Symmetry. 2-D Symmetry. 2-D Symmetry. Symmetry. EESC 2100: Mineralogy 1. Symmetry Elements 1. Rotation. Symmetry Elements 1. Rotation.

Crystal Chem Crystallography

Crystal Chem Crystallography Chemistry behind minerals and how they are assembled Bonding properties and ideas governing how atoms go together Mineral assembly precipitation/ crystallization and defects

TILES, TILES, TILES, TILES, TILES, TILES

3.012 Fund of Mat Sci: Structure Lecture 15 TILES, TILES, TILES, TILES, TILES, TILES Photo courtesy of Chris Applegate. Homework for Fri Nov 4 Study: Allen and Thomas from 3.1.1 to 3.1.4 and 3.2.1, 3.2.4

Symmetry Crystallography

Crystallography Motif: the fundamental part of a symmetric design that, when repeated, creates the whole pattern In 3-D, translation defines operations which move the motif into infinitely repeating patterns

The structure of liquids and glasses. The lattice and unit cell in 1D. The structure of crystalline materials. Describing condensed phase structures

Describing condensed phase structures Describing the structure of an isolated small molecule is easy to do Just specify the bond distances and angles How do we describe the structure of a condensed phase?

n-dimensional, infinite, periodic array of points, each of which has identical surroundings.

crystallography ll Lattice n-dimensional, infinite, periodic array of points, each of which has identical surroundings. use this as test for lattice points A2 ("bcc") structure lattice points Lattice n-dimensional,

Crystallographic Symmetry. Jeremy Karl Cockcroft

Crystallographic Symmetry Jeremy Karl Cockcroft Why bother? To describe crystal structures Simplifies the description, e.g. NaCl structure Requires coordinates for just 2 atoms + space group symmetry!

GEOL. 40 ELEMENTARY MINERALOGY

CRYSTAL DESCRIPTION AND CALCULATION A. INTRODUCTION This exercise develops the framework necessary for describing a crystal. In essence we shall discuss how we fix the position of any crystallographic

Crystallography Reading: Warren, Chapters 2.1, 2.2, 2.6, 8 Surface symmetry: Can be a clue to underlying structure. Examples:

Crystallography Reading: Warren, Chapters 2.1, 2.2, 2.6, 8 Surface symmetry: Can be a clue to underlying structure. Examples: Snow (SnowCrystals.com) Bismuth (Bao, Kavanagh, APL 98 66103 (2005) Hexagonal,

Mineralogy Problem Set Crystal Systems, Crystal Classes

Mineralogy Problem Set Crystal Systems, Crystal Classes (1) For each of the three accompanying plane patterns: (a) Use a ruler to draw solid lines to show where there are mirror planes on the pattern.

Mineralogy ( ) Chapter 5: Crystallography

Hashemite University Faculty of Natural Resources and Environment Department of earth and environmental sciences Mineralogy (1201220) Chapter 5: Crystallography Dr. Faten Al-Slaty First Semester 2015/2016

UNIT I SOLID STATE PHYSICS

UNIT I SOLID STATE PHYSICS CHAPTER 1 CRYSTAL STRUCTURE 1.1 INTRODUCTION When two atoms are brought together, two kinds of forces: attraction and repulsion come into play. The force of attraction increases

Tables of crystallographic properties of double antisymmetry space groups

Tables of crystallographic properties of double antisymmetry space groups Mantao Huang a, Brian K. VanLeeuwen a, Daniel B. Litvin b and Venkatraman Gopalan a * a Department of Materials Science and Engineering,

Axial Ratios, Parameters, Miller Indices

Page 1 of 7 EENS 2110 Tulane University Mineralogy Prof. Stephen A. Nelson Axial Ratios, Parameters, Miller Indices This document last updated on 07-Sep-2016 We've now seen how crystallographic axes can

GY-343 Petrology Petrographic Microscope Laboratory

Introduction to the Petrographic Microscope In this laboratory you will be using the petrographic microscope to analyze thin sections of various types of igneous rocks. You will be assigned a thin section

Applications of X-ray and Neutron Scattering in Biological Sciences: Symmetry in direct and reciprocal space 2012

Department of Drug Design and Pharmacology Applications of X-ray and Neutron Scattering in Biological Sciences: Symmetry in direct and reciprocal space 2012 Michael Gajhede Biostructural Research Copenhagen

