Neutron Scattering 102: SANS and NR

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Neutron Scattering 102SANS and NR
Paul Butler
Pre-requisites

• Fundamentals of neutron scattering 100
• Neutron diffraction 101
• Nobel Prize in physics

Grade based on attendance and participation
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Sizes of interest large scale structures 1
300 nm or more

• Mesoporous structures
• Biological structures (membranes, vesicles,
  proteins in solution)
• Polymers
• Colloids and surfactants
• Magnetic films and nanoparticles
• Voids and Precipitates

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SANS and NR assume elastic scattering
SANS and NR measures interference patterns from
structures in the direction of Q
?f ?i ?R kR kiQ?R Q?R 4? sin?R /
? Perpendicular to surface
Neutron Reflectometry (NR) Reflection mode
kS kiQs QsQs4? sin?s / ?
Small Angle Neutron Scattering (SANS)
Transmission mode
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Small Angle Neutron Scattering (SANS)
Macromolecular structures polymers,
micelles,complex fluids, precipitates,porous
media, fractal structures
Measure Scattered Intensity gt Macroscopic cross
section (Scattered intensity(Q) / Incident
intensity) T d
3-D Fourier Transform of scattering
contrast2 normalized to sample scattering volume
Reciprocity in diffraction Fourier features at
QS gt size d 2?/QS Intensity at smaller QS
(angle) gt larger structures
Slide Courtesy of William A. Hamilton
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Specular Neutron Reflection
Measure Reflection Coefficient Specularly
reflected intensity / Incident intensity
Layered structures or correlations relative to a
flat interface Polymeric, semiconductor and
metallic films and multilayers, adsorbed surface
structures and complex fluid correlations at
solid or free surfaces
1-D FT of depth derivative of scattering
contrast2 / Q?R4
Similar to SANS but ... This is only an
approximation valid at large Q?R of an Optical
transform - refraction happens
At lower Q?R, R reaches its maximum R1 i.e.
total reflection
Slide Courtesy of William A. Hamilton
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Specular Reflectivity vs. Scattering length
density profiles
a
sld step ? ?
Thin film
Multilayer
Thin film Interference fringes
Critical edge R1 for QRltQC QC4(???)1/2
Bragg peak
Fourier features (as per SANS)
Fresnel reflectivity
Slide Courtesy of William A. Hamilton
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What SANS tells us
S(Q) Structure factor (interactions or
correlations) or Fourier transform of g(r)
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P(Q) form factor (shape)
Q
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Sizes of interest large scale structures 1
300 nm or more 0.02 lt Q 2?/d lt 6
Q4? sin? / ?
Cold source spectrum ? 3-5lt ? lt20A
? small ? how

• Approaches to small ?
• Small detector resolution/Small slit (sample?)
  size
• Large collimation distance

Intensity ? balance sample size with instrument
length
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Sizes of interest large scale structures 1
300 nm or more
SANS Approach
2 ?
S1 2 S2
DETECTOR
S1
??
3m 16m
1m 15m
SSD
SDD

Optimized for ½ - ¾ inch diameter sample
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Sizes of interest large scale structures 1
300 nm or more
NR Approach
Q?R
ki
kR
Point by point scan
Ls
?
? Ls sin?
? 1mm for low Q
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Sizes of interest large scale structures 1
300 nm or more
Ultra Small Angle Approach when SANS isnt
small enough
Point by point scan - again
?
?
Fundamental Rule intensity OR resolution but
not both
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Sample Scattering

• Contribution to detector counts

1) Scattering from sample 2)
Scattering from other than sample (neutrons still
go through sample) 3) Stray neutrons and
electronic noise (neutrons dont go through
sample)
aperture
sample
Incident beam
air
Stray neutrons and Electronic noise
cell
Imeas(i) F t A e(i) ?O Tcs(dS/dO)s(i) ds
(dS/dO)c(i) dc Ibgd t
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SANS Basic Concepts
10 black 90 white
S/V specific surface are
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?i
2?f
Imeas F A e t R Ibgd t
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Summary

• SANS and NR measure structures in the direction
  of Q only
• SANS and NR assume elastic scattering
• SANS is a transmission technique that measures
  the average structures in the volume probed
• NR is a reflection technique that measures the z
  (depth) density profile of structures strongly
  correlated to the reflection interface
• Thinking aids
• SANS
• Imeas(i) F t A e(i) ?O Tcs(dS/dO)s(i) ds
  (dS/dO)c(i) dc Ibgd t
• NR
• Imeas F A e t R Ibgd t

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When measuring a gold layer on a Silicon
substrate for example, many reflectometers can go
to Q gt 0.4 Å-1 and reflectivities of nearly 10-8.
However most films measured at the solid
solution interface only get to 10-5 and a Qmax of
0.25Å-1 Why might this be and what might be
done about it. (hint think of sources of
background) SANS is a transmission mode
measurement, so with an infinitely thick sample
the transmission will be zero and thus no
scattering can be measured. If the sample is
infinitely thin, there is nothing to scatter
from. So what thickness is best? (hint look at
the Imeas equation) For a strong scatterer, a
large fraction of the beam is coherently
scattered. This is good for signal but how might
it be a problem? (hint think of the scattering
from the back or downstream side of the sample)
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USANS gets to very small angle. However SANS is
a long instrument in order to reach small angles.
Why not make the instrument longer? (Hint
particle or wave?)
Given the SANS pattern on the right, how can know
what Q to associate with each pixel? (hint use
geometry and the definition for Q)
NR and SANS measure structures in the direction
of Q. Given the NR Q is in the z direction, can
NR be used to measure the average diameter of the
spherically symmetric object floating randomly
below the interface?