R. Thetford, Philos. Mag. A 56 (1987) 15. [19] P.M. Derlet, D. Nguyen-Manh, S.L. Dudarev, Phys. Rev. B 76 (2007) 054107. [20] G. Bonny, D. Terentyev, A. Bakaev, P. Grigorev, D.V. Neck, Modell. Simul. Mater. Sci. Eng. 22 (2014) 053001. [21] D. Hull, D.J. Bacon, Introduction to Dislocations, Butterworth-Heinemann, Oxford, 2001. [22] P. Grigorev, D. Terentyev, G. Bonny, E.E. Zhurkin, G. Van Oost, J.-M. Noterdaeme, J. Nucl. Mater. 465 (2015) 364. [23] S. Alexander, V.B. Vasily, A. Athanasios, Modell. Simul. Mater. Sci. Eng. 20 (2012) 085007. [24] A. Stukowski, Modell. Simul. Mater. Sci. Eng. 18 (2010) 015012. [25] P. Grigorev, D. Terentyev, G. Bonny, E.E. Zhurkin, G. van Oost, J.-M. Noterdaeme, J. Nucl. Mater. 474 (2016) 143. [26] D. Terentyev, N. Anento, A. Serra, C.J. Ortiz, E.E. Zhurkin, J. Nucl. Mater. 458 (2015) 11. [27] D.F. Johnson, E.A. Carter, J. Mater. Res. 25 (2010) 315. [28] K. Heinola, T. Ahlgren, K. Nordlund, J. Keinonen, Phys. Rev. B 82 (2010) 094102. [29] C.S. Becquart, C. Domain, J. Nucl. Mater. 386–388 (2009) 109. [30] D. Terentyev, G. De Temmerman, T.W. Morgan, Y. Zayachuk, K. Lambrinou, B. Minov, et al., J. Appl. Phys. 117 (2015) 083302. [31] D. Terentyev, G. De Temmerman, B. Minov, Y. Zayachuk, K. Lambrinou, T.W. Morgan, et al., Nucl. Fusion 55 (2015) 013007. [32] O.V. Ogorodnikova, J. Appl. Phys. 118 (2015) 074902. [33] M. Shimada, Y. Hatano, P. Calderoni, T. Oda, Y. Oya, M.A. Sokolov, et al., J. Nucl. Mater. 415 (2011) S667.
Acknowledgements This work was supported by the European Commission and carried out within the framework of the Erasmus Mundus
Please cite this article in press as: P. Grigorev et al., Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.10.036
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations Petr Grigorev a,b,c,⇑, Alexander Bakaev a, Dmitry Terentyev a, Guido Van Oost b, Jean-Marie Noterdaeme b, Evgeny E. Zhurkin c a
SCKCEN, Nuclear Materials Science Institute, Boeretang 200, Mol 2400, Belgium Ghent University, Applied Physics EA17 FUSION-DC, St. Pietersnieuwstraat, 41 B4, B-9000 Gent, Belgium Department of Experimental Nuclear Physics K-89, Institute of Physics, Nanotechnology and Telecommunications, Peter the Great St. Petersburg Polytechnic University, 29 Polytekhnicheskaya str., 195251 St. Petersburg, Russia b c
a r t i c l e
i n f o
Article history: Received 4 August 2016 Received in revised form 24 October 2016 Accepted 25 October 2016 Available online xxxx Keywords: Hydrogen retention Helium Tungsten Dislocation loops Molecular Dynamics
a b s t r a c t The interaction of H and He interstitial atoms with ½h1 1 1i and h1 0 0i loops in tungsten (W) was studied by means of Molecular Static and Molecular Dynamics simulations. A recently developed interatomic potential was benchmarked using data for dislocation loops obtained earlier with two other W potentials available in literature. Molecular Static calculations demonstrated that ½h1 1 1i loops feature a wide spectrum of the binding energy with a maximum value of 1.1 eV for H and 1.93 eV for He as compared to 0.89 eV and 1.56 eV for a straight ½h1 1 1i{1 1 0} edge dislocation. For h1 0 0i loops, the values of the binding energy were found to be 1.63 eV and 2.87 eV for H and He, respectively. These results help to better understand the role played by dislocation loops in H/He retention in tungsten. Based on the obtained results, a contribution of the considered dislocation loops to the trapping and retention under plasma exposure is discussed. Ó 2016 Elsevier B.V. All rights reserved.
