Temperature-dependent bubble growth under synergistic interactions of hydrogen and helium in tungsten

A novel theoretical model based on modified diffusion rate equations is proposed to simulate the retention of hydrogen isotopes and the dynamics of bubble growth in tungsten (W) when exposed to simultaneous hydrogen (H) and helium (He) plasma irradiations. Simulation is conducted to assess the influence of temperature as well as simultaneous H and He irradiation at an increasing fluence. Not only to develop a holistic understanding but also to substantiate simulation findings about synergy between H and He plasma irradiation, a W sample is exposed sequentially to H and He plasma at 873 K using the large-power material irradiation experimental system. The topographical changes in the W sample are investigated using atomic force microscopy (AFM) after each plasma irradiation exposure sequence. Simulation results reveal that the ability of a bubble containing both H and He to trap adjacent H/He atoms is primarily governed by their individual partial pressure within the bubble. Furthermore, at elevated temperatures, the synergy between H and He significantly enhances the retention of H isotopes in W. AFM micrographs of the W sample exposed to both H and He plasma irradiation show a severely damaged and locally delaminated layer, absent in the sample exposed only to either H or He, conclusively establishing evidence of synergy between H and He irradiation effects. The average bubble radius computed using the model aligns excellently with experimentally determined values obtained through SEM/AFM analysis. The robustness of the proposed model is also assessed by comparing bubble radius and H isotopes retention at various temperatures with experimental data reported in the literature.

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Introduction
Tungsten (W) is specifically selected as material for the divertor in the International Thermonuclear Experimental Reactor (ITER) due to its low retention of hydrogen isotopes (H/D/T) and exceptionally high melting temperature [1,2].Tungsten's significance in studying plasma-material interactions has been pivotal for recognizing potential operational issues within ITER [3].Temperature [4], neutron irradiation [5], and hydrogen (H) or helium (He) ion implantation [6][7][8] are crucial factors influencing embrittlement in W. Understanding not only the influence of sample temperature and plasma composition on nanobubble formation but also identifying potential synergies among these factors is critical for predicting the performance of tungsten components in the ITER divertor.Numerous investigations have been conducted over the past two decades to understand the behaviour of H and He isotopes in W, especially on their roles in inducing bubble growth during exposure to H/He plasma with energy levels of 20 eV-200 eV [9][10][11].
Exposure to pure He plasma, even below the sputtering threshold energy, leads to distinct forms of surface damage such as the formation of nanoscale 'fuzz', the creation of micron-sized cavity, or a combination of both phenomena, often referred to as 'coral' [12].H blistering in W and other metals was identified well before the discovery of 'fuzz' [13].
Prior investigations [14] have shown that pre-irradiation with He significantly influences the retention properties of H isotopes in W, indicating the potential contribution of He bubbles to this phenomenon.These studies revealed that high-density bubbles induced by He + irradiation could serve as trapping sites for H atoms, significantly affecting the migration of solute H atoms within the material [15].Recently, Baldwin and Doerner [16] suggested that He bubble layers not only serve as trapping sites but also alter the migration energy of H isotopes in W.
H isotope retention should be minimized to prevent interference with fuel reactions and to reduce tritium (T) inventory.Recent research has established that H and He not only cause damage to W separately but also exhibit synergistic effects that further increase H isotope retention in W, thereby impairing material structure and performance [17,18].Experiments using mixed ion beam and plasma accelerators have demonstrated that under mixed H and He exposures, the interaction between H isotopes and He significantly enhances H retention [19,20].This synergistic effect of H and He differs markedly from the effects of pure H or He irradiation.Jiang et al [21] and Zhou et al [22] utilizing density functional theory (DFT) calculations as well as Li et al [23] employing molecular dynamics (MD) simulations have proposed that single heliumvacancy (He-V) complexes can continuously capture H atoms.The capture energy of these complexes increases with the number of H atoms until it reaches zero at the saturation.The critical number of H atoms for this saturation is 12, indicating that He-V complexes serve as effective capture sites for Zhou et al [22] calculated the isodensity surfaces of He in vacancies and the optimal configurations when capturing multiple H atoms.They found that single He atom occupies the centre of the vacancy, while H atoms are positioned near the tetrahedral interstitial sites within the vacancy.MD simulations by Li et al [24] have shown that vacancy clusters capture abundant amounts of H/He, with these clusters exhibiting a higher affinity for He compared to H. Theoretical investigations of the synergy between H and He have largely been restricted to DFT and MD studies, particularly on the stability of small vacancy-hydrogen-helium (VH n He m ) clusters [21,22].Computationally, research focusing on the synergistic effects of H and He in W has been quite limited [25,26].However, it is of paramount importance to develop a holistic understanding of the stability and mobility of larger clusters since its formation is inevitable under high flux plasma exposure, often resulting in the development of well-resolved bubbles.
Although numerous experimental and simulation studies have focused on the interaction between He and H isotopes [18][19][20][21][22][23][24][25][26], the physical mechanism underlying the synergistic effect in W remains unclear.Therefore, understanding and predicting the impact of simultaneous He and H irradiations on the structure and properties of W as a plasma-facing material, particularly considering the role of temperature in these processes, is of utmost importance.This research aims to elucidate the behaviour of H isotope retention and the dynamics of bubble growth in W under simultaneous He and H irradiation, with a special emphasis on effects of irradiation temperatures to develop insights into fuel recycling and the interaction of W with plasma.