INTRODUCTION TO THE PETROGRAPHIC MICROSCOPE AND RELIEF, BECKE LINE, AND OBLIQUE ILLUMINATION

GLY 4200C LAB EXERCISE 10 INTRODUCTION TO THE PETROGRAPHIC MICROSCOPE AND RELIEF, BECKE LINE, AND OBLIQUE ILLUMINATION Locate all of the following microscope parts. Refer to Figure1 1) Eyepiece (note the

Lecture course on crystallography, 2015 Lecture 5: Symmetry in crystallography

Dr Semën Gorfman Department of Physics, University of SIegen Lecture course on crystallography, 2015 Lecture 5: Symmetry in crystallography What is symmetry? Symmetry is a property of an object to stay

Crystallographic Calculations

Page 1 of 7 EENS 2110 Tulane University Mineralogy Prof. Stephen A. Nelson This page last updated on 07-Sep-2010 Crystallographic calculations involve the following: 1. Miller Indices (hkl) 2. Axial ratios

CRYSTAL MEASUREMENT AND AXIAL RATIO LABORATORY

CRYSTAL MEASUREMENT AND AXIAL RATIO LABORATORY George R. McCormick Department of Geology The University of Iowa Iowa City, Iowa 52242 george_mccormick@uiowa.edu Goals of the Exercise This exercise is designed

Chemical Crystallography

Chemical Crystallography Prof Andrew Goodwin Michaelmas 2014 Recap: Lecture 1 Why does diffraction give a Fourier transform? k i = k s = 2π/λ k i k s k i k s r l 1 = (λ/2π) k i r l 2 = (λ/2π) k s r Total

Low Frequency Properties of Dielectric Crystals

Landolt-Börnstein Numerical Data and Functional Relationships in Science and Technology New Series I Editor in Chief: O. Madelung Group III: Solid State Physics Volume 29 Low Frequency Properties of Dielectric

Analytical Methods for Materials

Analytical Methods for Materials Lesson 11 Crystallography and Crystal Structures, Part 3 Suggested Reading Chapter 6 in Waseda Chapter 1 in F.D. Bloss, Crystallography and Crystal Chemistry: An Introduction,

5 Symmetries and point group in a nut shell

30 Phys520.nb 5 Symmetries and point group in a nut shell 5.1. Basic ideas: 5.1.1. Symmetry operations Symmetry: A system remains invariant under certain operation. These operations are called symmetry

MSE 201A Thermodynamics and Phase Transformations Fall, 2008 Problem Set No. 7

MSE 21A Thermodynamics and Phase Transformations Fall, 28 Problem Set No. 7 Problem 1: (a) Show that if the point group of a material contains 2 perpendicular 2-fold axes then a second-order tensor property

Biaxial Minerals This document last updated on 27-Oct-2014

1 of 18 10/27/2014 1:10 PM EENS 2110 Tulane University Biaxial Minerals Mineralogy Prof. Stephen A. Nelson This document last updated on 27-Oct-2014 All minerals that crystallize in the orthorhombic, monoclinic,

Translational symmetry, point and space groups in solids

Translational symmetry, point and space groups in solids Michele Catti Dipartimento di Scienza dei Materiali, Universita di Milano Bicocca, Milano, Italy ASCS26 Spokane Michele Catti a = b = 4.594 Å; Å;

POINT SYMMETRY AND TYPES OF CRYSTAL LATTICE

POINT SYMMETRY AND TYPES OF CRYSTAL LATTICE Abdul Rashid Mirza Associate Professor of Physics. Govt. College of Science, wahdatroad, Lahore. 1 WHAT ARE CRYSTALS? The word crystal means icy or frozen water.

Chapter 9 Electro-Optics

Chapter 9 Electro-Optics Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging Electrical

X-ray analysis. 1. Basic crystallography 2. Basic diffraction physics 3. Experimental methods

X-ray analysis 1. Basic crystallography 2. Basic diffraction physics 3. Experimental methods Introduction Noble prizes associated with X-ray diffraction 1901 W. C. Roentgen (Physics) for the discovery

Fundamentals. Crystal patterns and crystal structures. Lattices, their symmetry and related basic concepts

Fundamentals. Crystal patterns and crystal structures. Lattices, their symmetry and related basic concepts Didactic material for the MaThCryst schools, France massimo.nespolo@univ-lorraine.fr Ideal vs.

