- Email: [email protected]
Recombination coefficient of hydrogen on tungsten surface
Journal of Nuclear Materials 522 (2019) 74e79
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Recombination coefficient of hydrogen on tungsten surface O.V. Ogorodnikova National Research Nuclear University “MEPHI”, 115409, Kashirskoe Sh. 31, Moscow, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 January 2019 Received in revised form 27 March 2019 Accepted 9 May 2019 Available online 10 May 2019
The recombination coefficient is an important parameter for modelling hydrogen-metal interaction. It is responsible for hydrogen desorption from the surface of the metal and, therefore, significantly affects the hydrogen penetration into the metal, accumulation in and permeation through the metal. In the present work, the recombination coefficient of hydrogen (H) on tungsten (W) surface is examined. It is shown that the recombination coefficient of H on a clean W surface is extremely high which indicates the rapid desorption of the hydrogen molecule from the surface. Simulation using a high recombination coefficient well describes a wide range of experimental data of gas and ions interaction of hydrogen isotopes with tungsten. Proof of incorrectness of the Anderl's recombination coefficient is presented by comparing it with both theory and experiment. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The hydrogen (H) migration and retention in a metal have been a subject of considerable attention in relation to plasma-surface interaction in nuclear reactors. A study of accumulation of hydrogen isotopes in plasma-facing materials appears necessary for assessment of safety of fusion reactor due to the radioactivity of tritium and material performance and for the plasma fuel balance. Currently, tungsten (W) is the reference material for the divertor of ITER and DEMO reactors. In order to assess of the tritium retention in future fusion devices, a comparison of the modelling results with the experimental data obtained under well defined laboratory conditions is important. H isotope migration and inventory in a metal under ion irradiation, is usually modelling by rate equations [1e10]. The input parameters in the rate equations are diffusivity, solubility, surface barrier, reflection coefficient, mean ion range, density of defects and binding energies of H with different types of defects. Such parameters can be defined by ab-initio calculations by DFT or MD or TRIM codes and can be validated by comparison with experiment. At steady state, the analytical solution of the retained H can be found as reported in Ref. [9]. In some cases, the analytical solution can be derived for the dynamic of H migration and retention [11,12]. Despite a drastic increase in publications on the H migration and retention in W, there are uncertainties in the interpretation and
E-mail address: [email protected]. https://doi.org/10.1016/j.jnucmat.2019.05.017 0022-3115/© 2019 Elsevier B.V. All rights reserved.
modelling of experimental data, especially, uncertainties in fundamental parameters govern the H retention and migration. Although, in early papers [1e9], it was shown that calculations based on the diffusion equation with trapping at different kinds of defects and second order thermal desorption using the recombination coefficient for a clean W surface describe well a wide range of experimental data, many authors, for example [13,14], continue to use the Anderl's recombination coefficient in spite of that such calculations lead to disagreement with their own experimental data or required artificial suggestions which are in contradiction with theoretical and experimental data. Therefore, the purpose of this work is to show invalidity to use the Anderl's recombination coefficient to describe the desorption of H from W surface. 2. Results and discussion Once implanted, H diffuses into the metal with trapping at different kinds of defects. One-dimensional diffusion equation with single trap was first given by McNabb & Foster [15]. Later, the description of the time dependent change of H in traps, has been given by Wilson & Baskes [16], Myers et al. [17], Doyle & Brice [18] and Longhurst [19]. Improved trapping equation was derived further by Ogorodnikova [5]. All equations are essentially the same but slightly different in details. This difference can result in more than one order of magnitude difference in H retention in some cases as it was reported in Ref. [5]. The rate of hydrogen thermodesorption from a surface is proportional to the square of the concentration of atoms chemisorbed on surface sites. However, to
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
75
According to Refs. [21,23], the sticking probability for the metal with a perfectly clean surface is generally non-activated, Ec ¼ 0, and is often close to unity, sz1. However, the surface properties is connected with the bulk properties for a pure metal. The sticking factor s0 on a clean metal is a fundamental constant which depends on the bulk parameters of the metal. The difference between the Pick&Sonnenberg’ recombination coefficient [21] and the improved Kr [6] is clearly shown in Fig. 1. Fig. 1 shows experimental [24,25] and theoretical recombination coefficient for Ni and Fe as a function of the temperature. The sticking coefficient for a clean metal surface equals to unity according to Ref. [21] and it is s0 ¼ D0K2s0l2 (2pmkT)1/2 according to Ref. [6]. Although the estimation of s0 depends on the accuracy of the measurement of D0 and Ks0, the use of self-consistent s0 which corresponds to the experimental data of D0 and Ks0 is seems to be more reliable than assuming s ¼ 1 for a clean metal surface. According to Fig. 1, the
Pick&Sonnenberg’ model overestimates the recombination coefficient but the model [6] is in a good agreement with experiments. In contrast to Pick&Sonnenberg's conclusion [21] that there is no difference between molecular and atomic hydrogen interaction with solid in the case of non-activated sorption (Ec ¼ 0), we state that even in the case of Ec ¼ 0, the pre-exponential sticking coefficient, s0, can be considerably less than unity and enhances the plasma-driven uptake and permeation compared to the gas-driven ones that was confirmed experimentally [9,12]. Surface contamination (adlayers of carbon, oxygen or sulfur) decreases the recombination coefficient by increasing the surface barrier Ec (eq. (1)) as schematically shown in Fig. 2. Other factors, for example, crystallographic orientation of the surface, surface defects, etc. can also affect the value of the recombination coefficient (for details see Refs. [6,12]). Please, note that the increase or decrease of subsurface barrier Es to be higher/lower than the diffusion barrier Em or higher/lower than the surface barrier Ec does not influence the recombination coefficient (see eq. (1)). This is due to the fact that the rate of establishing a local equilibrium between chemisorbed hydrogen on the surface and absorbed hydrogen in the subsurface layer is much faster than the rates of H desorption and diffusion. Fig. 3 shows the recombination coefficient for H on W derived using the Pick&Sonnenberg model (eq. (1)) for different surface barriers, Ec, in comparison with model [6] (eq. (2)) for a clean W surface in the case of Ec ¼ 0 and literature data [26,27]. The surface barrier of Ec ¼ 0 of deuterium adsorption-desorption on/from W was found experimentally in Ref. [28]. Using Fraunfelder's solubility [29], the recombination coefficient for a clean W surface is extremely high indicating a rapid H desorption from W surface. The Pick&Sonnenberg's model results in the same Kr as the model [6] in the case of W. The recombination coefficient for a ‘dirty’ W surface (Ec > Qs) increases with increasing the temperature. Franzen's Kr corresponds to a contaminated surface with the surface barrier of Ec ¼ 1.2 eV. However, the Anderl's Kr disagrees with the theory. It does not match any Ec value. Hence, the underlying physics of the Anderl's recombination coefficient is unclear. This is the first evidence of the incorrectness of the Anderl's Kr. Anderl et al. [26] used 3 keV D3þ ions on foils of reduction rolled, powder metallurgy tungsten with a purity of 99.95% for deuterium (D) permeation experiment. From comparison of the experimental data with modelling, the recombination coefficient for deuterium on tungsten was found. Fig. 4 shows the experimental data of permeation flux in comparison with modelling performed in Ref. [26] and the present calculations. The following input
Fig. 1. Comparison of experimental [24,25] and theoretical [6,21] recombination coefficient for Ni and Fe.
