Classification of Point Groups and Space Groups into Crystal Systems

Aug 11, 2012

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Classification of Point Groups and Space Groups into Crystal Systems

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1. Classification of Point Groupsand Space Groupsinto Crystal Systems

Space groups

Space groups. Translations T = u t 1 (1-D) u is an integer The set of all lattice vectors is a group (the set of all integers (±) is a group). Space groups . Quotient groups Thm: Cosets of an invariant subgroup form a group in which the subgroup is the identity element

383 views • 21 slides

Miller indices/crystal forms/space groups

Miller indices/crystal forms/space groups. Crystal Morphology. How do we keep track of the faces of a crystal? Sylvite a= 6.293 Å Fluorite a = 5.463 Å Pyrite a = 5.418 Å Galena a = 5.936 Å. Crystal Morphology. How do we keep track of the faces of a crystal?

918 views • 35 slides

POINT GROUPS & SPACE GROUPS

MATERIALS SCIENCE & ENGINEERING . Part of . A Learner’s Guide. AN INTRODUCTORY E-BOOK. Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016 Email: anandh@iitk.ac.in, URL: home.iitk.ac.in/~anandh.

536 views • 7 slides

Space Groups

Space Groups. Internal Symmetry of Crystals. Space Groups. If translation operations are included with rotation and inversion, We have 230 three-dimensional space groups. Translation operations Unit cell translations Centering operations (Lattices) ( A, B, C, I, F, R )

575 views • 25 slides

Introduction and point groups Stereographic projections Low symmetry systems Space groups

Crystallography. H. K. D. H. Bhadeshia. Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships Martensitic transformations. 180° rotation about horizontal axis. Invert rotated image.

1.04k views • 34 slides

Point Groups (Crystal Classes)

Point Groups (Crystal Classes). Stereographic Projections. Used to display crystal morphology. X for upper hemisphere. O for lower. Stereographic Projections. We will use stereographic projections to plot the perpendicular to a general face and its symmetry equivalents (general form hkl ).

1.37k views • 19 slides

From Point Groups to Space Groups

From Point Groups to Space Groups. How to expand from a point group to a space group Special and General Positions. Complete Hermann-Maugin Notation. Start with PtCl 4 2-. D4h Character Table. Add Unique Symmetry. The Features. The view is looking down the 4-fold axis

752 views • 22 slides