Scattering and Diffraction
|
|
- Neil Joseph
- 5 years ago
- Views:
Transcription
1 Scattering and Diffraction Andreas Kreyssig, Alan Goldman, Rob McQueeney Ames Laboratory Iowa State University All rights reserved, 2018.
2 Atomic scale structure - crystals Crystalline materials... atoms pack in periodic, 3D arrays typical of: -metals -many ceramics -some polymers crystalline SiO2 Adapted from Fig. 3.18(a), Callister 6e. Noncrystalline materials... atoms have no regular packing occurs for: -complex structures -rapid cooling "Amorphous" = Noncrystalline Distance between atoms ~ Å (10-10 m) noncrystalline SiO2 Adapted from Fig. 3.18(b), Callister 6e. 26
3 How we do study crystal structures? X-rays Visible light Resolution ~ wavelength So, m resolution requires λ ~ m
4 Diffraction Interference of two waves Double slit diffraction Constructive Destructive You can also do this with light (as well as neutrons and electrons). 2 slits 2 slits and 5 slits
5 Diffraction from periodic structures d(h k l ) Interference of waves crystalline SiO2 d(hkl) Constructive I Bragg equation: 2θ
6 Crystal structures and diffraction - PDF database PDF_DataBase 1; 2; 3; 4
7 Crystal structures and diffraction - PDF database PDF_DataBase 5; 6
8 Crystal structures and diffraction - PDF database PDF_Hanawalt 1; 2; PDF_Fink 1; 2
9 PDF database - Example: growth of PrAuSi out of Sn flux Which elements can/must be present? E. D. Mun: PM721-Ex1b
10 PDF database - Example: growth of PrAuSi out of Sn flux Oops is Au really present? E. D. Mun: PM721-Ex1c
11 PDF database - Example: growth of PrAuSi out of Sn flux Expected traces of Sn, but is the main phase right? E. D. Mun: PM721-Ex1e
12 PDF database - Example: growth of PrAuSi out of Sn flux Expected traces of Sn, but is the main phase right? E. D. Mun: PM721-Ex1f
13 PDF database - Example: growth of PrAuSi out of Sn flux If your phase is not in the database search for isostructural compounds... E. D. Mun: PM721-Ex1g
14 Diffraction from periodic structures 7 Crystal systems: with symmetry (cubic, hexagonal, trigonal, tetragonal, orthorhombic, monoclinic, triclinic) 14 Bravais lattices [above + centering (body, base, face)] 230 Space groups (14 Bravais lattices + 32 crystallographic point groups)
15 International Tables for Crystallography InternationalTables E1
16 International Tables for Crystallography InternationalTables E1
17 International Tables for Crystallography InternationalTables E2
18 International Tables for Crystallography InternationalTables 7_1
19 International Tables for Crystallography InternationalTables 7_2
20 International Tables for Crystallography InternationalTables 8
21 International Tables for Crystallography InternationalTables 9
22 International Tables for Crystallography Cullity 35, 36
23 International Tables for Crystallography InternationalTables E4
24 International Tables for Crystallography InternationalTables E3
25 Problems describing a structure Rhombohedral unit cell InternationalTables 84
26 Problems describing a structure Rhombohedral unit cell InternationalTables 146_11
27 Problems describing a structure Rhombohedral unit cell InternationalTables 146_11; 21
28 Problems describing a structure Rhombohedral unit cell InternationalTables 146_11; 12a; 21; 22
29 Problems describing a structure Origin of cell InternationalTables 129_11
30 Problems describing a structure Origin of cell InternationalTables 129_11; 21
31 Problems describing a structure Origin of cell InternationalTables 129_11; 12; 21; 22
32 Reciprocal space For an infinite 3D lattice defined by primitive vectors (a 1, a 2, a 3 ) we can define a reciprocal lattice generated by: For real space vector R = m 1 a 1 + m 2 a 2 + m 3 a 3 and reciprocal vector G = n 1 b 1 + n 2 b 2 + n 3 b 3 with all m s and n s integer is e ig R = 1 (G R = 2π x integer) G is normal to sets of planes of atoms. Each point (n 1, n 2, n 3 ) or (hkl) in the reciprocal lattice corresponds to a set of planes in the real space lattice.