Experimental details
Commercial polycrystalline tungsten (99.99% purity) was procured from Xiamen Honglu Tungsten Molybdenum Industry Co., Ltd.Specimens cut in size of 10 mm × 10 mm × 2 mm were mechanically polished to achieve a mirror-like finish and subsequently cleaned by ultrasonic in ethanol.Thereafter, samples were annealed at 1273 K for 2 h in vacuum (<10 −4 Pa) to reduce defect concentration and relieve stress from mechanical polishing.The inductively coupled plasma (ICP) source was developed specifically for steady-state H/He ion irradiation experiments.The design and primary parameters of the facility (LP-MIES) have been detailed in previous research work [27].To advance the understanding about the synergistic effects of the mixed H-He ion beam on damage induced in W, this research work adopts a technique involving the sequential implantation of H and He ions into W samples.This approach ensures precise determination of the H/He ion flux and irradiation fluence to understand synergy between them.All irradiations were performed with a sample holder bias of −80 V and an incident ion energy of 100 eV-it is below the threshold energy for sputtering yield of H/He on W. The ion flux, Γ i , was calculated from the ion saturation current to the sample, set at ≈ 1.0 × 10 20 m −2 s −1 in both pure H and He plasma.The single-step irradiation doses for H and He ions are quantified as 1.0 × 10 24 m −2 and 1.0 × 10 23 m −2 , respectively.The ion implantation procedure commenced with irradiation by H ions, subsequently followed by He ions, defining one complete cycle as a single alternation between H and He.This process was repeated for a total of 10 cycles.The irradiation temperature was consistently maintained at 873 K ± 30 K, monitored using thermocouples throughout the irradiation process.An irradiation temperature of 873 K is chosen because H bubbles do not form in W at temperatures above 700 K [28], while the typical growth temperature for He bubbles is above 1000 K [3].Thus, irradiation temperature of 873 K is favourable for observing the synergistic effects between H and He.
Atomic force microscopy (AFM, Veeco DI 3100) observations were uniformly performed on the same areas after each H/He plasma irradiation, facilitating in situ comparative analysis of topographical changes in samples by repetitive examination of the designated irradiation area.During conductive AFM measurements, a constant scan rate of 0.3 Hz and a voltage of 20 mV were applied between the platinum-iridium coated tip and the sample.This configuration enabled the simultaneous acquisition of surface morphology and conductivity mapping data.

