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Basics of Neutron Scattering
Solid State Physics Division Bhabha Atomic Research Centre
Mumbai, India
Veerendra K. Sharma
Email: [email protected]
Motivation
Our living highly depends on the materials Material properties depend on structure and dynamics of its constituents.
Designing new & better materials depends on understanding the correlation between structure/dynamics and material properties.
Q = ki - kf
hω = Ei - Ef
Neutron Scattering
Sample
Ei
Ef
ki
kf
2θ
Detector
λ ~ Å Structure Dynamics
Thermal Neutron
E ~ meV
)Å(81.81)( 2λ
=meVE
X-ray
λ ~ Å Structure
E ~ keV
)Å(4.12)(
λ=keVE
Light, X-ray, Neutron, etc
History of Neutrons
•1945 – diffraction (Shull, Wollan) •1955 – Triple Axis Spectrometers (Inelastic neutron Scattering)
1994 – Nobel Prize to Brockhouse and Shull
•1932 Chadwick discovered the neutrons
Nobel in 1935
1994 Nobel Prize in Physics- Shull and Brockhouse
Neutron Shows “where the atoms are”
.... “and what the atoms do”
Elastic Scattering ( Diffraction)
Shull
Inelastic Scattering ( Dynamics)
Brockhouse
Neutron Sources
1. Nuclear Fission
2. Spallation Source
High Energy Proton beam
High Z Target
λ ~ d (Å) Structure of Materials
Energy ~ excitations (meV) Dynamics of Materials
Neutral High Penetration (can
study bulk) Non-destructive
Magnetic moment (-1.913 µN)
Magnetic Structure
(interact mainly nuclei)
•Sensitive to light atoms; between neighbouring atoms •Contrast variation with isotopes
Neutron Advantages
Thermal neutrons: an ideal and unique probe in condensed matter
Microscopic Understanding of - Structural - Dynamic and - Magnetic properties
Neutron Advantages
Neutron Disadvantages
Neutron sources (Reactor/Spallation) are limited Neutron sources are weak => low signals, large samples. Some elements (e.g. Cd, B, Gd) absorb strongly
Theory of Neutron Scattering
Fermi’s pseudo-potential
V( r ) = (2πħ2/m) b δ(r)
Ψsc = – (b/r) ei k r
ψin = ei k z r λ ~ 10-10m
scatt. center bound at r=0
R0~10-14m Neutron Nucleus interaction s-wave scattering
b~ size of nucleus~10-15 m
Detector ΔΩ
ΩΩ
=Ω d .flux neutron Incident
delement angle into secper neutrons scattered ofNumber ddσ
Q = ki - kf ki
kf
For X-ray
For single atom
Q dependent
b=depends only on the nucleus
For single nucleus
Independent of Q
For Neutron
Theory of Neutron Scattering
Form factor
bN
f
What about neutron (magnetic) ?
All are Normalized at Q=0
Wave length~Å Nucleus size~fm
Neutron scattering from nucleus
No path difference Isotropic
λ >> size of scatterer/Potential width
X-ray Scattering from electron cloud
Wave length~Å Atom size~~Å
Finite path difference Form factor
λ ~ size of scatterer
for neutron it depends on Scattering length (b) which varies irregularly with Z
Scattering amplitude for X-ray increases with Z (Atomic number)
Neutron vs X-ray Scattering power
Sensitivity of low Z element in presence of High Z
Neighbouring elements https://www.ncnr.nist.gov/resources/n-lengths/
Atoms in FCC crystal
We are not taking photographs!!! We are working in Fourier space S(Q)
Length Scale ~ ( 2π/ Q ) Time Scale ~ 2πħ/ΔE
Fourier Transform Conjugate Variables
Structures in different length scales Dynamics in different time scales
Ref: Th. Brückel “Applications of Neutron Scattering - an Overview”
Structure and Dynamics
Elastic Scattering : Structure Monochromator
Sample
Detector
Neutrons
Ei Ki
Kf After scattering, detect the neutrons
I(Q)
Ei
Ef
Ki Kf
Inelastic Scattering : Dynamics
After scattering what is the energy of the neutrons ?
