Disorder, antistructure vacancy

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... 

A variety of defect formation mechanisms (lattice disorder) are known. Classical cases include the - Schottky and -> Frenkel mechanisms. For the Schottky defects, an anion vacancy and a cation vacancy are formed in an ionic crystal due to replacing two atoms at the surface. The Frenkel defect involves one atom displaced from its lattice site into an interstitial position, which is normally empty. The Schottky and Frenkel defects are both stoichiometric, i.e., can be formed without a change in the crystal composition. The structural disorder, characteristic of -> superionics (fast -> ion conductors), relates to crystals where the stoichiometric number of mobile ions is significantly lower than the number of positions available for these ions. Examples of structurally disordered solids are -> f-alumina, -> NASICON, and d-phase of - bismuth oxide. The antistructural disorder, typical for - intermetallic and essentially covalent phases, appears due to mixing of atoms between their regular sites. In many cases important for practice, the defects are formed to compensate charge of dopant ions due to the crystal electroneutrality rule (doping-induced disorder) (see also -> electroneutrality condition). 

The pyrochlore-type compounds, where the crystal structure is usually considered as a cation-ordered fluorite derivative with % vacant oxygen site per fluorite formula unit, constitute another large family of oxygen anion conductors [9, 33, 41—43, 84—88]. The unoccupied sites provide pathways for oxygen migration furthermore, the pyrochlore structure may tolerate formation of cation and anion vacancies, doping in both cation sublattices, and antistructural cation disorder. Regardless of these factors. 

TiAl-base alloys are in the range 160-180 GPa which is only 10-20% lower than that of the superalloys (see Table 2). Recently, it has been found by ab initio calculations that deviations from stoichiometry are due to accommodated antistructure atoms, i.e. constitutional disorder, instead of vacancies in the sublattices, and that the concentration of thermal vacancies is comparatively low because of the high formation energy (Fu and Yoo, 1993). The self-diffusion of Ti in TiAl has been studied (Kroll etal., 1992). 

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