33 Reciprocal space and Miller indices (0 K 0) (H 0 0) (100) Reflection = diffraction from planes of atoms spaced 2π/a apart (200) Reflection = diffraction from planes of atoms spaced 2π/2a apart
34 Diffraction from periodic structures d(h k l ) Interference of waves crystalline SiO2 d(hkl) Constructive k i G k f I Bragg equation: 2θ
35 Diffraction from periodic structures Ewald construction d(h k l ) crystalline SiO2 d(hkl) k i k f Q hkl 2q k i Scattering triangle: Q hkl = k f - k i Lifshin_31_1
36 Diffraction from periodic structures Ewald construction k f Q hkl k i k f Q hkl 2q k i Laue equation: G Q hkl = k f - k i Lifshin_31_1
37 Diffraction Basic equations Bragg equation: Laue equation: G Q hkl = k f - k i Structure Amplitude:
X-ray, Neutron and e-beam scattering
X-ray, Neutron and e-beam scattering Introduction Why scattering? Diffraction basics Neutrons and x-rays Techniques Direct and reciprocal space Single crystals Powders CaFe 2 As 2 an example What is the
More informationPhysical Chemistry I. Crystal Structure
Physical Chemistry I Crystal Structure Crystal Structure Introduction Crystal Lattice Bravis Lattices Crytal Planes, Miller indices Distances between planes Diffraction patters Bragg s law X-ray radiation
More informationBasic 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
More informationCrystallography 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,
More informationUNIT 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
More informationIntroduction 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
More informationThe 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?
More informationHandout 7 Reciprocal Space
Handout 7 Reciprocal Space Useful concepts for the analysis of diffraction data http://homepages.utoledo.edu/clind/ Concepts versus reality Reflection from lattice planes is just a concept that helps us
More informationCrystal planes. Neutrons: magnetic moment - interacts with magnetic materials or nuclei of non-magnetic materials. (in Å)
Crystallography: neutron, electron, and X-ray scattering from periodic lattice, scattering of waves by periodic structures, Miller indices, reciprocal space, Ewald construction. Diffraction: Specular,
More informationn-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,
More informationSOLID STATE 18. Reciprocal Space
SOLID STATE 8 Reciprocal Space Wave vectors and the concept of K-space can simplify the explanation of several properties of the solid state. They will be introduced to provide more information on diffraction
More informationAnalytical Methods for Materials
Analytical Methods for Materials Lesson 15 Reciprocal Lattices and Their Roles in Diffraction Studies Suggested Reading Chs. 2 and 6 in Tilley, Crystals and Crystal Structures, Wiley (2006) Ch. 6 M. DeGraef
More informationSymmetry 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
More information3.012 Structure An Introduction to X-ray Diffraction
3.012 Structure An Introduction to X-ray Diffraction This handout summarizes some topics that are important for understanding x-ray diffraction. The following references provide a thorough explanation
More informationPhys 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
More informationCrystallographic 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
More informationCrystallographic 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!
More informationChem 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
More informationNove 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
More informationOverview - 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
More informationCRYSTAL STRUCTURE, PHASE CHANGES, AND PHASE DIAGRAMS
CRYSTAL STRUCTURE, PHASE CHANGES, AND PHASE DIAGRAMS CRYSTAL STRUCTURE CRYSTALLINE AND AMORPHOUS SOLIDS Crystalline solids have an ordered arrangement. The long range order comes about from an underlying
More informationChemical 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
More informationNeutron Powder Diffraction Theory and Instrumentation
NTC, Taiwen Aug. 31, 212 Neutron Powder Diffraction Theory and Instrumentation Qingzhen Huang (qing.huang@nist.gov) NIST Center for Neutron Research (www.ncnr.nist.gov) Definitions E: energy; k: wave vector;
More information1 Crystal Structures. of three-dimensional crystals. Here we use two-dimensional examples to illustrate the concepts.
