Dr. Gavin Mountjoy, University of Kent, Canterbury, UK

Neutron techniques forstudying the structure of materials

Nell'ambito del programma "Visiting Professor", finanziato dalla Regione Sardegna.

Outline

1) IntroductionIntroduction

2) TheoryTheory of neutron interactions

3) ExperimentExperiment requirements for neutrons

4)4) TECHNIQUES:TECHNIQUES:

4.1) Neutron diffraction

4.2) Small angle neutron scattering

4.3) Neutron reflectometry

4.4) Inelastic neutron scattering

4.5) Magnetic neutron scattering

5) SummarySummary

1) Introduction

Study of materials

• our culture depends on materials

...relationships between the microstructure and the macroscopic properties

... are, in essence, what the materials science is all about.

This is best represented by the "materials science triangle": synthesissynthesis--microstructuremicrostructure--properties.properties.

• materials science depends on knowledge of structure

Techniques for studying structure use a Techniques for studying structure use a probeprobe::

probeprobe example techniquesexample techniques can also usecan also use

light:light: •• infrared spectroscopy infrared spectroscopy →→ neutronsneutrons

•• Raman spectroscopyRaman spectroscopy

XX--rays:rays: •• XX--ray diffractionray diffraction →→ neutronsneutrons

•• small angle neutron spectroscopysmall angle neutron spectroscopy →→ neutronsneutrons

•• XX--ray absorption spectroscopyray absorption spectroscopy

electrons: electrons: •• electron microscopyelectron microscopy

Structural techniques

Interaction of probe with material

• different probes → different interactions

• understanding of interaction → information about structure

probe:

interaction: rotation vibration electron transfer

molecule:

Properties of neutrons

• neutrons are fundamental particles – only found in the nucleus

– same size and mass as a proton

• neutrons have no electric charge– have no chemical properties

– are extremely penetrating though atoms

• neutrons interact only with nuclei of atoms– collide and transfer energy like gas molecules

– describe by energy E (meV) = 5.19 v2 where v (kms-1) is velocity

Sources of neutrons

• natural sources of neutrons– only radioactive elements, e.g. uranium

– neutron outside the nucleus will disappear after 18 minutes!

• artificial processes which produce neutrons– (1) nuclear fission: sustained reaction of radioactive elements, e.g. uranium

– (2) spallation: disintegration of heavy elements, e.g. tantalum

• artificial sources of neutrons– (1) nuclear reactor source: e.g. ILL laboratory in France

– (2) spallation source: e.g. ISIS laboratory in UK

Encountering neutrons

• neutrons are very harmful to living tissue– are extremely penetrating through materials

– require many metres of shielding

• in everyday life– not encountered!

• in laboratory– not encountered!

– note: α, β and γ radiation does not contain neutrons

Not to be confused with

• Mössbauer spectroscopy

• Nuclear magnetic resonance (NMR)

• Mass spectroscopy (e.g. isotopic analysis)

• these techniques are for studying nuclei but don't use neutrons

2) Theory of neutron interactions

Interactions of neutrons with nuclei of atoms

(1) elastic scattering – no energy transfer

(2) inelastic scattering – some energy transfer

(3) absorption – neutron is "captured" by nucleus to form a new nucleus

Notes on absorption:

– absorption increases strongly as energy of neutron decreases

– the new nucleus may be unstable and then undergo radioactive decay

*

elastic

inelastic

absorption

Neutron scattering cross sections

• amount of scattering is quantified as "cross section"– an imaginary "target" which the neutron can strike

– units of barns (10-28 m2) per atom

• scattering cross sections are tabulated– scattering cross sections vary randomly for different elements

neutron

X-rays

neutrons

Some complications

• incoherent scattering has an unpredictable variation– natural elements contain a mixture of different (nuclear) isotopes

– scattering also depends on spin of neutron and spin of nucleus

• coherent scattering is the part which is the same for all nuclei

• neutrons don't have electric charge, but do have a magnetic moment– neutrons can be scattered by "magnetic" elements, e.g. iron

