A critical review of experiments on deuterium retention in displacement-damaged tungsten as function of damaging dose

Experimental results from the literature on the evolution of deuterium retention in displacement-damaged tungsten as a function of damaging dose are presented. Except for a few outliers, retention is generally found to increase with the presence of displacement damage. However, total retention results scatter by three orders of magnitude for similar exposure temperatures and are difficult to compare, because they depend on experiment-specific parameters such as the irradiation energy used to produce the displacement damage or the deuterium exposure parameters such as fluence. Even local deuterium concentration measurements were found to scatter by more than one order of magnitude. An experimental methodology is proposed that allows robust conclusions about the evolution of deuterium retention with damage dose and the results are discussed in detail. Recrystallized tungsten is irradiated with 20.3 MeV self-ions at room temperature with different damage doses ranging from 0.001 to 2.3 displacements per atom. The defects are then decorated with a low flux, low-energy deuterium plasma at 450 K sample temperature. 3He Nuclear Reaction Analysis (NRA) shows that the deuterium concentration levels off from the linear increase already at very low damage dose of about 0.005 dpa. At a damage dose of 0.23 dpa a maximum deuterium concentration of about 1.4 at% is reached. Thermal Desorption Spectroscopy (TDS) shows that with damage increasing above 0.005 dpa, the overall shape of the desorption spectra does not change substantially, only their intensities increase. Total amounts derived from TDS are in quantitative agreement with results from 3He-NRA. Experimental results following this methodology also agree quantitatively with very recent parameter-free modeling of damage evolution.


Introduction
Among many other favorable properties of tungsten (W), its low intrinsic fuel retention makes it a promising candidate as a plasma-facing material for ITER as well as for a future demonstration reactor [1][2][3][4][5].However, during operation, defects will develop in the tungsten lattice that will trap hydrogen isotopes (HI), thereby increasing fuel retention.For present day confinement devices, this effect is small because low-energy ions and neutrals from the plasma only affect the very surface.Details of the interaction of hydrogen isotopes with tungsten can be found in the reviews by Causey [6], Skinner et al [7], Tanabe [8] and Roth and Schmid [9].They were all written in the light of the 700 g tritium regulatory limit for ITER.Recent calculations show that tritium self-sufficiency in a future fusion reactor with a 'burning' D-T plasma, will place a much more tighter limit on tritium loss than this regulatory limit for ITER [10,11].At the time these reviews were compiled, tungsten was only foreseen for parts of the divertor, and tritium loss in tungsten was considered to be small as compared to tritium co-deposition with carbon or beryllium.Current DEMO concepts foresee that the entire divertor as well as the main wall plasma-facing components should be protected with tungsten armor.Thus, the amount of tungsten in a future DEMO is much larger than in these early ITER considerations.For future nuclear devices increased retention is expected not only to take place at the very surface of the plasma-facing component, but throughout the whole bulk as a consequence of the neutron irradiation.In 2009 a panel of experts concluded that 'The current situation is therefore that there is a possibility of a large contribution to tritium inventory from trapping at neutron damage in tungsten to large depths, but also a large uncertainty whether this will actually occur since it has not been experimentally verified.Experiments to resolve this uncertainty should be a high priority.'[12].In the following years, several experimental studies tried to answer the question, whether the retention of hydrogen isotopes increases with radiation damage and, if so, how it depends on the dose.Since no intense neutron source with the expected energy spectrum was available, fission neutron irradiation and high energy ion implantation were used to mimic the aspects of the interaction of neutrons with tungsten [13,14].Since then, a plethora of experimental and theoretical studies were conducted to address the issue of displacement damage creation and evolution, transmutation, helium accumulation, and the consequences on the material properties such as hydrogen isotope retention, but also thermal conductivity and mechanical properties [15][16][17][18][19].This contribution critically reviews the existing data for a very fundamental aspect of the interaction of fusion neutrons with tungsten: the evolution of displacement damage with damage dose and its consequences on hydrogen isotope retention.
Early resistivity measurements showed a saturation behavior of damage with dose for many metals when irradiated at low temperatures.This was explained by simple geometric considerations of overlapping cascades of immobile atomic defects [20].The saturation of defect concentration in heavily damaged materials is an important issue in materials science in general.In the case of tungsten as a plasma-facing material, this implies an upper limit for tritium retention and is thus of great importance, e.g. for the licensing of future reactors.Very recent parameter-free calculations predict a saturation behavior of displacement damage at very low damage doses around 0.1 dpa (displacement per atom) [21].So far, these calculations are limited to low temperatures.However, in a future reactor, tungsten will be operated at elevated temperatures, and displacement damage is known to evolve with temperature [22].It is well known that atomic displacements due to energetic particle irradiation can produce a large variety of microstructural changes that do not lead to saturation when irradiation is performed at elevated temperatures, such as void growth [23].
The retention of hydrogen isotopes in tungsten is closely related to the presence of defects.Therefore, it seems obvious that the retention of hydrogen isotopes should closely follow the evolution of damage with the dose.However, hydrogen isotopes retention is a complicated phenomenon because it is the result of many different parameters such as the material grade (structure and impurity level) [24], the material temperature [25], surface condition [26], and it depends critically on the incoming particle flux, its energy and composition as hydrogen bubble formation occurs above a certain solute concentration [27,28].Eventually, macroscopic defects, such as blisters, develop [24,[29][30][31][32].Despite decades of research with significant progress, a quantitative description of many aspects is still lacking.Because of this complicated dependence of both phenomena-the evolution of displacement damage with dose and temperature and its influence on hydrogen isotope retentionit is not obvious that a clear conclusion can be drawn from hydrogen isotope retention measurements on damage evolution and vice versa.This article summarizes experimental results from different authors who studied deliberately the evolution of deuterium (D) retention with damage dose and discusses the differences and possible reasons for them.
The article is structured as follows: First, a number of experimental results from the literature on the evolution of deuterium retention with damage dose in tungsten are presented, discussed and compared with each other.From this analysis, conclusions are drawn for an optimal methodology that allows robust conclusions on the evolution of displacement damage with dose and the possible saturation behavior.Next, the results of an unpublished dataset from 2012 are described in detail where this methodology was applied to show its applicability and limitations.Finally, a summary and conclusions are provided.

