Perovskites cubic

Lead zirconate [12060-01 -4] PbZrO, mol wt 346.41, has two colorless crystal stmctures a cubic perovskite form above 230°C (Curie point) and a pseudotetragonal or orthorhombic form below 230°C. It is insoluble in water and aqueous alkaUes, but soluble in strong mineral acids. Lead zirconate is usually prepared by heating together the oxides of lead and zirconium in the proper proportion. It readily forms soHd solutions with other compounds with the ABO stmcture, such as barium zirconate or lead titanate. Mixed lead titanate-zirconates have particularly high piezoelectric properties. They are used in high power acoustic-radiating transducers, hydrophones, and specialty instmments (146). 

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+ ... 

This relationship can be generalized for any cubic perovskite ABX3 and provides a useful guide to the formation of these phases if it is written in the form ... 

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). 

Simple Cubic Perovskites. Since the work of Stotz and Wagner in 1966, the existence of protonic defects in wide-band-gap oxides at high... 

From the thermodynamics of such dynamical hydrogen bonds , one may actually expect an activation enthalpy of long-range proton diffusion of not more than 0.15 eV, provided that the configuration O—H "0 is linear, for which the proton-transfer barrier vanishes at 0/0 distances of less than 250 pm. However, the mobility of protonic defects in cubic perovskite-type oxides has activation enthalpies on the order of 0.4—0.6 eV. This raises the question as to which interactions control the activation enthalpy of proton transfer. 

The importance of the H/B repulsion is also witnessed by the observation that the activation enthalpies of proton mobility in cubic perovskites with pentavalent B-site cations (I—V perovskites) are significantly higher than for perovskites with tet-ravalent B-site cations (II—IV perovskites). - ... 

Fig. 6 Pulsed neutron PDF of PMN at T = 10 K (circles), compared to the PDF expected for the cubic perovskite average structure (solid line) [9]...

The structures of the compounds AMeFs are closely related to each other and can be derived from the well known perovskite structure. Therefore they may be generalizing referred to as fluoroperovskites, although some deformations of the cubic perovskite t e may occxir orthorhombic, tetragonal and hexagonal structures have been observed in ternary fluorides, in addition to the basic cubic type. 

As compared to the ReOs-type the cubic perovskite AMeFs contains an additional ion A in the center of the unit cell. The vacancies in the cubic close-packing of anions are thus filled up by insertion of similar sized cations A that complete the layers (111) to have the composition AF . 

The two mentioned ternary fluorides of cadmium with their tolerance factors of 1.00 and 0.88 resp. mark quite accurately the field of existence of cubic perovskites. As may be seen from the following Table 25 the tolerance factors of all cubic fluoroperovskites of the transition metals hitherto known lie within the range of these limits. 

As in all the perovskites — they might be defined that way — the A-and F-ions in the CsMnFs-structure form common close-packed layers AFs, in which the A-ion (Cs) displays a C. N. of 12 (Cs—F =3.12... 3.22 A in CsMnFs). The sequence ABC of three layers, characteristic of cubic perovskites, has been changed, however, to a hexagonal sequence of six layers ABC—ACB. This explains the relation found between the lattice constants ( hex = V2 eub Chex = 2 ]/3 acuu) from which follows Chex/ hex = ]/2 /3 = 2.45 or a value nearby. 

As a consequence of this repulsion the MnFe-octahedra of these groups MnaFg are distorted, the Mn—F-distances are 3 x 2 16 A and 3 X 2 12 A resp. The latter values correspond to the Mn—F-distances in the nearly undistorted MnFe-octahedra of the structure, which share comers only and like in the cubic perovskites bring about the three-dimensional netting of the lattice. 

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