Crystallographic Mismatch Nucleation

As can be seen in the following sections, nucleation is the initial step in the formation of crystalline materials. It is also very crucial in determination of the structural synergy between crystals and the substrate. It will be shown that the formation of a fibrous structure of some supramolecular materials is actually controlled by special type of nucleation—crystallographic mismatch nucleation, on the growing tips of fibers. Therefore, a decent understanding of nucleation is very important. 

In the following discussion, we will examine briefly some key factors controlling the crystallographic mismatch nucleation and growth ... 

Impurities. Adsorbed impurities may disturb the interfacial structural match between nucleating layers and the parent crystal surfaces. This gives rise to the lowering of m therefore, it will promote crystallographic mismatch nucleation (Sect. 4.1). 

The key question to be addressed is why and how crystallographic mismatch branching takes place. Obviously, the crystallographic mismatch branching takes place via the supersatmation-driven interfacial structural mismatch or the crystallographic mismatch nucleation and growth (Fig. 5). 

The occurrence of crystallographic mismatch branching is controlled by the following two steps (1) the growth of the surface of parent crystals (2) the crystallographic mismatch nucleation on the surface. 

As mentioned in Sect. 4.1, the crystallographic mismatch nucleation can be regarded as a special case of supersaturation-driven interfacial structural mismatch in heterogeneous 3D nucleation. Therefore, the nucleation rate can also be described by Eq. 17 with m given by Eq. 24. 

According to the 3D nucleation model, we should then have a linear relationship between In(fg) and l/(Afi/kT) (cf Eq. 19) for the nucleation associated with a given / (including crystallographic mismatch nucleation). In Fig. 13, the Unear fits between In(fg) and l/(A/x/fcT) obtained for both systems without and with EVACP indeed verify the nucleation control at the beginning of fiber network formation. 

Crystallographic Mismatch Nucleation Induced Fiber Branching... 

Supersaturation. Similarly to normal nucleation and growth, the kinetics of crystallographic mismatch nucleation and growth also depends on supersaturation. At low supersaturations, the crystallographic mismatch nucleation is difficult to occur due to the high AG jjjjg (Equations 2.15 and 2.16). As supersaturation increases, AG jj jg will drop rapidly (Equation 2.16). It follows that interfacial mismatch nucleation can occur much more easily in this case. 

This will trigger the crystallographic mismatch nucleation at the tips. 

As has been mentioned, crystallographic mismatch nucleation is a special case of heterogeneous nucleation where the substrate is the crystal fiber. Designating the induction time for the nucleation of new fibers on the host fibers as r (r 1/J, where J is the rate of the crystallographic mismatch nucleation), the average branching distance can be expressed as... 

Island growth also occurs with polycrystalline films, but in epitaxy, the islands combine to form a continuous single-crystal film, that is, one with no grain boundaries. In reality, nucleation is much more complex in the case of heteroepitaxy. Nucleation errors may result in relatively large areas, or domains, with different crystallographic orientations. The interfaces between domains are regions of structural mismatch called subgrain boundaries and will be visible in the microstructure. 

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