Diffusion studies with radioactive ions

An overview of the modified radiotracer based diffusion studies carried out at IGISOL is provided. The experimental procedures are briefly described followed by examples involving IGISOL as the key facility. In this respect the studies related to silicon-germanium (Si_1???xGe_x) alloys and on the related diffusion systematics are summarized. Another group of examples is related to mobility determination of lead isotopes in glass for verifying retrospective radon measurements. Finally an outlook to future possibilities related to employing radiotracers in solid state research is provided.     

Diffusion studies in liquids by holographic interferometry

Liquid diffusion coefficients are very important basic data for research and many applications in chemical engineering and in other fields, such as biological systems, pollution control and separation of isotopes. Holographic interferometry technique with accuracy and promptness is one of the most widely used techniques for diffusivity studies. We report an interferometric technique to determine the diffusion coefficient of transparent liquid solutions. As the diffusion progresses with time the refractive indices at different planes in the cell are different, and the characteristic extreme points of the fringe patterns shift outward. The interference fringes was obtained and recorded on a PC using a CCD camera. By judging the interferogram with a computer procedure the concentrations at different planes can be obtained by the relation between concentration and refractive indices, furthermore, the diffusion coefficient can be obtained by calculation. The obtained diffusivity values matched very well with the existing experimental results.     

Diffusion studies in liquids by multiple beam interferometer

A new method to determine the diffusion coefficients of transparent solutions using a multiple beam interferometer in real-time is reported. The experimental results are compared with existing diffusion coefficient values reported in the literature.     

Diffusion studies of Be-implanted GaAs by SIMS and electrical profiling

Secondary ion mass spectrometry (SIMS) has been used with differential resistivity and Hall effect measurements to study the 900°C diffusion of implanted Be in GaAs. Some outdiffusion of Be into the Si₃N₄ encapsulant occurs for surface Be concentrations above 1 × 10¹⁸cm^?3. However, excellent agreement between the electrical and atomic profiles indicates that 85–100% of the Be remaining after annealing is electrically active. The concentration-dependent diffusion observed for implanted Be in GaAs was not significantly altered in experiments using hot substrate implants, two-step anneals, or annealing with Ga and As overpressure.     

Diffusion studies in confined nematic liquid crystals by MAS PFG NMR

Pulsed field gradient (PFG) NMR and magic-angle spinning (MAS) NMR have been combined in order to measure the diffusion coefficients of liquid crystals in confined geometry. Combination of MAS NMR with PFG NMR has a higher spectroscopic resolution in comparison with conventional PFG NMR and improves the application of NMR diffusometry to liquid crystals. It is found that the confinement of the liquid crystal 5CB in porous glasses with mean pore diameters of 30 and 200 nm does not notably change its diffusion behavior in comparison with the bulk state.     

Diffusion studies in porous media with the "inside-out" technique

Diffusion measurements of water in a glass beads porous media were carried out by the "One-Sided Access" sensor. An approach to determine the long time mean square displacement of hydrogen molecules by measuring the ratio of stimulated echo to primary echo in a three pulse sequence in the presence of permanent static field gradient is analysed. The difference between the apparent diffusion coefficient in a pure water sample and in water/glass beads mixtures becomes visible.     

Diffusion of propylene adsorbed in Na-Y and Na-ZSM5 zeolites: Neutron scattering and FTIR studies

Here we report the quasielastic neutron scattering and FTIR studies on the dynamics of propylene adsorbed in Na-Y and Na-ZSM5 zeolites. QENS data show that although the mechanism of translational motion of propylene is jump diffusion in both the cases of Na-Y and Na-ZSM5 zeolites, the diffusivity is affected by the host size and is hindered in the case of Na-ZSM5. FTIR studies showed that guest-host interaction in Na-ZSM5 is stronger than that in Na-Y zeolite corroborating the QENS results.      

Diffusion flame-holes

Recent models of straight diffusion flame edges are extended to consider the effect of a curved edge forming the perimeter of an axisymmetric ‘hole’, where a burning flame surrounds a quenched inner region. For ‘free’ flame-holes (without a heat sink near the axis), at small Damköhler number (Da), the holes grow if the initial radius is large but shrink if it is small. For large Da, the holes shrink for any initial radius. Thus, free flame-holes are not stable for any Da, which is consistent with experimental observations. When the flame-hole is ‘anchored’ by a heat sink near to the axis, stationary holes of finite radius can exist for sufficiently high Da, but the solutions revert to ‘free’ hole behaviour for radii sufficiently larger than the heat sink radius. Based on these results, it is suggested that quasi-stationary flame-holes are not likely to be a common feature of turbulent diffusion flames, except possibly when large lateral gradients of Da are present due to intense vortices passing through the flame front.     

