Surface diffusion, or migration within the electrical double layer next to mineral surfaces, is often invoked as a significant contributor to the overall diffusion coefficient in compacted clays, particularly where model predictions underestimate measured diffusion coefficients. The potential for surface diffusion of Sr2+, Ca2+ and Na+ on three clays compacted to dry bulk densities of 1.25 and 1.60 Mg/m3 was examined. The clays were a bentonite, an illite/smectite, and a glacial lake clay (composed mainly of smectite, illite, kaolinite and quartz). The clays were saturated with a Na-Ca-Cl-dominated synthetic groundwater solution with an effective ionic strength of 220 mol/m3. Total intrinsic diffusion coefficients for the cations were determined from their steady-state flux through compacted clays, and apparent diffusion coefficients were obtained from the time-lag technique. Models of diffusive transport in compacted clays, based only on diffusion in the pore solution, adequately described the diffusion data for all clays and diffusants, and there was no need to invoke other transport mechanisms, like surface diffusion. The data indicate that surface diffusion is not a significant transport mechanism in compacted clays at least to a clay density of 1.60 Mg/m3.

We investigate a reaction–diffusion problem in a two-component porous medium with a nonlinear interface condition between the different components. One component is connected and the other one is disconnected. The ratio between the microscopic pore scale and the size of the whole domain is described by the small parameter $\epsilon$. On the interface between the components, we consider a dynamic Wentzell-boundary condition, where the normal fluxes from the bulk domains are given by a reaction–diffusion equation for the traces of the bulk solutions, including nonlinear reaction kinetics depending on the solutions on both sides of the interface. Using two-scale techniques, we pass to the limit $\epsilon \to 0$ and derive macroscopic models, where we need homogenisation results for surface diffusion. To cope with the nonlinear terms, we derive strong two-scale convergence results.

First-principles calculations were performed to determine the Fe on Fe (001) evaporation field and to characterize the surface diffusion of Fe and Cu on Fe (001) and on a step structure under an applied electric field. The evaporation field of Fe on Fe (001) was calculated by the nudged elastic band (NEB) method, using the combination of the effective screening medium and constant electrode potential methods to obtain a condition of constant electric field. The calculated evaporation field of Fe on Fe (001) was 32.4 V/nm, which agrees well with the experimental value. In the surface diffusion of Fe and Cu on Fe (001) and on a step structure, the activation barrier energies were determined by the NEB method with constant applied electric field. It was found that Cu diffuse more easily on the Fe (001) and step structure than Fe under an applied electric field. The activation barrier energy of surface diffusion in the saddle point configuration is small when the distance between Cu and Fe on the surface is larger, and the activation barrier energy becomes smaller when passing through a path far away from the surface due to the effect of the electric field.

We studied the diffusive transport of Cs, Np, Am and Co in compacted sandbentonite mixtures by using the through-diffusion method. The experiments for Cs were performed under various aqueous compositions. Effective diffusivity (De) values of 4.7×10–10 to 5.9×10–9 m2 s–1 were obtained with a somewhat large variation. Apparent diffusivity (Da) values, on the other hand, showed less variation, ranging from 2.0×10–12 to 6.2×10–12 m2 s–1. The results indicated that diffusive flux was proportional to the concentration gradient on the basis of the amount of Cs in the unit volume of the compacted sand-bentonite mixtures rather than the Cs concentration gradient in pore water. Because the former concentration gradient in the mixtures was nearly equal to that of adsorbed Cs, the diffusion of Cs in the mixtures was probably dominated by the concentration gradient of the Cs adsorbed on the mixtures. In addition, the effective/apparent diffusivity of 237Np(IV) and apparent diffusivity of 241Am(III) and 60Co(II) in the mixtures were determined in 0.3/0.03 mol l–1 (NH4)2CO3/Na2S2O4 solution.

