Nuclei, formation

These terms are obtained from die equation above by differentiation with respect to r, and setting the resultant equal to zero. This is equivalent to taking the point on the graph of the Gibbs energy of nucleus formation versus the size of the nucleus where the tangent has zero slope. 

Surface features can also be revealed by etching, which permits identification of points of intersection of line dislocations with the surface, and this is valuable in determining the role of these imperfections in chemical processes [45,214] and, in particular, nucleus formation. Smaller topographical details can be rendered visible by the evaporation of a thin (<0.5 nm) film of gold onto the surface [215,216]. Heights and depths of surface features can be determined by interferometry [203—205]. Microcinematography has also been used [217] to record the progress of solid phase reactions. 

The exponent n = j3 + X, where j3 is the number of steps involved in nucleus formation (frequently j3 = 1 or 0, the latter corresponding to instantaneous nucleation) and X is the number of dimensions in which the nuclei grow (X = 3 for spheres or hemispheres, 2 for discs or cylinders and 1 for linear development). Most frequently, it is found that 2 < n < 4. Since n is a compound term, the value determined does not necessarily provide a unique measurement of both j3 and X. Ambiguity may arise where, for example, n = 3 could be a consequence of (j3 = 2, X = 1), (j3 = 1,... 

While general agreement has been reached concerning the catalytic behaviour of the product metal in promoting reaction, other aspects of the rate process have been less satisfactorily characterized these include the changes which precede nucleus formation, the distribution of such sites and development of the reaction interface. 

The (en) compound developed nuclei which advanced rapidly across all surfaces of the reactant crystals and thereafter penetrated the bulk more slowly. Kinetic data fitted the contracting volume equation [eqn. (7), n = 3] and values of E (67—84 kJ mole"1) varied somewhat with the particle size of the reactant and the prevailing atmosphere. Nucleus formation in the (pn) compound was largely confined to the (100) surfaces of reactant crystallites and interface advance proceeded as a contracting area process [eqn. (7), n = 2], It was concluded that layers of packed propene groups within the structure were not penetrated by water molecules and the overall reaction rate was controlled by the diffusion of H20 to (100) surfaces. 

Farkas L (1927) The velocity of nucleus formation in superheated vapors. Z Phys Chem 125 236-240... 

Most nucleotide sugars are formed in the cytosol, generally from reactions involving the corresponding nucleoside triphosphate. GMP-sialic acids are formed in the nucleus. Formation of uridine diphosphate galactose (UDP-Gal) requires the following two reactions in mammahan tissues ... 

In some cases, an embryo must form before the nucleus formation is complete. 

W e know of many examples of the effect of impurities of crystallization. In many cases impurities will completely inhibit (2-4) nucleus formation. Reading the literature on this subject impresses one with the frequent occurrence of hydrocolloids as crystal modifiers, particularly where sugar or water is the material being crystallized. The use of gelatin, locust bean gum, or sodium alginate in ice cream is just one example of many practical applications of hydrocolloids in crystal modification. 

The validity of the Poisson distribution for silver nucleation is demonstrated in Fig. 5.48B. The assumption for this kind of treatment is that the nucleus formation is irreversible and that the event is binary consisting of a discontinuous process (nucleus formation) and a continuous process (flow of... 

These experimental results could not be confirmed by Lahav and co-workers they suggest that impurities in the starting materials have a much greater effect on the crystallisation process than the PVED (Parity Violating Energy Difference). Extensive experimental studies indicate the importance of small quantities of impurities, particularly in early phases of crystallisation nucleus formation. Amino acids from various sources were used, and the analyses were carried out using the enan-tioselective gas chromatography technique (M. Lahav et al 2006). 

Cyclic Voltammogram Feature for Random Adsorption and Nucleus Formation when the Process is Reversible (v -> 0)... 

Becker, R., and Doting, W. (1935). The kinetic treatment of nucleus formation in supersaturated vapors. Ann. Phys. Leipzig)[5 24, 719, 752. 

Farkas, L. (1927). The velocity of nucleus formation in supersaturated vapors. Z. Phys. Chem. 125, 236. 

Theofanous, T., Biasi, L., Isbin, H. S., and Fauske, H. (1969). A theoretical study on bubble growth in constant and time-dependent pressure fields. Chem. Eng. Sci. 24, 885. Trefetben, L. (1957). Nucleadon at a liquid-liquid interftice. J. Appl. Phys. 28,923. Volmer, M., and Weber, A. (1926). Nucleus formation in supersaturated systems. Z. Phys. Chem. 119, 277. 

Using specific metal combinations, electrodeposited alloys can be made to exhibit hardening as a result of heat treatment subsequent to deposition. This, it should be noted, causes solid precipitation. When alloys such as Cu-Ag, Cu-Pb, and Cu-Ni are coelectrodeposited within the limits of diffusion currents, equilibrium solutions or supersaturated solid solutions are in evidence, as observed by x-rays. The actual type of deposit can, for instance, be determined by the work value of nucleus formation under the overpotential conditions of the more electronegative metal. When the metals are codeposited at low polarization values, formation of solid solutions or of supersaturated solid solutions results. This is so even when the metals are not mutually soluble in the solid state according to the phase diagram. Codeposition at high polarization values, on the other hand, results, as a rule, in two-phase alloys even with systems capable of forming a continuous series of solid solutions. 

In the rate of crystallisation of a substance from a supersaturated solution two independent factors have to he considered, firstly the rate of nucleus formation from which crystallisation may proceed and secondly the rate of growth of a nucleus once it is formed. 

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