Simulation methodology
Our research group has previously developed theoretical models to study the H/He retention and bubble growth behaviour in W under either pure H or pure He plasma irradiation [29][30][31][32].These models consider three forms of H/He in W: solute H/He atoms, trapped atoms, and H/He bubbles.The models hypothesised that both H and He follow similar pathways as they diffuse within W and become trapped by defects, eventually causing the growth of bubbles.This process can be outlined as follows: when energetic H/He ions enter into W, they lose their energy and thermalize, transforming into solute atoms.These atoms diffuse within the W matrix and get trapped by defects causing their transformation into nanobubbles, leading to growth of H/He bubbles.Nonetheless, when both H and He atoms coexist in W, the dynamics of defect capture and bubble growth behaviours become more complex, requiring consideration of their interactions.The rate equation employed in the model to predict the nanobubble growth in W under individual H or He ion irradiation [30,32] is adapted to account for these interactions in this study.It is noteworthy that, considering the complexity of the model and computational feasibility, the current work is limited to the effects of intrinsic defects.Future work could extend the current model to include various trapping sites, account for dynamic effects such as surface and structural changes during implantation, saturation phenomena, and the migration of vacancies and bubbles at elevated temperatures.
It is established that H and He atoms preferentially cluster around defects in the W [21,33].This means that when H or He enters tungsten, it is quickly captured by the existing defects in W. Without considering the formation of new defects, the presence of H or He within existing defects inevitably leads to a decrease in the total number of available defect sites.It is also found experimentally that bubble formation occurs in tungsten exposed to low-energy D ions even without the creation of vacancies [8,34,35].This implicates that these bubbles form when intrinsic defects within W capture solute atoms of H or He until a critical size is reached.In the model developed in this study, the capacity of intrinsic defects in W to capture solute H/He atoms is assumed to be limited.Therefore, the total intrinsic defect site concentration (atomic fraction) C 0 t , set at 4.0 × 10 −4 [36], is composed of various elements: concentrations of hydrogen-filled defects (C t_H ), helium-filled defects (C t_He ), unfilled defects (C t ), and nanobubbles (C b ).The rate equation for each trapping site with a H/He atom incorporates terms for both generation and loss as follows: where C H is the concentration of solute H atoms, C He is the concentration of solute He atoms, and C W is the W atom concentration.a 0 is the lattice constant of W and is the diffusivity of solute atoms.The diffusion barrier energy (E m ) for solute H atoms is 0.25 eV [37].
The diffusion barrier energy for solute He atoms is quantified as 0.057 eV [38].T is the temperature and k b is the Boltzmann constant.For H in W, the binding energy (E Hd ) is defined as the energy difference between H atoms at a trap site and at a solute site [39].For He, P 1 is the He hopping rate between interstitial sites, while q 1 is the dissociation rate of He atom trapped into a defect [31].
The concentrations of solute H atoms (C H ) and solute He atoms (C He ) are expressed as follows: where R H/He is the backscattering coefficient of incident ions, Γ H/He is the incident ion flux, and the implantation profile (Φ H/He (z)) is obtained from SRIM simulation [30].r b_HHe is the radius of the H-He bubbles.For H, K 1 = K r K 2 s is the adsorption rate, K r is the recombination rate, and K s is the solubility [36].f is the pressure inside the bubble.For He, W is the number of surface sites [29].
is the dissociation rate of He atoms trapped into a bubble [29].H/He atoms implanted into the W bulk can either diffuse back to the surface, become trapped in defects, or migrate into H-He-V clusters or bubbles [29][30][31].Based on particle balance within W surface layer, the concentration of H or He solute atoms at the surface is governed by the boundary conditions expressed by following differential equations: where T L is the thickness of single W atom layer, and | 0,t denotes the boundary close to the W surface (z 0 = 0) at the time (t).Combining the equations ( 1)-( 6), we can obtain all the parameters selected in this paper, which are listed in table 1.
In W, He diffuses more rapidly than H, attributed to a lower diffusion energy barrier of approximately 0.06 eV [38], however, its solubility remains significantly low.Following He + implantation, He tends to aggregate near the W surface, and with sufficient implanted He + fluence, He bubble growth arises from accumulation in preexisting traps and at impurity sites.He bubbles that preferentially grow act as efficient capture sites for solute H atoms, resulting in a significant accumulation of H atoms at the He bubble interfaces.DFT simulations [21] reveal that a single He atom can attract up to twelve hydrogen H atoms.The trapping energy for the first H atom (−0.96 eV) is only slightly weaker than when H binds to a vacancy in W. Trapping energy reduces as more H atoms are captured, with the 12th H bound by an energy of −0.4 eV.You et al [42] have shown that multiple He atoms clustered within a vacancy can also bind strongly with H atoms. MD simulations [43] suggest that the ability of He bubbles to bind a significant amount of H at the bubble's edge indicates a critical role for He bubbles in H isotope retention.Therefore, it is proposed that small He bubbles are pre-existent in the bulk W, with loop punching being the primary mechanism for bubble growth.These pre-existent small He bubbles are assumed to be non-interconnected, and their density is consistently set to 1.0 × 10 20 m −3 [4,30].The prime reason of fixing the parameters in model in such a way is to prevent the bubbles from merging with each other as they grow.
The growth dynamics of bubbles under simultaneous H and He plasma irradiation adopted in the present model is depicted in figure 1. Preferentially formed He bubbles serve as abundant surface capture sites for surrounding solute H atoms, playing a pivotal role in the growth dynamics of bubble.The absorption of nearby solute H atoms by these He bubbles causes their internal pressure to rapidly increase.According to the Greenwood mechanical equilibrium condition, bubble growth is initiated when the internal pressure exceeds a critical threshold, as detailed in [30].When a bubble contains both H and He, its ability to capture adjacent H/He atoms is primarily determined by the respective partial pressures of H (P H ) and He (P He ) within the bubble.The number of H and He atoms as well as their respective molar volumes within the bubble are crucial in determining the partial pressures of H and He inside the bubble, which may be expressed as: where v H (P H , T) and v He (P He , T) are the molar volumes of H and He in the bubble (with units v (cm 3 mol −1 ), P [MPa]), respectively.The number of H atoms (N b_H ) and He atoms (N b_He ) in a bubble can be determined by The rate equation for each bubble containing N b−H /N b−He atoms have the generation and loss terms.It should be noted that the net flow of H entering the bubble may also be limited by the diffusion flux of H in tungsten [45,46].During the growth of the bubble, if the diffusion-limited flow is lower than the recombination-limited flow, equation (3) should be replaced by equation (11), and equation ( 9) by equation (12).
Furthermore, the size of the composite bubble (r b_HHe ) can be determined, being influenced collectively by the number of H and He atoms as well as their molar volumes within the bubble as: where N A is Avogadro's constant.It is hypothesized that the pressure in the composite bubble satisfies the Greenwood mechanical equilibrium conditions: where µ is the shear modulus of W [29], γ is the surface tension of the bubble interface [30], and b is the Burgers vector of the dislocation loop [30].
The solute H retention (T s_H ) in W bulk, H retention in trapped sites (T t_H ), and H retention in bubbles (T b_H ) are obtained as a function of t and T, H retention can be expressed as: Therefore, the total H retention (T H ) in the W at a given t can be expressed as:

