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By performing the first-principles calculations, we explore the dissolution and diffusion of hydrogen (H) in hexagonal closed packed zirconium (Zr) as well as its interaction with vacancy. We show that the tetrahedral (TE) interstitial site is the favorable trapping site for a single H atom with the solution energy of −0.45 eV. Such a negative solution energy is due to the strong electronic bond between H and neighboring Zr atoms. Moreover, the energy barrier for the migration of H from a TE site to its 1NN and 2NN TE site is 0.12 eV and 0.42 eV, respectively. It is noteworthy that the first path only slightly contributes to the experimentally measured H diffusivity in Zr, because the H atom is trapped by two nearest neighboring TE sites. Thus, the effective activation energy for H diffusion in Zr should be mainly determined by the second path, and the corresponding energy barrier is 0.42 eV. Furthermore, since the electronic density (available volume) in vacancy is lower (larger) than that of interstitial site, vacancy is a strong trap for H atoms in Zr. We demonstrate that the maximum of 8 H atoms can be accommodated in a mono-vacancy without the observation of H2 molecule. These results can provide a basis to develop Zr materials in nuclear cladding devices.

We have investigated the dissolution, diffusion, and retention of hydrogen (H) in tungsten-rhenium (W-Re) sigma (σ) phase using a first-principles method and thermodynamic models, in order to explore the influence of Re-rich precipitation on H behaviors in W. Taking the most stable W-Re σ phase (W-33.3 at.% Re) as an example, it is found that the solution energy of H at most interstitial sites (>80%) in W-Re σ phase is much lower than that in pure W. Specifically, the H solution energy at most stable interstitial site in W-Re σ phase is only 0.47 eV, ~54% lower than that in pure W. This can be attributed to that W-Re σ phase provides the larger available volume for interstitial H than the pure W, weakening the W-H repulsive interaction. Moreover, it has been demonstrated that this trend is almost independent on the Re concentration in W-Re σ phase. We have further determined the interaction between H atoms and mono-vacancy in W-Re σ phase based on the calculation of H trapping energies and the Polanyi-Wigner equation. The W-type and Re-type vacancy can accommodate 10 and 5 H atoms at room temperature (RT) in σ phase, respectively, and thus the average trapping capability of vacancy for H in σ phase is stronger than that in pure W (~6 H atoms at RT). Consequently, our calculations reveal that the Re-rich precipitation (both interstitial and vacancy sites) can serve as the strong trapping centers for H in W, significantly enhancing the H retention, which is entirely different from the negative effect of dispersed-Re/small Re clusters.

Here, we review recent computational findings focused on the behavior of transmutation elements (TEs) in Tungsten (W). W is chosen as one of the most promising materials for the divertor armor and plasma facing components in future fusion reactors. However, W in exposure of fusion neutrons can cause the transmutation reaction and produce TEs, such as rhenium and osmium. The presence of TEs can change chemical component of materials, and therefore inevitably influence the microstructure and properties of W materials. Multiscale simulation methods have been employed to investigate the dissolution, diffusion and radiation induced precipitation of TEs, as well as their effects on the behaviors of hydrogen isotopes in W. This systematic review can provide an insightful understanding to estimate the influence of TEs on the properties and performance of W-based materials. Keywords: Tungsten, Transmutation elements, Radiation induced precipitation, Point defects, Hydrogen

Seeding the impurity elements in W can affect the H behaviors. The effect of Ne on H behaviors in W bulk and W (110) surface has been investigated with the first-principles density functional theory (DFT) calculations in the present paper. It is found that the interactions between the interstitial Ne and H are attractive in bulk W. Ne atom can reduce the binding energies for H in the vacancy and divacancy, and the binding energies decrease linearly with the ratio of Ne and vacancy. In the W (110) surface without vacancy, the threefold hollow site is the most preferable site for H adsorption; Ne atom cannot be adsorbed on the W surface and in the subsurface because of the weak interaction. The substitutional Ne in subsurface can impede H absorption, and increase the diffusion barrier for H from the surface into subsurface.