1. Introduction Tungsten (W) is the material to be used for ITER plasma-facing components (PFCs) [1], selected due to its low sputtering yield, high melting point and high thermal conductivity. However, the impact of neutron irradiation in synergy with high heat flux plasma exposure is still to be assessed with respect to the structural integrity [2] and hydrogen isotope retention [3]. In the ITER divertor, the plasma-facing materials will be exposed to a very high plasma flux (1024 D/m2s) [4] with the ion energies lower than 100 eV, i.e., well below the atom displacement threshold (the energy needed to generate a stable Frenkel pair), and the implantation range will be limited to several nanometers. Subsequently, trapping of hydrogen (H) isotopes and helium (He) will be defined by the natural structural defects and neutron-induced defects. By now, many experimental and computational works have been dedicated to the assessment of trapping due to natural defects, such as vacancies, grain boundaries and dislocations (see e.g. [5–9]). Under neutron irradiation, besides the conventionally accepted traps, dislocations loops (DL) are to be accounted for because these ⇑ Corresponding author at: SCKCEN, Nuclear Materials Science Institute, Boeretang 200, Mol 2400, Belgium.
defects are the primary microstructural features observed directly by transmission electron microscopy (TEM) under in-situ irradiation of W in the ITER-relevant temperature range [10]. Dislocation loops of both types ½h1 1 1i and h1 0 0i are formed and their relative fraction depends on irradiation temperature as well as on tungsten purity. In addition to the cascade-producing damage, the dislocation loops have been regularly observed in tungsten under high flux plasma exposure [11] by TEM as well. Presumably, the DLs are formed either as a result of the loop-punching mechanism of H bubble growth or due to sub-surface plastic deformation induced by thermal shock. DLs should exhibit stronger binding as compared to straight screw dislocations, moreover h1 0 0i loops are expected to be stronger traps then ½h1 1 1i types. The purpose of this work is to clarify the strength of ½h1 1 1i and h1 0 0i dislocation loops as traps for H/He interstitial atoms as well as to investigate possible pipe-type diffusion mechanisms of H/He in the core of the loops.
2. Computational details Given the need to consider nano-metric sized dislocation loops, as experimentally observed, the work was carried out using classical Molecular Dynamics (MD). Simulations were performed using
http://dx.doi.org/10.1016/j.nimb.2016.10.036 0168-583X/Ó 2016 Elsevier B.V. All rights reserved.
Please cite this article in press as: P. Grigorev et al., Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.10.036
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LAMMPS [12]. The embedded atom method (EAM) (‘‘EAM2” version as stated in the original paper) interatomic potential for WH-He system from [13] was used. This potential uses the second version of the EAM potential for W-W interaction from [14]. Previously, the pure W potential was validated with respect to different properties including the dislocation relevant features (see [15] for a review) as well as the H/He-vacancy interaction has been fitted in the original work [13]. As of now, we are not aware of another WHe-H interatomic model for large-scale calculations wherein both dislocation and He/H features are incorporated and validated using ab initio data. Molecular Static (MS) calculations were performed by means of conjugate gradient algorithm implemented in LAMMPS with relative (DEtot/Etot) energy change between relaxation steps of 1010 as a stopping criterion. The size and the crystallographic orientation of the principal axes of the model crystal depended on the type of the loop considered. For the loops with Burgers vector h1 0 0i, cubic boxes with the axes orientation of x: h1 0 0i, y: h0 1 0i, z: h0 0 1i were used. The dislocation loop was created by replacing two atomic planes of atoms along x direction with h1 0 0i dumbbells within the required dislocation loop radius in the y-z plane. For the loops with Burgers vector ½h1 1 1i the model boxes with the axes orientation of x: h1 1 1i, y: h 1 1 2i, z: h1 1 0i were used. The dislocation loop was created by replacing three planes of atoms along x direction with h1 1 1i dumbbells within a required radius in y-z plane. The size of the box was varied from 104 to 1.5 106 atoms depending on the loop size. The lattice constant a0 was equal to 0.314 nm. The formation energy of the loop was calculated as the difference between the total energy of the system containing the loop and the total energy of the perfect crystal containing the same amount of atoms with the following formula:
Eform ¼ Eloop Nat Eat
ð1Þ
where Eloop is the total energy of the system containing the loop, Nat is the number of atoms in the system, Eat is the energy per atom in ideal bulk material predicted by the potential. The binding energy of H and He atoms with the loops was calculated by placing the He/H atom in a tetrahedral position close to the loop and relaxing the system. The region around the loop was scanned in this way in order to investigate all possible attractive positions. The value of the binding energy was calculated using the following expression:
EB ¼ EGA þ Eloop EGAloop N at Eat
ð2Þ
where EGAloop is the total energy of the system when a He/H atom is attached to the dislocation loop, Eloop and EGA the total energy of the system containing only a He/H atom in a tetrahedral position or only a dislocation loop, respectively. NatEat (same as above) is introduced to respect the particle number balance and to compensate for the different number of matrix W atoms present in the configurations corresponding to EGAloop, Eloop and EGA energies.
