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Transformation operators for symetry elements
- 1. Transformation operators for symetry elements KATHIA MARCELA CAMPO GIRALDO UNIVERSITY OF ANTIOQUIA COLLEGE OF PHYSICS
- 2. Content •Introduction •Transformation operators for the crystallographic symmetry elements •2-D point groups •3-D symmetry Operators •3-D point groups •Standard settings •The fourteen Bravais Networks •The forteen symmetry elements generate the 32 cristal clases •Curie groups symmetries •Bibliography
- 3. Introduction Since the pysical property tensors depend on symmetry, mathematical methods for determining the influence of symmetry are needed. More specifically, transformations matrices are required for the symmetry elements that generate the cristal class.
- 4. Transformation operators for the crystallographic symmetry elements There are four types of symmetry elements that require discussion: rotation axes, mirror planes, inversión centers, and inversión axes in which rotation is accompanied by inversión.
- 12. THE FOURTEEN BRAVAIS NETWORKS
- 13. The forteen symmetry elements generate the 32 cristal clases
- 14. Curie group symmetries In many practical applications engineers work with amorphous or polycrystalline materials rather than single crystals. Such materials are often processed in such a way that their properties are anisotropic. The symmetry of these textured materials can often be described by curie group symmetries.
- 15. The Curie groups all have a common symmetry element represented by an ∞-fold rotation axis. The transformation matrix for ∞- fold axis parallel to Z3 is
- 16. Polycrystalline metals and ceramics with randomly oriented grains possess spherical symmetry ∞ ∞m. Processed polycrystalline materials may also adopt crystallographics symmetry.
- 17. Liquids and liquid crystals exhibit a number of different Curie group symmetries
- 18. When sugar is dissolved in water it induces optical activity causing the plane of polarization of light to be rotated.
- 19. 19 NH3 Co NH3 H2OCl Cl H2O NH3 Co Cl ClH2O H3N H2O Examples of enantiomers
- 21. Bibliography Properties of materials_Robert E. Newnham Condensed matter physics lecture V and VI_Jorge M Osorio Guillen Inorganic Chemistry lecture_Juan Carlos M