Point defect: also Vacancy

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]... 

Two point defects may aggregate to give a defect pair (such as when the two vacanc that constitute a Schottky defect come from neighbouring sites). Ousters of defects ( also form. These defect clusters may ultimately give rise to a new periodic structure oi an extended defect such as a dislocation. Increasing disorder may alternatively give j to a random, amorphous solid. As the properties of a material may be dramatically alte by the presence of defects it is obviously of great interest to be able to imderstand th relationships and ultimately predict them. However, we will restrict our discussion small concentrations of defects. 

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 point defects are decisive for conduction in solid ionic crystals. Ionic migration occurs in the form of relay-type jumps of the ions into the nearest vacancies (along the held). The relation between conductivity o and the vacancy concentration is unambiguous, so that this concentration can also be determined from conductivity data. 

A number of the well-known y-induced centers in n-type Si are also neutralized by atomic hydrogen (Pearton, 1982). The A-center (oxygen-vacancy complex, Ec-0.18eV and divacancy level (Ec-0.23eV) are passivated, while the E-center (phosphorus-vacancy complex, Ec -0.44 eV) is thermally removed at relatively low temperatures and its susceptibility to hydrogenation could not be determined. Point defects... 

A block model of defects on a single-crystal surface is depicted in Figure 2.4.17 The surface itself in reality is a two-dimensional defect of the bulk material. In addition, one-dimensional defects in the form of steps which have zero-dimensional defects in the form of kink sites. Terraces, which are also shown in the figure, have a variety of surface sites and may also exhibit vacancies, adatoms, and point defects. Surface boundaries may be formed as a result of surface reconstruction of several equivalent orientations on terraces. 

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. 

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