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

Slides:

Advertisements

Similar presentations

INTRODUCTION TO CERAMIC MINERALS

Advertisements

Crystallography, Crystal Symmetry, and Crystal Systems

Equivalent Positions in 3-D

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

Introduction to Mineralogy Dr. Tark Hamilton Chapter 6: Lecture Crystallography & External Symmetry of Minerals Camosun College GEOS 250 Lectures:

Lecture 2: Crystal Symmetry

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

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

Symmetry Elements II.

Symmetry Elements Lecture 5. Symmetry Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern Operation: some.

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.

IT’S TIME FOR... CRYSTALLOGRAPHY TRIVIA!!

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

Lecture 11 (10/18/2006) Crystallography Part 4: Crystal Forms Twinning

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

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.

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?

Crystallography Gypsum Monoclinic Dolomite Triclinic Emerald Hexagonal

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

PH0101 UNIT 4 LECTURE 3 CRYSTAL SYMMETRY CENTRE OF SYMMETRY

Elementary Crystallography for X-ray Diffraction

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

Lecture 11 Crystallography

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.

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

Solid state physics Dr. Abeer Kamal Abd El-Aziz 1.

Crystal Morphology: External Form Klein, pages Geol 3055 Prof. Merle.

Lecture 12 Crystallography

Lecture 2 PH 4891/581, Jan. 9, 2009 This file has parts of Lecture 2. First, here is the link to Dr. Spears’ website on semiconductor physics. Look at.

Crystallography ll.

(1) Course of MIT 3.60 Symmetry, Structure and Tensor Properties of Materials (abbreviation: SST)

PHY1039 Properties of Matter Crystallography, Lattice Planes, Miller Indices, and X-ray Diffraction (See on-line resource: )

Symmetry, Groups and Crystal Structures

ESO 214: Nature and Properties of Materials

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.

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

بسم الله الرحمن الرحيم بسم الله الرحمن الرحيم  أفلا تبصرون  وفي الارض آيات للموقنين  أفلا تبصرون  وفي الارض آيات للموقنين من سورة الذاريات اية 20.

Inorganic Material Chemistry

المحاضرة 4 التركيب البلوري-التماثل

Crystal Structure and Crystallography of Materials

Crystal Structure NaCl Well defined surfaces

Periodic patterns.

X-ray Diffraction & Crystal Structure Analysis

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

Point Groups Roya Majidi 1393.

Miller indices/crystal forms/space groups

Crystal Structure and Crystallography of Materials

Crystalline state Symmetry in nature Symmetry in arts and industry

Crystalline state Symmetry in nature Symmetry in arts and industry

Symmetry Summary GLY 4200 Lab 5 - Fall, 2017.

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.

PHY 752 Solid State Physics

Symmetry Summary GLY 4200 Lab 5 - Fall, 2012.

Symmetry “the correspondence in size, form and

Operations of the 1st kind. no change in handedness. rotation Cn

Crystals and Symmetry.

Elementary Symmetry Operation Derivation of Plane Lattices

Elementary Symmetry Operation Derivation of Plane Lattices

Derivation of the 32 Point Groups

Crystallography lll.

A. The Solid State Classification of Solid Structures

Crystal Chem  Crystallography

Symmetry Summary GLY 4200 Lab 5 - Fall, 2019.

Presentation transcript:

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

Crystallography The study of crystalline solids and the principles that govern their growth, external shape, and internal structure Crystal – a solid bounded by geometrically-arranged smooth faces Perfection of crystal face development: Euhedral – perfect crystal faces Subhedral – imperfectly developed crystal faces Anhedral – no crystal faces

Recognition of Mineral Symmetry External Crystal Form (Morphology) - macroscopic observations/measurements of crystal faces - 32 crystal classes (point groups) possible symmetry elements or combinations of elements - 1st Half of Chapter 5 (p. 170-213) Internal Atomic Arrangement - determined from X-ray diffraction - takes into account 3D translation - 14 lattice types (Bravais lattices) - Combination of 32 point groups and 14 lattice types yields 230 space groups - 2nd Half of Chapter 5 (p. 213-239)

External Symmetry Elements Crystal Morphology Rotation Reflection Center of Symmetry Rotation with Inversion

External Symmetry Elements Motif Patterns Rotation Reflection Center of Symmetry Rotation with Inversion

Rotational Axes As an external symmetry element, rotation increments (n) range from 1 to ∞ When considering the limits of translation, rotation increments are limited to 1, 2, 3, 4, and 6-fold

Rotation with Inversion (Rotoinversion) Equivalent to other symmetry operations Equivalent to Center of Symmetry

Combination of Symmetry Elements – Multiple Rotational Axes Axes at 90º (except 3-fold axes in cubic symmetry at 54º44’) Axes intersect at point Possible symmetry combinations: 422, 622, 222, 32, 23, 432 (View 422 Symmetry.ai)

Combination of Symmetry Elements – Multiple Rotational Axes with 32 Symmetry motif projections do not require a second set of 2-fold axes

Combination of Symmetry Elements – Multiple Rotational Axes in the Cubic System 432 Point Group

Next Lecture External Symmetry (Continued) Combination of Rotation Axes and Mirror Planes 32 Crystal Classes/Point Groups 6 Crystal Systems Crystal Morphology Read: Chapter 5, p. 181-192