Diffraction: the Directors Cut

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Diffraction the Directors Cut

• Learning Outcomes
• By the end of this section you should
• know the basic principles of neutron electron
  diffraction
• be able to explain time-of-flight neutron
  diffraction and make calculations relating tof to
  d-spacing
• understand the uses of both techniques

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Not just X-rays

• Theres more to diffraction than X-rays, you know
• (but not much more)
• (with apologies to the Smiths)

As we (Dr Gibson) stated previously (HO3) For
diffraction from crystals Interatomic distances
0.1 - 2 Å so ? 0.1 - 2 Å X-rays, electrons,
neutrons suitable Matter waves!
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De Broglie

• Extended the idea of wave-particle duality
• 1923 particles can be wavelike
• Idea that everything has a wavelength!

Louis de Broglie 1892-1987
E mc2 (mc)c but momentum, pmv and for
a photon vc
E pc p f ? but Ehf (Planck/Einstein) hf
p f ? so
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Using de Broglie

• If we want a wavelength of 1.00 Å then
• h 6.626 x 10-34 J s
• mN 1.675 x 10-27 kg
• How fast do the neutrons need to be travelling?

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Neutron scattering

• Neutron can be scattered by atoms by
• interaction with nucleus
• interaction with spin of unpaired electrons -
  magnetic interaction, magnetic scattering. This
  happens because the neutron has a magnetic
  moment. (later)

• Also the interaction can be
• elastic (diffractometer) structural studies
• inelastic (spectrometer)
• loss of energy on scattering gives information
  on phonon dispersion (effect of vibrations in
  lattice) and stretching of bonds

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Scattering from neutrons

• X-rays fj ? Z - can be calculated
• Neutrons small dependence of fj on Z but major
  part Z independent. fj must be determined
  experimentally

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Good points/Bad points

• Can detect light atoms
• Can often distinguish between adjacent atoms
• Can distinguish between isotopes
• Can accurately find atoms in presence of very
  high Z atoms
• Covers a wide range of d-spacings - more hkl - BUT

• Some atoms/isotopes good neutron absorbers (e.g.
  Cd, Gd (Gadolinium), 6Li (so use 7Li)
• V has very low, 0 scattering (but..)
• need neutron source
• VERY expensive (10,000 per DAY!)
• Excellent complementary technique to XRD

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Neutron source

• Need nuclear reactor (and accelerators, amongst
  other things)
• Very expensive to set up!

Clifford Schull 1915-2001
Bertram Brockhouse 1918-2003
Nobel Prize 1994
"for the development of neutron spectroscopy"
for the development of the neutron diffraction
technique"
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ISIS schematic
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ISIS schematic
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(No Transcript)
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ILL, Grenoble, France
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IPNS, Argonne, Chicago IL

• Intense Pulsed Neutron Source

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Other neutron sources are also available

• e.g.
• Los Alamos Neutron Science Center (New Mexico,
  US)
• Lucas Heights (Sydney Australia)
• Oak Ridge (Tennessee, USA)
• KENS (Tsukuba, Japan)
• Chalk River (Ontario, Canada)
• Risø (Roskilde, Denmark)

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The experiment

• At many sources (e.g. ILL at Grenoble) neutrons
  are produced by fission in a nuclear reactor and
  then selected by wavelength - but with neutrons
  there are no characteristic wavelengths

..so by selecting a wavelength we lose neutrons
and lose intensity
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Alternative

• UK neutron source at Rutherford Appleton
  Laboratory uses time of flight neutron
  diffraction

U or Ta - 25 neutrons per proton (i.e. 5 x 1014
per pulse)
Electrons stripped ? protons (3 x 1013)
H- produced at source (pulsed)
Accelerator
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Time-of-flight neutron diffraction

• 2dhklsin? ?

