Activation energy for surface 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. 

Values at 1000 K of the pre-exponential factor A2 [eqn. (20)] for localised and mobile adsorption. The parameters for the localised state relate to tungsten, and p has been calculated assuming that the activation energy for surface diffusion (Em) is one-fifth the energy of desorption of atoms (— AUX i) [107] (K0)i 2 has been assigned the value 0.5 and Ns the value 1015 cm 2. 

Hydrogen, deuterium, neon, argon, and methane flow through saran charcoal by both Knudsen and surface flow. The latter is effected by the adsorbed molecules sliding from site to site across the surface. This is equivalent to a two-dimensional Knudsen flow where the adsorption site acts as the wall of the three-dimensional case, and a slide across the surface is the same as a flight across the pore. The activation energy for surface diffusion is 75 to 80% of the heat of adsorption. It is possible to calculate theoretically the relative contribution of each mechanism, while comparison with He, which does not adsorb, permits its experimental determination. The efficiency of surface flow is the ratio of the measured to the calculated value this decreases as the size of the molecule increases, being 80% for Ne and 12% for CH4. 

Both the adsorption of neon and its surface flow are small. The accuracy of determining the activation energy for surface diffusion is therefore poor. An average value of 1250 cal. is calculated from the data in Figure 8. This value is considerably greater than RT, indicating that we do have activated diffusion and not a mobile film. 

One would physically expect that as pressure increases the solid surface may get smoother due to the filling of small pores and cavities with adsorbed molecules, and as a result the reflection time of gas phase molecules from the surface may become shorter. The values of / in Table 1 are close to unity as expected and they are in an increasing order of n-hexane, carbon tetrachloride and benzene. On the other hand, the parameter a for n-hexane is much higher than that of the others. Since the parameter a in Eq. 3 represents how fast the Knudsen diffiisivity increases with pressure, one would expect a substantial contribution of the Knudsen diffusion for n-hexane to the total permeability at very low pressures. Also the parameter is a measure of how fast the activation energy for surface diffusion decreases with adsorbed concentration. As Table 1 indicates, the surface diffusion permeabilities of n-hexane and carbon tetrachloride are expected to increase more sharply than that of benzene. 

This equation shows that the observed or apparent activation energy for surface diffusion is related to by... 

From the overall perspective of the present chapter, our ambition in briefly describing the energetics of surface diffusion has been to illustrate the additional complexity that is ushered in as a result of the simultaneous action of more than one type of defect. In particular, we have shown that via a counterintuitive exchange mechanism, the activation energy for surface diffusion can be lowered by 0.4 eV relative to the intuitive motion associated with an imagined random walker on a surface. In addition, we have also shown that the presence of surface steps can have significant implications for the nature of diffusion on surfaces. 

Similarly, the Henney and Jones activation energy for surface diffusion in UO2.005 of 110,000 cal is definitely excessive, whereas reinterpretation as volume diffusion produced = 0.22 exp (—71,000// r), which is in good agreement with tracer data. ... 

In chemically reactive adsorbed overlayers, the probabilities of arrangements of adsorbed particles and accordingly the reaction rate are defined by the interplay between adsorption, reaction, and adsorbate diffusion. The activation energy for surface diffusion is often relatively low, therefore the adsorption overlayer is close to equilibrium giving a framework for analysis as presented above. When diffusion of some of the reactants is slow compared to other steps the arrangements of adsorbed particles is often far from equilibrium. In particular, immobile reactants may form islands (Figure 3.18). 

Competitive adsorption and mobility of adsorbates on the surface attribute to the coadsorption-induced reconstmction of adsorbate overlayers. If surface species is immobile because of a high activation energy for surface diffusion, coadsorption cannot take place. On the other hand, the adsorption energy of one adsorbate must be sufficient to compress the other adsorbate into a more compact layer. If coadsorbates have a very low heat of adsorption, the thermodynamic driving force for adsorbate overlayer reconstruction is absent. 

The periodic arrangement of atoms in a single-crystal surface causes a periodic sequence of potential wells separated by an energy barrier, the activation energy for surface diffusion E (Fig. 1.9). In fact, this barrier depends on the direction of motion, but the adsorbed particle will always jump to a neighboring site along the path of minimum activation energy, which is then... 

Heat of adsorption is usually greater the activation energy for surface diffusion, i.e. 

Since the heat of adsorption is usually larger than the activation energy for surface diffusion (Q > EJ, the ratio 5 will decrease as temperature increases, indicating that... 

The heat of adsorption usually ranges from 10 to 60 kJoule/mole and the activation energy for surface diffusion ranges from about one third of the heat of adsorption to the heat of adsorption. Thus the parameter y has the following practical range... 

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