Activation energy from 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... 

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 paper of Gordon describes a model for diffusion-controlled reaction based on the "hole concept in liquids of Jost (Ref 1, p 459). in which the activation energy for diffusion is equated simply to pV. The marked effect of density, therefore, results from the strong dependence of pressure on density (p varying about as the density cubed) and the appearance of this factor in an exponential term. On this basis, Gordon derived an approximate expression for dependence of detonation velocity D on explosive density pQ. This equation is given on pp 833 and 836 of Gordon s paper. From this expression the critical diameter dc for composite explosives is related to an exponential function of density by ... 

Figure 4.49 Activation energy for diffusion as a function of atomic radius of diffusing species in silica glass. From W. D. Kingery, H. K. Bowen, and D. R. Uhlmann, Introduction to Ceramics. Copyright 1976 by John WUey Sons, Inc. This material is used by permission of John Wiley Sons, Inc.

The diffusion coefficients of nitroglycerin and triacetin in doublebase propellant have been measured at 77°-140°F. Activation energies for diffusion ranged from 10 to 13 kcal./mole. Thus, cure rates for a given propellant composition can be expected approximately to double in going from 120° to 140°F. 

Thus ((Ax)2) becomes independent of the starting configuration of the cluster. The same equation is obtained if one averages over all configurations in a large number of events. The activation energy of diffusion of the center of mass of the cluster, A cm, as derived from an Arrhenius plot, is related to AE+ and AE by... 

This situation is very different from that representing Xe in zeolite Y, whereby the surface-mediated diffusion is characterized by a potential barrier to cage-to-cage crossings, consistent with the lower activation energy to diffusion of Ar in zeolite A. As was found for Xe, the surface-mediated... 

The results of experimental studies of the sorption and diffusion of light hydrocarbons and some other simple nonpolar molecules in type-A zeolites are summarized and compared with reported data for similar molecules in H-chabazite. Henry s law constants and equilibrium isotherms for both zeolites are interpreted in terms of a simple theoretical model. Zeolitic diffusivitiesy measured over small differential concentration steps, show a pronounced increase with sorbate concentration. This effect can be accounted for by the nonlinearity of the isotherms and the intrinsic mobilities are essentially independent of concentration. Activation energies for diffusion, calculated from the temperature dependence of the intrinsic mobilitieSy show a clear correlation with critical diameter. For the simpler moleculeSy transition state theory gives a quantitative prediction of the experimental diffusivity. 

To estimate the activation energy of diffusion at lower temperatures let us assume the pre-exponential factor Du to be independent of T and, by the order of magnitude, to be equal to D = A2vk % 10 4cm2s 1 (A % 10 8 cm is the characteristic value of a diffusion jump, vk 1012s 1 is the characteristic frequency of atomic oscillations in a solid). Then from the experimental values of D one can find the activation energy of diffusion Ea = 9 kcalmol 1... 

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