Isotope Effect For Diffusion Research Articles

Diffusion: Isotope Effect and Manning Factor in Liquids

In this paper, the diffusion isotope effect and the Manning factor are investigated by means of Molecular Dynamics simulations in liquid Cu-Ag alloys. The values for the diffusion isotope effect parameter allow for the estimate of the number of atoms that are moving cooperatively in a basic diffusion event as ‘seen’ by a given (tracer) atom. On average, in the considered alloys and considered temperatures, this is limited to between 5 and 15. This is consistent with results of Molecular Dynamics simulations on the average coordination number calculations. This would suggest that, together with a given atom, a majority of the neighbouring atoms are involved in a basic diffusion event. Results for the Manning factor (MD simulation) for Cu-Ag liquid alloys are seemingly in agreement with the direct exchange mechanism where only two atoms are involved in the elementary diffusion event. This is not in apparent agreement with the isotope effect results. It was shown, however, that any ring mechanism, or, more complex, cage mechanism are, in fact, a combination of several simultaneously happening direct exchanges. Any other possible mechanisms for diffusion in liquids is most likely a combination of direct exchanges as well. It can be seen then that the collective nature of all considered mechanisms is very similar and follows the direct exchange signature properties.

The Diffusion Isotope Effect and Diffusion Mechanism in Liquid Cu-Ag and Cu-Ni Alloys

In this paper, the diffusion isotope effect and diffusion mechanism are investigated by means of molecular dynamics simulations in two liquid alloys, Ni-Ag and Ni-Cu. The values for the diffusion isotope effect parameter allow for the estimate of the number of atoms which are moving cooperatively in a basic diffusion event as experienced by a given atomic species. It is shown that the composition dependence ofNDis typically very small. However, the temperature dependence of this parameter is much more pronounced. In addition, it is shown that, on average, in these alloys and temperatures considered,NDis limited to the range: 5<ND<17. This is consistent with results of molecular dynamics simulations on the average coordination number calculations. This would suggest that, together with a given atom, depending on temperature, the neighbouring atoms are all involved in the basic diffusion event.

Some Peculiarities of Isotopic Materials Science

The present status of the isotopetronics and its future application is briefly overviewed. Over of last five decades a great number of stable isotopes and well – developed method of their separation has made it possible to date to grow crystals of C, LiH, ZnO, ZnSe, CuCl, GaN, GaAs, CdS, Cu2 O, Si, Ge, α-Sn as well as graphene with a controllable isotopic composition. The use of such objects allows the investigate of not only the isotope effects in diffusion and lattice dynamics (vibrational, elastic and thermal properties) but also the influence of such effects on the electronic states via electron – phonon coupling (the renormalization of the band – to – band transition energy Eg as well as the exciton binding energy Eb) as well as strong nuclear force influence on elementary excitations. The thermal conductivity enhancement in the isotopically enriched materials amounts (C, Ge, Si) to almost 10% at room temperature and is close to a factor of six at the thermal conductivity maximum around 20K (Si-case). The change in the lattice constant is ∆a/a~10-3-10-4, while the change ∆cik in the elastic constants amounts to several percent. Very pronounced and general effects of isotope substitution are observed in phonon spectra. The scattering lines in isotopically mixed crystals are not only shifted (the shift of LO lines exceeds 100 cm-1) but are also broadened. Capture the thermal neutrons by isotope nuclei followed by nuclei decay produces new elements in a very large number of possibilities for isotope selective doping of different materials. Although the technology of isotopic materials science is still in its infancy, it is necessary underline that it has a very wide applications: beginning from optical fibre technology still modern development in isotope information storage and isotope quantum computers.

The isotope effect for Mg-Fe interdiffusion in olivine and its dependence on crystal orientation, composition and temperature

Isotopic fractionation associated with diffusion in crystals is the most reliable means of understanding the origin of mineral zoning in igneous and metamorphic rocks. We have experimentally determined the relative diffusivities of iron isotopes in olivine as a function of crystallographic orientation, composition, and temperature. For two isotopes i and j of an element, the isotope effect for diffusion is parameterized as Di/Dj = (mj/mi)β, where β is a dimensionless parameter, and D and m stand for diffusivity and mass, respectively. A series of single crystal diffusion couple experiments were conducted at an oxygen fugacity of QFM – 1.5 at temperatures of 1200, 1300, and 1400 °C. For the Fo83.4-Fo88.8 composition pair, βFe is isotropic and a value of 0.16 ± 0.09 can be used to describe diffusion along all major crystallographic axes in olivine. Based on our experiments and previously reported coupled Mg-Fe isotopic data, we also estimate βMg = 0.09 ± 0.05 for this range of olivine composition. For the Fo88.8-Fo100 composition pair, βFe becomes anisotropic with βFe [100] = 0.11 ± 0.03, βFe [010] = 0.14 ± 0.03 (both within error of the value measured for the Fo83.4-Fo88.8 pair), and βFe [001] = 0.03 ± 0.03. For Fo# between 83.4 and 100, βFe [100] and βFe [010] are thus independent of composition. The reason why βFe [001] transitions from ∼0.16 to ∼0.03 close to the Mg-endmember is unclear. Over the temperature range studied, a dependence of βFe on temperature was not resolved. General analytical expressions are introduced to calculate isotopic fractionation as a function of distance, time, β, and the concentration contrast between the diffusing media for spherical, cylindrical, and planar geometries.

