Confined diffusion

Summary An equation for the unidimensional confined diffusion is proposed. The equation coincides with the well-known homogeneous equation except the presence of a source term. This term which has the form of a dipole distribution is located on a moving front which sharply separates two distinct regions. In the first region (from the boundary up to the front) the confined solution coincides with a suitable solution of the homogeneous equation; in the second region (besides the front) it vanishes. The source term, moreover, switches off the diffusing flux at the front. The sharp confinement allows to relax the original boundary conditions of the homogeneous equation. Precisely, to the function depending on the time at the boundary, another arbitrary function depending on the space at the initial time is added. This new function (provided not vanishing) allows to obtain in general an acceptable evolution of the front and does not prevent the validity of the conservation law: flux at the boundary is equal to the time variation of the diffusing quantity contained between the boundary and the front. By a suitable choice of this new function, so that it results to be connected to the other boundary condition (that depending on time) it is possible to arrive at an evolution of the front such as: , where λ,K, corresponding, respectively, to a dimensionless parameter and diffusivity, depend on the medium. Under such simplifying assumption, it is possible to obtain an analytical expression for the confined solution. This solution, evaluated in a point of the space, arrives asymptotically at the same value reached by the solution of the homogeneous equation.     

Controlling the diffusion process via time-variable diffusion coefficient

The establishment of the steady-state dopant profile in a medium with a time-variable diffusion coefficient is considered within the approach proposed previously for estimating mass-and heat-transfer time characteristics. It is shown that the time it takes for the equilibrium concentration to set in may be increased or decreased by appropriately choosing the law of variation of the diffusion coefficient.     

Simultaneous magnetic resonance imaging of diffusion anisotropy and diffusion gradient

The theory of diffusion gradient-weighted MRI (DGWI) is presented in this paper. The Bloch-Torrey equation was modified to include the effect of intravoxel spatial-location variation of water diffusion (diffusion gradient) on MRI signal, in addition to the effect of intravoxel spatial-direction variation of water diffusion (diffusion anisotropy). An analytical solution for a diffusion-encoding spin-echo pulse sequence was derived. Unlike water diffusion which attenuates the image signal intensity, this newly derived solution relates the spatial gradient of the water diffusion with the phase of the image signal. This novel MRI technique directly measures both the water diffusion and its spatial gradient, and thus offers a noninvasive imaging tool to simultaneously investigate the intravoxel inhomogeneity and anisotropy of tissue structures. In addition, as demonstrated with our preliminary data, this new method may be utilized to delineate the interfaces of tissues with different diffusion. This method is an extension of the successful diffusion tensor MRI (DTI), but requires no additional data acquisition. In addition to the measured diffusion tensor, this new method provides measurements of the spatial derivatives of the three principal diffusivities of the tensor, thereby providing additional information for improving white matter fiber tractography.     

Quantum diffusion

Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities etc.) and they turn into quasiparticles of a new type—defectons, which are characterized not by their position in the crystal lattice but by their quasimomentum and dispersion law. Defecton-defecton and defecton-phonon scattering are considered and an interpolation formula for the diffusion coefficient valid in all interesting temperature and concentration regions is presented. A comparison with the experimental data is made. Some alternative points of view are discussed in detail and the inconsistency of the Kisvarsanyi-Sullivan theory is shown.     

Two-state random walk model of diffusion. 2. Oscillatory diffusion

Continuing our study of interrupted diffusion, we consider the problem of a particle executing a random walk interspersed with localized oscillations during its halts (e.g., at lattice sites). Earlier approaches proceedvia approximation schemes for the solution of the Fokker-Planck equation for diffusion in a periodic potential. In contrast, we visualize a two-state random walk in velocity space with the particle alternating between a state of flight and one of localized oscillation. Using simple, physically plausible inputs for the primary quantities characterising the random walk, we employ the powerful continuous-time random walk formalism to derive convenient and tractable closed-form expressions for all the objects of interest: the velocity autocorrelation, generalized diffusion constant, dynamic mobility, mean square displacement, dynamic structure factor (in the Gaussian approximation), etc. The interplay of the three characteristic times in the problem (the mean residence and flight times, and the period of the ‘local mode’) is elucidated. The emergence of a number of striking features of oscillatory diffusion (e.g., the local mode peak in the dynamic mobility and structure factor, and the transition between the oscillatory and diffusive regimes) is demonstrated.     

