Wave Vector Star Channel Associated with Superstructure of Crystal and Bravais Lattice Types

For developing new materials, high superconductor, ferroics such as ferroelectric, ferromagnetic, ferroelastic, and multi-ferroics such as ferroelectric- magnetic, mageneto-elastic, and so on, and for studying their features, the study of the symmetry is especially important. As well-known, all crystals belong to any group among 230 space groups. In this crystals, change of physical properties is related with the breaking of rotation, translational symmetry and is described to full irreducible representation of space group. For a long time, many researchers have been studying the possible superstructure that is practically significant. The superstructure is obtained during the translational symmetry breaking. The study of the superstructure phases aims at finding out the lattice types of the possible lower symmetry phases during translational symmetry breaking. This is directly associated with study of the wave vector star in reciprocal lattice space.