Tracer Diffusion Coefficients Research Articles

Atomic transport property of Fe–O liquid alloys in the Earth’s outer core P, T condition

The self-diffusion and tracer diffusion coefficients and viscosity of non-magnetic liquid Fe–O alloys were determined at 100–350GPa and 4000–8000K on the basis of the ab initio molecular dynamics simulation method. Those of pure liquid iron are found to be consistent with the results of former studies. We confirmed that the self-diffusivity of Fe monotonically increases with increasing oxygen fraction. Meanwhile, the viscosity monotonically decreases with increasing oxygen fraction. On the other hand, the depth dependence of diffusivities and viscosity in the outer core are not great along the geotherm because pressure and temperature conversely affect the transport coefficients. The calculated diffusivity suggests that an O-rich stratified layer with a thickness of ∼70km could be produced at the uppermost layer of the outer core if the layer was created from the diffusion of O from the mantle.

Relating surface chemistry and oxygen surface exchange in LnBaCo2O(5+δ) air electrodes.

The surface and near-surface chemical composition of electroceramic materials often shows significant deviations from that of the bulk. In particular, layered materials, such as cation-ordered LnBaCo2O(5+δ) perovskites (Ln = lanthanide), undergo surface and sub-surface restructuring due to the segregation of the divalent alkaline-earth cation. These processes can take place during synthesis and processing steps (e.g. deposition, sintering or annealing), as well as at temperatures relevant for the operation of these materials as air electrodes in solid oxide fuel cells and electrolysers. Furthermore, the surface segregation in these double perovskites shows fast kinetics, starting at temperatures as low as 400 °C over short periods of time and leading to a decrease in the transition metal surface coverage exposed to the gas phase. In this work, we use a combination of stable isotope tracer labeling and surface-sensitive ion beam techniques to study the oxygen transport properties and their relationship with the surface chemistry in ordered LnBaCo2O(5+δ) perovskites. Time-of-Flight Secondary-Ion Mass Spectrometry (ToF-SIMS) combined with (18)O isotope exchange was used to determine the oxygen tracer diffusion (D*) and surface exchange (k*) coefficients. Furthermore, Low Energy Ion Scattering (LEIS) was used for the analysis of the surface and near surface chemistry as it provides information from the first mono-atomic layer of the materials. In this way, we could relate the compositional modifications (e.g. cation segregation) taking place at the electrochemically-active surface during the exchange at high temperatures and the oxygen transport properties in double perovskite electrode materials to further our understanding of the mechanism of the surface exchange process.

An assessment of the ability of the obstruction-scaling model to estimate solute diffusion coefficients in hydrogels

The ability to estimate the diffusion coefficient of a solute within hydrogels has important application in the design and analysis of hydrogels used in drug delivery, tissue engineering, and regenerative medicine. A number of mathematical models have been derived for this purpose; however, they often rely on fitted parameters and so have limited predictive capability. Herein we assess the ability of the obstruction-scaling model to provide reasonable estimates of solute diffusion coefficients within hydrogels, as well as the assumption that a hydrogel can be represented as an entangled polymer solution of an equivalent concentration. Fluorescein isothiocyanate dextran solutes were loaded into sodium alginate solutions as well as hydrogels of different polymer volume fractions formed from photoinitiated cross-linking of methacrylate sodium alginate. The tracer diffusion coefficients of these solutes were measured using fluorescence recovery after photobleaching (FRAP). The measured diffusion coefficients were then compared to the values predicted by the obstruction-scaling model. The model predictions were within ±15% of the measured values, suggesting that the model can provide useful estimates of solute diffusion coefficients within hydrogels and solutions. Moreover, solutes diffusing in both sodium alginate solutions and hydrogels were demonstrated to experience the same degree of solute mobility restriction given the same effective polymer concentration, supporting the assumption that a hydrogel can be represented as an entangled polymer solution of equivalent concentration.