Literature review 2.1. Selection criteria
To mimic the displacement damage that neutrons will cause in the tungsten matrix, fission neutron and keV to MeV ion irradiation experiments have been used.Both of them have their advantages and limitations.Investigations with fission neutrons are laborious, time consuming and expensive, and fission neutrons do not resemble the energy spectrum of fusion neutrons [15].In addition, they typically do not allow for significant changes in irradiation conditions, which would be necessary to study the fundamentals of damage creation and evolution.They also do not allow, for example, to study the mutual interplay between tritium and deuterium with the displacement damage caused by the neutrons.Ion beam radiation is in principle able to overcome these limitations.Single beam and multiple beam irradiations have been successfully applied to simulate individual aspects of the interplay between the displacement damage caused by the neutrons and, e.g., the presence of other species such as hydrogen isotopes and helium [22,33,34].In addition, studies using ion irradiation are much easier to perform and much faster than experiments with fission neutrons.Heavy ions are often used because they allow for high damage rates on the order of dpa per hour and typically do not activate the material.However, it must be kept in mind that the orders of magnitude faster damage rates can also affect the observed result.Nevertheless, ions allow systematic variation of parameters such as the energy of the primary knock atom (PKA) or the irradiation temperature.However, their interaction is limited to a few micrometers from the surface which limits the diagnostic possibilities.Tungsten self-implantation is expected to be the most promising method to produce defects near the surface, as it does not alter the composition of the target.In addition, it produces dense collision cascades and the PKA energy spectrum is closer to those of neutron irradiation than it is for light ions [22,35].Nevertheless, the maximum PKA energy is much larger than that of fusion neutron irradiation.While a 14 MeV neutron can transfer at most 300 keV, self-ions can transfer up to their initial kinetic energy in a head-on collision.Typical energies used for W ions range from a few to several tens of MeV.Thus, the maximum PKA energies for self-ion irradiation are orders of magnitude larger than those in a fusion environment.However, so-called cascade splitting, which occurs above a PKA energy of 160 keV for tungsten, seems to extenuate this concern [35][36][37].
Deuterium or tritium retention has been studied in fission-neutron and ion-irradiated tungsten.This review is limited to ion irradiation experiments for two reasons: First, there is much more ion irradiation data available that can be compared with each other.Second, ion irradiation can easily be performed at low temperatures.Above a certain temperature, vacancies become mobile and displacement damage is expected to evolve [38].Heikinheimo et al [39] observed monovacancy recovery in tungsten starting at 550 K. Unfortunately, state-ofthe-art modeling of the microstructural evolution of radiation damage, including thermal effects, such as defect diffusion, is only possible for simplified defect structures [40,41].Thus, the evolution of a realistic microstructure at elevated temperatures and large doses, as well as the thermal evolution of heavily damaged materials during post-irradiation annealing, cannot yet be simulated.If tungsten is irradiated at sufficiently low temperatures where vacancies are immobile, it should be possible to compare the results with state-of-the-art modeling [21].In addition, at such low temperatures, dose rate effects should also play no or at least a minor role.Therefore, data sets were selected for this comparison where damage was created by ion irradiation close to room temperature.Similarly, only datasets where deuterium exposure was performed well below a sample temperature of 550 K were selected in order to minimize damage evolution and/or annealing during the deuterium loading.
Figure 1 shows deuterium retention results as a function of the damaging dose from seven different publications, presented on a double logarithmic scale.Overall, deuterium retention varies by nearly three orders of magnitude.Details of the damaging parameters are summarized in table 1 and the deuterium loading conditions are summarized in table 2. It is important to note that these publications used different procedures and various parameters were applied to calculate the damage dose from the ion fluence, as listed in table 1.A discussion of how to compare the reported dpa values with each other is provided in section 5. Here, the data are discussed with the originally reported dpa values for better traceability.
In the dataset of Hollingsworth et al [56] no conclusive dependence of deuterium retention on damage dose can be seen from their TDS data of 2 MeV W-irradiated samples after low fluence deuterium ion irradiation with 400 eV at 320 K (red circles).The deuterium retention in the undamaged, recrystallized tungsten was even greater than in the sample irradiated with 2 MeV W-ions to 1 dpa [56].In addition, the samples showed significant outgassing during storage at room temperature and the total retention was much lower than in the other data found in the literature.Similarly, Wampler and Doerner [42] saw no dependence of the deuterium areal density derived from 3 He-NRA on the damage dose for a dataset in which 12 MeV Si-irradiated tungsten was exposed to a medium-flux deuterium plasma at 314 K with an ion energy of 200 eV (olive open triangles) [42].However, at a target temperature of 473 K they found more retention and a clear dependence on the damage dose (solid olive triangles) [42].The sample with a peak damage of 0.6 dpa had a factor of 2.6 larger retention than the sample with 0.006 dpa.However, the undamaged reference sample had the same retention as the 0.006 dpa sample.Tyburska et al [44] reported that tungsten irradiated with 5.5 MeV W-ions to 1 dpa showed a factor of six higher retention after exposure to a medium flux deuterium plasma at 470 K and 38 eV ion energy as compared with an undamaged sample exposed to the same plasma.In this case, a clear increase in deuterium areal density derived from 3 He-NRA with damage dose was observed for a set of four samples (filled blue triangles).However, this was not observed for samples exposed to a low-flux ion beam between 320 and 350 K. Deuterium retention was even lower for the sample with the higher damage dose (open blue triangles in figure 1).Nevertheless, the authors claim a saturation behavior around 0.4 dpa from this study.'t Hoen et al [47] also claim to observe a saturation behavior, but at a lower damage dose of about 0.2 dpa.Their tungsten samples were irradiated with 10.8 MeV W-ions and cumulatively exposed to short pulses from a high flux linear plasma device (purple triangles) [47].The temperature across the sample varied between 470 and 520 K.The amount of deuterium derived from TDS varied by only 20% between the lowest (0.04 dpa) and the highest (0.4 dpa) damage doses applied.The retention in the undamaged sample was much lower than in any of the other data sets shown, being a factor of 70 less than in the 0.4 dpa sample.This is surprising since a high flux deuterium plasma Table 1.Damaging ion energy, species, and details for the damage calculations for the references of figures 1, 2, and 8. 'FC' stands for the 'Detailed Calculation with Full Damage Cascades' option, 'KP' stands for the 'quick calculation of damage' Kinchin-Pease option in SRIM [62].The order follows the publication date.The conversion factor f (for discussion see section 5) is listed with which the stated dpa value of the reference has to be divided in order to be compared with the SRIM 'Quick calculation of damage' Kinchin-Pease option with a displacement threshold energy E D = 90 eV and a lattice binding energy E L = 0 eV, as proposed by Stoller et al [63].was used, which can potentially create defects during the exposure [61].It is possible that defect creation was minimized due to the floating target arrangement and thus low deuterium ion energy.Oya et al [54] also saw a clear increase in retention with damage dose for their 6 MeV Fe-irradiated tungsten after 1 keV D 2 + low-flux ion implantation at 300 K (black circles).Even the lowest damage dose of 0.0003 dpa lead to an increase in retention determined by TDS by more than a factor of two.A further increase by a factor of 4.6 was reported for the highest dose of 1 dpa [54].They claim saturation above 0.1 dpa.Also with TDS, Shimada et al [48] found a clear increase of the total deuterium amount for 2.8 MeV Fe-irradiated tungsten with a stated damage dose of up to 3 dpa after exposure to a medium-flux deuterium plasma at 470 K (filled orange circles) and an ion energy of 100 eV.A slightly different dependence with damage dose was found for 20 MeV W-ion irradiated tungsten for the same deuterium exposures (open orange circles).No evidence for saturation was observed.Unfortunately, no data were presented for an undamaged, pristine sample to check for the damage caused by the plasma exposure itself.Möller et al [55] applied a focussed proton beam with 2.96 MeV to produce multiple small irradiation spots on the same sample with different doses and a relatively flat damage profile on the very same sample.The proton irradiation was performed at 320 K and the exposure to a medium flux deuterium plasma was performed at 420 K with an ion energy of about 40 eV.They observed a clear increase in retention with 3 He-NRA of more than one order of magnitude between undamaged samples and proton-irradiated samples.Two different data sets with multiple irradiation spots of variable dpa (maximum stated damage dose 0.65 dpa) are shown in figure 1 (open and filled green diamonds).The authors claim a saturation behavior at 0.2 dpa, but no such behavior is observed when the data are plotted on a double logarithmic scale as shown in figure 1.In summary, with the exception of two data sets where deuterium exposure was performed close to room temperature and at low deuterium fluences (Oya et al [54] and Hollingsworth et al [56]), a clear increase in total deuterium retention is observed for displacement-damaged tungsten as a function of damage dose.However, while all studies where deuterium exposure was conducted at elevated temperatures observed a substantial increase in deuterium retention compared with the undamaged tungsten, no conclusive results were derived regarding the actual dependence of deuterium retention as a function of the damage dose.Some of the authors observe a reduced increase at high damage levels and conclude from this a saturation behavior.Different damage doses are reported for this transition.