3. Results and discussion 3.1. Benchmark calculations In order to calculate the dislocation loop formation energy as well as the He/H atom binding energy it is important to eliminate any artefacts of the calculations related to the limited size of the model system. We tested different box sizes for each of the considered loops. The results are shown in Fig. 1(a). The box size is reported in lattice units. It can be seen that the formation energy decreases with the box size dimension reaching a plateau beyond a certain box size. This behavior is explained by elastic interaction of the loop with its image via periodic boundaries. From these calculations, we chose the box size to minimize the self-interaction and ensure constant formation energy of the loop vs. box size. Typically, it is enough that the loop is surrounded by 10 a0 of ideal atomic structure in all directions to accommodate the elastic stress. This is also confirmed by calculating the pressure distribution across the loop habit plane as shown in Fig. 1(b) for the ½h1 1 1i loop done by means of the virial calculation procedure embedded in LAMMPS [16]. As can be seen 80% (higher than 0.06 Mbar) of negative pressure is localized within 1 nm (~3a0)distance from the loop and within 2 nm (~6a0) within the positive pressure part, which substantiates our choice for the dimensions of the MD boxes. The pressure distribution for the h1 0 0i{1 0 0} loop is not shown here but remains qualitatively the same as for the ½h1 1 1i{1 1 1} loop. The stability of the nanometric dislocation loops was studied in [17] using the EAM potentials by Ackland [18] and by Derlet [19]. The Authors considered the loops with the Burgers vector h1 0 0i and the habit plane {100}, and the Burgers vector ½h1 1 1i with the habit plane {1 1 1} and {1 1 0}. In Fig. 2, we present the formation energy of the DLs calculated here and add data from [17] for comparison. We did not find any significant difference in the formation energy for the ½h1 1 1i{1 1 1} and the ½h1 1 1i{1 0 0} loops and thus we report only the formation energy for the ½h1 1 1i
Fig. 1. (a) Loop formation energy per atom depending on the size of the model box given in lattice units (L.U.) (b) pressure distribution around a ½h1 1 1i dislocation loop with 5 nm radius along the Burgers vector. The limits of dislocation loop are marked by the \ and > symbols. The red area of the colorcode corresponds to compressive and the blue area corresponds to tensile pressure. The contour plot is added for convenience and for the black and white version of the article.
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{1 1 1} loops. It can be seen from Fig. 2 that for the majority of the considered loops, the Ackland potential (green curves) predicts the lowest values of the formation energy, while the Derlet potential (red curves) predicts the middle value and presently used potential derived by Marinica et al. (blue curves) gives the highest values. This trend is consistent with the values for the formation energies reported in [20]: 8.87, 9.48, 10.46 eV for the h1 1 1i SIA dumbbell and 9.8, 11.34, 12.83 eV for the h1 1 0i SIA dumbbell as predicted, respectively, by the Ackland, Derlet and Marinica potentials. It is important to note that none of the considered potentials predict the stability of ½h1 1 1i (squares and triangles on Fig. 2) loops over h1 0 0i (circles on Fig. 2) loops as can be expected from the linear isotropic elasticity theory [21]. This important feature of the potentials should be kept in mind for the interpretation of MD simulations at finite temperatures.
