Hydrogen retention in tungsten
The experimental database concerning hydrogen retention in tungsten is rather extended as well as the scattering of the results. However, calculation of the hy-drogen inventory which is expected to accumulate in a reactor wall must be based on a good understanding of the physical processes governing hydrogen diffusion, trapping mechanisms and its release from the material. The aim of this section is to provide an introduction to the fundamental processes involved and existing ex-perimental data on diffusion, permeation and solubility, and trapping of hydrogen in tungsten. In figure 2.1, the main processes involved in recycling of hydrogen at the wall of a fusion device, are schematically depicted. Hydrogen atoms may get adsorbed in surface and sub-surface layers and subsequently get trapped in vacancies, grain boundaries, dislocations or interstitial sites.
Figure 2.1: Main processes involved in retention and recycling of hydrogen at the wall of a fusion reactor. Hydrogen atom sites in the lattice: (a) Surface adsorption, (b) sub-surface layers adsorption, (c) Interstitial, (e, d) Vacancies, (f) Grain boundary, (g) Dislocation The exhaust of high heat and particle fluxes to the plasma wetted areas erodes the material via sputtering or may cause material loss due to sublimation or melt-ing. A fraction of the eroded particles, after being ejected from the wall, may become ionized, enter the plasma and return back to the wall along the magnetic field lines, enabling the recycling process. In general, the particle bombardment process may bring along various scenarios . The impinging particles can be backscattered after the collision to the surface or implanted near the surface and released as thermal particles (usually at relatively low surface binding energy). If their energy is relatively high, they may implant deeper in the material and get released at a later time. Alternatively, they can get either deposited on the surface or eroded.
Physical sputtering occurs when energetic projectiles bombard the target and eject atoms by momentum transfer. The impinging particles transfer a fraction of their energy to the lattice, causing a collision cascade. If the recoil energy is higher than the surface binding energy, atoms may get ejected from the solid. The main parameter characterizing the physical sputtering is the sputtering yield which represents the number of sputtered particles per incident projectile. The process employs a “threshold energy” above which, sputtering is feasible: Eth = Es= (1 ). Es is the surface binding energy and is the fraction of energy transferred to the lattice after the collision. The factor depends on the mass ratio of the target m2 and projectile m1 as: = 4m1m2=(m1 + m2)2 . It is evident that the sputtering yield is related to the mass ratio of the target and projectile; it reaches its maximum for alike particle collisions for which the energy transfer is most efficient. For light impinging elements where the mass ratio of target atom to projectile ion is very high, the energy transfer is less efficient, leading to a reflection of the particle from the surface. Hydrogen sputtering of tungsten has a high threshold energy due to the large mass difference ( 1 u vs. 184 u). The factor calculated for hydrogen and its isotopes, yields: (H!W ) = 0:022, (D!W ) = 0:043, (T !W ) = 0:063. Hence, the sputtering threshold energy of i.e deuterium on tungsten is about 200 eV up to keV energy, well above the energy range expected in the divertor region .
A fraction of the incident particles will be reflected from the surface back into the plasma depending on their energy and type of material. The fraction of par-ticles which enter the implantation zone can get trapped in the crystallographic defects which are either intrinsic or generated from the neutron or other plasma species irradiation. Once the solubility limit is reached, trapped particles may ei-ther recombine and leave the surface or diffuse further in the bulk material, fill the existing traps and even diffuse deeper to the cooling structure. Hydrogen will reach either of the surfaces and recombine if the temperature or the recombination rate coefficient are sufficiently high.
Adsorption (on-surface) and absorption (in-bulk) are the principal states of hydrogen in the solid matter. When the diatomic H2 molecule gets in contact with the surface of a transition metal, it has the tendency to dissociate and create strong atomic-surface interaction. Energetically, this occurs when the binding en-ergy of atomic hydrogen with the surface is higher than the dissociation heat of the molecule. Adsorption is strongly affected by the presence of impurities and adatoms (loosely bound atoms to the metal surface) on the surface as they may alter the adsorption conditions or interfere with the dissociation sites .
Hydrogen diffuses from the implantation region to the bulk and occupies dif-ferent sites in the lattice, typically at the grain boundaries, vacancies, interstitial sites and dislocations, as depicted schematically in figure 2.1. In tungsten, which has a body-centered cubic lattice (bcc), interstitial hydrogen favors the tetrahedric sites with a jumping activation energy 0.4 eV between the two sites .
