Diffusion Coefficients Of Isotopes 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.

Hydrogen isotope permeation and retention behavior in the RAFM steel manufactured by laser powder bed fusion

Laser powder bed fusion (LPBF) has emerged as a promising additive manufacturing technique for producing complex components across various industries. This method is particularly instrumental in fabricating reduced activation ferritic/martensitic (RAFM) steel, a candidate structural material for the tritium breeding blanket. Hydrogen transport behaviors in the conventional RAFM steel have been largely investigated; however, they are not well understood in the LPBF-RAFM steel. In this work, we studied the hydrogen isotope permeation and retention behavior in the RAFM steel fabricated by LPBF, utilizing the deuterium gas driven permeation and thermal desorption spectroscopy experiments. The results show that the hydrogen isotope permeability of the LPBF-RAFM steel is close to the conventionally fabricated RAFM steel, but the diffusion coefficient is greatly lower and the retention is markedly higher in the LPBF-RAFM steel compared to the conventional RAFM steel. The large number density of microvoids and TiC precipitates in the LPBF-RAFM steel could be the predominant factors that result in the decrease in hydrogen isotope diffusion coefficient and the increase in the total amount of deuterium retention.

Electronic property and effective diffusion coefficient calculation model of hydrogen isotopes in multicomponent steel 2.25Cr1Mo from first-principles calculations

Chrome-molybdenum (2.25Cr1Mo) ferritic steel is one of the primary materials used in heat exchanger pipes in the steam generators of high-temperature gas-cooled reactors (HTGRs). Studying the tritium diffusion mechanism in 2.25Cr1Mo ferritic steel is of vital importance for the prediction and interpretation of tritium activity concentration in the reactor. However, the permeation of hydrogen isotopes in these alloys remains difficult to predict owing to the lack of understanding of the microscopic interactions between hydrogen isotopes and multicomponent alloys. In this study, the electronic and diffusion properties of the hydrogen isotopes in 2.25Cr1Mo alloy were investigated using first-principles calculations. Hydrogen preferentially intercalated into tetrahedral interstitial sites rather than octahedral ones in 2.25Cr1Mo alloy. The Cr and Mo dopants induced strong repulsion between H and the matrix. Interaction between H and 2.25Cr1Mo exhibited a combination of ionic and covalent bonds with electrons transferred from the steel to H atom. Dopants acted as scattering centers with local interaction with H and expanded the preventive effect of H diffusion to the second-nearest tetrahedral interstitials with a high energy barrier. The effective H diffusion coefficient in the alloy was calculated by an approximate model based on the volumetric ratio of the components for the first time. The obtained pre-exponential factor and activation energy agreed well with the experimental results. The current research provides a reliable way to determine the effective diffusion coefficient of hydrogen isotopes in multielement alloys, which can accelerate R&D of tritium-resistant materials in both fusion and fission reactors.

Measurement on Diffusion Coefficients and Isotope Fractionation Factors by a Through-Diffusion Experiment

For radioactive waste disposal, it is important that local groundwater flow is slow as groundwater flow is the main transport medium for radioactive nuclides in geological formations. When the groundwater flow is very slow, diffusion is the dominant transport mechanism (diffusion-dominant domain). Key pieces of evidence indicating a diffusion-dominant domain are the separation of components and the fractionation of isotopes by diffusion. To prove this, it is necessary to investigate the different diffusion coefficients for each component and the related stable isotope fractionation factors. Thus, in this study, through-diffusion and effective-porosity experiments were conducted on selected artificial materials and natural rocks. We also undertook measurements relating to the isotope fractionation factors of Cl and Br isotopes for natural samples. For natural rock samples, the diffusion coefficients of water isotopes (HDO and H218O) were three to four times higher than those of monovalent anions (Cl−, Br- and NO3−), and the isotope fractionation factor of 37Cl (1.0017–1.0021) was slightly higher than that of free water. It was experimentally confirmed that the isotope fractionation factor of 81Br was approximately 1.0007–1.0010, which is equivalent to that of free water. The enrichment factor of 81Br was almost half that of 37Cl. The effective porosity ratios of HDO and Cl were slightly different, but the difference was not significant compared to the ratio of their diffusion coefficients. As a result, component separation was dominated by diffusion. For artificial samples, the diffusion coefficients and effective porosities of HDO and Cl were almost the same; it was thus difficult to assess the component separation by diffusion. However, isotope fractionation of Cl and Br was confirmed using a through-diffusion experiment. The results show that HDO and Cl separation and isotope fractionation of Cl and Br can be expected in diffusion-dominant domains in geological formations.

