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N EUTRONS AND THEIR INTERACTION WITH MATTER Auteur - Date 1 I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N T HE CONTEXT Programme Neutron talks by Teresa Fernandez (yesterday) ME Ulli Koester (neutron prod.),

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SLIDE 1

Auteur - Date

I N S T I T U T M A X V O N L A U E - P A U L L A N G E V I N

1

NEUTRONS AND THEIR INTERACTION WITH MATTER

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2

Neutron talks by

  • Teresa Fernandez (yesterday)
  • ME
  • Ulli Koester (neutron prod.), Giovanna Fragneto (soft matter)
  • Juan Rodriguez-Carvajal (diffraction), Eddy Lelievre (instrumentation)
  • Andrew Wildes (spectroscopy), Mechtilde Enderle (inelastic scattering)
  • Gerry Lander (history)
  • Oliver Zimmer (nuclear and particle physics)

THE CONTEXT

Programme

05/09/2017

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3

  • History – neutrons and nuclear reactions
  • Production – reactors and spallation sources
  • Properties – as a particle and a probe
  • Instruments – exploiting the probe to do science

NEUTRONS AND THEIR INTERACTION WITH MATTER

Overview

05/09/2017

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4

  • 1932: J. Chadwick, after work by
  • thers, discovers the ‘neutron’, a

neutral but massive particle A BIT OF HISTORY

The neutron

05/09/2017

mHe +mB

( )c2 + T

He = mN +mn

( )c2 + T

N + T n

mn =1.0067 ± 0.0012 a.m.u

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5

  • 1938: O. Hahn, F. Strassmann & L. Meitner discovered the fission
  • f 235U nuclei through thermal neutron capture
  • 1939: H. v. Halban, F. Joliot & L. Kowarski showed that 235U nuclei

fission produced 2.4 n0 on average – chain reaction

  • 1942: E. Fermi & al. demonstrated first self-sustained chain

reaction reactor A BIT OF HISTORY

The nuclear reaction

05/09/2017

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6

NOBEL PRIZES, NEUTRONS AND THE ILL

Chadwick, Shull & Brockhouse

05/09/2017

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7

NOBEL PRIZES, NEUTRONS AND THE ILL

05/09/2017

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8

NOBEL PRIZES, NEUTRONS AND THE ILL

Haldane (1977 – 1981), Kosterlitz and Thouless for topological phase transitions and phases of matter (Electronic structure and excitation of 1D quantum liquids and spin chains)

05/09/2017

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9

  • Nuclear fission  chain reaction with excess

neutrons (1n  2.5n)

  • Slow neutrons split U-235 nuclei
  • Fission neutrons have MeV energies and

need to be moderated (thermalized) to meV energies by scattering from water

  • Thermalisation @ RT  thermal neutrons,

@ 25K  cold neutrons and @ 2400 K  hot neutrons

  • ILL – flux 1.5 x 1015 n/cm2/s

NEUTRON SOURCES

Fission reactors

05/09/2017

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10

  • Neutrons can be produced by

bombarding heavy metal targets

  • 2 GeV protons (90% speed-of-

light) produce spallation – evaporation of ~30 neutrons NEUTRON SOURCES

Spallation sources

05/09/2017

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11

NEUTRON SOURCES

05/09/2017 Berkeley 37-inch cyclotron 350 mCi Ra-Be source Chadwick

1930 1970 1980 1990 2000 2010 2020

105 1010 1015 1020 1

ISIS

Pulsed Sources

ZINP-P ZINP-P/ KENS WNR IPNS ILL X-10 CP-2

Steady State Sources

HFBR HFIR NRU MTR NRX CP-1

1940 1950 1960 Effective thermal neutron flux n/cm2-s

(Updated from Neutron Scattering, K. Skold and D. L. Price, eds., Academic Press, 1986) FRM-II SINQ SNS

ESS

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CONTINUOUS OR PULSED BEAMS

05/09/2017

Integrated vs peak flux – ESS will have a time-integrated flux comparable to ILL

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N VS X

ESRF (hard X-rays)

05/09/2017

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  • free neutrons are unstable: β-decay  proton, electron, anti-neutrino

life time: 886 ± 1 sec

  • wave-particle duality: neutrons have particle-like and wave-like properties
  • mass: mn = 1.675 x 10-27 kg = 1.00866 amu. (unified atomic mass unit)
  • charge = 0
  • spin =1/2
  • magnetic dipole moment: μn = -1.9 μN, μp = 2.8 μN, μe ~ 103 μn,
  • velocity (v), kinetic energy (E), temperature (T), wavevector (k),

wavelength (λ)

