Crystal nucleus formation

Crystal nucleus formation. When oxygen is captured from the oxide in the surface of catalyst the Me-0 ratio will have regional changes. The metal formed by reduction is dissociative at the initial stage, and separated out in single crystal... 

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. 

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. 

Polymer crystallization is usually initiated by nucleation. The rate of primary nucleation depends exponentially on the free-energy barrier for the formation of a critical crystal nucleus [ 110]. If we assume that a polymer crystallite is a cylinder with a thickness l and a radius R, then the free-energy cost associated with the formation of such a crystallite in the liquid phase can be expressed as... 

The initial transition of dissolved silicate molecules into solid nanoparticles is perhaps the least explored step in the synthesis of zeolites. One impediment to understanding this mysterious step is the poorly elucidated molecular composition of dissolved particles. The major mechanistic ideas for the formation of zeolites approach these structures differently i) many researchers believe that secondary building units (SBU) must be present to form initial nanoslabs [1,2] ii) some others prioritize the role of monomers to feed artificially introduced crystal nuclei or assume that even these nuclei form via appropriate aggregation of monomers [3] iii) silicate solutions are also frequently viewed as random mixtures of various siloxane polymers which condense first into an irregular gel configuration which can rearrange subsequently into a desired crystal nucleus at appropriate conditions [4,5],... 

The particle size of the resulting pigment can only be influenced to a limited extent by adjusting the reaction parameters, because the decisive factor is the ratio of the rate of formation of the crystal nucleus to the rate of crystal growth. 

In addition to the ability of polyphosphates to bond cations they also possess the important property of hindering the formation of large crystallites of CaCO i and of solid boiler scale, even when present at very small concentrations (239). This property, which is used in the threshold or in-noculation process, is based on the bonding or adsorption of polyphosphate chains on the surface of the crystal nucleus. These then hinder its further growth or aggregation. The effectiveness of detergents to which polyphosphates have been added must also be related to their adsorption on the... 

Such tendencies may be reduced by growing crystals very slowly, for instance, by extremely slow cooling or evaporation. In fact, when it is desired to obtain perfect crystals for goniometric or X-ray work, the golden rule is to grow them as slowly as possible. Excessive nucleus formation in solutions can often be avoided by removing dust particles in the following way. A solution saturated at, say, 30° C is made up and allowed to cool without disturbance to room temperature it is then suddenly disturbed, so that a shower of small crystals is formed these... 

Finally, it should be stressed that when the original supersaturated solution for crystallization was strictly racemic (0.0% ee), the probability for either the R or the S enantiomer to be enriched in solution after crystallization was 50% 9a this is because initial capricious formation of the very first nonracemic metastable crystal nucleus should doom which enantiomer is enriched in solution later. 

At a temperature below Tm the free enthalpy of the crystal is lower than that of the liquid hence the polymer will tend to crystallize. A crystal can, however, only be formed from a nucleus. The process of crystallization can thus be split-up into two different processes nucleus formation and crystal growth. 

Nucleus formation. Sometimes nuclei are already present, e.g. as contaminations, additives, or as deliberately added accelerators for crystallization. Sometimes nuclei... 

From the rate of nucleus formation and the rate of crystal growth the rate of crystallization results, which can be schematically represented as the product of both, as shown in Figure 4.7. The rate of crystallization is zero at Tg and at Tm, and shows a maximum somewhere in between, a maximum which is lower when the chains are longer. 

If the adsorption results in an organized deposit layer and a certain arrangement similar to the crystalline lattice we speak of epitaxy. A prerequisite of epitaxy is not only a two-dimensional lattice analogy of foreign lattice layers but also the mode of nucleus formation, fusing the nuclei, purity of crystal surface, and binding energy between lattice... 

Apart from the purely thermodynamic analysis, the description of the -> electro crystallization phenomena requires special consideration of the kinetics of nucleus formation [i-v]. Accounting for the discrete character of the clusters size alteration at small dimensions the atomistic nucleation theory shows that the super saturation dependence of the stationary nucleation rate /0 is a broken straight line (Figure 2) representing the intervals of Ap within which different clusters play the role of critical nuclei. Thus, [Ap, Apn is the supersaturation interval within which the nc -atomic cluster is the critical nucleus formed with a maximal thermodynamic work AG (nc). 

In the presence of dissolved aluminum ions, at not too high a temperature, the diflusion rate of the iron ions in the magnetite lattice is low. Hence, nucleus formation proceeds rapidly relative to crystal growth. Therefore, small iron crystallites, about 30 nm, form with correspondingly large specific surfaces. The aluminum probably remains partly in the iron crystallite in the form of very small FeAl204 areas statistically distributed over the lattice [262], [263], [294], [296], where an FeAl204 molecule occupies seven a Fe lattice positions [101]. 

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