April 19, 2023 1

Small-Angle Neutron Scattering in Materials Science

1 Nuclear Physics Institute and Research Centre Řež near Prague, Czech Republic2 IfW, TU Braunschweig, Germany

3 Helmholtz-Zentrum Berlin, Germany4 TU München, Forschungsneutronenquelle Heinz Maier-Leibnitz, Garching, Germany

5 ILL Grenoble, France

P. Strunz1, D. Mukherji2, G. Schumacher3, R. Gilles4 and A. Wiedenmann5

Outline:SANS and its applications to materials scienceExamples

–DT706 superalloy–core-shell nanoparticles –Porosity in thermal barrier coating

Projects supported by the European Commission under the 6th Framework Programme through the Key Action: Strengthening the European Research Area, Research Infrastructures. Contract n°: RII3-CT-2003-505925 '

April 19, 2023 2

Small-Angle Neutron Scattering

morphology size distance orientation volume fract.Scattering Length Density

ρ(r)

Q: Scattering vector (momentum transfer) magnitude Q roughly proportional to the scattering angle

Scattering curve. Evaluation:

2

– coherent elastic scattering on inhomogeneities of the size ≈ 10-20000 interatomic distances (i.e. 10 Å - 2 m) to small angles (up to 15°)

Scattering contrast (Δρ)2

April 19, 2023 3

Small-Angle Neutron Scattering – data analysis

morphology size distance orientation volume

fraction

or

April 19, 2023 4

Properties of neutron thermal neutrons:

wavelength 1.8 Å (0.18 nm) and to velocity 2200 m/s

cold neutrons: typically 9 Å and 437 m/s

no charge, weak interaction with matter

magnetic moment

non-monotonic dependence of scattering amplitude on at. number (and even isotop)

Why investigation of matter using neutrons?

interatomic distances and sizes of nanostructures in condensed matter similar to wavelength

often very small absorption => large depths (typically mm), volumes, in situ studies

study of magnetic structures

isotopic contrast variation, determination of “light” and “neighboring” elements

April 19, 2023 5

Applications: What can be investigated?

solid state physics - microstructure– Alloys, ceramics, glasses– Porosity, voids, microcracks– Semipermeable membranes– Porosity in ceramics– Phase transformations– Precipitates in metals, inclusions– Precipitate formation/dissolution in alloys– Nanoscaled materials, nanoparticles– Interfaces and surfaces of catalysts– Impurities in silicon

structural biology (biological macromolecules)– structure of biological macromolecular complexes e.g. DNA, protein, viruses; labeled subunits;

multiprotein complexes; stoichiometry of interactions, molecular weights; lipids.

chemistry and mesoscopic systems– colloids; micelle systems and microemulsions; polymers; membranes; gels

magnetism– Magnetic/non-magnetic inhomogeneities– Ferofluids– Flux line lattices in superconductors

sample environment– orientation and deformation by shear flow– experiments under high pressure– magnetic field, electric field– mechanical load– high/low temperatures– adsorption facilities

any structural, compositional or magnetic particle/inhomogeneity/ microstructural entity with size 1nm-2μm giving scattering contrast

April 19, 2023 6

SANS experimental techniquePin-hole facility

Typical rangeQ: (0.001 – 0.3) Å-1

D: (3000 - 10) Å

SANS II facility of SINQ, Paul-Scherrer Institute (PSI) Villigen, Switzerland

neutron guide

sampleexchangablediaphragms

detectorvelocity selector

Beam-stopVacuum chambers

neutron guides

April 19, 2023 7

Use neutrons (SANS) when: 1) bulk information or non-destructive testing is needed 2) sample cannot be prepared in the thin form necessary

for synchrotron without influencing the microstructure 3) absorption/scattering in sample-environment windows

too high for X-ray (in-situ experiments at extreme conditions)

4) scattering contrast for X-ray too low or does not allow to resolve details (easier contrast variation for neutrons)

5) magnetic microstructure

B

q

in D2O in H2O

Contrast variation

April 19, 2023 8

SANS magnetic scatteringExample of formula: scattering on homogenneous feromagnetic particle (M(r) = const.), polarized neutrons

2222sin2 MNMNPP ΔPΔΔΔQFVcQ

d

d

ΔN ... nuclear contrast

ΔM ... magnetic contrast

F(Q) ... common formfaktor

VP ... volume of one particle

cP ... volume fraction

... Angle between Q a MP ... beam polarization

B

Q

isotropic component component modulated by sin2

-0.2 -0.1 0.0 0.1 0.2-0.2

-0.1

0.0

0.1

0.2

QX, nm-1

QY,

nm

-1

BApplication:• voids and precipitates

in ferromagnetic alloys• radiation damage of

reactor vessel steels• ferrofluids• flux lines in superconductors...