On the substructure of diffusion zone in copper-alpha brass diffusion couple

The diffusion zone of a sample in the form of three layers was studied by electron microscopy, X-ray diffraction, light microscopy and microhardness test. Experimental results clearly show that in the diffusion zone there is a superposition of thermal stress and a stress due to the vacancies.     

Fractional nonlinear diffusion equation,solutions and anomalous diffusion

We devote this work to investigate the solutions of a generalized diffusion equation which contains spatial fractional derivatives and nonlinear terms. The presence of external forces and absorbent terms is also considered. The solutions found here can have a compact or long tail behavior and, in particular, for the last case in the asymptotic limit, we relate these solutions to the Lévy or Tsallis distributions. In addition, from the results presented here a rich class of diffusive processes, including normal and anomalous ones, can be obtained.     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Stability of nonlinear diffusion

The nonlinear diffusion equation in bounded geometry with time-independent boundary conditions has a uniquely determined stationary solution. We show that this solution is dynamically stable in the sense of Liapunov. Any initial distribution tends to the stationary one as time goes on. It is shown that the application of the Glansdorff-Prigogine stability criterion requires a more elaborate analysis. We develop a variational procedure which has application in a wide range of nonlinear transport problems.     

Nonlocality of relative diffusion

On the basis of numerical modeling, the hypothesis of the nonlocal character of Richardson relative diffusion is tested and confirmed. Zh. éksp. Teor. Fiz. 112, 163–166 (July 1997)     

Surface diffusion of adsorbates

The review covers studies of the surface diffusion of adsorbed species on single crystal substrates. Experimental techniques employed in investigations of the surface diffusion of adsorbates are discussed. Emphasis is placed on the analysis of data obtained at considerable degrees of coverage. These results demonstrate a close interrelation between surface diffusion and phase transitions in adsorbed layers. Possible mechanisms of surface diffusion are considered taking into account the structure of adsorbed layers. Findings on the effect of electric fields on surface diffusion processes are reviewed.     

The Harrison diffusion kinetics regimes in solute grain boundary diffusion

Knowledge of the limits of the principal Harrison kinetics regimes (Types A, B and C) for grain boundary diffusion is very important for the correct analysis of depth profiles in a tracer diffusion experiment. These regimes for self‐diffusion have been extensively studied in the past by making use of the phenomenological lattice Monte Carlo (LMC) method with the result that the limits are now well established. However, the relationship of these self‐diffusion limits to the corresponding ones for solute diffusion in the presence of solute segregation to the grain boundaries remains unclear. In the present study, the influence of solute segregation on the limits was investigated with the LMC method for the well‐known parallel grain boundary slab model by showing the equivalence of two diffusion models. It is shown which diffusion parameters are useful for identifying the limits of the Harrison kinetics regimes for solute grain boundary diffusion. It is also shown how the measured segregation factor from the diffusion experiment in the Harrison Type‐B kinetics regime may differ from the global segregation factor.     

Anomalous diffusion and thermal diffusion of light ions in a nonisothermal plasma

A turbulent state appearing upon the Cherenkov generation of slow ion acoustic waves by light ions and their induced scattering on heavy ions has been studied. The coefficients of the anomalous diffusion and thermal diffusion of light ions have been determined.     

Simulation of retarded diffusion of antimony and enhanced diffusion of phosphorus in silicon

The paper is concerned with the influence of point defects on dopant diffusion in silicon. This influence is analysed by means of comparing the experimental results of Mizuo and Higuchi with our simulation. The experiments deal with the oxidation retarded diffusion (ORD) of Sb and the oxidation enhanced diffusion (OED) ofP in FZ silicon at 1100°C. The simulation is carried out by using a physical model without simplifying assumptions. It is shown that simplifying assumptions are not admissible. A reasonable set of parameters is deduced from this analysis. As each parameter represents a physical effect, information about the importance of bulk and surface recombination of point defects and about the equilibrium concentration values and diffusion coefficients of diffusing species are obtained. It turns out that the influence of the surface is decisive for the distribution of point defects.Dedicated to Professor Karlheinz Seeger on the occasion of his 60th birthday     

Rotational diffusion microrheology

Examining the rotational diffusion of a microparticle suspended in a soft material opens up exciting new opportunities for locally probing the frequency-dependent linear viscoelastic shear modulus, G*(omega). We study the one-dimensional rotational diffusion of a wax microdisk in an aqueous polymer entanglement network using light streak tracking. By measuring the disk's time-dependent mean square angular displacement, , we predict the polymer solution's G*(omega) using a rotational generalized Stokes-Einstein relation. The good agreement of the predicted modulus with mechanical measurements confirms this new microrheological approach.