1.8 Other Cubic Structures

       There are a few structures, which appear as if they are based on cubic closed packing of anions.        However the actual structure is rather different and many of these structures are merely based on        the cubic packing of anions. Here, we discuss the perovskite structure based on ABO₃ structure,        CsCl structure and ReO₃ structure.

       1.8.1 Perovskite (ABO₃) Structure

• ABO₃ type compounds

• Examples are many titanates like BaTiO₃, SrTiO₃, PbTiO₃ etc. which happen to be technologically very useful compounds as we will see in later modules.

• In ABO₃ structured compounds, A ion is twelve fold coordinated by oxygen (like a dodecahedra) and B ion is octahedrally coordinated by oxygen ions.

• Oxygen atoms form an FCC-like (not FCC) cell with atoms missing from the corners which are occupied by A atoms.

• Bond strength check:
  Cation: Ba: ²⁄₁₂ = ¹⁄₆  and Ti: ⁴⁄₆ = ²⁄₃ 
  Oxygen valence = ¹⁄₆ x Coordination number by Ba + ²⁄₃ x coordination number by Ti .




Figure 1.31 Perovskite structure




Figure 1.32 Polyhedra model of perovskite structure

• Lattice type: Primitive Cubic (NOT FCC!)

• Motif:  A ion - 0 0 0, B ion – ½ ½ ½, O ion - ½ ½ 0, 0 ½ ½, ½ 0 ½

• One Formula unit per unit cell

• Coordination

• B cation is surrounded by oxygen octahedra which share corners.

• A cation is surrounded by oxygen dodecahedra which touch faces of octahedra.

• An important parameters about perovskites is the their “Tolerance Factor (t)” which is defined as

• This is derived from the geometry of a cube in which the atoms are of such sizes that they touch each other and hence, the face diagonal of the unit cell would be times the unit-cell length, as result t = 1 for a perfect cubic perovskite

  .

• However, due to variations in ionic radii of various ions, many perovskites show deviations from t = 1 and may not even have a cubic structure. Deviations from t = 1 signify the level of lattice distortion.

• For example, BaTiO₃ has cubic structure only above ~120°C while it is tetragonal at room temperature and further adopts orthorhombic and rhombohedral structure if cooled below RT.

• Perovskites can also have various combinations of ionic valence such as

  • e.g. A²⁺B⁴⁺O₄ , BaTiO_3, PbTiO₃, CaTiO₃, SrTiO₃ etc.

  • e.g. A³⁺B³⁺O₄ , LaAlO₃, LaGaO₃, BiFeO₃ etc.

  • Mixed Perovskites:

    • A²⁺(B²⁺_1/3B⁵⁺_2/3)O₃ eg. Pb(Mg_1/3Nb_2/3)O₃

    • A²⁺(B³⁺_1/2B⁵⁺_1/2)O₃ eg. Pb(Sc_1/2Ta_1/2)O₃