Point defect: also interstitial

In this section, the phenomenon of point defects, such as vacancies and interstitial, in crystals is briefly introduced. The oxide entropy change (A5) increases when more points defects, also known a imperfections, generate within a crystal. Metal oxides at equilibrium may contain nearly equal numbers of cations and anion vacancies. Thus, the number of point defects (n) producing a minimum free energy change, AG = AHf — TAS, can be modeled by the Arrhenius law [21-23]... 

However, most impurities and defects are Jalm-Teller unstable at high-symmetry sites or/and react covalently with the host crystal much more strongly than interstitial copper. The latter is obviously the case for substitutional impurities, but also for interstitials such as O (which sits at a relaxed, puckered bond-centred site in Si), H (which bridges a host atom-host atom bond in many semiconductors) or the self-interstitial (which often fonns more exotic stmctures such as the split-(l lO) configuration). Such point defects migrate by breaking and re-fonning bonds with their host, and phonons play an important role in such processes. 

Yakov Frenkel showed in 1926 that ideal crystals could not exist at temperatures above the absolute zero. Part of the ions leave their sites under the effect of thermaf vibrations and are accommodated in the interstitial space, leaving vacancies at the sites formerly taken up. Such point defects have been named Frenkel defects. These ideas were developed further by Walter Schottky in 1929, who pointed out that defects will also arise when individual ions or ion pairs are removed from the bulk... 

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... 

N is here the number of lattice defects (vacancies or interstitials) which are responsible for non-stoichiometry. AHfon is the variation of lattice enthalpy when one noninteracting lattice defect is introduced in the perfect lattice. Since two types of point-defects are always present (lattice defect and altervalent cations (electronic disorder)), the AHform takes into account not only the enthalpy change due to the process of introduction of the lattice defect in the lattice, but also that occurring in the Redox reaction creating the electronic disorder. 

Point defects are also highly prominent in the Tl,Pb,Bi/Ba,Sr,-Ca/Cu/O superconductors. Cation vacancies frequently occur. Some T1 is found on Ca sites, and there is evidence for Ca on the Sr/Ba site. Some Bi is found on both Sr and Ca sites. Both oxygen interstitials and vacancies apparently can occur. Present evidence suggests that compounds with the ideal structures and compositions would not be metallic or superconducting. There are also strong indications that these materials at their ideal compositions are in fact too unstable to be prepared. 

There is increasing experimental evidence for the superlattice ordering of vacant sites or interstitial atoms as a result of interactions between them. Superlattice ordering of point defects has been found in metal halides, oxides, sulphides, carbides and other systems, and the relation between such ordering and nonstoichiometry has been reviewed extensively (Anderson, 1974, 1984 Anderson Tilley, 1974). Superlattice ordering of point defects is also found in alloys and in some intermetallic compounds (Gleiter, 1983). We shall examine the features of some typical systems to illustrate this phenomenon, which has minimized the relevance of isolated point defects in many of the chemically interesting solids. 

If the vacancies are subsaturated, the dislocation tends to produce vacancies and therefore acts as a vacancy source. In that case, Eq. 11.5 will still hold, but fiy will be negative and the climb force and climb direction will be reversed. Equation 11.5 also holds for interstitial point defects, but the sign of will be reversed. 

Defects which have extent of only about an atomic diameter also exist in crystals—the point defects. Vacant lattice sites may occur—vacancies. Extra atoms—interstitials—may be inserted between regular crystal atoms. Atoms of the wrong chemical species—impurities—also may be present. 

Crystals contain two major categories of defect point defects and line defects. Point defects occur where atoms are missing (vacancies) or occupy the interstices between normal sites (interstitials) foreign atoms are also point defects. Line defects, or dislocations, are spatially extensive and involve disturbance of the periodicity of the lattice. 

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). 

The type and concentration of defects in solids determine or, at least, affect the transport properties. For instance, the -> ion conductivity in a crystal bulk is usually proportional to the -> concentration of -> ionic charge carriers, namely vacancies or interstitials (see also -> Nernst-Einstein equation). Clustering of the point defects may impede transport. The concentration and -> mobility of ionic charge carriers in the vicinity of extended defects may differ from ideal due to space-charge effects (see also - space charge region). 

The doped semiconductor materials can often be considered as well-characterized, diluted solid solutions. Here, the solutes are referred to as point defects, for instance, oxygen vacancies in TiC - phase, denoted as Vq, or boron atoms in silicon, substituting Si at Si sites, Bj etc. See also -> defects in solids, -+ Kroger-Vink notation of defects. The atoms present at interstitial positions are also point defects. Under stable (or metastable) thermodynamic equilibrium in a diluted state, - chemical potentials of point defects can be defined as follows ... 

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