Introduction to Crystallography and Mineral Crystal Systems by Mike and Darcy Howard Part 6: The Hexagonal System

Introduction to Crystallography and Mineral Crystal Systems by Mike and Darcy Howard Part 6: The Hexagonal System Now we will consider the only crystal system that has 4 crystallographic axes! You will

Lecture 3: Earth Materials and their Properties I: Minerals. Introduction to the Earth System EAS 2200

Lecture 3: Earth Materials and their Properties I: Minerals Introduction to the Earth System EAS 2200 Earth Materials Plan of the Why it matters Nature of the Earth/Composition The Solid Earth Mineral

ESS 439 Igneous Petrology/Optical Mineralogy

1 Lab # 3: Biaxial minerals ESS 439 Igneous Petrology/Optical Mineralogy In this laboratory session we will introduce the concepts of the Biaxial Indicatrix, Optic Axes, Vibration Directions and Ray Paths,

Structure of Earth Materials

12.108 Structure of Earth Materials I. Lecture 1: Minerals and Symmetry Operations Definition of a mineral A mineral is a naturally occurring homogeneous solid usually formed by inorganic processes. It

GY 302: Crystallography & Mineralogy

UNIVERSITY OF SOUTH ALABAMA GY 302: Crystallography & Mineralogy Lecture 7a: Optical Mineralogy (two day lecture) Instructor: Dr. Douglas Haywick This Week s Agenda 1. Properties of light 2. Minerals and

NMR Shifts. I Introduction and tensor/crystal symmetry.

NMR Shifts. I Introduction and tensor/crystal symmetry. These notes were developed for my group as introduction to NMR shifts and notation. 1) Basic shift definitions and notation: For nonmagnetic materials,

UNIVERSITY OF EDINBURGH. College of Science and Engineering School of GeoSciences. Earth Materials UO4824 DEGREE EXAMINATION (MOCK) xxxxxxxxxxxxxxxxx

UNIVERSITY OF EDINBURGH College of Science and Engineering School of GeoSciences Earth Materials UO4824 DEGREE EXAMINATION (MOCK) xxxxxxxxxxxxxxxxxxxx xxxxxxxxxxxxxxxxxxxxxx Chairman: External Examiners:

Crystallography basics

Crystallography basics 1 ? 2 Family of planes (hkl) - Family of plane: parallel planes and equally spaced. The indices correspond to the plane closer to the origin which intersects the cell at a/h, b/k

PX-CBMSO Course (2) of Symmetry

PX-CBMSO Course (2) The mathematical description of Symmetry y PX-CBMSO-June 2011 Cele Abad-Zapatero University of Illinois at Chicago Center for Pharmaceutical Biotechnology. Lecture no. 2 This material

Basics of crystallography

Basics of crystallography 1 Family of planes (hkl) - Family of plane: parallel planes and equally spaced. The indices correspond to the plane closer to the origin which intersects the cell at a/h, b/k

This Lab will not be marked so make sure to get anything you are unsure about checked by your TA!

Lab One. Microscope Refresher and Advanced Microscope Techniques Learning Goals. After this Lab, you should be able: Demonstrate the operation of the petrographic microscope in plane and crossed polarized

Chapter 4. Crystallography. 4.1 The crystalline state

Crystallography Atoms form bonds which attract them to one another. When you put many atoms together and they form bonds amongst themselves, are there any rules as to how they order themselves? Can we

Optical Mineralogy in a Nutshell

Optical Mineralogy in a Nutshell Use of the petrographic microscope Slides borrowed/adapted from Jane Selverstone (University of New Mexico) and John Winter (Whitman College) Why use the petrographic microscope?

