Three-Dimensional Symmetry

Slides:

Advertisements

Similar presentations

INTRODUCTION TO CERAMIC MINERALS

Advertisements

Equivalent Positions in 3-D

Crystal Morphology Remember: Space groups for atom symmetry

Watkins/Fronczek - Rotational Symmetry 1 Symmetry Rotational Symmetry and its Graphic Representation.

Ideas for Exercises for the K-12 Classroom

Symbols of the 32 three dimensional point groups

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

© T Madas. We can extend the idea of rotational symmetry in 3 dimensions:

Lecture 2: Crystal Symmetry

1 Watkins/Fronczek - Space Groups Translational + Rotational Symmetry Introduction to Space Groups.

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.

Symmetry Elements II.

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

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

Symmetry Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern Operation: some act that reproduces the.

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.

Rotation with Inversion (Rotoinversion) Equivalency to other symmetry operations

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?

Lecture 8 (10/09/2006) Crystallography Part 1: Symmetry Operations

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

The internal order of minerals: Lattices, Unit Cell & Bravais Lattices

PH0101 UNIT 4 LECTURE 3 CRYSTAL SYMMETRY CENTRE OF SYMMETRY

Practical I - A. Crystallographic axis  One of three lines (sometimes four, in the case of a hexagonal crystal), passing through a common point, that.

1. Crystals Principles of crystal growth 2. Symmetry Unit cells, Symmetry elements, point groups and space groups 3. Diffraction Introduction to diffraction.

Symmetry Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern Operation: some act that reproduces the.

Introduction to Crystallography

PH 0101 UNIT 4 LECTURE 1 INTRODUCTION TO CRYSTAL PHYSICS

CH4 – four-fold improper rotation

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.

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

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

Introduction to Crystallography and Mineral Crystal Systems PD Dr. Andrea Koschinsky Geosciences and Astrophysics.

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

Lecture 12 Crystallography

Chapter 4. Molecular Symmetry

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

Crystalline Solids :-In Crystalline Solids the atoms are arranged in some regular periodic geometrical pattern in three dimensions- long range order Eg.

Symmetry, Groups and Crystal Structures

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.

ESO 214: Nature and Properties of Materials

Crystal Structure of Solids

Key things to know to describe a crystal

Metallic –Electropositive: give up electrons Ionic –Electronegative/Electropositive Colavent –Electronegative: want electrons –Shared electrons along bond.

From Point Groups to Space Groups

Bonding in Solids Melting point (K) Molecular crystals MetalsIonic crystals Covalent crystals organic crystals W(3683) Mo(2883) Pt(2034)

Symmetry in crystals. Infinitely repeating lattices.

Point & Space Group Notations

WHY CRYSTALLORAPHY WHY CRYSTALLORAPHY? perfect order … the perfect order of particles in the space is amazing… crystals ground"as is" To think that such.

1 Crystals possess different symmetry elements. The definite ordered arrangement of the faces and edges of a crystal is known as `crystal symmetry’. CRYSTAL.

Periodic patterns.

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

Point Groups Roya Majidi 1393.

SOLID STATE By: Dr.DEPINDER KAUR.

SOLID STATE By: Dr.Bhawna.

Miller indices/crystal forms/space groups

Objectives • Written and graphic symbols of symmetry elements

Symmetry, Groups and Crystal Structures

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.

Chemical Bonding Molecular Geometry.

Symmetry, Groups and Crystal Structures

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

Symmetry Elements II.

Symmetry “the correspondence in size, form and

Crystal and Amorphous Structure

Elementary Symmetry Operation Derivation of Plane Lattices

Crystallography.

Presentation transcript:

Three-Dimensional Symmetry How can we put dots on a sphere?

The Seven Strip Space Groups

Simplest Pattern: motifs around a symmetry axis (5) Equivalent to wrapping a strip around a cylinder

Symmetry axis plus parallel mirror planes (5m)

Symmetry axis plus perpendicularmirror plane (5/m)

Symmetry axis plus both sets of mirror planes (5m/m)

Symmetry axis plus perpendicular 2-fold axes (52)

Symmetry axis plus mirror planes and perpendicular 2-fold axes (5m2)

The three-dimensional version of glide is called inversion

Axial Symmetry (1,2,3,4,6 – fold symmetry) x 7 types = 35 Only rotation and inversion possible for 1-fold symmetry (35 - 5 = 30) 3 other possibilities are duplicates 27 remaining types

Isometric Symmetry Cubic unit cells Unifying feature is surprising: four diagonal 3-fold symmetry axes 5 isometric types + 27 axial symmetries = 32 crystallographic point groups Two of the five are very common, one is less common, two others very rare

The Isometric Classes

The Isometric Classes

Non-Crystallographic Symmetries There are an infinite number of axial point groups: 5-fold, 7-fold, 8-fold, etc, with mirror planes, 2-fold axes, inversion, etc. In addition, there are two very special 5-fold isometric symmetries with and without mirror planes. Clusters of atoms, molecules, viruses, and biological structures contain these symmetries Some crystals approximate these forms but do not have true 5-fold symmetry, of course.

Icosahedral Symmetry

Icosahedral Symmetry Without Mirror Planes

Why Are Crystals Symmetrical? Electrostatic attraction and repulsion are symmetrical Ionic bonding attracts ions equally in all directions Covalent bonding involves orbitals that are symmetrically oriented because of electrostatic repulsion

Malformed Crystals

Why Might Crystals Not Be Symmetrical? Chemical gradient Temperature gradient Competition for ions by other minerals Stress Anisotropic surroundings

Regardless of Crystal Shape, Face Orientations and Interfacial Angles are Always the Same

We Can Project Face Orientation Data to Reveal the Symmetry

Projections in Three Dimensions are Vital for Revealing and Illustrating Crystal Symmetry