Fig. 2. Schematic diagram of potential energy for hydrogen chemisorption depending on the presence of an impurity on the surface that increases the surface barrier Ec. H solution and diffusion are shown as well. Qs is the heat of solution and Em is the diffusion barrier.
simplify the mathematical task, it was proposed that the desorption rate is proportional to the square of the bulk concentration of hydrogen under the surface [20]. The proportionality coefficient was named the recombination coefficient, Kr. In Ref. [21], it was shown that Kr is proportional to the probability of H atom to overcome the surface barrier, Ec, Kr ¼ sm/K2s
(1)
Where KS ¼ Ks0 expð Qs =kTÞ is the solubility, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisffi ¼ s0 expð 2Ec =kTÞ is the sticking coefficient and m ¼ 1= 2pmkT (m is the mass of hydrogen molecule and k ¼ 1.38 1023 J/K is the Boltzmann constant). In general, to derive the recombination coefficient, the kinetic description of the elementary processes of hydrogen adsorption, absorption, molecular dissociation, and recombination was proposed by several authors. A critical review of the existing models was done in Ref. [22]. It was shown that Kr is proportional to the probability of H atom either to overcome surface, Ec, or subsurface, Es, barriers. However, probability of H desorption from the surface is higher or equals to probability of H desorption from the bulk, thus, the validity of the Pick&Sonnenberg’ recombination coefficient [21] was confirmed. The improved expression for the self-consistent recombination coefficient was derived in Ref. [6]. It was shown that the recombination coefficient on a clean metal surface is a function of diffusion pre-factor, D0, square of the jumping length, l, and the heat of solution, Qs, Kclean ¼ D0l2exp(2Qs/kT) (molecules m4/atoms2 s) r
(2)
76
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
Fig. 3. Recombination coefficient for H on W derived using the Pick&Sonnenberg model (eq. (1)) for different surface barriers, Ec, in comparison with model [6] (eq. (2)) and Anderl's [26] and Franzen's [27] recombination coefficients.
Fig. 5. Comparison of experimental TDS with calculations using Anderl's parameters [26] and the parameters from Refs. [2,7]. TDS was done in-situ in 5e10 min after the implantation was off. Fig. 4. Experimental permeation flux measured in Ref. [26] in comparison with modelling in [26] and the present model using parameters from Refs. [2,7].
parameters were used in Ref. [26]: Kr ¼ 1,3 1017exp(-0.84/kT), and de-trapping energy of D from defects (presumably vacancies) Et ¼ 1,34 eV with defect density of Wt ¼ 2 105 at. fr. In the present calculations, the following parameters are used: the recombination coefficient for a clean W surface (eq. (2)) of Kclean ¼ 3 1025/T1/2exp(2.06/kT) and two types of defects with r de-trapping energies of Et ¼ 0,85 eV and Et ¼ 1,45 eV. The structural defects corresponding to de-trapping energies of 0.85 and 1.45 eV are distributed homogeneously over entire W thickness with densities of Wt ¼ 8 104 at. fr. and Wt ¼ 1 105 at. fr., respectively. The ion-induced defects are distributed near the implantation side up to the depth of hundreds nanometers and several micrometer. The ion-induced defect density increases with fluence up to the maximum values of Wmax ¼ 1 103 at. fr. and Wmax ¼ 6 102 at. t t fr. for defects with de-trapping energies of 0.85 and 1.45 eV, respectively. For details, see Refs. [2,7]. In both the Anderl's and the present models, diffusivity and solubility were taking from Ref. [29]. The experimental data on the D permeation through W foil are well described by both the Anderl‘s parameters and the present parameters. However, a reliable set of parameters (Kr, Et, Wt) should describe simultaneously permeation, depth profile and thermal desorption spectroscopy (TDS) measurements at different experimental conditions. Fig. 5 shows experimental TDS [2] versus calculated TDS using the Anderl‘s parameters and the parameters from Refs. [2,7]. Calculations with parameters from Ref. [26] lead to
disagreement with experimental data at both 320 and 773 K. This is the second evidence of the incorrectness of the Anderl‘s recombination coefficient. The third proof of the incorrectness of the Anderl‘s recombination coefficient is that the simulation using this Kr fails to reproduce experimental D depth profiles. To reproduce the D influx into W, the authors of [13,14] suggested the reduced reflection coefficient of D from W surface to four orders of magnitude compared to experimental and calculated data [12,30]. It is trying to suggest that extra knowledge can be inserted into the definition of the reflection coefficient. Assuming the Anderl‘s recombination coefficient in their simulations, the authors of [13,14] significantly overestimates the D penetrated flux into the bulk of W resulting in the disagreement with experimental depth profile of D. The fast recombination on a clear W surface allows to resolve this inconsistence because the high recombination coefficient of D on the W surface leads to high re-emission rate. The experimental D depth profile can be obtained with a reflection coefficient closer to theoretical one using the Kr for a clean W surface (eq. (2)). Modelling a wide range of experimental data [1e3,7e9,11,12] shows no need of such non-physical assumption as the reduction of the reflection coefficient by several orders of magnitude to reproduce the experimental data of the D depth profile and TDS. Moreover, it was shown in Ref. [9] using a wide range of experimental data that if the surface barrier Ec is lower than 1 eV, the desorption rate is high and kinetics of deuterium release is limited by detrapping from defects rather than to be limited by surface effects. As a final remark, we consider the modelling of experimental
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
data of [2,7,8,31] using different set of parameters. In general, the model should describe a wide range of experimental data with one set of parameters in order to exclude the freedom in the modelling parameters. In other words, reliable set of parameters (Kr, Eit, Wit) should describe simultaneously permeation, depth profile and TDS experiments at different fluences, ion energies and temperatures. From comparison of calculations with experiments, fundamental parameters can be extracted and several peculiar effects of H behaviour in materials can be predicted. The best validation of the model assumptions is the experimental confirmation of the model predictions. Fig. 6 shows experimental thermal desorption spectroscopy (TDS) data measured in-situ only 5e10 min after ion implantation at experimental facility HSQ [2,7] and in a few weeks after D plasma exposure at the experimental setup PlaQ [32] in comparison with modelling. Please, note that the W samples were held on air for several weeks after exposure to D plasma at PlaQ prior to start TDS measurements. The model (a) predicts that the D retention decreases after a few days between implantation and TDS measurements and this reduction is mainly