Activation energy bulk diffusion

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. 

It is particularly helpful that we can take the Cu-Ni system as an example of the use of successive deposition for preparing alloy films where a miscibility gap exists, and one component can diffuse readily, because this alloy system is also historically important in discussing catalysis by metals. The rate of migration of the copper atoms is much higher than that of the nickel atoms (there is a pronounced Kirkendall effect) and, with polycrystalline specimens, surface diffusion of copper over the nickel crystallites requires a lower activation energy than diffusion into the bulk of the crystallites. Hence, the following model was proposed for the location of the phases in Cu-Ni films (S3), prepared by annealing successively deposited layers at 200°C in vacuum, which was consistent with the experimental data on the work function. 

It is known that the activation energies for some processes taking place in nanoscale particles are different from ones for bulk substance. For example, the activation energy for diffusion of atoms in nanoparticles decreases with the particle size [1], In turn it can affect other processes related to mobility of atoms (molecules) in nanoparticles (e.g. absorption of foreign gases by nanoparticles, nanoparticle coalescence, chemical reactions in nanoparticles). 

We assume that relation between the activation energy for diffusion of oxygen in silicon nanoparticle (Dj) and in bulk silicon (E ) by analogy with [1] reads... 

A possible explanation of these results is that most of the surface of the Pd is contaminated after reduction at 773 K, with only a few sites remaining where H2 can be dissociated and then transferred to sub-surface positions. On a normal, clean Pd surface almost complete monolayer coverage occurs before any sub-surface can be formed because of the depth of the potential well for adsorbed H2 and the activation energy to diffusion. However, it is common knowledge that contaminated Pd wire or foil will not absorb H2 at room temperature, but that mechanical cleaning of the surface allows normal absorption to occur at a rate which is determined by the rate of diffusion of H atoms from surface portholes into the bulk metal. In contrast to the foregoing observations, an Exxon patent claims that Pd/Ti02 in the SMSl states does not form the 3-hydride phase. 

Evaporation of VCI speeds up with increased temperature. According to previous work [109], diffusion factors of G-2 in PE films obey the Arrhenius equation (Fig. 2.33) and the activation energy of diffusion decreases from 135.5 to 104 kJ/mole as the inhibitor concentration in the film bulk increases from 0.09 to 1.0 wt%. 

This is illustrated in Fig. 1, where we show two atoms moving in the neighbourhood of an ideal, unreconstructed surface, as well as a defect atom in the bulk. A calculation of the total energy as a function of the positions of the constituent atoms would yield the equilibrium structure of the surface and the distortions arising from the additional atoms. Furthermore, binding energies and the activation energies for diffusion of adsorbate and defect atoms would... 

By measuring water uptake, the diffusion coefficient and equilibrium concentration of water for the bulk adhesive were obtained at different temperatures. A value of 37 kJ/mol was also calculated for the activation energy of diffusion. A value for the plane-strain stress intensity factor, Kic, for the bulk adhesive was obtained using compact tension specimens. Tensile butt joints were prepared from mild steel blocks bonded with the epoxy adhesive and the fracture stress determined as a function of time of exposure to water at the different temperatures. An activation energy of 32 kJ/mol was calculated for joint failure, in close agreement with that obtained for the diffusion of water. This supports the view that the processes responsible for loss of joint strength are controlled by water diffusion. It was found that joints exposed to 20°C/55% RH showed no reduction in strength, even... 

It can be seen that, for a molecule to move in the bulk of the liquid it must obtain, as a result of a thermal fluctuation, an energy E. This is the activation energy of diffusion, and represents the energy needed by the molecule under consideration to push apart and climb over the two molecules in its way and escape from the attractions of the other molecules forming the cell that contains it. In the bulk of the liquid, on average, such movement is equally probable for all directions, so that the average molecular separation is unchanged by the molecular movement. 

However, the behavior of the catalysts measured in this work is different. At temperatures above 400 K the catalytic activity becomes limited, in agreem t with the Thiele theory. However, the apparent activation energy gradually decreases from 94 to 6 kJ/mol, rather than to 50 kJ/mol, which implies that the apparent activation energy of diffusion is exhibited. Nevertheless, the size of the wider pores in the pellet does appear to affect strongly the activity. Therefore, it is impossible that merely external diffusion limitation, that is, diffusion from the bulk of the gas flow to tiie external surface of the catalyst body, is rate-determining. Since the catalyst spheres had the same diameter, the activity of all catalysts should be equal if external transport is determining the activity. As the concentration of reactants inside the particle is nearly zero, the pore size should be of no importance. However, this is in contradiction with the measurements. 

The temperature dependence of the hydrogen permeability can be expressed by the well-known Arrhenius expression P exp( - )], formally similar to the self-diffusivity coefficient mentioned in Section 15.3. However, in this case, the activation energy for diffusion, E , is referred to the jumps of the hydrogen atoms in the bulk of the Pd-aUoy (the rate-determining step is the H diffusion according to the Richardson equation). Considering that 0 depends on the partial pressure of the carbon monoxide, in addition to the temperature of the mixture, that is 0 (T, ), the scaling factor g(T,p ) can... 

Film diffusion may influence the overall reaction because of the low gas flow rate. As the bulk concentrations change little with time along the length of the reactor, an assumption of constant difference between bulk and catalyst surface concentrations is used in this study and the rate constants will change with gas flow rates. Nevertheless, the activation energies will remain constant, and the proposed reaction kinetics still provides useful hint for understanding the reaction mechanism and optimizing the reactor and operation conditions. 

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