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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 Å so = Å X-rays, electrons, neutrons suitable Matter waves! In 1901 the very first Nobel Prize in Physics was awarded to Wilhelm Röntgen for his discovery of X-rays. Wilhelm Röntgen

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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 E = mc 2 = (mc)cbut momentum, p=mv and for a photon v=c How to prove? E = pc = p f but E=hf (Planck/Einstein) hf= p f so

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Using de Broglie If we want a wavelength of 1.00 Å then… h = x J s m N = x 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:f j Z - can be calculated Neutrons: small dependence of f j on Z but major part Z independent. f j must be determined experimentally V

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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 Bertram Brockhouse 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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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 H - produced at source (pulsed) Electrons stripped protons (~3 x ) U or Ta - 25 neutrons per proton (i.e. 5 x per pulse) Accelerator Synchrotron Target Ion Source Linear Accelerator Extracted Proton Beam Line

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Time-of-flight neutron diffraction 2d hkl sin = where m,v = mass, velocity of neutron L = length of flight patht = time of flight of neutron 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:

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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? Asso 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 Anti-ferromagnetic Ferrimagnetic Paramagnetic

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Magnetic transition Oxygen atoms missing for clarity > 120 K para AF

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Magnetic transition Oxygen atoms missing for clarity < 120 K para AF

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Magnetic transition Schull, Strauser & Wollan, Phys Rev B (1951)

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3d view – magnetic transition in YMn 2 With thanks to Prof Sue Kilcoyne: R Cywinski, S H Kilcoyne and C A Scott, J. Phys C (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 C (1991)

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More Complex Structures

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Heavy equipment Furnaces, cryostats, pressure cells, magnets, humidity chambers, etc. ReviewReview of sample environments Cryostat Cryomag High Pressure cell Paris-Edinburgh

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Heavy equipment Furnaces, cryostats, pressure cells, magnets, humidity chambers, etc. ReviewReview of sample environments Humidity chamber High Pressure for low angle work

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Electron Diffraction Similar principle – matter waves, but m e = x kg Also applied accelerating potential V such that: Typical values kV, so v up to 2.65 x 10 8 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) 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… George Paget Thomson

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Electron Diffraction Picture of diffraction taken by Thomson

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Braggs Law redux Since is very small, is also very small, so we can rewrite Braggs law as: = 2d D L 2 As previously, we can derive: d ~ L/D

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Instrument See applet at: Matter.org.ukMatter.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)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

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