Basics of Neutron Scattering

Solid State Physics Division Bhabha Atomic Research Centre

Mumbai, India

Veerendra K. Sharma

Email: sharmavk@barc.gov.in

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: sharmavk@barc.gov.in