Compacted bentonite is to be used as a component of an engineered barrier system to retard the migration of radionuclides in the geological disposal of radioactive waste. In such an environment, montmorillonite in compacted bentonite might be altered to illite due to the hydrothermal reactions caused by the decay heat of radionuclides. In the present study, the diffusion and retention behaviour of Cs in compacted montmorillonite containing illitewas investigated using through-diffusion experiments. The experimental results showed that the flux of Cs attributed to the surface diffusion was independent of the sorption of Cs on illite, indicating that the Cs sorbed on illite was immobile or considerably less mobile than the Cs sorbed on montmorillonite. Consequently, the illite content in compacted bentonite is expected to enhance the sorption capacity of Cs without causing surface diffusion.

Phase-field methods with a degenerate mobility have been widely used to simulate surface diffusion motion. However, apart from the motion induced by surface diffusion, adverse effects such as shrinkage, coarsening and false merging have been observed in the results obtained from the current phase-field methods, which largely affect the accuracy and numerical stability of these methods. In this paper, a flux-corrected phase-field method is proposed to improve the performance of phase-field methods for simulating surface diffusion. The three effects were numerically studied for the proposed method and compared with those observed in the two existing methods, the original phase-field method and the profile-corrected phase-field method. Results show that compared to the original phase-field method, the shrinkage effect in the profile-corrected phase-field method has been significantly reduced. However, coarsening and false merging effects still present and can be significant in some cases. The flux-corrected phase field performs the best in terms of eliminating the shrinkage and coarsening effects. The false merging effect still exists when the diffuse regions of different interfaces overlap with each other. But it has been much reduced as compared to that in the other two methods.

Coalescence is a significant pathway for the growth of nanostructures. Here we studied the coalescence of Bi nanoparticles in situ by liquid cell transmission electron microscopy (TEM). The growth of Bi nanoparticles was initiated from a bismuth neodecanoate precursor solution by electron beam irradiation inside a liquid cell under the TEM. A significant number of coalescence events occurred from the as-grown Bi nanodots. Both symmetric coalescence of two equal-sized nanoparticles and asymmetric coalescence of two or more unequal-sized nanoparticles were analyzed along their growth trajectories. Our observation suggests that two mass transport mechanisms, i.e., surface diffusion and grain boundary diffusion, are responsible for the shape evolution of nanoparticles after a coalescence event.

A lattice Kinetic Monte Carlo (KMC) approach is considered to study the statistical properties of the diffusion of Pt atom clusters on a Pt(111) surface. The interatomic potential experienced by the diffusing atoms is calculated by the embedded atom method and the hopping barrier for the allowed atomic movements are calculated using the Nudged Elastic Band method. The diffusion coefficient is computed for various cluster sizes and system temperatures. The obtained results are in agreement with the ones obtained in previous experimental and theoretical works. A simple scaling argument is proposed for the size dependence of the diffusion coefficient’s pre-factor. A detailed statistical analysis of the event by event KMC dynamics reveals two important and co-existing mechanisms for the diffusion of the cluster’s center of mass. At low temperatures (below T = 400K) the dominating mechanism responsible for the displacement of the cluster’s center of mass is the periphery (or edge) diffusion of the atoms. At high temperatures (above T = 800K) the dissociation and recombination of the clusters becomes more and more important.

We compare dewetting characteristics of a thin nonwetting solid film in theabsence of stress, fortwo models of a wetting potential: the exponential and the algebraic.The exponential model is a one-parameter (r) model, and the algebraic model isa two-parameter (r, m)model, where r is the ratio of the characteristic wetting length to the heightof the unperturbed film,and m is the exponent of h (film height) in a smooth function thatinterpolates the system's surfaceenergy above and below the film-substrate interface at z = 0. The exponentialmodelgives monotonically decreasing (with h) wetting chemical potential, whilethis dependence is monotonic only for the m = 1 case of the algebraic model.Linear stability analysis of the planar equilibrium surface is performed.Simulations of the surface dynamics in the strongly nonlinear regime(large deviations from the planar equilibrium) and for large surface energyanisotropies demonstrate that for any m the film is less prone to dewettingwhen it is governed by the algebraic model. Quasiequilibrium states similar tothe one found in the exponential model [M. Khenner, Phys. Rev. B, 77 (2008), 245445.] exist in the algebraic model as well, and the film morphologies are similar.