The diffusion of non-sorbing species in different crystalline rocks and fissure coating materials has been studied. The results show that the effective diffusivity of iodide, Uranine and Cr-EDTA in rock materials with fissure coating material is of the same magnitude or higher than in granites and gneisses. The results also show that it is not possible to assign one value to the diffusivity of a rock from a given area. The variations in properties are too large. The estimated effective diffusivity of iodide in rocks without fissure coating material was found to be in the range 1.10-14 m2/s to 70.10-14 m2/s.

To simulate the stress that exists in the bedrock at large depths, diffusion experiments with iodide and electrical resistivity measurements in rock materials under mechanical stress have been performed. It was found that the diffusivity in rock samples at 300–350 bars stress was reduced to 20–70% of the value in samples under atmospheric pressure.

Simple diffusion coefficients, D(θ), in most unsaturated media were found to be primarily a function of water content and not material characteristics except where the characteristics affect or determine water content. At high water contents, D(θ) gradually declines as water content decreases, from 10−5 cm2/sec at a volumetric water content of about 50% to 10−7 cm2/sec at a volumetric water content of about 5%, followed by a sharp decline as surface water films become thin and discontinuous and pendular water elements become very small, from 10−7 cm2/sec at a volumetric water content of about 5% to 10−9 cm2/sec at a volumetric water content of about 0.5% to 1%.

Besides some necessary reviewing of conventional diffusion theory, this paper deals with the modification of the mass and charge transport equations originating from the occurence of internal defect-chemical reactions (especially valence changes of the defects) which can be considered to be in local equilibrium. It is shown how the phenomenological transport coefficients for chemical diffusion, tracer diffusion and ionic conduction depend on the individual defect diffusivities under such general conditions. Moreover, the evaluation formulae of well-known electrochemical techniques such as Wagner-Hebb polarization and concentration cell experiments have to be modified. Application is made to the influence of trapping effects in doped SrTi03, to the valence changes in YBa2Cu3O6+x as well as to the mixed conduction in orthorhombic PbO.

Hydrogen diffusion in CuInSe 2 single crystals and CuInS2 thin films was studied by measuring the spreading of implantation profiles upon annealing. Deep implantation with an ion energy of 10 keV and sub-surface implantation with 300 eV were applied. The diffusion coefficients in both materials were found to be in the order of 10-14 to 10-13 cm2/s in the temperature range between 400 and 520 K.These fairly low diffusivities are typical for a trap and release transport process rather than intrinsic diffusion of interstitial hydrogen. In the polycrystalline CuInS2 films, hydrogen leaves the sample through the grain boundaries.

We address the problem of calculating the long-time-limit effective diffusivity in stable two- phase polycrystalline material. A phenomenological model is used where the high diffusivity interphase boundaries are treated as connected “coatings” of the individual grains. Derivation of expressions for the effective diffusivity with segregation is made along Maxwell lines. Monte Carlo simulation using lattice-based random walks is used to test the validity of the expressions. It is shown that for the case analysed the derived expressions for the effective diffusivity are in very good agreement with simulation results. The equivalent of the Hart equation is also derived. It is shown to be in poor agreement with simulation results.

Atomistic Molecular Dynamics are used to simulate diffusion of hydrocarbons inside the microporous structure of siliceous zeolite CIT-I, with chemical composition SiO2. CIT-1 is a crystalline microporous material containing channels formed by rings containing 12 and 10 Si atoms (Figure 1). The dimensions of these two channel systems are sufficient to cause substantial differences in the diffusion of para-xylene and ortho-xylene. Diffusion coefficients as a function of loading of each isomer, and activation energies have been calculated from the simulations. The effect of the isomer size in the diffusion path is also analysed.

Situations where a polymeric material is exposed to a solvent mixture so that the different components within the mixture can diffuse into the polymer are common both in industrial applications and in biological processes. Often one of the components is taken up preferentially and its presence affects the diffusion properties of the remaining components. The problem of accounting for processes of this type has not been dealt with in a systematic way. This may in part be due to the difficulty of characterizing experimentally the separate diffusion behavior of the various components: data of this kind are now becoming available for simple binary mixtures. In order to model this class of problems, a lattice model involving a polymer matrix (M) and two diffusing components (A and B) has been introduced. The Monte Carlo evolution of the system has been examined for different values of the local A–M, B–M and A–B interactions. These results shed light on the microscopic origin of selective uptake.

In this study we construct two new equations to describe the effective diffusivity in nanomaterials where diffusion proceeds via both the grains and the grain boundaries in comparable amounts. We analyze two very simple 2D grain configurations by Monte Carlo methods to test the validity of the equations. In addition, we also test the Hart and the recently extended Maxwell-Garnett equations. It is shown that one of the two new equations provides a very good description of diffusion in the grain models postulated.