April 19, 2023 9

Vortex lattice in type-II superconductors

•Higher magnetic field => field penetrates, flux is quantized into tubes •Generally: vortices move => resistance•Zero resistance <= enough flaws to "pin" the vortices: vortex lattice (2D)•Nature of vortex lattice and role of pinning: investigation also by SANS

•Higher magnetic field => field penetrates, flux is quantized into tubes •Generally: vortices move => resistance•Zero resistance <= enough flaws to "pin" the vortices: vortex lattice (2D)•Nature of vortex lattice and role of pinning: investigation also by SANS

R. Gilardi et al.: Small Angle Neutron Scattering Study of Vortex Pinning in High-Tc Superconductor

(La2−xSrxCuO4 (x=0.17, Tc=37 K). SINQ - experimental reports 2003.

K. Harada et al., Hitachi Lab, Science 274, 1167

(1996)

April 19, 2023 10

Ni-base superalloys

Composition: e.g. Cr 8.0, Co 4.0, Mo 0.5, Al 5.7, W 9.0, Ti 0.7, Ta 5.7, Ni balance; in wt%

High creep resistance

High-temperature applications

Two-phase microstructure:– -phase matrix strengthened by ’

precipitates (size nm-m)– optimized by heat treatment

– essential for mechanical properties

1. superallos are used at high-temperatures

2. they are processed before the use at HT

=> investigation of HT microstructure

April 19, 2023 11

size distribution (volume weighted)

SCA4335b1/4

HT experiment

melting point: 1350°C

April 19, 2023 12

In-situ SANS investigation of high-temperature precipitate morphology in

polycrystalline Ni-base superalloy DT706

new development of Ni-base superalloys: - improving their microstructural stability

- preserving their good mechanical properties

=>

Need to know the microstructure during heat treatment => the use of (in-situ) SANS

D. Mukherji, D. Del Genovese, P. Strunz, R. Gilles, A. Wiedenmann and J. RöslerJ. Phys.: Condens. Matter 20 (2008), 104220 (9pp)

April 19, 2023 13

Ex-situ treated samples DT706, SANS

We can model well the data => in-situ behavior can be well assessed

Volume fraction 5% 20% 13% 24%

April 19, 2023 14

DT706: in-situ SANS (HT furnace)

00:00 12:00 24:00 36:00 48:00 60:00 72:00 84:00-1000500

600

700

800

900

1000

1100

1200

0.5 K/min4 K/min20 K/min

temperature

Tem

pera

ture

(°C

)

Aim: Cooling rate (from solution treatment temperature) influence on precipitate microstructure

1E-3 0.01 0.10.01

0.1

1

10

100

1000

Q-4

DT7064 K/min

azimuthal average

Q (Å-1)

d/d

(cm

-1sr

-1)

measured, fit 1080°C 847°C 835°C, 1 min 835°C, 4 min 835°C, 38 min 835°C, 1 h 17 min 835°C, 8 h 45 min 835°C, 9 h 25 min room temperature after

0.0 0.3 0.6 0.9 1.2 1.50.0

0.3

0.6

0.9

1.2

1.5

y (

m)

x (m)0.0 0.3 0.6 0.9 1.2 1.5

x (m)

Model: η and γ’

April 19, 2023 15

20:00 24:00 28:00 32:00 36:00 40:00 44:00 48:00200

400

600

800

1000

1200

14001353K, 1080°C

1108K835°C

1163K890°C

1133K860°C

tem

pe

ratu

re (

K)20 K/min

0.5 K/min

Temperature

time

20:00 24:00 28:00 32:00 36:00 40:00 44:00 48:000.002

0.004

0.006

0.008

0.010

0.012

0.014

Integral intensity

Inte

gra

l in

ten

sity

(re

l.un

its)

time

Size (γ‘)

