Effect of the thermodynamic factor on the intrinsic and tracer diffusivities in binary mixtures.

Prediction of the mutual diffusivity in binary liquid mixtures containing one dimerising species, from the tracer diffusion coefficients

Prediction of the mutual diffusivity in binary non-ideal liquid mixtures from the tracer diffusion coefficients

Diffusion in the Ag-Cd system was investigated at 600°C with vapor-solid and solid-solid diffusion couples in the α-phase for the determination of intrinsic diffusion coefficients, atomic mobilities and interdiffus ion coefficients. Intrinsic diffusion coefficients, DCd and DAg, determined experimentally, were compared with those predicted from the models of Darken, Manning, and Dayananda with the aid of tracer diffusion and thermodynamic data. The experimental coefficients for various alpha alloys were found to be higher than those evaluated from each of the three models. On the other hand, the experimental values of the ratio, DCd/DAg were found to be in good agreement with the models of Manning and Dayananda where the vacancy wind effects on intrinsic diffusion are taken into account. Darken’s relations are considered inadequate to interrelate tracer and intrinsic diffusion coefficients in the Ag-Cd system, since vacancy wind effects are found to be appreciable in this system.

Tracer carbon diffusion, chemical diffusion and carbon activity data in austenite in terms of a four-frequency interstitial model first formulated by McKee is analysed. The later formulation by Okamura and Allnatt, which has recently been confirmed to be essentially exact, is made use of. In the revised analysis, the general finding of McKee that the increase of both tracer and chemical carbon diffusion coefficients with carbon composition at 1000°C is largely a result of a much higher rate of rotation of an interstitial pair compared with isolated carbon atoms is confirmed. It is found that carbon atoms move almost two times faster as a rotating pair than established originally by McKee. Information on the ratios of the exchange frequencies to other temperatures between 800°C and 1000°C using the available experimental data on the intrinsic diffusivities and the carbon activity is extrapolated.

Tracer diffusion coefficients D* of lithium ions in LixMn2O4 (0.2 < x < 1) thin films were measured as a function of the composition x by using secondary ion mass spectrometry. For this purpose, a new “step-isotope-exchange method” was developed to observe the time dependence of the 6Li isotope concentration ratio in the LixMn2O4 film which is in contact with a 6Li-enriched electrolyte to exchange Li+ ions. A steep decrease in D* depending on the Li composition was observed for LixMn2O4, with D* = 8 × 10–13 cm2 s–1 for x = 0.2 and decreasing to 1.5 × 10–17 cm2 s–1 for x = 1.0 (bulk diffusion coefficient, Db*). This behavior is well explained by a vacancy diffusion model for the α phase on LixMn2O4 (0.77 < x < 1.0). Chemical diffusion coefficients D̃ were also measured in the range of 0.2 < x < 1.0 by an electrochemical method, which was compared with the D* to evaluate the effect of thermodynamic factors. The thermodynamic factors and interactions between Li+ ions were found to strongly influence the chemical diffusion coefficient. The tracer diffusion measurements are important to understand the charge–discharge mechanism in the electrodes of lithium-ion batteries.

A simple and absolute closed capillary method is introduced for measuring tracer diffusion coefficients in liquids with both γ- and β-active tracers. In this method a narrow capillary is partially filled with a labelled solution and an unlabelled solution is used to fill the rest of the capillary. The diffusion coefficient is obtained from the time dependence of the monitored activity when the length of the capillary is known. The method has been tested by remeasuring the tracer diffusion coefficients of22NaCl and Na36Cl for solutions covering a wide range of total NaCl concentration. The average precision of the measurements was about 0.3%. The results obtained for Na36Cl tracer diffusion are in good agreement with the data found in literature. The22NaCl tracer diffusion coefficients that were measured in dilute solutions agree well with those obtained using the continuous open-ended capillary method but differ from results for solutions between 0.1 and 1M obtained with the diaphragm cell method.

Composition dependence of tracer diffusion coefficients in Fe–Ga alloys: A case study by a tracer-diffusion couple method

Atoms and molecules are not completely immobile within a solid material. They move by jumping into vacancies or interstitial sites in the crystal lattice. The laws describing their motion were discovered by Adolf Fick in the mid-19th century, modelled on analogous laws for the flow of heat (Fourier’s law) and electricity (Ohm’s law). According to Fick’s first law, the rate at which atoms move is proportional to the concentration gradient, with the diffusion coefficient defined as the constant of proportionality. Fick’s second law generalises the first law to a wide range of situations and is called the diffusion equation. This chapter examines a number of characteristic diffusion profiles; the difference between self, intrinsic, inter- and tracer diffusion coefficients; the Kirkendall effect and porosity formation when different components move at different speeds; and the Arrhenius temperature dependence of diffusion. Fick was a physiologist and derived his laws initially to describe the flow of blood through the heart. He made advances in anatomy, physiology and medicine, developing methods of monitoring blood pressure, muscular power, corneal pressure and glaucoma. He lived at the time of Bismarck’s post-Napoléonic unification of Germany and the associated flowering of German science, engineering, medicine and culture.

