Diffusion Coefficients Of Isotopes Research Articles

Isotopic fractionation of noble gases by diffusion in liquid water: Molecular dynamics simulations and hydrologic applications

Despite their great importance in low-temperature geochemistry, diffusion coefficients of noble gas isotopes in liquid water ( D) have been measured only for the major isotopes of helium, neon, krypton and xenon. Data on the diffusion coefficients of minor noble gas isotopes are essentially non-existent and so typically have been estimated by a kinetic-theory model in which D varies as the inverse square root of the isotopic mass ( m): D ∝ m −0.5. To examine the validity of the kinetic-theory model, we performed molecular dynamics (MD) simulations of the diffusion of noble gases in ambient liquid water. Our simulation results agree with available experimental data on the solvation structure and diffusion coefficients of the major noble gas isotopes and reveal for the first time that the isotopic mass-dependence of all noble gas self-diffusion coefficients has the power-law form D ∝ m − β with 0 < β < 0.2. Thus our results call into serious question the widespread assumption that the ‘square-root’ model can be applied to estimate the kinetic fractionation of noble gas isotopes caused by diffusion in ambient liquid water. To illustrate the importance of this finding, we used the diffusion coefficients determined in our MD simulations to reconsider the geochemical modeling of 20Ne/ 22Ne and 36Ar/ 40Ar isotopic ratios in three representative hydrologic studies. Our new modeling results indicate that kinetic isotopic fractionation by diffusion may play a significant role in noble gas transport processes in groundwater.

Diffusion‐driven kinetic isotope effect of Fe and Ni during formation of the Widmanstätten pattern

Abstract— Iron meteorites show resolvable Fe and Ni isotopic fractionation between taenite and kamacite. For Toluca (IAB), the isotopic fractionations between the two phases are around +0.1‰/amu for Fe and −0.4‰/amu for Ni. These variations may be due to i) equilibrium fractionation, ii) differences in the diffusivities of the different isotopes, or iii) a combination of both processes. A computer algorithm was developed in order to follow the growth of kamacite out of taenite during the formation of the Widmanstätten pattern as well as calculate the fractionation of Fe and Ni isotopes for a set of cooling rates ranging from 25 to 500 °C/Myr. Using a relative difference in diffusion coefficients of adjacent isotopes of 4‰/amu for Fe and Ni (β = 0.25), the observations made in Toluca can be reproduced for a cooling rate of 50 °C/Myr. This value agrees with earlier cooling rate estimates based on Ni concentration profiles. This supports the idea that the fractionation measured for Fe and Ni in iron meteorites is driven by differences in diffusivities of isotopes. It also supports the validity of the value of 0.25 adopted for β for diffusion of Fe and Ni in Fe‐Ni alloy in the temperature range of 400–700 °C.

Diffusion Coefficient of Tritium Through Molten Salt Flibe and Rate of Tritium Leak from Fusion Reactor System

Diffusion coefficients of hydrogen isotopes in Flibe were correlated with making reference to previous relating data of F- ion self-diffusivity and Flibe viscosity and so on. Rates of tritium permeation through structural materials in a fusion reactor system with Flibe blanket were estimated comparatively under conditions with or without a Flibe permeation barrier. A way to lower the tritium leak rate below a level regulated by law was proposed, and its effectiveness was discussed.

Mobility and diffusion of oxygen isotopes in YBa2Cu3O6+x : Monte carlo simulation

The self-diffusion (D0) and isotope diffusion (D*) coefficients of oxygen in YBa2Cu3O6+x are calculated as functions of the temperature (600–1200 K) and the oxygen content (0<x<1). The Monte Carlo simulation is performed with due regard for both the interaction of oxygen ions at lattice sites in the basal planes of YBa2Cu3O6+x and the interaction between a jumping ion at a saddle point and the environment. Equilibrium thermodynamic characteristics (including the phase diagram and the heat capacity) are calculated in terms of the Hamiltonian of interaction between oxygen ions at the lattice sites. It is found that an increase in the oxygen content leads to a decrease in the diffusion coefficients D0 and D*, an increase in the effective activation energies for diffusion by 0.3–0.5 eV, and a decrease in the Haven ratio from 1 to ∼0.5.

Release Behavior of Tritium from Graphite Material

The behavior of tritium at removal from graphite material for a fusion reactor is discussed. The mass transfer coefficient representing the isotope exchange reaction between hydrogen isotopes in the gas stream and tritium existing on graphite surfaces and that between water vapor in the gas stream and tritium on the surface are quantified. It was found that the reaction rate between hydrogen isotopes in the gas stream and tritium on the surface is much slower than that between water vapor in the gas stream and tritium on the surface. And, the release behavior of tritium from a graphite particle to the gas phase is calculated with the reaction rates obtained in this study using the solubility and the diffusion coefficient of hydrogen isotopes in graphite that have been presented in the previous report by the authors. A way to remove tritium from a graphite surface applying the isotope exchange reaction between water vapor in the gas stream and tritium on the surface turns out to be effective at the room temperature, although a temperature >1000 K is needed to release tritium from the bulk of a 10-μm graphite particle.