Reference
Looking at all the data together, as presented in figure 1, the increase follows the dose with a power law with an exponent ranging between 0.15 and 0.25.Absolute retention values vary by almost three orders of magnitude, despite the fact that only data sets were selected where very similar temperatures were applied during the displacement damage creation (room temperature and slightly above), as well as during the deuterium loading (mostly 470 K).The results seem to be hardly comparable.This is because damaging of different tungsten grades was performed with different ion species and with different energies resulting in different thicknesses of the damaged region.Table 1 summarizes the damaging ion species and energy and the applied method and paramteres used for the damage calculations.The deuterium energy, flux, fluence, exposure temperature and applied analysis methods are listed in table 2. It is important to emphasize that it cannot be concluded from this, that different ion species cause different damage.This was looked at recently in a dedicated study where tungsten was irradiated with protons, deuterium, helium, silicon, copper, iron and tungsten to similar depths and at the  3 He NRA Tyburska et al [44] 600 eV D 3 + 4 × 10 19 0.5-3 × 10 24 320 TDS, 3 He NRA Wright et al [45] few eV D? 1.1-2.7 × 10 24 0.9-2.2× 10 26 360-480 3 He NRA, TDS 'tHoen et al [47] few eV D? 1.2 × 10 24 1.2 × 10 26 470-520 TDS, 3 He NRA Shimada et al [48] 100 eV D ?+ ions 5-7 × 10 21 5-7 × 10 25 470 TDS Takagi et al [50] 1 eV D ?+ ions unknown unknown 376-600 3 He NRA same damage doses of 0.04 dpa and 0.5 dpa [59].The samples were exposed to the identical low-flux deuterium plasma at low energy.Despite the vastly different PKA energies, different damage rates, and different damaging species, the deuterium retention was very similar.Irradiation with medium to high mass ions resulted in indistinguishable deuterium retention values.Irradiation with light ions, i.e., protons, deuterons and helium, resulted in deuterium retention that was at most a factor of two higher.Thus, it can be concluded that the observed differences in absolute retention values in figure 1 are not due to different PKA energies or damaging dose rates, at least for the medium-to high-mass ion irradiations.The problem when discussing the released amounts measured by TDS or integral amounts from IBA methods is that the result also depends on the energy of the MeV ions, because the latter determines the width of the damage zone and, thus, the number of traps created.In addition, many other parameters during the deuterium loading influence the total retention.Deuterium retention beyond the deuterium implantation range proceeds by diffusion, and the diffusion front should penetrate into depth with the square root of time [42,52,64].It should therefore increase with fluence.The speed at which this diffusion front penetrates into depth depends not only on the source term defined by the impinging flux and the energy per deuteron, but also on the local trap concentration [42,52,64].The larger the defect density, the slower is the penetration into depth.Therefore, deuterium should penetrate deeper into the damaged zone for a smaller damage dose than for a larger one.As a consequence, the measured integrated amount does not necessarily reflect the total number of generated traps and additional information is required to determine the latter.To overcome this, one would have to expose to deuterium long enough for the damage zone to get filled to the end.However, if the exposure lasts too long, then deuterium could also penetrate beyond the damaged zone and decorate intrinsic defects in the bulk and again the total deuterium retention would not reflect the total number of traps generated.Thus, little can be inferred about the evolution of the damage with the dose from such total deuterium retention measurements.

Local D concentration
This ambiguity can be overcome by measuring the deuterium depth profile with absolute quantitative methods such as 3 He-NRA or Glow Discharge Optical Emission Spectroscopy (GDOES).If the local deuterium concertation is known, it can be related to the calculated damage dose at that location.In this case, the results of different studies should be comparable with each other.Likewise, such results can then be compared with cascade simulations and be used to make a statement about the displacement damage to be expected from fusion neutron irradiation.
Figure 2 shows the maximum deuterium concentration at the calculated damage peak as a function of the reported damage dose, again presented with a double logarithmic axis for the results from five datasets shown already in figure 1.
The remaining three data sets from figure 1 contain only TDS results and, therefore, this local information is not available.In addition, data from six other publications are included in figure 2. In general, the deuterium concentrations now only vary by a little more than one order of magnitude between the different data sets.This large variation is surprising, since the deuterium exposures were performed at very similar temperatures, and therefore the deuterium concentrations should not vary strongly.Since deuterium retention is a balance between the trapping of deuterium in the defects and the thermal release of deuterium from them, the so-called thermal de-trapping, one should find for a given defect density lower deuterium concentrations for data sets where the deuterium loading was performed at higher temperatures [52].This trend is not reflected in these data sets.However, the different data sets seem to be more concentrated around their average value, with a few data sets appearing more like outliers.Possible reasons for these outliers are discussed in the following in order to develop a methodology that should provide a consistent picture.
It can be seen that the conversion from total deuterium amounts to local deuterium concentrations changed some data sets significantly.In the case of the early work by Wampler and Doerner [42] (olive triangles), it shifted the curve from the upper end of the data set downwards to the lower end.It did not change the dependence on dose and still shows a clear increase.Thus, the traps created by the Si irradiation were filled to the end of the damage zone.However, the high deuterium concentration in the undamaged tungsten sample from their data set shows that the deuterium plasma exposure itself introduced substantial damage.That means, the deuterium exposure conditions they applied prevent sound conclusions about the influence of low damage doses on retention.This is in line with blisters the authors observed on the surfaces of the samples.However, although blisters are known to reduce the uptake into greater depths [64,65], they generally increase the deuterium concentration near the surface [29,31].Therefore, the reason why this data set shows lower concentrations than the others is unclear.Neither experimental details of the analysis setup, nor the cross section and the applied deconvolution method used for the absolute quantification are given.Consequently, the reason for the apparently low deuterium concentrations cannot be deduced.
The data from Tyburska et al [44] are in perfect agreement with the data from Wright et al [45] and part of the data from 'tHoen et al [47].Interestingly, the two data sets from 'tHoen et al that represent deuterium concentration measurements at different locations of the samples with different surface temperatures, follow a different trend.While the deuterium concentration in the center increases with the damage dose, the deuterium concentration a few millimeters away, where the sample temperature was 50 K lower, shows a maximum at 0.009 dpa and then decreases for higher dpa.Certainly, the integral information shown in figure 1 must be interpreted with great caution in this case.Nevertheless, the reported concentrations of slightly more than 1 at% for these three studies are also consistent with the measurements of Alimov et al [49], who found no difference in deuterium concentration between 0.5 and 50 dpa.These datasets alone would indicate saturation at a maximum deuterium concentration slightly above 1 at%.However, Takagi et al [50] observed a continuous increase in deuterium concentration with damage dose.They claim that defects migrate from the damaged region to greater depths.However, this data set is peculiar because it is from an in situ study where deuterium retention was measured with 3 He-NRA while the sample was exposed to deuterium plasma.Recent studies have shown, that the presence of helium can increase deuterium retention substantially [66,67].Therefore, large 3 He concentrations that accumulated beyond the initial W-ion implantation zone during the analysis could explain the increasing deuterium retention.Also, the data sets of Barton et al [53], Möller et al [55] and especially the single data point of Fukumoto et al [43] show deuterium concentrations significantly higher than the others.For the latter, it is not described how the absolute concentration was derived from the SIMS measurements.Therefore, it is not possible to conclude whether this is an accurate measurement and this data point has to be treated as an outlier.However, there is another important difference for this study [43], and for the one of Möller et al [55]: In both cases, protons are used to create the damage.For protons, the energy transfer to the lattice atom is substantially smaller than for heavy ions or neutrons.Consequently, the amount of damage created per incoming ion is much smaller and more isolated Frenkel pairs are produced, rather than dense damage cascades.In addition, significant amounts of protons are implanted along with the damage.While the concentration of implanted tungsten is 60 ppm per dpa for 20 MeV W-ion implantation it is close to one hydrogen per dpa for 0.3 MeV proton implantation as used by Fukumoto et al [43].It is known that the presence of hydrogen isotopes during radiation damaging increases retention significantly [34,58].Three times higher concentrations were observed for damaging of deuterium-containing tungsten compared with damaging of deuterium-free tungsten [58].Damaging in the presence of deuterium results in a deuterium concentration of up to 4 at% if deuterium loading is performed at 370 K [60].Möller et al [55] tried to circumvent the effect of the presence of protons in the lattice by using high irradiation energies and only looking at the so-called track region of the damage, where the hydrogen concentration per dpa is much smaller as compared with the Bragg peak.However, little is known about how little hydrogen is needed to influence damage evolution.Therefore, it cannot be concluded whether the presence of hydrogen or the different damage cascade is the reason for the larger retention [68].Also, for the data of Barton et al [53] it can only be speculated why the deuterium concentration is a factor of three higher than the one for the other data sets.Obvious reasons could be the shallow displacement damage of the 2 MeV Cu ions, which peaks below 400 nm, in combination with the high flux, high energy deuterium plasma.The latter could have created additional defects that could not be separated from the initial displacement damage due to the limited depth resolution of the 3 He-NRA arrangement used.It could also be a systematic experimental error of the applied analysis, but no experimental details are given that would allow to assess the cause of the apparent discrepancy.The only data set that covers a rather large dose range and shows a clear systematic change in the increase of deuterium concentration with dose is that of Ogorodnikova and Gann [51].In this work, tungsten was exposed to a low flux deuterium plasma (≈ 10 20 D/m 2 ) at 470 K with 25 eV per deuteron.The authors conclude saturation 'already at ≈ 0.45 dpa'.Neither the initial material grade, nor the preparation is specifically mentioned, but it is most likely polycrystalline tungsten that was 'recrystallized', as the undamaged reference sample showed a very low retention in the bulk of only 10 −3 at%.Already the lowest damaged dose of 0.005 dpa resulted in a clear increase of the deuterium concentration for these conditions, and the maximum concentration of 1.2 at% for the higher damage doses agrees very well with many of the other studies.It should be emphasized that these data and those from Tyburska et al [44], Wright et al [45], 'tHoen et al [47], Alimov et al [49], and Wang et al [57] were measured with the same setup at IPP Garching.Slightly different methodologies were applied.The resonance method, evaluating the proton integrals was used in [44,45,49,51] and the deconvolution method fitting the shapes of the proton spectra was used, e.g., in [47,57].A discussion of the two methods can be found in [69].While the analysis method may lead to small deviations in the shape of the derived depth profiles, the absolute maximum concentrations are not affected.Therefore, deviations between these data sets are not due to systematic errors of the 3 He-NRA method, but have to be attributed to sample preparation or the deuterium exposure conditions.At IPP Garching, absolute numbers derived by the 3 He-NRA depth profiling technique were cross-checked with calibrated TDS data in a dedicated study and showed excellent agreement [70].Comparable cross-checks and calibrations are repeated regularly.The deviation of the dataset of Alimov et al at 550 K [49] could be partly attributed to thermal detrapping.Another possible explanation is the very different experimental procedure applied.In this particular experiment, deuterium retention was measured at the back side of a 50 μm thick tungsten foil after displacement-damaging it with 20 MeV W. The front side was exposed to a medium-flux plasma at 550 K.
Overall, many reasons such as sample preparation, deuterium loading conditions, or systematic variations in the analysis might explain the discrepancies between the various published datasets.Unfortunately, the necessary experimental details are often missing to make a solid judgment.In general, the data set of Ogorodnikova and Gann [51] seems to fulfil most of the requirements that need to be applied for a sound study of the evolution of deuterium retention with the damage dose.These are: -Starting material with a low defect density -Damage creation well beyond the depth resolution of the applied deuterium analysis method -Damage creation at room temperature -Spanning a wide range of damage doses -Deuterium exposure to decorate the existing defects without creating additional defects (low enough sample temperature to significantly fill the defects, high enough temperature to facilitate deuterium transport, low enough deuterium flux and deuterium energy for that temperature to prevent defect creation) -Absolute quantitative deuterium depth profiling method to yield local information Unfortunately, this study [51] also lacks some details, e.g., the starting material and it was not unambiguously shown if the second last point about defect creation during the deuterium loading was really fulfilled.The following section describes a methodology that explicitly addresses this point.In addition, TDS is part of this proposed methodology to obtain information about the de-trapping energies of deuterium from the created defects and their evolution with damage dose.

