Energy, activation, for diffusion

Fig. XVIII-15. Oxygen atom diffusion on a W(IOO) surface (a) variation of the activation energy for diffusion with d and (b) variation of o- (From Ref. 136. Reprinted with kind permission of Elsevier Science-NL, Sara Burgerhartstraat 25, 1055 KV Amsterdam, The Netherlands.)...

The vacancy is very mobile in many semiconductors. In Si, its activation energy for diffusion ranges from 0.18 to 0.45 eV depending on its charge state, that is, on the position of the Fenni level. Wlrile the equilibrium concentration of vacancies is rather low, many processing steps inject vacancies into the bulk ion implantation, electron irradiation, etching, the deposition of some thin films on the surface, such as Al contacts or nitride layers etc. Such non-equilibrium situations can greatly affect the mobility of impurities as vacancies flood the sample and trap interstitials. 

The temperature dependence of the permeability arises from the temperature dependencies of the diffusion coefficient and the solubility coefficient. Equations 13 and 14 express these dependencies where and are constants, is the activation energy for diffusion, and is the heat of solution... 

Fig. 6. Activation energy for diffusion in poly(vinyl chloride) as a function of penetrant mean diameter (19). To convert to cal, divide by 4.184.

Normally the activation energy for diffusion in the gas phase is much smaller than the activation energy for a catalyzed reaction, and hence, according to Eqs. (38) and (46), the overall or apparent activation energy for the diffusion-limited process is half of what it would be without transportation limitation. If we plot the rate as a function of reciprocal temperature one observes a change in slope when transport limitations starts to set in. 

The pore size has a strong influence on the diffusion rate and the activation energy for diffusion, as illustrated by Fig. 3.39. In a simple view three types of diffusion can be distinguished ... 

Temperature influences skin permeability in both physical and physiological ways. For instance, activation energies for diffusion of small nonelectrolytes across the stratum corneum have been shown to lie between 8 and 15 kcal/mole [4,32]. Thus thermal activation alone can double the rate skin permeability when there is a 10°C change in the surface temperature of the skin [33], Additionally, blood perfusion through the skin in terms of amount and closeness of approach to the skin s surface is regulated by its temperature and also by an individual s need to maintain the body s 37° C isothermal state. Since clearance of percuta-neously absorbed drug to the systemic circulation is sensitive to blood flow, a fluctuation in blood flow might be expected to alter the uptake of chemicals. No clear-cut evidence exists that this is so, however, which seems to teach us that even the reduced blood flow of chilled skin is adequate to efficiently clear compounds from the underside of the epidermis. 

The values derived in this way for the diffusion coefficients exhibit surprising agreement with the experimental values, even for small ions, better than a coincidence in the order of magnitude. More detailed theoretical analysis indicates that the formation of holes required for particle jump is analogous to the formation of holes necessary for viscous flow of a liquid. Consequently, the activation energy for diffusion is similar to that for viscous flow. 

Diffusion activation energy for diffusion defined by equation 12.3.84... 

Using the data in Question 2, estimate the activation energy for diffusion if the vibration frequency is 1 x 1013 Hz and the temperature of the diffusion is 1200 K. 

The radioactive tracer diffusion coefficient of 22Na in glass is given in the following table. Estimate the activation energy for diffusion. 

The increase of the lateral diffusion rate with increasing temperature was used to estimate the activation energy for diffusion in the LC and GI phases. The temperature dependence of the correlation-time for molecular diffusion, Xd, can be formulated in terms of the activation energy E ) for the motion affecting Xd in an Arrhenius expression (t > = exp( a/R7 ))- Since D = a ldx ... 

One of the most important parameters when determining adsorption behavior is the operating temperature. For a linear isotherm, the permeance increases or decreases with increasing temperature, depending on the relative values of the heat of adsorption (Qj) and the activation energy for diffusion (T ) [7]. Eor a nonlinear isotherm (e.g., Langmuir) the permeance increases with increasing temperature when Qj < E. However, when > E, the permeance reaches a maximum and then decreases [7]. 

Calculate the activation energy for diffusion of a Pt adatom on Pt(100) via direct hopping between fourfold sites on the surface and, separately, via concerted substitution with a Pt atom in the top surface layer. Before beginning any calculations, consider how large the surface slab model needs to be in order to describe these two processes. Which process would you expect to dominate Pt adatom diffusion at room temperature ... 

It is relatively easier for a small neutral molecule (such as Fie or H2) to move through a liquid or solid structure, than for a large molecule (such as Xe). Hence, the activation energy for diffusion of small molecules is small and the diffusion coefficient is large. 

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