Isotopic Exchange and Oxygen Diffusion in the La0.88Sr0.12Ga0.82Mg0.18O3 – α–Molecular Oxygen System

The oxygen isotopic exchange kinetics in La0.88Sr0.12Ga0.82Mg0.18O3 – αand in the same electrolyte whose surface layer is enriched with cobalt ions is studied. Rates of different types of exchange and oxygen isotope diffusion coefficients in oxide are determined at 970–1200 K and oxygen pressures of 400–1200 Pa. The activation energy for the interphase oxygen exchange and the order of heteroexchange vs. oxygen pressure relationship are determined. The presence of cobalt ions in the near-surface layer alters the surface exchange parameters, such as the oxygen heteroexchange rate (which increases), order of the heteroexchange vs. oxygen pressure relationship, and the ratio between rates of different exchange types. The oxygen isotope diffusion coefficients coincide in both electrolytes but differ from those calculated from the electroconductivity data with the Nernst–Einstein equation.

A study of radon and thoron release from Egyptian building materials using polymeric nuclear track detectors

The free exhalation rates of both thoron and radon, the specific activities of 224Ra, and 226Ra, and the physical properties, such as the emanation coefficients and radon effective diffusion coefficient of several building material samples were determined using LR-115 and CR-39 polymeric nuclear track detectors. The free areal exhalation rate was measured by the sealed cup-technique, whereas the radium content was obtained by the alpha-autoradiographic method. The calibration coefficient for thoron measurements in air using cylindrical cup equipped with LR-115 detector was estimated. Moreover, the calibration coefficients for measurements of the specific activities of 224Ra and 226Ra were also evaluated. New method was developed for evaluating the emanation coefficient as well as the diffusion coefficient of radon isotopes in the studied materials.

Oxygen Transport Properties of La1 − xCaxCrO3 − δ as an Interconnect Material of a Solid Oxide Fuel Cell

Oxygen isotope diffusion coefficients were determined for via bulk and via grain‐boundary diffusion as functions of calcium content (x), temperatures from 1073 to 1273 K, and oxygen partial pressures from to at T = 1273 K. Both bulk and grain‐boundary diffusion coefficients increased with calcium content. For , the activation energy is 160 and for bulk and grain‐boundary diffusion, respectively. The bulk‐diffusion coefficient increased with decreasing oxygen partial pressure. The oxygen vacancy diffusion coefficient was calculated as at T = 1273 K, constant regardless of calcium content or oxygen‐vacancy content. The effect of surface exchange on the oxygen permeation through was quantitatively evaluated. © 2000 The Electrochemical Society. All rights reserved.

Isotope fractionation by diffusion in molten oxides

Laboratory diffusion experiments specifically designed to resolve small differences in the relative mobility of isotopes were used to measure the mobility of 76Ge vs. 70Ge in molten GeO 2 (1400°C, 0.5 GPa) and 48Ca vs. 40Ca in molten CaO–SiO 2–Al 2O 3 (1500°C, 1.0 GPa). When the mass ( m) dependence of the diffusion coefficient ( D) of isotopes 1,2 is written in the form ( D 1/ D 2) = ( m 2/ m 1) β, we find β ≤ 0.025 for Ge isotopes and β = 0.05 to 0.1 for Ca isotopes. The degree of isotope fractionation by diffusion between melts of the same initial isotopic composition but different elemental abundance depends not only on β but also on the ratio of the elemental concentrations in the two melts. Given our measured value of β for Ca isotopes, we predict that diffusion between melts with a factor of 5 to 10 difference in Ca content will produce variations in 44Ca/ 40Ca ratio of 2 to 5‰. To the extent that Ge is a good analogue for Si, we would not expect significant fractionation of Si isotopes. But even if the value of β for Si isotopes were as large as that for Ca, we would still not expect measurable diffusive isotopic fractionations of Si because the contrast in Si content between most natural melts is less than a factor of 2.

Influence of coexisting hydrogen isotopes on diffusion of tritium in niobium

The tracer diffusion coefficient of tritium in Nb has been measured at 523 K under the condition that tritium coexists with protium or deuterium. These data suggest the trend that the tracer diffusion coefficient of tritium in NbH x T y is somewhat larger than that in NbD x T y , though a definite conclusion has been reserved because their difference is small and comparable to the scattering of the experimental data. The concentration dependence of tracer diffusion coefficient of tritium in NbH x T y and NbD x T y can be practically considered to be equal to that of NbT x . On the basis of these experimental data and the data reported by Fukai et al., it has been suggested that the tracer diffusion coefficient of lighter hydrogen isotopes is appreciably influenced by coexisting heavier hydrogen isotopes but that of heavier hydrogen isotopes is scarcely influenced by coexisting lighter hydrogen isotopes.