Proposed experimental methodology
The experimental results on damage evolution presented in the following section were conducted in 2012.They were performed in preparation for deuterium-protium isotope exchange experiments in displacement-damaged W, but as they were intended as a preparatory study they were not published in this original study [71].They included the investigation of the evolution of deuterium retention with damage dose, and thus, the experimental prerequisites defined for this isotope exchange study apply also for the discussion here.The individual experimental steps developed for this study are outlined and justified in detail below.

Sample preparation
Hot-rolled polycrystalline tungsten samples with dimensions of 12 × 15 × 0.8 mm 3 manufactured from Plansee AG (Austria) [72] with a nominal purity of 99.97 wt.% were used.To improve comparability and to minimize the influence of microstructural effects, all samples were from the same manufacturing batch.Samples from this batch have been used in many other deuterium retention studies performed at IPP since approximately 2010.For this batch, A. Manhard et al tested and improved various polishing procedures, made a quantitative microstructure and defect density analysis and carefully investigated the influence of the microstructure on the deuterium retention [73][74][75].
For the results presented here, the surfaces were chemomechanically polished to a mirror-like finish following the procedure described in [74] to allow reliable determination of depth profiles with IBA methods.The goal of the present investigation was to study displacement damage in the near-surface layer which is only a few micrometers in thickness.To minimize defects and thus retention in this near surface layer, as well as in the bulk of the material, a heat treatment was performed prior to any implantation.The samples were heated by electron bombardment in vacuum at a pressure of 10 −6 Pa for 2 min at 2000 K.In addition to grain growth (size distribution ranging from 10 μm to 50 μm), a reduction of the dislocation line density by two orders of magnitude as compared with the initial value of 3 × 10 14 m m −3 was observed [75].

Displacement damage creation
Damaging was done by 20.3 MeV W 6+ ions (self-ion irradiation).Samples were mounted on a water-cooled copper substrate holder with molybdenum masks with an aperture of 10 × 14 mm 2 .Sample temperature remained below 290 K throughout the irradiation, as measured by a thermocouple attached to the holder.The background pressure in the chamber was below 10 −5 Pa.Homogeneous irradiation was achieved by scanning the beam with about 1 kHz in the x-and y-directions over the sample area.The acquired charge was measured in operando with four Faraday cups placed in front of the sample close to the four edges of it (see figure 2(c) in [76]).The implanted W-ion fluence was calculated from this charge, the charge state and the area of the corner cups.The average damage rate was 6 × 10 −5 dpa s −1 , and the peak damage rate was two orders of magnitude higher.The charge measurement was verified by implanting 1 MeV tungsten ions into carbon at a fluence of 1.6 × 10 20 ions m −2 and measuring the retained tungsten by Rutherford backscattering spectrometry.
To calculate the depth profile of the primary damage, the 'Quick Calculation of Damage' option of SRIM-2008.04was used and the output file 'vacancy.txt'was evaluated.A value of 90 eV for the displacement threshold energy E d , as recommended by the American Society for Testing and Materials [77], and 0 eV for the lattice binding energy, as recommended by Stoller et al [63,78], was used.Figure 3 shows that the calculated 0.036 displacements per ion and Å created directly by the incoming W-ions (green dotted line labeled 'ions') are negligible as compared with the 1.8 displacements per ion and Å created by the recoils.Both show a maximum around 1.35 μm and extend up to 2.3 μm.The sum of both displacements converts to a damage dose of 1 dpa in the maximum for a tungsten fluence of 3.4 × 10 18 ions m −2 and a tungsten density of 6.319 × 10 28 ions/m 3 .For this damage dose, the concentration of implanted tungsten is only 60 appm in the peak located at a depth of 1.65 μm and even much less within most of the damage zone, as can be seen in figure 3. Averaged over the entire depth, one W-ion creates in total 26500 primary displacements.Thus, the number of interstitials introduced by the implanted ions is more than four orders of magnitude smaller than the number of stable Frenkel pairs created and can, therefore, be neglected.Samples with six different damage doses were prepared, ranging from 0.001 dpa to 2.3 dpa (W-ion fluence between 3.1 × 10 15 and 7.87 × 10 18 ions m −2 ) and, hence, with a wider damage dose range than previously reported in the literature.

