Polynuclear growth

Nucleation followed by polynuclear growth (Nielsen, 1969 Sdhnel and Mullin, 1978)... 

FIGURE 6.13 Two-dimensional growth of sxuface nuclei by (a) mononuclear growth and fb) polynuclear growth models. Redrawn, with permission from Dirksen and Ring [4a]. 

Figure 13.27. Surface models for crystal growth (a) mononuclear growth, (b) polynuclear growth, and (c) screw dislocation growth. Along the step a kink site is shown. Adsorbed ions diffuse along the surface and become preferentially incorporated into the crystal lattice at kink sites. As growth proceeds, the surface step winds up in a surface spiral. Often the growth reaction observed occurs in the sequence c, a, b. (From Nielsen, 1964.) (d) Salient features and elementary processes at surfaces.

The induction time for nucleation followed by polynuclear growth is given by Sohnel and Mullin (1988). If the nucleation time is much smaller than the growth time, the induction times for various cases are given by Sohnel and Mullin (1988). For mononuclear growth, the induction time in this case is given by... 

Several growth models based on crystal surface (two-dimensional) nucleation, followed by the spread of the monolayers have been developed in recent years (O Hara and Reid, 1973 van der Eerden, Bennema and Cherepanova, 1978). The term birth and spread (B + S) model will be used here, but other names such as nuclei on nuclei (NON) and polynuclear growth may also be seen in the literature to describe virtually the same behaviour. As depicted in Figure 6.13, growth develops from surface nucleation that can occur at the edges, corners and on the faces of a crystal. Further surface nuclei can develop on the monolayer nuclei as they spread across the crystal face. 

Figure 6.13. Development of polynuclear growth by the birth and spread B + S) mechanism...

In the polynuclear growth mechanism, formation of nucleation steps on the particle surface is too fast, so that a new layer is created before the previous one has been completed. The growth rate is independent of the surface area of the particles, which is given by ... 

Figure 2.18 Nucleation of layers around a particle for (a) mononuclear growth and (b) polynuclear growth.

Surface reaction mechanisms include adsorption, desorption, surface nucleation, polynucleation, mononucleation and ion exchange reaction. The dependencies of amounts of precipitate and solution composition on time are different for each mechanism. For example, linear, exponential and logarithmic rate equations are established for volume diffusion, polynuclear growth and spiral growth, respectively. 

From the theoretical considerations above, for diffusion controlled growth g = 1, for crystal growth originating from screw dislocations g = 1 — 2 and for polynuclear growth g > 2. 

The overall growth kinetics is thus second order and exhibits diffusion dependence, with intrinsic surface integration kinetics (not shown) being greater than second order implying a polynuclear growth mechanism. 

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