Dislocation-Free Crystal Faces

The formation energy of 2D nuclei has been evaluated already (cf. eq. (4.25a)) as 

The J- ri relation is represented in Fig. 5.2. It is characterized by a relatively wide overvoltage range, in which / is practically zero. Only after exceeding a critical overvoltage does the nucleation rate show a sharp exponential rise (cf. Section 4.2). 

The existence of a supersaturation or overvoltage threshold is a characteristic feature of nucleation-induced processes as, e.g., electrochemical phase formation. Based on this phenomenon, several experimental techniques for electrociystallization studies have been developed (cf. Section 4.2). Before going into further details, however, let us discuss some technical skills that can lead to the preparation of well-developed low dislocation density single crystal faces. 

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The SECM theory for the first-order process was developed [66a] and applied to dissolution of the (100) face of copper sulfate single crystal, while the second-order kinetic model was shown to describe well the dissolution of potassium ferrocyanide trihydrate [66c]. By considering a dislocation-free crystal surface on which dissolution sites are only nucleated above a certain critical value of the undersaturation, one can also model an oscillatory dissolution process [66b]. In all cases, the change in geometry caused by dissolution of the substrate and electrodeposition at the tip was neglected. 

In addition to flame annealing methods for the preparation of single crystal faces of metals with extended atomically smooth terraces [5.10-5.13], the already traditional technique of electrolytic growth of single crystals [5.6-S.9] has remained unrivaled for the preparation of perfect, screw dislocation-free faces or faces with single, isolated screw dislocations. ... 

A perfect crystal face should be completely free of any surface defects. In view of its further application for crystal growth studies, however, a face not intersected by screw dislocations can be considered conditionally as perfect. All other defects have either little or no effect on the growth behavior of the face. To meet this situation, the term quasi-ideal or quasi-perfect" has been introduced for the description of faces free of screw dislocations [5.14]. A quasi-perfect face is characterized by extended atomically smooth terraces separated by monatomic steps and absence of emergence points of screw dislocations. A smooth quasi-perfect face without steps can be described as an intact quasi-perfect face". 

Adjusting the ac/dc ratio to the perfection degree, the face can be grown completely free of screw dislocations. At the moment, when the last dislocation grows out of the face, the electrochemical behavior of the crystal face changes abruptly ... 

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]... 

The kinetics of metal deposition on crystal faces free from screw dislocations is determined by the rate of nucleation /, nuclei cm sec of new lattice nets and their rate of propagation v, cm sec over the face. Almost simultaneously Nielsen/ Chernov/ and Hillig " showed that, depending on the values of these two parameters, two different mechanisms can be distinguished, whereby the extension of the surface plays a significant role (i) a layer by layer growth and (ii) a multinuclear multilayer growth. 

A dislocation free, atomically smooth face of a three-dimensional crystal can grow if after applying the supersaturation two-dimensional nuclei form and spread out to reach the face borders [4.1. 9],... 

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