832: Chemistry Solid State Structural Methods Outline Notes1 for the Spring 2000 Class Dr. Allen D. Hunter Youngstown State University Department of Chemistry
March 17th, 2000 Edition of Notes (i.e., Rough Draft to the end of Topic V)
1
Based partially on the text: Crystal Structure Analysis for Chemists and Biologists by J. P. Glusker, M. Lewis, and M. Rossi, VCH Publishers, New York, NY, 1994. Unless otherwise noted, chapter and page references are to this text.
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
2
Table of Contents
Section 1:
Table of Major Topics
Chemistry 832: Solid State Structural Methods Table of Contents Topic I: Introduction to Chemistry 832 Topic II: X-Ray Diffractometers Topic III: Single Crystals Topic IV: Diffraction by Crystals Topic V: Symmetry Topic VI: Physical Properties of Crystals Topic VII: Image Generation from Diffracted Waves Topic VIII: Amplitudes of Diffracted Waves Topic IX: Phases of Diffracted Waves Topic X: Electron Density Maps Topic XI: Least Squares Refinement Topic XII: Crystal and Diffraction Data Topic XIII: Atomic Coordinates and Molecular Structures Topic XIV: Absolute Structures Topic XV: Crystallographic Publications: Preparation and Analysis Topic XVI: Special Topics Index of Topics and Vocabulary
1 2 13 31 46 79 110 162 167 178 186 195 200 206 208 216 221 225 226
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
3
Section 2:
Complete Table of Contents
1 2 2 3 13 14 14 14 14 18 19 20 20 21 22 23 24 25 25 26 28 28 28 29 29 30 31 32 32 32 33
Chemistry 832: Solid State Structural Methods Table of Contents Section 1: Section 2: Section 1: Table of Major Topics Complete Table of Contents What is Chemistry 832?
Topic I: Introduction to Chemistry 832 Part a: Chemistry 832 Goals and Objectives Part b: Chemistry 832 Syllabus Part c: Chemistry 832 Resources Section 2: Section 3: Section 4: What Can Diffraction Methods Tell Us Speed and Cost What is a Single Crystal and Why is it Important?
Part a: Single Crystal Part b: Unit Cell Part c: Unit cells and diffraction data Section 5: Section 6: Block Diagram of an X-Ray Diffractometer X-Ray Generator
Part a: Goniometer Part b: Detector Section 7: Section 8: Basic Steps in X-Ray Diffraction Data Collection Basic Steps in X-Ray Diffraction Data Analysis
Part a: Data Analysis can be quite routine through impossibly difficult Part b: The Phase Problem Section 9: Main Steps in Data Analysis Part a: Procedural Steps Part b: Flow Chart for a Typical Structure Solution Topic II: X-Ray Diffractometers Section 1: What are X-Rays? Part a: Wavelengths of X-Rays Part b: Why are these Wavelengths chosen? Section 2: X-Ray Generators
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part a: X-Ray Lasers Part b: Conventional X-Ray Tubes Part c: Rotating Anode Generators Part d: Synchrotron Sources Section 3: X-Ray Monochromators Part a: Foil Filters (Ni foil) Part b: Crystal (Graphite) Monochromators Part c: Focusing Mirrors Section 4: X-Ray Collimators Part a: Graphite Crystal Monochromators and Pin Holes in Tubes Part b: Focusing Mirrors Section 5: Section 6: Section 7: Goniometers Low Temperature System X-Ray Detectors
4 33 33 34 35 36 36 36 36 37 37 37 38 39 40 40 41 42 43 44 45 45 45 45 46 47 48 50 53 66 71 73 73 77
Part a: Serial Detectors Part b: Film Based Area Detectors Part c: Multi-Wire Area Detectors Part d: CCD Detectors Part e: Imaging Plate Detectors Section 8: X-Ray Absorption in the Diffractometer Part a: Air Part b: Windows Part c: Sample, Glue, Fiber & Capillary Topic III: Single Crystals Section 1: Section 2: Perfect Crystals? Growing Single Crystals
Part a: General principles of growing single crystals Part b: Proven Methods for growing crystals Part c: What to do when proven methods fail Section 3: Section 4: The Unit Cell Crystal Shapes
Part a: Crystal Growth and Shapes Part b: Indexing Crystal Faces
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part c: The Crystal Lattice Topic IV: Diffraction by Crystals Section 1: Waves Part a: Generic Waves Part b: Water Waves Part c: Light Waves Section 2: Diffraction in Two Dimensions Part a: Diffraction Pattern from a Single Slit Part b: Diffraction Patterns from Two or More Slits Part c: Diffraction Patterns from Arrays of Slits Part d: Diffraction by Slits vs. Diffraction by Objects Section 3: Diffraction in Three Dimensions Part a: Laser Light Show Part b: The Influences of Object Patterns Part c: Quantum Mechanical Basketball Part d: The Influences of Objects, Periodicity, Array Size, and Disorder on Diffraction Patterns Section 4: X-Ray Diffraction Part a: What Diffracts X-Rays? Part b: The 180 Phase Shift for X-Rays Part c: Atomic Scattering Factors for X-Rays Section 5: Neutron Diffraction Part a: What Diffracts Neutrons? Part b: Atomic Scattering Factors for Neutrons Section 6: Part b: Braggs Law The Myth Taught in General Chemistry Part a: The Experimental Truth Part c: The Truth About Braggs Law Part d: Which planes are we talking about? Part e: Getting Unit Cell Parameters from Interplanar Spacings 106 Section 7: Anomalous Scattering
5 78 79 80 80 81 86 87 87 88 89 90 91 91 92 93 94 96 96 96 97 100 100 100 101 101 102 103 104 106 107 107
Part a: The Origins of Anomalous Scattering
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part b: Anomalous Scattering and Neutrons Part c: Anomalous Scattering and X-Rays Section 8: Section 1: The Ewald Sphere Introduction to Symmetry Topic V: Symmetry Part a: Origin and Choice of the Unit Cell Part b: Symmetry Operations Part c: Point Groups Part d: Space Groups Section 2: Point Symmetry Operations Part a: Rotation Axes Part b: Mirror Planes Part c: Inversion Centers Part d: Rotary Inversion Axes Part e: Point Groups and Chiral Molecules Section 3: Section 4: Section 5: Hermann-Mauguin vs. Schoenflies Symbols Symmetries of Regularly Repeating Objects Crystal Systems Space Groups
6 108 108 109 110 111 112 114 115 116 117 118 121 122 123 126 127 129 130 130 134 137 138 139 139 140 142 143 144 145 145 146 147
Part a: The 7 Crystal Systems Part b: Centering of Unit Cells Part c: The 14 Bravais Lattices Part d: The 230 Space Groups Section 6: Three Dimensional Symmetry Operations Part a: Translations Part b: Screw Axes Part c: Glide Planes Part d: Symmetry in some Real Crystals Part e: Review of Crystal Systems Space Groups Section 7: Symmetry in the Diffraction Pattern Part a: Equivalent Positions Part b: Friedel's Law Part c: Symmetry of Packing Symmetry of Diffraction Pattern
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part d: Laue Symmetry Part e: Examples of Using Laue Symmetry to Determine Crystal System: Diffraction Data, Unit Cell Parameters, and the Crystal System Section 8: Space Group Determination from Diffraction Data Part a: Systematic Absences Centering Part b: Systematic Absences Translational Symmetry Part c: Laue (Crystal System) Determination Part d: Bravais Determination Part e: Space Group Determination Part f: Space Group Ambiguity Topic VI: Physical Properties of Crystals Section 1: Mechanical Properties of Crystals Part a: Hardness of Crystals Part b: Cleavage of Crystals Section 2: Optical Properties of Crystals Part a: The Nature of Light Part b: Isotropic and Anisotropic Crystals Part c: Pleochromism Part d: Refraction of Light Part e: Birefringence of Light Part f: Polarization of Light Part g: Optical Activity and Crystals Section 3: Electrical Effects of Crystals Part a: Piezoelectric Effects Part b: Pyroelectric Effects Part c: Non-Linear Optical Phenomenon Section 4: Chemical Effects of Crystal Form Part a: Crystal Forms and Chemical Reactivity Part b: Different Faces Different Reactions Part c: Crystal Forms and Explosive Power Topic VII: Image Generation from Diffracted Waves Section 1: Waves
7 148 149 150 151 152 155 158 159 160 161 162 163 163 163 164 164 164 164 164 164 164 164 165 165 165 165 166 166 166 166 167 168
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part a: Amplitudes of Waves Part b: Lengths of Waves Part c: Phase Angles of Waves Part d: Summing Waves Section 2: Fourier Series Part a: Periodic Electron Density in Crystals Part b: Baron Fouriers Theorem Part c: Fourier Analysis Part d: Fourier Synthesis Section 3: Electron Density Calculations Part a: Electron Density is Periodic Part b: Equation for Electron Density as a Function of Structure Factors Part c: hkl values and Crystal Planes Section 4: Fourier Transforms Part a: Equation for Structure Factors as a Function of Electron Density Part b: Relationship Between Real and Reciprocal Space Part c: Summary of the Diffraction Structure Process Section 5: X-Ray Scattering Factors of Electrons in Orbitals Part a: Electron Distribution Curves for Orbitals Part b: Electron Scattering Curves for Orbitals Section 6: Section 7: Neutron Scattering Factors of Nuclei Kinematic and Dynamic Diffraction
8 168 168 168 168 169 169 169 169 169 170 170 170 170 170 170 170 170 171 171 171 172 173 173 173 173 174 174 174 174 175 175 176 176
Part a: Mosaic Blocks Part b: Kinematic Diffraction Part c: Dynamic Diffraction Section 8: Extinction Part a: Primary Extinction Part b: Secondary Extinction Part c: Renninger Effect and Double Reflections Section 9: Section 10: Structure Factors Displacement Parameters Part a: Structure Factor Amplitudes Part a: Vibration of Atoms in a Lattice
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part b: Disorder of Atoms and Molecules in a Lattice Part c: Isotropic Displacement Parameters Part d: Simple Anisotropic Displacement Parameters
9 176 176 176
Part e: Quadrupole Displacement Parameters and Evaluations of the Shapes of Electron Clouds 176 Section 11: Anomalous Scattering 177 177 177 177 178 179 179 179 179 179 179 180 180 180 180 181 181 181 181 182 183 184 185 186 187 187 187 187 Part a: Absorption Coefficients as a Function of Wavelength Part b: MAD Phasing of Protein Data Part c: Anomalous Scattering Topic VIII: Amplitudes of Diffracted Waves Section 1: Intensities of Diffracted Beams Part a: Equation for Intensities of Diffracted Beams Part b: Lorenz Factor Part c: Polarization Factor Part d: Absorption Factor Part e: Effects of Wavelength of Measured Intensities Section 2: X-Ray Sources Part a: X-Ray Spectrum of an X-Ray Tube Part b: Monochromatic X-Rays Part c: X-Ray Sources Section 3: X-Ray Detectors Part a: Scintillation Counters Part b: Beam Stop Part c: Area Detectors Section 4: Section 5: Section 6: Section 7: Section 1: Automated Diffractometers Effects of Temperatures on Collected Diffraction Data Peak Profiles Data Reduction Electron Density Distributions vs. Structure Factors and Phases
Topic IX: Phases of Diffracted Waves Part a: Flow Diagram Part b: With Known Structures Part c: Non-Centrosymmetric Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part d: Centrosymmetric Space Groups Section 2: Common Methods for Estimating Phase Angles Part a: The Role of Advances in Computers, Theory, and Software Part b: Direct Methods Part c: Patterson Methods Part d: Isostructural Crystals Part e: Multiple Bragg Diffraction Part f: Shake and Bake Section 3: Direct Methods Part a: Statistical Tools Part b: Mathematics of Phase Relationships Part c: Inequalities Part d: Where Works Best Section 4: Patterson Methods Part a: The Patterson Function Part b: Patterson Maps Part c: Where Works Best Part d: Heavy Atom Methods Section 5: Isomorphous Replacement Part a: Proteins: The Problem Structures Part b: Metal Salts Part c: Unnatural Amino Acids Part d: Related Protein Structures Section 6: Section 7: Section 1: Section 2: MAD Phasing of Proteins Shake and Bake Electron Density Function Electron Density Maps
10 187 188 188 188 188 188 188 188 189 189 189 189 189 190 190 190 190 190 191 191 191 191 191 193 194 195 196 197 197 197 197 197 197
Topic X: Electron Density Maps
Part a: General Features of Maps Part b: P(obs) Map Part c: F(calc) Map Part d: Difference Electron Density Maps Part e: Deformation Density Maps
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Section 3: Resolution
11 198 198 198 198 198 198 198 199 200 201 201 201 202 202 202 202 202 202 203 204 205 206 207 208 209 209 209 209 209 209 210 210 210
Part a: Conventional Definition Part b: Effects of Wavelength on Resolution and Intensities Part c: Mo Resolution Part d: Cu Resolution Part e: Ag and Synchrotron Data Part f: Effects of Resolution on the Structure Section 4: Section 1: Angles of Data Collection and Series Termination Errors What is Least Squares Refinement? Topic XI: Least Squares Refinement Part a: The Mathematics of Least Squares Refinement Part b: Qualitative Picture of Least Squares Refinement Section 2: Precision vs. Accuracy Part a: Precision Part b: Accuracy Part c: Random vs. Systematic Errors Part d: Gaussian Distribution Function Part e: Estimated Standard Deviations Section 3: Section 4: Section 5: Section 1: Section 1: Constraints Restraints Global vs. Local Minima in Solution The Standard Table Molecular Geometries
Topic XII: Crystal and Diffraction Data Topic XIII: Atomic Coordinates and Molecular Structures Part a: From xyz Coordinates to Bond Lengths, Bond Angles, etc. Part b: Vibrational Motion Part c: Fractional Coordinates Part d: Orthogonal Coordinates Part e: Complete Molecules? Section 2: Atomic Connectivities Part a: Derivation of Atomic Connectivity Tables Part b: International Tables for Typical Bond Distances
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter Part c: Bond Lengths Section 3: Section 4: Molecules in the Unit Cell and Z Estimated Standard Deviations
12 210 211 212 212 212 212 213 214 215 215 215 215 215 216 217 218 219 220 221 222 223 224 225 226
Part a: ESD Formula Part b: When are two values different? Part c: ESDs and Reliability of Data Section 5: Section 6: Section 7: Torsion Angles Molecular and Macromolecular Conformations Atomic and Molecular Displacements
Part a: Vibration Effects in Crystals Part b: Representations of Displacement Parameters Part c: Effects of Displacements on Molecular Geometries Part d: Uses of Anisotropic Displacement Parameters Topic XIV: Absolute Structures Section 1: Section 2: Section 3: Section 4: Section 1: Section 2: Section 3: Chirality of Molecules Optical Activity and Chiral Molecules Anomalous Dispersion Measurements Uses of Anomalous Dispersion Crystallographic Data Bases Crystallographic Papers Comparing Structures
Topic XV: Crystallographic Publications: Preparation and Analysis
Topic XVI: Special Topics Index of Topics and Vocabulary
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Topic I:
Introduction to Chemistry 832
Based primarily on: Chapter 1 (G, L, & R, pages 1-31) A. D. Hunters YSU Structure Solution Manual Other materials available (or referenced) on my WEB Site
Chapters 1 and Chapter 2 of G, L, & R need to be read on your own by the next class
Ask Students:
What do you know about the Application of
Diffraction Methods to Solving Chemical Problems?