00:00 04:00 08:00 12:00 16:00 20:00 24:00 28:00

400

500

600

700

800

900

1000

1100

1200

1300

1400

Te

mp

erat

ure

(K

) Temperature

00:00 04:00 08:00 12:00 16:00 20:00 24:00 28:000

200

400

600

800

1000

1200

1400

size - '

Time (hours)

size

(Å

)

after coolling rate 0.5 K/min after coolling rate 2.3 K/min after coolling rate 4 K/min after coolling rate 20 K/min

Integral intensity: determination at which temperature η and γ’ start to precipitate

29:00 30:00 31:00 32:00 33:00200

400

600

800

1000

1200

1400

1108K835°C

1138K865°C1160K

887°C

1134K861°C

tem

pe

ratu

re (

K)

0.5 K/min

Temperature

time

29:00 30:00 31:00 32:00 33:000.003

0.004

0.005

0.006

0.007

Integral intensity

Inte

gra

l in

ten

sity

(re

l.un

its)

time

April 19, 2023 16

Volume fraction

• increase in η at γ’ expense

• EM supports this observation00:00 04:00 08:00 12:00 16:00 20:00

0

500

600

700

800

900

1000

1100

1200

1300

1400

1500

Te

mp

era

ture

(K

)

Temperature

00:00 04:00 08:00 12:00 16:00 20:000.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

DT706_1cooling rate 4 K/min

Volume fraction × scattering contrast

Time (hours)

Vo

lum

e f

ract

ion

× s

catt

eri

ng

co

ntr

ast

(re

l.un

its.)

GAMMA PRIME

00:00 04:00 08:00 12:00 16:00 20:00

Time (hours)

ETA

0.5 K/min

outcome Evolution of size and volume fraction for various cooling

rates. γ’ size can be tuned using the in situ SANS results

start temperature of both η and γ’ determined

indication of growth of η at expense of γ’

April 19, 2023 17

Study of Ni3Si-type core-shell nanoparticles by contrast variation

in SANS experiment

Ni-Si alloy after two different heat treatments.

P. Strunz, D. Mukherji, G. Pigozzi, R. Gilles, T. Geue, K. PranzasAppl. Phys. A 88 [Materials Science & Processing], (2007) 277-284

electrochemical selective phase

dissolution

April 19, 2023 18

Extraction processExtraction process

TU Braunschweig and ETH Zurich

TU Braunschweig and ETH Zurich

Ni–Si or Ni–Si–Al alloys: Ni3Si particles covered by amorphous shell made of SiOx

bio-resistant => may be suitable for medical application

Ni–Si or Ni–Si–Al alloys: Ni3Si particles covered by amorphous shell made of SiOx

bio-resistant => may be suitable for medical application

1. Formation of nano-sized precipitates structure in bulk alloy by heat treatment

1. Formation of nano-sized precipitates structure in bulk alloy by heat treatment

2. Separating the nano-structure from the bulk: selective phase dissolution

2. Separating the nano-structure from the bulk: selective phase dissolution

3. Collection of nano-particles (ultrasound vibrations)

3. Collection of nano-particles (ultrasound vibrations)

shell: shell:

April 19, 2023 19

Shell formationShell formation

Possibilities : 1. Depletion of Ni from Ni-Si solid

solution matrix and re-deposition of Si on particle surface;

2. Depletion of Ni from Ni3Si precipitate surface.

Possibilities : 1. Depletion of Ni from Ni-Si solid

solution matrix and re-deposition of Si on particle surface;

2. Depletion of Ni from Ni3Si precipitate surface.

SANS: motivationSANS: motivation

confirm core-shell structure by an independent method

indicate which mechanism of shell formation takes place

confirm core-shell structure by an independent method

indicate which mechanism of shell formation takes place

comparison: precipitates in the bulk alloy and nanoparticles

contrast variation (masking the shell)

comparison: precipitates in the bulk alloy and nanoparticles

contrast variation (masking the shell)

methodmethod

April 19, 2023 20

Solid sample of Ni-13.3Si-2Al alloySolid sample of Ni-13.3Si-2Al alloy

The inter-particle interference peak at low Q magnitudes: dense population of precipitates

four precipitate populations necessary to describe the data

The inter-particle interference peak at low Q magnitudes: dense population of precipitates