Mixed cation effect in Ag2S–Tl2S–GeS–GeS2 glasses: Conductivity and tracer diffusion studies

Mixed cation effect has been studied for thallium–silver thiogermanate glasses in the (Ag2S)x(Tl2S)50-x(GeS)25(GeS2)25 system, where Ag2S fraction r=Ag2S/(Ag2S+Tl2S)=0, 0.25, 0.5, 0.75, and 1.0. The glass transition temperature changes from 160°C for r=0 to 231°C for r=1.0 and exhibits a negative deviation from additivity, with a slight minimum Tg≈157°C observed for compositions in the range 0.1≤r≤0.3. The room temperature conductivity σ298 increases by 5 orders of magnitude with increasing silver concentration, ranging between 10−8Scm−1 for the Tl–Ge–S system and 10−3Scm−1 for the Ag–Ge–S glass with a minimum at σ298≈10−9Scm−1. The activation energy decreases from 0.66 to 0.33eV, respectively, with the maximum at Eσ≈0.69eV. The minimum of both Tg and σ298 and the Eσ maximum are observed in the same composition range, 0.1≤r≤0.3. The 204Tl tracer diffusion coefficient at 170°C decreases with silver concentration from 10−10cm2s−1 for (Tl2S)50(GeS)25(GeS2)25 glass to 10−12cm2s−1 for (Ag2S)50(GeS)25(GeS2)25 glass. The obtained results indicate a classical mixed cation effect.

Insight into the Li Ion Dynamics in Li12Si7: Combining Field Gradient Nuclear Magnetic Resonance, One- and Two-Dimensional Magic-Angle Spinning Nuclear Magnetic Resonance, and Nuclear Magnetic Resonance Relaxometry

A comprehensive picture of the rather complex Li ion dynamics in the binary silicide Li12Si7 is presented. Long-range Li dynamics is probed by field gradient NMR methods. The obtained macroscopic tracer-diffusion coefficients are in good agreement with a jump process characterized by an activation energy of approximately 0.2 eV which was previously measured in 7Li NMR relaxometry—a microscopic method which probes ion dynamics on an atomic scale. From high-resolution magic-angle spinning (MAS) NMR, it can be concluded that 9 of the 13 crystallographically independent sites take part in this fast diffusion process. Li ions on the residual four sites are bound more tightly to the silicide Zintl anions with activation barriers ranging from 0.32 to 0.55 eV. Accordingly, the mean residence times of Li ions on these sites are considerably longer, which makes it possible to test their dynamics with 1D/2D MAS exchange NMR methods. We present a series of mixing-time-dependent 2D MAS exchange NMR measurements. The extracted Li jump rates are in very good agreement with those of dynamic processes investigated by NMR relaxometry. The data is interpreted in relation to the results of two recently published NMR studies on Li12Si7 and structural assignments based on one- and two-dimensional 29Si{7Li} heteronuclear correlation spectroscopy. These experiments assist in attributing different ionic mobilities to the different crystallographic lithium sites, suggesting preferred ion conduction pathways. Combining all these methods and their respective results, a consistent picture of the Li ion dynamics in Li12Si7 is obtained. Overall lithium species in the vicinity of the Si4 star unit tend to be more mobile than lithium species interacting with the Si5 ring units of the silicon framework structure.

Diffusion Coefficients of Carbon Dioxide in Brines Measured Using 13C Pulsed-Field Gradient Nuclear Magnetic Resonance

Tracer diffusion coefficients of CO2 in several brines were measured by 13C pulsed-field gradient NMR at a temperature of 298 K and at salt molalities of up to 5 mol·kg–1. The brines studied were NaCl(aq), CaCl2(aq), Na2SO4(aq), and a mixed brine prepared from seven salts: NaCl, CaCl2, MgCl2, KCl, Na2SO4, SrCl2, NaHCO3. The experimental results are compared with the predictions of a modified Stokes–Einstein relation in which the Stokes–Einstein number is 4 and the hydrodynamic radius of the CO2 molecule in aqueous solution is taken to be 168 pm, as determined in an earlier study of the (CO2 + H2O) binary system at the same temperature (Cadogan et al. J. Chem. Eng. Data 2014, 59, 519−525). This comparison shows agreement to within the experimental uncertainty, independent of salt type and molality. We conclude that the modified Stokes–Einstein relation provides a reliable means of estimating the tracer diffusion coefficient of CO2 in aqueous electrolyte solutions, based on knowledge of the brine viscosity ...