ＳＩＭＳによるセラミックス中の酸素拡散の測定

One of the most interesting features of secondary ion mass spectrometry (SIMS) is its ability to detect isotope ratio in a small area of a solid state sample. It enables to study isotope diffusion properties in solids. Experimental setup and data analysis for isotope exchange/SIMS measurement are introduced focusing on its application to oxygen transport study in ceramic materials. Fast diffusion paths and preferred surface reaction sites are visualized by sector type SIMS. Oxygen vacancy diffusion coefficient and chemical diffusion coefficient of nonstoichiometric oxides are also estimated from the isotope diffusion coefficient and thermodynamic data.

Analysis of the diffusion controlled growth of cobalt silicides in bulk and thin film couples

The solid state reaction between Co and Si has been studied in bulk diffusion couples between 850 and 1100 °C. At the scale of the observations made, the three phases Co2Si, CoSi, and CoSi2 are found to grow simultaneously, according to diffusion controlled kinetics. The results are analyzed in term of the Nernst-Einstein equation that directly relates diffusion fluxes to the free energy changes driving the formation. The growth rates obtained for CoSi2 at high temperatures, in the present bulk samples, are compared with those determined by others in thin films, at much lower temperatures. The comparison requires that attention should be paid to two factors. The first one is that the laws of growth are slightly different for a phase growing simultaneously with two other ones (bulk) and one phase growing alone (thin films). The second factor is the grain size of the various samples, which varies with the temperature of reaction. Once this is done, excellent agreement is obtained between the two sets of measurements. Moreover it is shown that knowing the grain size, it is possible to calculate quite accurately the growth rate from the respective isotope diffusion coefficients both for lattice and grain boundaries of Co and Si in CoSi2.

Measurements of Permeation of Hydrogen Isotopes through &amp;alpha;-Iron by Pressure Modulation and Ion Bombarding

Permeation response of hydrogen and deuterium through α-iron under the condition of pressure modulation was measured to determine the diffusion coefficient which contained no surface effects. The diffusion coefficients of hydrogen isotopes are obtained between 500 and 1000 K.Permeation under hydrogen ion bombardment was also studied to extend the temperature range of diffusion coefficient measurements.The ratio of the diffusion coefficients of hydrogen isotopes (DH⁄DD) depends on the temperature; the value of the ratio approaches unity with increasing temperature. This behavior differs from that of common fcc metals in which the value of the ratio approaches \sqrt2 with increasing temperature. The isotope effect of hydrogen diffusivity in α-iron can not be explained by the classical rate theory, and the quantum-mechanical correction is needed.

Transport in aqueous solutions of Group IIB metal salts. Part 7.—Measurement and prediction of isotopic diffusion coefficients for iodide in solutions of cadmium iodide

Isotopic diffusion coefficients for iodide have been measured in aqueous solutions of cadmium iodide over the concentration range 0.1–1.0 mol dm–3, using the diaphragm cell technique. The iodide diffusion coefficients are shown to decrease smoothly but steeply from the infinite dilution value of 2.046 × 10–5 cm2 s–1 to less than half that value in the concentration range above 0.1 mol dm–3. This remarkable decline has been assigned to the presence of complexes of the type CdI+2–xx(x= 1, 2, 3, 4). The irreversible thermodynamic analysis developed previously for cadmium diffusion in this same system (part 4) has been extended to include isotopic diffusion of labelled ligands on multiply substituted complexes. Using this analysis the observed iodide diffusion coefficients have been predicted within close limits over the whole concentration range up to ≈ 0.5 mol dm–3.

Transport in aqueous solutions of group IIB metal salts (298.15 K). Part 3.—Isotopic diffusion coefficients for cadmium-115 ions in aqueous cadmium iodide

Cadmium isotopic diffusion coefficients (Daa) were determined in aqueous cadmium iodide in the concentration range 0.1–0.6 mol dm–3. Daa passes through two maxima, one below 0.1 mol dm–3, the other at 0.4 mol dm–3. Irreversible thermodynamic analysis shows that these maxima are due to positive fluctuations in the isotope-to-isotope coupling contributions to Daa. For these studies a modified diaphragm cell technique was developed.