four precipitate populations necessary to describe the data

model: polydisperse 3D system of particles

2nd population: an extension of the 1st one

3rd and 4th populations in the channels between the larger precipitates

model: polydisperse 3D system of particles

2nd population: an extension of the 1st one

3rd and 4th populations in the channels between the larger precipitates

Polycrystalline alloy => isotropic => 3D cross section averaged

Polycrystalline alloy => isotropic => 3D cross section averaged

grey: precipitate white: matrix

1st population

2nd population

3rd population 4th population

April 19, 2023 21

nanopowder sample, contrast variationnanopowder sample, contrast variation

extracted nanoparticles dispersed in various mixtures of H2O/D2O

all mixtures except 80% D2O: the slope at medium-to-large Q deviates from Porod law

evolution with changing SLD cannot be explained without the presence of a shell

extracted nanoparticles dispersed in various mixtures of H2O/D2O

all mixtures except 80% D2O: the slope at medium-to-large Q deviates from Porod law

evolution with changing SLD cannot be explained without the presence of a shell

SLD of the shell: 49×109 cm−2SLD of the shell: 49×109 cm−21st population

2nd population

detail

model model

80% D2O80% D2O100% D2O100% D2O

April 19, 2023 22

comparison: precipitates vs.

nanopowder

comparison: precipitates vs.

nanopowder

1st and 2nd distributions (core) correspond well in size scale with the original populations in the solid sample

=> indication that the particle core was not attacked by the electrolyte during extraction process

1st and 2nd distributions (core) correspond well in size scale with the original populations in the solid sample

=> indication that the particle core was not attacked by the electrolyte during extraction process

distributions in solid sample compared to extracted nanoparticles

displayed distributions: the core and the core + shell

distributions in solid sample compared to extracted nanoparticles

displayed distributions: the core and the core + shell

April 19, 2023 23

In-situ SANS Study of Pore Microstructure in YSZ Thermal

Barrier CoatingsP. Strunz, G.Schumacher, R. Vassen and A. Wiedenmann,

Acta Materialia, Vol 52/11, 2004, pp.3305-3312

April 19, 2023 24

Ceramic Thermal Barrier Coatings

Preparation: – Air Plasma Spraying (APS), – Electron Beam Physical Vapor Deposition (EB PVD)

highly porous material, pore microstructure determines properties

April 19, 2023 25

1. large pores and cracks (radius > 100 nm)

2. medium-size pores (~20 nm)

3. nanometric pores (1-10nm)

TBC: samples (set 47) treated

ex-situ at 1200ºC

No thermal exposure: – hydrogen?

– extremely small pores?

– combination?

for 0, 1, 10 and 100 hours

Model:

April 19, 2023 26

in situ: creation of nanopores from ex-situ: there are nanopores after 1h at 1200 ºC

=> created between 400 and 1200ºC

nanopores created at 800ºC

00:00 04:00 08:00 12:00 100:000

200

400

600

800

1000

1200

800°C

in-situ ex-situ

1200°C

Te

mp

era

ture

(°C

)

Temperature

April 19, 2023 27

ZrO2 TBC (plasma sprayed): nanometric pores

in- and ex-situ measurement fit well together

800ºC: population of nm-sized pores created.

between 800°C and 1200ºC, this population is unchanged

annealing at 1200ºC: size increases, volume decreases

April 19, 2023 28

Applications (not exhaustive list): solid state physics - microstructure

– Alloys, ceramics, glasses– Porosity, voids, microcracks– Semipermeable membranes– Porosity in ceramics– Phase transformations– Precipitates in metals, inclusions– Precipitate formation/dissolution in alloys– Nanoscaled materials, nanoparticles– Interfaces and surfaces of catalysts– Impurities in silicon

magnetism– Magnetic/non-magnetic inhomogeneities– Ferofluids– Flux line lattices in superconductors

1) bulk information or non-destructive testing is needed 2) sample: cannot be prepared in the thin form necessary for

synchrotron without influencing the microstructure 3) absorption/scattering in sample-environment windows too high

for X-ray (in-situ experiments at extreme conditions) 4) scattering contrast for X-ray too low or does not allow to

resolve details (easier contrast variation for neutrons) 5) magnetic microstructure

What can be determined? Average particle size Surface area (I ~ S/Q4) Volume fraction Particle shape Internal structure (contrast variation) Size distributions

SAS in solid state physics: use neutrons when