Superstructure (condensed matter)

In solid state physics, a superstructure is some additional structure that is superimposed on a given crystalline structure. A typical and important example is ferromagnetic ordering.

In a wider sense, the term "superstructure" is applied to polymers and proteins to describe ordering on a length scale larger than that of monomeric segments.

In a crystal, a superstructure manifests itself through additional reflections in diffraction patterns, e.g., in low energy electron diffraction (LEED) or X-ray diffraction experiments. Often a set of weak diffraction spots appears between the stronger spots belonging to what is referred to as the substructure. In some cases a phase transition occurs, e.g., at higher temperatures, where the superstructure disappears and the material reverts to the simpler substructure. If not, usually compounds are known that exhibit only the substructure.

The superspots basically represent a modulation of the substructure that causes the translation symmetry inherent to the lattice of the substructure to be violated somewhat. One could speak of symmetry breaking of the translation symmetry of the lattice, although rotational symmetry may be lost simultaneously.

If the superspots are located at simple fractions of the vectors of the reciprocal lattice of the substructure, e.g., at q=(½,0,0), the resulting broken symmetry is a multiple of the unit cell along that axis. Such a modulation is called a commensurate superstructure.

In some materials, superspots will occur at positions that do not represent a simple fraction, say q=(0.5234,0,0). In such a case a structure results that strictly speaking has lost all translational symmetry in a particular direction. This is called an incommensurate structure.

There are basically three types of superstructures in crystals:

When a crystalline material that contains atoms with uncompensated electron spins is cooled down generally ordering of these spins will occur once the thermal energy is small enough not to overrule the interactions between neighboring spins. The ordering does not necessarily span the same unit cell as the original crystallographic subcell and a superstructure may occur. The superspots are typically only visible in neutron diffraction, because the neutron is scattered both by the nucleus and by the magnetic moments of the electron spins.

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