Geir Helgesen, Institutt for energiteknikk, 13.02.20081

Neutron:

• Uncharged elementary particle

• With an inner electric charge distribution

• Slightly heavier than a proton

• Lifetime 615 s → p + e

• Spinn S= ½

• Magnetic moment 1.91μN ~ μB/1836

• Can behave both as particle and wave

v ~ 2km/s

λ= wave length

k= wave number (vector || v), k=2π/λ

Proton - p:

2u + 1d quarks

charge= 2*(+2/3)+1*(-1/3)

Neutron – n:

1u + 2d quarks

charge= 1*(+2/3)+2*(-1/3)

λ

Geir Helgesen, Institutt for energiteknikk, 13.02.20082

....) magnons, (phonons,matter solidin stransition

energy tocomparable meV) 100(~ neutronsfor Energy

keV 4.12 )keV(

4.12)Å(

:rays-XFor

meV 81 )meV(

045.9)Å(

Å 1 Typical :neutronsFor

=⇒=

=⇒=

=

EE

EE

λ

λ

λ

For neutrons

Energy vs. wavelength

Geir Helgesen, Institutt for energiteknikk, 13.02.20083

a1) Fission

b) Spallation

Neutron production

a2) Neutron moderation

Energy spectra

liquid H2 ⇒ λ > 5 Å

λ ~ 1.8 Å

25 meV

Geir Helgesen, Institutt for energiteknikk, 13.02.20084

The JEEP-II reactor

250 kg UO2

D2O moderated

2 MW thermalpower

Geir Helgesen, Institutt for energiteknikk, 13.02.20085

Interactions of neutron and x-ray beams with matter

• Absorption – reduces beam intensity

• Refraction – bending beam when passing

• Scattering – almost all intensity transmitted in certain spatial directions dependent on the sample structure and orientation

Geir Helgesen, Institutt for energiteknikk, 13.02.20086

Neutron, x-ray, and electron penetration depths(intensity reduced to 1/e = 37% of original)

Geir Helgesen, Institutt for energiteknikk, 13.02.20087

NeutronsX-rays

114 μm241.4 mm22.535B

86 cm0.00364 μm402.7013Al

t1/2μ/ρ (cm/g)t1/2μ/ρ (cm/g)Density ρ(g/cm3)

ZElement

Pb

Gd

Cd

82

64

48

2.04 m !!3*10-42.5 μm24011.34

12 μm732.7 μm3307.9

57 μm144.0 μm2008.65

Absorption

( ) [ ]1/ 2

ln(2)Intensity reduced by 50%: cmt

μ ρρ

=⋅

Intensity: I(t) = I0 exp(-μt) t = ticknessμ = linear absorption coeffisient

Geir Helgesen, Institutt for energiteknikk, 13.02.20088

Scattering of neutrons

• happens in the atomic nucleus

• wave length of thermal neutrons ~ 1 Å = 0.1 nm = 10-10 m

• range of nuclear force ~ 1 fm = 10-15 m⇒ neutron is scattered from point source

• strength of scattering measured in the cross section σin unit of barn – 1 barn = 10-28 m2

• σ-values are measured experimentally– impossible to calculate in practice

• σ dependent on:i) atomic elementii) isotope of same elementiii) nuclear spin state

Scattering of x-rays

• scattered from the electrons around the nucleus by dipolar radiation

• depends on number of electrons and electron distribution

• scattering cross section often measured in units of Thomson length r0r0 = e2/mc2 = 2.8*10-15 m (Note: r0

2 ~ 0.1 barn)

Geir Helgesen, Institutt for energiteknikk, 13.02.20089

Geir Helgesen, Institutt for energiteknikk, 13.02.200810

Geir Helgesen, Institutt for energiteknikk, 13.02.200811

What can be studied by neutron techniques?

Geir Helgesen, Institutt for energiteknikk, 13.02.200812

Neutron detection processes

Two main detection techniques:

3He gas

or BF3

6Li

or ZnS

He-3: Scint. counter:

- high efficiency (75%) - high countrate

- low γ-sensitivity - can be big

Geir Helgesen, Institutt for energiteknikk, 13.02.200813

Neutron detectors

He-3 detectors – 1-dimensional 2-dimensional detectors- position sensitive

collect signal at both ends

Geir Helgesen, Institutt for energiteknikk, 13.02.200814

What can we learn from neutron scattering?

• Material structure

• crystal steructure

• disordered materials, alloys(grain size, form ….)

• structural defects

• liquid structure(molecular distances and orientations)

• Dynamics

• molecular rotations (NH2-, CH3-, …)

• vibrations

• sound waves – phonons in solids

• magnetization waves – magnons inmagnetic matter

• diffusion

Geir Helgesen, Institutt for energiteknikk, 13.02.200815

Geir Helgesen, Institutt for energiteknikk, 13.02.200816

Geir Helgesen, Institutt for energiteknikk, 13.02.200817

Elastic scattering

Model:

Two-axis diffractometer:

typical length scale in the sample L=1-5 Å

Bragg reflection from single crystal → one λ

i) measure intensity I(ϕ)

ii) calculate structure from I(ϕ)

ϕ

Geir Helgesen, Institutt for energiteknikk, 13.02.200818

• Nanoscale lengths are probed.

Adapted from A.V. Belushkin, Dubna

SANS instrumentation

spectrum of λ one λ

Geir Helgesen, Institutt for energiteknikk, 13.02.200819

Inelastic scattering

Model:

Triple-axis diffractometer:

1st Bragg reflection

2nd Bragg reflection

with E3 ≠ E1

ϕ

E1, λ1

E2, λ2

E3, λ3

- typical length scale in the sample L=1-5 Å

- energy changes ΔE= 1-5 meV

Two possibilities:

i) choose θ for E3=E1, scan ϕ (elastic)

ii) choose θ for E3 ≠ E1, scan ϕ (inelastic)

Geir Helgesen, Institutt for energiteknikk, 13.02.200820

Some references:Online refs.:1. An Introduction to Neutron Scattering by R. Pynn –

www.mrl.ucsb.edu/~pynn/2. NIST Neutron Techniques – www.ncnr.nist.gov/programs/

and www.ncnr.nist.gov/summerschool/3. Neutron Scattering Reference – www.neutron.anl.gov/reference.html4. Introduction to Neutron Powder Diffractometry –

www.iucr.org/iucr-top/comm/cteach/pamphlets/19/5. Introduction to Neutron and X-Ray Scattering by S.K. Sinha –

www.dep.anl.gov/nx/lectrnotes.pdf6. Interactive Tutorial about Diffraction –

www.pa.msu.edu/~proffen/teaching/teaching.html7. Neutron Diffraction by A. Hewat –

www.ill.fr/dif/AlanHewat/Budapest-Neutron-Diffraction.pdf8. European Neutron Portal – www.physik.uni-kiel.de/kfn/infos/cnews.php

Books:1. ”Neutron and Synchrotron Radiation for Condensed Matter Studies”, vol. 1-3

(Springer/EDP, 1993 – ISBN 2-86883-185-0)2. ”Introduction to the Theory of Thermal Neutron Scattering” by G.L. Squires

(Cambridge Univ. Press, 1978)3. ”Neutron Scattering”, Los Alamos Science, no. 19, 1990

(http://library.lanl.gov/cgi-bin/getfile?number19.htm)