Surface self-diffusion coefficient

The distribution of these impurities or minor alloy constituents near lattice discontinuities is known to affect the chemical and mechanical properties of the contaminated materials for example the presence of sulfur on a metal surface can promote ) or retard - o) corrosion, modify the surface energy ) or cause considerable increase in the surface self-diffusion coefficient ). Sulfur accumulation along grain boundaries may induce intergranular weakness and render otherwise ductile materials brittle ), either by formation of precipitates " ) or by enhancement of hydrogen adsorption >227)... 

One of the recent techniques most commonly used to measure diffusion in 2-dimensions is fluorescence recovery after photobleaching (FRAP). This method uses a laser beam focused through a fluorescence microscope to follow the diffusion of fluorescent molecules in a plane perpendicular to the laser beam. The fluorescence intensity from a laser spot of known diameter, typically a few microns, is measured. The laser intensity is then increased by approximately 1000 times. This irreversibly photobleaches any fluorophore in the spot. The intensity is then decreased again and the recovery in fluorescence intensity measured as unbleached molecules diffuse into the spot. The time function of fluorescence intensity is then analysed to give surface self-diffusion coefficient (Clark et al. 1990a, b, Wilde Clark 1993, Ladhaetal. 1994). 

For example, the surface self-diffusion coefficient can be measured by etching a periodic surface profile (e.g., sinusoidal) into a single-crystal surface. The amplitude of the profile is measured as a function of time via the intensity distribution of a laser diffraction pattern generated by the profile itself [52]. The self-diffusion coefficient can be evaluated from the change of the profile amplitude A (/) with time as the surface relaxes into its equilibrium surface structure upon heating ... 

FIGURE 7.65 The measurement scheme for the surface self-diffusion coefficient, D, using the groove healing method, which plots the decrease in the depth of the groove with an initial width, Wg, as a function... 

Figure 6.3 Correlations between surface self-diffusion coefficient and reduced temperature Tu/T for face-centered-cubic metals. (From Principles of Surface Chemistry, Somorjai 1972.)...

Lateral density fluctuations are mostly confined to the adsorbed water layer. The lateral density distributions are conveniently characterized by scatter plots of oxygen coordinates in the surface plane. Fig. 6 shows such scatter plots of water molecules in the first (left) and second layer (right) near the Hg(l 11) surface. Here, a dot is plotted at the oxygen atom position at intervals of 0.1 ps. In the first layer, the oxygen distribution clearly shows the structure of the substrate lattice. In the second layer, the distribution is almost isotropic. In the first layer, the oxygen motion is predominantly oscillatory rather than diffusive. The self-diffusion coefficient in the adsorbate layer is strongly reduced compared to the second or third layer [127]. The data in Fig. 6 are qualitatively similar to those obtained in the group of Berkowitz and coworkers [62,128-130]. These authors compared the structure near Pt(lOO) and Pt(lll) in detail and also noted that the motion of water in the first layer is oscillatory about equilibrium positions and thus characteristic of a solid phase, while the motion in the second layer has more... 

A width (compared to about 5 A for the free water surface). The authors observed a continuous change of the self-diffusion coefficient from liquidlike to solid-like values over this interval. The results have been extensively reviewed by Laird and Haymet [197]. 

Mechanisms of micellar reactions have been studied by a kinetic study of the state of the proton at the surface of dodecyl sulfate micelles [191]. Surface diffusion constants of Ni(II) on a sodium dodecyl sulfate micelle were studied by electron spin resonance (ESR). The lateral diffusion constant of Ni(II) was found to be three orders of magnitude less than that in ordinary aqueous solutions [192]. Migration and self-diffusion coefficients of divalent counterions in micellar solutions containing monovalent counterions were studied for solutions of Be2+ in lithium dodecyl sulfate and for solutions of Ca2+ in sodium dodecyl sulfate [193]. The structural disposition of the porphyrin complex and the conformation of the surfactant molecules inside the micellar cavity was studied by NMR on aqueous sodium dodecyl sulfate micelles [194]. 

Being formed in the gaseous phase medium, the electronically excited particles (EEPs) reach the solid surface by diffusion. The diffusion coefficients of EEPs are, as a rule, smaller than the self-diffusion coefficients of parent gas, a factor that is associated with increasing of the EEP elastic scattering cross-section at parent molecules due to the redis-... 

Since it was proposed in the early 1980s [6, 7], spin-relaxation has been extensively used to determine the surface-to-volume ratio of porous materials [8-10]. Pore structure has been probed by the effect on the diffusion coefficient [11, 12] and the diffusion propagator [13,14], Self-diffusion coefficient measurements as a function of diffusion time provide surface-to-volume ratio information for the early times, and tortuosity for the long times. Recent techniques of two-dimensional NMR of relaxation and diffusion [15-21] have proven particularly interesting for several applications. The development of portable NMR sensors (e.g., NMR logging devices [22] and NMR-MOUSE [23]) and novel concepts for ex situ NMR [24, 25] demonstrate the potential to extend the NMR technology to a broad application of field material testing. 

Staunton S. 1990. A comparison of the surface impedance factors of Ca, Na, Rb and Cs derived from their self-diffusion coefficients in various soils. Journal of Soil Science 41 643-653. 

The concept of transport resistances localized in the outermost regions of NS crystals was introduced in order to explain the differences between intracrystalline self-diffusion coefficients obtained by n.m.r methods and diffusion coefficients derived from non-equilibrium experiments based on the assumption that Intracrystalline transport is rate-limiting. This concept has been discussed during the past decade, cf. the pioneering work [79-81] and the reviews [2,7,8,23,32,82]. Nowadays, one can state that surface barriers do not occur necessarily in sorption uptake by NS crystals, but they may occur if the cross-sections of the sorbing molecular species and the micropore openings become comparable. For indication of their significance, careful analysis of... 

We note that (Dy v) is proportional to the self-diffusion coefficient of the cations in AO near the surface. 

Equation 5.18 offers a convenient technique for measuring self-diffusion coefficients. A thin layer of radioactive isotope deposited on the surface of a flat specimen serves as an instantaneous planar source. After the specimen is diffusion annealed, the isotope concentration profile is determined. With these data, Eq. 5.18 can be written... 

The dramatic increase of water density at a charged surface was observed by Toney et al. in their in situ X-ray scattering experiments, which has not yet been confirmed by simulation results.58,70 In another MD simulation work, Kiselev et al. found that selfdiffusion coefficient strongly decreases with increasing electric field.27 However, no difference between the self-diffusion coefficients for motion parallel and perpendicular to the external field was observed. 

Another descriptor of the mobility of water molecules in contact with the clay layers is the water self-diffusion coefficient. A fine recent review summarizes the theoretical and practical aspects of measurement by spin-echo nmr methods of this parameter (36) The plot of the decrease in the water self-diffusion coefficient as a function of C, the amount of suspended clay, for the same samples, is again a straight line going through the origin. By resorting once more to a similar analysis in terms of a two-state model (bound and "free water), one comes up (25) with a self-diffusion coefficient, for those water molecules pinched in-between counterions and the clay surface, of 1.6 10 15 m2.s 1,... 

MD and MC simulations have provided data on layer spacings, thermodynamic properties, as well as interlayer water configurations, interlayer-species self-diffusion coefficients, and total radial distribution functions that are consistent with experimental data. Most of the clay surface is relatively... 

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