Deuterium loading
Deuterium loading of the displacement-damaged zone of the samples was accomplished by implanting lowenergy and low-flux deuterium ions from a plasma into a shallow near-surface region (several Å, see [79]), from where they diffuse over time into deeper regions.For this purpose, the well-characterized, electrodeless lowtemperature plasma experiment PlaQ [80,81] was used.At the chosen operation pressure of 1.0 Pa, the resulting energy of the ions hitting the electrically floating sample holder is below 15 eV with a FWHM of about 4 eV [80].The absolute particle flux was calibrated for these conditions with a retarding field analyzer, the species distribution with an energy dispersive mass spectrometer.The ion flux consists mainly of D 3 + ions (94%) with small contributions from D 2 + (3%) and D + (3%).Therefore, the contributions to the total deuteron flux in form of ions are for these three ion species: 97%, 2%, and 1%.Since the kinetic energy is expected to be evenly distributed among the constituents of the molecular ions upon impacting the surface, these settings are referred to as < 5 eV/D.The resulting total flux of deuterium in the form of ions is 5.6 × 10 19 D/m 2 s.The flux of neutral atomic deuterium of low energy (< 1 eV) exceeds the flux of ions by at least one order of magnitude [80].However, this particle flux is considered being negligible for deuterium uptake at low sample temperatures [82] and only the ion flux or fluence is reported below.The temperature of the tungsten-coated copper substrate holder was controlled by a liquid heating circuit connected to a silicone oil-operated thermostat.Five samples were arranged radially around the central axis and were exposed simultaneously.Each sample was tightly bolted at the four corners with molybdenum screws to ensure good thermal contact.A thermocouple pressed against the back of the sample holder was used to monitor the temperature.In addition, an IR camera was used to monitor the surface temperature evolution of the samples, as well as the lateral homogeneity during the experiments.The temperature reading of the IR camera was calibrated with the thermostat prior to plasma operation.The influence of the plasma on the target temperature is negligible for the selected plasma conditions.The particle energy and substrate temperature were chosen with the aim to only decorate the defects which were created by the tungsten beam, but to avoid creation of additional defects.A recent study showed that for these deuterium fluxes and energies of 215 eV-and, hence, well below the kinetic energy of about 1 keV at which deuterium can displace a tungsten atom in the lattice -a ten nanometer thick, deuterium supersaturated layer can form with a deuterium concentration of 10 at% [83,84].To avoid this, the lowest possible energy was applied by keeping the substrate at a floating potential.In addition, an elevated temperature was used in this experiment.The chosen temperature was a compromise between, on the one hand, high enough temperature to promote diffusion for a fast uptake and low solute concentration to minimize defect formation for the given flux and energy, and low enough temperature to minimize thermal de-trapping of deuterium and still stay away from the temperature where vacancies become mobile and damage evolution sets in [85].A sample temperature of 450 K was chosen, which turned out to be a good choice, as was later shown by Kapser et al [79].They measured deuterium depth profiles in thin recrystallized foils exposed to the same plasma also at floating potential and observed a continuous increase in retention near the plasma-facing surface for exposures above fluences of 2 × 10 25 D/m 2 at 300 K, but not at 450 K. Microstructural analysis by scanning electron microscopy, assisted by focused ion beam, revealed sub-surface damage evolution at 300 K, but not at 450 K. Due to the fact that the plasma exposure does not create additional defects, these conditions are referred to 'gentle loading' or 'deuterium decoration' instead of 'deuterium implantation'.It must be emphasized that at lower temperatures, higher ion energies or higher ion fluxes, defect creation will occur during the deuterium exposure and will eventually not only alter the defect distribution, but also will significantly influence retention and transport, as features such as voids or blisters may develop [29-32, 65, 83, 84].

Deuterium depth profiling
Deuterium was analyzed ex situ with the D( 3 He,p)α nuclear reaction with nine different 3 He energies varying from 500 keV to 4.5 MeV to probe a sample depth of up to 7.4 μm.The lateral distribution was measured with a step width of 1 mm along the central axis of a sample yielding a variation of less than 7%.The deuterium concentration within the near-surface layer at depths of up to about 0.3 μm was determined on one location with 3 He energies of 500 keV and 690 keV by analyzing the emitted α particles with a PIPS detector at the laboratory scattering angle of 102°and a solid angle of 7.8 msr.For determining the deuterium concentration at larger depths, the high-energy protons were measured for all nine energies using a thick, large angle surface barrier detector at a scattering angle of 135°with a solid angle of 30 msr.A total charge of 10 μC was accumulated for each energy.NRADC [86] and SIMNRA 6.06 [87] were used for the deconvolution of the NRA spectra measured at different 3 He ion energies.In NRADC all α and proton spectra measured at different energies were evaluated simultaneously.Details about the data evaluation using NRADC can be found in [86].The theoretical depth resolution limit for the deuterium depth profile was calculated with RESOLNRA for the given reaction angle and detector geometry [88] and was used as prior knowledge for the thickness of the layers of constant concentration in NRADC.For the quantitative analysis, the cross section published by Alimov [89] was used.The total amount of retained deuterium within the information depth of the above given 7.4 μm was finally determined by integrating the deuterium profile over the measured depth.To check the performance of the detectors in terms of energy resolution and to compare measurements from day to day, an amorphous, deuterated carbon thin film calibration sample (a-C:D) of known deuterium content (1.25 × 10 22 D/m 2 ) was measured for each energy in addition.The accuracy of the beam current measurement (typically 3%-5%) together with the reported accuracy of the cross section of 5% and the counting statistics of about 1 to 3% (counts depending on 3 He energy and deuterium content) assures that the accuracy of the measurements stays within 10%.As mentioned earlier, in a dedicated study, the deuterium amount retained in magnetron-sputtered tungsten films of different thicknesses was measured with the same setup with 3 He-NRA and compared with absolutely calibrated TDS measurements [70].Excellent quantitative agreement was found for these two methods.

Thermal desorption spectroscopy
After the NRA measurement, the amount of deuterium in several selected samples was additionally measured by TDS in the quartz tube of the TESS device.A basic description of TESS is given in [90].The experimental procedure is similar to that described in [58] with two distinct differences for this early study: First, the furnace temperature was ramped up with a faster heating ramp of 15 K min −1 as compared to 3 K min −1 in the later studies.Samples are heated by conduction and radiation, so that the sample temperature lags behind the furnace temperature.The larger the ramp rate, the greater is this lag.Therefore, the temperature response of the samples to the linear furnace ramp must be carefully calibrated.This was done in independent experiments using a 125 μm thin pair of a type K thermocouple wire spot welded on a tungsten sample of identical size and surface finish that was subjected to an identical ramp.Second, because of this fast ramp, the maximum temperature of the ramp was set to 1275 K to ensure desorption of all retained deuterium from the samples (as verified by 3 He-NRA measurements after TDS).QMS signal recording, calibration and evaluation was identical as described in [58].As recently shown, desorbing deuterium converts with oxygen at the sample surface to HDO and D 2 O [91].For the present study, the contributions of HDO and D 2 O desorption were negligible.The secondary electron multiplier of the QMS was operated in a single ion counting mode to minimize the background noise and to be able to apply Poisson statistics to determine the error bars.The error bars are determined by successive calibration measurements and are governed by the stability of the detector and by the absolute flow reported on the calibration bottle.Consequently, the absolute amount of deuterium quantified with the QMS is considered to have an uncertainty of less than 10%.