Role of an acceptor impurity in the proton transfer in proton-conducting oxides

The influence of interaction of protons with defects (acceptor impurities, oxygen vacancies) and with each other on the proton transfer in acceptor-doped proton-conducting oxides A II B 1− IV R III O3 − δ with the perovskite structure and in oxides A 2− III R II O3 − δ with the structure of a distorted fluorite (bixbyite) has been investigated theoretically. The tracer diffusion coefficient D* and proton mobility have been calculated by the Monte Carlo method and analytically. It has been shown that the interaction of protons with defects substantially affects the magnitude and behavior of the transfer coefficients. The interaction with acceptor impurities plays the most important role. The proton mobility significantly decreases even at a low dopant concentration (x ∼ 1–3 at %). The dependence of the proton conductivity σ on the impurity concentration can exhibit maxima. For oxides with the bixbyite structure including nonequivalent cation sites, the distribution of the dopant over these sites has a strong influence on the dependence σ(x). The obtained results have been used to interpret the experimental data on the proton conductivity for a number of oxides.

Sodium-potassium interdiffusion in potassium-rich alkali feldspar II: Composition- and temperature-dependence obtained from cation exchange experiments

Na-K interdiffusion in disordered potassium-rich alkali feldspar was studied experimentally using cation exchange between gem quality sanidine from the Eifel and alkali-halide melt at temperatures of 800 °C to 1000 °C and at close to ambient pressure. Sodium-potassium interdiffusion coefficient DNaK was determined for potassium mole fractions in the range 0.65 ≤ XOr ≤ 0.99. At 0.65 ≤ XOr ≤ 0.95 the sodium-potassium interdiffusion coefficient is largely independent of composition. At XOr ≥ 0.95, it rises sharply with increasing potassium mole fraction. Diffusion perpendicular to (001) is about one order of magnitude faster and less strongly temperature dependent than perpendicular to (010). The parameters of the Arrhenius equation describing the temperature dependence of the sodium-potassium interdiffusion coefficient DNaK = D0Exp (−EA/RT) were estimated as The results of our direct determinations are compared with theoretical calculations using the corresponding sodium- and potassium tracer-diffusion coefficients, and the processes underlying the observed composition- and temperature dependence of sodium-potassium interdiffusion are discussed.

Oxygen tracer diffusion and surface exchange kinetics in Ba0.5Sr0.5Co0.8Fe0.2O3 − δ

The oxygen tracer diffusion coefficient, Db⁎, and the oxygen tracer surface exchange coefficient, k, were measured in Ba0.5Sr0.5Co0.8Fe0.2O3−δ (BSCF5582) over the temperature range of 310–800°C and the oxygen partial pressure range of 1.3×10−3–0.21bar. Several measurement techniques were used: isotope exchange followed by depth profiling (IEDP) within individual single grains or line scanning (IELS) along the sample cross-section and gas-phase analysis (GPA). Surface exchange kinetics was initially found to be slow and presumably inhibited by the formation of a passivating layer on the sample surface. High temperature pre-anneals (900–950°C) changed the nature of this layer and enhanced surface exchange. Fast bulk oxygen diffusion and surface exchange kinetics were observed after high temperature pre-anneals within the temperature range studied. The activation energies for 18O tracer diffusion and surface exchange at 0.21bar were 0.72±0.05 and 1.10±0.15eV, respectively. The tracer diffusion coefficient showed weak dependence upon oxygen partial pressure, whereas the surface exchange coefficient exhibited strong oxygen partial pressure dependence. The microstructure of the samples (the porosity and grain size) had a profound effect on the measured tracer diffusion coefficient.