due to a decrease in the D retention at the first peak of TDS. This reduction was observed experimentally by comparing TDS data measured at HSQ immediately after implantation and in a few weeks of time delay between the D plasma exposure at the experimental setup PlaQ and TDS measurements (Fig. 6a). TDS can also be simulated using only intrinsic traps with energies of 0.9 eV and 1.2 eV with trap densities of Wt ¼ 103 at. fr. and Wt ¼ 6 104 at. fr., respectively (Fig. 6b). However, as it was shown in Ref. [7], the D depth profiles cannot be modelled using only natural traps. Additionally, the model with only natural traps predicts that the D retention decreases insignificantly within a few days of time delay between implantation and TDS measurements that is in contradiction with experimental data. Experimental TDS data can also be described using low recombination coefficient (eq. (1)) with the surface barrier of Ec ¼ 1.12 eV and de-trapping energies of 0.85 eV and 1.3 eV. Both the D depth profile and TDS can be simulated using the recombination coefficient for a clean W surface as well as the recombination coefficient for contaminated W surface with the surface barrier of Ec ¼ 1.12 eV. The decrease of the D retention during storage at ambient room temperature measured in subsequent experimental work [33] indicates the correctness of the models (a) and (c) which take into account the formation of ion-induced defects during implantation [2,7]. The de-trapping energies obtained by comparing the experiment with the simulation are somewhat different in models (a) and (c): lower de-trapping energy Et ¼ 1.3 eV corresponds to lower recombination coefficient (higher surface barrier). As it was reported in Ref. [9], although the D concentration and TDS can be simulated with both high and low surface barriers, the D uptake from the gas cannot be simulated using the same parameters as for ion implantation with low recombination coefficient but can be simulated with high Kr. This is again an argument in favor of the model (a) with high Kr. In the modelling above, calculations include all stages of experimental procedure, namely, (i) implantation of deuterium into tungsten from ion beam or plasma, (ii) cool down of the sample in the case if the implantation was carried out at elevated temperature, (iii) time delay between the end of implantation and the start of post-implantation measurements and (iv) heating ramp for TDS measurements. The same set of parameters has been used to calculate all of those stages. Some authors make suggestions about the D depth distribution to simulate experimental TDS separetly, namely, ignore the stages of (i) - (iii). Such assumptions can lead to incorrect simulation and interpretation of the experimental data.
77
Fig. 6. Experimental TDS data from Refs. [2,7,31,32] (lines with symbols) and modelling (solid&dashed lines) using different set of parameters: a) high Kr (eq. (2)) and intrinsic and ion-induced defects from Refs. [2,7] with de-trapping energies of 0.85 eV and 1.45 eV, b) high Kr (eq. (2)) and only intrinsic defects with de-trapping energies of 0.9 eV and 1.2 eV and c) low Kr (eq. (1)) using the surface barrier of Ec ¼ 1.12 eV and intrinsic and ion-induced defects from Refs. [2,7] with de-trapping energies of 0.85 eV and 1.3 eV. Experimental parameters are: temperature of W sample of 320 K during implantation, ion energy of 200 eV Dþ and fluences of about 1024 D/m2. Additional experimental data for the fluence of 1022 D/m2 are presented in (b) and (c). TDS was done in-situ only in 5e10 min after the ion beam was switched off at HSQ, meaning without the time delay, and in a few weeks after the plasma exposure at PlaQ. The dashed lines show the simulated TDS after 2 days between the implantation and TDS measurement in HSQ аssuming that the sample was not taken out from the implantation vacuum chamber.
78
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
For example, the authors of [10] used experimental depth profile obtained by SIMS to simulate TDS using the Anderl's Kr. They suggested about negligible amount of D in solution, namely that all D are trapped in defects after implantation of 500 eV Dþ in single crystal W (SCW) at 300 K up to a fluences of 1024 D/m2. The calculated depth profiles, using the defect density and de-trapping energies from Ref. [10] combined with the Anderl's Kr, after 5 min and one day between implantation and TDS measurements are shown in Fig. 7. The calculated depth profile in one day after implantation looks similar to experimental SIMS depth profile measured up to 40 nm, but the D retention is much higher compared to experimental data due to deep D retention beyond the implantation depth. In experiment, it is 4.45 1020 D/m2 (see Ref. [10]) but according to the calculations it is about 9 1021 D/m2 in 1.15 days after implantation. The total D retention is mainly defined by D in solution. Hence, the suggestion about negligible amount of D in solution in several days after implantation is incorrect using the Anderl's Kr. Using this D depth distribution after a few days of time delay, the calculated TDS is shown in Fig. 8. Because post-irradiation time of a few days prior to TDS is not sufficient to release most of D from solution, majority of D is released from solution sites during TDS. Thus, calculations lead to higher D retention than experiment and TDS peaks are in disagreement with experimental TDS peaks. In contrast, the authors of [10] used experimental D depth profile measured by SIMS up to 40 nm for the modelling of TDS data without modelling the D depth profile during and after implantation. Figs. 7 and 8 demonstrate that the set of parameters in Ref. [10] used only for simulation of experimental TDS cannot be used for simulation of the experimental D depth profile after implantation and, consequently, fails to simulate experimental TDS. This clearly show the importance to perform calculations including all stages of experimental procedure. However, using Kr for a clean W surface, calculations including all stages of experimental procedure are in agreement with TDS experiment as shown in Fig. 9. The de-trapping energies derived from comparison of modelling with experiment are Et ¼ 1.3 eV and Et ¼ 1.55 eV for high Kr (eq. (2)). In the case of using the Anderl's Kr, the de-trapping energies obtained in Ref. [10] are Et ¼ 1.07 eV and of Et ¼ 1.34 eV. Again, as it was mentioned above, lower Kr leads to lower values of de-trapping energies. It should be mentioned that the values of the de-trapping energies also depend on the prefactors in the trapping coefficient in the rate equations [4,5,9,10,15e20]. For example, in TMAP code the value of 1013 1/s is usually used. Whereas in the present code, the self-consistent prefactor is used as
Fig. 8. Calculated TDS using the defect density and de-trapping energies from Ref. [10] combined with the Anderl's Kr in 5 min and one day after implantation. Calculations include all stages of experiment, namely, the implantation, the time delay between the implantation and TDS measurement and TDS measurements itself.
