Lecture notes on crystallography given to students of Moscow State University. M.V. Lomonosov (Faculty of Geology) geochemical flow in the 1st and 2nd semesters with the aim of giving students a natural science basis for subsequent study of mineralogy, petrography, geochemistry, a course in minerals, lithology and other sciences about the substance of the Earth; reveal the crystalline essence of minerals and the ensuing features of their physical properties, conditions of formation and behavior in the earth's crust, ways of searching for minerals and creating synthetic materials with the desired physical properties. ContentsUse the arrow to expand or collapse this sectionIntroductionGetting started .Textbooks.What do geologists study?Crystallography.Symmetry around us.Some definitions and notations.History of development crystallography. Projection of crystals. Euler's theorem Magic axes [of symmetry]. Projection of crystals and symmetry elements. Euler's theorem. Some basics of spherical trigonometry. Derivation of symmetry classes Warm-up. Derivation of symmetry groups (classes) in Bravais symbolism. Derivation of cubic symmetry groups (classes). Coordinate systems. Categories. Syngonies. Symbolism of Schönflies, Hermann - MogenCoordinate systems in crystallography. Categories. Syngonies. Symbols. Schönflies symbolism. Herman-Mogen symbolism (international) Various ways of representing symmetric operations - model, coordinate, matrix Cayley square Model method. Coordinate method. Cayley square. Simple forms of crystals. Simple form of crystal. Right-leftism in the mineral world. Appearance and habit. Simple forms cubic crystalsBasics of crystal growth and morphology. Synthesis methods Formation of crystals in nature. Morphological features of real crystals. Dendrites. Drusen. Epitaxites. Intergrowth twins. Symmetry of twins. Methods of growing crystals. Crystallization from solutions. Crystallization from melts. Symbols of faces and edges of crystals. Indication - assignment of a numerical crystallographic symbol to each face. Hayu's Law , the law of integers, or the law of rationality of relations between the parameters of crystal faces. Each individual face has its own index! Definition of face symbols in the absence of a single face in a crystal. Symbols of faces belonging to one simple crystal shape. Why is the U axis needed? Relationship between face symbols and crystal edges. Graphic method definitions of symbols of faces and edges of crystals. The essence of Weiss's law - the law of belts (zones). The method of zones - crystallographic [a Icosahedral symmetry groups All about L5. The magic of Platonic bodies. Quasicrystals. Carbon nanotubes. Hume-Rothery's rule. Icosahedral symmetry is present in living organisms. Limit symmetry groups. Curie, Neumann and Voigt principles. The beginning of a conversation about the physical properties of a crystalTo the question of our understanding of multidimensional spaces. Lineland and Flatland. Limit groups of Curie symmetry. Curie's principle. Neumann's principle. Voigt's principle. Physical properties of a crystal. Scalar, vector and tensor properties. Mechanical properties. Elastic properties of crystals. Acoustic properties. Symmetry of the microworld. Part 1Operation symmetry. Symmetry of crystal structures. Unit cell (Bravais cell). Rules for choosing a Bravais cell. Crystalline world in polyhedra. The theory of closest packing, its use to describe crystal structures. Different types of coordination polyhedra. The theory of closest packing. Types of closest packing. Relative sizes of atoms and ions. Atomic composition of the Earth's crust. Why is Si in charge? Silicates with finite motifsSizes of atoms and ions.Chemical element.Chemical composition of the Earth.Si is the main one.Crystal chemical classification of silicates.Silicates with infinite silicon-oxygen motifsChain silicates.Pyroxenoids.Layered silicates.Framework silicates.Granite.Zeolites.Physical properties of crystals (continued)Optical properties crystals. Refraction. Birefringence. Optically active crystals. Dispersion of light in crystals. Crystal brilliance. Crystal color. Main optical constants of a crystal. Electrical properties of crystals Zone energy structure of a crystal. Pyroelectric effect. Piezoelectric effect. Magnetic properties.