Theoretical constraints on the isotope effect for diffusion in minerals

Isotopes of the same element generally diffuse at slightly different rates within a mineral, due to the difference in their masses. The magnitude of the mass dependence of the diffusion coefficient depends on the product of the correlation coefficient f (representing the degree to which the diffusion process deviates from a random walk) and the coupling coefficient K (representing the degree to which the motion of an atom during a single jump is coupled to that of other nearby atoms). Whereas K has been found to vary over a relatively narrow range, f can vary over a wide range from ∼0 to 1.Diffusive isotope effects are expected to be large for trace and minor cations that diffuse slowly relative to the major cations that occupy the same sites and diffuse by the same mechanism. Diffusive isotope effects are also expected to be large for elements that diffuse rapidly by a simple interstitial mechanism. In both of these cases, the correlation coefficient is similar to or equal to unity. Diffusive isotope effects are reduced when the diffusion process is correlated, as for (1) rapid diffusion of trace and minor cations by a vacancy mechanism, with a low migration barrier for the jump to a vacancy; (2) diffusion by an interstitialcy process, or a process involving interstitial–vacancy pairs; (3) diffusion in grain boundaries and dislocations, where both dimensional restrictions and non-uniformity of the structure enhance correlation. The correlation coefficient can be determined from independent experimental data on the jump frequencies involved in the diffusion process, and/or from theoretical calculations of the jump energies. Quantitative estimates of the isotope effect are made for several cations in periclase, olivine, magnetite and rutile.

Thermal diffusion in a binary liquid due to rectified molecular fluctuations

The Soret motion in binary liquids is shown to arise to a large extent from rectified velocity fluctuations. From a hard-bead model with elastic collisions in a nonuniform temperature, we derive a net force on each molecule, which is proportional to the temperature gradient and depends on the ratio of the molecular masses and moments of inertia. Our findings agree with previous numerical simulations and provide an explanation for the thermal diffusion isotope effect observed for several liquids.

Analytical modelling of stable isotope fractionation of volatile organic compounds in the unsaturated zone

Analytical models were developed that simulate stable isotope ratios of volatile organic compounds (VOCs) near a point source contamination in the unsaturated zone. The models describe diffusive transport of VOCs, biodegradation and source ageing. The mass transport is governed by Fick's law for diffusion. The equation for reactive transport of VOCs in the soil gas phase was solved for different source geometries and for different boundary conditions. Model results were compared to experimental data from a one-dimensional laboratory column and a radial-symmetric field experiment. The comparison yielded a satisfying agreement. The model results clearly illustrate the significant isotope fractionation by gas phase diffusion under transient state conditions. This leads to an initial depletion of heavy isotopes with increasing distance from the source. The isotope evolution of the source is governed by the combined effects of isotope fractionation due to vaporisation, diffusion and biodegradation. The net effect can lead to an enrichment or depletion of the heavy isotope in the remaining organic phase, depending on the compound and element considered. Finally, the isotope evolution of molecules migrating away from the source and undergoing degradation is governed by a combined degradation and diffusion isotope effect. This suggests that, in the unsaturated zone, the interpretation of biodegradation of VOC based on isotopic data must always be based on a model combining gas phase diffusion and degradation.

Correlation effects for cation diffusion via vacancy-pairs in fluorite-related oxides

Recent research has suggested that diffusion via vacancy-pairs could be an important contribution to cation diffusion in fluorite-related oxides, such as yttria-stabilized zirconia. In this paper, a combination of analytical development and Monte Carlo computer simulation is used to analyze various diffusion correlation effects for cation and oxygen ion diffusion via tightly bound vacancy-pairs in the fluorite structure. It is shown that the application of sum-rule relations provides exact expressions for the collective correlation functions. It is also shown that a formalism inspired by Manning's diffusion kinetics formalism gives accurate expressions for tracer correlation factors when tested against Monte Carlo simulation results. It is also shown that the tracer correlation factors follow the impurity-form, thereby simplifying an interpretation of the diffusion isotope effect.