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
14
Section 1: Part a:
What is Chemistry 832? Chemistry 832 Goals and Objectives
6. See the Chemistry 832 Goals and Objectives Handout, available on my WEB Site
Part b:
Chemistry 832 Syllabus
7. See the Chemistry 832 Syllabus for Spring 2000, available on my WEB Site
Part c:
Chemistry 832 Resources
8. Texts and Monographs 9. See the list of reference materials: CrystallographyDiffraction Methods Texts List, available on my WEB Site
The Lab Manuals Copes are available in the Diffraction Lab or may be borrowed from Dr. Hunter
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
15
The Structure Solution Guide Copies are available as .pdf files for those who want their own, one is kept in each of the Diffraction Lab and NT Labs, and may be borrowed from Dr. Hunter
The NT Lab This lab is equipped with a dozen Windows NT computers, each loaded with all of the software needed for this course. It is available to Chemistry Majors (and other privileged undergraduates) and Graduate Students. To use this lab, you need to get an NT identity and password from Ray.
The WEB
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
16
Numerous excellent teaching materials on diffraction methods are available on the WEB, I will place links to some starting sites on my WEB page.
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
17
The Diffractometer Lab This lab is equipped with two Bruker AXS P4 Diffractometers. The southern instrument is equipped with a Cu X-Ray source and is usually used for powder studies. The northern instrument is equipped with a Mo X-Ray source and is our main single crystal instrument. The two PCs in this lab each control one of the diffractometers
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
18
Section 2:
What Can Diffraction Methods Tell Us
20.Diffraction methods can tell us much useful information about crystalline samples, including: 21.The size and shape of the repeating unit (unit cell) of the crystal 22. 23. 24. 25. Overall molecular structures Bond lengths, angles, torsions, etc. Atomic motion and disorder Intermolecular interactions
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
19
Section 3:
Speed and Cost
26.One generation ago, a single crystal study could take up most of a PhD and consequently was a rarely used technique 27.Now, a routine single crystal study is both quick and relatively inexpensive 28. 29. 1 second to 1 week for data collection 1 hour to several days to solve the data
30.A few hundred to a few thousand dollars for a small molecule, about ten to a hundred times more for a routine protein
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
20
Section 4: Part a:
What is a Single Crystal and Why is it Important? Single Crystal
Graphics from Text: Figure 1.3, page 5; single crystals of Quartz and Ammonium Dihydrogen Phosphate (NLO material)
Growing crystals is typically slowest and most unpredictable part of experiment Long distance order from one side to the other Defects in th crystal effect quality of data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
21
Part b: 34. 35. 36. 37.
Unit Cell Repeating motif of crystal Bricks in the wall Includes both dimensions and symmetry Made up of imaginary lattice points
38.Contains complete unique part(s) of molecules (sometimes more than one copy)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
22
Part c:
Unit cells and diffraction data
39.The more unit cells in the crystal the better the data quality
The less disorder the better the data quality
Graphics from Text: Figure 1.6, page 14; Unit cells of NaCl and KCl
Graphics from Text: Figures 1.7 and 1.8, pages 17 and 18; Crystal structures of Diamond and Graphite
Graphics from Text: Figures 1.9 - 1.11, pages 19 - 21; Crystal structures of Hexamethylbenzene, Hexachlorocyclohexane, and Steroids as representative examples of early diffraction results
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
23
Section 5:
Block Diagram of an X-Ray Diffractometer
X-Ray Source
Monochromator and Collimator
Crystal
2 Goniometer Detector Beam Stop
Graphics from Text: Figure 1.5, page 11; Texts diagram of an XRay Diffractometer
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
24
Section 6: 41.
X-Ray Generator Needs to produce intense X-ray beam
42. Needs to produce monochromatic X-ray beam 43. Needs to produce collimated X-ray beam
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
25
Part a:
Goniometer
44.Allows one to place a sample at a precisely controlled orientation in 3D space 45. Under computer control
Part b:
Detector
46.Allows one to measure the intensity of diffracted X-ray beams as a function of diffraction angle
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
26
Section 7: 47.
Basic Steps in X-Ray Diffraction Data Collection Grow Single Crystal
Mount Single Crystal on Diffractometer
Evaluate Crystal Quality
Collect Unit Cell information and Space Group information
Collect Diffraction Data
Collect Absorption Data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
27
Solve Structure
Graphics from Text: Figure 3.11, page 89; Relationship of Crystallographic Data to Structural Data
Prepare Structural Data for Publication
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
28
Section 8: Part a:
Basic Steps in X-Ray Diffraction Data Analysis Data Analysis can be quite routine through
impossibly difficult 55. 56. 57. 58. 59. Quality of Raw Data Advances? Theory Advances Software Advances Computer Advances Synergy of these changes
Part b:
The Phase Problem
60.Which is more important, Knowing the Intensities or Knowing the Phases of the Diffracted beams? 61. Data Solution Relationship
Experiment
Intensity Information + Phase Information
Results
Atomic Positions + Atomic Sizes/Shapes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
29
Section 9: Part a: 62.
Main Steps in Data Analysis Procedural Steps Process the Raw Data (XPREP) Determine Space Group Do Absorption Corrections
63. 64.
Determine an Initial Starting Solution (XS) Use one of the tricks to find at least one atom at near its actual position This will give you the first phase information
Evaluate the Trial Structure(s) (XP) and Refine the Trial Structure(s) (XL)
Evaluate the Final Answer
Prepare the Data for Publication
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
30
Part b:
Flow Chart for a Typical Structure Solution
XSCANS name.P4P name.RAW name.PSI
name._LG name.P4T name.PSR
Data Collection and Data Reduction Data Reduction, Space Group Determination, and Absorption Correction
XPREP
name.PRP name.PCF name.INT
name.INS name.HKL
XS
name.LST
Generate Trial Solutions
Cycle until good trial solution found
name.RES
XP
Analysis of trial Solutions
name.INS
XL
Cycle until the refined solution goes to convergence
name.LST name.CIF name.FCF
Structure Refinement
name.RES
XP
Analysis of Refined Solutions
name.RES
Final Solution XP
name.PLT name.ORT
Final Plots for Publication
name.CIF name.FCF name.PCF
XCIF
name.TBL name.SFT
Final Tables for Publication
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Topic II: X-Ray Diffractometers
Based primarily on: Chapter 7 (G, L, & R, pages 225-279) Other materials available (or referenced) on my WEB Site A. D. Hunters YSU Structure Solution Manual The Instruments in the Diffraction Lab.
Ask Students: What do you know about X-Ray Diffractometers?
X-Ray Source
Monochromator and Collimator
Crystal
2 Goniometer Detector Beam Stop
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
32
Section 1: Part a: 76.
What are X-Rays? Wavelengths of X-Rays Typically 0.5 to 2.0
77.Limited by X-Ray Generation Capabilities (i.e., target metal) 78. 79. 80. 81. Limited by Available X-Ray Flux 1.54 0.71 0.49 for Cu Targets for Mo Targets on Ag Targets
82. Tunable Wavelengths on Synchrotron Sources
Part b: 83.
Why are these Wavelengths chosen? They match intermolecular distances
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
33
Section 2: Part a:
X-Ray Generators X-Ray Lasers
Part b: 84.
Conventional X-Ray Tubes Cathode (Tungsten Filament) Provides electrons
85.
86.Slowly boils off Tungsten Vapor and this contaminates Metal Target and leads to filament breakage 87. 88. Accelerator Plates Metal Target (Anode)
89.Determines Wavelength distribution of X-Rays 90.Must be an excellent conductor of heat 91. 92. 93. 94. 95. Up to 3,000 Watts Cooling System Limiting variable on tube output Causes most operating problems Transports heat to a heat sink
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
34
Part c:
Rotating Anode Generators to overcome the cooling limitations of
96.Designed
Conventional Anodes
Their Anode is a Rotating Cylinder of the Target Metal
Rated Power Limits typically 12 to 18 kW Normally run at 6 to 10 kW to reduce maintenance
Maintenance Problems Seals have to deal with high voltages, high vacuum, and high speeds Filaments need to be changes every couple of months
Vacuum System maintenance Purchase and Operating Costs
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
35
Part d:
Synchrotron Sources
105.National Level Facilities costing hundreds of millions or even a Billion Dollars
Rely on wasted energy of rotating particle beam Early machines collected stray radiation from bending magnets (broad band) Current machines also use Wiglers to generate tunable radiation
Advanced Light Source, ALS, at the National Lab in Berkeley
Advanced Photon Source, APS, at the National Lab in Chicago
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
36
Section 3:
X-Ray Monochromators
111.Needed to reduce radiation to a single wavelength without unduly reducing the intensity
Part a: 112.
Foil Filters (Ni foil) Ni foil
Part b: 113.
Crystal (Graphite) Monochromators Large Graphite Single Crystal
Part c: 114.
Focusing Mirrors Highest Photon Yields
115.Catch a larger spread of X-rays from the tube
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
37
Section 4:
X-Ray Collimators
Part a: Tubes
Graphite Crystal Monochromators and Pin Holes in
Part b: 116.
Focusing Mirrors Much higher photon yields
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
38
Section 5:
Goniometers
117. Manual Goniometers on Picker Machines
118. 119. 120. 121. 122.
Automated Goniometers 4 Circle Goniometers on our P4s Kappa Geometry Goniometers Serial Detectors vs. Area Detectors Full computer control
123. 124.
Extremely precise machining Digital stepper motors
Goniometer Heads
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
39
Section 6: 126. 127. 128. 129.
Low Temperature System Why low temperatures? Data intensity at high angles Smaller Displacement Parameters Slower crystal decomposition
130. Decomposition from X-Ray Beam 131. 132. Decomposition from heat Decomposition from air
133. 134. 135. 136.
Limitations Icing Liquid N2 Systems to -150 C Liquid He Systems to 15 - 20 K
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
40
Section 7: Part a: 137. 138. 139. 140.
X-Ray Detectors Serial Detectors Scintillation Counters Excellent dynamic range Low cost Highly reliable
141.Only one reflection at a time and therefore long data collection times 142. The Multiplex Advantage
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
41
Part b: 143. 144.
