Vacancy-ordered structures

Anion-deficient perovskites and vacancy-ordered structures. Anion-vacancy... 

Consider a crystal of composition M0.5X, the metal vacancies are regularly arranged among the lattice sites at lower temperatures, shown in Fig. 1.18 as a basic model of a vacancy-ordered structure with a two-dimensional lattice (in this figure, the anion atoms are omitted for clarity). This structure is realized if the composition of the crystal is Mq 5X, and metal atoms M fully occupy the B-sites and metal vacancies fully occupy the A-sites, this only occurs at absolute zero temperature (perfect order). The occupation probabilities, p and Pg, denote the ratio of number of metal atoms on the A-sites (ma) to the number of lattice points of the A-sites ( 1V) and the ratio of number of metal atoms on the B-sites (Ug) to the number of lattice points of the B-sites (ilV), respectively. Thus p and pg can be expressed as... 

The crystal having the composition Mg 5X, which is the stoichiometric composition of the vacancy-ordered structure, shows disordering such as Pa and -< with increasing temperature. With decreasing number of vacancies in the composition Mj X, increases towards 1 at absolute zero temperature. (In this example <5 ranges from 0 to 0.5 in the expression... 

From the definition of p and pg, we obtain the following relationship vacancy-ordered structure pg > vacancy-disordered structure p = Pb... 

Fig. 1.73 Basic model structure for the definition of vacancy-ordered structures in the MX-MX2 system." ...

Ca2Fe205 and oxides of the CaMn03 v family are good examples of such vacancy-ordered structures. Complex intergrowth phases (ordered as well as disordered) involving brownmillerite and other related phases are commonly found in some of the anion-deficient oxides. Some of them also show polytypism due to different modes of stacking of the hexagonal and cubic layers. 

Table 1—Hexagonal Perovskite Oxides Exhibiting B-Site Vacancy-ordering Structural details...

Anion-Deficient Perovskites and Vacancy-Ordered Structures... 

Defects in MWCNTs are always present. We can briefly differentiate between topological defects which lead to rehybridization (C5 and C7 rings instead of C6 lead to rehybridization between sp2 and sp3) and incomplete bonding defects (vacancies, dislocation) (Fig. 16.2). Functionalization or doping with heteroelements may add further modifications with respect to the ideal ordered structure, but are also the sites which allow for anchoring supported metals or metal oxides, or to functionalize the CNTs with organic groups. 

In the brownmillerite structure, the oxygen vacancies order in such a way that half the iron of CaFe02.5 are octahedrally coordinated and half are tetrahedrally coordinated. This ordering is an expression of the tetrahedral-site stability of Fe ions. In a system like Lai yCayFe03 x < y/2, there is a tendency to form intergrowths of perovskite and brownmillerite structures the oxygen vacancies do not remain randomly distributed. Mossbauer spectra at 4.2 K for this complex system exhibit three sextets they have been interpreted in terms of 2 Fe and one Fe " ", or of an Fe and the disproportiona-... 

One of the best-characterized perovskite oxides with ordering of anion vacancies is the brownmillerite stmctme exhibited by Ca2Fe205 and Ca2FeA105 (Grenier et al, 1981). The compositions could be considered as anion-deficient perovskites with one-sixth of anion sites being vacant. The orthorhombic unit cell of the brownmillerite structure (a = 5.425, b = 5.598 and c = 14.768 A for Ca2Fe205) arises because of vacancy-ordering and is related to the cubic perovskite as a - c-... 

Figure 5.25 (a) Vacancy ordering in the ab plane of CajFejOj of brownmillerite structure (b) alternating sequence of octahedral and tetrahedral layers in the c direction. Small filled circles, iron large filled circles, oxygen open squares, oxygen vacancy. 

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