Thermo-Quantum Diffusion

A new approach to the thermo-quantum diffusion is proposed and a nonlinear quantum Smoluchowski equation is derived, which describes classical diffusion in the field of the Bohm quantum potential. A nonlinear thermo-quantum expression for the diffusion front is obtained, being a quantum generalization of the classical Einstein law. The quantum diffusion at zero temperature is also described and a new dependence of the position dispersion on time is derived. A stochastic Bohm-Langevin equation is also proposed.     

Diffusion reproduction processes

Interesting physics emerges from studying a population of reproducing individuals. Each can be regarded as a random walker, but it can either duplicate or die. Novel features of the collective behavior are quite surprising: if individuals reproduce or die freely, the life expectation is proportional to the size of the population, and if it is kept constant, the center of mass moves in space as if it were a single walker (i.e., the diffusion constant is independent of population's size). Biology-inspired interactions are also considered.     

Diffusion on surfaces

A commentary is presented on current progress towards understanding diffusion on surfaces. Recent work by field ion microscopy shows that interactions between diffusing adatoms lead to correlated motions and add unexpected complexity to the elementary diffusion mechanisms. Work on high temperature surface self-diffusion also suggests the importance of interactions between diffusing atoms. Mass transport, catalysed surface diffusion, giant diffusivities, impurity, tracer and adsorbed layer diffusion, diffusion in sintering and other applications, are briefly discussed.     

Diffusion by Turbulence

The turbulent diffusivity K of the atmosphere has first been studied by Richardson 1926 who empirically found that K depends on the scale l, K = Al^α, with α = 4/3 and A = 0.6 cm^2/3 s^?1. This empirical scaling law is derived here from a unified theory (based on the Navier-Stokes equation) together with an explicit result for the prefactor, A = 2.4 ?^1/3. The mean atmospheric dissipation rate compatible with this is ? = 0.016 cm² s^?3. For windtunnels with typical dissipation rates ? ? 1 m² s^?3 the turbulent diffusion coefficient should be K/cm² s^?1 = 52 (l/cm)^4/3.     

Diffusion with restrictions

A nonlinear diffusion equation is derived by taking into account hopping rates depending on the occupation of next neighbouring sites. There appears additional repulsive and attractive forces leading to a changed local mobility. The stationary and the time dependent behaviour of the system are studied based upon the master equation approach. Different to conventional diffusion it results in a time dependent bump the position of which increases with time described by an anomalous diffusion exponent. The fractal dimension of this random walk is exclusively determined by the space dimension. The applicability of the model to describe glasses is discussed.     

由扩散张量导出的各向异性扩散模型的隐式数值模拟

研究了由扩散张量导出的各向异性扩散的图像处理模型,并构造了隐式差分格式,形成了有13条对角线的大型稀疏矩阵.利用代数多重网格法求解了这个线性代数方程组.并进行了数值试验.     

Diffusion in disordered media

Diffusion in disordered systems does not follow the classical laws which describe transport in ordered crystalline media, and this leads to many anomalous physical properties. Since the application of percolation theory, the main advances in the understanding of these processes have come from fractal theory. Scaling theories and numerical simulations are important tools to describe diffusion processes (random walks: the 'ant in the labyrinth') on percolation systems and fractals. Different types of disordered systems exhibiting anomalous diffusion are presented (the incipient infinite percolation cluster, diffusion-limited aggregation clusters, lattice animals, and random combs), and scaling theories as well as numerical simulations of greater sophistication are described. Also, diffusion in the presence of singular distributions of transition rates is discussed and related to anomalous diffusion on disordered structures.     

Diffusion and two-particle correlations

Fluctuation signals of the QCD phase transition in nuclear collisions can be dissipated due to diffusion. Diffusive modes in the standard formulation of relativistic hydrodynamics propagate with infinite speed, violating causality. We develop a causal diffusion equation study the dissipation of net-charge fluctuations. We find that causality restricts the extent to which diffusion can dissipate these fluctuations.     

Diffusion in heterogeneous lattices

We present here the results of our investigations of particle diffusion over different heterogeneous lattices with deep and shallow adsorption sites. A general analytical expression for chemical diffusion coefficient has been derived for a number of inhomogeneous lattices of different dimensionality and symmetry. We have calculated coverage dependencies of diffusion coefficients. The analytical data have been compared with the numerical data obtained by the kinetic Monte Carlo simulations. Almost perfect agreement between the respective results has been found.     

Diffusion phase diffraction gratings

Ion exchange in glass is studied. The two-dimensional diffusion equation with periodic boundary conditions that describes the formation of a diffraction grating in glass is numerically solved. The existence of the optimum diffusion time providing the maximum diffraction efficiency in the first order is demonstrated. Dependences of the optimum diffusion time and the maximum diffraction efficiency on the space factor of a mask used for ion exchange are found.     

Diffusion coefficients in channeling

Making use of the general formula introduced by Ohtsuki, detailed calculations for diffusion coefficients in channeling are performed. The nuclear and single electron excitations are considered separately compared with the plasmon excitation. Some analytic expressions proposed in previous paper are confirmed.