THE NEUTRON

As a particle

05/09/2017

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15

  • velocity (v), kinetic energy (E), temperature (T), wavevector (k),

wavelength (λ) THE NEUTRON

As a particle

05/09/2017

 

n n B n

m / (h/λ m / π hk/ T k / v m E 2 ) 2 2 2

2 2 2

   

 

m L A λ μ v L tof

         sec 253

  • Neutron energy determines velocity and therefore time-of-flight (tof)
  • ver a given distance i.e. tof  energy determination
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16

THE NEUTRON

As a probe

05/09/2017

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  • Wavelengths on the scale of inter-atomic distances:

Å - nm wavelengths to measure Å - mm distances/sizes nl = 2dsin

  • Energies comparable to structural and magnetic

excitations: meV neutrons to meaure neV – meV energies

  • Neutral particle – gentle probe, highly penetrating

(e.g. 30 cm of Al), no radiation damage

  • Magnetic moment (nuclear spin) probes magnetism
  • f unpaired electrons (N.B. me ~ 1000x mN)

THE NEUTRON

As a probe

05/09/2017

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  • Neutron flux at reactor core
  • 1.5 x 1015 n/cm2/s
  • Flux at an instrument sample position
  • 108 n/cm2/s

 10-6 n/nm2/s 1 n/nm2/ms 10-6 - 10-3 n/nm3 (depending on v)

  • On these time and length scales,

neutrons are being scattered one at a time

  • Need wave-particle duality of

neutrons THE NEUTRON

As a probe – interacting with matter – scattering from at atom

05/09/2017

source plane waves in scattering system interference pattern in front of detector spherical waves emitted by scattering centres

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  • Nuclear size << neutron

wavelength  point-like s-wave scattering

  • b is the scattering length (‘power’)

in fm

  • #neutrons scattered per second

per unit solid angle : 2r2d ds /d = b2

  • s is the cross-section: 4pb2 (in

barns) THE NEUTRON

As a probe – interacting with matter – (elastic) scattering from a single fixed nucleus

05/09/2017

  • b eik f .r

r

V r

( ) = 2ph2

mr b d r

( )

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  • Q is called momentum

transfer

  • Q-dependence (eg angle)

gives info about atomic positions THE NEUTRON

As a probe – interacting with matter – scattering from a set of nuclei

05/09/2017

i f R R . Q i k j k j

k k Q e b b dΩ dσ

k j

           

  

  

 ,

source plane waves in scattering system interference pattern in front of detector spherical waves emitted by scattering centres

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  • Set of N similar atoms/ions –

spins/isotopes are uncorrelated at different sites

  • b depends on spin/isotope
  • Average is ‹b›
  • Incoherent scattering gives a Q

independent background

  • But it can be useful to probe the

dynamics of single particles (later) THE NEUTRON

As a probe – interacting with matter – scattering from a set of identical nuclei – coherent and incoherent scattering

05/09/2017

  

N

b b e b dΩ dσ

j,k R R iQ

k j

2 2 2

  

 

 

2 2 2

4 4 b b π σ b π σ

incoh coh

  

2 2

4 4

inc incoh coh coh

πb σ πb σ  

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22

  • If single isotope and zero nuclear spin,

no incoherent scattering

  • If single isotope and non-zero nuclear

spin I

  • nucleus+neutron spin: I+1/2 and I-1/2

scattering length b+ and b-

  • To reduce incoherent scattering

(background):

– use isotope substitution – use zero nuclear spin isotopes – polarise nuclei and neutrons

THE NEUTRON

As a probe – interacting with matter – scattering from a set of identical nuclei – coherent and incoherent scattering

05/09/2017

 

 

 

   Ib b I I b 1 1 2 1

    

2 2 2 2

1 2 1

 

    b b I I I b b

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THE NEUTRON

Scattering lengths

05/09/2017

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THE NEUTRON

Scattering lengths can be positive or negative (nuclear physics)

05/09/2017

  • Positive b (most nuclei): phase change
  • Negative b: no phase change at scattering point
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THE NEUTRON

Scattering lengths can be positive or negative  Contrast matching

05/09/2017

: = +

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  • Absorption – neutron capture
  • Several strong absorbers:

He, Li, B, Cd, Gd,…

  • Isotope dependent – choose to

your advantage THE NEUTRON

As a probe – interacting with matter - absorption

05/09/2017

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  • How to detect a weakly interacting,

neutral particle?

