Protonic Mobility of Neodymium Tungstate

Relating tracer and chemical diffusion coefficients in intermetallic compounds taking the DO 3 and A15 structures

Models of surface diffusion: I. Anisotropy in activated diffusion

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.

Quantities relevant to the chemical and tracer diffusion coefficients, namely the tracer correlation factor, the mobility correlation factor and the site-availability factor are calculated for an interacting lattice gas model using a Monte Carlo method. The origin and nature of the mobility correlation factor is discussed. Calculations are performed for diffusion by nearest-neighbour hopping between the tetrahedral sites in a BCC host, for each of four different site-blocking models (no double occupancy, multiple blocking to first, second or third neighbour). Comparisons are made with previous experimental work on NbHx and TaHx where it is found that for x<0.25 the measured correlations are greater than those calculated for any model, which is consistent with the presence of additional long range attractive interactions known to be important in this region; for 0.25<x<0.6 the results are consistent with multiple blocking to between the second and third neighbour, tending to the former at higher temperatures, while for x>0.6 the atoms are considerably more mobile than predicted by the third-neighbour blocking model. This is to be expected because at these concentrations the assumption of complete site exclusion is unrealistic.

Modeling of conductivity relaxation in oxide ceramics taking account of concentration dependent chemical diffusivities and surface exchange coefficients

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

Tracer, jump, and chemical diffusion coefficients D*, Dj, and D, respectively, were determined on a 50×50 square array of fixed sites by the fluctuation and Kubo–Green methods for the case of nearest-neighbor repulsions and numerically equal next-nearest-neighbor attractions. Both methods give the same D values except at θ=0.5 and T/Tc&amp;lt;0.9, where c(2×2) dominates and simulations are extremely sensitive to very small changes in the small amount of disorder. Activation energies are, in all cases, controlled by next-nearest-neighbor attraction, i.e., are positive relative to the noninteracting case and peak at θ=0.5. However, D has a maximum at θ=0.5 because of a deep minimum in 〈(δN)2〉/〈N〉. D* and Dj are very similar to each other and have a minimum at θ=0.5 and low T, because of the maxima in activation energies at this coverage, caused by the necessity to deform the c(2×2) structure.

Tracer, jump, and chemical diffusion coefficients have been determined by Monte Carlo simulations on a square lattice for the case of nearest-neighbor attraction and numerically equal next-nearest-neighbor repulsion. For this case only second-order θ vs μ/kBT isotherms were found, indicating that the system is in a single phase at all coverages. 〈(δN)2〉/〈N〉 varies only very slightly with temperature at all coverages indicating balance between repulsive and attractive adsorbate–adsorbate interactions. Tracer and jump diffusion coefficients also show only very slight temperature dependence, relative to the noninteractive case. The same is true for the chemical diffusion coefficient determined from the Kubo–Green equation as the product of jump diffusion coefficient and 〈N〉/〈(δN)2〉, DKG. For JNN/kBT&amp;lt;1, there is reasonably good agreement between DKG and DF, the chemical diffusion coefficient determined by the fluctuation method. For JNN/kBT&amp;gt;1, DF decreases markedly with decreasing T. It is hypothesized that this behavior results from the freezing in of enough long-range order for this particular set of interactions to make the fluctuation results differ from the Kubo–Green ones. The latter are more microscopic, and it may be that the fluctuation results depend on probe size.

The influence of adatom diffusion on coverage and emission current fluctuations

In this work we use the well‐known bivariate trap model with random topography in order to study the effects of surface heterogeneities on surface diffusion. Utilizing Monte Carlo simulations we characterize how the tracer, jump and chemical diffusion coefficients depend on temperature and concentration of deep traps, θ. In order to calculate the chemical diffusion coefficient we apply the fluctuation and the Kubo‐Green methods. Both methods are in good agreement at large values of θ only. The discrepancies are discussed and explained. The effects of heterogeneities are largely pronounced at low total coverage and low temperatures, where most of the adatoms are trapped by the deep traps. At high coverages the mobility of adatoms adsorbed on shallow traps dominate the diffusion behavior.

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.

Self-diffusion and collective diffusion of hydrogen in TaH x

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

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