Nucleation on dislocations

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 

Poisson s ratio v is approximately 0.3 for many solids, so to a fair approximation, the energy difference between edge and screw dislocations can be ignored. Following Cahn, 

Plotting AQ (r) vs. r in Fig. 19.15, two types of behavior are evident, depending on the value of the parameter, a, where 

For a 1, nucleation is barrierless—i.e., the transformation is controlled solely by growth kinetics. However, for a 1, a barrier exists. The local minimum of AQ (r) at point A in the plot corresponds to a metastable cylinder of /3 of radius r0 forming along the dislocation line. (In a sense, this is analogous to the Cottrell atmosphere described in Section 3.5.2.) In Eq. 19.54, the metastable cylinder s radius is 

The nucleation barrier for a 1 is then related to the difference in AQ r) between the states A and B in Fig. 19.15, where the radius rc corresponding to the unstable state at B is given from Eq. 19.54 as 

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Cahn also considered briefly the nucleation kinetics and showed that for reasonable values of the parameters in the theory, nucleation on dislocations in solids can be copious [19]. Typically, this occurs when a is in the range 0.4-0.7. 

Dick et al. [29] present additional data on the <100) shock compression of LiF which further establishes a threshold shear stress of between 0.24 GPa and 0.30 GPa for nucleation of dislocations in the shock front. 

Figure 11.1. Scanning tunnelling microscope image of a periodic array of Fe islands nucleated on the regular dislocation network of a Cu bilayer deposited on a platinum (111) face (after Urune...

The basic condition for experimental study of nucleation on an identical surface requires that this surface be a single crystal face without screw dislocations (page 306). Such a surface was obtained by Budevski et at. when silver was deposited in a narrow capillary. During subsequent deposition of silver layers the screw dislocations died out so that finally a surface of required properties was obtained. 

Tritium and its decay product, helium, change the structural properties of stainless steels and make them more susceptible to cracking. Tritium embrittlement is an enhanced form of hydrogen embrittlement because of the presence of He from tritium decay which nucleates as nanometer-sized bubbles on dislocations, grain boundaries, and other microstructural defects. Steels with decay helium bubble microstructures are hardened and less able to deform plastically and become more susceptible to embrittlement by hydrogen and its isotopes (1-7). 

Under conditions of low supersaturation (low driving force conditions) nuclea-tion/growth proceeds via dislocations (Burton-Cabrera-Frank (BCF) mechanism). With moderate supersaturation growth results from a two dimensional nucleation/ spreading mechanism nucleation on a flat face is fairly likely, but still rate limiting. At high levels of supersaturation, there is abundant nucleation on the crystal surface and the rate of growth is limited by the rate of diffusion of new material to the crystal surface. 

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. 

F.C. Larche. Nucleation and precipitation on dislocations. In F.R.N. Nabarro, editor, Dislocations in Solids, volume 4, pages 137-152, Amsterdam, 1979. North-Holland. 

Fig. 2. Dislocation sites and sites of oxide nucleation on a ill surface of germanium. Etched in CP4 and oxidized in poor vacuum.

A number of observations show that augite lamellae nucleate on other defects such as grain boundaries (Champness and Lorimer 1973), APBs (Carpenter 1978), and dislocations (Nord, Heuer, and Lally 1976). 

One of the problems with the analysis we have made thus far is its geometric simplicity. For the mode I case of primary interest here, the assumption that dislocations will be nucleated on the prolongation of the slip plane is overly... 

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