  • With a neutron absorber and measure

the resulting signal THE NEUTRON

As a probe – interacting with matter - absorption - Neutron detection

05/09/2017

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28

THE NEUTRON

Scattering and absorption cause attenuation of a neutron beam  imaging

05/09/2017

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THE NEUTRON

Scattering and absorption cause attenuation of a neutron beam  imaging

05/09/2017

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  • Interaction with nuclei:

– short range interaction  angle independent scattering (no form factor) – scattering length can be positive or negative ( contrast variation) – depends on isotope ( selectivity) and nuclear spin – Coherent and incoherent scattering – strength and weakness – Scattering contrast different from X-rays, favours light atoms

  • A gentle probe - meV neutron beam does not cause radiation damage

like a ~10 keV photon beam (what about XFEL!)

  • Magnetic moment probes magnetism of unpaired electrons

THE NEUTRON

As a probe – interacting with matter - summary

05/09/2017

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INSTRUMENTS & SCIENCE

Time and length scales

05/09/2017

?

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THE ILL’S INSTRUMENT SUITE

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Based on

  • Born approximation – kinematic theory: neutron

wavefunction un-perturbed inside sample

  • Fermi’s Golden Rule to calculate transitions of

neutron (k) and system (l) from initial and final state

  • Hamiltonian to describe the system states (l)

GENERAL EXPRESSION FOR SCATTERING FROM A COMPLEX SYSTEM

Deriving the general scattering function

05/09/2017

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  • Experiment measures double differential cross-

section which is simply related to S(Q,w) (or I(Q,t))

  • S(Q,w) is the double Fourier transform of the time-

dependent pair-correlation function GENERAL EXPRESSIONS FOR SCATTERING FROM A SET OF MOVING ATOMS

Deriving the scattering function – end up with (after much algebra and manipulations!)

05/09/2017

 

) , ( 2 1 exp exp exp 2 1

2 2

w w

      

                               

 

Q S π k k dΩ dE σ d dt t i (t) R Q i ) ( R Q

  • i

b b π k k dΩ dE σ d

i f +

  • k

j jk k j i f

 

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35

  • For a simple system with a single element but different b’s

GENERAL EXPRESSIONS FOR SCATTERING FROM A SET OF MOVING ATOMS

Deriving the scattering function – end up with – coherent & incoherent contributions

05/09/2017

 

 

     

                   

jk +

  • k

j i f coh coh f

dt t i (t) R Q i ) ( R Q

  • i

π k k π σ dE dΩ σ d w exp exp exp 2 1 4

2

 

 

     

                   

j +

  • j

j i f incoh incoh f

dt t i (t) R Q i ) ( R Q

  • i

π k k π σ dE dΩ σ d w exp exp exp 2 1 4

2

  • Scattering function determined by positions R of different atoms at

different times t

  • Incoherent scattering can be useful: it measures the correlation

between the same atom at different times  single particle dynamics

  • diffusion
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  • Q=kf - ki, ħw=Ef – Ei (E ~ k2, k =

2p/l)

  • Elastic scattering:

vary Q without changing w Ei = Ef vary 2 (monochromatic) vary |E| fix 2 (t.o.f.)

  • Quasi/in-elastic scattering:

vary w, normally Q will also change vary Ei or Ef and/or 2 GENERAL SCATTERING EXPERIMENT

Scattering triangle – handling Q and w

05/09/2017

sample

ki ki kf Q=kf-ki 2

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  • How to measure the energy of a neutron

beam?

  • Or, how to monochromate a beam?
  • Measure l with Bragg reflection

nl = 2dsin d = distance between scattering planes

  • Use neutron t.o.f. (or precession of

neutron magnetic moments in a magnetic field) GENERIC INSTRUMENT

Energy selection

05/09/2017

 

m L A λ μ v L tof

         sec 253

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DIFFRACTION

Instruments (don’t measure the final energy!) – D2b & LADI

05/09/2017

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DIFFRACTION

Example – Formation and properties of ice XVI

  • btained by emptying a type sII clathrate hydrate

05/09/2017

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DIFFRACTION

Instruments (don’t measure the final energy!) – D2b & LADI

05/09/2017

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DIFFRACTION

Example – Improving drug design: HIV-1 Protease in complex with clinical inhibitors (sample ~50 mg)

05/09/2017

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In previous scattering expressions R=R0+dR(t) For normal modes: dR(t)  displacement vectors e & frequencies w Coherent scattering - Phonons:

  • Short range coupling gives long range correlations
  • Dispersion as a function of q (or wavelength) – guitar string!