3 1 Crystal Structures A crystal is a periodic array of atoms. Many elements and quite a few compounds are crystalline at low enough temperatures, and many of the solid materials in our everyday life (like
More informationSolid State Physics Lecture 3 Diffraction and the Reciprocal Lattice (Kittel Ch. 2)
Solid State Physics 460 - Lecture 3 Diffraction and the Reciprocal Lattice (Kittel Ch. 2) Diffraction (Bragg Scattering) from a powder of crystallites - real example of image at right from http://www.uni-wuerzburg.de/mineralogie/crystal/teaching/pow.html
More informationGeneral theory of diffraction
General theory of diffraction X-rays scatter off the charge density (r), neutrons scatter off the spin density. Coherent scattering (diffraction) creates the Fourier transform of (r) from real to reciprocal
More information1/2, 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
More informationDiffraction. X-ray diffraction
Diffraction Definition (from Cambridge Advanced Learner s Dictionary ): - diffraction noun [U] SPECIALIZED (a pattern caused by) a change in the direction of light, water or sound waves - diffract verb
More informationBasic 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 Course Overview Basic Crystallography Part 1 n Introduction: Crystals and Crystallography n Crystal Lattices and
More informationX-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
More information3.012 Fund of Mat Sci: Structure Lecture 18
3.012 Fund of Mat Sci: Structure Lecture 18 X-RAYS AT WORK An X-ray diffraction image for the protein myoglobin. Source: Wikipedia. Model of helical domains in myoglobin. Image courtesy of Magnus Manske
More information2. Diffraction as a means to determine crystal structure
Page 1 of 22 2. Diffraction as a means to determine crystal structure Recall de Broglie matter waves: 2 p h E = where p = 2m λ h 1 E = ( ) 2m λ hc E = hυ = ( photons) λ ( matter wave) He atoms: [E (ev)]
More informationCHEM-E5225 :Electron Microscopy. Diffraction 1
CHEM-E5225 :Electron Microscopy Diffraction 1 2018-10-15 Yanling Ge Text book: Transmission electron microscopy by David B Williams & C. Barry Carter. 2009, Springer Outline Diffraction in TEM Thinking
More information... 3, , = a (1) 3 3 a 2 = a (2) The reciprocal lattice vectors are defined by the condition a b = 2πδ ij, which gives
PHZ646: Fall 013 Problem set # 4: Crystal Structure due Monday, 10/14 at the time of the class Instructor: D. L. Maslov maslov@phys.ufl.edu 39-0513 Rm. 114 Office hours: TR 3 pm-4 pm Please help your instructor
More informationCrystal Structure SOLID STATE PHYSICS. Lecture 5. A.H. Harker. thelecture thenextlecture. Physics and Astronomy UCL
Crystal Structure thelecture thenextlecture SOLID STATE PHYSICS Lecture 5 A.H. Harker Physics and Astronomy UCL Structure & Diffraction Crystal Diffraction (continued) 2.4 Experimental Methods Notes: examples
More informationWe need to be able to describe planes and directions.
We need to be able to describe planes and directions. Miller Indices & XRD 1 2 Determining crystal structure and identifying materials (B) Plastic deformation Plastic deformation and mechanical properties
More informationTILES, 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
More informationExperiment 3: Simulating X-Ray Diffraction CH3500: Inorganic Chemistry, Plymouth State University
Experiment 3: Simulating X-Ray Diffraction CH3500: Inorganic Chemistry, Plymouth State University Created by Jeremiah Duncan, Dept. of Atmospheric Science and Chemistry, Plymouth State University (2012).
More informationThe Reciprocal Lattice
59-553 The Reciprocal Lattice 61 Because of the reciprocal nature of d spacings and θ from Bragg s Law, the pattern of the diffraction we observe can be related to the crystal lattice by a mathematical
More information2. Diffraction as a means to determine crystal structure
2. Diffraction as a means to determine crystal structure Recall de Broglie matter waves: He atoms: [E (ev)] 1/2 = 0.14 / (Å) E 1Å = 0.0196 ev Neutrons: [E (ev)] 1/2 = 0.28 / (Å) E 1Å = 0.0784 ev Electrons:
More informationSolid State Physics 460- Lecture 5 Diffraction and the Reciprocal Lattice Continued (Kittel Ch. 2)
Solid State Physics 460- Lecture 5 Diffraction and the Reciprocal Lattice Continued (Kittel Ch. 2) Ewald Construction 2θ k out k in G Physics 460 F 2006 Lect 5 1 Recall from previous lectures Definition
More informationTranslational 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;
More informationIntroduction to X-ray and neutron scattering
UNESCO/IUPAC Postgraduate Course in Polymer Science Lecture: Introduction to X-ray and neutron scattering Zhigunov Alexander Institute of Macromolecular Chemistry ASCR, Heyrovsky sq., Prague -16 06 http://www.imc.cas.cz/unesco/index.html
More informationCrystallographic 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
More informationAxial 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
More information(Re-write, January 2011, from notes of S. C. Fain Jr., L. Sorensen, O. E. Vilches, J. Stoltenberg and D. B. Pengra, Version 1, preliminary)
Electron Diffraction (Re-write, January 011, from notes of S. C. Fain Jr., L. Sorensen, O. E. Vilches, J. Stoltenberg and D. B. Pengra, Version 1, preliminary) References: Any introductory physics text
More informationScattering Lecture. February 24, 2014
Scattering Lecture February 24, 2014 Structure Determination by Scattering Waves of radiation scattered by different objects interfere to give rise to an observable pattern! The wavelength needs to close
More informationPX-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
More informationRöntgenpraktikum. M. Oehzelt. (based on the diploma thesis of T. Haber [1])
Röntgenpraktikum M. Oehzelt (based on the diploma thesis of T. Haber [1]) October 21, 2004 Contents 1 Fundamentals 2 1.1 X-Ray Radiation......................... 2 1.1.1 Bremsstrahlung......................
