Diffusion of point defects

Let us finally mention that in polycrystalline samples, Nabarro-Herring(-Coble) creep occurs as already introduced in Section 14.3.2. The Nabarro-Herring creep rate is inversely proportional to the square of the average grain size, l2, if volume diffusion of point defects prevails. It is inversely proportional to /3 if grain boundary diffusion determines the transport. 

When GBS is accommodated by some of the mechanisms involving dislocation movement or diffusion of point defects, the grains retain almost the original size and shape even after large deformations. This GBS, as the primary mechanism for deformation, is the basis for the high ductility exhibited... 

Ungar P. J., HaUcioglu T. and Tiller W. A., Free Energies, Structures and Diffusion of Point Defects... 

Zakrzewska found that titanium dioxide doped with Nb and Cr should be considered as a bulk sensor. Its performance was governed by the diffusion of point defects, i.e. very slow diffusion of Ti vacancies for Ti02. 9.5 at% of Nb and fast diffusion of oxygen vacancies in the case of HOt. 2.5 at% Cr sensor. The corresponding response times were 55 min for TiOT. 9.5 at% of Nb and 20 s for HOt. 2.5 at% Cr [292]. 

It is necessary to emphasize that the effect of uphill diffusion should be distinguished from the directional diffusion of point defects that can also take place under conditions of a homogeneous stressed state (diffusive creep). Nevertheless, the indicated mechanisms of plastic deformation have a lot in common, because they both are diffusive mechanisms of plastic deformation of crystalline solids. 

Diffusion occurs by atomic defects moving through the crystal it is not a continuum process. We thus analyze diffusion as a statistical process. This is the kinetics part of the story. Diffusion of point defects is the key to understanding their properties. There are four basic mechanisms that can, in principle, occur these are illustrated in Figure 11.10. 

Diffusion of oxygen in oxidation scales occurs along grain boundaries. Corrosion of metals is controlled by formation and diffusion of point defects in the ceramic. Corrosion of polycrystalline ceramics also occurs most quickly along grain boundaries. 

There are also applications of quantum theory for instance in the onset of a failure in a material. The failure starts on the atomic scale when an interatomic bonding is stressed beyond its yield-stress threshold and breaks. The initiation and diffusion of point defects in crystal lattice turn out to be a starting point of many failures. These events occur in a stress field at certain temperatures. The phenomena of strain, fatigue crack initiation and propagation, wear, and high-temperature creep are of particular interest The processes of nucleation and diffusion of vacancies in the crystal lattice determines the material behavior at many operation conditions. 

When accommodated by some of the mechanisms involving dislocation movement or the diffusion of point defects, GBS forms the basis of the structural superplastic behavior of these materials (see Section 15.2). By taking advantage of the processes involved in superplasticity, it is possible to join ceramics super-plastically. For example, when two pieces of the same ceramics in contact are deformed within a superplastic regime (i.e., as soon as GBS is activated), the grains of one part interpenetrate those of the other part. This produces a rapid and perfect junction of the two, in such a way that a shorter time and a lower temperature can be used than are commonly required in other conventional process for ceramics joining [90]. 

Wagner s oxidation theory assumes that volume diffusion of point defects limits the growth of oxide layers. However, other transport mechanisms are possible, notably grain boundary diffusion. At relatively low temperatures, Tmelting temperature of the oxide, this mechanism contributes considerably to the transport, and the rate of oxidation exceeds that calculated using Wagner s theory. The rate of grain boundary diffusion depends on the microstructure of the oxide films formed, which is difficult to control [8]. For this reason, measured oxidation rates are often not well reproducible. 

D. Yamamoto, T. Uchihashi, N. Kodera, and T. Ando, Anisotropic diffusion of point defects in two-dimensional crystal of streptavidin observed by high-speed atomic force microscopy. Nanotechnology, 19, 384009 (2008). 

Most phenomena occur at the internal interface (A/B) however, in the case of decomposition, it is necessary to evacuate gas through layer B, which involves necessarily a diffusion zone (see Chapter 13). If there is gaseous emission, the process of adsorption-desorption is regarded as always present whereas in a gas-solid contact, it is necessary to consider the desorption of produced gas, located either on the surface of A if the gas diffuses through pores of B or on the stuface of B if the gas is produced at this interface after diffusion of point defects in B. 

Examine where this determining step can be located. It may be either at the internal interface or at the external one, but in these two cases, the space function is independent of time. It remains only the possibihty of difihsion as rate-determining step. This can be either a diffusion of point defects through the layer of formed sulfide or a diffusion of vacancies in the metal. It is indeed known that, for plates, a mode limited by a diffusion through thick layers leads to the parabolic law. 

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