Crystallographic Symmetry: The Fundamental Feature of Matter Organization Determining the Energy and Space Transformations in Condensed Atomic Systems

Abstract

Crystallization proceeds by ordering atomic positions by translational and point symmetry operations. By fixing the symmetrical atomic configuration, this process removes the degrees of freedom from the atoms and thereby minimizes their energy and space volume V* characterizing this configuration. The structure of corundum (Al₂O₃) is crystallographically analyzed and its parameters are compared with those for the other prevalent structures (spinel, garnet, apatite, tourmaline, etc.). The phenomenon of crystallographic symmetry in the space of three coordinates and energy minimizes the number of degrees of freedom, and hence, the energy of atomic systems, unifies their configuration by packing it into a minimum volume-an information cell. An “ideal” construction (stencil) stable with respect to variations in external conditions and atomic compositions forms.