Linear growth

FIG. 20-95 Batch dnim growth of limestone pellets hy layering with a size-independent linear growth rate [Capes, Chem. Eng., 45, CE78 (1967).]... 

The overall linear growth rate determined from these data is given by the following empirieal expression (Jones and Mydlarz, 1989)... 

This is the Wilson-Frenkel rate. With that rate an individual kink moves along a step by adsorbing more atoms from the vapour phase than desorbing. The growth rate of the step is then simply obtained as a multiple of Zd vF and the kink density. For small A/i the exponential function can be hnearized so that the step on a crystal surface follows a linear growth law... 

All reactions in which charge is transported through a film of reaction product on the metal surface —the film may or may not be rate determining (e.g. parabolic, logarithmic, asymptotic, etc. or linear growth laws, respectively). 

The volume ratio (see Section 1.9) for cuprous oxide on copper is 1 7, so that an initially protective film is to be expected. Such a film must grow by a diffusion process and should obey a parabolic law. This has been found to apply for copper in many conditions, but other relationships have been noted. Thus in the very early stages of oxidation a linear growth law has been observed (e.g. at 1 000°C) . 

First, on a purely physical basis, we determine when departures from a linear growth rate may be expected, that is when the crystal dimensions do not increase proportionally with time, but also depend on the size of the crystal (and maybe even other factors). Then we show how these limits relate to the possible values of i and g. 

Kinetic data for the decompositions of several metal hydrides are summarized in Table 12 to which the following information can be added. The acceleratory period in the decomposition of BeH2 (a < 0.35) is ascribed [673] to the random formation of metal nuclei followed by linear growth. The increase in rate consequent upon exposure to X-irradia-tion is attributed to enhanced nucleation. Grinding similarly increased the... 

In children, the diagnosis of GH deficiency is further supported if height is more than two standard deviations (SD) below the population mean (age- and sex-matched).35 Failure of linear growth is an almost universal presenting feature of childhood GH deficiency. 

Figure 17 Effect of branching on the secondary nucleation and linear growth rates from the work of Lambert and Phillips [58]. The effect of branching on the Regime l-ll transition can also be seen. Reprinted with permission from Lambert and Phillips [58]. Copyright 1994, American Chemical Society.

Figure 13 Top, plot of linear growth rates of polyfethylene adipate) spherulites as a function of crystallization temperature for indicated molecular weight fractions. Spherulites shown correspond to the indicated range of temperatures. (A) Crystallization at the lower temperature range (B) at intermediate temperatures (C) crystallization at high temperatures. Reproduced with permission from Ref. [216]. Copyright 1956,...

Moore SR, Lima AA, Conaway MR, Schorling JB, Soares AM, Guerrant RL Early childhood diarrhoea and helminthiases associate with long-term linear growth faltering. Int J Epidemiol 2001 30 1457-1464. 

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