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Point Groups

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Point Groups (Crystal Systems) Roya Majidi 1393
2D The five Bravais lattices in 2 dimensions
2D
2D P, C
2D P, C
2D
2D
2D
2-D Symmetry The original 6 elements plus the 4 combinations creates 10 possible 2-D Point Groups: 1 2 3 4 6 m 2mm 3m 4mm 6mm Any 2-D pattern of objects surrounding a point must conform to one of these groups
3D The 14 Bravais lattices in 3 dimensions

سه میلی

تک میلی

راست گوشی

چهار گوشی

مکعبی

سه گوشی / رومبوهدرال

شش گوشی

Crystallographic Point Groups Stereographic projections of point group symmetry (“+” is in the northern hemisphere and “o” is in the southern hemisphere)

Symmetry and the point groups

Symmetry and the point groups. Symmetry Elements and Symmetry Operations. Identity Proper axis of rotation Mirror planes Center of symmetry Improper axis of rotation. Symmetry Elements and Symmetry Operations. Identity =&gt; E. Symmetry Elements and Symmetry Operations.

2.85k views • 41 slides

Classification of Point Groups and Space Groups into Crystal Systems

699 views • 13 slides

Character Tables for Point Groups

Character Tables for Point Groups. Each point group has a complete set of possible symmetry operations that are conveniently listed as a matrix known as a Character Table . As an example, we will look at the character table for the C 2v point group. Point Group Label.

6.11k views • 25 slides

Ch 4 Lecture 1 Symmetry and Point Groups

Ch 4 Lecture 1 Symmetry and Point Groups. Introduction Symmetry is present in nature and in human culture. Using Symmetry in Chemistry Understand what orbitals are used in bonding Predict IR spectra or Interpret UV-Vis spectra Predict optical activity of a molecule

2.06k views • 17 slides

POINT GROUPS &amp; SPACE GROUPS

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

589 views • 7 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.

1.11k views • 34 slides

Lecture 10 REPRESENTATIONS OF SYMMETRY POINT GROUPS

Lecture 10 REPRESENTATIONS OF SYMMETRY POINT GROUPS. 1) Basis functions, characters and representations Each symmetry operation in a group can be represented by a matrix transforming a particular object ( basis function ) like the symmetry operation in the group does.

1.2k views • 4 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 ).

1.55k views • 19 slides

32 Crystallographic Point Groups

32 Crystallographic Point Groups. Point Groups. The 32 crystallographic point groups (point groups consistent with translational symmetry) can be constructed in one of two ways:.

1.95k views • 23 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

805 views • 22 slides

Identifying point groups

Identifying point groups. Special cases:. Perfect tetrahedral (T d ) e.g. P 4 , CH 4. Perfect octahedral (O h ) e.g. SF 6 , [B 6 H 6 ] -2. Perfect icosahedral (I h ) e.g. [B 12 H 12 ] -2 , C 60. Identifying point groups. Low symmetry groups:. Only* an improper axis (S n )

2.15k views • 16 slides

Certain physical properties associated with certain space groups or point groups

Certain physical properties associated with certain space groups or point groups · Piezoelectricity is the property of a crystal to develop an electric charge when subjected to pressure or tension in certain directions and is observed in crystals with polar axes.

359 views • 9 slides

The determination of point groups of molecules

The determination of point groups of molecules. two σ v but no σ h mirror planes means point group is C 2v. only one rotational axis = C 2. The point group of the water molecule is C 2v. Naming point groups:.

2.11k views • 33 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. HOMEWORK. Why do biological macromolecules often crystallize in space groups of higher symmetry than small molecules?

310 views • 24 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. Introduction. Form. Anisotropy. Ag. Mo. Polycrystals.

586 views • 50 slides

Point Groups (Crystal Classes)

373 views • 18 slides

Character Tables for Point Groups

757 views • 25 slides

Point Groups

Point Groups. Roya Majidi 1393. How symmetry operators without translation combine. Point Groups. 7 Crystal Systems. 32 point groups in 3D. Lattices have only 7 distinct point groups. How symmetry operators with translation combine. Space Groups. 14 Bravais Lattices.

1.38k views • 109 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 Reciprocal Lattice &amp; Diffraction Deformation and texture Interfaces, orientation relationships Martensitic transformations. P4mm.

305 views • 20 slides

Identifying point groups

352 views • 16 slides

Introduction and point groups Stereographic projections Low symmetry systems Space groups

753 views • 26 slides

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Presentation Transcript

Symmetry and the point groups

Classification of Point Groups and Space Groups into Crystal Systems

Character Tables for Point Groups

Ch 4 Lecture 1 Symmetry and Point Groups

POINT GROUPS &amp;amp; SPACE GROUPS

Introduction and point groups Stereographic projections Low symmetry systems Space groups

Lecture 10 REPRESENTATIONS OF SYMMETRY POINT GROUPS

Point Groups (Crystal Classes)

32 Crystallographic Point Groups

From Point Groups to Space Groups

Identifying point groups

Certain physical properties associated with certain space groups or point groups

The determination of point groups of molecules

From Point Groups to Space Groups

Introduction and point groups Stereographic projections Low symmetry systems Space groups

Point Groups (Crystal Classes)

Character Tables for Point Groups

Point Groups

Introduction and point groups Stereographic projections Low symmetry systems Space groups

Identifying point groups

Introduction and point groups Stereographic projections Low symmetry systems Space groups

POINT GROUPS & SPACE GROUPS