The Mirror: Mother of All Symmetries in Crystals

Abstract

Mirror symmetry is found to be the only fundamental symmetry in crystalline solids because all other symmetries, such as rotation, inversion, rotoreflection, rotoinversion and translational periodicity can be easily derived from suitable combinations of mirrors. Similarly, the point group symmetries can also be derived from the same. The mirror combination scheme is found to work in accordance with the principle of Wigner-Seitz cells and Brillouin Zones (and not with the conventional unit cells as proposed by Bravais), where the zone boundaries of a Brillouin zone represent different sets of Bragg planes obtained from diffraction pattern of the given crystal, while the diffraction of given crystal takes place in terms of decreasing interplanar spacing in reciprocal space. Because the Wigner Seitz cells, the Brillouin zones and the diffraction patterns possess defined origin and exhibit spherical symmetry, they cannot have translational symmetry of any kind (microscopic or macroscopic). Results obtained on the basis of this concept help us to remove the existing ambiguities in crystallography and make the crystal structure determination simple. Further, prima facie the diffraction patterns are found to take care of the proposed 'systematic absences' arising due to the so called lattice centering, glide planes and screw axes without actually taking them into consideration. This newly and first discovered concept is expected to explain all other complicated or less understood issues related to crystallography.