More informationThe Solid State. Phase diagrams Crystals and symmetry Unit cells and packing Types of solid
The Solid State Phase diagrams Crystals and symmetry Unit cells and packing Types of solid Learning objectives Apply phase diagrams to prediction of phase behaviour Describe distinguishing features of
More informationApplications 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
More informationIntroduction to Materials Science Graduate students (Applied Physics)
Introduction to Materials Science Graduate students (Applied Physics) Prof. Michael Roth Chapter Reciprocal Lattice and X-ray Diffraction Reciprocal Lattice - 1 The crystal can be viewed as made up of
More information9/13/2013. Diffraction. Diffraction. Diffraction. Diffraction. Diffraction. Diffraction of Visible Light
scattering of raiation by an object observe an escribe over 300 years ago illustrate with a iffraction grating Joseph von Fraunhofer German 80 slits new wavefront constructive interference exact pattern
More informationPOINT 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.
More informationEarth 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
More informationCrystals, X-rays and Proteins
Crystals, X-rays and Proteins Comprehensive Protein Crystallography Dennis Sherwood MA (Hons), MPhil, PhD Jon Cooper BA (Hons), PhD OXFORD UNIVERSITY PRESS Contents List of symbols xiv PART I FUNDAMENTALS
More informationFundamentals of X-ray diffraction
Fundamentals of X-ray diffraction Elena Willinger Lecture series: Modern Methods in Heterogeneous Catalysis Research Outline History of X-ray Sources of X-ray radiation Physics of X-ray scattering Fundamentals
More informationPROBING CRYSTAL STRUCTURE
PROBING CRYSTAL STRUCTURE Andrew Baczewski PHY 491, October 10th, 2011 OVERVIEW First - we ll briefly discuss Friday s quiz. Today, we will answer the following questions: How do we experimentally probe
More informationPhys 412 Solid State Physics. Lecturer: Réka Albert
Phys 412 Solid State Physics Lecturer: Réka Albert What is a solid? A material that keeps its shape Can be deformed by stress Returns to original shape if it is not strained too much Solid structure
More information5 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
More informationSolids. properties & structure
Solids properties & structure Determining Crystal Structure crystalline solids have a very regular geometric arrangement of their particles the arrangement of the particles and distances between them is
More informationPART 1 Introduction to Theory of Solids
Elsevier UK Job code: MIOC Ch01-I044647 9-3-2007 3:03p.m. Page:1 Trim:165 240MM TS: Integra, India PART 1 Introduction to Theory of Solids Elsevier UK Job code: MIOC Ch01-I044647 9-3-2007 3:03p.m. Page:2
More informationResolution: maximum limit of diffraction (asymmetric)
Resolution: maximum limit of diffraction (asymmetric) crystal Y X-ray source 2θ X direct beam tan 2θ = Y X d = resolution 2d sinθ = λ detector 1 Unit Cell: two vectors in plane of image c* Observe: b*
More informationLattice (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
More informationWave diffraction and the reciprocal lattice
Wave diffraction and the reciprocal lattice Dept of Phys M.C. Chang Braggs theory of diffraction Reciprocal lattice von Laue s theory of diffraction Braggs view of the diffraction (1912, father and son)
More informationChapter 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
More informationIntroduction to. Crystallography
M. MORALES Introuction to Crystallography magali.morales@ensicaen.fr Classification of the matter in 3 states : Crystallise soli liqui or amorphous gaz soli Crystallise soli : unique arrangement of atoms
More informationX-ray Crystallography BMB/Bi/Ch173 02/06/2017
1. Purify your protein 2. Crystallize protein 3. Collect diffraction data 4. Get experimental phases 5. Generate an electron density map 6. Build a model 7. Refine the model 8. Publish X-ray Crystallography
More informationStructure of Crystalline Solids