Dislocation, playing a crucial role in the plastic deformation of metals, can be significantly affected by introducing solute elements. Hydrogen (H) embrittlement is one such example, while the underlying mechanism for H affected dislocation structural stability and mobility remains unclear and the role of H has been controversial. Here, using first-principles calculations, we demonstrate that the effect of H on screw dislocation in bcc metals is H concentration-dependent, signified by a H-induced transition of SD core structure. At low concentrations of H segregation, dislocation maintains the intrinsic easy-core structure, and H atoms are attached to the "periphery" of dislocation to enhance dislocation motion. In contrast, at high H concentrations, dislocation transforms into a hard-core, metal hydride-like structure, as H atoms become the "body" of dislocation to significantly reduce the dislocation mobility. Further, such local easy-to-hard transition is found to be induced by just one solute of other elements, including helium, carbon, nitrogen and oxygen, independent of solute concentration. Our work sheds new light on the H-dislocation interactions in bcc metals, having broad implications in the interstitial solute-related phenomena.

We have investigated the effects of noble gas elements (helium, neon, argon and krypton) on the dissolution and accumulation behavior of hydrogen (H) in tungsten (W) using a first-principles method, as well as the behaviors of themselves. Noble gas atoms energetically prefer to occupy the tetrahedral interstitial site (TIS) in W, as the same of H. The TIS → TIS is their optimal diffusion path, and the diffusion energies increase with the increasing of atomic radius. All of them are energetically favorable clustering by self-trapping. It is found that the presence of the noble gas elements have significant effect on H behavior in W. Both interstitial noble gas atoms and their complex with vacancy can serve as strong trapping centers of H, which can be attributed to the redistribution of electron density and lattice distortion induced by noble gas. Most importantly, we have demonstrated that H trapping capability of noble gas clusters will increase with the increasing of the number of noble gas atoms in both interstitial and vacancy-complex cases. The H trapping energy surrounding the noble gas clusters with four atoms is comparable to that in noble gas-free vacancy. Further, the formation of noble gas clusters is much easier than that of vacancy due to the self-trapping interaction between noble gas atoms (>1 eV for interstitial case and >4 eV for vacancy-complex case), and thus the H trapping centers will rapidly increase after noble gas pre-irradiation/implantation. Consequently, the self-trapping character of noble gas induces their strong trapping effect on H.

International audience; We apply the Object Kinetic Monte Carlo method to simulate the hydrogen (H) clustering behaviour with large vacancy (V) clusters in tungsten. The main advantage of this method is to consider the temperature effects, large V clusters, and long-time evolution. It is thus a very useful tool to study the microstructure evolution of defects in irradiated materials covering from the atomic scale to mesoscale. Simulation results show that the number of trapped H atoms by V and V clusters decreases with the increase of temperature. This is expected because the de-trapping ability of H atoms increases when the temperature is increased. With the correction of the zero-point-energy in calculating binding energies, the present results show that the number of H atoms trapped by monovacancy decreases for all studied temperatures. We also found that the trapping ability of V clusters for H decreases with the increase of the sizes of V clusters, independent on temperature. The H concentration can largely affect the clustering behaviour of HmVn. When the H saturation concentration is reached, the clustering behaviour of HmVn is mainly determined by the sizes of V clusters.

We have investigated the hydrogen–beryllium (H–Be) interaction and the behavior of Be in tungsten (W) in order to explore the influence mechanism of Be on H using a first-principles method. A single Be atom is energetically favorable sitting at the octahedral interstitial site (OIS) instead of the tetrahedral interstitial site (TIS), and prefers to diffuse along the OIS → TIS → OIS path. Interestingly, it has been demonstrated that there is large binding energy between Be atoms in W (>1 eV), leading to them energetically clustering. This can be attributed to the strong Be–W repulsion and the intrinsic electrophobic properties of Be. Further, it is found Be has significant effect on H behavior in W. On the one hand, the interstitial Be atom can enhance the stability of H in W, and thus it can serve as a trapping center for H, due to the redistribution of electron density induced by Be. This will block H diffusing deeper into the bulk, leading to the decrease of H retention in W. On the other hand, the H trapping capability of vacancy will be severely weakened by Be, because Be will provide electrons to vacancy resulting in the increasing of the electron density. Hence, the Be-V complex only can hold 5H atoms, 58.3% less than that of the Be-free vacancy, and there is no H2 molecule formation. This indicates Be could suppress H bubbles formation in W. Consequently, H retention and blistering in W can be suppressed by doping Be.

