Charges on Defects

The position of a defect that has been substituted for another atom in the structure is represented by a subscript that is the chemical symbol of the atom normally found at the site occupied by the defect impurity atom. The impurity is given its normal chemical symbol, and the site occupied is written as a subscript, using the chemical symbol for the atom that normally occupies the site. Thus, an Mg atom on a Ni site in NiO would be written as MgNi. The same nomenclature is used if an atom in a crystal occupies the wrong site. For example, antisite defects in GaN would be written as GaN and NGa. 

Interstitial positions, positions in a crystal not normally occupied by an atom, are denoted by the subscript i. For example, F would represent an interstitial fluorine atom in, say, a crystal of fluorite, CaF2. 

It is possible for one or more lattice defects to associate with one another, that is, to cluster together. These are indicated by enclosing the components of such a cluster in parentheses. As an example, (VMVX) would represent a defect in which a vacancy on a metal site and a vacancy on a nonmetal site are associated as a vacancy pair. 

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To illustrate exactly how these mles work, a number of examples follow. In the first, the formation of antisite defects, a simple example that does not involve changes in atom numbers or charges on defects, is described. Secondly, two reactions involving oxides, nickel oxide and cadmium oxide, both of which are nonstoichio-metric, but for opposite reasons, indicate how to deal with a solid-gas interaction... 

FIGURE 12.16 Schematic showing local charge on defects in rocksalt. (a) A comer is always charged, (b and c) possibilities for jog on an edge dislocation. 

From these calculated displacements, the contributions to the energy from the ions in re 2a can be determined. Finally, it is necessary to determine the contribution from the io] region 2b. As we have mentioned, these are not included explicitly but are considers polarise due to the electrostatic field from the total charge on the defect. This contribr is gi en by the following summation ... 

Following the concepts of H. Helmholtz (1853), the EDL has a rigid structnre, and all excess charges on the solntion side are packed against the interface. Thus, the EDL is likened to a capacitor with plates separated by a distance 5, which is that of the closest approach of an ion s center to the surface. The EDL capacitance depends on 5 and on the value of the dielectric constant s for the medium between the plates. Adopting a value of 5 of 10 to 20 nm and a value of s = 4.5 (the water molecules in the layer between the plates are oriented, and the value of e is much lower than that in the bulk solution), we obtain C = 20 to 40 jjE/cm, which corresponds to the values observed. However, this model has a defect, in that the values of capacitance calculated depend neither on concentration nor on potential, which is at variance with experience (the model disregards thermal motion of the ions). 

In this equation, N is the number of ions per cm3, q is the charge on the ion, and a is a factor that varies from about 1 to 3 depending on the mechanism of diffusion. Because conductivity of a crystal depends on the presence of defects, studying conductivity gives information about the presence of defects. The conductivity of alkali halides by ions has been investigated in an experiment illustrated in Figure 8.11. 

What is the "effective charge on a defect What is an antisite defect ... 

This defect is therefore neutral in terms of effective charge. The same could be said of a neutral lithium atom introduced into an interstitial site in titanium disulfide, TiS2, which would be written Lip However, it is sometimes important to emphasize that the defect is neutral in terms of effective charge. This is made clear by the use of a superscript x. Thus a K+ ion substituted for a Na+ ion could be written K a when the effective charge situation needs to be specified. Similarly, an interstitial Li atom could be represented as Lif to emphasize the lack of an effective charge on the defect when it is essential to do so. 

The effective charges on an ionic defect can be considered to be linked to the defect by an imaginary bond. If the bond is weak, the effective charge can be liberated, say by thermal energy, so that it becomes free to move in an applied electric field and so contribute to the electronic conductivity of the material. Whether the effective charge on a defect is considered to be strongly associated with the defect or free depends upon the results obtained when the physical properties of the solid are measured. 

Calculations are now carried out routinely using a wide variety of programs, many of which are freely available. In particular, the charge on a defect can be included so that the formation energies, interactions, and relative importance of two defects such as a charged interstitial as against a neutral interstitial are now accessible. Similarly, computation is not restricted to intrinsic defects, and the energy of formation of... 

Although the high-temperature superconducting phases are formed from insulating materials by the introduction of defects, the precise relationship between dopant, structure, and properties is not fully understood yet. For example, in most of the cuprate phases it is extremely difficult to be exactly sure of the charges on the individual ions, and because of this the real defect structures are still uncertain. 

The interaction between a charged point defect and neighboring magnetic ions in magnetically doped thin films has been described in terms of a defect cluster called a bound magnetic polaron (Fig. 9.5a). The radius of a bound magnetic polaron due to an electron located on the defect, r, is given by... 

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