Diffusion Coefficient Of Tritium Research Articles

Thermal expansion, lattice vibration, and isotope effect on hydrogen diffusion in BCC Fe, Cr, and W from first-principles calculations.

Fe, Cr, and W are important elements in the alloys of in-reactor materials and operate in high-temperature environments with thermal expansion. Their tritium-impeding abilities are crucial to the radiation safety of various nuclear reactors. In this study, first-principles density functional theory is combined with quasi-harmonic approximation to evaluate factors that can affect the interstitial formation energy and diffusion coefficient of hydrogen isotopes in body-centered cubic (BCC) Fe, Cr, and W, including thermal expansion, metal host lattice vibrations, phonon density-of-states (pDOS) coupling diffusing atoms, and isotope effects. Calculation results indicate that the interstitial formation energy decreases as lattice expansion increases, whereas the jump barriers remain almost constant. Thermal expansion, host lattice vibration, and pDOS coupling minimally affect the diffusion coefficients of hydrogen isotopes in Fe, Cr, and W. The diffusion coefficient ratios between hydrogen isotopes are higher than the inverse ratio of the square root of the isotope mass at low temperatures. However, they decrease to the inverse ratio of the square root of the isotope mass at temperatures exceeding 800K. This study comprehensively investigates factors that affect the diffusion coefficients of hydrogen isotopes in BCC Fe, Cr, and W, thus providing a firm theoretical foundation for predicting the diffusion coefficients of tritium at different temperatures using protium/deuterium diffusion coefficients.

Reactor experiments on irradiation of two-phase lithium ceramics Li2TiO3/Li4SiO4 of various ratios

The design of future fusion reactors involves the production of tritium inside the breeder blanket. The most promising material for solid breeder blankets is a two-phase lithium ceramic containing orthosilicate Li4SiO4 (LOS) and metatitanate Li2TiO3 (LMT) of lithium in various proportions. Tritium is formed in lithium under neutron irradiation by the reaction 6Li(n,α)T. Further, this tritium is extracted from the blanket with a purge gas and returned to the fusion zone, realizing the concept of a closed fusion cycle.Irradiation under fission reactor conditions is still one of the few available methods for estimating the parameters of tritium generation and release from lithium-containing materials in the "in-situ" mode. This paper presents the results of experiments on neutron irradiation of two-phase lithium ceramics of various ratios (LOS + 35 mol. % LMT (pebble size 250–1250 μm), LOS + 35 mol. % LMT (pebble size 500–710 μm) and LOS + 25 mol. % LMT (pebble size 500–710 μm) at the WWR-K research reactor.Irradiation of each batch of samples lasted from 5 to 22 days. The experiments were carried out by the vacuum extraction method. This paper describes the main methodological aspects of the studies, namely the technical features of four irradiation campaigns, the sequence and scope of the studies. A comparison is also made of the initial sections of reactor experiments for all campaigns, where the reactor was sequentially brought to power, according to which the parameters of the Arrhenius dependence of the effective tritium diffusion coefficients were estimated.

Features of Helium and Tritium Release from Li2TiO3 Ceramic Pebbles under Neutron Irradiation.

