Fedorov Groups of Crystallographic Symmetry As Algorithms of Space and Energy Transformations in Realization of Stable Atomic Configurations
С. В. Борисов, С. А. Магарилл, Н. В. Первухина
Abstract
Abstract The effect of symmetry ordering of sites of material particles (atoms, chemically strong atomic groups) is shown on characteristic examples. This ordering leads to reduction of the degrees of their freedom and, therefore, minimizes the energy of a system during crystallization. The geometry of Fedorov groups, supplemented with the symmetry energy function, determines the processes occurring in condensed atomic medium (“Kingdom of crystals,” according to E.S. Fedorov). Criteria are proposed for comparative estimation of the stability of structures, including the structural stencils (structure types of tourmaline, apatite, et al.) abundant in nature.
Topics & Concepts
Realization (probability)Symmetry (geometry)CrystallizationSpace groupSymmetry operationDegrees of freedom (physics and chemistry)CrystallographyStability (learning theory)Function (biology)Space (punctuation)Theoretical physicsPhysicsChemistryGeometryMathematicsQuantum mechanicsX-ray crystallographyDiffractionComputer scienceThermodynamicsOperating systemBiologyEvolutionary biologyMachine learningStatisticsX-ray Diffraction in CrystallographyCrystal Structures and PropertiesChemical Thermodynamics and Molecular Structure