Theoretical research based on hydrogen-helium rate theory
Numerical simulations are performed to elucidate the evolution of nanobubbles and the retention of H isotopes across the temperature (T) range of 473 K-1273 K.For comparisons with experimental data, simulations are conducted with H + fluence varying from 1.0 × 10 24 m −2 -1.0 × 10 25 m −2 and He + fluence ranging from 1.0 × 10 23 m −2 to 1.0 × 10 24 m −2 .The irradiation fluence ratio of H + to He + is consistently maintained at 10:1.The incident energy for both H + and He + ions is 100 eV.Employing the proposed modified diffusion rate equations, the diffusion processes of H and He as well as the evolution of nanobubbles have been simulated accounting for variations in temperature and fluence.Figure 2    Previous research by our group [29][30][31] has established that solute He atoms exhibit a tendency to rapidly diffuse into He bubbles, thereby significantly restricting their diffusion deeper from the surface.For physical accuracy, the model incorporates a limitation where nanobubbles cannot interact.Initially, the model exclusively accounts for the existence of low-density He bubbles in W, disregarding the bubble nucleation.Such consideration is not physically invalid given the presence of low-density He bubbles minimally influences the diffusion of interstitial H and He atoms.Consequently, this leads to higher diffusion of these solute H/He atoms, particularly for He atoms, within W. .He atoms are trapped within defects with a binding energy ranging from ∼1.5 eV to 5.5 eV [40,47].As the T increases, these He atoms tend to dissociate into solute He atoms and single defects.Furthermore, the binding energy for trapped H atoms is significantly lower, approximately 0.85 eV [39].The ability of intrinsic defects to capture H and He atoms is limited, resulting in a competitive interaction during the trapping process of these atoms.

