Unit cell perovskite lattice

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). 

Characterization.— The LSFTO powder was calcined at a series of temperatures (1250, 1300, and 1400°C) in air to investigate phase purity and densification behavior. X-ray diffraction (XRD) powder patterns are shown in Fig. 1. The sample is single phase after heating at 1250°C. At the higher sintering temperatures, the lines become sharper and the density increases. The density measured by the Archimedes method was 90.3% relative to theoretical value after annealing at 1400°C for 10 h. The XRD pattern sintered at 1400°C was completely indexed with a cubic unit cell with lattice parameter a = 3.898(8) A and V= 59.2(6) A3. The weak XRD peaks at 31, 43, 55, and 65° 20 are also from the perovskite phase and arise from a small amount of WL radiation in the incident beam. 

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. 

BaTiOs crystallizes in the perovskite structure. This structure may be described as a barium-oxygen face-centered cubic lattice, with barium ions occupying the corners of the unit cell, oxide ions occupying the face-centers, and titanium ions occupying the centers of the unit cells, (a) If titanium is described as occupying holes in the Ba-O lattice, what type of hole does it occupy (b) What fraction of the holes of this type does it occupy (c) Suggest a reason why it occupies those holes of this type but not the other holes of the same type ... 

In order to calculate the lattice parameter for a noncubic substance, a system of linear equations with the help of the relations reported in Table 4.3 is formed, and then this system is solved. It is easier to understand the procedure with an example hence, we use the BaCe0 95Yb0 05O3 5 perovskite that crystallizes in an orthorhombic unit cell [34] to illustrate the methodology [32],... 

The compound LaMn03165 adopts a distorted perovskite structure, in which the unit cell has rhombohedral symmetry, with hexagonal lattice parameters a = 0.55068 nm, c = 1.33326nm, Z = 6 LaMn03165. The oxygen excess can arise either as oxygen interstitials or as metal atom vacancies. 

Perovskite is an example of a double oxide, it does not, as the formula might imply, contain [Ti03] ions, but is a mixed Ca(II) and Ti(IV) oxide. Figure 5.23a shows one representation of a unit cell of perovskite (see problem 5.13 at the end of the chapter). The cell is cubic, with Ti(IV) centres at the corners of the cube, and ions in the 12 edge sites. The 12-coordinate Ca ion lies at the centre of the unit cell. Each Ti(IV) centre is 6-coordinate, and this can be appreciated by considering the assembly of adjacent unit cells in the crystal lattice. 

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