Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1...

10
1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 – fold axes Unit cell edge mirror line

Transcript of Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1...

Page 1: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

1

Symmetry Elements of the 2D Space Groups

glide line2, 3, 4, 6 – fold axes

Unit cell edgemirror line

Page 2: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

2

Highestorder

rotation

Has reflection?

Yes No

6-fold p6m p6

4-foldHas mirrors at 45°?

p4Yes: p4m No: p4g

3-foldHas rot. centre off mirrors?

p3Yes: p31m No: p3m1

2-fold

Has perpendicular reflections?Has glide reflection?

Yes No

Has rot. centre off mirrors?pmg Yes: pgg No: p2

Yes: cmm No: pmm

noneHas glide axis off mirrors? Has glide reflection?

Yes: cm No: pm Yes: pg No: p1

Page 3: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

Find the plane groups in the following 10 patterns marked in the yellow squares (for 1 and 2 the same pattern is shown more than once to help you in seeing/finding the plane group). Draw the unit cell in the each pattern and show the mirror and/or the glide lines accordingly.

Page 4: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

1. 1.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

p4mm

Page 5: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

2.

2.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

No mirrors!

Page 6: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

2.

Pictures taken by Anke Zurn at Topkapi Palast, Istanbul

p6 No mirrors!

Page 7: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

kiosk, close to TopkapiPalast;Istanbul, 2009

3.

p6mm

Page 8: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

Bamboo basket image source: http://www.fz-juelich.de (modified)

Basket waving: kagome net

4.p6

http://www.fz-juelich.de/
http://www.fz-juelich.de/
http://www.fz-juelich.de/
Page 9: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

Kagome network

Page 10: Symmetry Elements of the 2D Space Groupsn.ethz.ch/~nielssi/download/4. Semester/AC II/Uebungen...1 Symmetry Elements of the 2D Space Groups glide line 2, 3, 4, 6 –fold axes Unit

10

6.

p4

7.

p4gm

8.

p31m

9.

cmm2

10.

cm


SYMMETRY AND SIMILARITY PROPERTIES OF 2D …examining the similarity of 2D-al configurations. 2.1 Method I search the symmetric axis of the configuration examined that I scanning the

SYMMETRY AND SIMILARITY PROPERTIES OF 2D …examining the similarity of 2D-al configurations. 2.1 Method I search the symmetric axis of the configuration examined that I scanning the

U. Pitt. MBSB-1 Fall-2014 Methods, Samples & Symmetry ...structbio.pitt.edu/.../MBSB-1_EMpart2_2014-Nov.pdf · Methods, Samples & Symmetry • 2D crystallography bacteriorhodopsin,

U. Pitt. MBSB-1 Fall-2014 Methods, Samples & Symmetry ...structbio.pitt.edu/.../MBSB-1_EMpart2_2014-Nov.pdf · Methods, Samples & Symmetry • 2D crystallography bacteriorhodopsin,

Microstructural design of 2D and 3D photonic …...II In the next step, 2D symmetric and asymmetric photonic crystals are optimized using BESO to study the influence of lattice symmetry

Microstructural design of 2D and 3D photonic …...II In the next step, 2D symmetric and asymmetric photonic crystals are optimized using BESO to study the influence of lattice symmetry

Lecture 2: Crystallization & Symmetry crystal growth theory symmetry symmetry operator symmetry operators space groups.

Lecture 2: Crystallization & Symmetry crystal growth theory symmetry symmetry operator symmetry operators space groups.

Robustness for 2D Symmetric Tensor Field Topologybeiwang/publications/Tensor_Field_Robustness... · Robustness for 2D Symmetric Tensor Field Topology ... a rotational symmetry with

Robustness for 2D Symmetric Tensor Field Topologybeiwang/publications/Tensor_Field_Robustness... · Robustness for 2D Symmetric Tensor Field Topology ... a rotational symmetry with

2D Symmetry (1.5 weeks)

2D Symmetry (1.5 weeks)

Symmetry OPEN CCESSA symmetry

Symmetry OPEN CCESSA symmetry

3-1 Symmetry. Symmetry All Around Us Symmetry at the Beach Symmetry at the Beach Line Symmetry & Rotational Symmetry - All you need to Know + Symmetry.

