Thermodynamic and structural aspects of precipitation

In order for precipitation phenomena to take place, a supersaturation must occur. This will, in general, arise as a result of the undercooling of a homogeneous solid solution into a two-phase region (i.e. as a result of the crossing of a solubility line). Further discussion will be based upon the situation shown in Fig. 7-8. 

In Fig. 7-8, the Gibbs free energy of the undercooled solution is shown as a function of composition. The common tangent line as drawn on this diagram gives the position of the miscibility gap on the T — Ni diagram as a result of the relationship (d G jd The spinodal 

Furthermore, the interfacial energy at the commencement of growth of the new phase will be strongly dependent upon whether the nucleation is fully coherent, partially coherent (nuclei formation by shear), or completely incoherent. The meaning of these terms is schematically illustrated in Fig. 7-9. 

The various transitions between nucleus and matrix (a) coherent, (b) partially coherent, (c) incoherent (see also reference [32]). 

Most precipitation phenomena appear to proceed either coherently or partially coherently, at least in their very early stages. This can be inferred from the continual recurrence of certain relationships in the orientations between the supersaturated matrix and the precipitated phase. An example is an orientational relationship named after Kurdjumov and Sachs which is 

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