Symmetry principles of the formation of ordered phases of crystals

General principles of the formation of low-symmetry ordered phases of crystals, such as the principle of a finite number of low-symmetry phases, the principle of phase diversity, the principle of a finite number of possible structure types of ordered phases, the principle of structural complexity, the compensation principle, and the generalized Fedorov-Groth law, are established in the framework of the Landau-Lifshitz theory of second-order phase transitions. The ranges of their applicability are determined. These principles are derived by extending the results of the structural calculations of the design of new inorganic materials with anomalous physicochemical properties.