Magnesium Diboride Crystal Structure

Magnesium diboride (MgB2) is a ceramic superconductor that consists of magnesium and boron atoms arranged in a crystal lattice structure. The crystal structure of MgB2 belongs to the hexagonal space group P6/mmm (No. 191), which means that it has a six-fold rotational symmetry around the c-axis and a mirror plane perpendicular to this axis.

The crystal lattice of MgB2 can be thought of as consisting of alternating layers of magnesium and boron atoms stacked along the c-axis. The magnesium atoms form a close-packed hexagonal lattice, with boron atoms occupying the trigonal prismatic voids between the magnesium atoms. Each boron atom is surrounded by six magnesium atoms, forming octahedral coordination geometry.

The unit cell of MgB2 contains two formula units, with each unit consisting of three magnesium atoms and two boron atoms. The lattice parameters for MgB2 are a=b=3.085 Å and c=3.524 Å. The crystal structure of MgB2 can also be described using the concept of a "superstructure," which arises due to the presence of boron-boron bonds in addition to magnesium-boron bonds.

In the superstructure model, the boron atoms form covalent bonds with each other to create triangular networks within each layer, while the magnesium atoms occupy the interstitial sites between these layers. This superstructure leads to a band structure that is highly anisotropic, with the two-dimensional π-band derived from the boron networks being responsible for the superconductivity observed in MgB2.