Surface crystallization growth model

Two proposals have been made for the mechanism of oxidation of apoferritin-bound Fe. In the crystal growth model, the bulk of the Fe is oxidized to Fe(0)(0H) on the surface of the growing crystallite." " It is initiated at catalytic sites on the interior surface of the protein. There is evidence that the mechanism of iron uptake by ferritin changes after the initial uptake. Initial uptake occurs more effectively with O2 as the oxidizing agent, but in the latter stages O2 and KIO3 are equally effective. 

This equation describes not only the crystal growth, but with an additional noise term it also describes the evolution of the surface width and is called the Edward-Wilkinson model. An even better treatment has been performed by renormalization methods and other techniques [44,51-53]. 

We have assumed so far, implicitly, that the interactions are strictly local between neighboring atoms and that long-ranged forces are unimportant. Of course the atom-atom interaction is based on quantum mechanics and is mediated by the electron as a Fermi particle. Therefore the assumption of short-range interaction is in principle a simplification. For many relevant questions on crystal growth it turns out to be a good and reasonable approximation but nevertheless it is not always permissible. For example, the surface of a crystal shows a superstructure which cannot be explained with our simple lattice models. 

D. J. Gates. Surface angle transitions and facets in a solvable TSK model of steady crystal growth. J Cryst Growth 180 36, 1997. 

Typical surfaces observed in Ising model simulations are illustrated in Fig. 2. The size and extent of adatom and vacancy clusters increases with the temperature. Above a transition temperature (T. 62 for the surface illustrated), the clusters percolate. That is, some of the clusters link up to produce a connected network over the entire surface. Above Tj, crystal growth can proceed without two-dimensional nucleation, since large clusters are an inherent part of the interface structure. Finite growth rates are expected at arbitrarily small values of the supersaturation. 

Crystal growth is a process where the polymer chains are continuously adsorbed to the growth surfaces. We must model both the polymer molecule and the growth substrate. The polymer chains we consider here are composed... 

Surface models for crystal growth (figures from Nielsen, 1964)... 

The geochemical fate of most reactive substances (trace metals, pollutants) is controlled by the reaction of solutes with solid surfaces. Simple chemical models for the residence time of reactive elements in oceans, lakes, sediment, and soil systems are based on the partitioning of chemical species between the aqueous solution and the particle surface. The rates of processes involved in precipitation (heterogeneous nucleation, crystal growth) and dissolution of mineral phases, of importance in the weathering of rocks, in the formation of soils, and sediment diagenesis, are critically dependent on surface species and their structural identity. 

Clearly this is a very interesting problem and of great practical relevance, very well suited to Monte Carlo simulation. At the same time, simulations of such problems have just only begun. In the context of crystal growth kinetics, models where evaporation-condensation processes compete with surface diffusion processes have occasionally been considered before . But many related processes can be envisaged which have not yet been studied at all. 

In this study, D-SCMC seed crystals were put in a racemic SCMC supersaturated solution in a batchwise agitated vessel and growth rates in longitudinal and lateral directions and the optical purity of D-SCMC crystals were measured. The growth rates and optical purity were discussed considering surface states of grown crystal observed by a microscope. The kinetics of crystal growth were measured and a model of inclusion of impurity was proposed. 

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