Diffusion volume 392 - energy

The mobility of the boundary should be closely related to die volume diffusion process in the solid, and would therefore be expected to show an Anlienius behaviour widi an activation energy close to the volume diffusion activation energy. 

The structure of a metallized layer is determined by the surface topography of the web substrate and by interaction of the involved condensation processes (shadowing, surface diffusion, volume diffusion, and desorption), which cause growth in the form of more or less densely packed pillars or conglomerates (Fig. 8.8) [8], Depending on which of the four condensation mechanisms is predominant, the structure will be more or less dense (Zones I—III). The activation energy for the surface and volume diffusion of metals is proportional to their respective melting... 

The following quantitative discussions will be based on a modified version of Eq. (4.4) (Myers and Swiatecki 1966 Friedlander et al. 1981) Eq. (4.5) differs from Eq. (4.4) by the fact that the asymmetry energy is not only subtracted from the volume energy (term 1) but also from the surface energy (term 2). This is consistent and follows from the definition of the surface energy. In addition, a further term, (fZ IA), is added, which takes into account that nuclear surface is somewhat diffuse. 

Fig. 8. Variation of activation energy with kinetic molecular diameter for diffusion in 4A 2eohte (A), 5A 2eohte (0)> carbon molecular sieve (MSC-5A) (A). Kinetic diameters are estimated from the van der Waals co-volumes. From ref. 7. To convert kj to kcal divide by 4.184.

The defects generated in ion—soHd interactions influence the kinetic processes that occur both inside and outside the cascade volume. At times long after the cascade lifetime (t > 10 s), the remaining vacancy—interstitial pairs can contribute to atomic diffusion processes. This process, commonly called radiation enhanced diffusion (RED), can be described by rate equations and an analytical approach (27). Within the cascade itself, under conditions of high defect densities, local energy depositions exceed 1 eV/atom and local kinetic processes can be described on the basis of ahquid-like diffusion formalism (28,29). 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

It can be seen drat the major difference lies in die activation energy being lower in the grain boundary. Data for a number of metals show that the activation energy for grain boundary diffusion is about one-half of that for volume diffusion. 

Ashby pointed out diat die sintering studies of copper particles of radius 3-15 microns showed clearly the effects of surface diffusion, and die activation energy for surface diffusion is close to the activation energy for volume diffusion, and hence it is not necessarily the volume diffusion process which predominates as a sintering mechanism at temperatures less than 800°C. 

Peclet number independent of Reynolds number also means that turbulent diffusion or dispersion is directly proportional to the fluid velocity. In general, reactors that are simple in construction, (tubular reactors and adiabatic reactors) approach their ideal condition much better in commercial size then on laboratory scale. On small scale and corresponding low flows, they are handicapped by significant temperature and concentration gradients that are not even well defined. In contrast, recycle reactors and CSTRs come much closer to their ideal state in laboratory sizes than in large equipment. The energy requirement for recycle reaci ors grows with the square of the volume. This limits increases in size or applicable recycle ratios. 

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