Overview - Macromolecular Crystallography

Overview - Macromolecular Crystallography 1. Overexpression and crystallization 2. Crystal characterization and data collection 3. The diffraction experiment 4. Phase problem 1. MIR (Multiple Isomorphous

REVIEW: CHAPTERS 1 TO 5. Sarah Lambart

REVIEW: CHAPTERS 1 TO 5 Sarah Lambart CHAPTER 1: MINERAL PROPERTIES AND CLASSIFICATION CHAP. 1: MINERAL PROPERTIES AND CLASSIFICATION Mineral: naturally occurring (always) a structure and a composition

Earth Materials Lab 2 - Lattices and the Unit Cell

Earth Materials Lab 2 - Lattices and the Unit Cell Unit Cell Minerals are crystallographic solids and therefore are made of atoms arranged into lattices. The average size hand specimen is made of more

GY 302: Crystallography & Mineralogy

UNIVERSITY OF SOUTH ALABAMA GY 302: Crystallography & Mineralogy Lecture 7b: Optical Mineralogy Instructor: Dr. Douglas Haywick Last Time 1. Properties of light 2. Minerals and light transmission Light

Optical Mineralogy. Optical Mineralogy. Use of the petrographic microscope

Optical Mineralogy Optical Mineralogy Use of the petrographic microscope John Winter, Whitman College with some slides Jane Selverstone, University of New Mexico, 2003 Why use the microscope?? Identify

NOMENCLATURE REMARKS ON CRYSTALLOGRAPHIC. M. A. PBacocr, (Jni,aersity of Toronto, Toronto, Canaila.* Assrnecr

REMARKS ON CRYSTALLOGRAPHIC NOMENCLATURE M. A. PBacocr, (Jni,aersity of Toronto, Toronto, Canaila.* Assrnecr In special cases the lattice (not structure) of a crystal in any system may be indistinguishable

Helpful resources for all X ray lectures Crystallization http://www.hamptonresearch.com under tech support: crystal growth 101 literature Spacegroup tables http://img.chem.ucl.ac.uk/sgp/mainmenu.htm Crystallography

EESC 4701: Igneous and Metamorphic Petrology IGNEOUS MINERALS LAB 1 HANDOUT

EESC 4701: Igneous and Metamorphic Petrology IGNEOUS MINERALS LAB 1 HANDOUT Sources: Cornell EAS302 lab, UMass Lowell 89.301 Mineralogy, LHRIC.org The Petrographic Microscope As you know, light is an electromagnetic

DIFFRACTION METHODS IN MATERIAL SCIENCE. PD Dr. Nikolay Zotov Lecture 4_2

DIFFRACTION METHODS IN MATERIAL SCIENCE PD Dr. Nikolay Zotov Email: zotov@imw.uni-stuttgart.de Lecture 4_2 OUTLINE OF THE COURSE 0. Introduction 1. Classification of Materials 2. Defects in Solids 3. Basics

St. Xavier s College Mumbai

St. Xavier s College Mumbai Syllabus for B.Sc I st Semester Courses in Geology (June 2016 onwards) Contents: Theory Syllabus for Courses: o S.Geo.1.01 - Introduction to Mineralogy and Crystallography o

Solids / Crystal Structure

The first crystal analysis proved that in the typical inorganic salt, NaCl, there is no molecular grouping. The inference that the structure consists of alternate ions of sodium and chlorine was an obvious

Phys 460 Describing and Classifying Crystal Lattices

Phys 460 Describing and Classifying Crystal Lattices What is a material? ^ crystalline Regular lattice of atoms Each atom has a positively charged nucleus surrounded by negative electrons Electrons are

MINERALOGY (EESC35) Course Outline. Dear all,

MINERALOGY (EESC35) Dear all, Welcome to the Mineralogy (EESC35) course! This course will bring to you the rich and colourful world of minerals, rocks and their associations. We shall have a look at basic

Basic Crystallography Part 1. Theory and Practice of X-ray Crystal Structure Determination

Basic Crystallography Part 1 Theory and Practice of X-ray Crystal Structure Determination We have a crystal How do we get there? we want a structure! The Unit Cell Concept Ralph Krätzner Unit Cell Description

Crystalline Solids. Amorphous Solids

Crystal Structure Crystalline Solids Possess rigid and long-range order; atoms, molecules, or ions occupy specific positions the tendency is to maximize attractive forces Amorphous Solids lack long-range

Chapter 2 Introduction to Phenomenological Crystal Structure

Chapter 2 Introduction to Phenomenological Crystal Structure 2.1 Crystal Structure An ideal crystal represents a periodic pattern generated by infinite, regular repetition of identical microphysical structural

Condensed Matter A Week 2: Crystal structure (II)