Transport in aqueous solutions of group IIB metal salts (298.15 K). Part 4.—Interpretation and prediction of isotopic diffusion coefficients for cadmium in dilute solutions of cadmium iodide

A method for predicting isotopic diffusion coefficients for component ions in a self-complexed electrolyte has been developed. In an irreversible thermodynamic analysis the diffusion coefficient has been shown to be a function of the mobility coefficients of the free ion and its complexes together with the interionic coupling coefficients between labelled and unlabelled species. It is shown that these coefficients may be evaluated by an extension of the methods developed earlier to predict isothermal transport in such systems. Cadmium ion diffusion coefficients in aqueous cadmium iodide, Daa, have been predicted (0.003–0.10 mol dm–3). These describe the maximum anticipated experimentally. Observed and calculated Daa agree to within 3 % at 0.1 mol dm–3.

Application of irreversible thermodynamics to isotopic diffusion. Part 1.—Isotope–isotope coupling coefficients for ions and water in concentrated aqueous solutions of alkali metal chlorides at 298.16 K

From literature sources irreversible thermodynamic parameters may be obtained for all alkali metal chloride salt solutions at 298.16 K in the concentration range 0–3.0 mol dm–3. Comparable data for isotopic diffusion coefficients of component ions and water are incomplete. These have been obtained in this study, using a diaphragm cell, for all but rubidium ion in rubidium chloride. It is shown that these two sets of data may be combined to yield Onsager frictional coefficients (rii*) or mobility coefficients (lii*) which measure the kinetic interaction between isotopes as a function of concentration for each salt solution. Interpretation of lii* for ions is made difficult because of large frame-of-reference contributions with water solvent, but these may be compared with values calculated from the Onsager limiting law. Frictional interpretations are more explicit. The main factor contributing to the experimental diffusion coefficient for ions, Dii, remains ion-water friction which amounts to some 90 % for many slats even at 3.0 mol dm–3. The primary cause is that interionic friction between ions of opposite charge is largely cancelled by isotope–isotope friction in the expression for Dii.

Investigation of the transport properties of a quaternary ammonium anion exchange membrane. Part 1.—Application of irreversible thermodynamics to the chloride form

A detailed study of the transport properties of the chloride form of a strong base quaternary ammonium anion exchange membrane has been completed. Experimental determination of isotope diffusion coefficients and electrical, salt diffusion, and osmotic properties has been made. From these data a complete irreversible thermodynamic analysis of the system in 0.1 and 1.0 mol dm–3 sodium chloride solutions has been obtained.Using primarily the frictional coefficient treatment, it is shown that the kinetic interaction between membrane ions and fixed charge contributes to a very large degree in reducing ion mobility, but that this contribution is large primarily because the membrane has very large internal ionic molality and not due to ion association. Equally, although there is considerable evidence for water structure enforcement around quaternary ammonium ions in aqueous solution, there is no evidence for this effect in the membrane. Water-to-water friction is similar to that obtained in other membrane studies on cation exchangers and to aqueous electrolyte solutions. The terminal hydroxyl groups on the quaternary ammonium fixed charges of the A104 membrane may do much to modify the unique solvation of alkyl substituted analogues. Pressure permeability and osmotic coefficients obtained by calculation indicate that the membrane is almost ideally semi-permeable with a reflection coefficient, σ, of 0.99 and 0.97 in 0.1 and 1.0 mol dm–3 salt solutions, respectively, and has a very low salt permeability.

Diffusion Coefficient in an Ordered Binary Alloy

The isotope diffusion coefficient of one of the components in a binary ordered alloy is derived for the vacancy mechanism by the path probability method. By introducing the concept of the transposed lattice and making full use of the symmetry of the system, the derivation is made transparent and simpler than the treatment reported previously. The new derivation leads quite naturally to decomposition of the correlation factor into two components related to the two sublattices; the decomposition leads to a detailed interpretation of the correlation factor. The vacancy availability factor and the effective jump frequency factor are defined and their importance in the diffusion in the ordered phase is pointed out.

Comparison of the transport properties of normal and expanded forms of a cation-exchange membrane. Part 2.—Self-diffusion and electrical properties of membranes in the sodium form in concentrated sodium chloride

The influence of shrinking and increasing salt uptake on the transport properties of normal and expanded membranes has been examined. Isotopic diffusion coefficients from sodium and chloride ions were found to be functions of changing tortuosity and membrane electrolyte molality. Tortuosity corrected coefficients agreed closely with those of sodium and chloride ions in aqueous sodium chloride at equal molalities. Diffusion coefficients for tritiated water were constant, when corrected for tortuosity, and equal to the diffusion coefficient of tritiated water in pure water. From electrical measurements, it is shown that the ratio of solvent-fixed velocities of sodium and membrane-sulphonate ions is constant over the experimental range of conditions. The sulphonate ion is more mobile than sodium on this frame of reference and similar in behaviour to chloride or nitrate in free aqueous solution. All data indicate the validity of a simple aqueous model for membrane transport phenomena.