Growth rate, linear, concentration dependence

In Fig. 19, the dependence of linear growth rate on concentration is shown. Below 0.4 mM (log C = —0.4) the rate increases proportional to the fourth power of the concentration. In a batch operation, since the concentration changes continually, the order of the reaction may also change, depending on the controlling mechanism. In view of this, and the... 

Fio. 19. Dependence of linear growth rate on concentration. After Nielsen (N5). 

Dependence of the growth rates on the aluminium in solution. Figure 8 shows the influence of the concentration of aluminium (mmol/1) on the rate of growth (nm/h) for the (001) and (hhO) faces at 115°C (the aluminium concentration taken into account corresponds to the average value between two consecutive analyses). If the experimental data are represented in In r versus In [Al] plots, satisfactory linear correlations are found. Growth rates may then be represented as ... 

Measurements of whisker crystallization rates by VLS have revealed that the linear growth rate is proportional to the whisker diameter, with larger fibers growing faster than smaller ones. The observed diameter-dependence has been attributed to differences in seed saturation concentration resulting from the curved interface of the seeds. The Gibbs-Thomson equation provides the relationship between the sphere diameter, d, and the chemical potential difference between the nutrient phase (e.g., molecular Si in the vapor) and the liquid alloy droplet Ap ... 

The addition of an antisoivent can be earned out in different ways, as indicated in Fig. 9-1, where the concentration of product is shown on the ordinate and the amount of antisoivent added is shown on the abscissa. A typical equilibrium solubility curve is indicated as A-B-C. (This curve could be concave or linear but is shown as convex for clarity.) The metastable region is indicated as the area between B-C and E-D. From point A to point B, addition of antisoivent will proceed without crystallization because the solution concentration is below the equilibrium solubility. At point B, equilibrium solubility is reached. As the addition of antisoivent continues, supersaturation will develop. The amount of supersaturation that can be developed without nucleation is system specific and will depend on the addition rate, mixing, primaiy and/or secondary nucleation rate, and growth rate, as well as the amount and type of impurities present in solution. 

The D" layer grows linearly, with the present volume taken as a free parameter. There is a constant mass inflow from subduction, with a U concentration related to the bulk mantle U concentration by a large enrichment factor operating during formation of ocean crust. There is a mass flux out (dependent upon the growth rate of the layer). Present isotopic compositions are those seen in HIMU basalts. 

It was determined that the rates of the nuclear centers formation and the nuclear centers growth are linearly depend on concentrations of ions hydroxides and silver ions. 

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