perovskite structure
Some of the most remarkable inorganic materials of the last century — superconductors, the piezoelectric ceramics in ultrasound and sonar, and the latest solar-cell absorbers — share one structural blueprint. It is named after the mineral perovskite, calcium titanate (CaTiO3), and it is the standard way nature packs many compounds with the general formula ABO3, where A and B are two different metal cations of very different sizes.
The structure is easiest to picture as a corner-sharing network of octahedra with a big cation rattling in the holes. The small, highly charged B cation (here Ti4+) sits at the centre of an octahedron of six oxide ions; these BO6 octahedra link by sharing every corner, building an open three-dimensional framework. The large A cation (here Ca2+) sits in the big cavity at the centre of eight such octahedra, surrounded by twelve oxide ions (coordination 12). One way to draw the unit cell: B at the corners, A at the body centre, oxide at the edge midpoints — a cubic cell with one ABO3 unit (Z = 1). So perovskite is a 12:6 cation coordination compound with a single shared oxide framework.
Perovskite earns its fame because tiny tweaks to that framework unlock dramatic properties. Slightly tilting or distorting the octahedra makes barium titanate (BaTiO3) ferroelectric and piezoelectric — squeeze it and it makes a voltage, used in microphones and sonar. Mixed-metal perovskites are the high-temperature superconductors (the cuprate YBa2Cu3O7 is a layered, oxygen-deficient perovskite). And organic-inorganic lead-halide perovskites such as CH3NH3PbI3 have become star materials for cheap, efficient solar cells. The single most important number is the tolerance factor, a ratio of ionic radii that predicts whether a given A and B pair will actually fit the perovskite cage or distort away from it.
Barium titanate, BaTiO3, is perovskite with a small twist: below about 120 degrees Celsius the Ti4+ shifts slightly off-centre in its octahedron, giving each cell a permanent electric dipole. That tiny off-centring is why BaTiO3 is ferroelectric and piezoelectric, the heart of countless capacitors and ultrasonic transducers.
A tiny off-centre shift of Ti4+ in perovskite BaTiO3 produces ferroelectricity and piezoelectricity.
The A cation is 12-coordinate, not 6 — a common error is to give A and B the same coordination. Many real perovskites are distorted (tilted octahedra) rather than perfectly cubic, and that distortion is exactly what makes them useful.