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X-Ray Diffraction
By Cade Grigsby
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What can X-ray diffraction tell us?
• Structure– Bonds
• Length• Type
– Arrangement• Geometry of crystal
• Picture– Electron density map
• Diffraction– Angle– Intensity
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From X-Rays to Structure
"X ray diffraction" by Thomas Splettstoesser (www.scistyle.com) - own work; the public domain image Myoglobindiffraction.png [1] was used; the other images were rendered with PyMol (www.pymol.org) based on PDB id 1MBO. Licensed under CC BY-SA 3.0 via
Wikimedia Commons - http://commons.wikimedia.org/wiki/File:X_ray_diffraction.png#/media/File:X_ray_diffraction.png
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X-Rays
• Short wavelength– 0.01 nm to 10 nm
• High frequency– 30 petahertz (3.0E16) to 30 exahertz (3.0E19)
• High energy– 100 eV to 100 keV– Excites core electrons– Ionizing radiation– Deep penetration
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Discovery of X-Rays
• Wilhelm Conrad Rӧntgan– Discovered in 1895– Nobel prize in physics
1901
• Cathode ray tube– Lit up fluorescent screen
• First X-ray image
http://www.auntminnie.com/index.aspx?sec=ser&sub=def&pag=dis&ItemID=99329
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X-Rays on EM Spectrum
http://blog.gwcollegedemocrats.com/picsvqzp/x-rays-waves-produced
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Production of X-Rays
• Tungsten filament emits electron beam at target metal– Cu or Mo
• Beam excites core electrons of target– 1s electrons ionized• X-rays emitted as higher level electrons fall
• Higher atomic number means higher energy X-rays
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Ejection of electron
http://radiologymasterclass.co.uk/tutorials/physics/x-ray_physics_production.html#top_second_img
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Other mechanism for x-rays
• High energy electron slowed as it approaches nucleus– Energy lost in ‘braking’
process released as x-ray photon
http://radiologymasterclass.co.uk/tutorials/physics/x-ray_physics_production.html#top_second_img
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X-Ray Tube
http://pubs.usgs.gov/of/2001/of01-041/htmldocs/xrpd.htm
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Diffraction of Light
• Light bends passing edge of object
• Effect of opening width on bending
• Interference creates dark and light spots– Constructive– Destructive
http://www.inkscapeforum.com/viewtopic.php?f=5&t=7222
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Effect of slit width
http://people.whitman.edu/~dunnivfm/FAASICPMS_Ebook/CH1/1_3_2.html
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Single-slit diffraction
http://cronodon.com/Atomic/Photon.html
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Double-slit experiment
• Light is diffracted• Slit width approximately
equal to wavelength• Diffraction pattern– Wave interference
• Constructive• Destructive
http://astarmathsandphysics.com/ib-physics-notes/waves-and-oscillations/ib-physics-notes-youngs-double-slit-experiment.html
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Diffraction Patterns
• Single-slit diffraction– Constructive
interference– Destructive interference
• Double-slit diffraction– Constructive
interference– Destructive interference
• What happens with multi-slit diffraction?
http://ffden-2.phys.uaf.edu/webproj/212_spring_2014/Khan_Howe/TheDoubleSlitExperiment_KhanHowe/Home.html
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Multi-slit diffraction
http://labman.phys.utk.edu/phys136/modules/m9/diff.htm
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The Problem with X-Rays
• Electromagnetic waves diffract• Early experiments could not diffract X-rays– Wavelength too small
• New method for diffracting x-rays
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The Solution
• Diffraction occurs when slit equals wavelength– X-ray wavelength equal to size of atom
• Use crystal lattice structure to diffract• Diffraction pattern obtained
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Evidence of Diffraction
• Max von Laue, Walter Friedrich, and Paul Knipping in 1912
• Pass X-rays through CuSO4 crystal and collect image on photographic plate– Known as X-Ray
Crystallography
http://www.chemistryviews.org/details/ezine/2064331/100th_Anniversary_of_the_Discovery_of_X-ray_Diffraction.html
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Bragg’s Law
• William Lawrence Bragg and William Henry Bragg
• 2dsin(Θ) = nλ• Nobel Prize in Physics
1915
http://www.chemistryviews.org/details/ezine/2064331/100th_Anniversary_of_the_Discovery_of_X-ray_Diffraction.html
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Single crystal X-Ray diffraction
http://serc.carleton.edu/research_education/geochemsheets/techniques/SXD.html
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Power Diffraction
http://chemwiki.ucdavis.edu/Analytical_Chemistry/Instrumental_Analysis/Diffraction/Powder_X-ray_Diffraction
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Powder Analysis
http://photojournal.jpl.nasa.gov/jpeg/PIA16217.jpg
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First X-Ray Diffraction Pattern
• Interference pattern– White dots show
constructive interference– Dark space destructive
interference
• Intensity of light– Amount of interference– Relates to amplitude and
phase of X-rays
http://blazelabs.com/f-xray.asp
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Mechanism of Diffraction
• X-rays interact with core electrons– Scatter photons
• Light diffracted at specific angles
http://en.wikipedia.org/wiki/Bragg's_law
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Why diffraction points at specific angles?
