Cubic structure vacancies

The path that the diffusing atom takes will depend upon the structure of the crystal. For example, the 100 planes of the face-centered cubic structure of elements such as copper are identical to that drawn in Figure 5.7. Direct diffusion of a tracer atom along the cubic axes by vacancy diffusion will require that the moving atom must squeeze between two other atoms. It is more likely that the actual path will be a dog-leg, in <110> directions, shown as a dashed line on Figure 5.7. 

The unit cell of pyrochlore can be considered as eight CaF2-type cells stacked as octants of a cube. There are two types of cells shown in Figure 6.21. They differ in the position of the oxygen vacancy and the relative positions of atoms A and B. Only two of the eight octants are shown to make it easier to visualize the relative positions of the three types of atoms. The octant on the lower left is type I and the other one is type II. There are four of each type, and they are not in adjacent cells. Atoms A and B are in ccp layers (a face-centered cubic structure) with oxygens in T layers. The type I cube has A ions located on face... 

For the stoichiometry U02.25, the structure can be simplified to an arrangement of4 3 2 clusters [25].These clusters are composed of four interstitial oxygen atoms in the (110) direction with three oxygen vacancies and two interstitial oxygen atoms in the (111) direction. The addition of this oxygen causes the expansion of the cubic structure so that the cell dimension for U4O9 is approximately four times that of UO2 [6], although the cubic structure is retained. 

Brauer ( ) reported a homogeneity range of x = 0.89-1.04 for NbO. NbO(cr) has a cubic structure, a NaCl type with ordered vacancies (j[3, 14). Further information may be found in the review of the Nb-0 system by Elliott (15). ... 

Fig. 2. Stabilised cubic structure of oxide electrolyte, showing a substituting cation and compensating anion site vacancy.

The unique property of solid solutions on the basis of zirconium oxide is oxygen-ionic conductivity and it is due to their crystal structure type. The solid solution of stabilized zirconium oxide has a cubic structure of fluorite type with anionic vacancies that leads to electrical conductivity abrupt increase at temperature increase of > 600° C. 

The implication is that it is possible to determine the diffusion coefficient from the easier measurement of ionic conductivity. However, the assumption that both processes utilise exactly the same mechanism is important In general, this is not true. In such a case, the relationship is slightly different from that in Equations (7.15) and (7.16) and depends on the details of the diffusion mechanism. For vacancy diffusion in a cubic structure. 

Point defects are particularly important in ceramics because of the role they can play in determining the properties of a material. The entire semiconductor industry is possible because of minute concentrations of point defects that are added to Si the dopants determine if the Si is n-type, p-type, or semi-insulating they determine the electrical properties. Solid-oxide fuel cells work because of the large concentrations of oxygen vacancies present the vacancies provide fast ion conduction pathways. CZ is cubic because of the presence of point defects that stabilize the cubic structure. 

Ionic conductivity is the transport of cations and/or anions across the perovskite under the influence of an electric field. As with diffusion, for ionic conductivity of cations and anions in perovskites to occur the structure must either contain open regions or a significant population of vacancies on the appropriate sublattice to allow ionic movement. Substitution is again widely used to create vacancies in perovskites with approximately cubic structures so as to increase conductivity. A further requirement, for strictly ionic conductivity, is the absence of cations with a variable valence. In cases where variable valence cations are present, electronic conductivity may also occur and in such cases will invariably dominate, in magnitude, the ionic conductivity (Sections 5.4 and 5.5). 

---