Fig. 9. Calculated TDS using the Kclean and de-trapping energies of Et ¼ 1.3 eV and r Et ¼ 1.55 eV that is in agreement with experimental data measured in Ref. [10]. Total D retention obtained by integrating of the D desorption rate over the time is 4.96 1020 D/m2 at fluence of 1024 D/m2 that is in agreement with experiment.
n ¼ D0/l2
(3)
In the case of deuterium in W, the pre-factor is 2.4 1013 1/s (using the Fraunfelder's diffusivity [29] and assuming the diffusion of D through tetrahedral interstitials in bcc W) that is slightly different from usually used value of 1013 1/s. This leads to lower detrapping energies compared to the case of use of 1013 1/s.
3. Conclusions
Fig. 7. Calculated depth profiles using the defect density and de-trapping energies from [10] combined with the Anderl's Kr after 5 min and one day between implantation and TDS measurements.
The recombination coefficient is an important parameter to model hydrogen-metal interaction. It is responsible for hydrogen desorption from the metal surface and, therefore, affect significantly on the hydrogen penetration into the metal, accumulation and permeation. In the present work, it is shown that the Anderls' recombination coefficient, often used in the simulation of hydrogen-tungsten interaction, does not satisfy the theory of hydrogen adsorption/desorption on a W surface. In addition, using the Anderls’ recombination coefficient in the simulations, the authors significantly overestimates the penetrated flux into the bulk
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
of W which leads to disagreement with experiment. Experimental data are well modelled using the recombination coefficient for a clean W surface without suggesting extra knowledge into the definition of the reflection coefficient or other physical values. Moreover, it is shown that the experimental data can be also modelled using the Pick&Sonnenberg recombination coefficient for a contaminated W surface. Contaminations on W surface or the presence of a surface barrier result in a decrease of the de-trapping energy of D with a defect in the modelling of TDS data. Taking into account that reliable set of parameters (Kr, Et, Wt) should describe simultaneously permeation, depth profile and TDS experiments at different experimental conditions of hydrogen-W interaction, it was shown that laboratory experiments can be well simulated using a high recombination coefficient that give us confidence in the correctness of high recombination of hydrogen on W surface. References [1] O.V. Ogorodnikova, J. Nucl. Mater. 390e391 (2009) 651. [2] O. Ogorodnikova, J. Roth, M. Mayer, Deuterium retention in tungsten in dependence of the surface conditions, J. Nucl. Mater. 34 (313e316) (2003) 469. [3] S.M. Myers, P.M. Richards, W.R. Wampler, F. Besenbacher, J. Nucl. Mater. 165 (1989) 9. [4] O.V. Ogorodnikova, M.A. Fuetterer, E. Serra, G. Benamati, J.-F. Salavy, G. Aiello, J. Nucl. Mater. 273 (1999) 66. [5] O.V. Ogorodnikova, Trapping effect in hydrogen retention in metals, in: A. Hassanein (Ed.), Hydrogen and Helium Recycling at Plasma Facing Materials, NATO Science Series vol. 54, Kluwer Academic Publishers, 2001, p. 7. [6] O.V. Ogorodnikova, J. Nucl. Mater. 277 (2000) 130. [7] O.V. Ogorodnikova, J. Roth, M. Mayer, J. Appl. Phys. 103 (2008) 034902. [8] O.V. Ogorodnikova, V. Gann, J. Nucl. Mater. 460 (2015) 60. [9] O.V. Ogorodnikova, J. Appl. Phys. 118 (2015) 074902. [10] M. Poon, A. Haasz, J. Davis, J. Nucl. Mater. 374 (2008) 390.
79
[11] O.V. Ogorodnikova, K. Sugyama, J. Nucl. Mater. 442 (2013) 518. [12] O.V. Ogorodnikova, S. Markelj, U. von Toussaint, J. Appl. Phys. 119 (2016) 054901. [13] M. Baldwin, R. Doerner, Nucl. Fusion 57 (2017) 076031. [14] M. Simmonds, J. Yu, Y. Wang, M. Baldwin, R. Doerner, G. Tynan, J. Nucl. Mater. 508 (2018) 472. [15] A. McNabb, P.K. Foster, Trans. Metal. Soc. AIME 227 (1963) 618. [16] K.L. Wilson, M.I. Baskes, J. Nucl. Mater. 76e77 (1978) 291. [17] S.M. Myers, S.T. Picraux, R.E. Stoltz, J. Appl. Phys. 50 (1979) 5710. [18] B.L. Doyle, D.K. Brice, Radiat. Eff. 89 (1985) 21. [19] G.R. Longhurst, R.A. Andrel, T.J. Dolan, M.J. Mulock, Fusion Technol. 28 (3) (1995) 1217. [20] I. Ali-Khan, K.J. Dietz, F.G. Waelbroeck, P. Wienhold, J. Nucl. Mater. 76e78 (1978) 337. [21] M.A. Pick, K. Sonnenberg, J. Nucl. Mater. 131 (1985) 208. [22] (a) A.A. Pisarev, O.V. Ogorodnikova, J. Nucl. Mater 248 (1997) 52; (b) O.V. Ogorodnikova, Simulation of Desorption and Retention of Hydrogen in Plasma - Solid Interaction (PhD thesis), Moscow Engineering Physics Institute, Moscow, 1997. [23] J.B. Taylor, I. Langmuir, Phys. Rev. 44 (1933) 423. [24] W.R. Wampler, J. Nucl. Mater. 145 (1987) 313. [25] K. Yamaguchi, T. Namba, M. Yamawaki, J. Nucl. Sci. Technol. 24 (11) (1987) 915. [26] R.A. Anderl, D.F. Holland, G.R. Longhurst, R.J. Pawelko, C.L. Trybus, C.H. Sellers, Fusion Technol. 21 (1992) 745. [27] P. Franzen, C. Garcia-Rosales, H. Plank, V.Kh Alimov, J. Nucl. Mater. (1997) 241e243, 1082. [28] P.W. Tamm, L.D. Schmidt, J. Chem. Phys. 55 (N9) (1971). [29] R. Frauenfelder, J. Vac. Sci. Technol. 6 (1969) 388. [30] W. Eckstein, J.P. Biersack, J. Appl. Phys. A38 (1985) 123. W. Eckstein, IPP 9/132, 2002. [31] (a) O. Ogorodnikova, ITPA SOL/DIV Garching, 2007; (b) O.V. Ogorodnikova, Modeling of hydrogen retention and permeation in tungsten, in: 9th International Workshop on Hydrogen Isotopes in Fusion Reactor Materials, Salamanca, Spain, June 2008. [32] O.V. Ogorodnikova, T. Schwarz-Selinger, K. Sugiyama, T. Dürbeck, W. Jacob, Phys. Scripta T138 (2009) 014053. [33] K.A. Moshkunov, K. Schmid, M. Mayer, V.A. Kurnaev, Yu M. Gasparyan, J. Nucl. Mater. 404 (2010) 174.