The effects of hydrogen induced vacancy formation in tungsten have been investigated with a first-principles method based on the density functional theory. Hydrogen is demonstrated to assist the formation of vacancy and such effect is enhanced with increasing of hydrogen concentration. Using the energy of a single tungsten atom for the bulk as the reference energy, a spontaneous vacancy formation in tungsten is observed when more than two hydrogen atoms are introduced. These results provide a good explanation for creation of super-abundant vacancies in tungsten and can contribute to understand the mechanism of hydrogen bubble formation.

We have explored the retention of hydrogen (H) in tungsten (W) by investigating its dissolution and aggregation in vacancy clusters (VCs) using a first-principles method and thermodynamic models. The solution energy of a single H in the VCs is in the range of -0.99 ~ -0.64 eV, much lower than that at a mono-vacancy (~ -0.37 eV) and interstitial site (~ 1.01 eV) in W. Such a remarkable discrepancy is rationalized on the electronic interaction of H with its neighboring W atoms, which varies from repulsion to attraction with H moving from perfect crystal to vacancy/VCs. Specifically, the solution/trapping energies of H in VCs can be well categorized by the coordination number of its neighboring W atoms, i.e. the lower the coordination number of W, the stronger is the H-W attraction and the lower is the H solution/trapping energy. Furthermore, taking the V_9^m cluster as an example, it is observed that the multiple H atoms form a multilayer nested cage configuration at VCs surface initially, and then the stable H2 molecules form in the center of VCs. Interestingly, the pre-existed H atoms in VCs inner surface has a shielding effect on the H-W interaction, decreasing the electron density of the central region of VCs and facilitating the formation of H2 molecules. Moreover, the desorption temperatures of H in VCs are also predicted based on the Polanyi-Wigner equation, which are in good agreement with the available thermal desorption spectroscopy experiments. Our calculations provide a good reference to understand the influence of VCs on the retention and evolution of H in W.

We have performed a first-principles investigation with a zero point energy correction on dissolution and diffusion of hydrogen (H) in a Σ5 (3 1 0)/[0 0 1] molybdenum (Mo) symmetrical tilt grain boundary (STGB). H prefers to stay at the interstitial site in the vacant space of the Mo GB with a negative solution energy (−0.42 eV) and segregation energy (−1.16 eV), which are decreased in the presence of vacancy in the GB. Furthermore, the H solution energy at the vacancy in the Mo GB is lower than that in the Mo bulk, suggesting a larger trapping capability for H of the vacancy in the Mo GB. The dissolving stability of H in the Mo GB can be explained by the low charge density that the GB provides for H. Kinetically, H prefers to easily diffuse within the vacant space along the Mo GB with a small diffusion barrier (0.04 eV), and to migrate to the GB from the bulk. These results provide a systematically exploration and analysis of H behaviors in the Mo GB at an atomic scale, which suggest that the Mo GB can serve as a trapping center for H, similar to the vacancy. In particular, a detailed comparison of H dissolution and diffusion behaviors in a Mo GB with those in a tungsten GB is performed. This can be helpful in understanding the experimentally observed H bubble formation in the Mo GB from the microscopic view.

We have investigated the dissolution and diffusion behaviors of hydrogen (H) in copper (Cu) based on first-principles calculations in combination with the classical thermodynamics models. A single H atom energetically prefers to occupy the octahedral interstitial site (OIS) instead of the tetrahedral interstitial site (TIS). This can be confirmed by the charge density results. The dissolved equilibrium concentration of H is 8.98 × 10−7 at a typical temperature 600 K. We demonstrate that the OIS → TIS → OIS path is the optimal diffusion path of H in Cu with diffusion barrier of 0.23 eV. Double H atoms tend to be paired up at the two neighboring OIS’s along the 〈1 1 0〉 direction with a distance of 2.59 A and a binding energy of 0.07 eV. This suggests a weak attractive interaction between H atoms, with the implication that self-trapping of H and thus formation of the H2 molecules are quite difficult in the bulk Cu.