– iron has unpaired electrons which have a magnetic moment

interactions betweenmagnetic moments

Neutron scattering from materials

• materials contain many atomic nuclei– not isolated atomic nuclei

– but molecules and solids

• need to include quantum mechanical effects

(i) neutrons have wave properties– elastic scattering → scattering of waves

(ii) molecules and solids have energy levels– inelastic scattering → transitions between energy levels

neutron

isolated atomic nuclei, i.e. gas

Elastic neutron scattering

• neutron wavelength λ (Å) = 9.11 ÷ E1/2 (meV)– wavelength λ increases as energy E decreases

• diffraction– example of "two slit" experiment

– waves scattered from two atoms at distance d

• scattering angle 2θ is inversely proportional to distance d– larger distance d gives smaller scattering angle 2θ

– Bragg's law: 2dsinθ = nλ

d2θ

probeprobe example techniquesexample techniques can also usecan also use

XX--rays:rays: •• XX--ray diffractionray diffraction →→ neutronsneutrons

• for diffraction want λ~Å

• need "thermal" neutrons

with E~kBT (0.025 eV)

Inelastic neutron scattering• neutron transfers energy to material

– energy causes motion of atoms:

translation, rotation, and vibration

• different vibrational modes have different energies– energy Evib (meV) = 0.124 ν (cm-1)

where ν (cm-1) is frequency of vibration,

K is bond strength, and µ (amu) is mass

*

( )µ

υK

cm 29131 =−

probeprobe example techniquesexample techniques can also usecan also use

light:light: •• infrared spectroscopy infrared spectroscopy →→ neutronsneutrons

• for vibrational spectroscopy want E~meV

• need "thermal" neutrons

with E~kBT (0.025 eV)

3) Experimental methods

Neutrons from nuclear reactor

• nuclear reactor source:– require nuclear fuel, e.g. uranium

– sustained nuclear fission reaction

– neutrons with range of energies

– neutrons produced continuously

• ILL laboratory, Grenoble, France

Neutrons from spallation source

• spallation or "pulsed" source:– require heavy nuclei, e.g. tantalum

– disintegration of nuclei by proton beam

– more high energy neutrons

– neutrons produced in pulses

• ISIS laboratory, Harwell, UK

Comparison of sources

Other equipment

• moderator– thermal bath at room temperature to reduce neutron energy E~meV

• monochromator– Bragg diffraction from a crystal to determine neutron wavelength λ

• neutron detectors– gas ionisation

– scintillator

– semiconductor

• samples– typically 1-10 grams

– sample containers to control temperature and pressure

Data analysis

• detectors record N counts for each point of data– counting statistics has random noise of N1/2

– counting times: several hours per sample

– also measure: empty container, background, calibration standard

• remove unwanted contributions to data– absorption: normally small

– multiple scattering: can be large

– inelastic scattering: (not wanted in diffraction)

hydrogen can be a big problem

– can replace hydrogen (11H0) with deuterium (2

1H1) if necessary

TECHNIQUES

4.1) Neutron diffraction• diffraction

– interference of elastically scattered waves

– same in principle as X-ray diffraction

• Bragg's law: 2dsinθ = nλ– 2θ is scattering angle

– d is interatomic spacing

– larger distance d gives smaller scattering angle 2θ

• measure counts as a function of 2θ

gives diffraction "pattern" or "spectrum"

• scattering vector Q is commonly used instead of 2θ– Q = 2π/d = 4πsinθ/λ

d2θ

0

5

0 2 4 6 8 10

G(r)

r (A)

-2

0

2

4

0 10 20 30 40

Q(S(Q

)-1)

Q (A-1)

• Fourier transform diffraction pattern– function of Q (or 2θ) → function of r (or d)

• example: neutron diffraction of SiO2 glass– Fourier transform shows peak at r=1.6A corresponding to Si-O bond

N. Afify et al (2009) PRB 79 024202

measured scattering as a function of Q(Å-1)

Information about distances d

analysed distancesas a function of r(Å)