Analysis of hydrogen-helium bubble growth dynamics during irradiation
The trapping of He in vacancies within W is energetically favourable, leading to the formation of variously sized He-V complexes [48].Moreover, He atoms demonstrate a propensity for self-clustering, a phenomenon that occurs even in the absence of vacancies [49].When trapped defects absorb He atoms and reach a critical size of 5-6 atoms, they eject a W atom and subsequently form stable He bubble [50].Numerous studies [51][52][53] suggest that the formation of He bubbles reduces H blistering. Further research [43,54] indicates that H is directly attracted to He bubble surfaces, potentially increasing H retention.These findings imply that during simultaneous H and He irradiation, He atoms are more effectively captured by defects than H, leading to the preferential formation   of He bubbles that strongly attract H atoms. Preferentially formed He bubbles serve as abundant surface capture sites for surrounding solute H atoms.This investigation additionally revealed that hydrogen-helium bubbles exhibit decreased mobility compared to those composed solely of He or H [55]. Figure 5 shows the averaged bubble radius (r b_HHe ) at different irradiation fluences as a function of position.Figure 6 displays the corresponding H atom number (N b_H ) inside bubbles versus depth (z).Notably, r b_HHe exhibits a dependence on both irradiation time and depth from the surface, with these bubbles in the near-surface layer showing rapid growth as the H/He ion fluence increases.At a given temperature and fluence, r b_HHe decreases with increasing z, while at a given T, r b_HHe increases with irradiation fluence.However, at a given fluence, r b_HHe significantly decreases as the T increases from 473 K to 1273 K. Comparative analysis of the number of H atoms (N b_H ) in bubbles under simultaneous H-He irradiation versus pure H irradiation is presented in figure 6.The H + fluence gradually increases from 1.0 × 10 24 m −2 to 1.0 × 10 25 m −2 , corresponding to irradiation time ranging from 100 s to 1000 s.Comparative analysis of figures 5 and 6 reveals that the reduction in r b_HHe with increasing T is attributable to a significant decrease in N b_H within these bubbles.The release of solute H atoms primarily occurs through recombination processes at the W surface. H release is highly dependent on the magnitude of the recombination rate, denoted as K r , which escalates exponentially with an increase in T. Equation (5) indicates that higher temperatures result in increased release of H atoms from the W surface, consequently leading to reduced H retention.A critical condition for bubble growth involves the diffusion of a solute H atom within W to the bubble's inner surface, where it recombines with another H atom, forming a molecule.This newly formed molecule then releases into the bubble [36].Therefore, the observed reduction in r b_HHe with increasing T can be attributed to the decrease in C H within W. It is noteworthy that irradiation with a combination of H and He ions markedly increases the retention of H in the bubbles, in contrast to irradiation with pure H.The present simulation results demonstrate that H atoms continue to contribute to the growth of composite bubbles even at elevated temperatures of 1273 K, as shown in figure 6(c).
This study provides a comparative analysis that focuses on the differences in bubble radii under conditions of H-He coirradiation compared to situations involving only H or He irradiation.Figure 7 shows the average bubble radius (r b ) as a function of z at various temperatures.In conditions of both pure H irradiation and simultaneous H-He irradiation, H + fluence is maintained at 1.0 × 10 25 m −2 .For pure He irradiation  and H-He co-irradiation, He + fluence is set at 1.0 × 10 24 m −2 .He solute atoms exhibit a rapid diffusion into He bubbles, influencing their concentration and growth.At a given T, the radius of He bubbles (r b_He ) decreases with increasing z, while at a given He + fluence, r b_He increases with increasing T, as shown in figure 7 for pure He irradiation.These findings are consistent with our previous research [31].Moreover, simulations revealed that He nanobubbles tend to grow rapidly at elevated temperatures, attributed to their abundance of surface sites.In pure H irradiation, the radius of H bubbles (r b_H ) significantly decreases with increasing T from 473 K to 1273 K. K r increases exponentially with rising T, facilitating the recombination of H atoms into H 2 molecules on the W surface.This process significantly enhances the release of H atoms in W. Our findings reveal that r b_HHe decreases with rising T, attributable to the reduced contribution of C H in bubble growth.It is noteworthy that r b_HHe consistently exceeds the sum of the radii of individual H and He bubbles, emphasizing a significant synergistic effect between H and He.At 473 K, the contribution of H to bubble growth predominates, whereas at 1273 K, the role of He becomes more pronounced.This variation can be attributed to the enhanced retention of H in W at lower temperatures and the increased mobility of He at higher temperatures [29,32].The growth of H-He bubbles is primarily driven by the higher internal pressure resulting from the increased number of H and He atoms within bubbles.According to Greenwood's equilibrium condition (equation ( 14)), P HHe decreases with increasing r b_HHe , which implies that it is easier for a bubble with a larger radius to keep growing.
Figure 7 shows that the formation of the largest bubbles occurs in the surface region of the plasma-facing wall, a phenomenon attributed to the highest concentration of solute H/He atoms in this area.This research includes a comparative analysis of the maximum bubble radii (r b_ max ) under simultaneous H-He irradiation versus pure H or He irradiation.r b_ max notably increases with irradiation fluence at a constant T, as shown in figure 8. Particularly at 873 K, the synergistic effect of H and He on bubble growth is clearly observable.At a given fluence, r b_HHe is observed to be two to three times larger than the summed radii of individual H and He bubbles.According to equations ( 15) and ( 16), when a bubble contains both H and He, its ability to capture adjacent H/He atoms is primarily determined by the respective partial pressures of H and He within the bubble.The dependence of P He /P H on T and fluence has been shown in figure 8 that pre-existing He bubbles serve as efficient capture sites for surrounding H atoms. H solute atoms can diffuse to the inner surface of the He bubble, where they recombine to form a H 2 molecule.This newly formed H 2 molecule is then released into the He bubble, thereby increasing the partial pressure of H within it.Concurrently, the increased internal pressure contributes to the bubble's volumetric expansion, which in turn creates additional surface capture sites for the absorption of adjacent solute atoms.Figure 8(d) shows that the partial pressure of He exceeds that of H within smaller bubbles, as indicated by the shaded area, leading to He-predominant bubble growth.However, the predominance of He gradually decreases with increasing r b_HHe .The partial pressure of H significantly exceeds that of He in larger bubbles.This shift is attributed to the enhanced capture efficiency of the H-He bubble for surrounding solute H atoms, a mechanism that significantly contributes to the further growth of H-He bubbles.

