Neutron Diffraction
Presented by Noël Harris
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History
• First experiment in 1945
– Ernest O. Wollan
• Additional work
– Clifford Shull
• Nobel prize in physics awarded in 1994
– ½ to Clifford Shull
– Wollan died in 1984
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History
• Same method of X-ray diffraction
– Discovered in 1895
– First experiment 1912
• Neutron discovered 1932
– 1945, First Reactors to generate free neutrons
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Neutron Diffraction
• Neutron scattering
• Free neutrons
– Diffraction pattern
• Emitted from
– Fusion
– Fission
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Neutrons
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Mass = 1.675 x 10–27 kg
Charge = 0
Spin = ½
Has a magnetic moment
Have wave properties
– λ=h/p
– Needed for diffraction
http://www.ncnr.nist.gov/summerschool/ss09/pdf/Dewey_FP09_Part1.pdf
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Diffraction
• Phenomena when wave encounters a slit
• Constructive and destructive interference
• Braggs Law
– Crystals
– 2d sinθn =nλ
http://en.wikipedia.org/wiki/Diffraction
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Why Neutrons
• X-rays get distorted with electron cloud
– Electrons even worse
– Heavy metals
• Neutrons have high penetrating power
– Due to no charge
• Can distinguish isotopes
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Interactions
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Penetration depth
LANSCE- Neutron scattering primer – Roger Pynn
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Isotopes
• X-rays react predictably with increase in Z
– Neutrons do not
• H has a largely different signal than D
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Review
• Neutron diffraction
– Same method as X-ray diffraction
• Better penetration
– Direct interaction with the nucleus
• Isotope distinguishing
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General set up
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Neutron Sources
• Reactors
– Uranium fission
• Spallation
– Linear accelerators
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Reactors
• Creates a continuous beam
• Must be reduced to a monochromatic beam
http://ap.smu.ca/demos/images/stories/Pics/Mousetrap/uranium_fission.gif
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http://www.manep-nccr.ch/img/photo/research-teams/il1swissneutronics2.jpg
http://web.ornl.gov/adm/partnerships/success_stories/ge-reuter.shtml
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Reactor Source: Grenoble, Institute
Laue-Langevin
http://www.lightsources.org/imagebank/image/esr054
http://hewat.net/science/ill-hewat.html
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Neutron monochrometers
• Pyrolytic graphite
• Germanium
• Copper
http://pd.chem.ucl.ac.uk/pdnn/inst3/monoc.htm
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Spallation
• Linear accelerator
– Proton ~ 800 MeV
• Hit heavy atoms
– Tungsten
• About 20 neutrons released
http://inspirehep.net/record/776811/files/spall_rys.png
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Spallation
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2006 Spallation Neutron Source at Oak
Ridge
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Types of neutrons
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Cold: 0.0-0.025 eV
Thermal: 0.025 eV
Slow: 1-10 eV
Fast: 1-20 MeV
Relativistic > 20MeV
• Neutrons produced
– ~25 MeV Spallation
– ~200 MeV Reactor
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Neutrons moderators
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Water- most common
Graphite
Heavy water
Liquid hydrogen
http://en.wikipedia.org/wiki/Neutron_moderator
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1975 NIST Reactor, Gaithersburg, MD
http://www.ncnr.nist.gov/NCNRHistory_Rush_Cappelletti.pdf
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Neutron moderator
• Material placed near source
• Neutrons lose energy through collisions
• Liquid Hydrogen cools to 5 MeV
– Neutron wavelength ~ 1.8Å
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Source: Reactor/Spallation
• Large Facilities providing neutrons for 30 to 50
neutron spectrometers
– “Small science at large facility”
• Locations
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Europe: 20
North America: 9
Asia: 8
South America: 3
Africa: 1
Australia: 1
http://neutronsources.org/neutron-centres.html
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Review
• Neutrons produced by
– Fission
– Spallation
• Neutrons temperatures
• Neutron moderators
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Nuclear Scattering - Basics
• Single fixed nucleus
• Neutron behavior is quantum
– Particle
– Wave
• Get same answer
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Scattering Nomenclature
• Cross section
– Effective area of nucleus
• Point scatter
– Ability to diffract in all directions
• Isotropic
– Wave length of neutron bigger than nucleus
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Single fixed nucleus
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Scattering in matter
• Nucleus is not fixed
• Elastic
• Inelastic
• (h/2π) Q
– Momentum transfer
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Elastic
• Same energy going in as going out
• “easiest”
–ɛ=0
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Inelastic
• Either a loss or gain of energy
• Moving matter
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Two types of scattering
• Coherent
– Interacts with sample as a whole
– Different nuclei
• And incoherent
– Independent nuclei
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Coherent Scattering
• Diffraction
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Neutrons going in same direction
Definite relative phase
Interference patterns
Elastic scattering
• Scattering
– Depends on distance between atoms
• Gives information of the material
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Figure 6 switch
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Structure determination
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i,j two atoms
r – their respective potions
Debye-Waller factor
b = Cross section of nucleus
