Effect on the Movement of Steps

Although the Cabrera-Vermilyea model represents an idealized picture of the growth and interaction process, experimental observations of the features and movement of the steps on crystal faces validate the model (van der Eerden and Muller-Krumbhaar 1986). A striking example is the effect of Al + adsorption on the 

With the assumption that the source of new steps on the crystal surface is a spiral defect, Cabrera and Vermilyea developed an approximate expression for the reduction in step velocity in the presence of immobile impurities. 

The Cabrera-Vermilyea model also implies the existence of a critical supersaturation below which no growth would take place in the presence of impurities. Mathematically, this is given by the condition 2pc, indicating that the density of impurities has reached the point where step movement by two-dimensional nucleation is prohibited. The size of the critical two-dimensional nucleus is relatable to supersaturation through the expression (Cabrera and Vermilyea 1958 Black et al. 1986) 

An intriguing class of compounds that exhibits many of the theoretical attributes of immobile impurities are the so-called tailor-made additives. These are compounds that are designed (i.e., synthesized) to have certain structural and chemical characteristics of the host (crystalline) phase. As a result of the relative host-impurity complementarity, these impurities have a tendency to strongly adsorb and, in some cases, incorporate into the bulk at concentrations as high as 20wt%. Consequently, the application of the Cabrera-Vermilyea model is particularly appropriate, and has been successfully used to model certain tailor-made additive systems (Black and Davey 1988). 

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