Growth rate of layer

Next, we must develop growth equations for the two oxide layers Lx and Ln. A decomposition of layer N is required in forming layer N — 1, as required by eqn. (261), and so in this respect layer N does not differ from the inner layers. On the other hand, there is no decomposition of a layer N + 1 required to obtain the requisite oxygen, since layer N is already in contact with the gaseous oxygen phase. Thus, there is no equivalent cation vacancy current to be considered, in contrast to the other layers. Neither is there an actual cation vacancy current J l, to be considered. However, there may be oxide evaporation which must be compensated for by the net growth rate of layer N. Thus we obtain... 

Considering now oxide layer 1, there will be no decomposition of that layer required since it is in contact with the parent metal. Thus (dLj /dt)- = 0. Also, we neglect the possibility of a cation vacancy current J(jcv) due to unannihilated vacancies which diffuse into the parent metal instead of annihilating with metal atoms in the parent metal at the metal-oxide interface. Such would constitute a loss of potential oxide formation for layer 1. Another consideration is the positive contribution to the growth rate of layer 1 due to the decomposition of layer 2, so that we can write... 

Consider, also, that layer i will likewise undergo solid-state decomposition at the interface xt = L, in the formation of layer i + 1, yielding a negative contribution (cLL,/df) to the growth of layer i. The net growth rate of layer j will be given by the difference in the formation rate of layer i at xt = 0 and the decomposition rate of layer i at xt = L,... 

We note in passing that this result holds for one of the extreme layers (namely, oxide layer 1 in contact with the parent metal) in addition to the inner layers this will be needed in developing the expression for the net growth rate of layer 1. 

The growth rate for layer 1 at x =0 requires an anion vacancy current J(jav) through layer 1. There are no growing oxide layers i for i < 1, so J)av) contributes entirely to the growth of layer 1. In addition, there is no oxide decomposition reaction at the phase boundary xt = 0 since this represents the metal interface thus, there is no equivalent current jJ°xv> to be considered. Therefore, we can write (dLj/d )+ = R av)J av), so the net growth rate of layer 1 is given by... 

This ignores any evaporation of oxide at the gas interface (xN = LN). If such occurs, the evaporation rate (dLN /dt)evap, considered to have a positive sign if evaporation is indeed occurring, will decrease the net growth rate of layer N, so that (dLN /dt) in eqn. (359) should then be replaced by [(cLLN /dt) + (dLN /dt)evaP ] Equivalently, we can write... 

Confirmation of the destmetion of ozone by chlorine and bromine from halofluorocarbons has led to international efforts to reduce emissions of ozone-destroying CPCs and Halons into the atmosphere. The 1987 Montreal Protocol on Substances That Deplete the Ozone Layer (150) (and its 1990 and 1992 revisions) calls for an end to the production of Halons in 1994 and CPCs, carbon tetrachloride, and methylchloroform byjanuary 1, 1996. In 1993, worldwide production of CPCs was reduced to 50% of 1986 levels of 1.13 x 10 and decreases in growth rates of CPC-11 and CPC-12 have been observed (151). 

Fig. 23. (I) Effect of water content on the growth rate of agglomerates sand granules grown by crushing and layering mechanism [from Capes and Danckwerts (C5)]. (II) Limestone nuclei by random coalescence [from Kapur (K2)]. (Ill) Limestone balls by nonrandom coale-scene [from Kapur (K4)]. (IV) Iron ore pelletized in a disk.[From Kanetkar (K1)].

For the special case of straight pores growing orthogonal to the electrode surface forming a flat interface to the bulk, the pore length l becomes equivalent to the layer thickness D. Equation (6.1) then also defines the growth rate of the whole porous layer rPS. The growth rate rPS of a porous layer depends on several... 

Equation 3.56 indicates that the biofilm essentially behaves like an immobilized water layer, with a resistance that is independent of the biofilm-water partition coefficient. Evidently, when the growth rate of the biofilm and the diffusion rate of the contaminants are of similar magnitude, this highly idealized model breaks down, and it can be expected in those cases that highly hydrophobic compounds will have more difficulty in reaching the membrane than less hydrophobic (more mobile) compounds. Also, Eq. 3.56 will likely fail to predict solute transport in biofilms with sizable populations of invertebrates because of bioturbation. 

With this model, it is predicted that there should be a liquid drop size which, if too large, will result in long delay times and excessive numbers of new embryos to vapor blanket the surface. Thus, small drops (or thin layers) are more prone to escape termination by vapor blanketing. Also, if experimental variables are modified so as to reduce the growth rate of embryos from A to B, e.g., by increasing pressure, again one would expect a lower probability of escalation. These two predictive conclusions appear to be substantiated by experiment. 

Electrode reactions are analogous to the growth of tarnishing (corrosion) layers (Weppner and Huggins, 1977). Assuming that bulk transport is the rate determining step, the growth rate of the reaction product is inversely proportional to the instantaneous thickness L... 

Here the so called ideal growth rate of the crystal layer is a calculated one. It is calculated from the linear dependence between the cooling rate of the surface and the resulting growth rate. The measured growth rate of crystal layer v includes all pos-... 

Several investigations (8.9 show, that the effective distribution coefficient can be described as a function of the growth rate. Own experiments show that a model to calculate the purity in dependence of the real growth rate is rather realistic. To considerate irregularities by the calculation of k ff, the effective distribution coefficient is presented as a function of the ideal growth rate of the crystal layer V, 3 and the growth rate deviation dy. ... 

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