Operando Isotopic Exchange in Solid Oxide Fuel Cells: Oxygen-Transport Dependency on Applied Potential.

The oxygen isotopic exchange technique is a powerful tool to investigate the oxygen transport kinetics in an oxide solid. In a solid oxide fuel cell, isotopic surface exchange and diffusion coefficients are classically determined by using the Isotopic Exchange Depth Profiling method followed by ex situ SIMS characterizations. Despite its relevance, the utilization of in situ or operando techniques to measure the isotopic exchange under an electrical bias remains marginal. We developed here a set-up which enables operando monitoring of oxygen exchange in SOFC type cells under polarization. The system has been used for studying the oxygen mobility dependency upon polarization on a symmetrical Pt/YSZ/Pt cell (YSZ: yttria-stabilized zirconia). Homomolecular and heterolytic exchange reactions were undertaken to investigate the oxygen activation step and discriminate the limiting step among the sequence of elementary steps which constitute the oxygen transport process in the SOFC system. Oxygen ions incorporation into the dense ionic conductor was identified to be the rate determining step, and its first order rate constant dependency on applied potential was established.

High-efficiency lithium isotope separation in an electrochemical system with 1-butyl-3-methylimidazolium dicyanamide, 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide, and diethyl carbonate as the solvents

Traditional Li isotope separation methods such as the column exchange process are environmentally hazardous because of the mercury involved. In this research, a high-efficiency Li isotope separation technique with a separation coefficient of 1.054 was developed based on the diffusion and migration of Li isotopes in various solvents. In many solutions, the difference in the diffusion coefficient is small; therefore, the separation effect is not satisfactory. However, due to their unique physical and chemical properties, ionic liquids such as 1-Butyl-3-methylimidazolium dicyanamide and 1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide and some organic solvents such as diethyl carbonate show higher differences in Li isotope diffusion coefficients and mobilities, hence they can be used to achieve the efficient separation of Li isotopes. The isotope separation with four Li salts (LiBF4, LiCl, LiBr, and LiI) in the three solvents was investigated utilizing these differences. The results show that some Li salts can achieve excellent separation effect in ionic liquids and organic solvents. The corresponding model simulation results also show that the separation effect increases with the increase of the diffusion coefficient difference, and the higher separation coefficient may be realized by searching for the solvent with more differences in the Li isotope diffusion coefficients and mobilities.

Isotope Effect on Diffusion in Nafion Studied by NMR Diffusometry

The isotope effect H → D on diffusion in proton-exchange membrane Nafion 212 is investigated using 1H and 2H nuclear magnetic resonance (NMR) diffusometry in a static magnetic field gradient in the temperature range from 200 to 332 K for proton and from 245 to 332 K for deuteron transport. The diffusion coefficients of both isotopes have identical temperature dependence, while proton diffusion is 1.4 times faster than deuteron diffusion at the same humidity. This difference indicates a significant influence of the mass of the diffusing particle and allows us to conclude that the Grotthuss mechanism or relay diffusion of H+ or D+ ions prevails over the vehicular mechanism involving H2O molecules or H3O+ ions.