Film Based Area Detectors Oldest type of X-Ray Detector Multiple layers of film
145.Visual estimation of intensities using Densiometer 146. Modern automated intensity readings
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
42
Part c:
Multi-Wire Area Detectors
147.X-1000 Multi-Wire Detector on Cu Machine in Lab 148.Grid of wires (512 by 512 or 1024 by 1024) 149. 150. 151. 152. Xe gas ionization Be Windows Poor Dynamic Range Low Cost
153.First major automated route for collecting Protein data 154. Good for collecting Powder Data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
43
Part d:
CCD Detectors
155. Developed by DOD and Astronomers 156.The current State of the Art for Small Molecules and Synchrotron data 157.Chip sizes range from 1k x 1k to 4k x 4k pixels and several cm on an edge 158.Fiber Optic Taper normally used to increase data collection area to about 10 cm x 10 cm 159.Data collected for 30 seconds to several minutes per frame and then read out to computer (this almost instantly) 160.A Phosphor (tailored for the wavelength(s) of interest) converts the impinging X-rays to multiple visible light photons (what is counted by the CCD chip) 161.Moderately expensive but price coming down rapidly 162.Significantly more maintenance than a serial detector 163. Good dynamic range
164.CCD chip needs to be cryocooled to function
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
44
Part e:
Imaging Plate Detectors
165.The detector of choice for most current protein diffraction studies 166.Very large data collection areas, typically 30 cm x 30 cm 167.This is especially important for large unit cells 168.X-rays strike a large Storage Phosphor (frame times can be up to tens of minutes) 169.Data read out by training an IR laser onto each pixel which causes optical photons to be released 170.Data read out times can be several minutes as this is done in a serial fashion 171.In compensation, many Imaging Plate systems have two phosphor screens and one is collecting data while the other is reading it out 172. Prices similar to CCD systems
173.Dynamic range smaller but data collection area larger
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
45
Section 8: Part a:
X-Ray Absorption in the Diffractometer Air
174.Not a problem for short wavelength radiation such as Mo or Ag 175.A significant problem for Cu, especially with large unit cell parameters where crystal to detector distances are large 176. Use a He beam path
Part b:
Windows
177.Typically use Be windows on detectors and X-ray tubes 178.May also use plastic films around He beam paths, etc.
Part c:
Sample, Glue, Fiber & Capillary
179.Larger samples with heavy atoms can absorb significantly 180.Glue used to mount the sample, any beam that passes through the mounting fiber, and any capillary glass can absorb significantly, especially for Cu radiation
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Topic III:
Single Crystals
Based primarily on Chapter 2 (G, L, & R, pages 33-71).
Crystal Growth Strategies based primarily on Chapter XIV in Allen Hunters YSU Structure Analysis Lab Manual, SALM, page 240 - 247
Ask Students: What do you know about Single Crystals
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
47
Section 1: 183. 184. 185.
Perfect Crystals? Single Crystals Have long range order Like bricks in a wall
One distinct orientation Typically a single degree or so of disorder across macroscopic dimensions
Graphics from Text: Figures 2.1 - 2.3, pages 34 - 36; Electron Micrograph pictures of three Virus Crystals
Graphics from Text: Figure 2.4, page 37; Scanning Tunneling Microscope, STM, images of Gallium Arsenide, GaAs, Single Crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
48
Section 2:
Growing Single Crystals
Stages of Crystal Growth Nucleation The key step Deposition on Surfaces of Individual Molecules Requires a Saturated Solution Requires that surface have similar metric parameters to the molecules being deposited
Graphics from Text: Figure 2.6, page 42; Sites of crystal growth on a crystal surface
Graphics from Text: Figure 2.8, page 48; Some methods of growing single crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
49
Crystal Growing Strategies from Chapter XIV in Allen Hunters YSU Structure Analysis Lab Manual, SALM, as a Separate Handout available from:
You Must Print out this Handout Modified Chapter XIV of ADH's Structure Analysis Lab Manual, SALM: Growing Single Crystals Suitable for Diffraction Analysis: In Color: 137KB.doc, 63KB.pdf Black and white: 143KB.doc, 62KB.pdf
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
50
Part a: 195. 196.
General principles of growing single crystals General view: Art rather than Science Green Thumb
197. Rational approach informed by understanding
Part i: Rates of Crystal Growth 198. 199. Slower is better Typically takes days to a week
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
51
Part ii: General Conditions for Crystal Growth 200. 201. 202. Best Conditions Constant temperatures Minimal vibration
203.Dark (often seems to help, especially avoid direct sunlight)
Impatience is the Enemy Convection is bad and should be suppressed Viscous solvents
Low Thermal Expansion Coefficient, dependence of density on temperature Narrower tubes
Dont check crystallizations too often
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
52
Part iii: Solvent Properties and Saturated Solutions 210. Grow crystals from Saturated Solutions 211.Like a bears porridge, concentration at saturation must be just right 212. Systematically explore solubility
Part iv: Master Several Favorite Methods 213. Success increases with experience
214. One learns to read subtle signals 215.Find a few methods and master them
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
53
Part b: 216.
Proven Methods for growing crystals The most common methods
Part i: Crystallization by Slow Evaporation 217. Most popular method
218.Works most easily with air stable materials 219. Slow solvent evaporation is the key
Part ii: Crystallization by Cooling 220.My personal favorite, alone or in combinations 221.Solubility typically decreases with temperature 222. 223. 224. Cool saturated solution of sample Freezer for organics/inorganics Furnace for extended solids
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
54
Part iii: Crystallization Using Mixed Solvents and Solvent Diffusion in the Gas Phase 225.Use a mixture of solvents to obtain the correct level of solubility 226. Mixed Solvents
227.One solvent is moderately good for the compound 228.Contains dissolved sample near saturation 229.One solvent is moderately bad for the compound 230.The two solvents must be fully miscible 231.The sample is fully dissolved in the better solvent and then through various means the concentration of the second, poorer, solvent is increased
Allow the two solvents to mix using a very slow solvent pump or dropwise solvent addition
Allow the better solvent to evaporate out of the system
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
55
Allow one or both of the solvents to diffuse into the other via the gas phase Typically takes longer and requires a moderately volatile solvent
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
56
Part iv: Crystallization by Solvent Layering 236. Solvent Layering
237.One solvent is moderately good for the compound 238.Contains dissolved sample near saturation 239.One solvent is moderately bad for the compound 240.The two solvents must be fully miscible 241. Layer one on top of the other
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
57
Part v: Crystallization by Diffusion Through Capillaries and Gels 242.Diffusion through a narrow capillary, constriction in the tube, or a gel 243.One solvent is moderately good for the compound 244.Contains dissolved sample near saturation 245.One solvent is moderately bad for the compound 246.The two solvents must be fully miscible 247.The sample is fully dissolved in the better solvent and then through various means the concentration of the second, poorer, solvent is increased
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
58
Part vi: Crystallization From Melts 248.Requires that the sample be thermally stable at the requisite melting point of the Melt
Used industrially to grow single crystals used in the electronics industry, e.g. Single crystal Silicon, Gallium Arsenide, etc.
Used to grow single crystals of high temperature extended solids, e.g. Minerals such as Diamond and Quartz in nature Metal oxides in Dr. Wagners group
Some work has been done on using low temperature ionic liquids (which may melt near room temperature) to apply this approach to less thermally stable ionic materials
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
59
Part vii: Crystallization by Sublimation 255.The compound must be sufficiently volatile at accessible pressures (vacuums) 256.Can be assisted by using heating of the sample and cooling of the receiver
Works best with the most volatile materials (typically quite nonpolar), e.g. Naphthalene Ferrocene Cr(CO)6
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
60
Part viii:
Crystallization Using Combinations
261.In Terminator II, Judgement Day, the boy is trying to teach Arnold Swartzenager, the Terminator, how to act more human 262.He first teaches him individual colloquial expression 263.He then tells him he can, like, use combos 264.Arnold gets the idea and comes up with Hasta La Vista - Baby (forgive my Spanish)
Like Arnold, dont be afraid to use combinations, combos, that your experience and intuition suggest, e.g. My favorite method is to layer the solution and then place it in the freezer
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
61
Part ix: Syntheses In Situ 267.Reactions at the Interface of Two Solutions 268.Can be at a boundary between to immiscible layers 269.Can be at a capillary junction between the same solvent 270.The starting materials are each dissolved in one solution 271. The product is insoluble in neither 272.It precipitates at the solution boundary 273.Works even for thermally unstable materials
Can be done with an electrochemical source as one reagent
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
62
Part x: The Magic of NMR Tubes 275.An amazingly large number of single crystals are grow in NMR tubes so always check them before cleaning.
Why is this true? NMR Tubes are: Typically very clean
Have few nucleation sites on their walls (no scratches) Thin and this suppresses convention The plastic caps have a very low permeability to most organic solvents that lets them evaporate out slowly over weeks or months Chemists run at near saturation to get the strongest signal Chemists use their cleanest samples for NMR to get the prettiest pictures for their bosses and themselves
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
63
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
64
Chemists, as a Rule, are Lazy They do not clean their tubes for months in dark quiet spot and let them sit around undisturbed in spots the boss cant see and they dont have to look at: perfect crystallization conditions
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
65
Part xi: Other Chance Methods 286. Dont look a gift horse in the mouth and keep a close watch: 287.dirty old flasks you have been avoiding washing 288. in old bottles of samples
289.in anything that might hold a sample
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
66
Part c:
What to do when proven methods fail
Part i: Purify Your Material 290.Impure materials greatly impede crystallization,
especially the formation of single crystals
If you crystallization doesnt work: Further purify the sample Keep the best solids and use them to start the next round
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
67
Part ii: Seed Crystals 294.Crystals grow by the addition of individual molecules to a surface having a similar structure
Crystals can be grown using Seed Crystals of your sample that were too small for diffraction analysis
Seed crystals are often produced accidentally from solutions splashed on the side walls of flasks
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
68
Part iii: The Role of Extraneous Materials 297.Interestingly, if one uses too clean of procedures (hard to do in practice) it is much harder for crystals to grow, they typically need a seeding/patterning agent, often provided accidentally
Dust, dandruff, and grease
Scratches and defects in the container walls
Surface treatments of the container walls
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
69
Part iv: Try, Try Again 301.When All Else Fails, Persistence Pays Off
Sequential crystal growing strategies
Systematic approaches to growing single crystals and the exploration of crystallization: the multiplex advantage Learning from Protein Crystallographers
Make Derivatives They synthetic chemists best friend
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
70
Solvates and Crystallization Agents Packing / Interacting solvents such as: Water or Alcohols Benzene Chlorocarbons
Inclusion Compounds and Supramolecular Complexes Thiourea, SC(NH2)2, Channel Compounds Calix[n]Arenes Cyclodextrins Porphyrins
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
71
Section 3:
The Unit Cell
Graphics from Text: Figure 2.5, page 38; Unit Cell Axial Lengths and Unit Cell Angles Axial naming follows the right hand rule The three axial vectors define a Parallelepiped The lengths can be the same or different Range from a few Angstroms to thousands of Angstroms The angle can be the same or different Often are not 90
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
72
z
c
b y
a
x
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
73
Section 4: Part a:
Crystal Shapes Crystal Growth and Shapes
Part i: Crystal Habits and Morphology 323.The relative rates that molecules are deposited onto the surface of growing crystals determines the final shape of the crystal
This final shape for a particular unit cell is referred to as: The Morphology of the Crystal The Habit of the Crystal These external forms are hard to directly relate to unit cell parameters
Graphics from Text: Figure 2.7, page 44; The relationship of crystal faces to the rates of face growth
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
74
Part ii: Polymorphism and Isomorphism 328.Some molecules are found with several different unit cells (typically because the energies of packing are similar and small changes in crystallization conditions favor one over the others) 329.These different forms are know as Polymorphs and this behavior is know as Polymorphism
Graphics from Text: Figure 2.14, pages 58 - 61; Variations of crystal shapes (crystal habits) from the same cubic unit cells
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
75
Isomorphism occurs when two different molecules crystallize in apparently identical crystals
Isomorphic Crystals typically have similar: Crystal Shapes Unit Cell Dimensions Similar molecular structures Similar molecular compositions
With enough similarity can grow mixed crystals via Isomorphic Replacement, e.g. Very common in minerals Mixed isotope compounds V(CO)6 in Cr(CO)6 Chromium Alum in Potash Alum Isomorphous Replacement in Protein Diffraction Studies using heavy atom salts, unnatural amino acids, etc.
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
76
Alums, (M1)2(SO4).(M3)2(SO4)3.24H20 M1 = K or NH4 M3 = Al+3 or Cr+3
Form large octahedral crystals by evaporating water solutions
Potash Alum, K2(SO4).Al2(SO4)3.24H20 Colorless Air Stable
Chromium Alum, K2(SO4).Cr2(SO4)3.24H20 Deep Purple Decays in Air
Isomorphic Replacement Layered Alums Mixed Alums
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
77
Part b:
Indexing Crystal Faces
355.Very widely done in geology as a way of identifying minerals 356.Contact Goniometer (two hinged straight edges used to measure angles) 357.Graphics from Text: Figure 2.10, page 52; Diagram of a Contact Goniometer
358. 359.
Indexing Crystal Faces The xyz face of a crystal is
360.Parallel to all of the xyz planes in the crystal 361.Intersects to axes of the unit cell at 1/x, 1/y, and 1/z 362. 363. 364. Examples: 100 Face 134 Face
365. Good Exam Type Question 366.Graphics from Text: Figure 2.11 and 2.12, page 53 and 54; Indexing Crystal Faces
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
78
Part c:
The Crystal Lattice
367.The Crystal Lattice is an imaginary three dimensional array of points, lattice points, that repeats to give the three dimensional order of the crystal
When convoluted with the unit cell contents, it build the full three dimensional structure of the crystal
Graphics from Text: Figures 2.15 and 2.16, pages 62 and 63; The crystal lattice and real crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Topic IV:
Diffraction by Crystals
Based primarily on Chapter 3 (G, L, & R, pages 73-103).