Contents lists available at ScienceDirect
Journal of Nuclear Materials journal homepage: www.elsevier.com/locate/jnucmat
Recombination coefficient of hydrogen on tungsten surface O.V. Ogorodnikova National Research Nuclear University “MEPHI”, 115409, Kashirskoe Sh. 31, Moscow, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 January 2019 Received in revised form 27 March 2019 Accepted 9 May 2019 Available online 10 May 2019
The recombination coefficient is an important parameter for modelling hydrogen-metal interaction. It is responsible for hydrogen desorption from the surface of the metal and, therefore, significantly affects the hydrogen penetration into the metal, accumulation in and permeation through the metal. In the present work, the recombination coefficient of hydrogen (H) on tungsten (W) surface is examined. It is shown that the recombination coefficient of H on a clean W surface is extremely high which indicates the rapid desorption of the hydrogen molecule from the surface. Simulation using a high recombination coefficient well describes a wide range of experimental data of gas and ions interaction of hydrogen isotopes with tungsten. Proof of incorrectness of the Anderl's recombination coefficient is presented by comparing it with both theory and experiment. © 2019 Elsevier B.V. All rights reserved.
1. Introduction The hydrogen (H) migration and retention in a metal have been a subject of considerable attention in relation to plasma-surface interaction in nuclear reactors. A study of accumulation of hydrogen isotopes in plasma-facing materials appears necessary for assessment of safety of fusion reactor due to the radioactivity of tritium and material performance and for the plasma fuel balance. Currently, tungsten (W) is the reference material for the divertor of ITER and DEMO reactors. In order to assess of the tritium retention in future fusion devices, a comparison of the modelling results with the experimental data obtained under well defined laboratory conditions is important. H isotope migration and inventory in a metal under ion irradiation, is usually modelling by rate equations [1e10]. The input parameters in the rate equations are diffusivity, solubility, surface barrier, reflection coefficient, mean ion range, density of defects and binding energies of H with different types of defects. Such parameters can be defined by ab-initio calculations by DFT or MD or TRIM codes and can be validated by comparison with experiment. At steady state, the analytical solution of the retained H can be found as reported in Ref. [9]. In some cases, the analytical solution can be derived for the dynamic of H migration and retention [11,12]. Despite a drastic increase in publications on the H migration and retention in W, there are uncertainties in the interpretation and
E-mail address: [email protected]. https://doi.org/10.1016/j.jnucmat.2019.05.017 0022-3115/© 2019 Elsevier B.V. All rights reserved.
modelling of experimental data, especially, uncertainties in fundamental parameters govern the H retention and migration. Although, in early papers [1e9], it was shown that calculations based on the diffusion equation with trapping at different kinds of defects and second order thermal desorption using the recombination coefficient for a clean W surface describe well a wide range of experimental data, many authors, for example [13,14], continue to use the Anderl's recombination coefficient in spite of that such calculations lead to disagreement with their own experimental data or required artificial suggestions which are in contradiction with theoretical and experimental data. Therefore, the purpose of this work is to show invalidity to use the Anderl's recombination coefficient to describe the desorption of H from W surface. 2. Results and discussion Once implanted, H diffuses into the metal with trapping at different kinds of defects. One-dimensional diffusion equation with single trap was first given by McNabb & Foster [15]. Later, the description of the time dependent change of H in traps, has been given by Wilson & Baskes [16], Myers et al. [17], Doyle & Brice [18] and Longhurst [19]. Improved trapping equation was derived further by Ogorodnikova [5]. All equations are essentially the same but slightly different in details. This difference can result in more than one order of magnitude difference in H retention in some cases as it was reported in Ref. [5]. The rate of hydrogen thermodesorption from a surface is proportional to the square of the concentration of atoms chemisorbed on surface sites. However, to
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
75
According to Refs. [21,23], the sticking probability for the metal with a perfectly clean surface is generally non-activated, Ec ¼ 0, and is often close to unity, sz1. However, the surface properties is connected with the bulk properties for a pure metal. The sticking factor s0 on a clean metal is a fundamental constant which depends on the bulk parameters of the metal. The difference between the Pick&Sonnenberg’ recombination coefficient [21] and the improved Kr [6] is clearly shown in Fig. 1. Fig. 1 shows experimental [24,25] and theoretical recombination coefficient for Ni and Fe as a function of the temperature. The sticking coefficient for a clean metal surface equals to unity according to Ref. [21] and it is s0 ¼ D0K2s0l2 (2pmkT)1/2 according to Ref. [6]. Although the estimation of s0 depends on the accuracy of the measurement of D0 and Ks0, the use of self-consistent s0 which corresponds to the experimental data of D0 and Ks0 is seems to be more reliable than assuming s ¼ 1 for a clean metal surface. According to Fig. 1, the
Pick&Sonnenberg’ model overestimates the recombination coefficient but the model [6] is in a good agreement with experiments. In contrast to Pick&Sonnenberg's conclusion [21] that there is no difference between molecular and atomic hydrogen interaction with solid in the case of non-activated sorption (Ec ¼ 0), we state that even in the case of Ec ¼ 0, the pre-exponential sticking coefficient, s0, can be considerably less than unity and enhances the plasma-driven uptake and permeation compared to the gas-driven ones that was confirmed experimentally [9,12]. Surface contamination (adlayers of carbon, oxygen or sulfur) decreases the recombination coefficient by increasing the surface barrier Ec (eq. (1)) as schematically shown in Fig. 2. Other factors, for example, crystallographic orientation of the surface, surface defects, etc. can also affect the value of the recombination coefficient (for details see Refs. [6,12]). Please, note that the increase or decrease of subsurface barrier Es to be higher/lower than the diffusion barrier Em or higher/lower than the surface barrier Ec does not influence the recombination coefficient (see eq. (1)). This is due to the fact that the rate of establishing a local equilibrium between chemisorbed hydrogen on the surface and absorbed hydrogen in the subsurface layer is much faster than the rates of H desorption and diffusion. Fig. 3 shows the recombination coefficient for H on W derived using the Pick&Sonnenberg model (eq. (1)) for different surface barriers, Ec, in comparison with model [6] (eq. (2)) for a clean W surface in the case of Ec ¼ 0 and literature data [26,27]. The surface barrier of Ec ¼ 0 of deuterium adsorption-desorption on/from W was found experimentally in Ref. [28]. Using Fraunfelder's solubility [29], the recombination coefficient for a clean W surface is extremely high indicating a rapid H desorption from W surface. The Pick&Sonnenberg's model results in the same Kr as the model [6] in the case of W. The recombination coefficient for a ‘dirty’ W surface (Ec > Qs) increases with increasing the temperature. Franzen's Kr corresponds to a contaminated surface with the surface barrier of Ec ¼ 1.2 eV. However, the Anderl's Kr disagrees with the theory. It does not match any Ec value. Hence, the underlying physics of the Anderl's recombination coefficient is unclear. This is the first evidence of the incorrectness of the Anderl's Kr. Anderl et al. [26] used 3 keV D3þ ions on foils of reduction rolled, powder metallurgy tungsten with a purity of 99.95% for deuterium (D) permeation experiment. From comparison of the experimental data with modelling, the recombination coefficient for deuterium on tungsten was found. Fig. 4 shows the experimental data of permeation flux in comparison with modelling performed in Ref. [26] and the present calculations. The following input
Fig. 1. Comparison of experimental [24,25] and theoretical [6,21] recombination coefficient for Ni and Fe.