• diffraction from crystalline materials– (h,k,l) planes of atoms with spacings dhkl = a ÷ (h2+k2+l2)1/2

– gives series of Bragg peaks 2θhkl

– crystal structure can be found using Rietveld refinement

• example: LiMn2O4

http://www.phy.cmich.edu/people/petkov/nano.html

Fouriertransform

Neutron diffractometer

• measure counts as function of λ and 2θ– λ depends on neutron energy

– 2θ depends on detector position

• nuclear reactor source– λ fixed by monochromator

– 2θ varied by moving detector

• spallation or "pulsed" source– fixed 2θ due to fixed detector

– range of λ due to neutron energies

2θ

λ

Example 1: ferrihydrite

• iron oxide phases – important in technology and in the environment

• ferrihydrite (FeOOH) – poorly crystalline iron oxyhydroxide phase

– structure is uncertain and still being discussed

The Structure of Ferrihydrite,

a Nanocrystalline Material

F. Marc Michel et al (2007) Science, Vol. 316, pp. 1726

Evaluation of the structural model

for ferrihydrite

A. Manceau (2009) Clay Minerals, Vol. 44, pp. 19

Neutron diffraction of ferrihydrite

• study by Anna Corrias et al, University of Cagliari– measured using GEM instrument at ISIS laboratory

• additional information compared to X-ray diffraction– due to neutron scattering cross sections

– no O-O contributions below 3Å

X-ray diffraction neutron diffraction

Example 2: phosphate glasses

• phosphate glasses have a network of PO4 tetrahedra

• use diffraction to find interatomic distances d– e.g. PO4 tetrahedra has 4 P-O bonds with bond lengths 1.5Å

– cations like Ca have variable coordination to oxygen

• advantages of neutron diffraction– additional information due to neutron scattering cross sections

– good counting statistics to large 2θ gives more precise d

Ca

P

P-Obondlengths

P-Obondlengths

– measured using

GEM instrument

at ISIS laboratory

X-ray

K.M. Wetherall et al (2009)JPCM Vol. 21 pp. 035109

neutron

Neutron diffraction with isotopic substitution• example: 10mol% silver-doped phosphate glass

– normal material contains elements with a mixture of isotopes

– isotopic enrichment gives scattering cross section specific to isotope

– silver isotopes 107Ag and 109Ag have cross sections of 0.57 and 0.17 barns

– comparison of neutron diffraction shows distances involving silver

R.M. Moss et al (2008)Adv. Func. Mat. Vol. 18 pp. 634

Advantages of neutron diffraction

compared to XRD:

• scattering cross section– has no atomic number dependence

• strong scattering for hydrogen

• neutrons are highly penetrating– large samples

– special sample environments

e.g. high temperature or high pressure

• but expensive

residual elastic strain in a 12 mm thick steel plate.

4.2) Small angle neutron scattering

• distances d much larger than interatomic distances, i.e. d>>Å– principle is the same as neutron diffraction

– scattering angle 2θ is much smaller

• large scale structure in molecular and solid materials– examples:

zeolitesmesoporous silicas

block copolymersamphiphilic liquids

clustersaggregates

Example 1: oil in ionic liquids• oil/ionic liquid (IL) microemulsion

– ionic liquids are salts which are molten at room temperature

– oil droplets included to enhance solubility of apolar compounds

• small angle neutron scattering gives microemulsion structure– measured using LOQ instrument at ISIS laboratory

S.E. Rogers (2009) Materials Today "Neutron Scattering Special Issue" pp. 92

Example 2: amorphous calcium phosphate

• amorphous calcium phosphate– a biomineral precipitated from solutions containing PO4 and Ca

– forms aggregates with main particles ~100 nm in diameter

– measured using

LOQ instrument

at ISIS laboratory

X-ray neutron

4.3) Neutron reflectometry

• principle is similar to reflection of light

• elastic scattering from surface or interface – change in scattering cross section at the boundary