Experimental study of hydrogen-helium bubble growth in tungsten
The irradiation exposed surface of W sample was examined after each step (mentioned in table 1) using AFM. Figure 9 shows the evolution of H-He bubbles in W during sequential irradiation by H and He ions at 873 K with an energy of 100 eV.In this study, the single-step irradiation doses for H and He ions are quantified as 1.0 × 10 24 m −2 and 1.0 × 10 23 m −2 , respectively.The experimental procedure begins with the implantation of H + into W, followed by He + , with subsequent alternation between the two types of ion irradiation.AFM observations are consistently performed on the same areas after each H/He plasma irradiation to ensure comparability.The conductivity in regions containing nanobubbles within the W near-surface layer is higher than in surrounding areas, particularly at the bubble edges as depicted in current images (see figure 10).This indicates the formation of nanometre-sized H-He bubbles within W [56].As reported by Roth and Schmid [57], H diffusion in W occurs relatively quickly, but its solubility within W is comparably low.This suggests that H, drawn toward W surfaces, tends to accumulate in regions with high He bubble concentrations near the surface, rather than penetrating deeper into the material.This aligns with the findings of this study.However, the introduction of excessive H into W often results in a notable decrease in its surface conductivity.Consequently, AFM was primarily utilized to observe the changes in the surface morphology of W post-irradiation. Figure 9 indicates that the radius of H-He bubbles significantly expands as the H + fluence increases from 2.0 × 10 24 m −2 to 8.0 × 10 24 m −2 , concurrently with an increase in He + fluence from 2.0 × 10 23 m −2 to 8.0 × 10 23 m −2 .Unexpectedly, localized delamination on the W surface is observed during the irradiation process, as  depicted in figure 11.The W experiences severe damage, with local delamination occurring on their surface at H + fluences ranging from 3.0 × 10 24 m −2 to 1.0 × 10 25 m −2 .Previous research demonstrated that increases in both bubble density and size in the W near-surface layer correlate with a significant rise in tensile stress perpendicular to the surface of the material [30].Present simulations reveal that the critical conditions for fracturing the surface layer depend on the size and concentration of bubbles in the irradiated material.The interaction between the surface layer and the underlying W matrix weakens under surface stress, resulting in local delamination once the stress exceeds a specific threshold.This phenomenon is not observable under irradiation with either H or He alone, providing compelling evidence for the synergistic promotion of bubble growth by the combined presence of H and He.