In figure 2.2, a qualitative diagram of potential energy of hydrogen transport in tungsten is given, which is an endothermic material for hydrogen intake. From this diagram can be seen that once the H2 molecule dissociates at the surface, it goes through an energy barrier ESB to enter the bulk material. Energetic particles however, don’t account on the implantation profile . Thermal dif-fusion of “free” hydrogen in tungsten is often described by the relation: D 107 exp(E diff =kBT ) (m2s1 ) where Ediff is the diffusion activation energy and T is the temperature. Traps are generated by lattice imperfections, impuri-ties, grain boundaries and hydrogen atoms can get released from such traps if they overcome the Etr energy barrier (de-trapping rate: dt 1013exp(E tr=kBT ) (s1 )).
Hydrogen diffuses very fast in tungsten and it desorbs even at room temperature from the metal. Diffusion rate coefficients have been derived from various ex-periments and modeling but they are largely scattered and the most reliable to be used are the Frauenfelder’s results . He measured the desorption rate of hy-drogen from loaded tungsten wires at temperatures 1200-2400 K and proposed the diffusion coefficient: D = 4:1 107 exp(0:39eV =k BT ) m2s1 . At such high temperature, diffusion is not affected by trapping and surface recombination is insignificant. Causey  recommends using the activation energy -0.39 eV and pre-exponential factor 4:1 107 m2s1  for the diffusion coefficient. How-ever, density functional theory (DFT) calculations suggest faster diffusion with an activation energy of 0.2 eV and pre-exponential factor 1:9 107 m2s1 .
The extrapolation of Frauenfelder’s data have been used at lower tempera-tures. In his review on hydrogen retention in tungsten, Tanabe  adds the re-cent results on tritium tracer technique from Ikeda et al.  which fall on Frauen-felder’s extrapolation to lower temperatures (see figure 2.3). They suggested an upper limit for the diffusion, relevant in the temperature range 250-2500 K: D = (3:8 0:4) 107 exp(0:4 0:015eV =kBT ) m2s1 . The fact that hydrogen diffuses out of tungsten at any temperature, starting from the room temperature, indicates that the experimental data on tungsten mobility could be strongly af-fected by the sample treatment and time lag between the loading and desorption processes.
In figure 2.4, permeation rate coefficients for hydrogen in tungsten, are plotted (  and references herein). The suggested activation energy for permeation from Ikeda et al. , derived from the tritium tracer technique, is 65 kJ/mol ( 0.67 eV) and the pre-exponential factor is (1:21 0:24) 105 molm1 s1 . This value is in a good agreement with Frauenfelder’s data when extrapolated to higher temperatures. Frauenfelder’s data for permeation suggest an activation energy of 1-1.4 eV in the high temperature range but it is not relevant when extrapolated to lower temperatures where trapping and surface effects become dominant.
Modeling of the thermal desorption spectroscopy data
Thermal desorption spectroscopy (TDS) is a commonly used method to evaluate the total gas retention in a metal, as well as desorption activation energies. Typi-cally, the sample is heated in vacuum at a certain temperature ramp rate, and the released gas is detected by a mass-spectrometer. Before gas atoms are detected by the mass-spectrometer, they must overcome the de-trapping energy barrier in the metal, diffuse to the surface and possibly get re-trapped on the way out, and finally leave the surface after recombining to molecules. The measured desorption flux is usually plotted either as a function of time or as a function of the sample tem-perature. The shape, position and number of peaks of such a TDS profile depend on the interplay of all above-listed process and only in rare cases can be deduced, based solely on the knowledge of the dominant process.
De-trapping of hydrogen atoms from trapping sites in a metal is a thermally ac-tivated process, so the de-trapping rate is typically described by an Arrhenius type equation, e.g. as a product of a temperature independent pre-exponential factor, of-ten referred as the attempt frequency, and the Boltzmann factor exp(E a=kBT ), with an activation energy Ea. In the publication from A.M. de Jong and J.W. Niemantsverdriet  it is demonstrated that the derivation of the activation en-ergy and the pre-exponential factor based on the analysis of the peak tempera-ture, peak width and shape for a single TDS profile, performs poorly. The rea-son for this is the release of hydrogen from the depth of the material and its diffusion and re-trapping during desorption. More reliable data on the activa-tion energy and pre-exponential factor may be derived from the shift of the TDS peak temperature, when several desorption measurements on equal samples are performed at different heating rates (T (t) = T0 + t). Considering a linear heating ramp with Tmax at maximal desorption and the Arrhenius relation for the desorption flux, implying that desorption is limited by de-trapping, yields: ln( =Tmax2) = ln(kBA=Ea) Ea=kBTmax. Ea is the activation energy and A is the pre-exponential factor. The activation energy would therefore be the slope of the graph =Tmax2 plotted as a function of 1=Tmax in a semi-log scale . Also in this case, the applicability of the method is limited as it depends on the surface recombination and re-trapping processes . The relevance of such measure-ments is, however, the generation of additional data for modeling and reduction of the number of the free parameters.
