Incoherent nucleation

Incoherent Nucleation. Consider first incoherent nucleation on dislocations [19]. For linearly elastic isotropic materials, the energy per unit length Ei inside a cylinder of radius r having a dislocation at its center is given by... 

Figure 19.17 Lowering of the activation barrier for heterogeneous incoherent nucleation at dislocations with increasing values of the parameter a (see Eq. 19.55). From Cahn [19].

Nucleation arid Crystal Growth. When a new phase forms dining the reduction process, the first step is phase nucleation. If the structure of the new phase does not match the host matrix, phase nucleation problems can occur (incoherent nucleation). The... 

Internal nucleation and growth can occur coherently or incoherently while the reaction volume can be negative or positive. The severe constraints which the matrix crystal exerts on the internal reaction can lead to the formation of metastable (or even unstable) phases, which do not exist outside the matrix. Often, heavy plastic flow and anisotropic growth has been found. 

In crystalline solids, only coherent spinodal decomposition is observed. The process of forming incoherent interfaces involves the generation of anticoherency dislocation structures and is incompatible with the continuous evolution of the phase-separated microstructure characteristic of spinodal decomposition. Systems with elastic misfit may first transform by coherent spinodal decomposition and then, during the later stages of the process, lose coherency through the nucleation and capture of anticoherency interfacial dislocations [18]. 

Coherent Nucleation. The elastic interaction between the strain field of the nucleus and the stress field in the matrix due to the dislocation provides the main catalyzing force for heterogeneous nucleation of coherent precipitates on dislocations. This elastic interaction is absent for incoherent precipitates. 

Derive Eq. 19.36 for the free-energy change due to the annihilation of excess vacancies at nucleating incoherent clusters during precipitation. 

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. 

Why do the GP zones and then the 0" phase form before the 9 and the 9 phase Recall from Section 11.4 that the barrier to nucleation is directly proportional to the interfacial energy. The small clusters of Cu atoms and coherent 9" phase have much lower interfacial energy than the incoherent 9 phase. However, the 9 phase is the stable phase so that eventually the metastable 9" and 9 will proceed to the stable 9 phase. 

As one Gaussian sphere touches less than one NA, the nuclei on each NA do not interact with each other, that is, each nuclei should be incoherent (Fig. 4.30a). The probability of nucleation on a NA (Pna) is independent and the same on any NA in the melt. Therefore should be independent of Cna,... 

It is also possible for the molecules to be deposited incoherently, so that the surfaces of the nucleus and crystal are not in register. In this case the top and bottom surfaces do not completely compensate one another. There is a net interfacial free energy between the pillbox and substrate that we will designate as a. Therefore, for this type of nucleation (125,126)... 

Here the constant kj specifies several quantities. These are the geometry of the nucleus whether it is formed homogeneously or heterogeneously in certain situations whether it is deposited coherently or incoherently and the enthalpy of fusion per repeating unit. Two-dimensional steady-state nucleation (initiation or growth) can be expressed as... 

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