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?