Point defect: also combinations

The notion of point defects in an otherwise perfect crystal dates from the classical papers by Frenkel88 and by Schottky and Wagner.75 86 The perfect lattice is thermodynamically unstable with respect to a lattice in which a certain number of atoms are removed from normal lattice sites to the surface (vacancy disorder) or in which a certain number of atoms are transferred from the surface to interstitial positions inside the crystal (interstitial disorder). These forms of disorder can occur in many elemental solids and compounds. The formation of equal numbers of vacant lattice sites in both M and X sublattices of a compound M0Xft is called Schottky disorder. In compounds in which M and X occupy different sublattices in the perfect crystal there is also the possibility of antistructure disorder in which small numbers of M and X atoms are interchanged. These three sorts of disorder can be combined to give three hybrid types of disorder in crystalline compounds. The most important of these is Frenkel disorder, in which equal numbers of vacancies and interstitials of the same kind of atom are formed in a compound. The possibility of Schottky-antistructure disorder (in which a vacancy is formed by... 

Point defects have zero dimension line defects, also known as dislocations, are onedimensional and planar defects such as surface defects and grain boundary defects have two dimensions. These defects may occur individually or in combination. 

Intrinsic point defects are deviations from the ideal structure caused by displacement or removal of lattice atoms [106,107], Possible intrinsic defects are vacancies, interstitials, and antisites. In ZnO these are denoted as Vzn and Vo, Zn and 0 , and as Zno and Ozn, respectively. There are also combinations of defects like neutral Schottky (cation and anion vacancy) and Frenkel (cation vacancy and cation interstitial) pairs, which are abundant in ionic compounds like alkali-metal halides [106,107], As a rule of thumb, the energy to create a defect depends on the difference in charge between the defect and the lattice site occupied by the defect, e.g., in ZnO a vacancy or an interstitial can carry a charge of 2 while an antisite can have a charge of 4. This makes vacancies and interstitials more likely in polar compounds and antisite defects less important [108-110]. On the contrary, antisite defects are more important in more covalently bonded compounds like the III-V semiconductors (see e.g., [Ill] and references therein). 

Very recently, based on a combined use of chemical evidence, IR and EPR spectroscopies, as well as of ab initio calculations it has been suggested that oxygen vacancies form preferentially at low coordinated sites (steps, edges, comers) [133] it has also been observed that the nature of the point defects at the surface changes dramatically depending on the pretreatment conditions [135]. 

In atomic or molecular sohds, common types of point defects are the absence of an atom or molecule from its expected position at a regular lattice site (a vacancy), or the presence of an atom or molecule in a position which is not on the regular lattice (an interstitial). In ionic solids, these point defects occur in two main combinations. These are Schottky defects, in which there are equal numbers of cation and anion vacancies within the crystal, and Frenkel defects, in which there are cation vacancies associated with an equal number of "missing" cations located at non-lattice, interstitial positions. Both are illustrated in Figure 1.1. Point defects are also found in association with altervalent impurities, dislocations, etc., and combinations of vacancies with electrons or positive holes give rise to various types of colour centres (see below). 

Zero-dimensional defects or point defects conclude the list of defect types with Fig. 5.87. Interstitial electrons, electron holes, and excitons (hole-electron combinations of increased energy) are involved in the electrical conduction mechanisms of materials, including conducting polymers. Vacancies and interstitial motifs, of major importance for the explanation of diffusivity and chemical reactivity in ionic crystals, can also be found in copolymers and on co-crystallization with small molecules. Of special importance for the crystal of linear macromolecules is, however, the chain disorder listed in Fig. 5.86 (compare also with Fig. 2.98). The ideal chain packing (a) is only rarely continued along the whole molecule (fuUy extended-chain crystals, see the example of Fig. 5.78). A most common defect is the chain fold (b). Often collected into fold surfaces, but also possible as a larger defect in the crystal interior. Twists, jogs, kinks, and ends are other polymer point defects of interest. 

As is seen, the approach described combines both superceU and cycUc-cluster models of the defective crystal and differs from the traditional supercell calculations by an attempt to exclude in stage 3 the spnrious point-defect periodicity. This exclusion allows us formally to escape periodic repeating of the crystalUne lattice relaxation around the point defect. Furthermore, the different charge states of the point defect could be also considered in stage 3 without principal difficulties since in CCM the charge is not periodically repeated over the lattice. 

Thus, the growth of an external oxide scale by the reaction between a pure metal or a metallic alloy and a gaseous or liquid oxidant phase at high temperature is also a combination of diffusion processes and interfacial reactions, and Fig. 2.1 also applies to such corrosion processes that are formally similar to solid-state reactions in poly-phase and multi-constituent systems. Such a similarity will be considered to extend the treatment of the Kirkendall effect for two-phase diffusion couples to the growth of an oxide scale on a pure metal or on an alloy. The roles of interfaces will be analysed more particularly in relation to some specific topics related to oxide scaling processes such as interface displacement, growth stresses and injection of point defects (vacancy or interstitial). 

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