shown in Fig. 3(a), where the binding energy map in the {1 0 0} plane around the h1 0 0i{1 0 0} loop with a radius of 2.5 nm is shown. It can be seen that H is attracted to the loop core in the tensile region (see Fig. 1(b)) while there is a repulsive interaction in the compression zone. The binding energy distribution of scanned positions is shown in Fig. 3(b, upper bar). It demonstrates that there is a wide range of the binding energies with a maximum value of 1.64 eV. Upon the relaxation of H attached next to the ½h1 1 1i{1 1 1} loop, the loop was seen to transform into the ½h1 1 1i{1 1 0} configuration so that the orientation of the habit plane normal was tilted at 35o from the Burgers vector orientation. The visualization of the dislocation loop core and the rotation of the habit plane in the as-relaxed crystal is shown in Fig. 4. The dislocation loop is represented by a green line, obtained with the dislocation identification algorithm [23] implemented in the OVITO tool [24], and H positions are shown by red spheres. No such rotation was seen for the h1 0 0i loops. In Fig. 3(b, lower bar) we present the binding energy distribution for H - ½h1 1 1i loop (with a radius of 5 nm) and compare it with the results for a straight ½h1 1 1i{1 1 0} edge dislocation already reported in [22]. In the case of the edge dislocation, the distribution has a higher number of counts near the two energy channels: 0.8 and 0.55 eV. This means that the majority of the scanned H positions relaxed into two types of stable positions. At the same time the distribution for the loop is more uniform, reflecting less rigorous structure of the loop core and availability of the trapping sites with the binding energy exceeding the maximum binding energy with the straight dislocation line. The maximum binding energy for the loop reaches 1.1 eV. These high binding energy positions correspond to the groups of positions shown in Fig. 4. The same MS calculations for He showed similar trends as for H. The maximum binding energy with the ½h1 1 1i and h1 0 0i dislocation loop was determined to be, respectively, 1.93 eV and 2.87 eV. The latter values are significantly higher as compared to the binding energy with the straight ½h1 1 1i{1 1 0} edge dislocation being 1.56 eV.
3.2. Interaction of H and He atoms with dislocation loops
3.3. Finite temperature dynamic calculations
The binding energy of H and He atoms to the DLs was calculated using the methodology described above. The results for H are
MD simulations at finite temperature were performed to study the interaction of H and He interstitials with the core of dislocation
Fig. 2. Comparison of the loops formation energies predicted by different potentials. The h1 0 0i{1 0 0} loops are shown with circles, the ½h1 1 1i{1 1 1} loops are shown with squares and the ½h1 1 1i{1 1 0} loops are shown with triangles. The results for the Ackland potential are shown in green, for the Derlet potential in red and the present study results are shown in blue.
Fig. 3. (a) The binding energy map around the h1 0 0i{100} loop with radius 2.5 nm, positive values of binding energies are shown in red and represent attraction positions, negative values are shown in blue and represent repulsion positions. (b) the H and h1 0 0i{111} loop binding energy distribution (top x axis), H binding energy distribution for a ½h1 1 1i dislocation loop and a ½h1 1 1i edge dislocation are reported in [22] (bottom x axis). The distributions were normalized to 1.
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Fig. 4. Visualization of initial configuration (most left picture) and final configurations demonstrating the transformation of ½h1 1 1i{1 1 1} loops to ½h1 1 1i{1 1 0} loops when H is in the vicinity if the loop.
loops in dynamics, in particular to clarify whether pipe diffusion occurs and how the association of H/He with a loop affects its mobility (if any). Due to the high mobility of h1 1 1i crowdions, the ½h1 1 1i DLs are seen to move already at the relatively low temperature of 600 K in a short MD run for 1 ns. H and He atoms also have low migration barriers in W [25]. However, the relatively strong loop-H/He binding energy implies suppression of the loop diffusion, unless pipe diffusion of H/He enables the movement of the loopH/He complex (see example studied in iron [26]). MD simulations involving both ½h1 1 1i and h1 0 0i loops with H/He attached were performed at 600, 1200 and 1800 K for 10 ns. In all the cases, the H/He-loop complex remained immobile within the whole timespan. Diffusion of H/He was also not detected. Increasing the simulation temperature did not activate pipe diffusion and detachment events were observed instead. As of now, there is no evidence for pipe diffusion of H and He in the core of either ½h1 1 1i or h1 0 0i dislocation loops. On the contrary, MD simulations performed in [22] for a H atom attached to a straight ½h1 1 1i{1 1 0} dislocation core demonstrated one dimensional diffusion along the core with the migration barrier calculated to be 0.17 eV. 3.4. Hierarchy of defects trapping H To structure the obtained results and to assess the role of the dislocation loops in the trapping and release of H isotopes, we con-
