Mean diffusion length

By the pulsed field gradient spin echo method (1) it is possible to measure mean diffusion lengths ( /(l2)) for molecules in a given time interval in systems without a concentration gradient. The application of the method is limited to... 

The mean diffusion length of the minorities is drastically dependent on crystal imperfections. It may also be dependent on surface orientation, if they have an anisotropic mobility. Optical anisotropy is necessary for seeing an influence of crystal orientation on the penetration depth of the light while crystal imperfections will only affect the penetration depth in a range of wave lengths where light absorption in the crystal is very weak. The photocurrents are very small in this case which will not be discussed here. 

Figure 9 Adsorption process of NO on Pd particles supported on MgO(l 00). (a) Global adsorption probability as a function of surface temperature and for various particle sizes (from Ref. [89]). (b) Schematic representation of die elementary processes in die molecular adsorption of NO on supported Pd particles (1) quasi-elastic redection on die bare support, (2) physisorption-diffusion-desorption from the bare support, (3) direct chemisorption on die Pd particles, (4) NO chemisorption on the Pd particles via a precursor physisorbed state on die bare support. Xs is die mean diffusion length of die NO molecules on the support and p is die width of die collection zone around die Pd particles.

The mean diffusion length of the positron or Ps undergoing onedimensional Brownian motion can be expressed as [44] ... 

While 8 is somewhat greater than 1, both p and / are somewhat smaller than 1. Therefore, for approximate calculations, epf can be set 1. The fission factor rj varies appreciably with the energy of the neutrons, as shown in Fig. 11.4 for The neutron losses in a reactor of finite dimensions can be taken into account approximately by the sum L +1 , where Ls is the mean slowing-down length of the fission neutrons in the moderator and L the mean diffusion length in the fuel-moderator mixture. For a spherical reactor of radius R the approximate relation is... 

The support plays an important effect in the adsorption kinetics of CO on supported clusters. Indeed CO physisorbed on the support is captured by surface diffusion on the periphery of the metal clusters where it becomes chemisorbed. The role of a precursor state played by CO adsorbed on the support is a rather general phenomenon. It has been observed first on Pd/mica [173] then on Pd/alumina [174,175], on Pd/MgO [176], on Pd/silica [177], and on Rh/alumina [178]. This effect has been theoretically modeled assuming the clusters are distributed on a regular lattice [179] and more recently on a random distribution of clusters [180]. The basic features of this phenomenon are the following. One can define around each cluster a capture zone of width Xg, where is the mean diffusion length of a CO molecule on the support. Each molecule physisorbed in the capture zone will be chemisorbed (via surface diffusion) on the metal cluster. When the temperature decreases, Xg increases, then the capture zone increases to the point where the capture zones overlap. Thus the adsorption rate increases when temperature decreases before the overlap of the capture zones that occurs earlier when the density of clusters increases. Another interesting feature is that the adsorption flux increases when cluster size decreases. It is worth mentioning that this effect (often called reverse spillover) can increase the adsorption rate by a factor of 10. We later see the consequences for catalytic reactions. 

We see the global adsorption to increase when the temperature decreases. At high temperature it is equal to Ac, the fraction of the substrate covered by the metal clusters. In that case, the width of the capture zone, p, is zero and only molecules directly impinging on the clusters are chemisorbed and Og is equal to nR n. When the temperature decreases, the mean diffusion length, Xg, grows and p increases. Finally, the global adsorption probability reaches saturation when the capture zones overlap. The maximum value of the adsorption probability is given by ... 

If the mean diffusion length and the penetration depth 1/a of the light exceed largely the extension of the space charge layer, the flux of the minority carriers to the surface outside the space charge layer can be calculated from the following differential equation ... 

Mean diffusion length at room temperature for the defect-free material. For the free positron lifetimes, we used the bulk Ufetimes calculated by GGA and the experimental ones shown in Table 4.17. If the non-negbgible defect concentration is included, the parameter L+ will be smaller. 

The mean diffusion length L+ of the positron is defined as the mean distance from the point of thermalisation that the positron reaches by diffusion movement. This quantity is related to the diffusion coefficient by the relation [72]... 

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