3-1 Symmetry. Symmetry All Around Us Symmetry at the Beach Symmetry at the Beach Line Symmetry & Rotational Symmetry - All you need to Know + Symmetry.

2D Symmetry (1.5 weeks). From previous lecture, we know that, in 2D, there are 3 basics symmetry elements: Translation,mirror (reflection),and rotation.

2D Symmetry (1.5 weeks). From previous lecture, we know that, in 2D, there are 3 basics symmetry elements: Translation,mirror (reflection),and rotation.

Constructing crystals in 1D, 2D & 3D Understanding them using the language of: Lattices Symmetry LET US MAKE SOME CRYSTALS .

Constructing crystals in 1D, 2D & 3D Understanding them using the language of: Lattices Symmetry LET US MAKE SOME CRYSTALS .

2D Kac-Moody Symmetry of 4D Yang-Mills Theory · PDF file2D Kac-Moody Symmetry of 4D Yang-Mills Theory ... 18 Oct 2016 act nontrivially at null in nity and comprise the four-dimensional

2D Kac-Moody Symmetry of 4D Yang-Mills Theory · PDF file2D Kac-Moody Symmetry of 4D Yang-Mills Theory ... 18 Oct 2016 act nontrivially at null in nity and comprise the four-dimensional

Symmetry and Aesthetics in Contemporary Physicsweb.physics.ucsb.edu/~jatila/sym-lectures/Class_02_2016.pdf · symmetry translational symmetry reflection symmetry screw symmetry =

Symmetry and Aesthetics in Contemporary Physicsweb.physics.ucsb.edu/~jatila/sym-lectures/Class_02_2016.pdf · symmetry translational symmetry reflection symmetry screw symmetry =

Vocabulary symmetry line symmetry line of symmetry rotational symmetry center of symmetry order of symmetry magnitude of symmetry.

Vocabulary symmetry line symmetry line of symmetry rotational symmetry center of symmetry order of symmetry magnitude of symmetry.

Symmetry Section 3.1. Symmetry Two Types of Symmetry:

Symmetry Section 3.1. Symmetry Two Types of Symmetry:

Symmetry and Properties of Crystals (MSE638) Symmetry ...home.iitk.ac.in/~bsomnath/mse638/WWW/2dsym.pdfSymmetry and Properties of Crystals (MSE638) Symmetry operations in 2D and planar

Symmetry and Properties of Crystals (MSE638) Symmetry ...home.iitk.ac.in/~bsomnath/mse638/WWW/2dsym.pdfSymmetry and Properties of Crystals (MSE638) Symmetry operations in 2D and planar

Symmetry and Properties of Crystals (MSE 638) 2D Space Grouphome.iitk.ac.in/~bsomnath/mse638/WWW/2dsg.pdf · Symmetry and Properties of Crystals (MSE 638) 2D Space Group Somnath Bhowmick

Symmetry and Properties of Crystals (MSE 638) 2D Space Grouphome.iitk.ac.in/~bsomnath/mse638/WWW/2dsg.pdf · Symmetry and Properties of Crystals (MSE 638) 2D Space Group Somnath Bhowmick

MTH 3-19a MTH 4-19a Symmetry Line Symmetry Rotation (Turn) Symmetry Translational Symmetry Creating Rotational Symmetry.

MTH 3-19a MTH 4-19a Symmetry Line Symmetry Rotation (Turn) Symmetry Translational Symmetry Creating Rotational Symmetry.

Symmetry Line Symmetry Rotational (Order) Symmetry Creating Rotational Symmetry S4.

Symmetry Line Symmetry Rotational (Order) Symmetry Creating Rotational Symmetry S4.

Topological Insulators in 2D and 3D - Lancaster UniversityTopological Insulators in 2D and 3D I. Introduction - Graphene - Time reversal symmetry and Kramers’ theorem. II. 2D quantum

Topological Insulators in 2D and 3D - Lancaster UniversityTopological Insulators in 2D and 3D I. Introduction - Graphene - Time reversal symmetry and Kramers’ theorem. II. 2D quantum

Czerny Carl-40 Taegliche Uebungen Op 337 Peters 6985 Scan

Czerny Carl-40 Taegliche Uebungen Op 337 Peters 6985 Scan