In order to simulate the implantation and desorption processes, diffusion and trapping of hydrogen in tungsten are usually described with a set of 1D rate equa-tions . One partial differential equation that describes the time evolution of the solute hydrogen concentration in tungsten is given in 2.2, as a combination of a diffusion term, an implantation source and trapping-detrapping reactions: @ sol(x; t) @ D(T) @ sol(x; t) N @ trapped(x; t) = X i + source(x; t) @t @x @x i=1 @t.
Plasma loading conditions expected in the ITER divertor
In ITER, the divertor plasma will contain large amounts of hydrogen isotopes (D, T), He and impurities with flux densities and energies, varying by several orders of magnitude along the divertor surface. Exposed to such conditions, tungsten may undergo erosion, cracking and other surface modifications affecting its thermal and mechanical properties. Another concern is the retention of implanted radioactive fuel atoms (tritium) in the material surface and their diffusion through the bulk. Therefore, detailed knowledge on the plasma parameters at the plasma edge and the impact on the plasma-material interaction is required.
Figure 2.8: Plasma profile (temperature, density, particle and heat flux) along the inner and outer ITER divertor for a semi-detached plasma scenario (highly radiative divertor operation ). Low and high flux notations represent the deuterium particle fluxes selected to be studied in the experiments.
Plasma parameters as modeled with B2-EIRENE code on the ITER divertor, where the particle and heat fluxes are expected to be critical for the plasma fac-ing components, are plotted in figure 2.8. Electron temperature, density, particle and heat fluxes along the inner and outer ITER divertor are simulated for a semidetached plasma scenario with 100 MW power entering the scrape-of-layer . As seen from the graph, the particle fluxes will vary by several orders of magni-tude, reaching up to 1024 m2 s1 . The question raised, after a large amount of investigations on the deuterium retention, is related to its impact on the particle flux and temperature. It was found that the total deuterium retention has a maximum in the temperature range 400-600 K at fluxes above 1021 m2 s1  (see figure 2.11). The aim of the present work is to distinguish the role of the particle flux on deuterium retention and surface morphology on tungsten when the fluence is kept constant. In the figure 2.8, low and high flux notations represent the deuterium particle fluxes which are selected to be studied in the experiments, namely 1021 and 1024 m2 s1 . The selected ion fluence to be studied is 1026 m2 due to the large existing database and possibility of comparing the results and the relevance to the fluence accumulated after one ITER plasma discharge. Another reason is the feasibility to achieve this fluence in a linear plasma device from the technical point of view. Simulations based on the thermo-hydraulic calculations (RACLETTE code) for He and DT plasma operations , predict a temperature range 600-1000 K for major part of the profiles along the outer divertor, coinciding with the temper-ature of bubble layer formation. In figure 2.9 the surface temperature variation along the outer target at ITER divertor during He and DT phase of operation, is plotted. In addition to the surface modifications, also deuterium retention has a strong dependence on the exposure temperature therefore the selected temperature range in the present experiments is 500-1170 K.
Table of contents :
2 Basic mechanisms of plasma-material interaction
2.1 Hydrogen retention in tungsten
2.1.1 Hydrogen mobility
2.1.2 Trapping and surface effects
2.1.3 Modeling of the thermal desorption spectroscopy data
2.2 Mechanisms for blister formation
2.3 Plasma loading conditions expected in the ITER divertor
2.4 Plasma loading impact on surface modifications and retention .
2.4.1 Ion fluence and surface temperature
2.4.2 Material microstructure
2.4.3 Combined He/D exposure
2.4.4 Transient heat and particle loads
3 Experimental setup and analysis techniques
3.1 Linear plasma devices
3.1.2 PSI-2 .
3.1.3 PISCES-A .
3.2 Analysis techniques
3.2.1 Electron microscopy
3.2.3 Secondary Ion Mass Spectrometry (SIMS)
3.2.4 Nuclear Reaction Analysis (NRA)
3.2.5 Thermal Desorption Spectroscopy (TDS)
3.3 Sample preparation
4 Experimental results and discussion
4.1 Deuterium plasma exposure
4.1.1 Small Grain Tungsten (SGW)
4.1.2 Large Grain Tungsten (LGW)
4.1.3 Recrystallized Tungsten (RecW)
4.1.4 Single Crystal Tungsten (SCW)
4.1.5 Summary and modeling results
4.2 Mixed D/He plasma exposure of recrystallized tungsten
4.3 He and H transient heat and particle loads on polycrystalline tungsten
5 Conclusions and outlook
A Material selection
A.1 Chemical content and material specifications of tungsten bars
B D experiments
B.1 TDS profiles of tungsten samples after exposure to pure D plasma
C He/H experiments
C.1 Surface analysis of Mo-deposited tungsten samples after exposure to H and He plasma