Structure of Crystalline Solids Solids- Effect of IMF s on Phase Kinetic energy overcome by intermolecular forces C 60 molecule llotropes of Carbon Network-Covalent solid Molecular solid Does not flow
More informationSuggested Reading. Pages in Engler and Randle
The Structure Factor Suggested Reading Pages 303-312312 in DeGraef & McHenry Pages 59-61 in Engler and Randle 1 Structure Factor (F ) N i1 1 2 i( hu kv lw ) F fe i i j i Describes how atomic arrangement
More informationRoger Johnson Structure and Dynamics: X-ray Diffraction Lecture 6
6.1. Summary In this Lecture we cover the theory of x-ray diffraction, which gives direct information about the atomic structure of crystals. In these experiments, the wavelength of the incident beam must
More informationGeometry of Crystal Lattice
0 Geometry of Crystal Lattice 0.1 Translational Symmetry The crystalline state of substances is different from other states (gaseous, liquid, amorphous) in that the atoms are in an ordered and symmetrical
More informationCrystal Structure and Electron Diffraction
Crystal Structure and Electron Diffraction References: Kittel C.: Introduction to Solid State Physics, 8 th ed. Wiley 005 University of Michigan, PHY441-44 (Advanced Physics Laboratory Experiments, Electron
More informationMaterials Science and Engineering 102 Structure and Bonding. Prof. Stephen L. Sass. Midterm Examination Duration: 1 hour 20 minutes
October 9, 008 MSE 0: Structure and Bonding Midterm Exam SOLUTIONS SID: Signature: Materials Science and Engineering 0 Structure and Bonding Prof. Stephen L. Sass Midterm Examination Duration: hour 0 minutes
More informationLecture Note on Crystal structures Masatsugu Sei Suzuki and Itsuko S. Suzuki Department of Physics, SUNY at Binghamton (Date: February 03, 2012)
Lecture Note on Crystal structures Masatsugu Sei Suzuki and Itsuko S. Suzuki Department of Physics, SUNY at Binghamton (Date: February 03, 2012) This is a part of lecture note on solid state physics (Phys.472/572)
More informationStructure and Dynamics : An Atomic View of Materials
Structure and Dynamics : An Atomic View of Materials MARTIN T. DOVE Department ofearth Sciences University of Cambridge OXFORD UNIVERSITY PRESS Contents 1 Introduction 1 1.1 Observations 1 1.1.1 Microscopic
More informationChap 3 Scattering and structures
Chap 3 Scattering and structures Dept of Phys M.C. Chang Von Laue was struck in 1912 by the intuition that X-ray might scatter off crystals in the way that ordinary light scatters off a diffraction grating.
More informationChapter 2. X-ray X. Diffraction and Reciprocal Lattice. Scattering from Lattices
Chapter. X-ray X Diffraction and Reciprocal Lattice Diffraction of waves by crystals Reciprocal Lattice Diffraction of X-rays Powder diffraction Single crystal X-ray diffraction Scattering from Lattices
More informationSymmetry. 2-D Symmetry. 2-D Symmetry. Symmetry. EESC 2100: Mineralogy 1. Symmetry Elements 1. Rotation. Symmetry Elements 1. Rotation.
Symmetry a. Two-fold rotation = 30 o /2 rotation a. Two-fold rotation = 30 o /2 rotation Operation Motif = the symbol for a two-fold rotation EESC 2100: Mineralogy 1 a. Two-fold rotation = 30 o /2 rotation
More informationChapter 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
More informationApplication Note SC-XRD 505 Single Crystal Diffraction
Application Note SC-XRD 505 Single Crystal Diffraction Introduction Single-crystal X-ray diffraction, commonly referred to as X-ray crystallography, is an analytical technique in which X-ray methods are
More informationX-ray Diffraction. Diffraction. X-ray Generation. X-ray Generation. X-ray Generation. X-ray Spectrum from Tube
X-ray Diffraction Mineral identification Mode analysis Structure Studies X-ray Generation X-ray tube (sealed) Pure metal target (Cu) Electrons remover inner-shell electrons from target. Other electrons
More informationFROM DIFFRACTION TO STRUCTURE
3.012 Fund of Mat Sci: Structure Lecture 19 FROM DIFFRACTION TO STRUCTURE Images removed for copyright reasons. 3-fold symmetry in silicon along the [111] direction. Forward (left) and backward (right)
More informationRoad map (Where are we headed?)