Numerical investigation for lithium isotope effect in ionic superconductor

The lithium isotope effect in ionic superconductors is numerically investigated. Using first-principles and kinetic Monte–Carlo simulations, the diffusion coefficients of 6Li and 7Li ions are calculated. Two important effects that cause the difference in the mobilities of lithium isotopes are also shown: the quantum effect, which decreases the activation barrier energy for lithium ion in a certain structure and increases the ratio of the diffusion coefficient of Li isotopes, as well as the correlation effect between 6Li and 7Li ions and vacancies. These results will assist in finding materials that exhibit large lithium isotope effect. The preferred chemical composition of lithium isotopes required to enhance the lithium isotope effect and the application of these isotopes as a separation membrane for the lithium ionic superconductors are discussed.

SIMULATION OF THE PROCESSES OF HYDROGEN ISOTOPES ABSORPTION IN SORPTION EXPERIMENTS

This paper presents a model that allows to describe the absorption of hydrogen isotopes by the investigated sample under the following conditions: a thin sample with known geometric dimensions is saturated from the gas phase with hydrogen isotopes at the given temperature in a chamber of known volume and the initial hydrogen isotope pressure in the chamber. Using the developed model, it was possible to describe perfectly the experimental results on the absorption of a three-component mixture of hydrogen isotopes and to determine the interaction parameters of hydrogen isotopes with vanadium V4Cr4Ti alloy. In particular, the solubility constant and the diffusion coefficient of hydrogen isotopes in the alloy were determined, as well as the parameters of their Arrhenius dependences. In the future, the proposed model can be used to simulate the processes of hydrogen storage in nuclear reactor facilities (NR), thermonuclear reactors (TNR) and petrochemical industries.

Diffusion coefficients of Mg isotopes in MgSiO3 and Mg2SiO4 melts calculated by first-principles molecular dynamics simulations

The mass dependence of diffusion coefficient (D) can be described in the form of DiDj=mjmiβ, where m denotes masses of isotope i and j, and β is an empirical parameter as used to quantify the diffusive transport of isotopes. Recent advances in computation techniques allow theoretically calculation of β values. Here, we apply first-principles Born-Oppenheimer molecular dynamics (MD) and pseudo-isotope method (taking mjmi=124,624,4824,12024) to estimate β for MgSiO3 and Mg2SiO4 melts.Our calculation shows that β values for Mg calculated with 24Mg and different pseudo Mg isotopes are identical, indicating the reliability of the pseudo-isotope method. For MgSiO3 melt, β is 0.272 ± 0.005 at 4000 K and 0 GPa, higher than the value calculated using classical MD simulations (0.135). For Mg2SiO4 melt, β is 0.184 ± 0.006 at 2300 K, 0.245 ± 0.007 at 3000 K, and 0.257 ± 0.012 at 4000 K. Notably, β values of MgSiO3 and Mg2SiO4 melts are significantly higher than the value in basalt-rhyolite melts determined by chemical diffusion experiments (0.05). Our results suggest that β values are not sensitive to the temperature if it is well above the liquidus, but can be significantly smaller when the temperature is close to the liquidus. The small difference of β between silicate liquids with simple compositions of MgSiO3 and Mg2SiO4 suggests that the β value may depend on the chemical composition of the melts. This study shows that first-principles MD provide a promising tool to estimate β of silicate melts.

Evaluation of isotope diffusion coefficient and surface exchange coefficient of ScSZ series oxide by oxygen isotope exchange method

In this work, the Isotope diffusion coefficient (D*) and surface exchange coefficient (k*) of Sc2O3 stabilized ZrO2 (ScSZ) series oxide, 6mol% Sc2O3-ZrO2 (6ScSZ), 10mol% Sc2O3-ZrO2 (10ScSZ) and 10mol% Sc2O3- 1mol% CeO2-ZrO2 (10Sc1CeSZ) were evaluated by using oxygen isotope exchange method. It was found that these ScSZ oxides showed a relatively higher D* value; 10Sc1CeSZ showed 1.1×10−7cm2s−1, 10ScSZ showed 9.3×10−8cm2s−1 and 6ScSZ showed 6.1×10−8cm2s−1 at 711°C, respectively. In addition, its activation energy was 1.0eV for 10Sc1CeSZ, 1.1eV for 10ScSZ and 1.0eV for 6ScSZ, respectively. The rapid change of D* due to the phase transition was also confirmed at around 600°C in the case of 10ScSZ. The surface exchange coefficient (k*) of these ScSZ oxides showed a relatively high value at lower temperature. 10Sc1CeSZ showed 1.3×10−8cms−1 at 498°C under lower vapor pressure of less than 20Pa.