Comparative analysis of simulated and experimental data
Figure 12 shows the simulated data for bubble radius and H isotopes retention across the temperature range of 400 K-1000 K, compared with the experimental data from the literature [8,39,[58][59][60][61][62][63][64].The simulation values for r b_HHe correspond closely with the experimental results obtained using SEM/AFM, as shown in figure 12(a).Localized delamination significantly complicates the statistical analysis of bubbles.To minimize this impact, not only careful manual selection of specific regions but also multiple regions are selected in this research.H-He bubbles are manually counted from AFM images across the selected regions to calculate the average size and number density of bubbles, with a minimum radius threshold of 2.0 nm.The error is estimated by calculating the arithmetic mean deviation for values obtained from 10 different regions.Figures 12(b) and (c) provide a comparative analysis of the total H retention (T H ) in W under simultaneous H-He irradiation and pure H irradiation, respectively, to  further substantiate the validity of our model.However, the model initially underestimates the retention of H isotopes in W for time less than 300 s.This deviation is attributed primarily to the initial assumption of the model focusing solely on capture by low-density, small hydrogen bubbles.The ability of He bubbles to incorporate substantial amounts of H suggests that they can play a crucial role in H retention.Our findings confirm that the synergistic effect between H and He contributes to an increased retention of H isotopes in W at elevated temperatures.

Conclusions
Understanding the behaviour of tungsten (W) under plasma irradiation is crucial for various applications, especially in fusion reactors.This study has investigated the synergistic effects of hydrogen (H) and helium (He) plasma irradiation on bubble growth and H isotopes retention in W at different temperatures using the novel theoretical method proposed based on the modified diffusion rate equations.To substantiate the findings of the model, experiments are performed on polycrystalline W sample at 873 K in which it was sequentially exposed to 100 eV H and He ion irradiations with fluences of 1.0 × 10 24 m −2 and 1.0 × 10 23 m −2 , respectively.Sample is characterized using atomic force microscopy after each irradiation sequence.The model findings for the average bubble radius and H isotopes retention at various temperatures is compared with experimental data reported in the literature.Based on the combination of theoretical and experimental results, the major outcomes are as follows: • The incorporation of H into He bubbles leads to a significant increase in their internal pressure, promoting the bubble growth.It is observed that the capacity of a bubble containing both H and He to trap adjacent H/He atoms is largely governed by their respective partial pressures within the bubble.• The average bubble radius is dependent on both irradiation temperature and fluence as well as on depth from the surface.Bubbles in the vicinity of surface layer show rapid growth with an increase in fluence at a given temperature.For certain fluence, the average bubble radius considerably decreases with increase in temperature from 473 K to 1273 K. • AFM micrographs of the W sample exposed to both H and He plasma irradiation show a severely damaged and locally delaminated layer-absent in the sample exposed only to either H or He-providing compelling evidence of synergy between H and He plasma irradiation effects.• The average bubble radius computed using the model aligns excellently with experimentally determined values obtained through SEM/AFM analysis.• The average bubble radius and H isotopes retention at various temperatures are also compared with experimental data reported in the literature, it shows good agreement.However, more complexity may be incorporated in the model accounting for the formation of He bubbles in the presence of H, and the long-term ability of the H rich layer surrounding the bubble.