Road map (Where are we headed?) oal: Fairly high level understanding of carrier transport and optical transitions in semiconductors Necessary Ingredients Crystal Structure Lattice Vibrations Free Electron
More information3a 2. a 1 = 3a. a 2 = 3a
Physics 195 / Applied Physics 195 Assignment #4 Professor: Donhee Ham Teaching Fellows: Brendan Deveney and Laura Adams Date: Oct. 6, 017 Due: 1:45pm + 10 min grace period, Oct. 13, 017 at the dropbox
More informationAnalytical Methods for Materials
Analytical Methods for Materials Laboratory Module # Crystal Structure Determination for Non-Cubic Crystals Suggested Reading 1. Y. Waseda, E. Matsubara, and K. Shinoda, X-ray Diffraction Crystallography,
More informationIntroduction 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:
More informationMP464: Solid State Physics Problem Sheet
MP464: Solid State Physics Problem Sheet 1) Write down primitive lattice vectors for the -dimensional rectangular lattice, with sides a and b in the x and y-directions respectively, and a face-centred
More informationKeble College - Hilary 2012 Section VI: Condensed matter physics Tutorial 2 - Lattices and scattering
Tomi Johnson Keble College - Hilary 2012 Section VI: Condensed matter physics Tutorial 2 - Lattices and scattering Please leave your work in the Clarendon laboratory s J pigeon hole by 5pm on Monday of
More informationDiamond. There are four types of solid: -Hard Structure - Tetrahedral atomic arrangement. What hybrid state do you think the carbon has?
Bonding in Solids Bonding in Solids There are four types of solid: 1. Molecular (formed from molecules) - usually soft with low melting points and poor conductivity. 2. Covalent network - very hard with
More informationUnderstanding Single-Crystal X-Ray Crystallography Exercises and Solutions
Understanding Single-Crystal X-Ray Crystallography Exercises and Solutions Dennis W. Bennett Department of Chemistry and Biochemistry University of Wisconsin-Milwaukee Chapter Crystal Lattices. The copper
More informationThere are four types of solid:
Bonding in Solids There are four types of solid: 1. Molecular (formed from molecules) - usually soft with low melting points and poor conductivity. 2. Covalent network - very hard with very high melting
More informationClass 27: Reciprocal Space 1: Introduction to Reciprocal Space
Class 27: Reciprocal Space 1: Introduction to Reciprocal Space Many properties of solid materials stem from the fact that they have periodic internal structures. Electronic properties are no exception.
More informationPSD '18 -- Xray lecture 4. Laue conditions Fourier Transform The reciprocal lattice data collection
PSD '18 -- Xray lecture 4 Laue conditions Fourier Transform The reciprocal lattice data collection 1 Fourier Transform The Fourier Transform is a conversion of one space into another space with reciprocal
More informationX-Ray Diffraction. Parkland College. Reuben James Parkland College. Recommended Citation
Parkland College A with Honors Projects Honors Program 2014 X-Ray Diffraction Reuben James Parkland College Recommended Citation James, Reuben, "X-Ray Diffraction" (2014). A with Honors Projects. 115.
More informationMolecular Biology Course 2006 Protein Crystallography Part I
Molecular Biology Course 2006 Protein Crystallography Part I Tim Grüne University of Göttingen Dept. of Structural Chemistry November 2006 http://shelx.uni-ac.gwdg.de tg@shelx.uni-ac.gwdg.de Overview Overview
More informationPraseodymia on non-passivated and passivated Si(111) surfaces
Praseodymia on non-passivated and passivated Si(111) surfaces Dissertation (kumulativ) zur Erlangung des Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) dem Fachbereich Physik der Universität
More informationCrystal Structure Determination II
Crystal Structure Determination II Dr. Falak Sher Pakistan Institute of Engineering and Applied Sciences 09/10/2010 Diffraction Intensities The integrated intensity, I (hkl) (peak area) of each powder
More informationExperimental Determination of Crystal Structure
Experimental Determination of Crystal Structure Branislav K. Nikolić Department of Physics and Astronomy, University of Delaware, U.S.A. PHYS 624: Introduction to Solid State Physics http://www.physics.udel.edu/~bnikolic/teaching/phys624/phys624.html
More informationX-ray Diffraction. Interaction of Waves Reciprocal Lattice and Diffraction X-ray Scattering by Atoms The Integrated Intensity
X-ray Diraction Interaction o Waves Reciprocal Lattice and Diraction X-ray Scattering by Atoms The Integrated Intensity Basic Principles o Interaction o Waves Periodic waves characteristic: Frequency :
More information