I(Q,ω)
One additional variable ħω ( Energy transfer)
2
Eσ∂
∂ ∂Ω
θ
( )2/sin4 θλπ
=Q
1 Å 1 nm 100 nm 1 micron
Crystal structure
Precipitates Porous media
Micelles/R
Proteins
polymers
Nano particles Self-assembled
Bacteria
Virus
Grains
Relevant Structures in Condensed Matter
Structure: Elastic Neutron Scattering
Wide angle diffraction (crystallography, magnetism)
Very large angle diffraction (glasses, liquids)
Small angle scattering (large macromolecules, nanoparticles)
0.00 0.05 0.10 0.15 0.200.0
0.4
0.8
1.2
Dilute System
I(Q)
Q (Å-1)
∆Q ~ 1/R
S(Q
)-1
Q(Å-1) 0 10 20 30 40
SANS Mesoscopic
objects
WAS/NPD Arrangements of Atoms
neutrons
Length Scale ~ ( 2π/ Q )
Low Q
Intermediate Q
)2/sin(4 θλπ
=Q
Structure: Elastic Neutron Scattering
SANS Applications
Soft Matter
Biological Systems
Nanomaterials
Superconductor Flux Lines
Polymers, Colloids
Lipid Membranes, Proteins DNA, Drugs
Nanoparticles Carbon Nanotube Phase separation in Alloys Microporosity in Ceramic
Vortex Structure, Flux Lines Pinning
Lipid membranes
f
Mag. Cell same as Chemical Cell
Mag. Cell is not same as chemical cell
More contribution at low Q
Magnetic Diffraction
Applications of Diffraction
Condensed Matter Physics Structure and its correlation with properties (e.g. Magnetic materials, High TC Superconductor, etc.)
Biology
Structure of proteins, binding of ligands
Chemistry & Energy Materials Structure determination of new compounds, structure of catalysts, Hydrogen storage
Dynamics
Periodic motion ( e.g. vibration)
Stochastic motion (e.g. diffusion, reorientation)
Quasielastic Neutron Scattering Inelastic
Neutron Scattering
Dynamics
Map of dynamical modes
Applications of QENS spectroscopy
Soft Matter &
Biological Systems
Polymers, Colloids, Liquid crystals
Lipid Membranes, Proteins DNA, Drugs
Lateral diffusion
Bending
Thickness fluctuations
Internal
Chemistry & Materials
Catalyst, Hydrogen storage, Li-ion battery materials, Nanoporous Materials (e.g. Zeolites, Clay), deep eutctic solvents
Application of Inelastic neutron Scattering
Lattice or Spin dynamics
Interatomic potentials & bonding
Phase transitions & critical phenomena (soft modes)
Magnetic Exchange interactions
Phonon dispersions Phonon Density of States Spin-wave dispersion
To study
Provides :
Negative Thermal Expansion Materials
(Ex. Water 0-4 °C; ZrW2O8)
Summary
Neutron techniques cover a very large range of length and time scales relevant for research on condensed matter systems.
Length Scale ~ (Å to µm) Time Scale ~ (10-14 s to 10-7 s)
Assets of neutrons structure as well dynamics sensitivity to magnetism, gentle non-destructive probe, sensitivity to light elements, contrast for neighboring elements, etc
Ref: Th. Brückel “Applications of Neutron Scattering - an Overview”
Summary
Significance of research with neutrons in fundamental research and modern technologies
References: G. E. Bacon, Neutron Diffraction (Oxford University Press)
L. A. Feigin and D. Svergun Structural Analysis by Small-Angle X-Ray and
Neutron Scattering, (Plenum Press, New York). Th. Brückel “Applications of Neutron Scattering - an Overview”
M. Bee “Quasielastic Neutron Scattering and its applications”
Thank You Email: [email protected]