Ask Students: What do you know about the Process of Diffraction of Waves?
Graphics from Text: Figure 1.2, page 4; Image Generation in Optical Microscopy and X-Ray Diffraction
X-Ray Source
Monochromator and Collimator
Crystal
2 Goniometer Detector Beam Stop
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
80
Section 1: Part a: 372. 373.
Waves Generic Waves Parameters that define a wave: Wavelength,
374. In Diffraction is typically near 1 375. (Frequency, (remember: C = )) 376. 377. Amplitude, A Relative Phase,
Graphics from Text: Figure 3.1, page 75; The Amplitude, A, Wavelength, , and Relative Phase, , of a Sinusoidal Wave
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
81
Part b:
Water Waves
378.Apply your intuition/real world experience/Physics to thinking about planar waves, such as water waves, moving through holes in a barrier (breakwater) 379.Note: The same thing happens when they go through a field of poles in the water
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
82
Part i: Non-parallel sets of waves on open water 380.Areas of unexpectedly high and low amplitudes (can be very dangerous to boaters) 381. 382. Constructive Interference Destructive Interference
Later
Constructive Inteference Destrcutive Interference
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
83
Part ii: Parallel waves passing through a hole in a breakwater 383.Areas of unexpectedly high and low amplitudes (can be very dangerous to boats at dock) 384. 385. Constructive Interference Destructive Interference
386.Graphics from Text: Figure 3.2a, page 76; Spreading of Plane Waves passing through a slit
Direction of Travel
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Breakwater
Breakwater
Chemistry 832: Solid State Structural Methods, Dr. Hunter
84
Part iii: Parallel waves passing through two holes in a breakwater 387.Areas of unexpectedly high and low amplitudes 388. 389. Constructive Interference Destructive Interference
390.Graphics from Text: Figure 3.2b, page 76; Spreading of Plane Waves passing through two slits
Breakwater
200
100
000 Direction of Travel
-1 0 0 Breakwater
-2 0 0
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
85
Part iv: Parallel waves passing through two holes of varying spacings 391.The further apart the slits are the closer together will be the sites of constructive and destructive interference 392.Graphics from Text: Figure 3.2b and c, page 76; Effects of slit spacing on interference pattern
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
86
Part c:
Light Waves
Graphics from Text: Figure 1.4, page 9; Diffraction of light through a fine metal mesh sieve
Note the wavelength does not change
Constructive Interference and Destructive Interference
Graphics from Text: Figures 1.1 and 3.3, pages 3 and 77; Constructive and Destructive Superposition of Waves
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
87
Section 2: Part a:
Diffraction in Two Dimensions Diffraction Pattern from a Single Slit
Part i: Influence of Slit Width on Diffraction Pattern
Narrow Slits Wide patterns Wide Slits Narrow patterns Note: the inverse relationship characteristic of diffraction
Graphics from Text: Figure 3.5, page 79; Diffraction Patterns of a Single Slit
Part ii: Reason for the Observed Diffraction Pattern Shapes 400.Constructive and Destructive Interference from light coming through different parts of the slit
Graphics from Text: Figure 3.6, page 80; Reason for the Diffraction Patterns of a Single Slit
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
88
Part b:
Diffraction Patterns from Two or More Slits
401.Much like with water waves, pairs of slits give rise to interference patterns.
Part i: Influence of Slit Spacing 402.Wide spacing of slits leads to closely spaced maxima 403.Close spacing of slits leads to widely space maxima
Graphics from Text: Figure 3.6, page 80; Diffraction Pattern Spacing from Larger and Smaller Spacings of Slits
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
89
Part c:
Diffraction Patterns from Arrays of Slits
404.The overall influences of slit width and pattern are a convolution of the influences of slit width and slit spacing 405.Slit Width Overall Envelope of Diffraction Pattern 406.Slit Spacing Spacing of Maxima within that Envelope
Graphics from Text: Figure 3.6, page 80; Diffraction Pattern Spacing from Arrays of Slits
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
90
Part d:
Diffraction by Slits vs. Diffraction by Objects
407.These discussions have focused on models of slits in walls
They also work equally well with objects that cause the bending, for example: A field of Telephone Poles planted in a lake for water waves A pattern of glass or plastic rods for light waves
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
91
Section 3:
Diffraction in Three Dimensions
Part a:
Laser Light Show
Diffraction patterns form by shining light through two dimensional patterns and projected onto a screen
Laser Light Show: Laser Pointer and ICE Slides
Graphics from Text: Figure 3.7, page 82; Diffraction Patterns from Arrays of Points on a Slide
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
92
Part b:
The Influences of Object Patterns
412.It is most apparent that there is a reciprocal relationship between the diffracting array and the observed pattern 413. A square array a square pattern
414.A rectangular array a rectangular pattern rotated 90 415. A hexagonal array a hexagonal pattern 416.A closely spaced array a widely spaced pattern 417.A widely spaced array a closely spaced pattern
418. Hence the origin of the term Reciprocal Space
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
93
Part c:
Quantum Mechanical Basketball
419.Influences of the patterns on the court on who in the stands will get hit 420.Influences of the player orientation, size, and shape on who in the stands will be hit
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
94
Part d:
The Influences of Objects, Periodicity, Array Size,
and Disorder on Diffraction Patterns Part i: Objects in the Array 421.The size, shapes, and orientations or the objects in the array a continuously varying intensity of diffracted light 422. This is like a topographic map
Part ii: Pattern of the Array 423.The periodicity of the pattern determines the angles at which diffracted beams will be observable and hence set a mask over which the continuously varying intensity pattern can be sampled 424.This is like a piece of paper with holes punched out of it through which one looks at a topographic map
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
95
Part iii: Size of the Array 425. The more objects in the array:
426.the narrower will be each beam of light 427.the stronger will be the total diffracted beam
Part iv: Disorder of the Array 428.The more disordered (both dynamically and statically) the array the weaker will be the diffracted beams at higher diffraction angles
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
96
Section 4:
X-Ray Diffraction
Part a:
What Diffracts X-Rays?
429.X-rays are diffracted by electrons not the nucleus so an Xray structure solution tells you where the electrons are in the sample not where the centers of the atoms are
Part b:
The 180 Phase Shift for X-Rays
430.When a wave is reflected (e.g., a water wave off of a wall or a light wave off of a mirror) that wave gets a 180 phase shift relative to the incoming wave 431.The same 180 Phase Shift is typical for X-ray diffraction
Graphics from Text: Figure 3.8, page 84; the Phase Shift during XRay Scattering
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
97
Part c:
Atomic Scattering Factors for X-Rays
432.Since X-ray are diffracted by electrons, the size and shape of the electron cloud will influence the diffracted intensity
Graphics from Text: Figure 3.12, page 90; The relationship of Relative Object Size and Wavelength to High Angle Scattering of Waves
Graphics from Text: Figure 3.13a, page 91 and Table 3.2 page 92; Some Atomic Scattering Factors and Atomic Scattering Curves for X-Rays
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
98
Part i: Maximum Atomic Scattering Factor, ASF 433.More total electrons corresponds to a stronger diffracting ability 434.Thus, the maximum Atomic Scattering Factor, ASF, will follow the order W > Mo > Cr, etc., O-2 >O- > O 435.The maximum ASF value for an atom/ion is equal to the total number of electrons 436.Because ASF is determined by the electron cloud and not by the nuclear composition, it is largely independent of the isotope
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
99
Part ii: Shapes of the Atomic Scattering Factor Curves 437.The size of the atom strongly influences the angular dependence of the diffracted intensity 438.As with slit width effects, this is due to destructive interference between X-rays scattered from different parts of the electron cloud 439.With the same total number of electrons, larger atoms drop off more quickly (i.e., due to Zeff) 440.The effects of different orbitals can be calculated to give calculated ASF curves 441.Because atoms are large with respect to the size of Xrays, X-Ray ASF curves drop off fairly rapidly and one tends not to see a lot of diffracted intensity at high angles 442.ASF curves are typically plotted as ASF vs. sin/ and are thus useful for all X-ray wavelengths
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
100
Section 5:
Neutron Diffraction
Part a: 443.
What Diffracts Neutrons? Neutrons are diffracted by nuclei
Part b:
Atomic Scattering Factors for Neutrons
444.Neutrons used for diffraction have a wavelength of about 1 while nuclei have diameters of about 10-4 and therefore act a point diffraction objects 445.This means that their scattered intensity is largely independent of angle 446.Because it is nuclei that do the scattering, Neutron ASF values are different for different isotope 447.However, they are independent of the charge on the atom/ion
Graphics from Text: Figure 3.13b, page 91 and Table 3.2, page 92; Atomic Scatting Factors for Neutrons
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
101
Section 6:
Braggs Law
Part a:
The Experimental Truth
Braggs Law states for diffraction to occur it is observed experimentally that: n = 2 d sin Where n Any integer, 0, 1, 2, 3, 4, etc. The Wavelength of Diffracted Light d The Interplanar Spacing
The Angle between the Incident Ray and the Planes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
102
Part b:
The Myth Taught in General Chemistry
Diffraction Off of Planes gives Braggs Law (may mention this is due to constructive and destructive interference)
sin = x/d 2dsin = 2x 2x = n n = 2dsin plane
d d plane x x
d
plane
Graphics from Text: Figure 3.10b, page 87; Diffraction off of Planes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
103
Part c:
The Truth About Braggs Law
Graphics from Text: Figure 3.9, page 85; Conditions for Diffraction so as to get Constructive Interference - Relating Diffraction Through Slits to Diffraction off of Planes
Graphics from Text: Figures 3.10a and b, pages 86 and 87; Interference and Braggs Law
d d
x
x
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
104
Part d:
Which planes are we talking about?
455.Diagram of planes from a section of crystal
Pl an e
an e
an e
an e
0
0
1
0
1
1
1
1
1
1
1
1
1
0
Pl an e
Pl
Pl
0
Pl
1 0 0 Plane
2 0 0 Plane
y 3 0 0 Plane Axis System x 4 0 0 Plane
5 0 0 Plane 0 1 0 Plane
Graphics from Text: Figure 2.12, page 34; the Indexing of Crystal Faces
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
105
The minimum incidence angle reflections off of pairs of planes that are one layer apart and would be the 1 0 0 reflections
The next angle reflections off to pairs of planes two layers apart and would be referred to as the 2 0 0 reflection
The third smallest angle reflections off to pairs of planes three layers apart and would be referred to as the 3 0 0 reflection
Thus the 1 0 0, the 2 0 0, the 3 0 0, etc., reflections all come off of a set of parallel planes that intersect the x axis but not the y and z axes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
106
Part e: Spacings
Getting Unit Cell Parameters from Interplanar
461.Once one measures the observed angles of a dozen or so reflections, it is an exercise in geometry to calculate the unit cell parameters 462.Obviously the more accurate the angles (and the larger the number) the more accurate will be the unit cell parameters
Graphics from Text: Table 3.1, page 88; Obtaining Unit Cell Dimensions from dhkl Values
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
107
Section 7: Part a:
Anomalous Scattering The Origins of Anomalous Scattering
463.Upon diffraction from an array of atoms, most of the time the phase shift is approximately 180
In the ideal case, the absorption of radiation by an element increases smoothly with increasing wavelength Occasionally, when the incident radiation is similar in energy to the energy required to excite or ionize a bound electron, there will be a spike in the absorption curve called an Absorption Edge Graphics from Text: Figure 6.23, page 219; Absorption Curves for some representative atoms
If the wavelength of the incident radiation is near the absorption edge of an element then the phase shift is likely to be significantly different than 180, more later
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
108
Part b:
Anomalous Scattering and Neutrons
468.For neutrons, anomalous scattering is dependent on the isotope one uses and can be used to readily distinguish isotopes in different positions 469.Graphics from Text: Table 3.2, page 92; Atomic Scattering Factor Table including an example of Anomalous Scattering for 6Li
Part c:
Anomalous Scattering and X-Rays
470.As we will see later, this is very important for X-rays both in helping to estimate phases of complex molecules such as proteins and in absolute structure determinations where anomalous scattering makes reflection h k l -h -k -l
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
109
Section 8:
The Ewald Sphere
The Ewald Sphere is a way of thinking about when a crystal will be at the right orientation for a reflection to occur
Graphics from Text: Figure 3.17, pages 98 and 99, The Origin of the Ewald Sphere
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Topic V: Symmetry
Based primarily on: Chapter 4 (G, L, & R, pages 105-141)
XSCANS Tutorial Guide and Reference Guide (BrukerAXS) The International Tables (Symmetry and Space Group Determination Sections) Software Package: Crystallographic CourseWare (M. Kastner, Bucknell University): An exceptionally useful and user friendly package to learn about symmetry and many aspects of diffraction methods
Ask Students: What do you know about Symmetry?