Ion diffusion across material interfaces is considered in a sequence of approximations with increasing complexity. First, the one-dimensional lattice gas model of particle diffusion is generalized to include a finite width interface region, and the possible existence of an energy barrier at the interface. Overvoltage measurements on InSe, and dielectric loss measurements on B2O3 - 0.5Li20 - 0.15Li2SO4 are used to determine the field-free hopping rates in the two materials. It is shown that the energy barrier is a dominant parameter. This model is then modified by considering the disorder of the glass structure and the blocking effect resulting from the ion interaction. Next, a more rigorous treatment is presented by solving the Poisson equation with appropriate boundatry conditions, and a self-consistent theory of the ionic diffusion is proposed. To clarify this problem, an intermediate step and two additional models with increasing sophistication are considered: first, the potential φ(x) of the moving charge density n(x) is calculated and it is shown that φ(x) is not negligible. Then, a feed-back is provided by including this potential in the diffusion equation. This treatment is already self-consistent and more realistic but leads to long computations even for the simple one dimensional lattice-gas model. A remedy of this difficulty is proposed whereby the theory is reformulated in order to guarantee from the beginning the self-consistency of the solution of the non-linear diffusion problem. Straightforward extensions to the two-dimensional case are then possible. The results of the computations are illustrated with numerical examples for different values of the physical parameters.

A diffusion multiple is an assembly of three or more different metal blocks, in intimate interfacial contact, that is subjected to a high temperature to allow thermal interdiffusion. The power of using a diffusion multiple approach in the efficient mapping of phase diagrams and materials properties for multicomponent alloy systems is illustrated in this article using several examples. It is now possible to map phase diagrams and materials properties at an efficiency some 3 orders of magnitude higher than the conventional one-alloy-at-a-time approach. With this high efficiency, many critical materials data that otherwise would be too time-consuming and expensive to acquire can be obtained and employed to accelerate our understanding of a system's materials physics and chemistry. It is postulated that coupling the diffusion multiple approach with the CALPHAD (calculation of phase diagrams) method will have a significant impact on the computational design of materials.

At long times the effective solute diffusivity can be described by the (modified) Hart-Mortlock and Maxwell-Garnett equations for diffusion parallel and perpendicular to the grain boundary respectively. In this paper we analyze for the first time the time dependence of the effective solute diffusivity for these conditions. We assume that there are local regions (delineated by the diffusion length) in the grains adjacent to the grain boundary where the solute is equilibrated with the grain boundary. We write equations for the effective solute diffusivity with this assumption. Comparison with Monte Carlo simulations shows that this is quite a reasonable approximation for solute diffusion parallel to the grain boundary. For diffusion perpendicular to the grain boundary it is only a fair approximation unless the segregation is weak.

Diffusion coefficients were measured (Dm) for Pu(IV) in dense mixtures of bentonite and sand (soil) saturated with a synthetic groundwater solution (SGW) at a pH of 8 and at 25°C. The Dm values were approximately 10-14 m2/s. The clay content of the soil, in the range of 10 to 50%, did not have a significant effect on Dm. The Dm values were also compared with diffusion coefficients calculated (Dc) from a model based on a distribution coefficient. Fair agreement between Dm and Dc for Pu(IV) was found for the soils and SGW examined here. It is unlikelv. however, that the model will accurately estimate Dm for Pu, which has a complex solution and sorption chemistry, over a wide range of conditions.

The diffusion of cesium(I), strontium(II), pertechnetate and europium in brine-saturated backfill materials was measured. Plastic diffusion cells containing cylindrical diffusion columns were used for low density backfill materials. The diffusion of gamma-emitters was followed by a gamma scanning technique. Metal diffusion cells constructed entirely from Hastelloy C-276 were used for the diffusion of pertechnetate in highly compacted bentonite. Apparent distribution coefficients calculated from diffusion data are (a) 0.02 m3 /kg for cesium(I) in 40 wt.% mordenite and 60 wt.% bentonite; (b) 0.04 m3/kg for strontium(II) in 10 wt.% sodium titanate and 90 wt.% bentonite; (c) 0.5 m3/kg for pertechnetate in 70 wt.% charcoal and 30 wt.% bentonite; and (d) 3 m3/kg for europium in 100% bentonite. Backfill effectiveness estimates based on batch sorption measurements were supported by these results;however, the diffusion results for europium did not agree well with a model for diffusion retarded by linear sorption. First measurements of pertechnetate diffusion in highly compacted bentonite suggest that anion exclusion may play a role in reducing mass transport rates of anions in this material. Needs for diffusion measurements that take into account site-specific materials interactions are described.

Carbon steel is one of the candidate overpack materials for high-level waste disposal and is expected to assure complete containment of vitrified waste glass during an initial period of 1000 years in Japan. The lifetime of the carbon steel overpack will depend on its corrosion rate. The corrosion rate of carbon steel is reduced by the presence of buffer material such as bentonite. Buffer material will delay the supply of corrosive materials and discharge of corrosion products through it. Carbon steel overpack will be corroded by consuming oxygen introduced by repository construction after closure of repository and then will keep the reducing environment in the vicinity of repository. The reducing condition will be expected to retard the migration of redox-sensitive radionuclides by lowering their solubilities. Therefore, the diffusion of corrosion products of iron in buffer material is important to discuss the corrosion rate of overpack, migration of redox-sensitive radionuclides and properties of buffer material. The purpose of this paper is to study diffusion behavior of a corrosion product of iron in compacted bentonites under a reducing condition with a carbon steel. The diffusion mechanism of iron in the compacted bentonites were discussed by estimation of iron species in the bentonite pore water. There were two diffusion paths of iron in the compacted bentonites used in this study; the fast path has low capacity of iron, ca. 1wt%, and large apparent diffusion coefficient, ca. 10−12 m2/s and the slow path has high capacity of iron, ca. 10wt%, and small apparent diffusion coefficient, ca. 10−14 m2/s.