The operation of fusion reactors is based on the reaction that occurs when two heavy hydrogen isotopes, deuterium and tritium, combine to form helium and a neutron with an energy of 14.1 MeV D + T → He + n. For this reaction to occur, it is necessary to produce tritium in the facility itself, as tritium is not common in nature. The generation of tritium in the facility is a key function of the breeder blanket. During the operation of a D-T fusion reactor, high-energy tritium is generated as a result of the 6Li(n,α)T reaction in a lithium-containing ceramic material in the breeder blanket. Lithium metatitanate Li2TiO3 is proposed as one of the promising materials for use in the solid breeder blanket of the DEMO reactor. Several concepts for test blanket modules based on lithium ceramics are being developed for testing at the ITER reactor. Lithium metatitanate Li2TiO3 has good tritium release parameters, as well as good thermal and thermomechanical characteristics. The most important property of lithium ceramics Li2TiO3 is its ability to withstand exposure to long-term high-energy radiation at high temperatures and across large temperature gradients. Its inherent thermal stability and chemical inertness are significant advantages in terms of safety concerns. This study was a continuation of research regarding tritium and helium release from lithium metatitanate Li2TiO3 with 96% 6Li during irradiation at the WWR-K research reactor using the vacuum extraction method. As a result of the analysis of experiments regarding the irradiation of lithium metatitanate in vacuum conditions, it has been established that, during irradiation, peak releases of helium from closed pores of the ceramics are observed, which open during the first 7 days of irradiation. The authors assumed that the reasons samples crack are temperature gradients over the ceramic sample, resulting from the internal heating of pebbles under the conditions of their vacuum evacuation, and contact with the bottom of the evacuated capsule. The temperature dependence of the effective diffusion coefficient of tritium in ceramics at the end of irradiation and the parameters of helium effusion were also determined.

Tritium Desorption Behavior and Microstructure Evolution of Beryllium Irradiated at Low Temperature Up to High Neutron Dose in BR2 Reactor

The present study investigated the release of tritium from beryllium irradiated at 323 K to a neutron fluence of 4.67 × 1026 m−2 (E > 1 MeV), corresponding up to 22,000 appm helium and 2000 appm tritium productions. The TPD tests revealed a single tritium release peak during thermal desorption tests, irrespective of the heating mode employed. The tritium release peaks occurred at temperatures ranging from 1031–1136 K, depending on the heating mode, with a desorption energy of 1.6 eV. Additionally, the effective tritium diffusion coefficient was found to vary from 1.2 × 10−12 m2/s at 873 K to 1.8 × 10−10 m2/s at 1073 K. The evolution of beryllium microstructure was found to be dependent on the annealing temperature. No discernible differences were observed between the as-received state and after annealing at 473–773 K for 5 h, with a corresponding porosity range of 1–2%. The annealing at temperatures of 873–1373 K for 5 h resulted in the formation of large bubbles, with porosity increasing sharply above 873 K and reaching 30–60%.

Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium

The contribution of nuclear quantum effects (NQEs) to the kinetics and dynamics of interstitial H isotopes in face-centered cubic Pd was intensively investigated using several path-integral techniques, along with a newly developed machine-learning interatomic potential based on artificial neural networks for Pd–H alloys. The diffusion coefficients (D) of protium, deuterium, and tritium in Pd were predicted over a wide temperature range (50–1500 K) based on quantum transition-state theory (QTST) combined with path-integral molecular-dynamics simulations. The importance of NQEs even at high temperatures was illustrated in terms of the characteristic temperature dependence of the activation free energies for H-isotope migration in Pd. This illuminates the overall picture of anomalous D crossovers among the three H isotopes in Pd. In addition, the D of protium in Pd was directly computed using two approximate quantum-dynamics methods based on Feynman’s path-integral theory, i.e. centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), in the temperature range 370–1500 K. The D values obtained from the CMD and RPMD simulations were very similar and agreed better with the reported experimental values than the QTST results in this temperature range. Our machine learning-based path-integral calculations elucidate the underlying quantum nature of the ‘reversed S’-type nonlinear behavior of D for the three H isotopes in Pd on the Arrhenius plots.

Phase composition control of biphasic tritium breeding ceramics and correlation behavior of lithium and tritium