Iron and nickel isotope fractionation by diffusion, with applications to iron meteorites

Mass-dependent, kinetic fractionation of isotopes through processes such as diffusion can result in measurable isotopic signatures. When these signatures are retained in geologic materials, they can be used to help interpret their thermal histories. The mass dependence of the diffusion coefficient of isotopes 1 and 2 can be written as (D1/D2)=(m2/m1)β, where D1 and D2 are the diffusion coefficients of m1 and m2 respectively, and β is an empirical coefficient that relates the two ratios. Experiments have been performed to measure β in the Fe–Ni alloy system. Diffusion couple experiments between pure Fe and Ni metals were run in a piston cylinder at 1300–1400 °C and 1 GPa. Concentration and isotopic profiles were measured by electron microprobe and ion microprobe respectively. We find that a single β coefficient of β=0.32±0.04 can describe the isotopic effect in all experiments. This result is comparable to the isotope effect determined in many other similar alloy systems. The new β coefficient is used in a model of the isotopic profiles to be expected during the Widmanstätten pattern formation in iron meteorites. The results are consistent with previous estimates of the cooling rate of the iron meteorite Toluca. The application of isotopic constraints based on these results in addition to conventional cooling rate models could provide a more robust picture of the thermal history of these early planetary bodies.

Isotopic effect at oxygen diffusion in imperfect crystals of cerium oxide

The surface and volume diffusion of oxygen isotopes in different phase states of Ce1 − xGdxO2 − x/2 crystals are studied with the high-speed molecular dynamics method (using graphics processors). It is shown that the ratio between the oxygen isotope diffusion coefficients (the so-called isotopic effect) in the volume of simulated crystals, D(O16)/D(O18) ≈ 1.05, agrees well with the well-known ratio \(\sqrt {M(O^{18} )/M(O^{16} )} = 1.06\) and does not depend on the temperature, phase state, and particle-particle interaction potential. On the surface of nanocrystals, the isotopic effect is a linear function of temperature. The ratio between diffusion coefficients of light and heavy isotopes grows with decreasing temperature and equals D(O16)/D(O18) ≈ 1.12 at T = 1000 K.

