QUASIPERIODIC LATTICES AND QUASISYMMETRY SPACE GROUPS. I.N. Mochtchenko, North Caucasus Scientific Center, 140, Pushkinskaya, Rostov-on-Don, 344006, Russia

The method allowing to describe the quasicrystals as a discrete and quasiperiodic disposition of structural elements and to characterize the quasicrystal structure by means of a few parameters is presented. The central point of elaborated theory is a quasiperiodic lattice. We propose a constructive algorithm determinating the 2-dim and 3-dim discrete lattices in which the knots are disposed by quasiperiodic law with finite distance between them. The structure of quasicrystal is described by one or several such lattices occupated by atoms of different sorts and characterized by coordinates of these sublattices, the basis vectors of quasiperiodicity and space group of quasisymmetry. The last consists of one subgroup of point symmetry (it may containes noncrystallography elements such as 5-, 7-, 8-, 12-fold axises), subgroups of quasitranslations and subgroups of point quasisymmetry. The quasisymmetry elements are the approximate symmetry operations and transform lattice into itself with some error. The proposed theory is demonstrated on the example of quasicrystal with 5-fold axis symmetry. The calculated high-resolution TEM micrographs and difraction diagrams are well corresponded to experemental ones. The elaborated method is computible with the conseption of pointlike atoms which is the basis of difraction structural analysis.