Lesson 11: Adding Translation Define pure translation within a cell—centering Combine translation with other symmetry operations to produce a new operations.

Slides:

Advertisements

Similar presentations

More on symmetry Learning Outcomes:

Advertisements

Equivalent Positions in 3-D

In this section we’ll consider space groups Pm, Cm, Pc and Cc

Symbols of the 32 three dimensional point groups

t1 t2 6 t1 t2 7 8 t1 t2 9 t1 t2.

3D Symmetry _2 (Two weeks).

Lesson 12—Working with Space Groups How to convert a space group to a point group Adding the translational elements Calculating the coordinates of the.

Why Study Solid State Physics?

III Crystal Symmetry 3-1 Symmetry elements (1) Rotation symmetry

Lecture 2: Crystal Symmetry

CONDENSED MATTER PHYSICS PHYSICS PAPER A BSc. (III) (NM and CSc.) Harvinder Kaur Associate Professor in Physics PG.Govt College for Girls Sector -11, Chandigarh.

Crystals and Symmetry. Why Is Symmetry Important? Identification of Materials Prediction of Atomic Structure Relation to Physical Properties –Optical.

Lecture 13 (11/1/2006) Crystallography Part 6: 3-D Internal Order & Symmetry Space (Bravais) Lattices Space Groups.

Mineralogy Carleton College Winter Lattice and its properties Lattice: An imaginary 3-D framework, that can be referenced to a network of regularly.

How to read and understand… Title.

Lecture 12 (10/30/2006) Crystallography Part 5: Internal Order and 2-D Symmetry Plane Lattices Planar Point Groups Plane Groups.

Title How to read and understand…. Page Left system crystal system.

17-plane groups When the three symmetry elements, mirrors, rotation axis and glide planes are shown on the five nets, 17-plane groups are derived.

Crystal Chem  Crystallography Chemistry behind minerals and how they are assembled –Bonding properties and ideas governing how atoms go together –Mineral.

CRYSTALLOGRAPHY TRIVIA FINAL ROUND!. Round 3 – Question 1 Twins are said to add another level of symmetry to a crystal. Why is this?

Homework Discussion Read pages 372 – 382 Page 394: 1 – 6, 11 – 12,

Crystallography Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern In 3-D, translation defines operations.

Symmetry of Single-walled Carbon Nanotubes. Outline Part I (November 29) Symmetry operations Line groups Part II (December 6) Irreducible representations.

I. Structural Aspects Space GroupsFranzen, pp Combine Translational and Rotational symmetry operations  230 Space Groups Both types must be compatible.

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.

“International Tables of Crystallography”

Crystallography and Diffraction Theory and Modern Methods of Analysis Lectures 1-2 Introduction to Crystal Symmetry Dr. I. Abrahams Queen Mary University.

1 Internal Order and Symmetry GLY 4200 Fall, 2015.

Chem Lattices By definition, crystals are periodic in three dimensions and the X-ray diffraction experiment must be understood in the context of.

Chapter 1 Crystal Structures. Two Categories of Solid State Materials Crystalline: quartz, diamond….. Amorphous: glass, polymer…..

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

8-11 Symmetry Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation.

Transformation in Geometry Transformation A transformation changes the position or size of a shape on a coordinate plane.

Lecture 12 Crystallography

Lesson 12—Working with Space Groups

Warm Up 1. Give the coordinates of triangle ABC with vertices (7, 2), (1, 2), (4, –5) reflected across the y-axis. 2. Give the coordinates of triangle.

Lesson 13 How the reciprocal cell appears in reciprocal space. How the non-translational symmetry elements appear in real space How translational symmetry.

Lesson 13 How the reciprocal cell appears in reciprocal space. How the non-translational symmetry elements appear in real space How translational symmetry.

Crystallography ll.

Homework Look at the Space Group P21/c (#14). This is the most common space group for small molecules. 1. No protein has ever been found to crystallize.

