Diffusion length, surface

Assuming that the average diffusion length of particles to the cavity from the shell surface is equal to tire thickness of the shell, and conversely tlrat there is a counter-cutTent of vacancies from tire cavity to the shell surface, the rate of densification dp/dt is given by... 

Many inorganic solids lend themselves to study by PL, to probe their intrinsic properties and to look at impurities and defects. Such materials include alkali-halides, semiconductors, crystalline ceramics, and glasses. In opaque materials PL is particularly surface sensitive, being restricted by the optical penetration depth and carrier diffusion length to a region of 0.05 to several pm beneath the surface. 

This length is apparently related to the capture time by the relation Pi J Tc and il A physical meaning of the free diffusion length 4 is that the maximum size of a stable adsorbed two-dimensional nucleus on a facet cannot essentially exceed this free diffusion length. If the nucleus is smaller, all atoms depositing on the surface can still find the path to the boundary of a nucleus in order to be incorporated there. If the nucleus is larger, a new nucleus can develop on its surface. 

A serious point is the neglect of surface tension and anisotropy in these derivations. In the experiments analyzed so far the relation VX const, seems to hold approximately, but what happens when the capillary anisotropy e goes to zero Numerically, tip-splitting occurs at lower velocities for smaller e. Most likely in a system with anisotropy e = 0 (and zero kinetic coefficient) the structures show seaweed patterns at velocities where the diffusion length is smaller than the short wavelength hmit of the neutral stability curve, as discussed in Sec. V B. 

Here, D is the diffusion constant for heat or material and the kinematic viscosity of the liquid. A consequence of the existence of such a diffusive surface barrier is that the diffusion length = D/F is to be replaced by in all formulas, as soon as growth rate V the more important become the hydrodynamic convection effects. 

Equations 4.31 and 4.32 also suggest another important fact regarding NEMCA on noble metal surfaces The rate limiting step for the backspillover of ions from the solid electrolyte over the entire gas exposed catalyst surface is not their surface diffusion, in which case the surfacediffusivity Ds would appear in Eq. 4.32, but rather their creation at the three-phase-boundaries (tpb). Since the surface diffusion length, L, in typical NEMCA catalyst-electrode film is of the order of 2 pm and the observed NEMCA time constants x are typically of the order of 1000 s, this suggests surface diffusivity values, Ds, of at least L2/t, i.e. of at least 4 10 11 cm2/s. Such values are reasonable, in view of the surface science literature for O on Pt(l 11).1314 For example this is exactly the value computed for the surface diffusivity of O on Pt(lll) and Pt(100) at 400°C from the experimental results of Lewis and Gomer14 which they described by the equation ... 

At low temperatures, donors and acceptors remain neutral when they trap an electron hole pair, forming a bound exciton. Bound exciton recombination emits a characteristic luminescence peak, the energy of which is so specific that it can be used to identify the impurities present. Thewalt et al. (1985) measured the luminescence spectrum of Si samples doped by implantation with B, P, In, and T1 before and after hydrogenation. Ion implantation places the acceptors in a well-controlled thin layer that can be rapidly permeated by atomic hydrogen. In contrast, to observe acceptor neutralization by luminescence in bulk-doped Si would require long Hj treatment, since photoluminescence probes deeply below the surface due to the long diffusion length of electrons, holes, and free excitons. 

T. Tiedje, Information about Band-Tail States from Time-of-Flight Experiments Arnold R. Moore, Diffusion Length in Undoped a-Si H W. Beyer and J. Overhof, Doping Effects in a-Si H H. Fritzche, Electronic Properties of Surfaces in a-Si H CR. Wronski, The Staebler-Wronski Effect... 

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