Impact of W on structural evolution and diffusivity of Ni–W melts: an ab initio molecular dynamics study

Effects of W on structural evolution and diffusivity of Ni–10W and Ni–20W (at.%) melts are studied via ab initio molecular dynamic simulations. The atomic local topology is characterized in terms of pair correlation functions, structure factors, bond pairs, and topological structures. It is observed that the Ni–20W melt is more closely packed than the Ni–10W, showing higher average coordination number and more Voronoi polyhedra with high coordination numbers. The tracer diffusion coefficients of Ni and W calculated by the mean-squared displacement are very close to each other in both Ni–W alloys. Comparing with their self-diffusion coefficients of pure Ni and pure W, the tracer diffusion coefficient of Ni in Ni–W melts decreases, while that of W increases. Nearly identical tracer diffusivities of Ni and W in Ni–W melts attribute to the formation of local solute-centered polyhedra with high deformation electron density severing as bridges between various atomic clusters and strengthening the atomic bonding, indicating the collective motion of Ni and W in those melts. Moreover, atomic bonds of Ni–W metallic melts characterized by the deformation electron density present the network among different atomic clusters, revealing the physical nature of the collective motions between W and Ni.

Simultaneous tracer diffusion and interdiffusion in a sandwich-type configuration to provide the composition dependence of the tracer diffusion coefficients

In this paper, a new formalism of a combined tracer and interdiffusion experiment for a binary interdiffusion couple is developed. The analysis requires an interdiffusion couple that initially contains a thin layer of tracers of one or both of the constituent elements at the original interface of the couple (sandwich interdiffusion experiment). This type of interdiffusion experiment was first performed in 1958 by J.R. Manning. The theoretical analysis presented in this paper is based on a newly developed phenomenological theory of isotopic interdiffusion combined with the Boltzmann–Matano formalism. This new analysis now provides the means to obtain the composition dependent interdiffusion coefficient and tracer diffusion coefficients simultaneously from analysis of the interdiffusion and tracer profiles in a single sandwich interdiffusion experiment. The new analysis is successfully applied to the results of Manning’s original ‘sandwich interdiffusion’ experiment in the Ag–Cd system (six couples in total) and is validated with an independent determination of the Ag and Cd tracer diffusion coefficients by Schoen using the conventional thin film technique. Suggestions for further development of the sandwich interdiffusion experiment and analysis to the case of multicomponent alloys are provided.

Experiments on tracer diffusion in aqueous and non-aqueous solvent combinations.

Forced Rayleigh scattering is used to study the tracer diffusion of an azobenzene in binary combinations of polar solvents, including water. In the absence of water, the tracer diffusion coefficient D in the mixture lies between the diffusion coefficients within the pure solvents, on a curve that is reasonably close to the prediction of free-volume theory. If water is present, on the other hand, the diffusion coefficient displays a minimum that is less than the smaller of the two pure-solvent values. We attempt to understand the different behavior in water by concentrating on the fairly hydrophobic nature of the solute, leading to a first solvent shell that is hydrophobic on the inside and hydrophilic on the outside. We also believe that clusters of amphiphiles explain the observation that, in aqueous combinations, D is nearly constant above a certain amphiphile mole fraction.