Internal Symmetry of Crystals

Symmetry in two-dimension  2D unit cell Periodicity in 3-dim. – smallest repeated unit  unit cell.

ESO 214: Nature and Properties of Materials

Space Groups Internal Symmetry of Crystals. Space Groups If translation operations are included with rotation and inversion, We have 230 three-dimensional.

Key things to know to describe a crystal

Crystallography lll. 230 space groups Combine 32 point groups (rotational symmetry) with a. 14 Bravais lattices (translational symmetry) b.glide planes.

From Point Groups to Space Groups

Symmetry in crystals. Infinitely repeating lattices.

المحاضرة 4 التركيب البلوري-التماثل

3-D Lattices a x z c    y b shortest translation vectors each corner of the unit cell : point with equal surroundings = lattice point cell defined.

Crystal Structure and Crystallography of Materials

Parameters235 Formula MW cryst syst Space group a /Å b /Å c /Å α (°) β (°) γ (°) V /Å 3 Z T /K λ /Å ρ c (g/cm3) μ (mm-1) Goodness of fit θ range Total.

Crystal Structure and Crystallography of Materials

PRESENTATION ON SYMMETRY IN CRYSTAL STRUCTURE REPRESENTED BY SATYAM CHAUHAN BT/ME/1601/011.

9.5 & 9.6 – Compositions of Transformations & Symmetry

Point Groups Roya Majidi 1393.

Miller indices/crystal forms/space groups

c Symmetry b  a   a b The unit cell in three dimensions.

Crystal Structure and Crystallography of Materials

Crystalline state Symmetry in nature Symmetry in arts and industry

Textbook: Condensed matter physics, 2nd ed. By M. Marder

Crystals Crystal consist of the periodic arrangement of building blocks Each building block, called a basis, is an atom, a molecule, or a group of atoms.

NOTE: Symbolism In Schönflies notation, what does the symbol S2 mean?

Symmetry of position: periodic order

Crystals and Symmetry.

Composition of Transformations

Crystallography.

Crystallography lll.

Crystal Chem  Crystallography

Presentation transcript:

Lesson 11: Adding Translation Define pure translation within a cell—centering Combine translation with other symmetry operations to produce a new operations  Rotation + translation = screw axis  Reflection + translation = glide plane

Look at the Space Group P21/c (#14). 1. No protein has ever been found to crystallize in this space group. Why is that? P21/c is centric while proteins are optically active 2. Someone reports a crystal in P21/c with Z=1.Is this possible? Why or why not. Impossible. Only special positions have 2 in the cell 3. What is the symmetry of the special positions in this space group? Inversion

Centering Types Centering is indicated by a capital letter at the start of the H-M cell name. Face Centering –A centering (0, ½, ½)‏ –B centering (½, 0, ½)‏ –C centering (½, ½, 0)‏ –F centering – A+B+C centering (Face centered)‏ Body Centering –I centering –(½, ½, ½) (Body Centered)‏ No Centering P for primitive

Rhombohedral Centering It is always possible to take a rhombohedral cell (a=b=c  and convert it to a hexagonal cell (a=b . The hexagonal cell will have 3 times the volume and be rhomohedral centered—R (2/3, 1/3, 1/3) (1/3, 2/3, 2/3)‏ Today rhombohedral cells are always reported in their hexagonal form.

A translation by 2/3 generates a point at 1/3

Glide Planes A glide plane is a mirror followed by a translation of ½ the length of the vector in the plane of the mirror. The translation can be along an axis in the plane (a,b,c) or along the diagonal (n)‏ The glide plane is indicated by a lower case letter indicating the direction of translation. The axis perpendicular to the plane is found from the position in the H-M symbol The translation is never perpendicular to m

An example

Diamond Glide Symbol d Reflection followed by ¼ translation along the diagonal of the mirror plane Very Rare—thank goodness

Homework Is there anything wrong with the proposed space group Pbac? If so what. Is there a difference between 2 1 and 6 3 ? If so what is it.