Deuterium retention as function of deuterium fluence
In a first series of experiments, the uptake of deuterium in self-damaged tungsten was investigated.A set of four recrystallized samples was implanted with 20.3 MeV W 6+ at room temperature with a fluence of 7.87 × 10 17 W-ions/m 2 (calculated peak damage dose of 0.23 dpa).Four samples were simultaneously exposed to the lowtemperature ECR plasma described above (energy < 5 eV/D, flux 5.6 × 10 19 D/m 2 s, substrate temperature 450 K).After 5, 20, and 72 h, one sample at a time was removed from the plasma and the exposure of the remaining samples was continued until a total exposure time of 114 h was reached, corresponding to a total deuterium fluence of 2.25 × 10 25 D/m 2 .Two additional samples were independently prepared and deuteriumloaded in a separate plasma exposure for 72 or 78 h using the same parameters to check for reproducibility.Given the resolution of the method, this depth coincides well with the calculated maximum range of the displacement damage.Longer exposure to deuterium plasma does not significantly change the deuterium depth profile.This is attributed to the fact, that the depth profile is determined by the ion-irradiation induced traps.Obviously, after an exposure to about 10 25 D/m 2 , all of the created traps are filled.
All profiles show a first thin layer containing about 2 × 10 19 D/m 2 .The actual thickness of this layer cannot be resolved due the limited depth resolution of about 20 nm.This amount of deuterium can be attributed to either adsorption at the surface or implantation within the ion range (≈ 15 Å for the minority species D + with 15 eV).This feature of the deuterium exposure will be omitted in the following, as it is not relevant for the discussion of the displacement damage.
The maximum deuterium concentration is in all cases about 1 at%.At the lowest deuterium fluence step it is 1.1 at% and increases to 1.4 at% when the deuterium has reached the end of the damage zone.Samples prepared separately and exposed for 72 and 78 h show very similar deuterium depth profiles.The variation of the concentration in the individual layers is at most 0.12 at%, which provides a margin for the error bar and thus provides an insight into the reproducibility of the whole procedure applied.
Figure 5 shows the integrated amount of deuterium within the 3 He-NRA information depth derived for the depth profiles in figure 4. The total amount increases steeply at the beginning of the exposure, but the difference between the last two fluence steps is marginal.It can therefore be concluded that for the chosen deuterium loading conditions, a fluence of 1.5 × 10 25 D/m 2 is sufficient to fill the available traps in these samples with a maximum peak damage dose of 0.23 dpa.

Evolution of deuterium retention as a function of damage dose
In a second series of experiments, samples were prepared in the same way as described above and irradiated with 20.3 MeV W 6+ at six different damage doses ranging from 0.001 dpa to 2.3 dpa.Based on the result of the previous deuterium fluence series, they were then exposed to a fluence of 1.5 × 10 25 D/m 2 (72 h) at 450 K and deuterium energies < 5 eV/D.Figure 6 shows the deuterium depth profiles as derived with 3 He-NRA for six samples from this series along with the one of an undamaged reference sample.
For the undamaged reference sample, deuterium retention in the bulk is very low, just slightly above the detection limit for the present conditions of about 10 −3 at%.This retention is attributed to residual defects and/ or impurities that trap hydrogen isotopes.The flat profile and the low bulk deuterium concentration shows that the plasma exposure parameters were chosen such that they do not introduce additional defects.Macroscopic defects, such as blisters, typically lead to increased retention at depths of a few μm, as was observed, e.g., by Manhard et al [81].For all W-irradiated samples, the surface peak is followed by a rather flat concentration profile extending approximately to the maximum damage depth of 2.3 μm as calculated by SRIM.Even the lowest damage dose of 0.001 dpa leads to a significant increase of the deuterium concentration by one order of magnitude as compared with the undamaged reference sample.With further increase of the damage dose, the maximum deuterium concentration increases and reaches the identical saturation value of 1.4 at% as in the preceding deuterium fluence variation of the 0.23 dpa samples.This deuterium concentration is thus three orders of magnitude greater than the deuterium concentration in the undamaged reference sample.For the larger damage dose of 2.3 dpa, this value is not exceeded.However, for this 2.3 dpa sample deuterium penetrated only about one micron into the material within the 72 h.The reason is not clear, but the experiment was  repeated two more times, always showing the same reduced penetration.Even at 144 h exposure, the damage zone was only partially filled.This is surprising, since for the same deuterium particle flux and defect density transport into depth should be the same for the same number of trap sites.One explanation would be a reduced uptake due to, e.g., contamination or amorphization at the very surface layer.Neither higher carbon concentrations than for the other samples (typically few times 10 19 C m −2 ) were observed with 3 He-NRA, nor were there any indications of near-surface defects, as checked with electron channeling contrast imaging.A slight increase in deuterium concentration at depths beyond the calculated damage range is seen when the depth profiles are plotted on a logarithmic scale as in figure 6.It is not certain whether this increase is an artefact of the deconvolution procedure or real.A justification for the latter could be strain building up beyond the displacement-damaged layer [92], which would favor deuterium retention.Clearly, there is no evidence for a large fraction of defects propagating to greater depths which would prevent saturation of the deuterium concentration, as speculated by Takagi et al [50].
Figure 7 shows the maximum deuterium concentrations D max taken from the depth profiles of figure 6 at a depth of 1.25 μm as a function of damage dose with a double logarithmic scale.The bisector is plotted as a dashed line to illustrate the linear increase.The deuterium concentration levels off from the linear increase already at a very low damage dose of about 0.005 dpa, which could indicate that cascades are already beginning to overlap.Finally, at 0.23 dpa a maximum concentration of about 1.4 at% is reached.In addition to D max , the total amount of deuterium within the 3 He-NRA information depth of 7.4 μm is plotted, denoted as 'D areal density'.As expected for the cases where the depth profiles are very similar in shape, the curve follows the D max curve very closely.Exceptions are the undamaged sample and the 0.001 dpa sample, where the retention beyond the displacement damage influences the areal density already.This again emphasizes the limitation of using total deuterium amounts as discussed earlier.
Figure 8 shows the corresponding TDS release spectra for all six samples from figure 6.In general, the deuterium release starts above the exposure temperature of 450 K and ends for all samples just above 1000 K.All samples show two distinct release peaks.For samples with a damage dose of 0.005 dpa and higher, the low temperature peak is more intense.For the undamaged reference sample and the sample with the lowest damage dose, both peaks are also visible, but their intensities are nearly equal.As the damage increases above 0.005 dpa, the overall shape of the desorption spectra does not change significantly, but only their intensities increase.For this ramp rate, the low temperature release peak has its maximum at 670 K and the high temperature release peaks at 800 K. Macroscopic rate equation modeling can describe the spectra of samples prepared in an almost identical manner with de-trapping energies ranging between 1 and 2 eV [58,60].There is much speculation in the literature as to what type of defects would be responsible for such TDS spectra, ranging from dislocations to single vacancies, vacancy clusters or voids.It is important to note that for the samples investigated here, the position of the left flank of the spectra is not determined by the nature of the trap, but only by the exposure temperature.For the experiments shown here, deuterium release can only start above 450 K. Possible traps with lower de-trapping energies are thermally de-trapping already during the exposure and in the cool-down phase.To emphasize this point figure 9 shows TDS spectra of two samples with a peak damage dose of 0.23 dpa that were exposed to the same plasma conditions (5.6 × 10 19 D/m 2 s, 450 K, 72 h) for two different exposure temperatures.In one case, at 450 K like all samples in the damage dose series shown in figure 8 and in the other case at 400 K.Both spectra resemble each other nearly perfectly, except for a shift of the left flank.For the sample exposed at 50 K lower temperature, the left flank is shifted by 50 K to lower temperature.The right flank matches in both cases perfectly, underlining the excellent reproducibility of the experimental procedures.
Integrating the TDS spectra of figure 8 over time gives the total amount of deuterium released from the samples.Figure 7 shows this total amount of deuterium as a function of the damage dose, in addition to the maximum deuterium concentration and the deuterium areal density as derived with 3 He-NRA and discussed above.From 0.005 dpa on both techniques show the same trend: deuterium retention initially increases steeply with dose and flattens out to a constant value in the sub-dpa range.Dividing the amount of deuterium released by the sample area of 1.38 cm 2 even gives a perfect quantitative agreement between the total amount of deuterium derived from TDS and NRA for these samples.However, one clear difference between the two techniques is immediately apparent.While D max from 3 He-NRA has a dynamic range of three orders of magnitude for these samples, TDS is limited to only one order of magnitude.This is not due to any inherent limitation of the technique itself, but is due to the fact that at these low damage doses the effect of damage from the only a few μm thick self-damaged layer on deuterium retention is overcast by the deuterium retention in the  800 μm tungsten bulk below.Therefore, the deuterium release from the 0.001 dpa sample is nearly as large as the that from the undamaged sample.This is despite the fact that these samples were annealed at 2000 K and therefore had very few defects as mentioned above.Without recrystallizing the material, the dynamics would have been even worse.Subtracting the contribution of the bulk from the other spectra is not straightforward.For each sample prepared with a different damage dose, this bulk contribution is different and almost impossible to quantify accurately.As discussed earlier, deuterium is expected to penetrate deeper for samples with lower damage dose than for samples with higher damage dose.However, there is no diagnostic available that would allow deuterium depth profiling to such large depths with the required sensitivity.To improve the dynamics of TDS measurements, one would therefore need to work with either very thin samples or even purer samples with negligible trap density for deuterium, such as high purity single crystals.Only then can the contribution of the deuterium bulk retention be reduced and the retention in the displacement-damaged layer would be noticeable even for smaller damage doses.This aspect is emphasized here because it is often ignored in the literature.Therefore, the interpretation of TDS spectra from ion irradiation experiments have to be considered with great care.