• High purity of the Li2TiO3-xLi4SiO4 ( x = 0.5, 1) biphasic ceramic powders . • A dependence on the phase ratio for the high-temperature stability. • Favourable tritium diffusion coefficient for the biphasic Li2TiO3-xLi4SiO4. • Fast prediction of the tritium release property by the electrical characteristics. Biphasic tritium breeding ceramics were prepared by the microwave-induced solution combustion (MSCS) method in a single step. The phase ratio of lithium titanate and lithium silicate can be effectively controlled by changing the Si/Ti atom ratios in the aqueous precursor. The combustion process is completed within ∽100 s, and the nano-structure Li 2 TiO 3 -Li 4 SiO 4 ceramic power can be obtained directly after the combustion reaction. This preparation approach is promising for the scale production of tritium breeding ceramics with various chemical compositions. Besides, as Li 4 SiO 4 absorbs CO 2, which leads to the formation of Li 2 SiO 3 and Li 2 CO 3 , the powder needs further calcination treatment at 983 – 1023 K. For the ceramic bodies sintered at 1073 K and 1223 K, the Li 2 TiO 3 - x Li 4 SiO 4 ( x = 1) ceramic shows high phase stability and small grain size of ∽200 nm. However, for the case of Li 2 TiO 3 - x Li 4 SiO 4 ( x = 0.5) ceramic, the Li 4 SiO 4 phase is transformed into Li 2 TiSiO 5 and Li 2 SiO 3 with a lithium loss in sintering process. On the other hand, the evaluation of the tritium migration behavior using the electrochemical workstation is performed. The calculation results show that the lithium diffusion coefficient ( D Li ) can reflect the D tritium for the ceramics with various phase compositions. It is found that the D tritium is not proportional to the lithium density in the ceramic. The Li 2 TiO 3 - x Li 4 SiO 4 ( x = 1) ceramic has a favorable tritium migration behavior than mono-Li 4 SiO 4 ceramic.

Determination of the activation energy of tritium diffusion in ceramic breeders by reactor power variation

In this work, the analysis of experimental results on the irradiation of lithium ceramics Li2TiO3 is presented. Lithium ceramics samples were irradiated at the WWR-K research reactor (Almaty, Kazakhstan) under continuous pumping conditions at a temperature of ~610°C for ~21 days with a thermal neutron flux of ~5•1013 n/(cm2•s). During the experiment, the release of tritium-containing molecules (HT, T2, HTO and T2O) was recorded by a mass-spectrometric method. During the reactor experiment with a frequency of about one to two times a day, a short-term (less than 10 minutes) reduction of reactor power by 25-50 % was conducted, with subsequent regain. In this case, as expected, samples temperature and the released flows of tritium-containing molecules decreased. This mode of reactor operation and obtained data allowed us to propose a method for assessing the temperature dependence of the diffusion coefficient of tritium in ceramics under reactor irradiation. This method assumes that with a rapid change in the reactor power and the sample temperature, the tritium concentration in the surface region does not change much. In contrast, the diffusion coefficient (which has an Arrhenius temperature dependence) varies greatly. It determines the decrease in tritium flows from the sample. In the paper, several sections of reactor power decrease/increase are analyzed, which are used to evaluate the diffusion coefficients of tritium in ceramics under reactor irradiation.

Tritium diffusion in a Li2TiO3 crystal terminated with the (001) surface from first-principles calculations.

The tritium release behavior of the Li2TiO3 crystal has become an important index to evaluate its comprehensive performance as a solid breeder material in nuclear fusion reactors. The tritium diffusion on the surface (surface diffusion) and diffusion from the inside to the surface (hopping diffusion) in Li2TiO3 crystals with a 1/3-Li(001) surface are systematically investigated by the first-principles method. Possible adsorption sites, diffusion pathways and energy barriers of surface diffusion and hopping diffusion have been calculated and analyzed, respectively. Tritium atoms are found to diffuse preferentially along the [100] direction on the surface and two equivalent pathways across the surface were identified. The obtained activation energies are about 0.50 eV for surface diffusion and 1.56 eV for hopping diffusion. The local density of states and Bader charge for typical surface diffusion and hopping diffusion pathways are calculated and analyzed. The results reveal that the tritium (T) atom bonds with neighboring oxygen (O) atoms during the surface diffusion, while the T-O interaction is significantly weakened in the hopping diffusion which results in the higher activation energy than that of surface diffusion. In combination with our previous work, a complete tritium diffusion model for the Li2TiO3 crystal is proposed and the corresponding tritium diffusion coefficients are obtained. Our obtained activation energies are in the same range as previous experimental data and could provide theoretical support for the future related experiments.