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Structure determination
• Only certain values give a non zero
• Q vectors perpendicular to the plane in
multiples of 2π/d
• Simplifies into Bragg's law
– nλ=2dsinθ
• Determines atoms:
– Spacing
– Density
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Bragg’s law
• When wavelength matches d
• Primary scattering
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Elastic scattering
• Bucky ball
• a.) 3.25 Å
• b.)5.5 Å
• c.)3.55 Å
http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.67.3808
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Incoherent scattering
• Random distribution of nuclear spins
– Isotopes
– Natural products
• Two thirds will have moments flipped
• Polarization analysis
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Representative spectra
http://pubs.rsc.org/services/images/RSCpubs.ePlatform.Service.FreeContent.ImageService.svc/ImageService/Articleimage
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/2015/CP/c4cp04112g/c4cp04112g-f1_hi-res.gif
Inelastic spectrum
• Globular protein
• Measured at different temperatures
• Decrease temperature
– Inelastic peak visible
• Increase temperature
– Broader elastic peak
http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.65.1080
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Intensity
• Intensity of scattered neutrons is proportional
to the square of the density of the atoms
• Neutron Fluxes smaller than X-rays
• Therefore signal limiting
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Problems
• Real life
– More than one atom type
– Varying crystal structure
– Placing crystal
• Computers – unit cells
• Sample prep
• Analysis technique
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Review
• Inelastic/Elastic Scattering
– Coherent
– Incoherent
• Coherent simplifies to Braggs law
– When wavelength = d
– 2d sinθn =nλ
• Incoherent
– Polarized neutrons
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Techniques
• No standard technique
• Elastic scattering
– Powder diffraction
– Small angle
• Inelastic scattering
– Three axis
– Magnetic
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Powder diffraction
• Avoid sample placement issue
• Sample is powder
• Small samples
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Reactor source
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http://journals.aps.org/prb/pdf/10.1103/PhysRevB.54.15149
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Spallation source
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Difference?
• Pulse vs continuum source
– Get same answer
• Independent variable is different
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Small Angle Scattering
• Coherent scattering
– Ideal for proteins
• Wavelength is larger
• Diffraction angle is less than 1 degree
• Contrast matching
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Contrast matching
• Mix matrix with sample
• Only certain parts are “visible”
• Diffraction is usually matched with water with
varying amounts of deuterium
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Contrast matching
• Example: an Egg
• Yolk is “invisible”
• White is “invisible”
• Segmenting aids in analysis
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Small Angle Spectra
• Varying matrix composition
http://www.sfu.ca/physics/research/workarea/frisken/Research_Files/Macromolecules2006Diblocks.pdf
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Review
• Elastic coherent scattering techniques
• Rely on Braggs law
• Many techniques
– Independent axis changes
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Moving matter
• One moves the others are affected
• Chorus line where dancers have to look to
their neighbor to see how they move.
• Effective waves through out the compound
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Phonons
• This movement gives rise to inelastic coherent
scattering
• Neutrons frequency = molecular
• Appreciable fractionation
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Three axis spectroscopy
• Monochromator
• Sample
• Analyzer
• Measures at constant Q
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http://nmi3.eu/index.php?rex_img_type=content_noresize&rex_img_file=three-axis_spectroscopy.jpg
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Inefficient
• Each measurement takes several minutes
– Scan each wavelength
• Complete scan takes several hours to days
• Time allows for making adjustment on the fly
• In the works is to make a simultaneous
measurement.
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Three axis spectra
http://journals.aps.org/prb/pdf/10.1103/PhysRevB.6.4332
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Incoherent scattering
• Usually unwanted back ground
• Nucleus at different locations
• Isotopes
• Magnetic material
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Magnetic Scattering
• Neutron has magnetic moment
• Interact with electrons
– Unpaired
• Ferromagnetic
• Antiferromagnetic
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Ferromagnetic interactions
• Ferromagnetic- all electrons in same direction
• Non-isotropic interaction
• Dipole interaction
• Sensitive to magnetic field
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Antiferromagnetic
• Spins are in random up and down positions
• Distance is twice as long
• Bragg λ is half
• Can easily distinguish between regular
splitting
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Flat- Coil Neutron Flipper
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Using polarized Neutrons
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Magnetic scattering
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Magnetic Scattering spectra
• Spin density
http://pubs.acs.org/doi/pdf/10.1021/ja00084a048
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Other Types of Neutron Spectrometry
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Magnetic Reflectometer
Liquid Reflectometer
Neutron spin echo
Backscattering Spectrometer
Ultra High Pressure Diffractometer
Disordered Materials Diffractometer
Chopper Apps:
– High Resolution Fermi Spectrometer
– Wide-Angle Fermi Spectrometer
– Microvolt Muli-Chopper Spectrometer
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Questions?
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