Surface nucleus nucleation

When the attachment of the substrate to the precipitate to be formed is strong, the clusters tend to spread themselves out on the substrate and form thin surface islands. A special limiting case is the formation of a surface nucleus on a seed crystal of the same mineral (as in surface nucleation crystal growth). As the cohesive bonding within the cluster becomes stronger relative to the bonding between the cluster and the substrate, the cluster will tend to grow three-dimensionally (Steefel and Van Cappellen, 1990). 

In addition to the matching of the structures of the surfaces of the mineral to be nucleated and the substrate, adsorption or chemical bonding of nucleus constituents to the surface of the substrate can be expected to enhance the nucleation. Surface... 

In electrochemical phase formation nucleation must be on a surface of a foreign or native substrate. If the nucleus formed on a surface is a cluster that grows in all three dimensions, one speaks of a three-dimensional nucleation. The nucleus is a cluster of only a few atoms and can be depicted as a semi-sphere (Figure 7.1). 

After completion of a layer on the surface of the crystal, a new surface nucleus must be created for the formation of a new layer. This is called a secondary nucleation process. The growth of the crystal is then a series of secondary nucleation events and completions of new layers. The most widely accepted expression for the secondary nucleation rate is given by... 

Figure 6.30 Surface nucleation and substrate completion with reptation in regime I. where one surface nucleus deposited at rate /causes completion of substrate of length L, giving overaii growth rate G, = b iL Multiple surface nuclei occur in regime II (not shown) and lead to Gn = lo(2/g) where g is the substarte completion rate. The substrate completion rate, g, is associated with a "reeling in rate r= (l /ao)g for the case of adjacent reentry (77).

The resistance to nucleation is associated with the surface energy of forming small clusters. Once beyond a critical size, the growth proceeds with the considerable driving force due to the supersaturation or subcooling. It is the definition of this critical nucleus size that has consumed much theoretical and experimental research. We present a brief description of the classic nucleation theory along with some examples of crystal nucleation and growth studies. 

The formation of a liquid phase from the vapour at any pressure below saturation cannot occur in the absence of a solid surface which serves to nucleate the process. Within a pore, the adsorbed film acts as a nucleus upon which condensation can take place when the relative pressure reaches the figure given by the Kelvin equation. In the converse process of evaporation, the problem of nucleation does not arise the liquid phase is already present and evaporation can occur spontaneously from the meniscus as soon as the pressure is low enough. It is because the processes of condensation and evaporation do not necessarily take place as exact reverses of each other that hysteresis can arise. 

Models used to describe the growth of crystals by layers call for a two-step process (/) formation of a two-dimensional nucleus on the surface and (2) spreading of the solute from the two-dimensional nucleus across the surface. The relative rates at which these two steps occur give rise to the mononuclear two-dimensional nucleation theory and the polynuclear two-dimensional nucleation theory. In the mononuclear two-dimensional nucleation theory, the surface nucleation step occurs at a finite rate, whereas the spreading across the surface is assumed to occur at an infinite rate. The reverse is tme for the polynuclear two-dimensional nucleation theory. Erom the mononuclear two-dimensional nucleation theory, growth is related to supersaturation by the equation. 

A pre-factor 1/r contains a time scale r or a frequency which for instance corresponds to the hard phonon or to an atomic frequency. The growth rate of the crystal is proportional to this rate (23). As will be shown later, the nucleus once formed expands in a time scale shorter than the one necessary for nucleation. If the process consists of a series of sequential subprocesses, the global velocity is governed by the slowest one. Therefore, this nucleation process determines the growth rate of a faceted surface. 

In the secondary nucleation stage, the remaining amorphous portions of the molecule begin to grow in the chain direction. This is schematically shown in Fig. 16. At first, nucleation with the nucleus thickness /i takes place in the chain direction and after completion of the lateral deposition, the next nucleation with the thickness k takes place, and this process is repeated over and over. The same surface nucleation rate equation as the primary stage can be used to describe these nucleation processes. 

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