Unit cell perovskite

We emphasize a special aspect of this investigation which is of general importance for the fabrication of any type of epitactic system in which a simple single unit cell perovskite is combined with a multi-sub-unit cell compound. We find in the present case that the upper interface contains a higher density of defects and a higher level of strain than the lower one. This originates from the different surface geometry, as shown schematically in Fig. 13.25. 

Figure 6. Structure of the perovskite-type lithium-ion conductor Li 2yLa057TiO3. The lithium ions (small, gray) and the lanthanum ions (large, gray) are randomly distributed over the A sites, of which 14 percent are vacancies, enabling the lithium ions to be mobile. Titanium forms TiOh octahedra, as shown in yellow. The unit cell is indicated.

A unit cell of the mineral perovskite, which has a structure similar to that of some of the ceramic superconductors, is shown here. What is its formula ... 

Structure of YBa2Cu307. The perovskite structure is attained by inserting O atoms between the strings of Y atoms and between the Cu04 squares. Two unit cells are shown in each direction (stereo image) r... 

Figure 11.6 Views of perovskite crystal structure. Top—conventional cubic unit cell white circles = oxygen black circle = transition metal gray circles = alkali or alkaline earth metal. Bottom—extended unit cell to show the cage formed by the oxygen octa-hedra. Adapted from Bragg et al. (1965).

RbCaF3 has the perovskite structure with the Ca in the center of the unit cell. What is the electrostatic bond character of each of the Ca-F bonds How many fluoride ions must surround each Ca2+ ion What is the electrostatic bond character of each Rb-F bond How many F ions surround each Rb+ ... 

Figure 4.27 Idealized structures of the AnB 03 +2 phases (a) AB03, (perovskite) unit cell (b) n = 4, Ca4Nh4014 (c) n = 5, Ca5(Ti, Nb)5Oi7 and (d) n = 4.5, Ca Ti, Nb)9029. The shaded squares represent (Ti, Nb)06 octahedra and the shaded circles represent Ca atoms.

Modular structures are those that can be considered to be built from slabs of one or more parent structures. Slabs can be sections from just one parent phase, as in many perovskite-related structures and CS phases, or they can come from two or more parent structures, as in the mica-pyroxene intergrowths. Some of these crystals possess enormous unit cells, of some hundreds of nanometers in length. In many materials the slab thicknesses may vary widely, in which case the slab boundaries will not fall on a regular lattice and form planar defects. 

Table 11.1 lists the resulting low-temperature phases calculated for this set of compounds. Where experimental data are available (marked with a star) the predicted structures are those observed at low temperatures. Inverse denotes a perovskite structure in which a large divalent ion is 12-coordinate and a smaller univalent ion 6-coordinate. Unit cell dimensions are predicted to within 1% of the measured values. 

Figure 10. Unit cell of ABO3 perovskite structure. (Reprinted with permission from Nature Materials (http //www.nature.com/nmat), ref 128. Copyright 2003 Nature Publishing Group.)...

Oxides and Sulphides.—The synthesis of SrNiO, and SrNiO, has been reported. The former has a perovskite structure whereas the latter is hexagonal. The structure of a-Ni.,S shows three non-equivalent sulphur sites and five non-equivalent nickel sites per unit cell. Four of the nickel sites are square-pyramidally disposed and the other tetrahedrally disposed towards sulphur. There is evidence for metal-metal bonding. ... 

The often mentioned relations between the structure types of cryolite and perovskite (page 41) may be explained best with the example of the elpasoHte type. The elpasoUte structure is really a superstructure of the perovskite-lattice, generated by substituting two divalent Me-ions in KMeFs by two others of valency 1 (Na) and 3 (Me) resp. The resulting compound K (Nao.5Meo.5)F3 crystallizes with an ordered distribution of Na+ and Me + because of the differences in size and charge of the ions. Thus to describe the unit cell the lattice constant of the perovskite ( 4 A) has to be doubled to yield that of the elpasohte structure ( 8 A). 

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 structure of these compounds was elucidated by the work of Okazaki and Suemune (236) on the fluoride KCuFj. The unimolecular tetragonally compressed perovskite cells of previous reports (90) do not account for additional reflections observed in single crystal work. Instead one has to conceive a unit cell containing z = A formula units... 

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. 

The Perovskite Structure, ABXS Systems. Cubic Pm3m (Space Group 221) A cubic structure was assigned to the mineral perovskite, CaTiOj, but this particular compound was later found to actually possess orthorhombic symmetry. Today, however, we refer to the perovskite structure in its idealized form as having cubic symmetry and it is normally represented by a simple unit cell (Figure 10). 

Figure 10 The Perovskite (CaTi03) structure. A polyhedral representation for an unit cell having different origins. From Reference 169. 

Several other research groups (89-91) picked up on this discovery and obtained Ba/K/Bi/O materials with an onset transition temperature of 34 K. The structure of this oxide superconductor is cubic, perovskite-type, having unit cell dimensions, 4.288-4.293 A. This system appears to be a three-dimensional superconductor and has... 

The simplest quaternary derivative with the perovskite structure would be one in which two different transition metals might occupy the B-site position. This can be formulated as A(B,1 2B1 2)03, or preferably A2(B B0O6. These compounds can then crystallize with a doubled unit cell, if ordering occurs on the octahedral metal sites. Further compositional and structural adaptions could be obtained, as shown below, all possessing an overall 1 1 3 ratio of A B 0 atoms. In all the following examples and formulations, the proper stoichiometry will be maintained, and oxygen will be the principal anionic species. 

Figure 11 Models of the structures of Ba2YCu3Ox for x = 6.85 (Figure a) and x = 6.15 (Figure b). Both structures are based on a unit cell of parameters 2>/2ac 2y/2ac 3ac where a is the basic perovskite parameter. Also in this case some of the Cu(l) atoms are in three-fold coordination.

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