Modelling the Diffusion Coefficients of Dilute Gaseous Solutes in Hydrocarbon Liquids

In this work, we present a model, based on rough hard-sphere theory, for the tracer diffusion coefficients of gaseous solutes in non-polar liquids. This work extends an earlier model developed specifically for carbon dioxide in hydrocarbon liquids and establishes a general correlation for gaseous solutes in non-polar liquids. The solutes considered were light hydrocarbons, carbon dioxide, nitrogen and argon, while the solvents were all hydrocarbon liquids. Application of the model requires knowledge of the temperature-dependent molar core volumes of the solute and solvent, which can be determined from pure-component viscosity data, and a temperature-independent roughness factor which can be determined from a single diffusion coefficient measurement in the system of interest. The new model was found to correlate the experimental data with an average absolute relative deviation of 2.7 %. The model also successfully represents computer-simulation data for tracer diffusion coefficients of hard-sphere mixtures and reduces to the expected form for self-diffusion when the solute and solvent become identical.

Techniques of Tracer Diffusion Measurements in Metals, Alloys and Compounds

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.

Effect of Hofmeister Ions on Transport Properties of Aqueous Solutions of Sodium Hyaluronate

Tracer diffusion coefficients obtained from the Taylor dispersion technique at 25.0 °C were measured to study the influence of sodium, ammonium and magnesium salts at 0.01 and 0.1 mol dm−3 on the transport behavior of sodium hyaluronate (NaHy, 0.1%). The selection of these salts was based on their position in Hofmeister series, which describe the specific influence of different ions (cations and anions) on some physicochemical properties of a system that can be interpreted as a salting-in or salting-out effect. In our case, in general, an increase in the ionic strength (i.e., concentrations at 0.01 mol dm−3) led to a significant decrease in the limiting diffusion coefficient of the NaHy 0.1%, indicating, in those circumstances, the presence of salting-in effects. However, the opposite effect (salting-out) was verified with the increase in concentration of some salts, mainly for NH4SCN at 0.1 mol dm−3. In this particular salt, the cation is weakly hydrated and, consequently, its presence does not favor interactions between NaHy and water molecules, promoting, in those circumstances, less resistance to the movement of NaHy and thus to the increase of its diffusion (19%). These data, complemented by viscosity measurements, permit us to have a better understanding about the effect of these salts on the transport behaviour of NaHy.

Tracer diffusion coefficients of Li+ ions in c-axis oriented LixCoO2 thin films measured by secondary ion mass spectrometry

Lithium diffusion is a key factor in determining the charge/discharge rate of Li-ion batteries. Herein, we study the tracer diffusion coefficient of lithium ions in the c-axis oriented LiCoO2 thin film using secondary ion mass spectrometry (SIMS).

Fick’s Laws

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.

Mg diffusion in forsterite from 1250–1600 °C

26Mg tracer diffusion coefficients were determined in single crystals of pure synthetic forsterite (Mg2SiO4). Isotopically enriched powder sources both acted as the 26Mg source and buffered the activities of silica (aSiO2) at forsterite + protoenstatite (Mg2Si2O6) (high aSiO2) and forsterite + periclase (MgO) (low aSiO2). Experiments were conducted at atmospheric pressure between 1250 and 1600 °C, and at oxygen fugacities (fO2s) between 10–12 bars (CO-CO2 mix) and 10–0.7 bars (air). The resulting diffusion profiles were measured along the three principal crystallographic axes (a, b, and c; ||[100], ||[010], ||[001]) using laser ablation–inductively coupled plasma–mass spectrometry (LA-ICP-MS), with a quadrupole mass spectrometer. These measurements were corroborated by ion microprobe using the sensitive high resolution ion microprobe-reverse geometry (SHRIMP-RG) instrument. Mg tracer diffusion is anisotropic, with D[001] > D[010] > D[100], the difference in diffusion coefficients varying by about one order of magnitude at a given temperature with crystallographic orientation. Diffusion is faster in protoenstatite-buffered than periclase-buffered conditions, again with around one order of magnitude difference in diffusivity between buffering conditions. There is no apparent effect of fO2 on diffusion. A global fit to all data, including data from Chakraborty et al. (1994) and Morioka (1981) yields the relationship: log 10 D = log 10 D 0 ( m 2 s - 1 ) + 0 . 61 ( ± 0 . 03 ) log 10 a SiO 2 + - 359 ( ± 10 ) kJ / mol 2 . 303 R T where log10D0 is –3.15 (±0.08), –3.61 (±0.02), and –4.01 (± 0.05) m2 s–1 for the [001], [010], and [100] directions, respectively (1 s.d.). The LA-ICP-MS technique reproduces diffusion coefficients determined by SHRIMP-RG, albeit with slightly different absolute values of isotope ratios. This shows that LA-ICPMS, which is both accessible and rapid, is a robust analytical method for such tracer diffusion studies.

Diffusion Rates of Components in Metal-Silicides Depending on Atomic Number of Refractory Metal Component

Interdiffusion studies conducted in group IVB, VB and VIB metal-silicon systems are discussed in detail to show a pattern in the change of diffusion coefficients with the change in atomic number of the refractory metal (M) component. MSi2and M5Si3phases are considered for these discussions. It is shown that integrated diffusion coefficients increase with the increase in atomic number of the refractory component when the data are plotted with respect to the melting point normalized annealing temperature. This indicates the increase in overall defect concentration facilitating the diffusion of components. This is found to be true in both the phases. Additionally, the estimated ratios of tracer diffusion coefficients indicate the change in concentration of antisite defects in certain manner with the change in atomic number of the refractory components.