In this study a simple model of a long range ordered alloy, in which the sublattics exist a priori, is considered for the purposes of describing chemical diffusion. Diffusion is assumed to take place via the agency of vacancies. Four atom-vacancy exchange frequencies are specificed. Manning's formalism for describing diffusion in the random alloy is adapted and extended to the present model. The thermodynamic factors are calculated by adapting the Widom formalism. The average jump frequencies and thermodynamic factors are calculated exactly; the calculated collective correlation factors, which appear in combination in the vacancy wind terms in the intrinsic diffusivities, are found to be in good agreement with Monte Carlo computer simulation results which are also presented.

In this paper, extensive Monte Carlo simulation results are reported on tracer and collective diffusion correlation effects in the random ternary alloy, as an example of a multicomponent alloy system. The problem of analytically describing both collective and tracer diffusion kinetics is also addressed for the random multicomponent alloy by application of a combination of the Manning theory and Holdsworth and Elliott theory. It is found that the overall results from the combined theory agree reasonably well with Monte Carlo results. This combined approach is much more accurate than Manning’s approach itself and much more manageable than the almost exact, but unfortunately difficult to use, self-consistent theory of Moleko, Allnatt and Allnatt. Some relations between the Onsager phenomenological coefficients and tracer diffusion coefficients are derived and are tested with our Monte Carlo data. Good agreement is found.

The effect of large vacancy concentration on intrinsic and interdiffusion coefficients: A first-principle study of B2-NiAl

Diffusion studies were made in the alpha and beta phases of the silver-zinc system at 600°C with vapor-solid and solid-solid diffusion couples in order to determine intrinsic diffusion coefficients and interdiffusion coefficients. Intrinsic diffusion coefficients, DZn and DAg, determined experimentally for bothα andβ alloys, were compared with those predicted from the models of Darken, Manning, and Dayananda with the aid of thermodynamic and single crystal tracer diffusion data. The experimental values of Dzn were close to those predicted by the models of Darken and Manning, while the experimental DAg values were higher than those determined by both models. The experimental values of the ratio, DZn/DAg, were found to be lower than those predicted by either Darken’s or Manning’s relations. Also, Dayananda’s model was found to be inapplicable with the available tracer diffusion data. This disagreement is considered to reflect the inadequacy of the single crystal tracer diffusivities in the analysis of intrinsic diffusion in polycrystalline Ag-Zn alloys.

Intrinsic diffusion coefficients have been calculated for a solid solution binary fcc metal alloy with vacancies using grand canonical and kinetic Monte Carlo (MC) methods for a variety of model Hamiltonians. Model Hamiltonians include a kinetically and thermodynamically ideal case, solute-vacancy attraction and repulsion, and solute-solute attraction and repulsion. These model Hamiltonians are chosen to have constant average activation energies in order to focus on contributions from other thermodynamic and kinetic factors. The thermodynamic factor calculated using MC is compared to a mean-field regular solution model. It is shown that the mean-field model accurately predicts the thermodynamic factors for each model alloy Hamiltonian except for the alloys with a solute-solute interaction and concentration that are in the spinodal region (as predicted by the regular solution model). The MC determined concentration-dependent intrinsic diffusion coefficients are compared to values determined from the dilute five-frequency model and Darken and Manning analytical approximations. The results indicate that for a solid solution with known average barriers and vacancy concentration, Darken and Manning approximation-based analytic expressions and mean-field theory can be used to predict concentration-dependent diffusion coefficients within a factor of approximately three, provided the system is outside of the spinodal region. The good accuracy of this approximate approach follows from the fact that the thermodynamic factor is the main contribution to the concentration dependence of the diffusion constants, and that this thermodynamic factor is well described by mean-field theory.

Describing diffusion in fluid mixtures at elevated pressures by combining the Maxwell–Stefan formulation with an equation of state

Tracer diffusion is one of most reliable techniques for providing basic kinetic data in solids. In the present review, selected direct methods, in particular the radiotracer measurements as a superior technique due to its high sensitivity, Secondary-Ion-Mass-Spectroscopy (SIMS) profiling, X-Ray Diffraction measurements and Rutherford Backscattering Spectrometry are presented and discussed. Special attention is put on the radiotracer technique describing the currently used sectioning techniques in detail with a focus on the experimental applications and complications. The relevant experimental results are exemplary shown. Furthermore, the most recent developments and advances related to the combined tracer/inter-diffusion measurements are highlighted. It is shown that this approach offers possibilities to provide the concentration-dependent tracer diffusion coefficients of the constituting elements in multi-component alloys in high-throughput experiments. Possibilities of estimating the tracer diffusion coefficients following different types of diffusion couple methods in binary and multicomponent systems are briefly introduced. Finally, specificity of SIMS analysis of diffusion in fine-grained materials are carefully analyzed. If applicable, a direct comparison of the results obtained by different techniques is given.