We have investigated site occupancy and mechanical properties of a vanadium (V) Σ5(310)/[001] grain boundary (GB) with hydrogen (H) using a first-principles method. The segregation energy is calculated to be −0.29 eV for the energetically favorable V GB interstitial site, indicating that H energetically prefers to segregate into the V GB. We demonstrate that H can largely affect the mechanical properties of the V GB. The tensile strength and the Griffith fracture energy are reduced by approximately 13% (to 18.42 GPa) and 10% (to 1.74 J/m2) because of H segregation in comparison with that of the clean V GB, respectively. Our total energy calculations show that H acts as an embrittler to the V GB based on the Rice-Wang model. The atomic configurations and charge transfer analysis show that the segregated H weakens the surrounding interfacial V-V bonds, leading to the V GB mechanical properties degradation.

We have investigated structure and solubility of H, as well as H–vacancy interaction in tungsten (W) single crystal employing a first-principles method. Single H atom is shown to be energetically favorable sitting at the tetrahedral interstitial site (TIS). The solubility of H is estimated in W according to the Sieverts’ law. We found that the solution concentrations are 2.3 × 10 −10 and 1.8 × 10 −7 at the typical temperatures of 600 K and 1000 K, respectively. The calculated results are basically consistent with the experiments. The vacancy can be found to play a key role on the trapping of H in W. There exists a very strong binding between single H and vacancy with the binding energy of 1.18 eV. With the H atoms added, the H n V complexes can be easily formed in the vacancy. A monovacancy is shown to be capable of trapping as many as 7 H atoms. Kinetically, we show that the H jumps into the vacancy from the first nearest neighboring TIS into vacancy with a much reduced barrier of 0.02 eV, which indicates a down-hill “drift” diffusion of H towards vacancy. The physical mechanism underlying H assisted vacancy formation is originated from that H atoms can stimulate the formation and growth of vacancy or void by binding with vacancy to decrease the effective formation energy of vacancy in W.

The effects of carbon (C) on hydrogen (H) trapping in tungsten (W) have been investigated by using a first-principles method, C exhibits a weak attractive interaction with H at a distance of ∼2.5 A in intrinsic W. H is energetically favorable to be far away from C, and prefers to bind onto an isosurface of an optimal charge density of 0.10 electrons/A 3 at the vacancy with C. Such optimal charge density region shrinks when more H atoms are added, and disappears with the addition of a sixth H, which bonds strongly with C characterized by a much higher C–H charge density. The presence of C increases the trapping energy of H at the vacancy, indicating a strong effect of C on H trapping in W.

We perform first-principles calculations to investigate the stress effects on stability and diffusion of H in W. Both the solution energy and the diffusion barrier of H decrease with increasing tensile stress. We show that the stress will not alter the site preference and the relative stability, with ∼0.4 eV stress-independent energy difference between the TIS and the OIS. We demonstrate the solution and the diffusion of H in W becomes more difficult under the applied compressive stress, which theoretically provides a possible way to suppress the H retention in W.

A first-principles computational tensile test has been preformed to investigate the effects of hydrogen on a tungsten grain boundary. It has been found that the maximum ideal tensile strength of the tungsten grain boundary with hydrogen atom segregation was 32.85 GPa, which was about 9% lower than that of the clean tungsten grain boundary (36.23 GPa). This indicated that the theoretical strength of the tungsten grain boundary became weaker in the presence of the hydrogen atom. Atomic configuration analysis showed that the grain boundary fracture was caused by the interfacial bond breaking. The Griffith fracture energy was calculated to be 161 meV/A 2 (2.58 J/m 2 ) and 155 meV/A 2 (2.48 J/m 2 ) for the tungsten grain boundary without and with the hydrogen atom segregation, respectively. The solution energy of the hydrogen atom in a fracture free surface was −0.31 eV, which was 0.08 eV lower than that of the hydrogen atom in a tungsten grain boundary. This indicated that hydrogen was a grain boundary embrittler according to the Rice-Wang thermodynamic theory. The Bader charge analysis suggested that the physical origin for hydrogen-induced embrittlement was the charge transfer induced by hydrogen in the tungsten grain boundary.