Overview of SIMS-Based Experimental Studies of Tracer Diffusion in Solids and Application to Mg Self-Diffusion

Tracer diffusivities provide the most fundamental information on diffusion in materials, and are the foundation of robust diffusion databases that enable the use of the Onsager phenomenological formalism with no major assumptions. Compared to traditional radiotracer techniques that utilize radioactive isotopes, the secondary ion mass spectrometry (SIMS)-based thin-film technique for tracer diffusion is based on the use of enriched stable isotopes that can be accurately profiled using SIMS. An overview of the thin-film method for tracer diffusion studies using stable isotopes is provided. Experimental procedures and techniques for the measurement of tracer diffusion coefficients are presented for pure magnesium, which presents some unique challenges due to the ease of oxidation. The development of a modified Shewmon-Rhines diffusion capsule for annealing Mg and an ultra-high vacuum system for sputter deposition of Mg isotopes are discussed. Optimized conditions for accurate SIMS depth profiling in polycrystalline Mg are provided. An automated procedure for correction of heat-up and cool-down times during tracer diffusion annealing is discussed. The non-linear fitting of a SIMS depth profile data using the thin-film Gaussian solution to obtain the tracer diffusivity along with the background tracer concentration and tracer film thickness is demonstrated. An Arrhenius fit of the Mg self-diffusion data obtained using the low-temperature SIMS measurements from this study and the high-temperature radiotracer measurements of Shewmon and Rhines (Trans. AIME 250:1021-1025, 1954) was found to be a good representation of both types of diffusion data over a broad range of temperatures between 250 and 627 °C (523 and 900 K).

Experimental investigation of water self-diffusion coefficient and tracer diffusion coefficient of tert-butanol in water-based silica nanofluids

Water self-diffusion coefficient and tracer diffusion coefficient of tert-butanol in water-based silica nanofluids were measured by using pulsed field gradient nuclear magnetic resonance (PFG-NMR) method for silica nanoparticle volume fractions ranged from 0.005% to 1% at three different temperatures (15, 25 and 35 °C). In this work, formation of dye–nanoparticle complexes was minimized and undesirable primary advection effects induced by solute injection were also eliminated. Insignificant enhancement (mostly less than 10% increase) in both water self-diffusion coefficient and tracer diffusion coefficient of tert-butanol in nanofluids was observed. These results indicate that probably Brownian motion of nanoparticles and induced micro-convection tend to enhance mass transfer but the obstruction effect of solid nanoparticles limits this enhancement by reducing the free volume face to diffusion path of molecules.

Diffusion behavior in Nickel–Aluminum and Aluminum–Uranium diluted alloys

Impurity diffusion coefficients are entirely obtained from a low cost classical molecular statics technique (CMST). In particular, we show how CMST is appropriate in order to describe the impurity diffusion behavior mediated by a vacancy mechanism. In the context of the five-frequency model, CMST allows to calculate all the microscopic parameters, namely: the free energy of vacancy formation, the vacancy-solute binding energy and the involved jump frequencies, from them, we obtain the macroscopic transport magnitudes such as: correlation factor, solvent-enhancement factor, Onsager and diffusion coefficients. Specifically, we perform our calculations in f.c.c. diluted Ni–Al and Al–U alloys. Results for the tracer diffusion coefficients of solvent and solute species are in agreement with available experimental data for both systems. We conclude that in Ni–Al and Al–U systems solute atoms migrate by direct interchange with vacancies in all the temperature range where there are available experimental data. In the Al–U case, a vacancy drag mechanism could occur at temperatures below 550K.

Diffusion kinetics in dilute binary alloys with the h.c.p. crystal structure

In this paper, an extended version of the matrix method is derived in order to address diffusion kinetics for the full anisotropic three-dimensional h.c.p. structure. It is shown that the diffusion anisotropy can be properly addressed with a model of 13 atom-vacancy frequencies which is an extended version of the well-known 5-frequency model for the f.c.c. lattice. Both tracer and phenomenological diffusion coefficients are calculated using this new approach. Extended Monte Carlo simulations are performed in order to cross-check some of the results of the matrix method. Applications of the proposed model to experimental diffusion data are discussed.

Self-intermediate scattering function of strongly interacting three-dimensional lattice gases: time- and wave-vector-dependent tracer diffusion coefficient.