structed a plot where the binding energy of H to different microstructural defects such as straight dislocation lines, vacancy, vacancy-HN clusters, voids and dislocation loops is presented. In addition, in Fig. 5, the right hand Y axis corresponds to the temperature at which detrapping is expected to occur given the heating ramp of 0.5 K/s (which was typically used in many works to measure the thermal desorption spectra). It was estimated by integrating the release equation:
dCðtÞ Eb þ Em ¼ CðtÞm exp dt kT
ð3Þ
where Eb is the binding energy, Em is the H bulk migration energy, k is the Boltzmann factor, m is the Debye frequency, T is temperature. In this estimation temperature varied in time as T(t)=T0 + 0.5t to mimic TDS measurements. The detrapping activation temperature was estimated as a temperature at which the release rate from the trap has a maximum. One can see that the binding energy to the ½h1 1 1i loop lays in the range of binding energies calculated for the vacancy-HN clusters [27–29], which therefore contribute to the detrapping stage occurring around 450–550 K and in fact is seen to magnify in the plastically-deformed samples [30,31]. The binding energy for the h1 0 0i loops is placed in between vacancy-H pair and void, and therefore the detrapping temperature is around 700 K, clearly above the stage typically attributed to the trapping from the dislocations and vacancies [32]. Notably, the first results for
Fig. 5. The binding energy of H to different microstructural defects such as straight dislocation lines, vacancy, vacancy-HN clusters, voids and dislocation loops. The right hand side Y axis corresponds to the temperature at which detrapping is expected to occur given the heating ramp of 0.5 K/s.
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the desorption of deuterium after the high flux plasma exposure in neutron irradiated tungsten, reported by Shimada et al. [33], identified a need to introduce new types of traps (as compared to standard two-trap parameterization sufficient to describe nonirradiated material) with the low energy (<1.1 eV) and high energy (>1.7 eV). Note that the neutron irradiation in those experiments was carried out at 50 °C and up to 0.025 dpa. The presence of voids for such conditions has never been reported, since both irradiation temperature and dose are low enough to induce sufficient vacancy migration to form visible voids. Dislocation loops on the other hand, are formed directly in cascades induced by fast neutrons and therefore might be responsible for the high energy detrapping stages together with vacancy clusters (also formed in cascades and upon annealing induced by thermal desorption experiment). 4. Conclusions The interaction of H and He interstitials with ½h1 1 1i and h1 0 0i dislocation loops of circular shape was studied by means of atomistic simulations. Molecular Static simulations demonstrated that the dislocation loops can act as traps with a wide spectrum of the binding energy. Both DLs are stronger taps for He/H as compared to a straight edge or screw dislocation with Burgers vector ½h1 1 1i. With respect to H trapping, a 5 nm ½h1 1 1i loop binds with H with a maximum energy of 1.1 eV, which is 0.2 eV higher than the binding energy with a straight dislocation line (0.89 eV), while a h1 0 0i loop has a binding energy of 1.64 eV. The computational analysis of the TDS spectra for neutron irradiated samples reported by Shimada et al. [33], demonstrated that multiple lowenergy (<1.1 eV) traps are required to reproduce the structure of the temperature peaks around 300–600 K well, and our results suggest that ½h1 1 1i loops can explain the origin of such traps. Indeed, ½h1 1 1i loops provide a wide spectrum of the binding energy with a maximum value of 1.1 eV and these loops are formed directly in cascades during neutron irradiation at the temperature applied in Shimada’s experiment. The assessment of the H release stages that are affected by the presence of the dislocation loops in the material was made on the basis of the obtained binding energies. It can be concluded that ½h1 1 1i loops might contribute to the desorption stage occurring around 450 K, usually assigned to dislocations, while h1 0 0i loops release H at higher temperatures, in the temperature range attributed to H-vacancy complexes or even higher. Molecular Dynamic simulations at finite temperature did not reveal pipe diffusion of H or He in the core of the dislocation loops (of either type). In all the cases, the H/He-loop complex remained immobile within the whole timespan of the MD run. Increasing the simulation temperature did not activate pipe diffusion and detachment events were observed instead.
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Acknowledgements This work was supported by the European Commission and carried out within the framework of the Erasmus Mundus
Please cite this article in press as: P. Grigorev et al., Interaction of hydrogen and helium with nanometric dislocation loops in tungsten assessed by atomistic calculations, Nucl. Instr. Meth. B (2016), http://dx.doi.org/10.1016/j.nimb.2016.10.036