Employing a first-principles method, we have investigated dissolution and diffusion properties of hydrogen (H) in molybdenum (Mo), one of potential candidates for plasma facing materials in a nuclear fusion Tokamak. We show that single H atom is energetically favorable sitting at the tetrahedral interstitial site (TIS) instead of octahedral interstitial site and diagonal interstitial site. This can be confirmed by the electron localization function result. Bader charge analysis suggests that the bonding between H and surrounding Mo is mainly ionic mixed with slight covalent component. Double H atoms tend to be paired up at the two neighboring TIS’s along the 〈1 1 0〉 direction with the distance of ∼0.221 nm and the binding energy of 0.03 eV. This suggests a weak attractive interaction between H atoms, with the implication that self-trapping of H and thus formation of the H2 molecules are quite difficult in an intrinsic Mo environment. We demonstrate that the diffusion barrier of H that jumps between the TIS’s is 0.16 eV, and the dissolved concentration of H in the intrinsic Mo is 2.6 × 10−8 at a typical temperature of 600 K. The diffusion coefficients of H, D, and T are different due to the different masses, which are calculated to be 1.3 × 10−7 m2/s, 9.2 × 10−8 m2/s, and 7.5 × 10−8 m2/s at 600 K.

A series of batch experiments were conducted in 125 mL serum bottles to assess the toxicity of different concentrations of ammonia nitrogen to the specific methanogenic activity of anaerobic granular sludge from upflow anaerobic sludge bed(UASB) and expanded granular sludge bed(EGSB) reactors. The effects of pH value and temperature on toxicity of ammonia nitrogen to anaerobes were investigated. The results show that the specific methanogenic activity of anaerobic granular sludge suffers inhibition from ammonia nitrogen, the concentrations of ammonia nitrogen that produce 50% inhibition of specific methanogenic activity for sludge from UASB and EGSB reactor are 2.35 and 2.75 g/L, respectively. Hydrogen utilizing methanogens suffers less inhibition from ammonia nitrogen than that of acetate utilizing methanogens. Hydrogen-producing acetogens that utilize propionate and butyrate as substrates suffer serious inhibition from ammonia nitrogen. The toxicity of ammonia nitrogen to anaerobic granular sludge enhances when pH value and temperature increase. Anaerobic granular sludge can bear higher concentrations of ammonia nitrogen after being acclimated by ammonia nitrogen for 7 d.

We investigate the effects of carbon (C) on hydrogen (H) solubility in copper (Cu) using a first-principles method. We show C can increase the solution energy of H in the bulk Cu originated from the charge density redistribution, which leads to a weak repulsion between H and C in Cu. On the contrary, we demonstrate the C-vacancy (C-V) complex can serve as a trapping centre of H, and one C-V complex can hold up to six H atoms. Moreover, it is found that C can effectively decrease the solution energy of a single H in the vacancy, 0.68 eV lower than that of H in the C-free vacancy, changing the solution process of H in the vacancy from endothermic to exothermic. This can be attributed to the strong bonding interaction between H and C in the vacancy. Based on analyzing the role of C in different metals, we propose that the effects of C on the H solubility in the vacancy mainly depend on the difference between the H-C interaction and the C-metal atom interaction. These indicate that C plays a key role in H trapping behavior in Cu.

When an impurity is doped in a solid, it inevitably induces a local stress, tending to expand or contract the lattice. Consequently, strain can be applied to change the solubility of impurity in a solid. Generally, the solubility responds to strain ``monotonically,'' increasing (decreasing) with the tensile (compressive) strain if the impurity induces a compressive stress or vice versa. Using first-principles calculations, however, we discovered that the H solubility can be enhanced by anisotropic strain in some bcc metals, almost independent of the sign of strain. This anomalous behavior is found to be caused by a continuous change of H location induced by anisotropic strain. Our finding suggests a cascading effect of H bubble formation in bcc metals: the H solution leads to H bubble formation that induces anisotropic strain that in turn enhances H solubility to further facilitate bubble growth.

Employing a first-principles method, we have studied the stability, diffusivity, and permeation properties of hydrogen (H) and its isotopes in bcc vanadium (V). A single H atom is found to favor the tetrahedral interstitial site (TIS) in V. The charge density distribution exhibits a strong interaction between H and its neighbor V atoms. Analysis of DOS and Bader charge reveals that the occupation number of H-induced low energy states is directly associated with the stability of H in V. Further, H is shown to diffuse between the neighboring TISs with a diffusion barrier of 0.07 eV. Diffusion coefficients and permeabilities of H isotopes in V are estimated with empirical theory. At a typical temperature of 800 K, the diffusion coefficient and the permeability of H are 2.48 × 10(-4) cm(2) s(-1) and 2.19 × 10(-9) mol m(-1) s(-1) Pa(- 1/2), respectively.

