Cubic perovskite structure

The disordered structure can be stabilized to room temperature by inclusion of substitutional impurities on the In sites. Thus the oxide formed when Ga is substituted for In, Ba2(ln1 xGaJt-)205+s to form Galn defects has a disordered cubic perovskite structure even at room temperature for values of x between 0.25 and 0.5, and the similar Ba2iln1 vCox)205+3 with Coin defects has a disordered cubic perovskite structure at room temperature when x lies between 0.2 and 0.8. The defects present in the In sites hinder oxygen ordering during the timescale over which the samples cool from the... 

The same analysis can be applied to compounds with a more complex formula. For example, the oxide LaCoCL, which adopts the cubic perovskite structure, usually shows a large positive Seebeck coefficient, of the order of +700 jjlV K-1, when prepared in air (Hebert et al., 2007). This indicates that there are holes present in the material. The La ions have a fixed valence, La3+, hence the presence of holes must be associated with the transition-metal ion present. Previous discussion suggests that LaCo03 has become slightly oxidized to LaCoCL+j, and contains a population of Co4+ ions (Co3+ + h or Coc0)- Each added oxygen ion will generate two holes, equivalent to two Co4+ ... 

In this equation rA is the radius of the cage site cation, rB is the radius of the octahedrally coordinated cation, and rx is the radius of the anion. The factor l is called the tolerance factor. Ideally, t should be equal to 1.0, and it has been found empirically that if t lies in the approximate range 0.9-1.0, a cubic perovskite structure is stable. However, some care must be exercised when using this simple concept. It is necessary to use ionic radii appropriate to the coordination geometry of the ions. Thus, rA should be appropriate to 12 coordination, rB to octahedral coordination, and rx to linear coordination. Within this limitation the tolerance factor has good predictive power. 

Figure 11.6 AMF3 crystal structures, (a) Ideal cubic perovskite structure, (b) Tilting of MXg octahedra in orthorhombically distorted AMF3 perovskites. (c) RbNiF3 CSC0F3 and CsNiF3 crystal structures, (d) Crystal structure of lithium niobate.

The perovskite structure and its variant and derivative structures, and superstructures, are adopted by many compounds with a formula 1 1 3 (and also with more complex compositions). The ideal, cubic perovskite structure is not very common, even the mineral CaTi03 is slightly distorted (an undistorted example is given by SrTi03). 

Fig. 17a-c. The ideal cubic-perovskite structure for ABX3 and ordered A2BB Xs... 

The familiar cubic perovskite structure of ABO3 has of course just one structural parameter, the unit cell edge a. This requires the ratio of the A-O to the B-O bond lengths to be equal to y/2. When this condition cannot be met, the structme distorts in (one of) a number of well-documented ways . By far the largest of the families of derivative structures that arise when A is too small [/(A-0)//(B-0) < /2] is that of the orthorhombic perovskites (GdFeOa type) exemplified by the mineral perovskite (CaTi03) itself. 

This material, which has the ideal cubic perovskite structure, has been extensively investigated from both theoretical and experimental points of view (see Dougier... 

Fluorescence from the Do and Di levels of Eu3+ in doped SrTiOa (cubic perovskite structure) has been observed [618]. The fluorescence decay from the 5Di level consists of radiative transitions to the 7F states and a nonradiative dominant transition to the 5Do level. The decay of the 5X>o state is mainly radiative and is composed of both zero-phonon and phonon-assisted transitions, the latter accounting for much of the temperature dependence of its lifetime. For temperatures upto 300° K, the decrease in the sZ>o lifetime has been correlated [618] with the increased intensity of the vibronic bands [619]. Both 5Z>o 7Fi and 5Do 7F2 transitions as well as 5Di 7F, bD - 7F2 and 5Z>o - 7F show vibronic structures at room temperatures [619] and below. 

Barium titanate, BaTi03, is probably the most widely studied ferroelectric oxide. Extensive studies were conducted on this compound during World War II in the United States, England, Russia, and Japan, but the results were not revealed until after the war. Barium titanium(IV) oxide was found to be a ferroelectric up to a temperature of 120°C., which is its Curie point. Above 120°C., barium titanium(IV) oxide has the cubic perovskite structure, and below this temperature the oxygen and titanium ions are shifted and result in a tetragonal structure with the c axis approximately 1% longer than the a axis. Below 0°C., the symmetry of barium titanate becomes orthorhombic, and below —90°C., it becomes trigonal. 

Fig. 1. (a) The ideal cubic perovskite structure and (b) the n = 1 Ruddlesden-Popper phase AO AMO3. 

Figure 3b Sheared Sr03-substructure of the cubic perovskite structure as model for the hypothetical compound Na3N. N -ions are surrounded by Nations forming cubic close packed distorted cube-octahedra. Nations are depicted as white spheres (not drawn to scale). Average Na-Na- and Na-N-distance about 2.6 A (space group P42/mmc, no. 131).

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