Birth and spread model

Figure 3.10. Schematic to show the layer-by-layer growth model due to two-dimensional nucleation. This figure assumes the mode of nucleation to be the mononuclear model. Other models, such as the poly-nuclear or birth and spread models, as explained in the text, may also be considered.

A birth and spread model, which allows nucleation and advancement of one growth layer at a time on one surface. 

The birth and spread model and its modifications predicts that the growth rate G increases with increasing supersaturation and increasing temperature. The dependence of growth rate on these variables is not a simple function of supersaturation and the model does not have the obvious problems of the other two models. For this reason, some semiempirical relations obtained from Eq. (2.41) are sometimes used to correlate experimental growth data and obtain the needed constants. 

In the mononuclear model, the limiting step is the formation of a nucleus. Once one is formed, the subsequent growth spreading across the crystal surface is infinitely rapid. For the polynuclear model, the spreading velocity is taken as zero and the crystal surface can only be covered by the accumulation of a sufficient number of nuclei. These two growth models represent two extreme cases. A third model, known as the birth-and-spread model, allows for formation of nuclei and their subsequent growth at a finite rate. In this case, new nuclei can form on top of uncompleted layers. 

The birth and spread model (B+S) describes the formation of critical nuclei on a smooth crystal surface and their subsequent growth. The so-called nucleus above nucleus model leads to... 

Figure 6 A schematic of the birth and spread model of crystal growth (after Mullin ).

Of the three models for the growth via 2D nucleation, only the birth-and-spread model will be discussed here, as it is the most plausible and the free enthalpy of nucleation for this mechanism is the lowest. In this model, 2D surface nuclei are generated on the flat faces. The nuclei are limited by steps that will spread out. It is allowed that new nuclei generate on growing islands (Figure 2.32). 

Figure 2.32 Model for the growth via 2D surface nuclei according to the birth-and-spread model. These 2D nuclei are limited by steps and spread laterally. The nucleation of islands that are still not grown out is allowed.

Figure 2.33 Dependence of the growth rate R on supersaturation for growth via the birth-and-spread model. Note that a certain supersaturation is necessary for growth to start...

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. 

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