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Simplified expressions for the scattering function – coherent scattering

05/09/2017

     

                      

     

 

τ q Q δ ω ω δ / / n ω e Q W M v π k k π σ dE dΩ σ d

s τ s s s s i f coh coh f

  2 1 2 1 2 exp 2 1 2 4

3 1 2

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43

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Instruments – varying ki & kf – TAS, TOF

05/09/2017

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SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – phonon lifetimes in thermoelectrics - Complex Metallic Alloy - Al13Co4 Quasicrystal approximant

05/09/2017

[001]

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SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – phonon lifetimes in thermoelectrics - Complex Metallic Alloy - Al13Co4 Quasicrystal approximant

05/09/2017

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In previous scattering expressions R=R0+dR(t) For normal modes: dR(t)  displacement vectors e & frequencies w Incoherent scattering - Internal (molecular) modes:

  • No long range correlations due to weak coupling
  • No dispersion

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Simplified expressions for the scattering function – incoherent scattering

05/09/2017

     

 

        

   r r r r r incoh s s s s i f incoh f

W e Q M π σ ω / / n ω ω δ k k dE dΩ σ d 2 exp 1 4 2 2 1 2 1

2 1 2

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47

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Instruments – TOF, Lagrange

05/09/2017

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48

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – endofullerenes

05/09/2017

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SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – endofullerenes

05/09/2017

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50

SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Instruments – Back-Scattering

05/09/2017

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SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – oxide ion conductors

05/09/2017

Anode Electrolyte Cathode

H2 O2 H2O

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SPECTROSCOPY – TIME/FREQUENCY DOMAIN

Example – oxide ion conductors

05/09/2017

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GENERIC INSTRUMENT

Energy selection - precession of neutron magnetic moments in a magnetic field (depends on t.o.f. in B)

05/09/2017

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54

MAGNETISM

Structure and dynamics – double differential cross-section

05/09/2017

 

f i f f i i

λ λ f i i i i m f f f n i f λ σ λ σ f

E E E E δ λ σ k V λ σ k π m k k dΩ dE σ d                  

 2 2 2 2

2 

As for interactions with nuclei but

  • Neutron spin probes local magnetic fields due to electron spin

and orbital contribution

  • Atomic form factor – scattering from an atom is angular

dependent due to electron cloud

  • No incoherence effects
  • N.B. s and V in these equations

                   

2 2

1 2 4 R R p R R s curl μ μ γ π μ B μ V

B N n m

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55

MAGNETISM

Polarised neutrons – separate nuclear and magnetic signals & more precise information on magnetic structures

05/09/2017

  • Typically measure 4 polarised

scattering channels: uu, dd, ud, du

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56

MAGNETISM

Polarised neutrons – separate nuclear and magnetic signals & more precise information on magnetic structures

05/09/2017

  • Polarised (optically pumped) 3He

selectively absorbs one neutron spin state – more versatile polariser

  • Cryopad allows full control of incident and

scattered neutron polarisation – spherical polarimetry

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57

MAGNETISM

Example – Ground state selection under pressure in the quantum pyrochlore magnet Yb2Ti2O7

05/09/2017

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58

MAGNETISM

Example – How do electrons/spins organise in a triangular lattice? Spins pair into quantum-mechanical bonds and fluctuate…

05/09/2017

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59

The neutron Is Highly penetrating Interacts with nuclei – favourable for light atoms (H, Li, O,…) Incoherent scattering is ideal for proton dynamics Isotopes provide selectivity – contrast matching Interacts with unpaired electrons – magnetism Probes 15 orders of magnitude in length & 10 in time Neutron sources have relatively low intensity and are only available in large scale facilities – ILL, ISIS, PSI, FRM2 in Europe, SNS & NIST in US SUMMARY – KEY MESSAGES

05/09/2017

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60

  • Introduction to the Theory of Thermal Neutron Scattering
  • G.L. Squires Reprint edition (1997) Dover publications ISBN 04869447
  • Experimental Neutron Scattering
  • B.T.M. Willis & C.J. Carlile (2009) Oxford University Press ISBN 978-0-19-851970-6
  • Neutron Applications in Earth, Energy and Environmental Sciences
  • L. Liang, R. Rinaldi & H. Schober Eds Springer (2009) ISBN 978-0-387-09416-8
  • Methods in Molecular Biophysiscs
  • I.N. Serdyuk, N. R. Zaccai & J. Zaccai Cambridge University Press (2007) ISBN 978-0-521-81524-6
  • Thermal Neutron Scattering
  • P.A. Egelstaff ed. Academic Press (1965)

ADDITIONAL READING

Search the web! Plus…

05/09/2017

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I N S T I T U T L A U E L A N G E V I N

ENJOY YOUR MONTH ON THE EPN CAMPUS

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