Pm3m

Pm3m, also written as Pm-3m, is a space group in crystallography. It represents a highly symmetric cubic arrangement with a primitive lattice and the Oh point group, and it is designated No. 221 in the International Tables for Crystallography. The symbol denotes a space group setting in which the lattice is primitive (P) and the full cubic symmetry is present.

Structure and symmetry: The lattice is primitive cubic, containing one lattice point per unit cell. The corresponding point group is m-3m (Oh), which contributes the 48 distinct symmetry operations of the cubic Oh group when considering point symmetry. In space-group terms, Pm-3m describes crystals with high-translational and orientational symmetry, where atoms may occupy high-symmetry positions and simple bases can generate common structures. The origin is typically chosen at a high-symmetry point, such as a lattice site.

Representations and features: Pm-3m is used to describe high-symmetry cubic phases and is compatible with simple two- or multi-atom basis arrangements within a primitive cubic framework. It is one of the most common settings for describing idealized cubic phases in inorganic materials, particularly when the structure exhibits full cubic symmetry without octahedral tilts or distortions.

Applications and examples: Materials with CsCl-type structures are often described by Pm-3m, as are ideal cubic phases of certain perovskites at high temperatures (ABO3 with A at the corners, B at the body center, and X at the face centers). The space group serves as a standard reference in crystallographic analysis and in the interpretation of diffraction data for high-symmetry cubic materials.