– causes interference of scattered waves

http://www.ncnr.nist.gov/AnnualReport/FY2003_html/RH10/

4.4) Inelastic neutron scattering

• measure counts as function of

neutron change in energy ∆E– due to change in wavelength ∆λ

– determine λ before and λ' after

(requires monochromator after)

• conservation of energy– neutron ∆E = vibration Evib

• gives vibrational spectrum– energy units of meV

– or frequency units of cm-1 or THz

inelastic neutron scattering spectrometer

Example 1: polymers

• different vibrational modes

have different energies– e.g. 1500cm-1

• inelastic neutron scattering cross sections are simple– infrared spectroscopy: require change in dipole moment

– Raman spectroscopy: require change in polarisability

infrared

Raman

neutron

polyethylene

In-plane bending or scissoring(δs CH2)

• advantages of neutrons– see all vibrational modes

– good detail for low energy vibrations

– strong scattering for hydrogen

isotactic

polypropylene

atactic

• high frequency part of spectrum– vibrations of molecular fragments, e.g. CH2 bend at ~1500cm-1

• low frequency part of spectrum– vibrations of entire molecule(s), or lattice vibrations

Vibrational modes in crystalline solids

• vibrational modes are called "phonons"– atoms vibrate together in waves called "phonons"

– described by energy Evib=hωvib and wavevector kvib=2π/λvib

• measure counts as a

function of neutron ∆E

and scattering vector Q– conservation requires

∆E = Evib and Q = kvib

• gives "dispersion relation"– neutron ∆E vs. Q

or phonon ω vs. k

energy hwphonon

=2π/λphonon

Example 2: aluminium

• inelastic neutron scattering gives dispersion relation (ω vs. k)– measured as dynamical structure factor S(∆E,Q)

energy hwphonon

phonon wavevector k

phonon energy hwphonon

Example 3: vibrational modes in silica glass

• silica glass (SiO2) has a network of SiO4 tetrahedra

• use inelastic neutron scattering to study vibrational modes– based on vibrational modes of SiO4 tetrahedra and Si-O-Si bridges

asym. stretch - sym. stretch - bend

asym. stretch - sym. stretch - bendO

O

OO

O

Si

Si

Si

• computer modelling has predicted the different contributions

• best to compare models with inelastic neutron scattering– because infrared and Raman cross sections are difficult to calculate

• change isotope to from O16 to O18 to change vibrational frequency– gives an experimental probe of the role of oxygen

ab initiomodelling

inelasticneutronscattering

LIGHT = O16 isotope

DARK = O18 isotope

vibrational mode due to SiO4 bendingwith less oxygen motion

– measured using

MARI instrument

at ISIS laboratory

4.5) Magnetic neutron scattering

• Example: YMn2O5

– contains Mn3+ and Mn4+ both with unpaired electrons, i.e. magnetic "spins"

– normal neutron diffraction depends only on arrangement of nuclei

– diffraction of polarised neutrons reveals orientation of magnetic "spins"

magnetic scattering

T. Perring (2009) Materials Today "Neutron Scattering Special Issue" pp. 100

Inelastic scattering

• magnetic excitations– material containing unpaired electrons with magnetic "spins"

– unpaired electrons spin together in waves

– "spin wave" defined by energy Emag and wavevector kmag

– can be measured using inelastic neutron scattering

• Example: KCuF3

– Cu2+ located along chains

has unpaired electrons

T. Perring (2009) Materials Today "Neutron Scattering Special Issue" pp. 100

5) Summary

• neutrons can be used as probes of structure– applications to neutron sources to do an experiment

• diffraction and small angle scattering – same principles as for X-rays

– advantages: neutron scattering cross sections different to X-rays

sample containers

good probe of hydrogen

• inelastic scattering– same principles as infrared spectroscopy

– advantages: all vibrational modes are visible

good details at low frequencies (lattice vibrations)

Acknowledgements

• colleagues (University of Kent):– R.C. Haworth, K.M. Wetherall

• neutron source (ISIS laboratory) :– A.C. Hannon (GEM instrument), J. Taylor (MARI instrument)

• funding organisations:– EPRSC (UK)