Fig. 2. Schematic diagram of potential energy for hydrogen chemisorption depending on the presence of an impurity on the surface that increases the surface barrier Ec. H solution and diffusion are shown as well. Qs is the heat of solution and Em is the diffusion barrier.
simplify the mathematical task, it was proposed that the desorption rate is proportional to the square of the bulk concentration of hydrogen under the surface [20]. The proportionality coefficient was named the recombination coefficient, Kr. In Ref. [21], it was shown that Kr is proportional to the probability of H atom to overcome the surface barrier, Ec, Kr ¼ sm/K2s
(1)
Where KS ¼ Ks0 expð Qs =kTÞ is the solubility, pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffisffi ¼ s0 expð 2Ec =kTÞ is the sticking coefficient and m ¼ 1= 2pmkT (m is the mass of hydrogen molecule and k ¼ 1.38 1023 J/K is the Boltzmann constant). In general, to derive the recombination coefficient, the kinetic description of the elementary processes of hydrogen adsorption, absorption, molecular dissociation, and recombination was proposed by several authors. A critical review of the existing models was done in Ref. [22]. It was shown that Kr is proportional to the probability of H atom either to overcome surface, Ec, or subsurface, Es, barriers. However, probability of H desorption from the surface is higher or equals to probability of H desorption from the bulk, thus, the validity of the Pick&Sonnenberg’ recombination coefficient [21] was confirmed. The improved expression for the self-consistent recombination coefficient was derived in Ref. [6]. It was shown that the recombination coefficient on a clean metal surface is a function of diffusion pre-factor, D0, square of the jumping length, l, and the heat of solution, Qs, Kclean ¼ D0l2exp(2Qs/kT) (molecules m4/atoms2 s) r
(2)
76
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
Fig. 3. Recombination coefficient for H on W derived using the Pick&Sonnenberg model (eq. (1)) for different surface barriers, Ec, in comparison with model [6] (eq. (2)) and Anderl's [26] and Franzen's [27] recombination coefficients.
Fig. 5. Comparison of experimental TDS with calculations using Anderl's parameters [26] and the parameters from Refs. [2,7]. TDS was done in-situ in 5e10 min after the implantation was off. Fig. 4. Experimental permeation flux measured in Ref. [26] in comparison with modelling in [26] and the present model using parameters from Refs. [2,7].
parameters were used in Ref. [26]: Kr ¼ 1,3 1017exp(-0.84/kT), and de-trapping energy of D from defects (presumably vacancies) Et ¼ 1,34 eV with defect density of Wt ¼ 2 105 at. fr. In the present calculations, the following parameters are used: the recombination coefficient for a clean W surface (eq. (2)) of Kclean ¼ 3 1025/T1/2exp(2.06/kT) and two types of defects with r de-trapping energies of Et ¼ 0,85 eV and Et ¼ 1,45 eV. The structural defects corresponding to de-trapping energies of 0.85 and 1.45 eV are distributed homogeneously over entire W thickness with densities of Wt ¼ 8 104 at. fr. and Wt ¼ 1 105 at. fr., respectively. The ion-induced defects are distributed near the implantation side up to the depth of hundreds nanometers and several micrometer. The ion-induced defect density increases with fluence up to the maximum values of Wmax ¼ 1 103 at. fr. and Wmax ¼ 6 102 at. t t fr. for defects with de-trapping energies of 0.85 and 1.45 eV, respectively. For details, see Refs. [2,7]. In both the Anderl's and the present models, diffusivity and solubility were taking from Ref. [29]. The experimental data on the D permeation through W foil are well described by both the Anderl‘s parameters and the present parameters. However, a reliable set of parameters (Kr, Et, Wt) should describe simultaneously permeation, depth profile and thermal desorption spectroscopy (TDS) measurements at different experimental conditions. Fig. 5 shows experimental TDS [2] versus calculated TDS using the Anderl‘s parameters and the parameters from Refs. [2,7]. Calculations with parameters from Ref. [26] lead to
disagreement with experimental data at both 320 and 773 K. This is the second evidence of the incorrectness of the Anderl‘s recombination coefficient. The third proof of the incorrectness of the Anderl‘s recombination coefficient is that the simulation using this Kr fails to reproduce experimental D depth profiles. To reproduce the D influx into W, the authors of [13,14] suggested the reduced reflection coefficient of D from W surface to four orders of magnitude compared to experimental and calculated data [12,30]. It is trying to suggest that extra knowledge can be inserted into the definition of the reflection coefficient. Assuming the Anderl‘s recombination coefficient in their simulations, the authors of [13,14] significantly overestimates the D penetrated flux into the bulk of W resulting in the disagreement with experimental depth profile of D. The fast recombination on a clear W surface allows to resolve this inconsistence because the high recombination coefficient of D on the W surface leads to high re-emission rate. The experimental D depth profile can be obtained with a reflection coefficient closer to theoretical one using the Kr for a clean W surface (eq. (2)). Modelling a wide range of experimental data [1e3,7e9,11,12] shows no need of such non-physical assumption as the reduction of the reflection coefficient by several orders of magnitude to reproduce the experimental data of the D depth profile and TDS. Moreover, it was shown in Ref. [9] using a wide range of experimental data that if the surface barrier Ec is lower than 1 eV, the desorption rate is high and kinetics of deuterium release is limited by detrapping from defects rather than to be limited by surface effects. As a final remark, we consider the modelling of experimental
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
data of [2,7,8,31] using different set of parameters. In general, the model should describe a wide range of experimental data with one set of parameters in order to exclude the freedom in the modelling parameters. In other words, reliable set of parameters (Kr, Eit, Wit) should describe simultaneously permeation, depth profile and TDS experiments at different fluences, ion energies and temperatures. From comparison of calculations with experiments, fundamental parameters can be extracted and several peculiar effects of H behaviour in materials can be predicted. The best validation of the model assumptions is the experimental confirmation of the model predictions. Fig. 6 shows experimental thermal desorption spectroscopy (TDS) data measured in-situ only 5e10 min after ion implantation at experimental facility HSQ [2,7] and in a few weeks after D plasma exposure at the experimental setup PlaQ [32] in comparison with modelling. Please, note that the W samples were held on air for several weeks after exposure to D plasma at PlaQ prior to start TDS measurements. The model (a) predicts that the D retention decreases after a few days between implantation and TDS measurements and this reduction is