Correlated tracer diffusion in an ordered interface structure

In this paper, we postulate a simple two-dimensional structure that attempts to capture the character of many of the qualitative findings from computer simulations of diffusion paths in grain boundaries. We postulate two types of mechanism: those where single atom jumps occur and those where multiple atom jumps occur. We derive analytical expressions for the tracer correlation factors, including those correlation factors that appear in the analysis of the diffusion isotope effect. We also carry out Monte Carlo simulations of these correlation factors. We find very good agreement between the derived expressions for the correlation factors and the simulation results. We are able to show that, in the absence of knowledge about the kinetic energy factor ΔK, isotope effect experiments cannot differentiate between a simple atom-jump mechanism and multiple-atom-jump mechanism.

Collectivity of motion in undercooled liquids and amorphous solids

The motion of the structure determining components is highly collective, both in amorphous solids and in undercooled liquids. This has been deduced from experimental low temperature data in the tunneling regime as well as from the vanishing isotope effect in diffusion in glasses and undercooled liquids. In molecular dynamics simulations of glasses one observes that both low frequency resonant vibrations and atomic jumps are centered on more than 10 atoms which, in densely packed materials, form chain-like structures. With increasing temperature the number of atoms jumping collectively increases. These chains of collectively jumping atoms are also seen in undercooled liquids. Collectivity only vanishes at higher temperatures. This collectivity is intimately related to the dynamic heterogeneity which causes a non-Gaussianity of the atomic displacements.

Isotope effect of diffusion in the supercooled liquid state of bulk metallic glasses

The isotope effect, E=(Dα/Dβ−1)/(mβ/mα−1), of cobalt diffusion in the deeply supercooled liquid state of the bulk metallic glass formers Zr46.7Ti8.3Cu7.5Ni10Be27.5 and Zr65Cu17.5Ni10Al7.5 has been measured employing the radiotracers 57Co and 60Co in conjunction with serial sectioning by means of ion-beam depth profiling. In both alloys a small mass dependence with E≈0.10 is observed. This dependence has no temperature dependence in a range of 120 K in the supercooled liquid state encompassing four orders of magnitude in the diffusivity. We suggest that these results show that long-range diffusion in a deeply supercooled liquid is not mediated by viscous flow but proceeds by collective hopping processes involving about 10 atoms.

Isotope effect in diffusion of methyl radicals in glassy ethanol-1,2 d5 at low temperatures

The kinetics of methyl radicals decay has been studied at 77 K and at 90 K in glassy mixtures 0.9( xC 2H 5OH+(1− x)C 2D 5OH)+0.1H 2O. It has been shown that in matrices with a small content of H-component ( x≲0.02) the decay rate of CD 3 radicals is noticeably higher than that of CH 3. Upon H/D substitution in the methyl radical the rate of radical migration and the rate of deuterium atom abstraction from matrix molecules change simultaneously. As the fraction of C 2H 5OH in the mixture increases, the difference in the rates of the decay of methyl radical isotopomers vanishes. The unusual “inverse” isotope effect in the methyl radical diffusion is considered in the framework of the transition state theory.

The relationship between 18O/16O and 13C/12C ratios of ambient CO2 in two Amazonian tropical forests

Oxygen and carbon isotopic compositions of ambient carbon dioxide in two tropical forests in the Amazonian basin were determined at the beginning and the end of the dry season. One site, Fazenda Vitoria, is typical of a seasonal forest with a pronounced dry season from May to November whereas the other site, Reserva Ducke, has a milder dry season. Samples collected at night revealed that in the beginning of the dry season, when the forest is still relatively wet, isotopic exchange between carbon dioxide and wet surfaces or fog is possible. Oxygen isotope ratios of ambient carbon dioxide collected during the day were correlated with the carbon isotope ratios. These correlations are representative of the mixing line between tropospheric and respired CO2. The mixing lines were used to extrapolate the δ18O values of soil-respired CO2. These values were compared with those derived from the isotopic composition of bulk soil water (as reflected by plant stem water) and a diffusion isotopic effect of 8.8‰. It was observed that δ18O values of respired CO2 derived by extrapolation were greater than those calculated by using δ18O values of bulk soil water and the associated diffusion isotope effect. The results show that in tropical forests, assumptions used in previous studies of temperate regions to derive the oxygen isotopic composition of respired CO2 do not hold.