We investigate the self-intermediate scattering function (SISF) in a three-dimensional (3D) cubic lattice fluid (interacting lattice gas) with attractive nearest-neighbor interparticle interactions at a temperature slightly above the critical one by means of Monte Carlo simulations. A special representation of SISF as an exponent of the mean tracer diffusion coefficient multiplied by the geometrical factor and time is considered to highlight memory effects that are included in time and wave-vector dependence of the diffusion coefficient. An analytical expression for the diffusion coefficient is suggested to reproduce the simulation data. It is shown that the particles' mean-square displacement is equal to the time integral of the diffusion coefficient. We make a comparison with the previously considered 2D system on a square lattice. The main difference with the two-dimensional case is that the time dependence of particular characteristics of the tracer diffusion coefficient in the 3D case cannot be described by exponentially decreasing functions, but requires using stretched exponentials with rather small values of exponents, of the order of 0.2. The hydrodynamic values of the tracer diffusion coefficient (in the limit of large times and small wave vectors) defined through SIFS simulation results agree well with the results of its direct determination by the mean-square displacement of the particles in the entire range of concentrations and temperatures.

Atomistic simulations of the decomposition kinetics in Fe–Cr alloys: Influence of magnetism

Magnetism plays a crucial role in the thermodynamic and kinetic properties of ferritic alloys. In fact, magnetism increases the solubility limit of Cr in Fe, inducing an asymmetrical phase diagram. Moreover, the phase transition from ferromagnetic to paramagnetic (F/P) iron alloys modifies to a large extent the system response to different environmental conditions by modification of the alloy diffusion properties. Indeed, experimental tracer diffusion coefficients deviate from an Arrhenius law during the F/P magnetic transition, leading to a large increase in the paramagnetic regime compared to the extrapolated value from the ferromagnetic domain. Furthermore, as the Curie temperature decreases with the Cr concentration, this evolution of the diffusion properties affects the decomposition kinetics in different ways depending on the alloy composition. An atomic diffusion model, with pair interactions that depend on the local composition and on temperature, has been developed to take into account this magnetic transition effect. The interaction model has been implemented in an atomistic kinetic Monte Carlo algorithm to study the diffusion coefficients and precipitation kinetics of the Fe–Cr alloys. This model has been successfully compared to decomposition kinetic experiments for a wide range of concentrations and temperatures.

Oxide ion and electron transport properties in lanthanum silicate oxyapatite ceramics

An oxygen-excess-type lanthanum silicate (LSO) solid electrolyte with high chemical stability as well as high ion conductivity was developed by optimizing the chemical composition, La9.333+x(Si6−yAly)O26+1.5x−0.5y. It was found that La10(Si5.8Al0.2)O26.9 (x=0.667, y=0.2) exhibited the highest conductivity among them, and addition of a small amount of iron was effective for the improvement of its chemical stability. The LSO specimen of x=0.667 and y=0.2 with iron addition (0.5mol%) was chemically stable and had a conductivity of 5.6×10−2Scm−1 under air at 1073K, while its electronic conductivity was less than 2.0×10−4Scm−1 at the same temperature. The oxygen tracer diffusion coefficient, DO* of this material was determined as 2.0×10−8cm2s−1 at 1073K.

Diffusion pattern in MSi2 and M5Si3 silicides in group VB (M = V, Nb, Ta) and VIB (M = Mo, W) refractory metal-silicon systems

Group VB and VIB M–Si systems are considered to show an interesting pattern in the diffusion of components with the change in atomic number in a particular group (M = V, Nb, Ta or M = Mo, W, respectively). Mainly two phases, MSi2 and M5Si3 are considered for this discussion. Except for Ta–silicides, the activation energy for the integrated diffusion of MSi2 is always lower than M5Si3. In both phases, the relative mobilities measured by the ratio of the tracer diffusion coefficients, , decrease with an increasing atomic number in the given group. If determined at the same homologous temperature, the interdiffusion coefficients increase with the atomic number of the refractory metal in the MSi2 phases and decrease in the M5Si3 ones. This behaviour features the basic changes in the defect concentrations on different sublattices with a change in the atomic number of the refractory components.