Lithium isotope fractionation by diffusion in minerals. Part 1: Pyroxenes

Several recent studies found large lithium isotopic fractionations correlated with concentration gradients in pyroxene minerals from lava flows and mantle nodules that were interpreted as indicating diffusion of lithium into the grains. Motivated by these findings experiments were undertaken in which powdered spodumene (LiAlSi2O6) or Li2SiO3 was used to diffuse lithium into Templeton augite or Dekalb diopside grains at 900°C and oxygen fugacity ranging from logfO2=−17 to logfO2=−12. The purpose of these experiments was to determine the diffusion coefficient of lithium in pyroxene minerals and to measure the isotopic fractionation of lithium in the diffusion boundary layer due to the relative mobility of 6Li compared to 7Li. The diffusion profiles of lithium that had not yet reached the center of Templeton augite grains were in most cases sharp steps propagating in from each boundary. In one case a more usual profile with smoothly decreasing lithium concentration with distance from the grain boundary was found. A model in which lithium occupies two different sites – one being fast diffusing interstitial lithium, the other much less mobile lithium in a metal site, reproduced both types of profiles. The step-like profiles arise in the model when interstitial lithium diffusing into the grain is strongly partitioned into abundant metal sites and thus does not penetrate further into the grain until all the metal sites at a given distance become filled. While the rate of propagation of the concentration step can be used to calculate an effective diffusivity for the penetration of lithium into the augite grains, the multiple speciation of lithium precludes making a separate precise determination of the diffusion coefficient of the interstitial lithium. Isotopic fractionations of 7Li/6Li of about 30‰ were found in the step-like diffusion boundary layers, which translate into a ratio of the isotope diffusion coefficients D7Li/D6Li=0.9592 (i.e., (6/7)β with β=0.27). The same value of β=0.27 was also able to fit the isotopic fractionation data from the experiment with the smoothly decreasing lithium concentration profile. The laboratory experiments confirmed that diffusion of lithium produces large kinetic isotopic fractionations and thus highlight the importance of isotopic measurements for discriminating when a particular instance of chemical zoning in minerals was the result of diffusion or some other process such crystal growth from an evolving melt. The experiments also showed that, contrary to conventional wisdom, isotopic gradients do not dissipate faster than gradients in the parent element, indeed the contrary is seen in several of the Templeton experiments where very large lithium isotopic fractionations persisted after the lithium concentration had become effectively homogenized. Published data of lithium isotopic fractionation of zoned augite grains from a Martian meteorite and in clinopyroxene grains from both lava flows on the Solomon Islands and from a San Carlos mantle xenolith were modeled in terms of lithium diffusion with an isotope fractionation parameter β between 0.25 and 0.30, which is very similar to that derived from the laboratory experiments.

Oxygen Transport in Perovskite Type Oxide La0.6Sr0.4Co0.2Fe0.8O3-δ

Oxygen isotope diffusion coefficient, D *, of La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF6428) was measured as a function of p(O2) and temperature. Vacancy diffusion coefficient, D V, was calculated from D * and reported values of oxygen nonstoichiometry, δ. There was little dependence of D V on δ or p(O2) while D V by conductivity relaxation method was reported to drastically decrease with decreasing p(O2) below 10-2 bar. The absolute values of D V in this study were about an order of magnitude larger than those by conductivity relaxation method.

Theory of isotope diffusion in a material with multiple species and its implications for hydrogen-enhanced electrical conductivity in olivine

The relationship between isotope diffusion coefficient and electrical conductivity is examined for a material where a dominant charge-carrying atomic species (e.g., hydrogen) is present as various forms with different diffusion coefficients (e.g., two protons trapped at M-site vacancy, one proton trapped at M-site vacancy etc.). It is shown that the isotopic diffusion occurs keeping the concentration ratio of each species fixed as determined by the thermo-chemical environment. Consequently, the isotope diffusion coefficient is the harmonic average of diffusion coefficients of individual species and is dominated by the slowest diffusing species. In contrast, when electric current is carried by charged species, the concentrations of individual species do not change. Therefore, electrical conductivity is related to the arithmetic average of individual diffusion coefficients dominated by the fastest diffusing species. The difference between these two cases can be large when different species have largely different diffusion coefficients. This model provides an explanation for the observed differences between experimental observations on isotopic diffusion (of H-D) and hydrogen-enhanced electrical conductivity and supports a hybrid model of hydrogen-enhanced electrical conduction where electrical conductivity is dominated by the fast moving hydrogen-related species. The species with the largest mobility may change with temperature leading to a change in anisotropy of conductivity. The degree of enhancement of electrical conductivity by hydrogen is high enough to explain most of the geophysically observed electrical conductivity of Earth’s upper mantle.

Experimental determination of the role of diffusion on Li isotope fractionation during basaltic glass weathering

