Andrew Jackson Instrument Scientist ESS Introduction to Neutron Scattering Neutrons and Food, Jan 30th 2012 Delft University of Technology
Andrew JacksonInstrument Scientist
ESS
Introduction to Neutron Scattering
Neutrons and Food, Jan 30th 2012
Delft University of Technology
The Neutron
Fission
Can use fission or spallation to generate beams of neutrons for experiments
The neutron:● Is a spin 1/2 sub-atomic particle● Has a mass equivalent to 1839 electrons (1.674928 x 10-27 kg)● Has a magnetic moment of -1.9130427 μn (-9.6491783 x 1027JT-1)● Has a lifetime of 15 minutes (885.9 s).
Why Neutrons?
1) Ability to measure both energy and momentum transfer Geometry of motion
2) Neutrons scatter by a nuclear interaction => different isotopes scatter differently H and D scatter very differently
3) Simplicity of the interaction allows easy interpretation of intensities
Easy to compare with theory and models
4) Neutrons have a magnetic moment H
D O Si
C
What do we measure?
1. A source of neutrons 2. A method to prescribe the wavevector (ki) of the neutrons incident on
the sample 3. A well-chosen sample
4. A method to determine the wavevector (kf) of the scattered neutrons 5. A detector
Sample Ei ki
momentum = hk energy = (hk)2/(2m) ! k=2π/λ#
Ef kf
Q = ki - kf
hω = Ei - Ef
y
xk
k’
r
Incident plane wave: eikx
Scattered circular wave:
Nucleus at r=0
2θ
k'
k
qq = 2k sinθ =
λ4π sinθ
|q|2 |k|
1sinθ =
-b r eikr
Measure number of neutrons scattered as function of Q and ω
Intensity of scattering as function of Q is related to the Fourier transform of the spatial arrangement of matter in the sample
Elastic vs Inelastic
Contrast Variation and Matching
ρ solvent = ρ shell!
or!
ρ solvent = ρ core! (shell visible)!
(core visible)!
Contrast Matching - reduce the number of phases �visible�
The two distinct 2-phase systems can be easily understood
Neutron Scattering Techniques
Neutron scattering methods probe structural features over 5 orders of magnitude
and
dynamic phenomena over 8 orders of magnitude in time USANS!
Neutron reflectivity!
DiffractionSizes probed = “atomic structures” = 0.1 nm - 10 nm
Position and intensity of diffraction peaks gives atomic positions
Diffraction Example
Kovalevsy et al., Structure, 18 (2010) 688-699
Mechanism of D-Xylose Isomerase
Small Angle Scattering
Sizes probed = “large-scale structures” = 1 nm - 10 µm
1!
Q!
S(Q) = Structure factor (interactions or correlations)!or Fourier transform of g(r)!
P(Q) = form factor (shape)!
SANS Examples
Mesoporous structuresBiological structures (membranes, vesicles, proteins in solution)
PolymersColloids and surfactants
Magnetic films and nanoparticlesVoids and Precipitates
Reflectometry
x
z
θ0
θ1
x
z
θ0
θ1
θ1
θ2
n0
n1
n2
n0
n1
k0k0
k1
kz = k0 sinθ0
qz = 2kz = 4π/λ sin θ0
θ0
(a) (b)
d
Sizes probed = 1 nm - 100 nm
Specular = Incident and Reflected Angles Equal => Structure perpendicular to surface
Offspecular = Incident and Reflected Angles Not Equal => Structure in plane of surface
Reflectometry Examples
Biological structures (lipid membranes, adsorbed proteins)Polymers
SurfactantsMagnetic films
Solid Substrate
Neutron Spectroscopy
Sr3Cr2O8 measured at LET (ISIS)Bella Lake and Diana Lucia Quintero Castro
Reveals a plethora of excitations 4D information (x,y,z and time)
TOFTOF @ FRMII
4m
Neutron Spectroscopy
Time and spatial resolution are well matched
Useful for investigation of diffusive versus confined motion
Trajectory of a C32H66 Molecule on different timescales (T. Unruh et al).
Imaging
Radiographic technique
Sizes probed = 100 μm and larger
Summary
Neutron scattering is particularly sensitive to hydrogen
Varying the hydrogen/deuterium ratio (contrast variation) provides extra information
Neutron scattering techniques can study atomic to macroscopic dimensions and motions from atomic vibration to macromolecular diffusive motions
Questions?