Crystallites, hemispherical

Figure 3.48. An artist impression of possible shapes of catalyst particles present on a support a. spherical particle with only one point contact to support, b. hemispherical particle, strongly bonded to support and partially poisoned, c. metal crystallite, strongly bonded to and partially encapsulated in support, d. complete wetting of the support by the active phase. After Scholten et al, 1985 and Ba.stein cr a/., 1987.

When the charge-transfer step in an electrodeposition reaction is fast, the rate of growth of nuclei (crystallites) is determined by either of two steps (I) the lattice incorporation step or (2) the diffusion of electrodepositing ions into the nucleus (diffusion in the solution). We start with the first case. Four simple models of nuclei are usually considered (a) a two-dimensional (2D) cylinder, (b) a three-dimensional (3D) hemisphere, (c) a right-circular cone, and (d) a truncated four-sided pyramid (Fig. 7.2). 

Previously, Stonehart11 had described the mechanism for diffusion of oxygen to an individual platinum crystallite on the carbon support surface. In this instance, at low current-densities, it was anticipated that hemispherical diffusion conditions operate, since the base of the platinum crystallite is shielded by the carbon support and thereby is inactive. 

Identity of the angles of diffraction maximums and equality of their hemispheres show that introduction of XLY does not change interplane distances of polymer crystallites and their sizes. 

Before discussing these techniques, it is perhaps wise to comment on the practice of calculating active surface areas from crystallite size measurements. This is unreliable for several reasons. First, instrumental techniques such as SEM, TEM, and x-ray line broadening all have their limitations. Monolayer-type dispersions are not detected and ultrasmall crystallites are below the range for accurate determination. Second, shape must be assumed in the calculations. Theoretical and experimental evidence indicates that the most stable shapes are spherclike cubo-octahedra. However, depending on the interaction with the support, crystallites may exist as full spheres, hemispheres, or intermediate structures. For very small sizes, this cannot be resolved easily with TEM. Also, a distribution of sizes and shapes may exist. Calculation of the surface from size measurements is, at its best, an indication of an upper limit. 

To control the size and geometry of the prepared nanoparticles, another important parameter is the kind of substrate used. According to Markov et al. when metal crystallites or drops nucleate or grow onto a foreign substrate, in their immediate vicinity zones of zero nucleation probability exist [30]. Nucleation under these conditions occurs under the influence of the external electrical field. The growth of nuclei causes deformations in the field, resulting in an overpotential drop in the screened surface segments. When the overpotential is lower than the minimum value for nucleation, further nucleation is impossible. It was shown that for a hemispherical drop on a flat substrate, nucleation is impossible inside a zone of radius r, defined as... 

For t values very close to to (zone Ila), where the nucleation process becomes very important, a linear relationship (/ — iof = at + b was found. At the same time, the formation of small hemispherical crystallites whose radius increases with t until the electrode is covered completely was observed by scanning electron microscopy (SEM) [148]. The fact that the current is proportional to t indicates that nucleation is progressive and that crystallite formation is kinetically controlled by planar or spherical diffusion [166]. When a rotating electrode was used, a sharp decrease in the current was observed in zone lib while no significant change of i occurred in zone Ila, a result which proves that nucleation is controlled by the spherical diffusion of the monomer. 

A change in the form of the metal crystallites from hemispherical to rafts. ... 

The model of Custodio et al. [74] describes every crystallite as a cylinder with a hemispherical cap at each end. The length of the cylindrical part then determines whether the crystallite will look more like a spherulite or more like a shish-kebab. In Figure 14.11, this concept for the morphological development is illustrated. The growth mechanisms for isotropic (spherulites) and ori-... 

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