QUEEN MARY, UNIVERSITY OF LONDON SCHOOL OF PHYSICS AND ASTRONOMY Condensed Matter A Week : Crystal structure (II) References for crystal structure: Dove chapters 3; Sidebottom chapter. Last week we learnt

M\1any arguments have been concerned with what these symbols mean, and how they

SOME DESIRABLE MODIFICATIONS OF THE INTERNATIONAL SYMMETRY SYMBOLS* BY MARTIN J. BUERGER MASSACHUSETTS INSTITUTE OF TECHNOLOGY Communicated August 21, 1967 With the publication of Hilton's Mathematical

Chem 728 Introduction to Solid Surfaces

Chem 728 Introduction to Solid Surfaces Solids: hard; fracture; not compressible; molecules close to each other Liquids: molecules mobile, but quite close to each other Gases: molecules very mobile; compressible

Homework 1 (not graded) X-ray Diffractometry CHE Multiple Choice. 1. One of the methods of reducing exposure to radiation is to minimize.

Homework 1 (not graded) X-ray Diffractometry CHE 380.45 Multiple Choice 1. One of the methods of reducing exposure to radiation is to minimize. a) distance b) humidity c) time d) speed e) shielding 2.

Crystals! Table of Contents. Vocabulary 2. Word Search 6. What is a Crystal? 7. Atoms, Ions, Molecules. and the Unit Cell 13.

Crystals! Table of Contents Vocabulary 2 Word Search 6 What is a Crystal? 7 Atoms, Ions, Molecules and the Unit Cell 13 Crystal Shapes 15 X-Ray Crystallography 17 Recipes for Making A Booklet for Elementary

Lecture 2 Symmetry in the solid state -

Lecture 2 Symmetry in the solid state - Part II: Crystallographic coordinates and Space Groups. 1 Coordinate systems in crystallography and the mathematical form of the symmetry operators 1.1 Introduction

ESS 439 Lab 2 Examine Optical Properties of Minerals

ESS 439 Lab 2 Examine Optical Properties of Minerals The optical properties depend on the manner that visible light is transmitted through the crystal, and thus are dependent on mineral s Crystal Structure

Lecture 21 Reminder/Introduction to Wave Optics

Lecture 1 Reminder/Introduction to Wave Optics Program: 1. Maxwell s Equations.. Magnetic induction and electric displacement. 3. Origins of the electric permittivity and magnetic permeability. 4. Wave

1/2, 1/2,1/2, is the center of a cube. Induces of lattice directions and crystal planes (a) Directions in a crystal Directions in a crystal are

Crystallography Many materials in nature occur as crystals. Examples include the metallic elements gold, copper and silver, ionic compounds such as salt (e.s. NaCl); ceramics, rutile TiO2; and nonmetallic

Resolution of Ambiguities and the Discovery of

ISST Journal of Applied hysics, Vol. 6 No. 1, (January - June), p.p. 1-10 ISSN No. 0976-90X Intellectuals Society for Socio-Techno Welfare Resolution of Ambiguities and the Discovery of Two New Space Lattices

Crystallographic structure Physical vs Chemical bonding in solids

Crystallographic structure Physical vs Chemical bonding in solids Inert gas and molecular crystals: Van der Waals forces (physics) Water and organic chemistry H bonds (physics) Quartz crystal SiO 2 : covalent

Symmetry in 2D. 4/24/2013 L. Viciu AC II Symmetry in 2D

Symmetry in 2D 1 Outlook Symmetry: definitions, unit cell choice Symmetry operations in 2D Symmetry combinations Plane Point groups Plane (space) groups Finding the plane group: examples 2 Symmetry Symmetry

Last Time. GY 302: Crystallography & Mineralogy. Polymorphs & Polymorphism. Other Crystal Structures. Other Crystal Structures. This Week s Agenda

UNIVERSITY OF SOUTH ALABAMA Last Time GY 302: Crystallography & Mineralogy 1. Polymorphs and Polymorphism 2. Pseudomorphs and other definitions 3. Crystal Habit Lecture 7: Optical Mineralogy (two day lecture?)

