Screw dislocation crystal growth

Burton, Cabrera, and Frank [56] and Bennema and Gilmer [57] have developed a theory to predict the crystal growth rate for screw dislocations. The growth rate will depend on the shape of the growth spiral. For an Archimedian spiral, shown in Figure 6.14 [58], the distance between the steps of the spiral yo is... 

If the crystals are free of screw dislocations, their growth is then governed by the mechanism of 2D nucleation [22,23,38,39]. This implies that the growth of crystal faces takes place by growing crystal layers one on top of the other, and the occurrence of a new layer on the existing layer is via 2D nucleation [38,39]. According to this model, the growth rate of the fibers can be expressed as [38,39]... 

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. 

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. 

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... 

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. 

Stack of lamellar crystals generated by spiral growth at one or more screw dislocations. Note The axial displacement over a full turn of the screw (Burgers vector) is usually equal to one lamellar thickness. 

There are two layer-spreading models. In these models, the crystal surface is atomically flat except at screw dislocations or steps of a partially grown surface layer. If there are screw dislocations, growth would continue on the screw... 

It is often observed in tiny crystals of micrometer order, such as clay minerals, that the entire surface of a crystal face is covered by elementary spiral layers originating from one screw dislocation (Fig. 5.3). Figure 5.10(a) shows such an exceptional case observed on a (0001) face of a SiC crystal synthesized by the Acheson method. However, such a situation is almost exceptional on crystal faces larger than millimeter size, and is encountered only on crystals synthesized under very precisely controlled conditions. In general, there are many growth centers on one crystal face, and steps from these centers bunch together to form macro-steps, which constitute the step patterns of the face. 

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