• Angle of diffraction decreases as distance of planes increases– Reciprocal relationship
• Diffraction point distance from center decreases as distance between planes increases
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Patterns in Patterns
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
• Patterns of in benzene• Diffraction spots
perpendicular to planes
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Greater Plane Distance
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
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Along Planes of Symmetry
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
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Other Scattering
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
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Explained with Waves
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Greater distance between planes
• Increase distance of planes– Light goes in phase again– 5.0 cm distance between
planes– 45o angle of diffraction
from the horizontal
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Smaller Distance between Planes
• Higher angle of diffraction– Planes 2.0 cm apart– Angle 60o
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Crystal Structure
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
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Other Compounds
• Rosalind Franklin– X-Ray cystallographer
• B-form DNA• Dark spots areas of
constructive interferance• Strong bands top and
bottom– Base stacking– Small distance between
planes, high angle
http://undsci.berkeley.edu/article/0_0_0/dna_checklist
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Reason for Pattern
http://doublehelix.me/about/http://undsci.berkeley.edu/article/0_0_0/dna_checklist
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Further Reasoning
http://undsci.berkeley.edu/article/0_0_0/dna_checklist http://doublehelix.me/about/
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Watson and Crick
• Shown diffraction pattern by colleague of Franklin, Maurice Wilkins
• Recognized pattern– Worked with helical proteins
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What does this tell us?
• Interactions with core electrons• Electron density– Location of atoms• Center of electron density
– Type of bonds• Specific angles of diffraction– Unique to specific crystals– Miller indices
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From X-Rays to Structure
"X ray diffraction" by Thomas Splettstoesser (www.scistyle.com) - own work; the public domain image Myoglobindiffraction.png [1] was used; the other images were rendered with PyMol (www.pymol.org) based on PDB id 1MBO. Licensed under CC BY-SA 3.0
via Wikimedia Commons - http://commons.wikimedia.org/wiki/File:X_ray_diffraction.png#/media/File:X_ray_diffraction.png
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The Transition
• How do you get from a diffraction pattern to an electron density map?– Computer programs
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Detection of Angles of Diffraction
• Diffractometers equipped with X-ray counters– Angle relative to crystal– Intensity of X-rays– Modern instruments coupled with CCD detectors
• Each element has specific angles of diffraction
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Diffraction Spectra of Si
http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm
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Diffraction of NaCl
https://universe-review.ca/F13-atom04.htm
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Zinc Oxide Nano particles
http://openi.nlm.nih.gov/detailedresult.php?img=3289443_ijn-7-845f2&req=4
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Miller Indices
• Describes planes in a crystal
• Assign origin point• H, K, and L– Written (hkl)– Each distance written as
its reciprocal
http://commons.wikimedia.org/wiki/File:Miller_Indices_Cubes.svg
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More Miller Indices
http://oregonstate.edu/instruct/engr321/Exams/ExamsF02/ENGR321F02MTTwo.html
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Determination of Lattice Structure
• ‘a’ is lattice constant of cubic crystal
• ‘h’, ‘k’, and ‘l’ are the Miller indices of Bragg plane
• Without computer– Trial and error
http://en.wikipedia.org/wiki/Bragg%27s_law
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Body Centered Cube (BCC)
• h+k+l must equal an odd number
• Fe and W crystals
http://ecee.colorado.edu/~bart/book/bravais.htm
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Iron Crystal
http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/diffraction/bcc.html
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Face Centered Cube (FCC)
• h, k, l must be all odd or all even values
• Cu, Al, NaCl crystals
http://ecee.colorado.edu/~bart/book/bravais.htm
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Diffraction of NaCl
https://universe-review.ca/F13-atom04.htm
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Diamond FCC
• Atoms quarter of diagonal length apart
• h+k+l = 4n– Values must be all even
or all odd
• Si crystals
http://ecee.colorado.edu/~bart/book/bravais.htm
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Diffraction Spectra of Si
http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm
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Electron Density Map• Constructed from
diffraction pattern• Slice of the crystal• Can be used to
determine information on bonds– Length and type
http://www.mdpi.com/1422-0067/8/2/103/htm
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Modern Electron Density Mapping
http://www.spring8.or.jp/wkg/BL41XU/solution/lang-en/SOL-0000001166?set_language=en&cl=en
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Other uses
http://www.portlandpress.com/pp/books/online/tiepac/session6/ch2.htm
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Analysis of Electron Density Map
• Contour rings– One represents 1e/Å
• Electronegative atoms– More contour rings
• Determination of bonds– Shortest are double bonds– Intermediate bonds are
resonance– Longest bonds are single
bonds
• No hydrogens– Too few electrons
https://webspace.yale.edu/chem125/125/xray/diffract.html
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Measuring Bonds
• Interpretation by comparison
• Measure from center of contours– Aromatic C—C bonds 1.5
cm– Double C=O bond 1.5 cm– Double C=C bond 1.1 cm– Single C—C and C—O
bonds 1.9 cm
• Computers can also perform calculations
https://webspace.yale.edu/chem125/125/xray/diffract.html
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Conclusion• Structure
– Miller Indices and computer programs• Crystal geometry
– Electron density map• Diffraction pattern
– Arrangement based on plane distance– Diffraction angle
• Identification of atoms– Specific diffraction angle– Rough estimate with electron density
• Bonds– Length– Type
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Questions?