//root/15989/25d5a23251801d6c804dae69c1a5b12da6ac1e32.doc
Chemistry 832: Solid State Structural Methods, Dr. Hunter
111
Section 1:
Introduction to Symmetry
477.Symmetry tell us about patterns in shapes in a very concise way and is very important in interpreting crystallographic data
We will not be discussing symmetry in detail in 2000 (but will in the Semester version of the course) but will look at some high points
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
112
Part a:
Origin and Choice of the Unit Cell
479.The Origin of the Unit Cell is entirely arbitrary but for the sake of simplicity it is usually chosen as the point of highest symmetry in the unit cell
Note: The molecule(s) in the unit cell do not have to be in the center and in fact are often split between adjacent unit cells
For each lattice, one can choose an infinite number of unit cells The only criterion is that, when duplicated side by side, the unit cell must reproduce the structure of the whole crystals The unit cell can be chosen with different sizes and shapes The Primitive Unit Cell is the smallest unit cell possible with its angles being as close to 90 as possible
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
113
Graphics from Text: Figures 4.1a and b, pages 106 and 107; Examples of Choices of Unit Cells
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
114
Part b:
Symmetry Operations
486.Symmetry operations are geometric activities that convert an object back into itself 487. It can be a point, a line, or a plane
Graphics from Text: Figure 4.2, page 108; The Symmetry of Benzene
Graphics from Text: Table 4.1, page 116; Table of Symmetry Operations
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
115
Part c:
Point Groups
490.Point Groups are a collection of symmetry operations characteristic of an object that is fixed in space 491.These are widely used in Physical Chemistry and Spectroscopy to simplify calculations and predict spectra 492.There are 32 Unique Point Groups relevant to the Crystalline State
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
116
Part d:
Space Groups
493.Space Groups are a collection of Symmetry Operations characteristic of an object that is arranged periodically in space 494.These are widely used in Solid State Chemistry and Materials Science to simplify calculations and understand extended solids 495. There are 230 Unique Space Groups
496.Some of these are very commonly found while others have yet to be observed in nature
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
117
Section 2:
Point Symmetry Operations
497.Point Symmetry Operations are a symmetry elements characteristic of an individual object 498.No Translational Symmetry Operations are allowed
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
118
Part a:
Rotation Axes
499.Rotation Axes occur when one rotates an object about a line passing through its center
A n-fold rotation rotates an object through 360/n leaving the object unchanged n=1 A Onefold Rotation rotates the object through 360 This rotation is also referred to as the Identity Operation
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
119
n=2 A Twofold Rotation rotates the object through 180 Graphics from Text: Figure 4.3, page 110; Two Fold Rotation Axes
z
xyz
-x -y z
Twofold Rotation about z axis
z
y
180o
x
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
120
n=3 A Threefold Rotation rotates the object through 120
n=4 A Fourfold Rotation rotates the object through 90
n=5 A Fivefold Rotation rotates the object through 72 This is allowed in individual molecules but not allowed in crystalline materials
n=6 A Sixfold Rotation rotates the object through 60
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
121
Part b:
Mirror Planes
510.A Mirror Plane converts an object into its Mirror Image 511.Objects may have more than one mirror planes in them
z
xyz
x -y z
z
A Mirror Plane
x x
y
Graphics from Text: Figure 4.4, page 111; Mirror Planes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
122
Part c:
Inversion Centers
513.An Inversion Center turns a molecule inside out 514. It is often referred to as i or as 1bar
An Inversion Center
*
-x -y -z
xyz
z
y x
Graphics from Text: Figure 4.5, page 112; Center of Symmetry
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
123
Part d:
Rotary Inversion Axes
516.A Rotatory Inversion Axis is a Rotation by 360/n followed by an inversion across a center of symmetry
517.A n-fold rotation rotates an object through 360/n followed by inversion leaving the object unchanged 518.n=1 A Onefold Rotatory Inversion rotates the object through 360 and then inverts it 519.This rotation is the same as the Inversion Center 520. This is referred to as 1bar
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
124
n=2 A Twofold Rotatory Inversion rotates the object through 180 and then inverts it This is referred to as 2bar This is equivalent to a Mirror Plane
Graphics from Text: Figure 4.6, pages 113 and 114; Twofold Rotatory Inversion Axis
n=3 A Threefold Rotatory Inversion rotates the object through 120 and then inverts it This is referred to as 3bar
n=4 A Fourfold Rotatory Inversion rotates the object through 90 and then inverts it This is referred to as 4bar
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
125
n=5 A Fivefold Rotatory Inversion rotates the object through 72 and then inverts it This is referred to as 5bar This is allowed in individual molecules but not allowed in crystalline materials
n=6 A Sixfold Rotatory Inversion rotates the object through 60 and then inverts it This is referred to as 6bar
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
126
Part e:
Point Groups and Chiral Molecules
Part i: Proper Symmetry Operations 534.Proper Symmetry Operations do not change the handedness of objects 535. 536. Translations Rotations
Part ii: Improper Symmetry Operations 537.Improper Symmetry Operations do change the
handedness of objects (i.e., they convert it to its mirror image) 538. 539. Reflections Inversions
Part iii: Point Groups and Handedness 540.If a molecule is Chiral, it can never be in a Point Group that includes Improper Symmetry Operations because they would then be superimposable on their mirror image
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
127
Section 3:
Hermann-Mauguin vs. Schoenflies Symbols
541.Point Groups can be indicated by one of two systems of nomenclature 542.Schoenflies is what is used most commonly by Chemists such as Spectroscopists 543.Hermann-Mauguin is used by Crystallographers 544.Graphics from Text: Table 4.1, page 116; Conversions from Schoenflies to Hermann-Mauguin Symbols for Point Groups
Graphics from Text: Figure 4.7, page 117; The Symmetry of a Cube
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
128
Rotation
Rotation + Perpendicular Reflections
Rotation + Plane(s) Through the Axis
Rotatory Inversion
Rotation (n) + n Perpendicular Twofold Axes
Rotation (n) + n Perpendicular Twofold Axes + Perpendicular Reflections
Rotation (n) + n Perpendicular 2 Fold Axes + Perpendicular Reflections + Diagonal
Cubic Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
129
Section 4:
Symmetries of Regularly Repeating Objects
554.Crystallographic Point Groups (i.e., those in solids) must leave the whole crystal unchanged 555.As a consequence only 2, 3, 4, and 6 fold symmetries are allowed (Fivefold Symmetry) is forbidden 556.As a consequence, there are only 32 Allowed Point Groups in the Crystalline State
Graphics from Text: Figure 4.8, page 119; Fivefold Symmetry vs. Threefold, Fourfold, and Sixfold Symmetry
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
130
Section 5:
Crystal Systems Space Groups
Part a:
The 7 Crystal Systems
558.The Seven Crystal Systems are characterized by their Lattice Symmetries (which also constrain their allowed unit cell axial lengths and angles)
Graphics from Text: Table 4.2, page 120; The Seven Crystal Systems
Part i: Triclinic 560. Symmetry is the Identity or Inversion 561. 562. 563. Lattice (Laue) Symmetry 1bar a b c
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
131
Part ii: Monoclinic 564.Symmetry is a single Twofold Rotation or Rotatory Inversion axis along b 565. 566. 567. 568. Lattice (Laue) Symmetry 2/m a b c = = 9 0 9 0
Part iii: Orthorhombic 569.Symmetry is three mutually perpendicular Twofold Rotation or Rotatory Inversion axes along a, b, and c 570. 571. 572. Lattice (Laue) Symmetry mmm a b c = = = 9 0
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
132
Part iv: Tetragonal 573.Symmetry is a single Fourfold Rotation or Rotatory Inversion axis along c 574. 575. 576. 577. A face stretched cube Lattice (Laue) Symmetry 4/mmm a=b c = = = 9 0
Part v: Cubic 578.Symmetry is four Threefold axes along a+b+c, -a+b+c, a-b+c, and -a-b+c 579. 580. 581. Lattice (Laue) Symmetry m3m a=b= c = = = 9 0
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
133
Part vi: Trigonal 582.Symmetry is a single Threefold Rotation or Rotatory Inversion axis along a+b+c 583. 584. 585. 586. = = 90 A corner stretched cube Lattice (Laue) Symmetry 3(bar)m a=b= c Table in Text Incorrect??? Table in Text Incorrect???
587. 9 0 , < 1 2 0
Part vii: Hexagonal 588.Symmetry is a single Sixfold Rotation or Rotatory Inversion axis along c 589. 590. 591. 592. Lattice (Laue) Symmetry 6/mmm a=b c = = 90 = 1 2 0
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
134
Part b:
Centering of Unit Cells
593.Centering relates to how many lattice points are in each unit cell and where are any additional lattice points located 594.There are four possible types: P, (C, A, or B), I, and F (plus R) 595.When Primitive Centering is found with the Trigonal Crystal System, this is referred to as Primitive
Rhombohedral, R, rather than Primitive, P, Centering
Graphics from Text: Table 4.3, page 121; Diagrams at the bottom of the table of the five types of Centering
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
135
Part i: Primitive Centering 597.The Primitive Unit Cell contains only a single lattice point (at its corners (the other centerings have this same corner lattice point)) 598.This means that each unit cell has only 1 lattice point 599.This type of centering is designated as P 600.When Primitive Centering is found with the Trigonal Crystal System, this is referred to as Primitive
Rhombohedral, R, rather than Primitive, P, Centering
Part ii: Body Centered 601.The Body Centered Unit Cell contains a second lattice point at the center of the unit cell 602.This means that each unit cell has 2 lattice points 603.This type of centering is designated as I
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
136
Part iii: Face Centered 604.The Face Centered Unit Cell contains a second lattice point in the middle of two opposite faces of the unit cell 605.This means that each unit cell has 2 lattice points 606. This may be the C, A, or B faces 607.This type of centering is designated as C
Part iv: All Face Centered 608.The All Face Centered Unit Cell contains centering on all faces 609.This means that each unit cell has 4 lattice points 610.This type of centering is designated as F
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
137
Part c:
The 14 Bravais Lattices
611.If one combines the 7 Crystal Systems with the 4 Types of Centering, there are only 14 combinations consistent with three dimensional ordered arrays 612.These are referred to as the 14 Bravais Lattices 613.Each is associated with two to seven unique
Crystallographic Point Groups 7 Crystal Systems + 4 Centering Types 14 Bravais Lattices Graphics from Text: Table 4.3, page 121; The 14 Bravais Lattices, 32 Crystallographic Point Groups (Crystal Classes), and Some Representative Space Groups
Graphics from Text: Figure 4.9, page 122; The 14 Bravais Lattices (7 Primitive and 7 Nonprimitive)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
138
Part d:
The 230 Space Groups
616.The 32 Crystallographic Point Groups must fit into the Symmetries of the 14 Bravais Lattices 617.Each Crystallographic Point Group is used only once 618.They must be consistent with translational symmetry 619.This produces the 230 Crystallographic Space Groups
14 Bravais Lattices + 32 Crystallographic Point Groups 230 Crystallographic Space Groups
Graphics from Text: Table 4.3, page 121; The 14 Bravais Lattices, 32 Crystallographic Point Groups (Crystal Classes), and Some Representative Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
139
Section 6:
Three Dimensional Symmetry Operations
621.With crystalline arrays, additional symmetry elements that involve translations are introduced
Part a:
Translations
622.Straight Translations must be present to get a lattice and occur in each dimension to build up the three dimensional lattice from the unit cell contents
Graphics from Text: Figure 4.10, page 123; Translational Symmetry
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
140
Part b:
Screw Axes
624.Screw Axes involve translations some small fraction of the unit cell length while rotating around an axis 625. The symbol for a Screw axis is nq
626.n tells us the amount of rotation (i.e., 360/n) 627.q tells us the fraction of the unit cell translated (i.e., a q/n translation, thus 43 involves a 3/4 translation) 628.This does not change the handedness of objects
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
141
A 41 screw axis involves a 90 rotation while moving 1/4 the way along the unit cell length
A 42 screw axis involves a 90 rotation while moving 2/4 (1/2) the way along the unit cell length
A 43 screw axis involves a 90 rotation while moving 3/4 the way along the unit cell length Note: 41 and 43 are equivalent (i.e., referred to as enantiomorphic)
Graphics from Text: Figure 4.11, page 124; A Twofold Screw Axis Graphics from Text: Figure 4.13, page 126; The Relationship Between Symmetry Operations with and without a Translation, the Relationship between a Twofold Rotation Axis and a Twofold Screw Axis
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
142
Part c:
Glide Planes
635.Glide Planes involve translations some small fraction of the unit cell length while inverting through the mirror plane 636.a Glides, b Glides, and c Glides involve a a/2, b/2, and c/ 2 axis translation 637.i.e., a Glide involves a translation 1/2 of the length of the a axis and reflection through a plane 638.Graphics from Text: Figure 4.12, page 125; A Glide Plane
639.n Glides involve a translation 1/2 the length of the diagonal 640. 1/2(b+c), 1/2(c+a), or 1/2(a+b)
641.d Glides involve a translation 1/4 the length of the diagonal 642. 1/4(b c), 1/4(c a), or 1/4(a b)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
143
643.Graphics from Text: Figure 4.13, page 126; The Relationship Between Symmetry Operations with and without a Translation, the Relationship between a Mirror Plane and a Glide Plane
Part d:
Symmetry in some Real Crystals
644.Graphics from Text: Figures 4.14a and b, pages 129 and 130; The Symmetry found (and Equivalent Positions) in Hydrated Citric Acid and Anhydrous Citric Acid Crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