Comparison with literature data and discussion
In the following, the maximum deuterium concentration from the data set described above is compared with all of the literature data shown in figure 2. However, as mentioned above, the original publications used different procedures and input parameters to calculate the damage dose and therefore cannot be directly compared in a quantitative manner.In older studies, the 'Full cascade' option of SRIM was often used, which is known to yield a factor of two higher, unphysical values for the dose [63].In addition, very different values for the displacement threshold energy E D have been used, ranging from the standard SRIM setting of 25 eV, which has little scientific justification, up to the 90 eV recommended by ASTM when the kinetic energy available to generate atomic displacements T d is much larger than E D [93,94].The variation of the SRIM-calculated peak displacement damage with the displacement energy E D is shown in figure 10 for the 20.3 MeV tungsten on tungsten irradiation used here.As expected, the data points scale inversely proportional to E D .In addition to the number of displacements, figure 10 shows the correction factor to convert reported values to the present values when displacement energies other than 90 eV were used.When the standard SRIM setting of 25 eV is used for the displacement threshold, the calculated dpa value is a factor of 3.6 greater than when the STM recommended 90 eV is used.
Very few publications report the parameters used to calculate the damage dose.In order to allow for a meaningful comparison, the reported damage doses of the original studies were recalculated using the ion species, fluence and energy as stated in the original publication, but using the damage dose calculation method (SRIM 2008.4 [62]) and the same parameters as applied in the methodology described in section 3.2.(displacement threshold energy E D = 90 V and lattice binding energy E L = 0 eV).To emphasize the difference, the ratio between the original dpa and the dpa calculated here is listed in table 2 as the 'conversion factor'.The deviations range from only 1.14 in the case of Ogorodnikova and Gann [51] up to a factor of nearly 7 in the case of Wampler and Doerner [42] and Fukumoto et al [43].With this correction, the literature data sets shown in figure 2 can finally be quantitively compared with each other and with the experimental datasets described in section 4.
Figure 11 shows the local deuterium concentration at the peak damage for all these data sets as a function of the recalculated damage dose with double logarithmic scales.Overall, the data sets agree slightly better than in figure 2, although the improvement is small.Those that were considered outliers in the discussion of figure 2 did not improve as only the x values were changed by the conversion factor, but not the deuterium concentration.However, the other data sets are now closer together, especially from about 0.01 to about 10 dpa.From this comparison it can be concluded that the maximum deuterium concentration reaches more than 1 at% at damage doses greater than about 0.1 dpa.In addition, the dataset of the present study agrees very well with the values of Ogorodnikova and Gann [51], not only in terms of the relative dependence of the deuterium concentration on the damage dose, but also with respect to the absolute values.In addition, it also extends to smaller dpa values.
Overall, it can be concluded, that the proposed methodology has successfully demonstrated that -The deuterium retention increases almost linearly with the damage dose only in the milli-dpa range.
-The increase begins to flatten out already at very low damage dose of around 0.005 dpa.
-Saturation is reached above a damage dose of about 0.1 dpa.
-The saturation value for this maximum deuterium concentration is about 1.4 at% for a D exposure temperature of 450 K Very recent parameter-free calculations of damage evolution combining the relaxation-creation algorithm with massive molecular dynamics cascade calculations, provide quantitative agreement with these experimental results in several ways [21].First, a saturation behavior for the equivalent vacancy density was observed at a similar low damage dose.Second, the calculated maximum of the absolute vacancy density of about 0.4 at% agrees very well with the present 1.4 at% deuterium, assuming that several deuterium atoms are trapped in a single vacancy.Heinola et al [95] and Fernandez et al [96] determined the binding energies of hydrogen to point defects in tungsten.They found that five to six hydrogen atoms can be trapped in a single vacancy at room temperature.The number is reduced to about four at a sample temperature of 450 K (used in the work presented The reported damage dose was converted using the conversion factors listed in table 1.Note the break in the x-axis to show the deuterium retention for the undamaged reference sample.Values were taken at a depth where the damage maximum would be located for the irradiated samples.here).Thus, assuming that in the self-damaged tungsten dominantly single vacancies are present, a maximum deuterium concentration of 4 times 0.4 at% = 1.6 at% would be expected as compared with the 1.4 at% found in the experiment.
It is important to mention that the results of this study cannot be used directly to predict tritium retention in a future fusion device.Traps will evolve at elevated temperatures and may anneal, reducing the density of point defects.In addition, as mentioned above, the concentration of tritium in defects will not only depend on the trap density, but is a balance between the incoming tritium (depending on flux and energy) and the thermal release from the defects (depending on de-trapping energy and temperature).At most, the derived vacancy densities of about 0.4 at% can be used as an upper limit for first tritium loss calculations, as was done in [11].However, this approach implies that vacancy-type defects dominate hydrogen isotope retention and that no macroscopic voids evolve at elevated temperatures that could retain tritium even in molecular form [97,98].To address this issue, the same methodology is currently being applied to damaging at elevated temperature.
It is also important to stress that the use of such a tungsten grade with low initial defect density is mandatory for a benchmark experiment as discussed here, despite the fact that such a material grade will not prevail in the bulk tungsten tiles of a possible divertor or in the foreseen tungsten coatings of the main wall.If defect rich tungsten were used for such a benchmark experiment, retention in the bulk would compete with retention in the near surface layer, making interpretation difficult or even impossible for the lower damage doses applied.Importantly, the initial defect density does not influence the final maximum deuterium retention and, therefore does not influence the final defect concentration at large damage doses when irradiation-damaging is performed at room temperature as shown by Ogorodnikova et al [99] and Pečovnik et al [100].Naively, an influence is only expected, if the damaging temperature is high enough to start vacancy diffusion and the vacancy diffusion length becomes comparable or smaller than the average distance to ,e.g., the next grain boundary where the vacancy can annihilate.Therefore, it is important to emphasize that the relative increase in deuterium retention is of little use since it depends on the initial state of the material.What is important is the final absolute deuterium retention value for a given deuterium exposure temperature.Only this measure can be used to derive defect densities and should therefore be used for comparison with modeling.