In order to use lithium isotopes as tracers of silicate weathering, it is of primary importance to determine the processes responsible for Li isotope fractionation and to constrain the isotope fractionation factors caused by each process as a function of environmental parameters (e.g. temperature, pH). The aim of this study is to assess Li isotope fractionation during the dissolution of basalt and particularly during leaching of Li into solution by diffusion or ion exchange. To this end, we performed dissolution experiments on a Li-enriched synthetic basaltic glass at low ratios of mineral surface area/volume of solution ( S/ V), over short timescales, at various temperatures (50 and 90 °C) and pH (3, 7, and 10). Analyses of the Li isotope composition of the resulting solutions show that the leachates are enriched in 6Li (δ 7Li = +4.9 to +10.5‰) compared to the fresh basaltic glass (δ 7Li = +10.3 ± 0.4‰). The δ 7Li value of the leachate is lower during the early stages of the leaching process, increasing to values close to the fresh basaltic glass as leaching progresses. These low δ 7Li values can be explained in terms of diffusion-driven isotope fractionation. In order to quantify the fractionation caused by diffusion, we have developed a model that couples Li diffusion with dissolution of the glassy silicate network. This model calculates the ratio of the diffusion coefficients of both isotopes ( a = D 7/ D 6), as well as its dependence on temperature, pH, and S/ V. a is mainly dependent on temperature, which can be explained by a small difference in activation energy (0.10 ± 0.02 kJ/mol) between 6Li + and 7Li +. This temperature dependence reveals that Li isotope fractionation during diffusion is low at low temperatures ( T < 20 °C), but can be significant at high temperatures. However, concerning hydrothermal fluids ( T > 120 °C), the dissolution rate of basaltic glass is also high and masks the effects of diffusion. These results indicate that the high δ 7Li values of river waters, in particular in basaltic catchments, and the fractionated values of hydrothermal fluids are mainly controlled by precipitation of secondary phases.

Diffusion processes in a liquid mixture of lithium isotopes

The quantum mechanical theory of diffusion, as recently developed for liquid metals [M. Omini, Phil. Mag. 86 1643 (2006); Phil. Mag. 87 5249 (2007)], is now presented in a final version that improves and clarifies the original formulation. The new formulation uses a convergent variational method to solve the transport equation and confirms, through a rigorous analysis, the validity of the approximations introduced in the quoted papers. As a consequence, all previous calculations, concerning the self diffusion coefficients of liquid lithium isotopes, are automatically confirmed. The possibility of obtaining, as a limit of a convergent procedure, the true solution of the transport equation allows a reliable prediction of all isotope effects. In particular, it provides numerical values for the interdiffusion coefficients of 6Li and 7Li, which were not explicitly deduced in the previous works. The total consistency of these values with those measured by Feinauer et al. [Phys. Condens. Matter 6 L355 (1994)] further supports the theory. It is concluded that the whole set of experimental data on liquid lithium, as provided by the above authors, is theoretically explained within the experimental uncertainties.

Studies on a synthetic sitinakite-type silicotitanate cation exchanger: Part 1: Measurement of cation exchange diffusion coefficients

A commercially available synthetic silicotitanate (IONSIV ® IE-911), with a sitinakite-like structure, is a candidate material for the remediation of aqueous nuclear waste streams. These streams are often complex in their cation composition. This work investigates the effect of the presence of Na, K, Mg, Ca and Ba on the rates of removal of Cs and Sr radioisotopes as cations of importance in aqueous nuclear waste streams. Results are compiled as isotopic diffusion coefficients, and by analysis of changes in pH with time, observed as the systems reach equilibrium. This kinetic treatment provides necessary data for use in the modelling of plant performance and for the accurate determination of distribution coefficients which will be the subject of the second part in this series.

Solubility, Diffusivity, and Isotopic Exchange Rate of Hydrogen Isotopes in Li-Pb

The diffusion, solution and permeation coefficients of hydrogen isotopes in liquid Li-Pb which is a candidate liquid blanket material for fusion reactors were determined in the temperature range 573-973K using an unsteady permeation method. Each coefficiens was correlated to temperature as follows:The hydrogen permeation flux depends on the square root of pressure at 773-973K. Although the power of pressure declined below 0.4 when temperature was below 673K, the effects of surface resistance were neglected above 673K.The hydrogen solubility in liquid Li-Pbwas found to correlate with a Sievert’s constant.We calculated a height-equivalent to theoretical-plate of a gas-liquid countercurrent extraction tower for tritium recovery rates in liquid Li-Pb to be