mainly due to a decrease in the D retention at the first peak of TDS. This reduction was observed experimentally by comparing TDS data measured at HSQ immediately after implantation and in a few weeks of time delay between the D plasma exposure at the experimental setup PlaQ and TDS measurements (Fig. 6a). TDS can also be simulated using only intrinsic traps with energies of 0.9 eV and 1.2 eV with trap densities of Wt ¼ 103 at. fr. and Wt ¼ 6 104 at. fr., respectively (Fig. 6b). However, as it was shown in Ref. [7], the D depth profiles cannot be modelled using only natural traps. Additionally, the model with only natural traps predicts that the D retention decreases insignificantly within a few days of time delay between implantation and TDS measurements that is in contradiction with experimental data. Experimental TDS data can also be described using low recombination coefficient (eq. (1)) with the surface barrier of Ec ¼ 1.12 eV and de-trapping energies of 0.85 eV and 1.3 eV. Both the D depth profile and TDS can be simulated using the recombination coefficient for a clean W surface as well as the recombination coefficient for contaminated W surface with the surface barrier of Ec ¼ 1.12 eV. The decrease of the D retention during storage at ambient room temperature measured in subsequent experimental work [33] indicates the correctness of the models (a) and (c) which take into account the formation of ion-induced defects during implantation [2,7]. The de-trapping energies obtained by comparing the experiment with the simulation are somewhat different in models (a) and (c): lower de-trapping energy Et ¼ 1.3 eV corresponds to lower recombination coefficient (higher surface barrier). As it was reported in Ref. [9], although the D concentration and TDS can be simulated with both high and low surface barriers, the D uptake from the gas cannot be simulated using the same parameters as for ion implantation with low recombination coefficient but can be simulated with high Kr. This is again an argument in favor of the model (a) with high Kr. In the modelling above, calculations include all stages of experimental procedure, namely, (i) implantation of deuterium into tungsten from ion beam or plasma, (ii) cool down of the sample in the case if the implantation was carried out at elevated temperature, (iii) time delay between the end of implantation and the start of post-implantation measurements and (iv) heating ramp for TDS measurements. The same set of parameters has been used to calculate all of those stages. Some authors make suggestions about the D depth distribution to simulate experimental TDS separetly, namely, ignore the stages of (i) - (iii). Such assumptions can lead to incorrect simulation and interpretation of the experimental data.
77
Fig. 6. Experimental TDS data from Refs. [2,7,31,32] (lines with symbols) and modelling (solid&dashed lines) using different set of parameters: a) high Kr (eq. (2)) and intrinsic and ion-induced defects from Refs. [2,7] with de-trapping energies of 0.85 eV and 1.45 eV, b) high Kr (eq. (2)) and only intrinsic defects with de-trapping energies of 0.9 eV and 1.2 eV and c) low Kr (eq. (1)) using the surface barrier of Ec ¼ 1.12 eV and intrinsic and ion-induced defects from Refs. [2,7] with de-trapping energies of 0.85 eV and 1.3 eV. Experimental parameters are: temperature of W sample of 320 K during implantation, ion energy of 200 eV Dþ and fluences of about 1024 D/m2. Additional experimental data for the fluence of 1022 D/m2 are presented in (b) and (c). TDS was done in-situ only in 5e10 min after the ion beam was switched off at HSQ, meaning without the time delay, and in a few weeks after the plasma exposure at PlaQ. The dashed lines show the simulated TDS after 2 days between the implantation and TDS measurement in HSQ аssuming that the sample was not taken out from the implantation vacuum chamber.
78
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
For example, the authors of [10] used experimental depth profile obtained by SIMS to simulate TDS using the Anderl's Kr. They suggested about negligible amount of D in solution, namely that all D are trapped in defects after implantation of 500 eV Dþ in single crystal W (SCW) at 300 K up to a fluences of 1024 D/m2. The calculated depth profiles, using the defect density and de-trapping energies from Ref. [10] combined with the Anderl's Kr, after 5 min and one day between implantation and TDS measurements are shown in Fig. 7. The calculated depth profile in one day after implantation looks similar to experimental SIMS depth profile measured up to 40 nm, but the D retention is much higher compared to experimental data due to deep D retention beyond the implantation depth. In experiment, it is 4.45 1020 D/m2 (see Ref. [10]) but according to the calculations it is about 9 1021 D/m2 in 1.15 days after implantation. The total D retention is mainly defined by D in solution. Hence, the suggestion about negligible amount of D in solution in several days after implantation is incorrect using the Anderl's Kr. Using this D depth distribution after a few days of time delay, the calculated TDS is shown in Fig. 8. Because post-irradiation time of a few days prior to TDS is not sufficient to release most of D from solution, majority of D is released from solution sites during TDS. Thus, calculations lead to higher D retention than experiment and TDS peaks are in disagreement with experimental TDS peaks. In contrast, the authors of [10] used experimental D depth profile measured by SIMS up to 40 nm for the modelling of TDS data without modelling the D depth profile during and after implantation. Figs. 7 and 8 demonstrate that the set of parameters in Ref. [10] used only for simulation of experimental TDS cannot be used for simulation of the experimental D depth profile after implantation and, consequently, fails to simulate experimental TDS. This clearly show the importance to perform calculations including all stages of experimental procedure. However, using Kr for a clean W surface, calculations including all stages of experimental procedure are in agreement with TDS experiment as shown in Fig. 9. The de-trapping energies derived from comparison of modelling with experiment are Et ¼ 1.3 eV and Et ¼ 1.55 eV for high Kr (eq. (2)). In the case of using the Anderl's Kr, the de-trapping energies obtained in Ref. [10] are Et ¼ 1.07 eV and of Et ¼ 1.34 eV. Again, as it was mentioned above, lower Kr leads to lower values of de-trapping energies. It should be mentioned that the values of the de-trapping energies also depend on the prefactors in the trapping coefficient in the rate equations [4,5,9,10,15e20]. For example, in TMAP code the value of 1013 1/s is usually used. Whereas in the present code, the self-consistent prefactor is used as
Fig. 8. Calculated TDS using the defect density and de-trapping energies from Ref. [10] combined with the Anderl's Kr in 5 min and one day after implantation. Calculations include all stages of experiment, namely, the implantation, the time delay between the implantation and TDS measurement and TDS measurements itself.
