P63mc

P63mc, often written P6_3mc, is a space group in crystallography that describes a hexagonal, non-centrosymmetric crystal structure. It belongs to the hexagonal crystal system and is used to characterize materials with a primitive hexagonal lattice that exhibit a sixfold screw axis along the c axis, combined with mirror and glide symmetries. The combination of these symmetry elements yields the full set of symmetry operations associated with the group.

In P6_3mc, the primary symmetry operation is the 6_3 screw axis along the c direction, along with a mirror plane perpendicular to c and a glide plane (c) that together generate the remaining operations. The group lacks an inversion center, placing it among non-centrosymmetric space groups. Because of this, crystals with P6_3mc symmetry often display polar or piezoelectric properties, and they may exhibit distinctive optical responses in nonlinear processes.

Wyckoff positions in this space group depend on the specific material, but structures described by P6_3mc typically involve atoms occupying low-to-medium symmetry sites that support non-centrosymmetric arrangements. The parameters a and c define the hexagonal lattice, with a typical relationship a = b and c distinct, though exact values vary by material.

Common materials adopting the P6_3mc (wurtzite-type) structure include ZnO, GaN, and AlN, as well as other nitrides and oxides that crystallize in this hexagonal, non-centrosymmetric framework. The space group is central to understanding their piezoelectric, pyroelectric, and certain optical properties, and is frequently used in crystallographic descriptions of wurtzite-related compounds.