diffraction: the directors cut learning outcomes by the end of this section you should: know the...
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Diffraction: the Director’s 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
Not just X-rays
There’s 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 Åso = 0.1 - 2 ÅX-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
1845-1923
De Broglie
• Extended the idea of wave-particle duality• 1923 – particles can be wavelike• Idea that everything has a wavelength!
Louis de Broglie
1892-1987E = mc2 = (mc)c but momentum, p=mv
and for a photon v=c
mv
h
p
h
How to prove?
E = pc = p f but E=hf (Planck/Einstein)hf = p f
so
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?
mv
h
p
h
1
ms4000m
hv
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
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
V
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
Neutron source
• Need nuclear reactor (and accelerators, amongst other things)
• Very expensive to set up!
Clifford Schull
1915-2001
Bertram Brockhouse
1918-2003Nobel Prize 1994
"for the development of neutron spectroscopy"
“for the development of the neutron diffraction technique"
ISIS schematic
ISIS schematic
ILL, Grenoble, France
IPNS, Argonne, Chicago IL
Intense Pulsed Neutron Source
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)
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
Alternative
UK neutron source at Rutherford Appleton Laboratory uses “time of flight” neutron diffraction
H- produced at source (pulsed)
Electrons stripped protons (~3 x 1013)
U or Ta - 25 neutrons per proton (i.e. 5 x 1014 per pulse)
Accelerator
Synchrotron
Target
Ion Source
Linear Accelerator
Extracted Proton Beam Line
Time-of-flight neutron diffraction
2dhklsin =
mv
h
where m,v = mass, velocity of neutron
L = length of flight path t = time of flight of neutron
t
Lv
• 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:
Time-of-flight equation
Combine: sind2
mL
ht
sindh
mL2t
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
Data
• e.g. from Polaris, ISIS (Medium resolution, high intensity diffractometer)
Range of d-spacings
• They thus interact with unpaired electrons in atoms• This leads to additional (magnetic) scattering
ExampleA 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?
As sindh
mLt2
so
sinmL
thd
2
d = 4.90 Å
sin14510101.6752
106.6261014200d
27
346
Polaris at ISIS
Errors
• The biggest error in the experiment is where the neutrons originate
• This gives an error in the flight path, L• typical value ~5cm
d
d
t
t
L
L
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
Magnetic Diffraction
• Neutrons possess a magnetic dipole moment
Example:
MnO (also NiO, FeO)
Rock salt structure
Basics of magnetism
Ferromagnetic
Anti-ferromagnetic Ferrimagnetic
Paramagnetic
Magnetic transition
• Oxygen atoms missing for clarity• > 120 K
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 100 200 300T / K
Ma
gn
eti
c s
us
ce
pti
bil
ity
paraAF
Magnetic transition
• Oxygen atoms missing for clarity• < 120 K
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0 100 200 300T / K
Ma
gn
eti
c s
us
ce
pti
bil
ity
paraAF
Magnetic transition
Schull, Strauser & Wollan, Phys Rev B 83 333 (1951)
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)
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)
More Complex Structures
Heavy equipment
• Furnaces, cryostats, pressure cells, magnets, humidity chambers, etc.
Review of sample environments
CryostatCryomag
High Pressure cell “Paris-Edinburgh”
Heavy equipment
• Furnaces, cryostats, pressure cells, magnets, humidity chambers, etc.
Review of sample environments
Humidity chamber
High Pressure for low angle work
Electron Diffraction
Similar principle – matter waves, but me = 9.109 x 10-31 kg
• Also applied “accelerating potential” V such that:
em
eVv
2
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)
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
1892-1975
Electron Diffraction
Picture of diffraction taken by Thomson
Bragg’s Law redux
• Since is very small, is also very small, so we can rewrite Bragg’s law as:
= 2d
D
L
2
As previously, we can derive:
d ~ L/D
Instrument
See applet at: Matter.org.uk
Schematic
Unlike X-ray diffraction we can refocus to produce an image, as well as producing a diffraction pattern.
HREM
Refocussed image
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
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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