the perovskite structure
/ puh-ROV-skite /
The perovskite structure, named after the mineral perovskite (calcium titanate, CaTiO3), is one of the most versatile and important structures in all of materials science. It houses two different cations, a large A and a small B, together with an anion X (usually oxygen). Picture a scaffold of corner-linked octahedra with a big ion rattling in the cavity between them, and you have the essential image.
In the ideal cubic form, the small B cation sits at each corner of the cube, oxygens sit at the midpoints of the cube edges (so each B is surrounded by six oxygens forming a BO6 octahedron), and the large A cation sits at the body centre with twelve oxygen neighbours. There is 1 formula unit of ABO3 per cell, coordination 12 for A and 6 for B, and the BO6 octahedra share every corner to build a continuous framework. Whether the cube stays perfect or distorts is captured by the Goldschmidt tolerance factor, t = (rA + rO) divided by sqrt(2) times (rB + rO); a value near 1 gives cubic perovskite, while smaller values make the octahedra tilt and the symmetry drop.
This one structure hosts an astonishing range of functional materials: barium titanate (ferroelectric, the heart of ceramic capacitors), lead zirconate titanate or PZT (the standard piezoelectric), lanthanum manganites (colossal magnetoresistance), strontium titanate, high-temperature superconducting cuprates (layered perovskites), and the halide perovskites now revolutionising solar cells. The tilting and off-centring of the octahedra drive displacive phase transitions that switch ferroelectric and ferroelastic behaviour on and off.
Barium titanate (BaTiO3) is a perovskite: cooling below 120 C shifts the Ti4+ off-centre in its octahedron, making the crystal ferroelectric, the basis of multilayer capacitors.
A corner-sharing octahedral framework with a big cation in the cage: the most functional structure known.
Very few perovskites are actually cubic at room temperature; most tilt or distort, and it is exactly these small departures from the ideal cube that produce ferroelectricity, piezoelectricity, and their useful properties.