Summary and conclusions
Experimental results from the literature on the evolution of deuterium retention in MeV-ion implanted tungsten were critically reviewed and compared with unpublished data.Except for a few outliers, retention is generally found to increase with displacement damage.Total retention results scatter by three orders of magnitude and cannot be compared with each other as they depend on experiment-specific parameters such as the irradiation energy or the deuterium fluence.Even local deuterium concentration measurements performed at similar deuterium exposure temperatures, which should be potentially suitable to provide reliable results, were found to scatter by more than one order of magnitude.Unfortunately most studies lacks experimental details that would allow for a solid judgment about the absolute D concentration.A saturation behavior is postulated in many studies, but with the exception of the study by Ogorodnikova and Gann [51], a narrow range of damage doses or the applied deuterium plasma exposure conditions and/or analysis methods do not give a clear overall trend.
An optimal methodology for the experimental procedures and data evaluation is proposed that allows robust conclusions on the evolution of displacement damage and consequently on the evolution of deuterium retention with damage dose and the possible saturation behavior.This methodology includes to: -Use of high purity tungsten material with a low defect density.
-Create damage well beyond the depth resolution of the applied deuterium analysis method used.
-Create damage at room temperature for comparison with state-of-the-art modeling.
-Cover a wide range of damage doses.
-Use low-flux, low-energy deuterium exposure at a sample temperature low enough to decorate defects but high enough to avoid additional defect creation.
-Apply an absolute quantitative deuterium depth profiling method to obtain local information on the deuterium concentration.
Experimental results are discussed in detail where displacement damage was created in 2000 K annealed tungsten with 20.3 MeV-energy self-ions at room temperature.The deuterium decoration of the defects was performed at low ion energy (< 5 eV/D) and low flux (<10 20 D/m 2 s) to minimize gas precipitation and blister growth and thus the possible production of additional trap sites.The sample temperature was chosen to be 450 K, which is low enough to avoid defect annealing by vacancy migration (onset temperature about 550 K) and high enough to allow for diffusive transport during deuterium loading.Deuterium exposures are performed until the complete depth of the damage zone is filled.Two absolute quantitative analysis methods are applied: 3 He-NRA is used to measure the evolution of deuterium concentrations a function of the damage dose and has a dynamic range of three orders of magnitude.It is shown that the deuterium retention increases almost linearly with the damaging fluence in the milli-dpa range, but the increase starts to level off already at very low damage doses of about 0.005 dpa.A maximum deuterium concentration of 1.4 at% is reached at a damage dose of 0.23 dpa for the chosen exposure temperature of 450 K. TDS is used to learn about the kinetics of release and to measure the total amount released from the samples.However, for the present methodology, it has only a limited dynamic range of only one order of magnitude due to the contribution of the undamaged bulk tungsten below the displacement damage.Yet it shows that as the displacement damage dose increases above 0.005 dpa, the overall shape of the desorption spectra does not change significantly, but only their intensities increase.The total amounts derived from TDS agree very well with the results from 3 He-NRA.The described data set agrees quantitatively with that of Ogorodnikova and Gann [43] as well as with parameter-free modeling of damage evolution by Mason et al [21].

Figure 1 .
Figure1.Deuterium retention data from the literature for displacement-damaged tungsten for plasma or ion exposures as a function of the damage dose reported in the original publication, plotted on a double logarithmic scale.The temperatures given in the text box represent the temperature of the deuterium ion or plasma exposure.Displacement damage was created near room temperature in all cases.For details see text and tables 1 and 2. Note the break in the x-axis to show the deuterium retention for the undamaged reference samples, where available.

Figure 2 .
Figure 2.Local deuterium concentration at the peak damage for displacement-damaged tungsten as a function of reported damage dose for plasma or ion exposures from the literature.The data are plotted on a double logarithmic scale.The temperature given in the text box represents the temperature of the deuterium ion or plasma exposure.Displacement damage was created at room temperature in all cases.See text and tables 1 and 2 for details.Note the break in the x-axis to show the deuterium retention for the undamaged reference sample.Values were taken at a depth where the damage maximum would be located for the irradiated samples.

Figure 3 .
Figure 3. SRIM-2008.04calculated primary damage profile (green axis) for 20.3 MeV W-ions on tungsten (light green dotted line), the damage created by the recoils (light green solid line) and the sum of both (green solid line).In addition, the calculated damage dose (red axis and red line) and the concentration of implanted ions (blue axis and blue line) are shown for an implanted W-ion fluence of 3.4 × 10 18 W-ions/m 2 .Displacement threshold E D = 90 eV, lattice binding energy 0 eV, 'Quick Calculation of Damage' option.

The 3
He-NRA depth profiles of the retained deuterium are shown in figure 4 as a function of the deuterium fluence.As the fluence increases, the deuterium penetrates deeper into the sample.While most of the deuterium reaches only about 600 nm after 0.1 × 10 25 D/m 2 (5 h exposure), it finally fills the end of the damage zone at about 2.5 μm between 0.4 and 1.5 × 10 25 D/m 2 (20 and 72 h respectively).

Figure 4 .
Figure 4. 3 He-NRA deuterium depth profiles as a function of deuterium fluence in self-damaged, recrystallized tungsten (max.damage dose 0.23 dpa) exposed to a low-temperature plasma at constant energy (< 5 eV/D), flux (5.6 × 10 19 D/m 2 s) and substrate temperature (450 K) (left scale).The dashed green lines show the result of independent preparations and exposures to check reproducibility.In addition, a SRIM 2008.04 calculated damage dose depth profile is shown as a gray line (right scale).The longest exposure of 114 h corresponds to a total deuterium fluence of 2.25 × 10 25 D/m 2 .

Figure 5 .
Figure 5. Integrated deuterium amount derived from the depth profiles of figure 4 as a function of deuterium fluence.The open symbols represent the amounts of the two independent sample preparations exposed to D plasma for 72 and 78 h.The color scheme is identical to figure 4.

Figure 6 .
Figure 6.Deuterium concentration depth profiles in logarithmic scale from 3 He-NRA of 20.3 MeV self-damaged recrystallized tungsten for different damage doses after decoration with a low-temperature plasma with 5.6 × 10 19 D/m 2 s at 450 K for 72 h (left scale).The SRIM 2008.04 calculated damage dose depth profile is shown as a gray line in addition (right scale).

Figure 7 .
Figure 7. Deuterium retention measurements in self-damaged, recrystallized tungsten as a function of the calculated damage dose after decoration with a low-temperature plasma with 5 eV/D and 5.6 × 10 19 D/m 2 s at 450 K for 72 h.Red axis and data points: Maximum deuterium concentration; Blue axis and data points: Deuterium areal density, both derived from 3 He-NRA.Green axis and data points: Total amount from TDS.The 2.3 dpa sample was only partially filled, so the data point is shown with open symbols.Note the break in the x-axis of this double logarithmic plot, which allows the results for the undamaged reference sample to be shown.

Figure 8 .
Figure 8. Left scale: Deuterium desorption flux as a function of time for samples prepared with different damage doses.Same samples as shown in figure 6.The furnace ramp rate was 15 K min −1 in all cases.Right scale: Evolution of furnace and sample temperature.

Figure 9 .
Figure 9. Deuterium desorption fluxes for two tungsten samples irradiated with 20.3 MeV to a peak damage dose of 0.23 dpa at room temperature and decorated with deuterium at 400 (blue) and 450 K (red).The inset shows an enlarged view of the same data with logarithmic y-scale.
[77].According to the theory, the number of atomic displacements (N d ) should follow the relationship =

Figure 10 .
Figure 10.Peak displacement damage calculated with the 'Quick Calculation of Damage' option of SRIM 2008.04 for 20.3 MeV tungsten on tungsten for different values of the displacement threshold E D (left axis).The right axis gives the conversion factor for E D ≠ 90 eV.

Figure 11 .
Figure 11.Local deuterium concentration at the peak damage for displacement-damaged tungsten from figure 2 with recalculated dpa values compared with the data of the present study (light blue open circles).The temperature given in the text box represent the temperature of the deuterium ion or plasma exposure.Displacement damage was created at room temperature in all cases.The reported damage dose was converted using the conversion factors listed in table 1.Note the break in the x-axis to show the deuterium retention for the undamaged reference sample.Values were taken at a depth where the damage maximum would be located for the irradiated samples.

Table 2 .
Deuterium ion energy, flux, fluence, exposure temperature and analysis method applied for the references in table 1, figures 1, 2, and 11. * Exposure of the back side of a 50 μm thin tungsten foil.