144
Part e:
Review of Crystal Systems Space Groups
7 Crystal Systems + 4 Centering Types 14 Bravais Lattices + 32 Crystallographic Point Groups (Translational Symmetry) 230 Crystallographic Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
145
Section 7: Part a:
Symmetry in the Diffraction Pattern Equivalent Positions
645.The Asymmetric Unit is the smallest unit from which the actions of the Space Group Symmetry will produce the entire contents of the crystal When the complete set of Space Group Symmetry Elements acts upon the Asymmetric Unit each position x y z in the asymmetric unit may be converted into other Equivalent Positions within the Unit Cell
Graphics from Text: Table 4.4, page 128; Table of Equivalent Positions in some Common Space Groups Graphics from Text: Figures 4.14a and b, pages 129 and 130; The Symmetry found (and Equivalent Positions) in Hydrated Citric Acid and Anhydrous Citric Acid Crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
146
Part b:
Friedel's Law
649.It commonly occurs that not all reflections in the data set have different intensities, rather we often see in Friedel Symmetry that sets of reflections have exactly equal intensities For many crystals, the intensity pattern in the data is exactly Centrosymmetric This is called Friedels Law which states I(h k l) = I(-h -k -l) This means that in these cases one half of the data should be an exact duplicate of the other The only exceptions to Friedels Law occur when one or more atoms in the structure Anomalous Scatterers (from which one may deduce Absolute Configurations) Graphics from Text: Figure 4.15, page 131; An example to Illustrate Friedel Symmetry in Diffraction Data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
147
Part c: Pattern
Symmetry of Packing Symmetry of Diffraction
655.All of the Symmetry of Crystal Packing will be reflected (in an inverse manner) in the Symmetry of the Diffracted Data
Thus, from the Symmetry of the Diffracted Data we can infer the Symmetry of the Crystal Packing
This is how one determines the Space Group and even some structural information
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
148
Part d:
Laue Symmetry
658.Laue Symmetry is all of the Symmetry of the Diffracted Data other than Friedel Symmetry 659.This extra symmetry can be used to reduce the amount of data collected or help to be sure of the Crystal System (i.e., the axial lengths and angle are not enough because they may be accidentally these values)
Graphics from Text: Figure 4.16, page 131; An example to Illustrate the Fourfold Laue Symmetry in Diffraction Data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
149
Part e:
Examples of Using Laue Symmetry to Determine
Crystal System: 661.Graphics from Text: Figure 4.17, page 132; Laue Symmetry in the Diffraction Data of Monoclinic and Orthorhombic Crystals Monoclinic Crystals will have: I(h k l) = I(-h k -l) But I(h k l) I(-h k l) [Of course from Friedel I(h k l) = I(-h -k -l)]
Orthorhombic
Crystals
(three
mutually
perpendicular
Twofold Axes) will have: I(h k l) = I(-h k l) = I(h -k l) = I( h k -l)
Therefore is one observes that I(h k l) = I(-h k l) (within statistical error for a representative collection of reflections) then we can be certain a crystal is really Orthorhombic and not just a Monoclinic Crystal that just happens to have = 90
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
150
Diffraction Data, Unit Cell Parameters, and the Crystal System
The Laue Symmetry of the Diffraction Data, and not the Unit Cell Dimensions, is the best way to Determine the Crystal System (see example above)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
151
Section 8:
Space Group Determination from Diffraction Data
670.In 2000 we will not look at this in detail due to time limitations but you do need to be familiar with the general principles
Graphics from Text: Figure 4.18, page 133; Three examples to Illustrate the use of Symmetry in Diffraction Data to Determine Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
152
Part a:
Systematic Absences Centering
Part i: Centering as Translational Symmetry 672.Centering of Unit Cells leads to easily predicted changes in the diffraction data 673.The different Lattice Points in a Nonprimitive Unit Cell can be thought of as a type of Translational Symmetry
Part ii: Example: A Centering 674.Thus A Centering can be thought of as a translation of the Corner Lattice Point from the corners of the unit cell half way up both the b and c axes to give the second Lattice Pont in the middle of the A Face 675.This is stated as a b/2 + c/2 Translation
This Translation means that all reflections having the Sum of the k and l indices being odd will be Systematically Absent
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
153
This is stated as a k = l odd Systematic Absence
Part iii: Getting Centering from Systematic Absences 678.These absences will be found in all of the data whatever the values of h k and l (i.e., none have to be zero) 679.No general absences P Centering (no translation) k + l odd absent A Centering (b/2 + c/2 translation) l + h odd absent B Centering (c/2 + a/2 translation) h + k odd absent C Centering (a/2 + b/2 translation) h k l two odd or two even absent (all odd or all even present) F Centering ((a + b)/2, (b + c)/2, and (a + c)/2 translations) h + k + l odd absent I Centering ((a + b + c)/2 translation)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
154
Graphics from Text: Table 4.5, page 134; Examples of Using Systematic Absence Data to Determine Centering (Bravais Lattice) Information
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
155
Part b:
Systematic Absences Translational Symmetry
Part i: Systematic Absences when One or Two Indices are Zero 686.Translational Symmetry gives rise to Systematic Absences that are observed when either one or two of the indices are zero
Graphics from Text: Table 4.5, page 134; Examples of Using Systematic Absence Data to Determine Translational Symmetry Elements (Screw Axes and Glide Planes)
A complete listing of these rules is given in the International Tables
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
156
Part ii: Screw Axis Determinations from Systematic Absences 689.A Twofold Screw Axis, 21, along a will make h 0 0 be systematically absent when h is an odd number due to the a/2 translation
A Twofold Screw Axis, 21, along b will make 0 k 0 be systematically absent when k is an odd number due to the b/2 translation
A Twofold Screw Axis, 21, along c will make 0 0 l be systematically absent when l is an odd number due to the c/2 translation
A Threefold Screw Axis, 31 or 32, along c will make 0 0 l be systematically absent when l = 3n + 1 or l = 3n + 2 due to the c/3 or a 2c/3 translation
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
157
Part iii: Glide Plane Determinations from Systematic Absences 693.A Glide Plane Perpendicular to axis a translating along b, b glide, will make 0 k l be systematically absent when k is an odd number due to the b/2 translation
A Glide Plane Perpendicular to axis a translating along c, c glide, will make 0 k l be systematically absent when l is an odd number due to the c/2 translation
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
158
Part c:
Laue (Crystal System) Determination
695.When one collects the full diffraction data in either tabular or graphical form, one can look for Patterns in Equivalent Intensities of the Diffraction Data and from these determine the Laue Symmetry (i.e., the Crystal System; Triclinic, Monoclinic, Orthorhombic, Tetragonal, Cubic, Trigonal, and Hexagonal) 696.This can initially be done by looking at a representative set of reflection intensities 697.Graphics from Text: Table 4.2, page 120; The Seven Crystal Systems
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
159
Part d:
Bravais Determination
698.When one collects the full diffraction data in either tabular or graphical form, one can look for Systematic Absences and from these deduce the various types of Translational Symmetry present 699.This can initially be done by looking at a representative set of reflection intensities 700.From the General Systematic Absences (i.e., for all nonzero values of h k and l) one can deduce the Centering Type from the 4 unique possibilities (i.e., P, A, B, C, F, or I) 701.From the Crystal System and Centering Type
information one gets which of the 14 Bravais Lattice Types one has 702.Graphics from Text: Table 4.3 and Figure 4.9, pages 121 and 122; The Fourteen Bravais Lattice Types (and their associated Point Groups as well as some representative Space Groups)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
160
Part e:
Space Group Determination
703.When one collects the full diffraction data in either tabular or graphical form, one can look for Systematic Absences in the data for cases when one or two of the Indices are zero (i.e., h 0 0, 0 k 0, 0 0 l, h k 0, h 0 l, and 0 k l) and from these deduce the various types of Translational Symmetry present (i.e., Screw Axes and Glide Planes present (symmetry of the Point Group))
This really needs to be done with a fairly complete data set but one can get a good idea but just collecting these Special Classes of Reflections
From this information one can reduce the possible of choices 230 Space Groups to (ideally) one or a few
Graphics from Text: Table 4.6, page 135; Space Groups and the Symmetry Elements of Objects in Them
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
161
Part f: Space Group Ambiguity 707.When two or more Space Groups fit, you have a Space Group Ambiguity (which often revolves around whether you have a Center of Symmetry; which must be resolved otherwise)
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
162
Topic VI:
Physical Properties of Crystals
Based primarily on Chapter 5 (G, L, & R, pages 143-183).
Ask Students: What do you know about the Physical Properties of Crystals?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
163
Section 1:
Mechanical Properties of Crystals
Part a:
Hardness of Crystals
Part b:
Cleavage of Crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
164
Section 2:
Optical Properties of Crystals
Part a:
The Nature of Light
Part b:
Isotropic and Anisotropic Crystals
Part c:
Pleochromism
Part d:
Refraction of Light
Part e:
Birefringence of Light
Part f: Polarization of Light
Part g:
Optical Activity and Crystals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
165
Section 3:
Electrical Effects of Crystals
Part a:
Piezoelectric Effects
Part b:
Pyroelectric Effects
Part c:
Non-Linear Optical Phenomenon
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
166
Section 4:
Chemical Effects of Crystal Form
Part a:
Crystal Forms and Chemical Reactivity
Part b:
Different Faces Different Reactions
Part c:
Crystal Forms and Explosive Power
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
167
Topic VII:
Image Generation from Diffracted Waves
Based primarily on Chapter 6 (G, L, & R, pages 185-223).
Ask Students:
What do you know about How an Optical
Microscope Works?
Ask Students: What do you know about How X-Ray Diffraction Data is Transformed into Structural Information?
Graphics from Text: Figure 1.2, page 4; Imaging object using microscopes and diffraction methods
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
168
Section 1:
Waves
Part a:
Amplitudes of Waves
Part b:
Lengths of Waves
Part c:
Phase Angles of Waves
Part d:
Summing Waves
Graphics from Text: Figure 1.1, page 3; Effect of relative phases when summing waves
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
169
Section 2:
Fourier Series
Part a:
Periodic Electron Density in Crystals
Part b:
Baron Fouriers Theorem
Part c:
Fourier Analysis
Part d:
Fourier Synthesis
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
170
Section 3:
Electron Density Calculations
Part a:
Electron Density is Periodic
Part b:
Equation for Electron Density as a Function of
Structure Factors
Part c:
hkl values and Crystal Planes
Section 4:
Fourier Transforms
Part a:
Equation for Structure Factors as a Function of
Electron Density
Part b:
Relationship Between Real and Reciprocal Space
Part c:
Summary of the Diffraction Structure Process
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
171
Section 5:
X-Ray Scattering Factors of Electrons in Orbitals
Part a:
Electron Distribution Curves for Orbitals
Part b:
Electron Scattering Curves for Orbitals
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
172
Section 6:
Neutron Scattering Factors of Nuclei
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
173
Section 7:
Kinematic and Dynamic Diffraction
Part a:
Mosaic Blocks
Part b:
Kinematic Diffraction
Part c:
Dynamic Diffraction
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
174
Section 8:
Extinction
Part a:
Primary Extinction
Part b:
Secondary Extinction
Part c:
Renninger Effect and Double Reflections
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
175
Section 9:
Structure Factors
Part a:
Structure Factor Amplitudes
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
176
Section 10: Displacement Parameters
Part a:
Vibration of Atoms in a Lattice
Part b:
Disorder of Atoms and Molecules in a Lattice
Part c:
Isotropic Displacement Parameters
Part d:
Simple Anisotropic Displacement Parameters
Part e:
Quadrupole
Displacement
Parameters
and
Evaluations of the Shapes of Electron Clouds
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
177
Section 11: Anomalous Scattering
Part a:
Absorption
Coefficients
as
a
Function
of
Wavelength
Part b:
MAD Phasing of Protein Data
Part c:
Anomalous Scattering
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
178
Topic VIII:
Amplitudes of Diffracted Waves
Based primarily on Chapter 7 (G, L, & R, pages 225-279).
Ask Students: What do you know about How the Amplitudes of Diffracted Waves are Related to Crystal Structures and Molecular Structures?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
179
Section 1:
Intensities of Diffracted Beams
Part a:
Equation for Intensities of Diffracted Beams
Part b:
Lorenz Factor
Part c:
Polarization Factor
Part d:
Absorption Factor
Part e:
Effects of Wavelength of Measured Intensities
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
180
Section 2:
X-Ray Sources
Part a:
X-Ray Spectrum of an X-Ray Tube
Part b:
Monochromatic X-Rays
Part c:
X-Ray Sources
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
181
Section 3:
X-Ray Detectors
Part a:
Scintillation Counters
Part b:
Beam Stop
Part c:
Area Detectors
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
182
Section 4:
Automated Diffractometers
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
183
Section 5: Data
Effects of Temperatures on Collected Diffraction
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
184
Section 6:
Peak Profiles
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
185
Section 7:
Data Reduction
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
186
Topic IX:
Phases of Diffracted Waves
Based primarily on Chapter 8 (G, L, & R, pages 281-343).
