Indexing crystal faces

Using single crystals it has been shown that different low-index crystal faces see Section 20) exhibit different corrosion rates. However, the relative corrosion rate of the different faces varies with the environment and these structural effects are of little practical significance. On the other hand, the fact that polycrystal grains of different crystallographic orientation may corrode at different rates, is of some importance. 

The temperature behavior of low446,491,503 558 as well as high Miller index crystal faces of Au447,448 has been examined in 0.01 M perchloric acid solutions. For all gold surfaces studied, C, was found to decrease and Ea=Q moved to less negative values with increasing t 446-448 491503-558... 

Figure 3.16. Some simple defects found on a low-index crystal face 1, the perfect flat face, a terrace 2, an emerging screw dislocation 3, the intersection of an edge dislocation with the terrace 4, an impurity adsorbed atom 5, a monatomic step in the surface, a ledge 6, a vacancy in the ledge 7, a kink, a step in the ledge 8 an adatom of the same type as the bulk atoms 9, a vacancy in the terrace 10, an adatom on the terrace. (From Ref. 12, with permission from Oxford University Press.)...

With regard to the attachment and detachment energies, the corners of a crystal or a rough interface that is constructed by kinks alone are sites where the process proceeds most quickly, whereas the low-index crystal faces, corresponding to smooth interfaces, represent the direction with the minimum rate of normal growth and dissolution. As a result, if a single crystalline sphere is dissolved in an isotropic environmental phase, a dissolution form bounded by both flat and curved crystal faces appears. This is called the dissolution form, which is not the same as the growth form. 

Low Miller index surfaces of metallic single crystals are the most commonly used substrates in LEED investigations. The reasons for their widespread use are that they have the lowest surface free energy and therefore are the most stable, have the highest rotational symmetry and are the most densely packed. Also, in the case of transition metals and semiconductors they are chemically less reactive than the higher Miller index crystal faces. 

Fig. 1. Surface structure often found on low-index crystal faces. 1, A terrace perfectly flat crystal face. 2, An emerging screw dislocation. 3, The intersection of an edge dislocation with a terrace. 4, A ledge or monatomic step, 5. A kink a step in a ledge. 6, A vacancy in a ledge. 7, An adsorbed growth unit on a ledge.

When a polycrystalline Pt wire electrode is electropolished and annealed, faceting may be expected to produce essentially a statistical mixture of the <100>, <110>, and <111> low-index crystal faces as its surface. To estimate a for such a surface, we must identify a structure-related pattern of adsorption sites for each type of face and weight the resultant site densities appropriately. 

A single crystal surface exhibits terraces (T) with low Miller index crystal faces and high surface density. They are separated by ledges (L) which may have kinks (K). A terrace between two ledges is a step. Defects on terraces consist of vacancies or adsorbed atoms. Thus the smooth surface may indeed be rough on an atomic scale. This model is called as TLK model (Fig. 2.6). The systematic... 

There have been a number of diverse applications of EAs within crystallography reported in the literature. Heavy-atom replacement is a common procedure for phase assignment in protein crystallography. Chang and Lewis use a GA to search for heavy-atom sites that are consistent with the observed Patterson function difference. The coordinates of putative heavy-atom sites were encoded as binary numbers on the GA string. Another application is detailed by Tam and Compton, who successfully index crystal faces using a GA. Face indices were encoded in a binary lookup table and the best results were obtained using two GA runs, with the first... 

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