Nucleation and growth rates

Whether it is homogeneous or heterogeneous growth, the nucleation rate J is difficult to measure, as the critical clusters formed correspond to a small number of molecules and hence are very small. In practice, the induction time (t) is determined, which is the time between supersaturation and the first appearance of visible crystals. Assuming that the first appearance of the crystals is primarily controlled by the nucleation step, then t is inversely proportional to the rate of nucleation  

Using eqn (2.26), the interfacial energy can be evaluated from measurements of the induction time as a function of supersaturation. The radius of the critical nucleus can be derived from eqn (2.12). 

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Crystal Morphology. Size, shape, color, and impurities are dependent on the conditions of synthesis (14—17). Lower temperatures favor dark colored, less pure crystals higher temperatures promote paler, purer crystals. Low pressures (5 GPa) and temperatures favor the development of cube faces, whereas higher pressures and temperatures produce octahedral faces. Nucleation and growth rates increase rapidly as the process pressure is raised above the diamond—graphite equiUbrium pressure. 

Analysis of equation 48 shows that a single sample taken either from inside the crystallizer or from the product stream will allow evaluation of nucleation and growth rates at the system conditions. Figure 12 shows a plot of typical population density data obtained from a crystallizer meeting the stated assumptions. The slope of the plot of such data maybe used to obtain the growth rate, and the product of the intercept and growth rate gives the nucleation rate. 

Although magma density is a function of the kinetic parameters fP and G, it often can be measured iadependentiy. In such cases, it should be used as a constraint ia evaluating nucleation and growth rates from measured crystal size distributions (62), especially if the system of iaterest exhibits the characteristics of anomalous crystal growth. 

A. D. Randolph and D. Etherton, Study of Gypsum Crystal Nucleation and Growth Rates in Simulated Flue Gas Desulfurization Eiquors, EPRI Report CS1885, Electric Power Research Institute, Palo Alto, Calif., 1981. 

Aoun, M., Plasari, E., Davis, R. and Villenuaux, I., 1999. A simultaneous determination of nucleation and growth rates from batch spontaneous precipitation. Chemical Engineering Science, 54, 1161-1180. 

The complexity of these chemical and mechanical interactions is such that each metal-environment system must be examined on an individual basis to determine the important processes influencing corrosion fatigue crack nucleation and growth rates. Thus, in the ensuing sections, examples are quoted to illustrate commonly occurring phenomena or establish more general principles with reasonably wide applicability for particular classes of metal/environment combinations. It should be noted, however, that when... 

Substitution of appropriate functions for nucleation and growth rates into eqn. (1) and integration yields the f(a)—time relation corresponding to a particular geometry of interface advance. In real systems, the reactant... 

The purpose of this review is to solve these two unresolved problems by confirming the nucleation during the induction period of nucleation and the important role of the topological nature with experimental facts regarding the molecular weight (M)- or number density of the entanglement (independence of nucleation and growth rates. 

Figure 9.8 (a) Influence of supersaturation on nucleation and growth rate (b) influence of supersaturation on homogeneous and heterogeneous nucleations. 

Kelly, BJ., "Study of Ct Oy AH O Nucleation and Growth Rates in Simulated Flue-Gas Desulfurization Liquors," M.S. Thesis, University of Arizona, Tucson (1983). 

Figure 4-7 Comparison of crystal nucleation and growth rate 350...

Disodium Tetraborate Decahydrate (Borax Decahydrate). Disodium tetraborate decahydrate, Na2B40 101I, 0 or Na20 2B203 1 HI I (). formula wt, 381.36 monoclinic sp gr, 1.71 specific heat 1.611 kj/ (kg-K) [0.385 kcal/(g°C] at 25—50°C (68) heat of formation, —6.2643 MJ/mol (—1497.2 kcal/mol) (69) exists in nature as the mineral borax. Its crystal habit, nucleation, and growth rate are sensitive to inorganic and surface active otganic modifiers (70). 

Applying supercritical fluids in CSS allows one to obtain supersaturation and to control nucleation- and growth rates by temperature-induced variation of the concentration of the solute in systems where no liquid solvents (e.g., VOC = volatile organic compounds) are present. 

Expressions for Transformation Rate when Nucleation and Growth Rates are Constant. If the growth velocity R is isotropic and constant, Eq. 21.5 can be integrated and the time cone is the set of points r that obey... 

Substituting the appropriate factors from Eq. 21.10 into Eqs. 21.11 and 21.4 gives expressions for the fraction transformed in one, two, and three dimensions for the case of constant nucleation and growth rates J and R. The resulting expressions for the untransformed volume are... 

Temperature dependence of pearlite nucleation and growth rates in a 0.78% C, 0.63% Mn steel of ASTM grain size 5.25. Data from R. F. Mehl and A. Dube, Phase Transformations in Solids (New York Wiley, 1951), 545. Reprinted with permission of John Wiley Sons, Inc. 

The rate of reaction is dependent on the nucleation and growth rates of calcite, not the dissolution rate of aragonite. Curiously, it has also been observed that absolute rates are strongly dependent on the aragonitic material used. This observation appears to contradict the generally held conclusion that rates are strictly dependent on calcite nucleation and precipitation rates, not the dissolution rate of aragonite. 

The higher the pressure over equilibrium, the higher the diamond nucleation and growth rate and the smaller and less perfect the crystal. Lower synthesis temperatures favor cubes and higher ones, octahedra. Suitable control of these variables permits the growth of selected types of... 

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