Ask Students:
What do you know about How the Phases of
Diffracted Waves are Related to Crystal Structures and Molecular Structures?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
187
Section 1: and Phases
Electron Density Distributions vs. Structure Factors
Part a:
Flow Diagram
Part b:
With Known Structures
Part c:
Non-Centrosymmetric Space Groups
Part d:
Centrosymmetric Space Groups
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
188
Section 2:
Common Methods for Estimating Phase Angles
Part a: Software
The Role of Advances in Computers, Theory, and
Part b:
Direct Methods
Part c:
Patterson Methods
Part d:
Isostructural Crystals
Part e:
Multiple Bragg Diffraction
Part f: Shake and Bake
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
189
Section 3:
Direct Methods
Part a:
Statistical Tools
Part b:
Mathematics of Phase Relationships
Part c:
Inequalities
Part d:
Where Works Best
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
190
Section 4:
Patterson Methods
Part a:
The Patterson Function
Part b:
Patterson Maps
Part c:
Where Works Best
Part d:
Heavy Atom Methods
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
191
Section 5:
Isomorphous Replacement
Part a:
Proteins: The Problem Structures
Part b:
Metal Salts
Part c:
Unnatural Amino Acids
Part d:
Related Protein Structures
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
192
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
193
Section 6:
MAD Phasing of Proteins
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
194
Section 7:
Shake and Bake
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
195
Topic X: Electron Density Maps
Based primarily on Chapter 9 (G, L, & R, pages 345-387).
Ask Students:
What do you know about the Relationship of
Electron Density Maps to Molecular Structures?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
196
Section 1:
Electron Density Function
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
197
Section 2:
Electron Density Maps
Part a:
General Features of Maps
Part b:
P(obs) Map
Part c:
F(calc) Map
Part d:
Difference Electron Density Maps
Part e:
Deformation Density Maps
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
198
Section 3:
Resolution
Part a:
Conventional Definition
Part b:
Effects of Wavelength on Resolution and Intensities
Part c:
Mo Resolution
Part d:
Cu Resolution
Part e:
Ag and Synchrotron Data
Part f: Effects of Resolution on the Structure
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
199
Section 4: Errors
Angles of Data Collection and Series Termination
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
200
Topic XI:
Least Squares Refinement
Based primarily on Chapter 10 (G, L, & R, pages 389-411).
Ask Students:
What do you know about How Least Squares
Refinement Works?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
201
Section 1:
What is Least Squares Refinement?
Part a:
The Mathematics of Least Squares Refinement
Part b:
Qualitative Picture of Least Squares Refinement
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
202
Section 2:
Precision vs. Accuracy
Part a:
Precision
Part b:
Accuracy
Part c:
Random vs. Systematic Errors
Part d:
Gaussian Distribution Function
Part e:
Estimated Standard Deviations
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
203
Section 3:
Constraints
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
204
Section 4:
Restraints
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
205
Section 5:
Global vs. Local Minima in Solution
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
206
Topic XII:
Crystal and Diffraction Data
Based primarily on Literature References
Ask Students: What do you know about How to Interpret Tables of Crystal and Diffraction Data?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
207
Section 1:
The Standard Table
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
208
Topic XIII:
Atomic Coordinates and Molecular Structures
Based primarily on Chapters 11 to 13 (G, L, & R, pages 413571).
Ask Students: What do you know about How one Interprets Raw Crystallographic Data to Get Molecular Structure Information?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
209
Section 1:
Molecular Geometries
Part a:
From xyz Coordinates to Bond Lengths, Bond
Angles, etc.
Part b:
Vibrational Motion
Part c:
Fractional Coordinates
Part d:
Orthogonal Coordinates
Part e:
Complete Molecules?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
210
Section 2:
Atomic Connectivities
Part a:
Derivation of Atomic Connectivity Tables
Part b:
International Tables for Typical Bond Distances
Part c:
Bond Lengths
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
211
Section 3:
Molecules in the Unit Cell and Z
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
212
Section 4:
Estimated Standard Deviations
Part a:
ESD Formula
Part b:
When are two values different?
Part c:
ESDs and Reliability of Data
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
213
Section 5:
Torsion Angles
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
214
Section 6:
Molecular and Macromolecular Conformations
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
215
Section 7:
Atomic and Molecular Displacements
Part a:
Vibration Effects in Crystals
Part b:
Representations of Displacement Parameters
Part c:
Effects of Displacements on Molecular Geometries
Part d:
Uses of Anisotropic Displacement Parameters
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
216
Topic XIV:
Absolute Structures
Based primarily on Chapter 14 (G, L, & R, pages 573-625).
Ask Students:
What do you know about How the Absolute
Structures of Molecules are Determined?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
217
Section 1:
Chirality of Molecules
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
218
Section 2:
Optical Activity and Chiral Molecules
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
219
Section 3:
Anomalous Dispersion Measurements
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
220
Section 4:
Uses of Anomalous Dispersion
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
221
Topic XV: Analysis
Crystallographic Publications: Preparation and
Based primarily on Chapter 16 (G, L, & R, pages 689-729).
Ask Students:
What do you know about Using the
Crystallographic Literature?
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
222
Section 1:
Crystallographic Data Bases
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
223
Section 2:
Crystallographic Papers
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
224
Section 3:
Comparing Structures
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
225
Topic XVI:
Special Topics
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
226
Index of Topics and Vocabulary
0
0 0 l.........................................................................160 0 k 0........................................................................160 0 k l.........................................................................160
6
6/mmm...................................................................133 6bar.........................................................................125
1
1/2(a+b)..................................................................142 1/2(b+c)..................................................................142 1/2(c+a)..................................................................142 1/4(a(b)...................................................................142 1/4(b(c)...................................................................142 1/4(c(a)...................................................................142 14 Bravais Lattice Types........................................159 14 Bravais Lattices.................................137, 138, 144 180 Phase Shift .....................................................96 1bar.................................................................122, 130
7
7 Crystal Systems...........................................137, 144
A
A 80, 134, 136, 159 a ( b ( c...........................................................130, 131 a = b ( c...........................................................132, 133 a=b c .........................................................132, 133 A Centering....................................................152, 153 A Face....................................................................152 a Glide....................................................................142 a Glides..................................................................142 A Sixfold Rotation.................................................120 a-b+c.......................................................................132 a/2...........................................................................142 a/2 + b/2 translation................................................153 a+b+c..............................................................132, 133 Absolute Configurations........................................146 absolute structure determinations...........................108 Absolute Structures................................................216 Absolute Structures of Molecules..........................216 Absorption Coefficients as a Function of Wavelength ...........................................................................177 Absorption Correction..............................................30 Absorption Corrections............................................29 Absorption Curves for some representative atoms 107 Absorption Data.......................................................26 Absorption Edge....................................................107 Absorption Factor..................................................179 Accelerator Plates....................................................33 Accuracy................................................................202 Advanced Light Source............................................35 Advanced Photon Source.........................................35 Ag.............................................................................45 Ag and Synchrotron Data.......................................198 Ag Targets................................................................32 Air............................................................................45 Al+3.........................................................................76 Alcohols...................................................................70 All Face Centered...................................................136 All Face Centered Unit Cell...................................136 Allen D. Hunter..........................................................1 Allen Hunters YSU Structure Analysis Lab Manual .............................................................................49 ALS..........................................................................35
2
2/m.........................................................................131 21 156 230 Crystallographic Space Groups...............138, 144 230 Space Groups..................................................160 230 Unique Space Groups......................................116
3
3(bar)m...................................................................133 31 156 32 156 32 Allowed Point Groups.......................................129 32 Crystallographic Point Groups..........137, 138, 144 32 Unique Point Groups.........................................115 360/n.......................................................................140 360/n9 ...........................................................118, 123 3bar.........................................................................124
4
4 Centering Types..........................................137, 144 4 Circle Goniometers...............................................38 4 Types of Centering..............................................137 4/mmm...................................................................132 41 screw axis..........................................................141 42 screw axis..........................................................141 43 screw axis..........................................................141 4bar.........................................................................124
5
5bar.........................................................................125
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
Alums.......................................................................76 Ammonium Dihydrogen Phosphate.........................20 Amplitude.................................................................80 Amplitudes of Diffracted Waves...........................178 Amplitudes of Waves.............................................168 Analysis of Refined Solutions..................................30 Analysis of trial Solutions........................................30 Angles of Data Collection and Series Termination Errors.................................................................199 angular dependence of the diffracted intensity........99 Anode.................................................................33, 34 Anomalous Dispersion Measurements...................219 Anomalous Scatterers............................................146 anomalous scattering..............................................108 Anomalous Scattering....................................107, 177 Anomalous Scattering and Neutrons......................108 Anomalous Scattering and X-Rays........................108 Application of Diffraction Methods to Solving Chemical Problems?............................................13 APS..........................................................................35 Area Detectors..................................................38, 181 Art rather than Science.............................................50 ASF..........................................................................98 Asymmetric Unit....................................................145 Atomic and Molecular Displacements...................215 Atomic Connectivities............................................210 Atomic Coordinates and Molecular Structures......208 Atomic motion and disorder....................................18 Atomic Positions......................................................28 Atomic Scattering Factor.........................................98 Atomic Scattering Factors for Neutrons................100 Atomic Scattering Factors for X-Rays.....................97 Atomic Scatting Factors for Neutrons...................100 Atomic Sizes/Shapes................................................28 Automated Diffractometers....................................182 Automated Goniometers..........................................38 Axial naming............................................................71 axial vectors.............................................................71
227
Berkeley...................................................................35 Birefringence of Light............................................164 Block Diagram of an X-Ray Diffractometer............23 Body Centered........................................................135 Body Centered Unit Cell........................................135 Bond Lengths.........................................................210 Braggs Law...................................................101, 102 Bravais Determination...........................................159 breakwater................................................................81 Bricks.......................................................................21 bricks in a wall.........................................................47 Bruker AXS..............................................................17 Bruker-AXS...........................................................110 Bucknell University...............................................110
C
C 134, 136, 159 C Centering............................................................153 c Glides..................................................................142 c/2...........................................................................142 c/2 + a/2 translation................................................153 Calix[n]Arenes.........................................................70 capillary........................................................45, 57, 61 Cathode....................................................................33 CCD chip..................................................................43 CCD Detectors.........................................................43 Center of Symmetry.......................................122, 161 Centering........................................................134, 152 Centering (Bravais Lattice) Information................154 Centering as Translational Symmetry....................152 Centering of Unit Cells..........................................134 Centering Type.......................................................159 Centrosymmetric Space Groups.............................187 Channel Compounds................................................70 Chapter 1..................................................................13 Chapter 10..............................................................200 Chapter 14..............................................................216 Chapter 16..............................................................221 Chapter 2............................................................13, 46 Chapter 3..................................................................79 Chapter 4................................................................110 Chapter 5................................................................162 Chapter 6................................................................167 Chapter 7..........................................................31, 178 Chapter 8................................................................186 Chapter 9................................................................195 Chapter XIV.............................................................46 Chapters 1................................................................13 Chapters 11 to 13...................................................208 Chemical Effects of Crystal Form.........................166 Chemistry 832............................................................1 Chemistry 832 Goals and Objectives.......................14 Chemistry 832 Resources.........................................14 Chemistry 832 Syllabus...........................................14 Chemists.................................................................127
B
B 134, 136, 159 B Centering............................................................153 b Glides..................................................................142 b/2...........................................................................142 b/2 + c/2.................................................................152 b/2 + c/2 translation................................................153 Baron Fouriers Theorem.......................................169 Basic Steps in X-Ray Diffraction Data Analysis.....28 Basic Steps in X-Ray Diffraction Data Collection. .26 Be windows..............................................................45 Be Windows.............................................................42 Beam Stop..............................................................181 bears porridge.........................................................52 bending magnets......................................................35 Benzene............................................................70, 114
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
Chicago....................................................................35 Chip sizes.................................................................43 Chiral......................................................................126 Chirality of Molecules...........................................217 Chlorocarbons..........................................................70 Choices of Unit Cells.............................................113 Chromium Alum................................................75, 76 Citric Acid..............................................................143 Cleavage of Crystals..............................................163 collimated X-ray beam.............................................24 combinations............................................................60 combos.....................................................................60 Common Methods for Estimating Phase Angles...188 Comparing Structures............................................224 Complete Molecules..............................................209 Complete Table of Contents......................................3 Computer Advances.................................................28 Constant temperatures..............................................51 Constraints.............................................................203 Constructive and Destructive Superposition of Waves .............................................................................86 Constructive Interference...............82, 83, 84, 86, 103 Contact Goniometer.................................................77 Convection...............................................................51 Conventional Anodes...............................................34 Conventional Definition.........................................198 Conventional X-Ray Tubes......................................33 convoluted................................................................78 Cooling System........................................................33 Corner Lattice Point...............................................152 Costs.........................................................................34 Cr(CO)6.............................................................59, 75 Cr+3.........................................................................76 cryocooled................................................................43 Crystal (Graphite) Monochromators........................36 Crystal and Diffraction Data..................................206 Crystal Classes...............................................137, 138 crystal decomposition..............................................39 crystal faces..............................................................73 Crystal Forms and Chemical Reactivity................166 Crystal Forms and Explosive Power......................166 Crystal Growing Strategies......................................49 crystal growth...........................................................48 Crystal Growth and Shapes......................................73 crystal habits............................................................74 Crystal Habits and Morphology...............................73 crystal lattice............................................................78 Crystal Lattice..........................................................78 Crystal Packing......................................................147 Crystal Quality.........................................................26 crystal shapes...........................................................74 Crystal Shapes....................................................73, 75 Crystal Structure Analysis for Chemists and Biologists...............................................................1 Crystal Structures...........................................178, 186 crystal surface..........................................................48