First-Principles Study of Tritium Diffusion in the Li3TaO4 Crystal.

Li3TaO4 with a high melting point, good thermal stability, and higher lithium content has become a possible choice for breeder materials, which have potential applications in future fusion reactors. Perfect and defect crystal models of Li3TaO4 are set up, and all of the tritium-diffusion pathways have been studied by the first-principles method. The activation energy barriers of different diffusion pathways are calculated and analyzed considering the pathway length and tritium–oxygen interactions. The obtained minimum energy barrier for tritium diffusing in the perfect Li3TaO4 crystal is only 0.34 eV. The minimum energy barrier is less than 0.72 eV when tritium diffuses in the defect Li3TaO4 crystal in the presence of a lithium vacancy. Finally, the diffusion coefficients of tritium in the Li3TaO4 crystal are calculated, which further confirm that it is easy for tritium to escape from the trap of the lithium vacancy and diffuse in the crystal. Such a tritium-diffusion behavior is in favor of the tritium-release process of the Li3TaO4 crystal and could provide theoretical guidance for the future applications of Li3TaO4 materials.

Diffusion of hydrogen isotopes in 3C-SiC in HTR-PM: A first-principles study

Silicon carbide (SiC) is the main diffusion barrier of tri-isotropic particles in high-temperature gas-cooled reactor pebble-bed modules (HTR-PMs). When analyzing the source term of tritium in a HTR-PM primary circuit, it is essential to determine the amount of tritium released, which requires the diffusion coefficient of tritium in SiC. In the present work, the diffusion behavior of hydrogen in 3C-SiC is investigated using density functional theory-based first-principles calculations, which can be used to estimate the diffusivity of tritium while ignoring the neutron and mass effects. Different charge states of hydrogen (i.e., H0, H− and H+) and all possible low-energy configurations and diffusion paths are also considered in the calculations. The results indicate that the charge state of hydrogen changes from negative to positive with the increase in Fermi energy. In addition, the most stable position of H− in SiC is a tetrahedral site surrounded by four Si atoms. Furthermore, minimum diffusion barriers of 0.45, 0.46 and 1.52 eV are determined for H0, H− and H+, respectively. The calculated diffusion coefficients from the present work agree well with those computed in the literature. In addition, the experimental results are closer to the negative hydrogen values computed in this study, indicating that the most likely charge state of hydrogen is negative. Our calculations provide a good reference for nuclear safety evaluation in HTR-PMs using the diffusivity of hydrogen in SiC.

Molecular dynamics simulation of diffusion of hydrogen and its isotopic molecule in polystyrene

Polystyrene is one of the target materials used in Inertial Confinement Fusion (ICF). Molecular dynamics simulations are performed in this report to study the diffusion of gases, including hydrogen and its isotopic molecule under normal temperature and pressure. According to the Mean Square Displacement (MSD) of the gas moving in polystyrene, the diffusion coefficient of hydrogen, deuterium and tritium in different molecular weight polystyrene were obtained. The calculated diffusion coefficients agree well with the results of former simulation studies. The diffusion coefficients of polystyrene of the same molecular weight gradually decrease along with the increase of mass fraction of hydrogen isotopes (hydrogen, deuterium and tritium). The study also finds that diffusion coefficients will decrease along with the increasing of polystyrene molecular weight. Moreover, the pair correlation functions, cohesive energy density and fractional free volume were studied corresponding to hydrogen isotopes diffusion coefficients.