• We are measuring d, so two variables, ? and ?
• In lab X-ray powder diffraction, ? is constant, ?
  variable
• In time-of-flight (t.o.f), ? is constant, ?
  variable
• This takes advantage of the full white spectrum

• Two basic equations

where m,v mass, velocity of neutron L length
of flight path t time of flight of neutron
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Time-of-flight equation

• Combine

L is a constant for the detector, h, m are
constants so t ? d d-spacings are discriminated
by the time of arrival of the neutrons at the
detector
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Data

• e.g. from Polaris, ISIS (Medium resolution, high
  intensity diffractometer)

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Range of d-spacings

• They thus interact with unpaired electrons in
  atoms
• This leads to additional (magnetic) scattering

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Example

• A neutron detector is located at a distance of
  10m from the sample and at 145º. We measure a
  reflection with a tof of 14,200 ?s. What is its
  d-spacing?

d 4.90 Å
Polaris at ISIS
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Errors

• The biggest error in the experiment is where the
  neutrons originate
• This gives an error in the flight path, L
• typical value 5cm

Hence as L increases, error in d is reduced -
resolution of the instrument is improved e.g.
instrument at 10m compared to instrument at
100m 100m HRPD, currently highest resolution in
the world
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Magnetic Diffraction

• Neutrons possess a magnetic dipole moment

Example MnO (also NiO, FeO) Rock salt structure
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Basics of magnetism

• Ferromagnetic

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Magnetic transition

• Oxygen atoms missing for clarity
• gt 120 K

para
AF
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Magnetic transition

• Oxygen atoms missing for clarity
• lt 120 K

para
AF
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Magnetic transition

• Schull, Strauser Wollan, Phys Rev B 83 333
  (1951)

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3d view magnetic transition in YMn2
With thanks to Prof Sue Kilcoyne R Cywinski, S
H Kilcoyne and C A Scott, J. Phys C33 6473 (1991)
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3d view doping loses transition
With thanks to Prof Sue Kilcoyne R Cywinski, S
H Kilcoyne and C A Scott, J. Phys C33 6473 (1991)
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More Complex Structures
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Heavy equipment

• Furnaces, cryostats, pressure cells, magnets,
  humidity chambers, etc.

Cryomag
High Pressure cell Paris-Edinburgh
Cryostat
Review of sample environments
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Heavy equipment

• Furnaces, cryostats, pressure cells, magnets,
  humidity chambers, etc.

Humidity chamber
High Pressure for low angle work
Review of sample environments
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Electron Diffraction

• Similar principle matter waves, but me 9.109
  x 10-31 kg
• Also applied accelerating potential V such that

Typical values 10-200 kV, so v up to 2.65 x 108
ms-1 Relativistic speeds! Calculate v for an
accelerating voltage of 10 kV. What is ??
(Question sheet)
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G. P. Thomson

• Experiments performed at Marischal College in the
  late 1920's
• (also Lester Werner and Clinton Davisson at Bell
  labs in New York)

George Paget Thomson 1892-1975
100 keV electrons. His father had won the Nobel
prize for proving electrons were particles. G.
P. won the prize for proving that they were waves
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Electron Diffraction

• Picture of diffraction taken by Thomson

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Braggs Law redux

• Since l is very small, q is also very small, so
  we can rewrite Braggs law as
• l 2d q

As previously, we can derive d ?L/D
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Instrument

• See applet at Matter.org.uk

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Schematic

• Unlike X-ray diffraction we can refocus to
  produce an image, as well as producing a
  diffraction pattern.

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HREM

• Refocussed image

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Uses

• Can be used to look at individual crystallites
  must be thin (why?)
• Useful to help determine unit cell parameters
  need many orientations (see animation here)
• Shape of spots streaking can give information on
  crystal size and shape
• Can identify packing defects (see later)

• Added extra EDX for elemental analysis
• Electrons knock out inner shell electrons
• Characteristic X-rays emitted as outer shell
  electron drops down to fill gap

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Conclusions

• Both neutron and electron diffraction are very
  useful complementary techniques to X-ray
  diffraction
• Neutron diffraction has a number of advantages
  over X-ray diffraction but cost is a major
  disadvantage!
• Both fission and spallation sources are used
• Magnetic diffraction is possible due to the
  dipole present with neutrons
• Electrons can be focussed, allowing high
  resolution imaging as well as diffraction
• Information on defects and unit cells