228
Crystal System...............................148, 150, 158, 159 Crystal Systems ( Space Groups............................130 Crystalline State.....................................................129 crystallization...........................................................66 Crystallization Agents..............................................70 Crystallization by Cooling.......................................53 Crystallization by Diffusion Through Capillaries and Gels......................................................................57 Crystallization by Slow Evaporation.......................53 Crystallization by Solvent Layering.........................56 Crystallization by Sublimation.................................59 Crystallization From Melts......................................58 Crystallization Using Combinations........................60 Crystallization Using Mixed Solvents and Solvent Diffusion in the Gas Phase..................................54 Crystallographers...................................................127 Crystallographic CourseWare................................110 Crystallographic Data Bases..................................222 Crystallographic Literature....................................221 Crystallographic Papers.........................................223 Crystallographic Point Groups.......................129, 137 Crystallographic Publications\..................................... Preparation and Analysis..................................221 Crystallography-Diffraction Methods Texts List.....14 Cu45 Cu Machine..............................................................42 Cu radiation..............................................................45 Cu Resolution.........................................................198 Cu Targets................................................................32 Cu X-Ray source......................................................17 Cube.......................................................................127 Cubic..............................................................132, 158 Cubic Space Groups...............................................128 cubic unit cells.........................................................74 Cyclodextrins...........................................................70
D
d ( The Interplanar Spacing ..................................101 d Glides..................................................................142 dandruff....................................................................68 Data ( Solution Relationship....................................28 Data Analysis can be quite routine through impossibly difficult.............................................28 data collection..........................................................19 data collection area...................................................44 data collection areas.................................................44 Data for Publication.................................................29 Data intensity at high angles....................................39 Data read out times..................................................44 Data Reduction.................................................30, 185 Decomposition from air...........................................39 Decomposition from heat.........................................39 Decomposition from X-Ray Beam..........................39 Defects in th crystal..................................................20
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
Deformation Density Maps....................................197 Densiometer.............................................................41 Department of Chemistry...........................................1 Deposition on Surfaces............................................48 Derivation of Atomic Connectivity Tables............210 Derivatives...............................................................69 Destructive Interference.........................82, 83, 84, 86 Detector....................................................................25 dhkl Values............................................................106 Diagonal.................................................................128 Diamond.............................................................22, 58 Difference Electron Density Maps.........................197 Different Faces Different Reactions......................166 Diffracted beams......................................................28 Diffracted Data...............................................147, 148 diffraction angle.......................................................25 Diffraction by Crystals.............................................79 Diffraction by Slits vs. Diffraction by Objects........90 Diffraction Data...............................................26, 167 Diffraction Data, Unit Cell Parameters, and the Crystal System...................................................150 Diffraction in Three Dimensions.............................91 Diffraction in Two Dimensions...............................87 Diffraction Lab...................................................14, 15 Diffraction off of Planes........................................103 Diffraction Pattern from a Single Slit......................87 Diffraction Pattern Spacing......................................88 Diffraction Pattern Spacing from Arrays of Slits.....89 Diffraction Patterns from Arrays of Points on a Slide .............................................................................91 Diffraction Patterns from Arrays of Slits.................89 Diffraction Patterns from Two or More Slits...........88 Diffraction Patterns of a Single Slit.........................87 Diffraction Through Slits.......................................103 Diffractometer Lab...................................................17 diffuse.......................................................................55 Direct Methods...............................................188, 189 disorder.....................................................................22 disorder across macroscopic dimensions.................47 Disorder of Atoms and Molecules in a Lattice......176 Disorder of the Array...............................................95 Displacement Parameters.................................39, 176 dropwise solvent addition........................................54 Dust..........................................................................68 Dynamic Diffraction..............................................173 dynamic range....................................................40, 43 Dynamic range.........................................................44 Dynamic Range........................................................42
229
Effects of Temperatures on Collected Diffraction Data...................................................................183 Effects of Wavelength of Measured Intensities.....179 Effects of Wavelength on Resolution and Intensities ...........................................................................198 Electrical Effects of Crystals..................................165 electrochemical source.............................................61 Electron Density Calculations................................170 Electron Density Distributions vs. Structure Factors and Phases.........................................................187 Electron Density Function.....................................196 Electron Density is Periodic...................................170 Electron Density Maps...................................195, 197 Electron Distribution Curves for Orbitals..............171 Electron Micrograph................................................47 Electron Scattering Curves for Orbitals.................171 electrons...................................................................96 enantiomorphic.......................................................141 Equation for Electron Density as a Function of Structure Factors...............................................170 Equation for Intensities of Diffracted Beams.........179 Equation for Structure Factors as a Function of Electron Density................................................170 Equivalent Positions...............................................145 ESD Formula..........................................................212 ESDs and Reliability of Data.................................212 Estimated Standard Deviations......................202, 212 evaporate..................................................................54 Ewald Sphere.........................................................109 Example\...................................................................... A Centering.......................................................152 Examples of Using Laue Symmetry to Determine Crystal System...................................................149 Extinction...............................................................174
F
F 134, 136, 159 F Centering.............................................................153 F(calc) Map............................................................197 Face Centered.........................................................136 Face Centered Unit Cell.........................................136 face stretched cube.................................................132 Ferrocene..................................................................59 Fiber Optic Taper.....................................................43 Figure 1.2.................................................................79 Figure 1.3.................................................................20 Figure 1.4.................................................................86 Figure 1.5.................................................................23 Figure 1.6.................................................................22 Figure 2.10...............................................................77 Figure 2.11 and 2.12................................................77 Figure 2.12.............................................................104 Figure 2.14...............................................................74 Figure 2.4.................................................................47
E
Edition of Notes.........................................................1 Effects of Displacements on Molecular Geometries ...........................................................................215 Effects of Resolution on the Structure...................198
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
Figure 2.5.................................................................71 Figure 2.6.................................................................48 Figure 2.7.................................................................73 Figure 2.8.................................................................48 Figure 3.1.................................................................80 Figure 3.10b...........................................................102 Figure 3.11...............................................................27 Figure 3.12...............................................................97 Figure 3.13a.............................................................97 Figure 3.13b...........................................................100 Figure 3.17.............................................................109 Figure 3.2a...............................................................83 Figure 3.2b...............................................................84 Figure 3.2b and c......................................................85 Figure 3.5.................................................................87 Figure 3.6.....................................................87, 88, 89 Figure 3.7.................................................................91 Figure 3.8.................................................................96 Figure 3.9...............................................................103 Figure 4.10.............................................................139 Figure 4.11.............................................................141 Figure 4.12.............................................................142 Figure 4.13.....................................................141, 143 Figure 4.15.............................................................146 Figure 4.16.............................................................148 Figure 4.17.............................................................149 Figure 4.18.............................................................151 Figure 4.2...............................................................114 Figure 4.3...............................................................119 Figure 4.4...............................................................121 Figure 4.5...............................................................122 Figure 4.6...............................................................124 Figure 4.7...............................................................127 Figure 4.8...............................................................129 Figure 4.9.......................................................137, 159 Figure 6.23.............................................................107 Figures 1.1 and 3.3...................................................86 Figures 1.7 and 1.8...................................................22 Figures 1.9 - 1.11.....................................................22 Figures 2.1 - 2.3.......................................................47 Figures 2.15 and 2.16...............................................78 Figures 3.10a and b................................................103 Figures 4.14a and b........................................143, 145 Figures 4.1a and b..................................................113 Filaments..................................................................34 Film Based Area Detectors......................................41 Final Plots for Publication........................................30 Final Tables for Publication.....................................30 Fivefold Rotation...................................................120 Fivefold Rotatory Inversion...................................125 Fivefold Symmetry................................................129 Flow Chart for a Typical Structure Solution............30 Flow Diagram........................................................187 Focusing Mirrors................................................36, 37 Foil Filters (Ni foil)..................................................36 Fourfold Laue Symmetry in Diffraction Data........148
230
Fourfold Rotation...................................................120 Fourfold Rotation or Rotatory Inversion axis........132 Fourfold Rotatory Inversion...................................124 Fourier Analysis.....................................................169 Fourier Series.........................................................169 Fourier Synthesis....................................................169 Fourier Transforms................................................170 Fourteen Bravais Lattice Types.............................159 Fractional Coordinates...........................................209 Frequency.................................................................80 Friedel....................................................................149 Friedel Symmetry...........................................146, 148 Friedel Symmetry in Diffraction Data...................146 Friedel's Law..........................................................146 From xyz Coordinates to Bond Lengths, Bond Angles, etc.........................................................209
G
GaAs.........................................................................47 Gallium Arsenide...............................................47, 58 Gaussian Distribution Function.............................202 General Conditions for Crystal Growth...................51 General Features of Maps......................................197 General principles of growing single crystals..........50 General Systematic Absences................................159 Generate Trial Solutions..........................................30 Generic Waves.........................................................80 geology.....................................................................77 Getting Centering from Systematic Absences.......153 Getting Unit Cell Parameters from Interplanar Spacings............................................................106 gift horse..................................................................65 Glide Plane.............................................142, 143, 157 Glide Plane Determinations from Systematic Absences............................................................157 Glide Planes...........................................142, 155, 160 Global vs. Local Minima in Solution.....................205 Glue..........................................................................45 Goals and Objectives Handout.................................14 Goniometer...............................................................25 Goniometer Heads....................................................38 Goniometers.............................................................38 Graphics from Text. 20, 22, 23, 27, 47, 48, 71, 73, 74, 77, 78, 79, 80, 83, 84, 85, 86, 87, 88, 89, 91, 96, 97, 100, 102, 103, 104, 106, 107, 108, 109, 113, 114, 119, 121, 122, 124, 127, 129, 130, 134, 137, 138, 139, 141, 142, 143, 145, 146, 148, 149, 151, 154, 155, 158, 159, 160, 167, 168 Graphite....................................................................22 Graphite Crystal Monochromators and Pin Holes in Tubes...................................................................37 Graphite Single Crystal............................................36 grease.......................................................................68 Green Thumb...........................................................50 Grow Single Crystal.................................................26
2000, Dr. Allen D. Hunter, Department of Chemistry, Youngstown State University
Chemistry 832: Solid State Structural Methods, Dr. Hunter
Growing crystals......................................................20 growing single crystals.............................................48 Growing Single Crystals..........................................48 Growing Single Crystals Suitable for Diffraction Analysis...............................................................49
231
H
h + k odd absent....................................................153 h + k + l odd absent................................................153 h 0 0........................................................................160 h 0 l.........................................................................160 h k 0........................................................................160 h k l two odd or two even absent..........................153 h k l ( -h -k -l..........................................................108 Habit of the Crystal..................................................73 handedness.............................................................140 handedness of objects.............................................126 Hardness of Crystals..............................................163 He beam path...........................................................45 heat sink...................................................................33 Heavy Atom Methods............................................190 Hermann-Mauguin.................................................127 Hermann-Mauguin vs. Schoenflies Symbols.........127 Hexachlorocyclohexane...........................................22 Hexagonal......................................................133, 158 Hexamethylbenzene.................................................22 High Angle Scattering of Waves.............................97 high speeds...............................................................34 high vacuum.............................................................34 high voltages............................................................34 hkl values and Crystal Planes.................................170
I
i 122 I 134, 135, 159 I Centering..............................................................153 I(h k l) ( I(-h k l).....................................................149 I(h k l) = I(-h -k -l).........................................146, 149 I(h k l) = I(-h k -l)...................................................149 I(h k l) = I(-h k l)....................................................149 I(h k l) = I(-h k l) = I(h -k l) = I( h k -l).................149 ICE Slides................................................................91 Identity Operation..................................................118 Image Generation from Diffracted Waves.............167 Image Generation in Optical Microscopy and X-Ray Diffraction...........................................................79 Imaging Plate Detectors...........................................44 Imaging Plate systems..............................................44 immiscible layers.....................................................61 Impatience is the Enemy..........................................51 Improper Symmetry Operations.............................126 Impure materials......................................................66 incidence angle.......................................................105 Inclusion Compounds..............................................70 Index of Topics and Vocabulary............................226
Indexing Crystal Faces.............................................77 Indexing of Crystal Faces......................................104 Indices are zero............................................