First-principles study of the stability and diffusion properties of hydrogen in zirconium carbide

The stability and diffusion properties of interstitial hydrogen atom in bulk ZrC have been investigated by first-principles calculations. In energy, hydrogen atoms prefer to occupy the carbon substitutional site (C-SS) with a negative formation energy, consistent with the experimental observations. In the C-SS, the hydrogen atom obtains 0.702 electrons from its 1 NN Zr atoms, tending to achieve the most stable 1s2 electronic state. Two hydrogen atoms in the same tetrahedral interstitial site are able to form a pairing cluster along the 〈110〉 direction with the HH pair equilibrium distance of 1.30 Å, nearly twice the length of H2 bond, suggesting a relatively weak interaction between the HH pair. The diffusion energy barriers of hydrogen in pure and vacancy pre-existing ZrC matrix are calculated. It is found that the presence of native vacancies will capture the hydrogen atoms due to the large energy barrier to jump out the vacancy. Furthermore, the temperature-dependent diffusion coefficients of interstitial hydrogen, deuterium, and tritium in ZrC are predicted using the transition state theory.

Application of thermally expanded graphite for the cementation of cesium- and tritium-containing waste oils

Thermally expanded graphite (TEG) may be used for solidification of radioactive waste oils produced by the nuclear industry. TEG synthesized within the scope of this work retains the properties of a loose powder-like material when saturated with oil at the ratio of 20 g of oil per 1 g of TEG. At this ratio, the effect of wetting of the cement particles with oil, inhibiting the formation of a monolithic structure, is not manifested. As a result, the required compression strength of a cement compound is retained at the oil content of up to 27 vol %. The effective diffusion coefficients of 137Cs and tritium are calculated on the basis of the experimental data on leaching. For the compounds without additives, these diffusion coefficients are (1.4–1.6) × 10−13 m2/s for both radionuclides. The reason for the coincidence of the diffusion coefficients is the nature of molecular motion inside the winding transport pores of TEG determined by its structure. The diffusion coefficients decrease with time for tritium. The leaching rate of 137Cs does not exceed the value specified by GOST for the addition of bentonite to the compound in the amount of 6% by weight of the cement. Application of other mineral and organic additives does not give the desired effect and even increases the leaching rate. The leaching rate of tritium does not depend on additives (including bentonite).

Tritium through-diffusion test in non steady state: Can the effective diffusion coefficient be determined?

The diffusion coefficient of tritium in its liquid form through cementitious materials is an indicator of durability in the domain of nuclear waste disposal. Because the cement-based materials designed for the waste storage have very high confinement properties, diffusion tests tend to last several months if not years in some cases. Therefore, basing the determination of the tritium diffusion coefficient on the experimental data measured during non steady state is tempting. The aim of this work is to demonstrate that the determination during the transient regime of the effective diffusion coefficient and the material porosity leads to non-negligible underestimation of these quantities. Moreover, it appears that, when using a numerical model for the determination, their validity can only be judged on the basis of more than one criterion, whether those criteria are obtained from the experimental data or from a numerical model.

Determination of tritium diffusion coefficients in irradiated beryllium of S-200F grade

The work presents study of helium and tritium interaction with irradiated S-200F beryllium grade. The goal of research is related to solving the problem of detritiation of stored beryllium material. Also it is aimed to explain the mechanisms of processes occurring during tritium interaction with beryl-lium which is planned to be used in the future fusion-type reactor (FTR). The study consists of following stages: thermodesorption xperiments on gas release from irradiated beryllium, calculation of helium and tritium generated in beryllium; processing and analysis of experimental data; determination of basic pa-rameters of tritium interaction with irradiated beryllium. These data is needed for estimation of high-temperature degassing procedure such as detritiation method in case of S-200F eryllium grade as well as for calculation of tritium distribution in beryllium materials.

