Nucleation fractional

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

In an amorphous material, the aUoy, when heated to a constant isothermal temperature and maintained there, shows a dsc trace as in Figure 10 (74). This trace is not a characteristic of microcrystalline growth, but rather can be well described by an isothermal nucleation and growth process based on the Johnson-Mehl-Avrami (JMA) transformation theory (75). The transformed volume fraction at time /can be written as... 

Crystal growth is a layer-by-layer process, and the retention time required in most commercial equipment to produce crystals of the size normally desired is on the order of 2 to 6 h. On the other hand, nucleation in a supersaturated solution can be generated in a fraction... 

If the particles are initially monodisperse and the total solids volume fraction (e = ttL N16) remains constant in the absence of crystal growth and nucleation then... 

X = vapor quality of fluid = 0 for pool boiling and is a low fraction, about 0.1 to 0.3, for most nucleate boiling... 

Measurements of overall reaction rates (of product formation or of reactant consumption) do not necessarily provide sufficient information to describe completely and unambiguously the kinetics of the constituent steps of a composite rate process. A nucleation and growth reaction, for example, is composed of the interlinked but distinct and different changes which lead to the initial generation and to the subsequent advance of the reaction interface. Quantitative kinetic analysis of yield—time data does not always lead to a unique reaction model but, in favourable systems, the rate parameters, considered with reference to quantitative microscopic measurements, can be identified with specific nucleation and growth steps. Microscopic examinations provide positive evidence for interpretation of shapes of fractional decomposition (a)—time curves. In reactions of solids, it is often convenient to consider separately the geometry of interface development and the chemical changes which occur within that zone of locally enhanced reactivity. 

Topley and Hume [453], in a study of the dehydration of CaC03 6 H20, assumed the rapid initial formation of (on average) a single nucleus on the surface of each particle of reactant, represented as a sphere of radius a. In the absence of preferential surface development, the reaction interface penetrates the reactant at equal rates in all inward directions (kG = dr/df) and the volume of material reacted at time t is that volume of a sphere, having its centre at the site of surface nucleation and of radius kGt, which falls within the reactant. The fractional reaction, the zone of interpenetrating spheres, at time t is... 

Solar energy, 6, 488 surface modified electrodes, 6, 30 Sol-Gel process fast reactor fuel, 6, 924 Solid state reactions, 1, 463-471 fraction of reaction, 1, 464 geometric, 1, 464 growth, 1, 464 nucleation, 1, 464 rate laws, 1,464 Solochrome black T metallochromic indicators, 1,555 Solubility... 

We define a nucleation overpotential rjN EN E0 (Fig. 36) required to make the N0 oxidation nuclei appear. The nucleation overpotential is related to the degree of closure (compaction) of the polymeric entanglement ( ), expressed as the fraction of interchain free volume destroyed after polarization at a given potential Ec, compared with the amount of free volume present at Es. 

The kinetics of F-actin-Si assembly from G-actin and Si via nucleation of actin filaments, followed by Si binding are not observed in a low ionic strength medium. Instead, the mechanism involves condensation of high affinity (G-actin)2 S complexes rapidly preformed in solution. Assembly of F-actin-Si in the presence of Si > G-actin is a quasi-irreversible process. This mechanism is therefore different from that involving the assembly of F-actin filaments, which is characterized by the initial, energetically unfavorable formation of a small number of nuclei representing a minute fraction of the population of actin molecules, followed by endwise elongation from G-actin subunits. 

The frequency-dependent spectroscopic capabilities of SPFM are ideally suited for studies of ion solvation and mobility on surfaces. This is because the characteristic time of processes involving ionic motion in liquids ranges from seconds (or more) to fractions of a millisecond. Ions at the surface of materials are natural nucleation sites for adsorbed water. Solvation increases ionic mobility, and this is reflected in their response to the electric field around the tip of the SPFM. The schematic drawing in Figure 29 illustrates the situation in which positive ions accumulate under a negatively biased tip. If the polarity is reversed, the positive ions will diffuse away while negative ions will accumulate under the tip. Mass transport of ions takes place over distances of a few tip radii or a few times the tip-surface distance. 

In Nature, however, we always have a contiiinous distribution of particles. This means that we have all sizes, even those of fractional parentage, i.e.-18.56n, 18.57p, 18.58 p, etc. (supposing that we can measure 0.01 p differences). The reason for this is that the mecheuiisms for particle formation, i.e.- precipitation, embryo and nucleation growth, Ostwald ripening, and sintering, are random processes. Thus, while we may speak of the "statistical variation of diameters", and while we use whole numbers for the particle diameters, the actuality is that the diameters are fractional in nature. Very few particle-size" specialists seem to recognize this fact. Since the processes are random in nature, we can use statistics to describe the... 

Layadi et al. have shown, using in. situ spectroscopic ellipsometry, that both surface and subsurface processes are involved in the formation of /xc-Si [502, 503]. In addition, it was shown that the crystallites nucleate in the highly porous layer below the film surface [502, 504], as a result of energy released by chemical reactions [505, 506] (chemical annealing). In this process four phases can be distinguished incubation, nucleation, growth, and steady state [507]. In the incubation phase, the void fraction increases gradually while the amorphous fraction decreases. Crystallites start to appear when the void fraction reaches a maximum... 

As mentioned previously, scale-up of crystallization processes from the laboratory is far from straightforward. Various parameters need to be maintained to be as close to those used in the laboratory as possible in order to reproduce the results from the laboratory. For scale-up, supersolubility, agitation (and its effect on secondary nucleation throughout the vessel), fraction of solids in the slurry, seed number and sizes, contact time between growing crystals and liquid all need to be maintained. 

For liquid metals the superiority of nucleate boiling heat transfer coefficients over those for forced-convection liquid-phase heat transfer is not as great as for ordinary liquids, primarily because the liquid-phase coefficients for liquid metals are already high, and the bubble growth period for liquid metals is a relatively short fraction of the total ebullition cycle compared with that for ordinary fluids. In the case of liquid metals, the initial shape of the bubbles is hemispheric, and it becomes spherical before leaving the heating surface. This is because of very rapid... 

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