X-Ray Diffraction
By Cade Grigsby
1
What can X-ray diffraction tell us?
• Structure
– Bonds
• Length
• Type
– Arrangement
• Geometry of crystal
• Picture
– Electron density map
• Diffraction
– Angle
– Intensity
2
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
3
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
4
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
5
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
7
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
12
Single-slit diffraction
http://cronodon.com/Atomic/Photon.html
13
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-physicsnotes-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
15
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
17
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
18
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_Xray_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 20
Single crystal X-Ray diffraction
http://serc.carleton.edu/research_education/geochemsheets/techniques/SXD.html
21
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
26
Patterns in Patterns
• Patterns of in benzene
• Diffraction spots
perpendicular to planes
https://webspace.yale.edu/chem125/125/xray/laserdiffraction.htm
27
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
29
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
32
Smaller Distance between Planes
• Higher angle of
diffraction
– Planes 2.0 cm apart
– Angle 60o
33
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://undsci.berkeley.edu/article/0_0_0/dna_checklist
http://doublehelix.me/about/
36
Further Reasoning
http://undsci.berkeley.edu/article/0_0_0/dna_checklist
http://doublehelix.me/about/
37
Watson and Crick
• Shown diffraction pattern by colleague of
Franklin, Maurice Wilkins
• Recognized pattern
– Worked with helical proteins
38
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
39
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
41
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
42
Diffraction Spectra of Si
http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm
43
Diffraction of NaCl
https://universe-review.ca/F13-atom04.htm
44
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
46
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
48
Body Centered Cube (BCC)
• h+k+l must equal an
odd number
• Fe and W crystals
http://ecee.colorado.edu/~bart/book/bravais.htm
49
Iron Crystal
http://pwatlas.mt.umist.ac.uk/internetmicroscope/micrographs/diffraction/bcc.html
50
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
51
Diffraction of NaCl
https://universe-review.ca/F13-atom04.htm
52
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
53
Diffraction Spectra of Si
http://www.mrc.iastate.edu/research_programs/nanocrystalline.htm
54
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
55
Modern Electron Density Mapping
http://www.spring8.or.jp/wkg/BL41XU/solution/lang-en/SOL-0000001166?set_language=en&cl=en
56
Other uses
http://www.portlandpress.com/pp/books/online/tiepac/session6/ch2.htm
57
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
58
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
59
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
60
Questions?
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