Screw dislocation growth

Three basic models were developed to describe crystal growth rates normal growth, screw dislocation growth, and surface crystallization. 

A number of theories have been put forth to explain the mechanism of polytype formation (30—36), such as the generation of steps by screw dislocations on single-crystal surfaces that could account for the large number of polytypes formed (30,35,36). The growth of crystals via the vapor phase is beheved to occur by surface nucleation and ledge movement by face specific reactions (37). The soHd-state transformation from one polytype to another is beheved to occur by a layer-displacement mechanism (38) caused by nucleation and expansion of stacking faults in close-packed double layers of Si and C. 

The screw dislocation theory (27), often referred to as the BCE theory (after its formulators), shows that the dependence of growth rate on supersaturation can vary from a paraboHc relationship at low supersaturation to a linear relationship at high supersaturation. In the BCE theory, growth rate is given by... 

Figure 3.22. Screw dislocation and crystal growth, after W.T. Read.

Figure 3.23. A growth spiral on a silicon carbide crystal, originating from the point of emergence of a screw dislocation (courtesy Prof, S, Amelinckx).

Charles Frank and his recognition, in 1949, that the observation of ready crystal growth at small supersaturations required the participation of screw dislocations emerging from the crystal surface (Section 3.2.3.3) in this way the severe mismatch with theoretical estimates of the required supersaturation could be resolved. 

The other major defeets in erystalline solids oeeupy mueh more of the volume in the lattiee. They are known as line defeets. There are two types viz. edge dislocations and screw dislocations (Figure 1.4). Line defeets play an important role in determining erystal growth and seeondary nueleation proeess (Chapter 5). 

Figure 5.5 Development of a crystal growth spiral staring from a screw dislocation...

One can now immediately deduce the normal growth rate of a crystal due to the screw dislocation. Whenever a step edge passes by a fixed point on the crystal surface, this point gains the height of a lattice unit. The normal growth rate V of the crystal is then... 

If spiral growth occurs due to the existence of screw dislocations, the results depend upon whether the diffusion length ijy is smaller or larger than the typical separation of the spiral arms i. In the first case the situation hardly changes from the purely kinetic situation without diffusion, but in the second case interaction between steps comes into effect [90] and phenomena such as step bunching [91] take place. We can estimate qualitatively the... 

The electrocrystallization on an identical metal substrate is the slowest process of this type. Faster processes which are also much more frequent, are connected with ubiquitous defects in the crystal lattice, in particular with the screw dislocations (Fig. 5.25). As a result of the helical structure of the defect, a monoatomic step originates from the point where the new dislocation line intersects the surface of the crystal face. It can be seen in Fig. 5.48 that the wedge-shaped step gradually fills up during electrocrystallization after completion it slowly moves across the crystal face and winds up into a spiral. The resultant progressive spiral cannot disappear from the crystal surface and thus provides a sufficient number of growth... 

Screw dislocations play an important part in crystal growth. The theoretical background to this fact was first developed in 1949 by Frank and colleagues. It was apparent that crystal growth was rapid as long as ledges and similar sites existed on the face of a crystal because these form low-energy positions for the addition of new atoms or... 

Figure 3.8 Crystal growth at a screw dislocation (a) addition of new material at a step is energetically favored, and (b) a step is always present at an emerging screw dislocation.

Edge dislocations play an important role in the strength of a metal, and screw dislocations are important in crystal growth. Dislocations also interact strongly with other defects in the crystal and can act as sources and sinks of point defects. 

Heterogeneous nucleation of CaC03 on 5-AI2O3. Example for the sequence of nucleation and subsequent crystal growth. The latter is plotted as a 2nd order reaction (as is typical for screw dislocation catalysis). 

The classical crystal growth theory goes back to Burton, Cabrera and Frank (BCF) (1951). The BCF theory presents a physical picture of the interface (Fig. 6.9c) where at kinks on a surface step - at the outcrop of a screw dislocation-adsorbed crystal constituents are sequentially incorporated into the growing lattice. 

Dislocations. Screw dislocations are the most important defects when crystal growth is considered, since they produce steps on the crystal surface. These steps are crystal growth sites. Another type of dislocation of interest for metal deposition is the edge dislocation. Screw and edge dislocations are shown in Figure 3.4. 

Eig. 2.22 Continuous crystal growth around a central screw dislocation axis. The small blocks are unit cells of the crystalline material and are usually well organized. The displacement site acts as a site for nucleation. 

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