Scattering and Diffraction

Scattering and Diffraction Andreas Kreyssig, Alan Goldman, Rob McQueeney Ames Laboratory Iowa State University All rights reserved, 2018. Atomic scale structure - crystals Crystalline materials... atoms

THE FIVE TYPES OF PLANAR 2-D LATTICES. (d) (e)

THE FIVE TYPES OF PLANAR 2-D LATTICES (a) (d) (b) (d) and (e) are the same (e) (c) (f) (a) OBLIQUE LATTICE - NO RESTRICTIONS ON ANGLES BETWEEN THE UNIT CELL EDGES (b) RECTANGULAR LATTICE - ANGLE BETWEEN

Lattice (Sieć) A collection of nodes, i.e. points with integral coordinates. In crystallography, a lattice is an

Prof. dr hab. Mariusz Jaskólski GLOSSARYUSZ TERMINÓW KRYSTALOGRAFICZNYCH (dla osób nie znających jeszcze krystalografii, ale znających język angielski) Symmetry (Symetria) Property of physical and mathematical

Nove fizickohemijske metode. Ivana Radosavljevic Evans Durham University, UK

Nove fizickohemijske metode Ivana Radosavljevic Evans Durham University, UK Nove fizickohemijske metode: Metode zasnovane na sinhrotronskom zracenju Plan predavanja: Difrakcione metode strukturne karakterizacije

Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras

Condensed Matter Physics Prof. G. Rangarajan Department of Physics Indian Institute of Technology, Madras Lecture - 03 Symmetry in Perfect Solids Worked Examples Stated without prove to be in the lecture.

St. Xavier s College Mumbai. Syllabus for B.Sc I st Semester Courses in Geology (June 2017 onwards)

St. Xavier s College Mumbai Syllabus for B.Sc I st Semester Courses in Geology (June 2017 onwards) Contents: Theory Syllabus for Courses: o S.Geo.1.01 - Introduction to Mineralogy and Crystallography o

Crystal Structure. Dr Bindu Krishnan

Solid State Physics-1 Crystal Structure Dr Bindu Krishnan CRYSTAL LATTICE What is crystal (space) lattice? In crystallography, only the geometrical properties of the crystal are of interest, therefore

Tensorial and physical properties of crystals

Tensorial and physical properties of crystals Michele Catti Dipartimento di Scienza dei Materiali, Universita di Milano Bicocca, Milano, Italy (catti@mater.unimib.it) MaThCryst Nancy 2005 International

Electromagnetic Properties of Materials Part 2

ECE 5322 21 st Century Electromagnetics Instructor: Office: Phone: E Mail: Dr. Raymond C. Rumpf A 337 (915) 747 6958 rcrumpf@utep.edu Lecture #3 Electromagnetic Properties of Materials Part 2 Nonlinear

Chapter 1. Crystal structure. 1.1 Crystal lattices

Chapter 1 Crystal structure 1.1 Crystal lattices We will concentrate as stated in the introduction, on perfect crystals, i.e. on arrays of atoms, where a given arrangement is repeated forming a periodic

Raman and IR spectroscopy in materials science. Symmetry analysis of normal phonon modes Boriana Mihailova

University of Hamburg, Institute of Mineralogy and Petrology Raman and IR spectroscopy in materials science. Symmetry analysis of normal phonon modes Boriana Mihailova Outline. The dynamics of atoms in

Tim Hughbanks CHEMISTRY 634. Two Covers. Required Books, etc.

CHEMISTRY 634 This course is for 3 credits. Lecture: 2 75 min/week; TTh 11:10-12:25, Room 2122 Grades will be based on the homework (roughly 25%), term paper (15%), midterm and final exams Web site: http://www.chem.tamu.edu/rgroup/

Introduction to Twinning

S.Parsons@ed.ac.uk Introduction to Twinning Simon Parsons School of Chemistry and Centre for Science at Extreme Conditions, The University of Edinburgh, Edinburgh, UK. Introduction Although twinning has

CHAPTER 5: CRYSTAL DEFECTS AND TWINNING. Sarah Lambart

CHAPTER 5: CRYSTAL DEFECTS AND TWINNING Sarah Lambart RECAP CHAP. 4 Hermann-Mauguin symbols 32 crystal classes Miller indices Crystal forms RECAP CHAP. 4 Crystal System Crystal Class Symmetry Name of Class