New photopolymers have contributed significantly to the recent growth of holographic and lithographic applications. Photopolymerizable organic-inorganic hybrid materials, based on methacrylate functionalized silane and zirconia particles as holographic recording material, are presented. Thick films of this composite system were prepared and volume diffractive gratings were fabricated by a two laser beam interference technique. The formation of the gratings is based on the diffusion of high refractive index components (ZrO2-nanoparticles) to areas with high irradiation intensity with subsequent immobilization by full irradiation of the film. The influence of the zirconia particles as the main component for obtaining highly efficient gratings is presented and the correlation between particle concentration and refractive index profile is shown.

Experimental results are presented on the diffusion of Cu in silicon and Black Diamond¶ (BD). Cu coated silicon samples, with and without the BD layer, are annealed at various temperatures and times. It is concluded that Cu diffusion in silicon is inhibited in the presence of a copper silicide formed during annealing and/or low solubility at temperatures less than 400°C. On the other hand, the incorporation of Cu in the BD film is observed to be strongly dependant on the method of deposition of the Cu layer. It is further concluded, based on device reliability data, that intentional backside Cu contamination does not pose serious device reliability problems even when subjected to annealing at temperatures typically used for backend processing.

The diffusion of non-sorbing species in different rock materials and fissure coating materials have been studied. The results show that the effective diffusivity of iodide in granites with fissure coating materials is of the same magnitude or higher as the effective diffusivity for iodide in granites without fissure coating material. Also the porosities of the granites with fissure coating material were higher. The effective diffusivity for iodide in rock materials without fissure coating material was determined to be from 1.i0-14 m2/s to about 7.10-13 m2/s.To simulate the stress that exists in the bedrock at large depths diffusion experiments with iodide in rock materials under mechanical stress, and electrical resistivity measurements in salt-water-saturated rock cores under stress have been started. Electrical resistivity measurements is an indirect method to determine the diffusivity.Results from some initial measurements show that the effective diffusivity is reduced to about 40 % of the value for unstressed samples at pressures of 230-280 bar. This is the expected stress at repository depths.

Our study is motivated by the need for development and deployment of reliable and efficient energy storage devices, such as lithium-ion batteries. However, the rate-capacity loss is the key obstacle faced by current lithium-ion battery technology, hindering many potential large-scale engineering applications, such as future transportation modalities, grid stabilization and storage systems for renewable energy. During electrochemical processes, diffusion-induced stress is an important factor causing electrode material capacity loss and failure. In this study, we present models that are capable for describing diffusion mechanisms and stress formation in LiFePO4 nanoparticles, a lithium-ion battery cathode material which promises an alternative, with the potential for reduced cost and improved safety. To evaluate mechanics of diffusion-induced fractures, a plate-like model is adopted with anisotropic materials properties and volume misfits during the phase transformation are considered. Stress distribution at phase boundaries and fracture mechanics information (energy release rates and stress intensity factors) are provided to further understand the stress development due to lithium-ion diffusion during discharging. This study contributes to the fundamental understanding of kinetics of materials in lithium-ion batteries, and results from our stress analysis provides better electrode materials design rules for future lithium-ion batteries.

The essence of fluid-mechanical mixing of diffusing and reacting fluids can be traced back to kinematics, connectedness of material volumes and transport processes occurring across deforming material surfaces. Descriptions based on kinematics of homoeomorphic deforming material surfaces (tracers) are restricted solely to continuous motions and conveniently analysed by transport equations in Lagrangian frames.

Connectedness of material volumes restricts the mixing topology and generates bicontinuous structures characterized by intermaterial-area and striation-thickness distributions. Upper bounds for area generation and material-line elongation are related to mean values of viscous dissipation and govern the average reaction rate in diffusion-controlled reactions. Two concepts are introduced: micromixing, related to local flows, rate of stretching and local viscous dissipation, and macromixing, associated with connectedness of isoconcentration surfaces, vorticity and average viscous dissipation.

Several small-scale flows can be used to typify the interplay between fluid mechanics, mass and energy transport, and chemical reactions: elliptically symmetrical stagnation flows, vortex decay, and swirling flow with uniform stretching. It is proposed that complex fluid motions might be interpreted in terms of integrated behaviour of populations of small-scale flows distributed in space and time to simulate mixing behaviour.

The objective of this work is to present the foundations of a continuum mixing description making reference to earlier approaches to demonstrate computational applicability and practical significance.