Point defect definition

These examples indicate that it is necessary to keep the possible effect of point defects on bulk and mechanical properties in mind. Although less definitive than electronic and optical properties, they may make the difference in the success or failure of device operation. 

A unit, or perfect, dislocation is defined by a Burgers vector which regenerates the structure perfectly after passage along the slip plane. The dislocations defined above with respect to a simple cubic structure are perfect dislocations. Clearly, then, a unit dislocation is defined in terms of the crystal structure of the host crystal. Thus, there is no definition of a unit dislocation that applies across all structures, unlike the definitions of point defects, which generally can be given in terms of any structure. 

VO2 and Ti02) leads to the formation of extended defects, i.e. CS planes, rather than to point defects. In the early literature reports, the definition of CS involved the removal of a complete sheet of anion sites to form an extended CS plane defect (Wadsley 1964, Anderson and Hyde 1967). Consequently, the role played by true point defects in non-stoichiometric oxides was not obvious from these earlier reports and answer to this was sought by Anderson (1970, 1971), Anderson et al (1973) (1.13.2). However, although this definition of CS is a convenient one, the situation is not so straightforward as we now demonstrate. 

The second type of impurity, substitution of a lattice atom with an impurity atom, allows us to enter the world of alloys and intermetallics. Let us diverge slightly for a moment to discuss how control of substitutional impurities can lead to some useful materials, and then we will conclude our description of point defects. An alloy, by definition, is a metallic solid or liquid formed from an intimate combination of two or more elements. By intimate combination, we mean either a liquid or solid solution. In the instance where the solid is crystalline, some of the impurity atoms, usually defined as the minority constituent, occupy sites in the lattice that would normally be occupied by the majority constituent. Alloys need not be crystalline, however. If a liquid alloy is quenched rapidly enough, an amorphous metal can result. The solid material is still an alloy, since the elements are in intimate combination, but there is no crystalline order and hence no substitutional impurities. To aid in our description of substitutional impurities, we will limit the current description to crystalline alloys, but keep in mind that amorphous alloys exist as well. 

Figure 5.1 Point defects in ionic solids Schottky defect, vacancy pair, Frenkel defect and aliovalent impurity (for definitions see Section 5.2).

Let us now discuss some details of practical relevance. From the Gibbs phase rule, it is evident that crystals consisting of only one component (A) become nonvariant by the predetermination of two thermodynamic variables, which for practical reasons are chosen to be Pand T. In these one-component systems, it is easy to recognize the (isobanc) concentration dependence of the point defects on temperature. From the definition of the vacancy chemical potential for sufficiently small vacancy mole fractions Nv, namely //v = /A (P, T) + RT- In Vv, together with the condition of equilibrium with the crystal s inerL surroundings (gas, vacuum), one directly finds... 

Figure 18. In the same way as the concentration of protonic charge carriers characterizes die acidity (basicity) of water and in the same way as the electronic charge carriers characterize the redox activity, the concentration of elementary ionic charge carriers, that is of point defects, measure the acidity (basicity) of ionic solids, while associates constitute internal acids and bases. The definition of acidity/basicity from the (electrochemical potential of the exchangeable ion, and, hence, of the defects leads to a generalized and thermodynamically firm acid-base concept that also allows to link acid-base scales of different solids.77 (In order to match the decadic scale the levels are normalized by In 10.) (Reprinted from J. Maier, Acid-Base Centers and Acid-Base Scales in Ionic Solids. Chem. Eur. J. 7, 4762-4770. Copyright 2001 with permission from WILEY-VCH Verlag GmbH.)...

The first question to address is the definition of a defect in an amorphous material. In a crystal any departure from the perfect crystalline lattice is a defect, which could be a point defect, such as a vacancy or interstitial, an extended defect, such as a dislocation or stacking fault, or an impurity. A different definition is required in an amorphous material because there is no perfect lattice. The inevitable disorder of the random network is an integral part of the amorphous material and it is not helpful to think of this as a collection of many defects. By analogy with the crystal one can define a defect as a departure from the ideal amorphous network which is a continuous... 

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. 

In compound crystals, balanced-defect reactions must conserve mass, charge neutrality, and the ratio of the regular lattice sites. In pure compounds, the point defects that form can be classified as either stoichiometric or nonstoichiometric. By definition, stoichiometric defects do not result in a change in chemistry of the crystal. Examples are Schottky (simultaneous formation of vacancies on the cation and anion sublattices) and Frenkel (vacancy-interstitial pair). 

In these equations, r is a so-called "partition coefficient , co is a degeneracy, k is Boltzsmann s constant, and T is in degrees Kelvin. The first equation in 2.5.3. is a statistical mechanical definition of work, whereas the last two describe total energy states. Having these definitions and equations allows us to define point defects firom a Statistical Mechanical viewpoint. 

In the majority of mechanical applications of materials, their surfaces experience contact with another material and take the external load before the bulk of the material is influenced. In some cases, surface interactions influence the bulk (e.g., propagation of cracks dislocations or point defects from the surface in depth). In many cases, only the outermost surface layer is affected by the surface contact with no detectable changes in the bulk of the material. This is like a storm that is frightening and destructive on the ocean surface, but does not have any influence on deep-water life. We are primarily concerned in this review with that kind of interaction. The surface layer thickness affected by external mechanical forces ranges from nanometers to microns. Thus, in our case, the definition of surface is different from the one used by surface scientists, that is, physicists and chemists. We introduce here an engineering definition of surface the outermost layer of the material that can be influenced by physical and/or chemical interaction with other surfaces and/or the environment. In this chapter, we consider only mechanical effects, but both mechanical and chemical interactions are possible and their synergy can lead to mechanochemical alteration of a material surface. 

With respect to standard molecular-cluster techniques, this approach has some attractive features explicit reference is made to the HF LCAO periodic solution for the unperturbed (or perfect) host crystal. In particular, the self-embedding-consistent condition is satisfied, that is, in the absence of defects, the electronic structure in the cluster region coincides with that of the perfect host crystal there is no need to saturate dangling bonds the geometric constraints and the Madelung field of the environment are automatically included. With respect to the supercell technique, this approach does not present the problem of interaction between defects in different supercells, allows a more flexible definition of the cluster subspace, and permits the study of charged defects. The perturbed-cluster approach is implemented in the computer code EMBEDOl [703] and applied in the calculations of the point defects both in the bulk crystal, [704] and on the surface [705]. The difficulties of this approach are connected with the lattice-relaxation calculations. 

The regular atoms on their normal sites and the point defects occupy particular sites in the crystal structure and these have been termed structural elements by Kroger, Stieltjes, and Vink (1959) (see also Kroger (1964)). As discussed in Chapter 2, the rules for writing defect reactions require that a definite ratio of sites is maintained due to the restraint of the crystal structure of the compounds. Thus if a normal site of one of the constituents in a binary compound MO is created or annihilated, a normal site of the other constituent must simultaneously be created or annihilated. 

The concentrations of point defects, and therefore the direction and degree of nonstoichiometry, are determined by the thermodynamic activities of external phases in equilibrium with the nonstoichiometric compound. For example, the concentration of X vacancies may be controlled by maintaining the crystal in equilibrium with another phase containing X at a definite activity. The external phase may be X2 gas (e.g., O2). The equation for formation of X vacancies then may be written... 

---