Figure 1 .
Figure 1.Illustration depicts the formation of H-He bubbles achieved through the capture of surrounding solute H atoms by He bubbles.

Figure 4
presents the spatial distributions of C t_H and C t_He at varying temperatures.The H/He diffusion depth and concentration exhibit a strong dependence on T. At a given T, C t_H exhibits slight dependence on H + fluence ranging from 1.0 × 10 24 m −2 to 1.0 × 10 25 m −2 .The capture of solute H atoms within defects leads to the formation of trapped H.This process predominantly dictates that C t_H is governed by C H at a specific temperature.Furthermore, the He atoms are relatively stable when trapped into defects and these trapped He are produced during the frequent hopping of solute He atoms in W.This leads to a consistent correlation between the distribution of C t_He and C He along the penetration depth.However, with increasing T, there is a significant decrease in both C t_H and C t_s .At z 0 , C t_H decreases from ≈ 10 25 m −3 to 10 19 m −3 (figures 4(a)-(c)), while C t_He decreases from ≈ 10 24 m −3 to 10 20 m −3 as T rises from 473 K to 1273 K (figures 4(d)-(f ))

Figure 7 .
Figure 7. Comparative analysis of bubble radii under simultaneous H-He irradiation versus pure H and pure He irradiation.H + fluence is consistently maintained at 1.0 × 10 25 m −2 , while the He + fluence is set at 1.0 × 10 24 m −2 .Temperature is (a) 473 K, (b) 873 K, and (c) 1273 K.

Figure 8 .
Figure 8.The radius of maximum bubbles (r b_ max ) dependence on temperature and fluence.The temperature is (a) 473 K, (b) 873 K, and (c) 1273 K. Additionally, (d) shows the dependence of He to H partial pressure ratio (P He /P H ) on temperature and ion fluence under simultaneous H-He irradiation.In (d), shading emphasizes areas where He partial pressure surpasses H within the bubbles.

Figure 9 .
Figure 9. AFM micrographs of W samples exposed to H/He plasma at a surface temperature of 873 K.The single-step irradiation doses for H and He ions are quantified as 1.0 × 10 24 m −2 and 1.0 × 10 23 m −2 , respectively.

Figure 10 .
Figure 10.Surface topography (a) and simultaneously measured current images (b) of W are presented, following sequential irradiation by H and He ions at 873 K with an energy of 100 eV.

Figure 11 .
Figure 11.Microstructural changes in the W surface post-irradiation were examined using AFM.The single-step irradiation doses for H and He ions are quantified as 1.0 × 10 24 m −2 and 1.0 × 10 23 m −2 , respectively.The temperature and H/He ions flux are 873 K and ≈ 1.0 × 10 20 m −2 s −1 , respectively.

Figure 12 .
Figure 12.Simulated data for the radius of bubble (a) and H isotope retention, compared with experimental measurements in the literature [8, 39, 58-64].(b) and (c) illustrate a comparison of H isotope retention in W under simultaneous H-He irradiation and pure H irradiation, respectively, to further substantiate the validity of our model.

Table 1 .
Parameters of H/He atoms in W material utilised in this work.