Isotope effects in the diffusion of hydrogen

Isotope effects in diffusion of hydrogen atoms are investigated theoretically. It is shown that isotope effect is reduced by a nonadiabatic effect of the heat bath so that the classical‐quantum crossover temperature and quantum tunneling rate lose their mass dependence. On the other hand, isotope effect is reversed in classical hopping rate under strong spatial confinement at the barrier top. These results indicate that isotope effects can be the means of observing influences of many degrees of freedom characterizing environment in diffusion process.

Separation of protium/deuterium and oxygen-16/oxygen-18 by membrane distillation

An attempt to explain the significant isotope effect of deuterium and heavy oxygen observed in the MD process was undertaken. A study of the transport mechanism through porous PTFE membranes showed that membrane mass transfer coefficients can be well estimated from the molecular diffusion model or from the combination of Knudsen and molecular diffusion models. the existence of a diffusion isotope effect in membrane distillation enhances the separation factors for H 2O HDO and H 2 16O H 2 18 O enrichment. The discussion of the nature of the isotope effect in MD is presented.

Isotope effect of diffusion and electromigration of hydrogen in nickel

Isotope effect of diffusion and electromigration of hydrogen in nickel

Isotope effect for diffusion of gold in lead-indium alloys

The effect of isotopic mass on the diffusion of Au in Pb-In alloys has been studied over a composition range of 0–2.0 at.% indium. It has been found that the strength of the isotope effect E is 0.18 ± 0.03 for pure lead with negligible temperature dependence. This result is consistent with other isotope effect measurements for “fast diffusers” in polyvalent materials. The isotope effect increases with increasing In concentration, reaching 0.4 ± 0.04 with 2.0 at.% In added, and the variation with temperature is again less than the experimental error. Since the anticipated value of the isotope mass is near unity for a simple interstitial mechanism for pure lead, it is clear that the diffusion mechanism for Au in Pb-In alloys cannot be accounted for by this mechanism.

Isotope Effect of Diffusion during Stuctural Relaxation of Metallic Glasses

Isotope Effect of Diffusion during Stuctural Relaxation of Metallic Glasses

Kinetic isotope effects for hydrogen diffusion in bulk nickel and on nickel surfaces

Diffusion coefficients for H, D, and T on a Ni(100) surface and in bulk Ni are calculated using variational transition state theory with semiclassical ground-state transmission coefficients using two potential energy surfaces obtained by the embedded atom method (EAM). The original EAM potential reproduces experimental bulk diffusion coefficients, but greatly overestimates the diffusion coefficients for H and D on Ni(100). By refining the empirical potential parameters, a new EAM potential is developed that accurately reproduces both the bulk and surface diffusion coefficients. The variational transition state theory calculations are used to analyze the unusually low (compared to gas phase) H/D kinetic isotope effects for diffusion in bulk and on the Ni(100) surface. For the temperature range for which experiments have been carried out, quantum mechanical tunneling contributes negligibly to the diffusion and, in these cases, the kinetic isotope effect is determined largely by the change in zero-point energy between the reactant equilibrium binding sites and the transition state. A near equality of the reactant and transition state zero-point energies leads to the unusually low kinetic isotope effects. Using the same refined EAM potential energy surface, the energetics of diffusion on the Ni(111) and Ni(110) surfaces are also presented. The barriers for diffusion on these two surfaces are sufficiently low, about 1.0 kcal/mol, that the approximation of uncorrelated hops needed to relate the computed hopping rate to the diffusion coefficient is suspect. Although diffusion coefficients were not computed, based upon an analysis of the zero-point energies at the reactants and saddle points, we predict that the H/D kinetic isotope effects for diffusion on these two surfaces will also be close to unity.

Tritium permeation through iron

Abstract An experimental method for measuring diffusion coefficients and permeation rates of tritium in metals around room temperature has been established, and their values in iron have been obtained by using the method. Permeation rates of tritium and hydrogen through iron were measured by the electrochemical method in which a tritiated aqueous solution was used as a cathodic electrolyte. Tritium and hydrogen were introduced from one side of a membrane specimen by cathodic polarization, while at the other side of the specimen the permeating tritium and hydrogen were extracted by potentiostatical ionization. The amount of permeated hydrogen was obtained by integrating the anodic current, and that of tritium was determined by measuring the radioactivity of the electrolyte sampled from the extraction side. Diffusion coefficients of tritium (DT) and hydrogen (DH) were determined from the time lag of tritium and hydrogen permeation. DT = 9×10−10m2/s and DH = 4×10−9m2/s at 286 K for annealed iron specimens. These values of DT and DH were compared with the previous data of the diffusion coefficients of hydrogen and deuterium, and the isotope effect in diffusion was discussed.