An ABO₃ crystal structure in which the B-site cation sits at the center of an oxygen octahedron (coordination number 6) and the A-site cation in the space between octahedra (coordination number 12). BaTiO₃ is an example.
Japanese name: ペロブスカイト構造
Perovskite structure appears in 1 practice question across 1 topic, including Ceramics and glasses.
Field: Ceramics and glasses
The ideal perovskite structure is cubic and can be drawn with the B-site cation at the body center of the unit cell, oxide ions at the six face centers and A-site cations at the eight corners. The BO₆ octahedra share corners to form a three-dimensional network, and the large A cations sit in the spaces between them. SrTiO₃ is cubic at room temperature, with a lattice parameter of about 0.3905 nm. The name comes from the mineral CaTiO₃, found in the Ural Mountains in 1839 and named after the Russian mineralogist Perovski.
The balance of ion sizes is expressed by the Goldschmidt tolerance factor t = (r_A + r_O)/(√2(r_B + r_O)). With t = 1 the ions fit the ideal cubic structure exactly, and empirically the perovskite structure forms readily for t from roughly 0.8 to slightly above 1, while other structures form when t is far outside this range. Calculated with Shannon ionic radii, t is about 1.00 for SrTiO₃, about 1.06 for BaTiO₃ and about 0.97 for CaTiO₃. In BaTiO₃, with t above 1, the Ti moves easily within its octahedron and ferroelectricity appears; in CaTiO₃, with t below 1, the octahedra tilt and the structure becomes orthorhombic.
By changing the combination of A, B and X, the perovskite structure shows a wide variety of properties. BaTiO₃ is used as the dielectric in multilayer ceramic capacitors, PZT in piezoelectric elements and (La,Sr)MnO₃ in the air electrodes of solid oxide fuel cells. Copper-oxide high-temperature superconductors and manganese oxides showing colossal magnetoresistance are also derived from this structure. Furthermore, halide perovskites such as CH₃NH₃PbI₃, in which X is replaced by a halogen, are being researched and commercialized as the light-absorbing layers of solar cells.
When part of the A or B site is replaced by ions of different valence, oxygen vacancies or electrons and holes form to compensate the charge, allowing electronic and ionic conduction to be tuned. For example, replacing La with Sr increases oxygen vacancies or holes. BaTiO₃ changes from cubic to tetragonal at its Curie temperature of about 120 °C, and additives are used to adjust this temperature and the temperature dependence of permittivity to give capacitors uniform characteristics. There are also many derived structures built from this structure as a basic unit, such as the layered Ruddlesden–Popper type.
Answer: C. 6
In the ideal perovskite structure, the small B-site cation (Ti⁴⁺) is surrounded by 6 oxide ions, forming TiO₆ octahedra that share corners and link up in three dimensions. The large A-site cation (Ba²⁺) sits in the space between the octahedra, surrounded by 12 oxide ions. Twelve is the A-site coordination number, an easy value to confuse. Four is the tetrahedral coordination number of the wurtzite and zinc blende structures. In BaTiO₃, a slight displacement of Ti from the center of the octahedron produces spontaneous polarization, the origin of ferroelectricity, a large dielectric constant and piezoelectricity.
It is the same ABX₃-type structure. Solar cells use halide perovskites in which X is a halogen such as iodine instead of oxygen, A is an organic cation such as methylammonium or Cs⁺, and B is Pb²⁺ or a similar ion.
Insert ionic radii appropriate to the coordination number into t = (r_A + r_O)/(√2(r_B + r_O)). Use 12-coordinate values for A and 6-coordinate values for B; for SrTiO₃ (Sr²⁺ 0.144 nm, Ti⁴⁺ 0.0605 nm, O²⁻ 0.140 nm), t ≈ 1.00.
No. The ideal cubic form occurs only in some, such as SrTiO₃; many are distorted to tetragonal, orthorhombic or rhombohedral by octahedral tilting or displacement of the B ion. Many substances change crystal system with temperature, and BaTiO₃ undergoes several phase transitions as temperature changes.
In the ideal perovskite structure, the small B-site cation (Ti⁴⁺) is surrounded by 6 oxide ions, forming TiO₆ octahedra that share corners and link up in three dimensions.
In the perovskite structure (ABO₃), as in BaTiO₃, what is t…Piezoelectric effect Sintering Transformation toughening Weibull modulus