Growth independent nuclei

From the experimental fact that the lamellar thickening growth rate (17) of ECSC of PE is independent of l [8], we can regard ve on the end surface of the nucleus as constant and independent of l. For simplicity, we assume that the shape of ECSC is rectangular parallelepiped (Fig. 28). ve is given by the ratio of the volume of the crystal to the surface area of the crystal as shown below,... 

The exponent n is Unked to the munber of steps in the formation of a nucleus (this is a zone in the soUd matrix at which the reaction occurs), ft, and the number of dimensions in which the nuclei grow, X. It can be difficult to distinguish ft and X without independent evidence, and ft can fall to zero following the consumption of external nuclei sites. Hulbert has analysed the possible values of the exponent, n, for a variety of conditions of instantaneous (/3 = 0), constant (ft = 1) and deceleratory (0 < /I < 1) nucleation and for growth in one, two and three dimensions (X = 1 - 3) [ 17]. He also considered the effects of a diffusion contribution to the reaction rate. This reduces the importance of the acceleratory process and reduces the value of n. For diffusion controlled processes, n = ft + Xjl, whereas for a phase boimdary controlled process n = ft + X. Possible values of n are summarised in Table 1. Interpretation of these values can be difficult, and a given value does not unequivocally allow the determination of the reaction mechanism. 

Growth of Independent Nuclei, In the initial stages of growth of the nuclei it can be assumed that nuclei grow independent of each other. In this case the rate of growth of a single (free) 2D cylindrical nucleus is given by... 

The foreign species act in solution and usually retard nucleation or growth of goethite by competing with soluble Fe " species for sites on the subcritical nucleus or on the growing crystal. This mechanism is independent of the presence of ferrihydrite. 

In the rate of crystallisation of a substance from a supersaturated solution two independent factors have to he considered, firstly the rate of nucleus formation from which crystallisation may proceed and secondly the rate of growth of a nucleus once it is formed. 

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