Tritium permeation in EUROFER in EXOTIC and LIBRETTO irradiation experiments

The reduced activation martensitic steel (RAFM) EUROFER is foreseen as a structural material in test breeder module (TBM) in ITER and breeder blanket in DEMO design. In a number of irradiation experiments conducted in high flux reactor (HFR) in Petten EUROFER was used as a containment wall of the breeder material, through which tritium permeation was monitored on line. Thus in EXOTIC-9/1 (EXtraction Of Tritium In Ceramics) experiment where Li2TiO3 pebbles were the breeder material, EUROFER was irradiated up to 1.3dpa at 340–580°C. In LIBRETTO experiments (LIBRETTO-4/1, -4/2 and -5) the breeder material was lead lithium eutectic which was in direct contact with the EUROFER containment wall. The neutron damage in steel achieved in the LIBRETTO experiments varied from 2 to 3.5dpa. The irradiation temperature was 350°C (LIBRETTO-4/1), 550°C (LIBRETTO-4/2), and 300–500°C (LIBRETTO-5).Tritium permeability was studied by varying the irradiation temperature and hydrogen concentration in the purge gas. From the analysis of the temperature transients performed in all four experiments yielded the tritium diffusion coefficients were derived, which appear to be factor ten lower than the literature data obtained in the gas driven permeation experiments.

Tritium release kinetics in lithium orthosilicate ceramic pebbles irradiated with low thermal-neutron fluence

Tritium release kinetics in lithium orthosilicate (Li4SiO4) ceramic pebbles irradiated with low thermal-neutron fluence was studied by out-of-pile annealing experiments. It was found that the tritium produced in Li4SiO4 pebbles was mainly released as tritiated water vapor (HTO). The apparent desorption activation energy of tritium on the pebble surface was consistent with the diffusion activation energy of tritium in the crystal grains, indicating that tritium release was mainly controlled by diffusion process. The diffusion coefficients of tritium in the crystal grains at temperatures ranging from 450K to 600K were obtained by isothermal annealing tests, and the Arrhenius relation was determined to be D=1×10−7.0 exp(−40.3×103/RT) cm2s−1.

Quantum–Thermal Crossover of Hydrogen and Tritium Diffusion in α-Iron

The diffusion coefficients of hydrogen (H) and tritium (T) in α-Fe have been computed using two approximate quantum dynamical techniques, that is, centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD), in the temperature range of T = 100–1000 K using the embedded atom method (EAM) potential. It has been found that the RPMD and CMD methods give very similar results. From a further analysis based on quantum transition-state theory (centroid density QTST) combined with path integral molecular dynamics (PIMD), it has been clear that there is a crossover between thermal and quantum mechanisms at about T = 500 and 300 K for H and T diffusions, respectively. The importance of nuclear quantum effects at low temperatures has been illustrated in terms of the effective free-energy surface map.

Study on oxidation of hydrogen over commercial catalyst for tritium recovery system

For the establishment of the D-T fusion reactor technology, recovery of tritium released into the working area of fusion power plants is quite important. When tritium leaks to working areas, the last barrier is the wall of the building. Due to higher diffusion coefficient of tritium, it diffuses through the wall and would be readily liberated to the environment. Thus, the tritium recovery system is indispensable for the D-T fusion reactor. The objective of the present study is to develop the advanced technology of the tritium recovery system.In the near future, deuterium plasma discharge experiments scheduled be conducted with Large Helical Device (LHD) in National Institute for Fusion Science. A small amount of tritium is produced by D-D reaction in LHD. Tritium in plasma exhaust gases and process gas during discharge needs to be recovered, and thus the design and construction of the tritium recovery system used for that purpose is a matter of considerable urgency.The tritium recovery system usually consists of catalysts and adsorbents, which is the most conventional and reliable method for removing tritium that is accidentally released into the working area of these facilities. However, more recent and advanced type of catalysts on the market cannot be directly applied to the design of tritium recovery system, because of paucity of design data for tritium recovery system. In this study, the authors performed oxidation experiments of hydrogen over a catalyst. The experiments were performed by changing various experimental parameters.

Carbon sorbents for immobilization of tritium-containing waste oils

Emission of tritium from the pump oil-carbon sorbent-cement compositions (where the carbon sorbent is thermally expanded graphite or charcoal fabricated by thermal or radiation evaporation of a cellulose material) was studied. The compositions are characterized by a high hold-up ability with respect to oil components, when the matrix is contacted with water. The apparent diffusion coefficients of tritium are equal to 10−15–10−16 m2 s−1. The compositions are found to be resistant to radiation and can be recommended for solidification of radioactive waste oils.