Fig. 9. Calculated TDS using the Kclean and de-trapping energies of Et ¼ 1.3 eV and r Et ¼ 1.55 eV that is in agreement with experimental data measured in Ref. [10]. Total D retention obtained by integrating of the D desorption rate over the time is 4.96 1020 D/m2 at fluence of 1024 D/m2 that is in agreement with experiment.
n ¼ D0/l2
(3)
In the case of deuterium in W, the pre-factor is 2.4 1013 1/s (using the Fraunfelder's diffusivity [29] and assuming the diffusion of D through tetrahedral interstitials in bcc W) that is slightly different from usually used value of 1013 1/s. This leads to lower detrapping energies compared to the case of use of 1013 1/s.
3. Conclusions
Fig. 7. Calculated depth profiles using the defect density and de-trapping energies from [10] combined with the Anderl's Kr after 5 min and one day between implantation and TDS measurements.
The recombination coefficient is an important parameter to model hydrogen-metal interaction. It is responsible for hydrogen desorption from the metal surface and, therefore, affect significantly on the hydrogen penetration into the metal, accumulation and permeation. In the present work, it is shown that the Anderls' recombination coefficient, often used in the simulation of hydrogen-tungsten interaction, does not satisfy the theory of hydrogen adsorption/desorption on a W surface. In addition, using the Anderls’ recombination coefficient in the simulations, the authors significantly overestimates the penetrated flux into the bulk
O.V. Ogorodnikova / Journal of Nuclear Materials 522 (2019) 74e79
of W which leads to disagreement with experiment. Experimental data are well modelled using the recombination coefficient for a clean W surface without suggesting extra knowledge into the definition of the reflection coefficient or other physical values. Moreover, it is shown that the experimental data can be also modelled using the Pick&Sonnenberg recombination coefficient for a contaminated W surface. Contaminations on W surface or the presence of a surface barrier result in a decrease of the de-trapping energy of D with a defect in the modelling of TDS data. Taking into account that reliable set of parameters (Kr, Et, Wt) should describe simultaneously permeation, depth profile and TDS experiments at different experimental conditions of hydrogen-W interaction, it was shown that laboratory experiments can be well simulated using a high recombination coefficient that give us confidence in the correctness of high recombination of hydrogen on W surface. References [1] O.V. Ogorodnikova, J. Nucl. Mater. 390e391 (2009) 651. [2] O. Ogorodnikova, J. Roth, M. Mayer, Deuterium retention in tungsten in dependence of the surface conditions, J. Nucl. Mater. 34 (313e316) (2003) 469. [3] S.M. Myers, P.M. Richards, W.R. Wampler, F. Besenbacher, J. Nucl. Mater. 165 (1989) 9. [4] O.V. Ogorodnikova, M.A. Fuetterer, E. Serra, G. Benamati, J.-F. Salavy, G. Aiello, J. Nucl. Mater. 273 (1999) 66. [5] O.V. Ogorodnikova, Trapping effect in hydrogen retention in metals, in: A. Hassanein (Ed.), Hydrogen and Helium Recycling at Plasma Facing Materials, NATO Science Series vol. 54, Kluwer Academic Publishers, 2001, p. 7. [6] O.V. Ogorodnikova, J. Nucl. Mater. 277 (2000) 130. [7] O.V. Ogorodnikova, J. Roth, M. Mayer, J. Appl. Phys. 103 (2008) 034902. [8] O.V. Ogorodnikova, V. Gann, J. Nucl. Mater. 460 (2015) 60. [9] O.V. Ogorodnikova, J. Appl. Phys. 118 (2015) 074902. [10] M. Poon, A. Haasz, J. Davis, J. Nucl. Mater. 374 (2008) 390.
79
[11] O.V. Ogorodnikova, K. Sugyama, J. Nucl. Mater. 442 (2013) 518. [12] O.V. Ogorodnikova, S. Markelj, U. von Toussaint, J. Appl. Phys. 119 (2016) 054901. [13] M. Baldwin, R. Doerner, Nucl. Fusion 57 (2017) 076031. [14] M. Simmonds, J. Yu, Y. Wang, M. Baldwin, R. Doerner, G. Tynan, J. Nucl. Mater. 508 (2018) 472. [15] A. McNabb, P.K. Foster, Trans. Metal. Soc. AIME 227 (1963) 618. [16] K.L. Wilson, M.I. Baskes, J. Nucl. Mater. 76e77 (1978) 291. [17] S.M. Myers, S.T. Picraux, R.E. Stoltz, J. Appl. Phys. 50 (1979) 5710. [18] B.L. Doyle, D.K. Brice, Radiat. Eff. 89 (1985) 21. [19] G.R. Longhurst, R.A. Andrel, T.J. Dolan, M.J. Mulock, Fusion Technol. 28 (3) (1995) 1217. [20] I. Ali-Khan, K.J. Dietz, F.G. Waelbroeck, P. Wienhold, J. Nucl. Mater. 76e78 (1978) 337. [21] M.A. Pick, K. Sonnenberg, J. Nucl. Mater. 131 (1985) 208. [22] (a) A.A. Pisarev, O.V. Ogorodnikova, J. Nucl. Mater 248 (1997) 52; (b) O.V. Ogorodnikova, Simulation of Desorption and Retention of Hydrogen in Plasma - Solid Interaction (PhD thesis), Moscow Engineering Physics Institute, Moscow, 1997. [23] J.B. Taylor, I. Langmuir, Phys. Rev. 44 (1933) 423. [24] W.R. Wampler, J. Nucl. Mater. 145 (1987) 313. [25] K. Yamaguchi, T. Namba, M. Yamawaki, J. Nucl. Sci. Technol. 24 (11) (1987) 915. [26] R.A. Anderl, D.F. Holland, G.R. Longhurst, R.J. Pawelko, C.L. Trybus, C.H. Sellers, Fusion Technol. 21 (1992) 745. [27] P. Franzen, C. Garcia-Rosales, H. Plank, V.Kh Alimov, J. Nucl. Mater. (1997) 241e243, 1082. [28] P.W. Tamm, L.D. Schmidt, J. Chem. Phys. 55 (N9) (1971). [29] R. Frauenfelder, J. Vac. Sci. Technol. 6 (1969) 388. [30] W. Eckstein, J.P. Biersack, J. Appl. Phys. A38 (1985) 123. W. Eckstein, IPP 9/132, 2002. [31] (a) O. Ogorodnikova, ITPA SOL/DIV Garching, 2007; (b) O.V. Ogorodnikova, Modeling of hydrogen retention and permeation in tungsten, in: 9th International Workshop on Hydrogen Isotopes in Fusion Reactor Materials, Salamanca, Spain, June 2008. [32] O.V. Ogorodnikova, T. Schwarz-Selinger, K. Sugiyama, T. Dürbeck, W. Jacob, Phys. Scripta T138 (2009) 014053. [33] K.A. Moshkunov, K. Schmid, M. Mayer, V.A. Kurnaev, Yu M. Gasparyan, J. Nucl. Mater. 404 (2010) 174.