Roger Johnson Structure and Dynamics: The 230 space groups Lecture 3

Roger Johnson Structure and Dnamics: The 23 space groups Lecture 3 3.1. Summar In the first two lectures we considered the structure and dnamics of single molecules. In this lecture we turn our attention

Introduction to point and space group symmetry

Workshop on Electron Crystallography, Nelson Mandela Metropolitan University, South Africa, October 14-16, 2013 Introduction to point and space group syetry Hol Kirse Huboldt-Universität zu Berlin, Institut

Introduction to crystallography The unitcell The resiprocal space and unitcell Braggs law Structure factor F hkl and atomic scattering factor f zθ

Introduction to crystallography The unitcell The resiprocal space and unitcell Braggs law Structure factor F hkl and atomic scattering factor f zθ Introduction to crystallography We divide materials into

11/29/2010. Propagation in Anisotropic Media 3. Introduction. Introduction. Gabriel Popescu

Propagation in Anisotropic Media Gabriel Popescu University of Illinois at Urbana Champaign Beckman Institute Quantitative Light Imaging Laboratory http://light.ece.uiuc.edu Principles of Optical Imaging

Uniaxial Minerals Descriptions

Uniaxial Minerals Descriptions Look at 6 uniaxial minerals Quartz Nepheline Calcite Apatite Tourmaline Zircon Examine composition, relief, colour, form, cleavage, twinning, birefringence, occurrence Quartz

GY 302: Crystallography & Mineralogy

UNIVERSITY OF SOUTH ALABAMA GY 302: Crystallography & Mineralogy Lecture 20: Class VIII-Silicates Soro- and Cyclosilicates Instructor: Dr. Douglas Haywick Mineral Quiz 4 results 1: Witherite (21%) 2: Cerussite

Crystallographic Point Groups and Space Groups

Crystallographic Point Groups and Space Groups Physics 251 Spring 2011 Matt Wittmann University of California Santa Cruz June 8, 2011 Mathematical description of a crystal Definition A Bravais lattice

Optics and Optical Design. Chapter 6: Polarization Optics. Lectures 11-13

Optics and Optical Design Chapter 6: Polarization Optics Lectures 11-13 Cord Arnold / Anne L Huillier Polarization of Light Arbitrary wave vs. paraxial wave One component in x-direction y x z Components

Fun with Asbestos 1. Table 1: Asbestos Minerals. Mineral Asbestos Variety Mineral Group Comments. monoclinic amphibole. monoclinic amphibole

1 Fun with Asbestos 1 WARNING: DO NOT OPEN BOTTLES CONTAINING ASBESTOS. Asbestos may cause lung damage. Do not breathe fibers. The crocidolite (blue asbestos) is considered most hazardous, but the other

Florida Atlantic University MINERALOGY -- FINAL EXAMINATION KEY

GLY4200C Name 108 points December 2, 2011 16 took exam - Numbers to the left of the question number in red are the number of incorrect responses. Instructor comments are in blue. Florida Atlantic University

Introduction to Crystal Structure and Bonding. Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India

Introduction to Crystal Structure and Bonding 1 Prof.P. Ravindran, Department of Physics, Central University of Tamil Nadu, India http://folk.uio.no/ravi/semi2013 Fundamental Properties of matter 2 Matter:

Solid Earth materials:

Solid Earth materials: Elements minerals rocks Nonuniform distribution of matter Molten core Contains most heavy elements Iron, nickel Thin surface crust Mostly lighter elements 8 elements make up 98.6%

Saveetha Engineering College, Thandalam, Chennai. Department of Physics. First Semester. Ph6151 Engineering Physics I (NOV/DEC 2014)

Saveetha Engineering College, Thandalam, Chennai. Department of Physics First Semester Ph6151 Engineering Physics I (NOV/DEC 2014) Part A (Questions and Answers) 1. Distinguish between Crystalline and

INVESTIGATION OF MANIFESTATION OF OPTICAL ACTIVITY IN ANISOTROPIC CRYSTALS. Moscow, Russia,

INVESTIGATION OF MANIFESTATION OF OPTICAL ACTIVITY IN ANISOTROPIC CRYSTALS A.F. Konstantinova 1, E.A. Evdishchenko 1, K.A. Kaldybaev, K.B. Imangazieva, K.K. Konstantinov 1 1 Shubnikov Institute of Crystallography,