Point defect Subject

Dislocation theory as a portion of the subject of solid-state physics is somewhat beyond the scope of this book, but it is desirable to examine the subject briefly in terms of its implications in surface chemistry. Perhaps the most elementary type of defect is that of an extra or interstitial atom—Frenkel defect [110]—or a missing atom or vacancy—Schottky defect [111]. Such point defects play an important role in the treatment of diffusion and electrical conductivities in solids and the solubility of a salt in the host lattice of another or different valence type [112]. Point defects have a thermodynamic basis for their existence in terms of the energy and entropy of their formation, the situation is similar to the formation of isolated holes and erratic atoms on a surface. Dislocations, on the other hand, may be viewed as an organized concentration of point defects they are lattice defects and play an important role in the mechanism of the plastic deformation of solids. Lattice defects or dislocations are not thermodynamic in the sense of the point defects their formation is intimately connected with the mechanism of nucleation and crystal growth (see Section IX-4), and they constitute an important source of surface imperfection. 

Materials that contain defects and impurities can exhibit some of the most scientifically interesting and economically important phenomena known. The nature of disorder in solids is a vast subject and so our discussion will necessarily be limited. The smallest degree of disorder that can be introduced into a perfect crystal is a point defect. Three common types of point defect are vacancies, interstitials and substitutionals. Vacancies form when an atom is missing from its expected lattice site. A common example is the Schottky defect, which is typically formed when one cation and one anion are removed from fhe bulk and placed on the surface. Schottky defects are common in the alkali halides. Interstitials are due to the presence of an atom in a location that is usually unoccupied. A... 

The vast subject of dislocations, particularly with respect to mechanical properties, will not be considered in this book, and only a few aspects of dislocations, especially interactions with point defects, will be explored. 

A dislocation is generally subjected to another type of force if nonequilibrium point defects are present (see Fig. 11.2). If the point defects are supersaturated vacancies, they can diffuse to the dislocation and be destroyed there by dislocation climb. A diffusion flux of excess vacancies to the dislocation is equivalent to an opposite flux of atoms taken from the extra plane associated with the edge dislocation. This causes the extra plane to shrink, the dislocation to climb in the +y direction, and the dislocation to act as a vacancy sink. In this situation, an effective osmotic force is exerted on the dislocation in the +y direction, since the destruction of the excess vacancies which occurs when the dislocation climbs a distance Sy causes the free energy of the system to decrease by 8Q. The osmotic force is then given by... 

Point Defect Generation During Phosphorus Diffusion. At Concentrations above the Solid Solubility Limit. The mechanism for the diffusion of phosphorus in silicon is still a subject of interest. Hu et al. (46) reviewed the models of phosphorus diffusion in silicon and proposed a dual va-cancy-interstitialcy mechanism. This mechanism was previously applied by Hu (38) to explain oxidation-enhanced diffusion. Harris and Antoniadis (47) studied silicon self-interstitial supersaturation during phosphorus diffusion and observed an enhanced diffusion of the arsenic buried layer under the phosphorus diffusion layer and a retarded diffusion of the antimony buried layer. From these results they concluded that during the diffusion of predeposited phosphorus, the concentration of silicon self-interstitials was enhanced and the vacancy concentration was reduced. They ruled out the possibility that the increase in the concentration of silicon self-interstitials was due to the oxidation of silicon, which was concurrent with the phosphorus predeposition process. 

While the preceding statements apply to the bulk of the crystal, the surface of the crystal is subject to the same constraints with some additional complexity. Specifically, because different point defects are likely to have different free energies of formation, there is an enhanced concentration of one of the two defects in the near surface region and a compensating layer of charge on the... 

Catalytic applications of ceria and ceria-based mixed oxides depend primarily upon the nature and concentration of the defects present in the material. Although experimental techniques are available for the study of these defects, the characterization of their physical properties at the atomic level is often very difficult. The most important point defects in ceria are oxygen vacancies, reduced Ce centers and dopant impurities. The formation energy of such defects and the energetics of their mutual interactions within the bulk oxide have been the subject of several computational studies. 

An alternative perspective on the subject of point defects to the continuum analysis advanced above is offered by atomic-level analysis. Perhaps the simplest microscopic model of point defect formation is that of the formation energy for vacancies within a pair potential description of the total energy. This calculation is revealing in two respects first, it illustrates the conceptual basis for evaluating the vacancy formation energy, even within schemes that are energetically more accurate. Secondly, it reveals additional conceptual shortcomings associated with... 

Of course, the results given above are advanced not so much as the final word on the subject of point defect formation energies, but rather to illustrate the... 

Point Defects and Diffusion by C. P. Flynn, Clarendon Press, Oxford England, 1972. A definitive treatise on the subject of point defects and diffusion as seen from the perspective which predates the routine use of first-principles simulations to inform models of diffusion. 

Atom Movements by Jean Philibert, Les Editions de Physique, Les Ulis Cedex A Prance, 1991. My personal favorite on the subject of diffusion. This book is filled with both descriptive and quantitative accounts of point defects and their motion. 

Some of the transition metal-oxide systems have become a subject of intensive research in the last two decades. The relation between the parabolic oxidation kinetics and the predominating point defect in the oxide was verified. To discuss the high-temperature oxidation mechanism of non-noble metals it is appropriate to start with a brief survey of some of the literature on the point defect dependent properties of, for example, nickel oxide. 

The mechanism by which defects concentrate impurities is a subject of research that has important bearing on crystal growth, especially related to formation of crystalline materials for use in the electronics industry. Besides imperfections associated with isolated impurities (i.e., point defects), the other major types of structural defects are line defects (both edge and screw), planar defects, grain boundaries, and structural disorder (Wright 1989). The connection between defect formation and impurity uptake is evident in two of these defects in particular the edge defect and point defect. 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

The measured properties of polycrystalline ceramics are greatly influenced by the microstructure of the material. Of particular importance are the grain size of the crystallites, porosity, voids or gas bubbles within the ceramic and any impurity phases present. In addition, chemical defects such as point defects and mobile charge carriers within grains and the physics and chemistry of the grain botmdaries will all have an influence on the measured properties of the solid. Because of this, ceramics are subjected to carefully controlled fabrication routes and the sintering temperature and time have a considerable effect upon the measured properties (Figure 6.3c). 

---