We reveal the microscopic vacancy trapping mechanism for H bubble formation in W based on first-principles calculations of the energetics of H-vacancy interaction and the kinetics of H segregation. Vacancy provides an isosurface of optimal charge density that induces collective H binding on its internal surface, a prerequisite for the formation of ${\text{H}}_{2}$ molecule and nucleation of H bubble inside the vacancy. The critical H density on the vacancy surface before the ${\text{H}}_{2}$ formation is found to be ${10}^{19}--{10}^{20}\text{ }\text{H}$ atoms per ${\text{m}}^{2}$. We believe that such mechanism is generally applicable for H bubble formation in metals and metal alloys.

Employing a thermodynamic model with previously calculated first-principle energetics as inputs, we determined the hydrogen (H) concentration at the interstitial and monovacancy as well as its dependence on temperature and pressure in tungsten and molybdenum. Based on this, we predicted the critical H concentration for H bubble formation at different temperatures. The critical concentration, defined as the value when the concentration of H at a certain mH-vacancy complex first became equal to that of H at the interstitial, was 24 ppm/7.3 GPa and 410 ppm/4.7 GPa at 600 K in tungsten and molybdenum in the case of a monovacancy. Beyond the critical H concentration, numerous H atoms accumulated in the monovacancy, leading to the formation and rapid growth of H-vacancy complexes, which was considered the preliminary stage of H bubble formation. We expect that the proposed approach will be generally used to determine the critical H concentration for H bubble formation in metals.

Tungsten (W) is considered to be one of the most promising plasma-facing materials (PFMs) for next-step fusion energy systems. However, as a PFM, W will be subjected to extremely high fluxes of low-energy hydrogen (H) isotopes, leading to retention of H isotopes and blistering in W, which will degrade the thermal and mechanical properties of W. Modelling and simulation are indispensable to understand the behaviour of H isotopes including dissolution, diffusion, accumulation and bubble formation, which can contribute directly to the design, preparation and application of W as a PFM under a fusion environment. This paper reviews the recent findings regarding the behaviour of H in W obtained via modelling and simulation at different scales.

We investigate the physical origin of H–He interaction in W in terms of optimal charge density by calculating the energetics and diffusion properties using a first-principles method. On the one hand, we show a strong attraction between H and He in W originated from the charge density redistribution due to the presence of He, driving H segregation towards He. This can block the permeation of H into deeper bulk and thus suppress H blistering. On the other hand, we demonstrate that He, rather than H, energetically prefers to occupy the vacancy centre due to its closed-shell structure, which can block H2 formation at the vacancy centre. This is because He causes a redistribution of charge density inside the vacancy to make it ‘not optimal’ for the formation of H2 molecules, which can be treated as a preliminary nucleation of the H bubbles. We thus propose that H retention and blistering in W can be suppressed by doping the noble gas elements.

We have investigated the dissolution, segregation and diffusion of hydrogen (H) in a tungsten (W) grain boundary (GB) using a first-principles method in order to understand the GB trapping mechanism of H. Optimal charge density plays an essential role in such a GB trapping mechanism. Dissolution and segregation of H are directly associated with the optimal charge density, which can be reflected by the H solution and segregation energy sequence for the different interstitial sites. To occupy the optimal-charge-density site, H can be easily trapped by the W GB with the solution and segregation energy of −0.23 eV and −1.11 eV, respectively. Kinetically, such a trapping is easier to realize due to the much lower diffusion barrier of 0.13–0.16 eV from the bulk to the GB in comparison with the segregation energy, suggesting that it is quite difficult for the trapped H to escape out of the GB. However, the GB can hold no more than 2 H atoms because the isosurface of optimal charge density almost disappears with the second H atom in, leading to the conclusion that H2 molecule and thus H bubble cannot form in the W GB. Taking into account the lower vacancy formation energy in the GB as compared with the bulk, we propose that the experimentally observed H bubble formation in the W GB should be via a vacancy trapping mechanism.