Koch-Cohen cluster

Single crystal X-ray diffraction and neutron diffraction studies of a quenched sample indicated that the vacancies were not spread statistically over the structure, but were arranged in clusters (Koch/Cohen clusters) consisting of 13 vacancies and four... 

FIGURE 5.26 The Koch-Cohen cluster illustrated with the back and front planes cut away for clarity. The central section with four tetrahedrally coordinated Fe ions is picked out in bold. 

Figure 5.44 depicts the central section of a possible defect cluster for FeO. (a) Determine the vacancy interstitial ratio for this cluster, (b) Assuming that this section is surrounded by Fe ions and oxide ions in octahedral sites as in the Koch-Cohen cluster, determine the formula of a sample made totally of such clusters, (c) Determine the numbers of Fe and Fe ions in octahedral sites. 

Figure 5.14 Koch-Cohen cluster of defects in (wiistite.) Hatched circles...

The ions in the tetrahedral sites have been shown by Mossbauer spectroscopy to have an oxidation state of +3. In a way similar to the uranium oxide structure, the distance between the closest octahedral holes and the tetrahedral hole is too short to allow both sites to be occupied simultaneously. In this case, four vacancies on the octahedral sites are created for every interstitial tetrahedral ion, as shown in Figure 6.8. This type of cluster occurs at low values of x. As x increases, larger clusters form in which there are thirteen vacancies and four interstitial ions. This is called a Koch-Cohen cluster (Figure 6.9). 

Defects often cluster together. This can occur randomly, as in Koch-Cohen clusters, or in an ordered way by crystallographic shear to form, for example, Mo,gO,g. 

The defect structure of Fei O with the NaCl-type structure had been estimated to be a random distribution of iron vacancies. In 1960, Roth confirmed, by powder X-ray diffraction, that the defect structure of wiistite quenched from high temperatures consists of iron vacancies (Vp ) and interstitial iron (Fcj) (there are about half as many FCj as Vpe). This was a remarkable discovery in the sense that it showed that different types of crystal defects with comparable concentrations are able to exist simultaneously in a substance, Roth also proposed a structure model, named a Roth cluster, shown in Fig. 1.84. Later this model (defect complex = vacancy -F interstitial) was verified by X-ray diffraction on a single crystal and also by in-situ neutron diffraction experiments. Moreover, it has been shown that the defect complex arranges regularly and results in a kind of super-structure, the model structure of which (called a Koch-Cohen model) is shown in Fig. 1.85 together with the basic structures (a) and (b). 

Fig. 1.85 Defect complexes of wustite. (a) Basic structure (Roth cluster) (b) edge-sharing tetrahedra (6 2 complex) (c) cornersharing tetrahedra (Koch-Cohen complex).

In the case of large deviations from stoichiometry, simple associates or more extended defect clusters can be formed. One example is the Koch-Cohen defect cluster in nonstoichi-ometric wiistite (FeO). This defect cluster bears a strong resemblance to the structure of Fc304. One can think of nonstoichiometric FeO as fragments of FCjOj intergrown in the rock salt stmcture of FeO. Another well-known cluster in the oxide-interstitial defect cluster is... 

Figure 1.11. Schematic diagrams of (a) and (b) Fei j O point defect clusters (after Koch and Cohen 1969) (c) clustering in fluorite-type structures and (d) the Cap2 structure.

Fig. 23. Cation vacancy cluster in Fco 902O- Cations in tetrahedral interstitial sites are associated with the cluster. One octant of the defect is shown. The defect consists of 13 octahedral vacancies (open circles) and four associated tetrahedral cations (shaded circles). The large and small filled circles represent, respectively, oxygen and iron ions in octahedral sites. The ions surrounding the defect are displaced as indicated by the arrows. Fe " ions in the vicinity of the defect and in the tetrahedral sites neutralize the excess negative charge. From Koch and Cohen. ...

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