Introduction toSmall Angle Scattering - FHI toSmall ... XRD Optical microscopy Electron microscopy...

Introduction to Small‐Angle Scattering

Dr. Armin Hoell

Lecture series: Modern Methods in heterogeneous catalysis research: FHI, WS 2014‐2015

SAXS & ASAXS

Lecture: Introduction to Small‐Angle Scattering: FHI Berlin WS 2014‐2015

Helmholtz Zentrum Berlin für Materialien und Energie

Liese-Meitner-Campus Wannsee-Neutron reaktor as neutron source:

BER II-solarenergie research

Wilhelm-Conrad-Roentgen CampusAdlershof-Synchrotron source: BESSY II-solarenergie research

2


Outline

Introduction SAS: -some historical remarks

-when can small-angle scattering be used

-kind of samples

Small-Angle Scattering:

-scattering vector, size range to be investigated

-theoretical remarks

-structural parameters, the scattering contrast

-Which are possible structural results of SAS

Model scattering curves:

Example of instrumentation: -ASAXS instrument at BESSY II

Contrast variation: -ASAXS; resonant Small-Angle X-ray Scattering

Examples: -RuSe – catalyst for fuel cells

-degradation of PtNi3 catalysts studied by ASAXS

3


References: Small‐Angle Scattering (SAS)

Guinier (1956/1994) “X-ray diffraction. In crystals, imperfect crystals, and amorphous bodies”, Chapter 10 Small-angle x-ray scattering.

Glatter & Kratky (ed.) (1982) “Small Angle X-ray Scattering”. (http://physchem.kfunigraz.ac.at/sm/Software.htm)

Feigin & Svergun (1987) “Structure analysis by small-angle X-ray and neutron scattering”,(http://www.embl-hamburg.de/ExternalInfo/Research/Sax/reprints/feigin_svergun_1987.pdf)

Guinier & Fournet, (1955), “Small-angle scattering of X-rays”, New York

Otto Kratky (1983) “Die Welt der vernachlässigten Dimensionen und die Kleinwinkelstreuung der Röntgen-Strahlen und Neutronen an biologischen Makromolekülen”, Nova Acta Leopoldina, Halle.

27. IFF-Ferienkurs (1996) “Streumethoden zur Untersuchung kondensierter Materie”, Jülich.ISBN 3-89336-180-4

Software to analyse the Small-Angle Scattering curves. SASFIT / Joachim Kohlbrecher: PSIhttps://kur.web.psi.ch/sans1/SANSSoft/sasfit.html

4

Heimo Schnablegger: „The SAXS Guide“ Firma Anton Paar, Austriaonline available from institute ILL / Grenoble in France


1 m 1 pm1 nm1 mm 1 m

SAXSUSAXS WAXSXRD

Optical microscopy

Electron microscopy

Static and dynamic light scattering

Structural determination of different materials

Atomic force microscopy

Electron diffractionBiggest advantage of X-ray scattering:-In situ measurements-Statistical average

ProteinsLiquid crystals

DNA

5


History: SAXS and Anomalous SAXS

1980

1991

3/2006

Stuhrmann (EMBL Hamburg; instrument X15) first ASAXS on Ferritin and Hemoglobin

J.P. Simon; O. Lyon; FranceASAXS on alloys and theory

A. Bienenstock; Stanford, USA

JUSIFA instrument at B1 (Haubold; FZ Juelich)ASAXS at A1 (lower energy range, organic materials) Stuhrmann

HMI - SAXS instrument at BESSY: dedicated to anomalous and grazing incidence SAXS

HASYLAB

No real dedicated ASAXS instruments furthermore: ID01 & BM02 @ ESRF; 12ID at APS

Our goals:- Application of ASAXS in the material science field and materials for renewable energy sources- Increase the sensitivity and accuracy of ASAXS - Further development of ASAXS theory

1930

7MPW-SAXS at BESSY

1940 –1960

Guinier, Debye, Luzatti, Porod and others develop interpretation for the basic features in SAXS patterns

6


What can be characterized by Small Angle Scattering?

-in general all nanostructures containing materials

(in state of solid plates, powders, or liquids)

Examples:-immiscibility regions and beginning crystallization in e.g. glasses

-precipitations in alloys

-concentrations fluctuations at phase boundaries (e.g. hydrogen storage)

-grain boundaries in polycrystalline materials

-pore structures in aero gels, porous glasses …

-morphology of biological cells, DNS, bones, woods

-polymers

-colloidal liquids: protein structures, magnetic fluids

-catalysts; especially nonoparticles on different supports

7


Some Examples

Luminescent Nano- crystals:

ZnCdSe CdTe

Different catalysts:

8

PtNi3


Historical Gold‐Ruby Glass: old roman

Motivation: Gold nanoparticles

Lycurgus cup

9


Principle of Small‐Angle Scattering (SAS)

Monochromator/

2

DetectorSample(containing nanostructures)

d

Neutrons

or X-rays

Collimation

Inhomogeneity of densities, composition fluctuations and

magnetisation in size ranges of d: ~ 0.5 – 100 nm

One can get: Size distributions, distances, compositions, volume fractions

Intensity I(q) q = 2/d

Scattering angle 2: 0.1 – 6°

|q| =4 sin/

important: sample properties

Beamstop

10


Small‐Angle Scattering (SAS)

Scattering cross-section

12 kkQ

)sin(4

QQ

maxmin Q

r

AdQ 0

Scattering vector:

Resolution limit:

SAS range:

Colloidal dimensions: ~ 1 – 100 nm

1k

2k

Q

11

Material: that containsnanostructures


How can colloidal structures be investigated?

)sin(4

q )sin(2d

Magnitude of the scattering vector Bragg-equation

dq 2

Threshold value: dq 0

Scattering also allows to investigate structures in the nm- and µm- range.

Small-Angle Scattering (SAXS, SANS, USAXS, USANS)

12


(r)

(r)

particle matrix r

-

Inhomogenities of scattering lenghtdensity, ,in a size range of: ~ 0.5 - 200 nm

Small‐Angle Scattering (SAS)

Qmax

I(Q)

Q=(4/)sin()Qmin

SAXS

WAXS(resolution of colloidal

dimensions)

(resolution of atomic dimensions)

maxmin Q

r

minmax Q

r

Resolution limit:

View field limit:

SAS does not have resolution for interatomicdistances.

Therefore, SAS alone can not distinguish whether a nanostructure is crystalline or amorphous.

13

[introduction scattering length density later]


Small‐ and Wide‐Angle X‐ray Scattering (SAXS & WAXS)

14

q (nm-1)

SAXS WAXS


Porod region( I(q) q-4 )

Guinierregion

q > 3.5/Rg

15


Particle scattering

41 /)( QKQI

VQSQIQK 24

1 )(2)(lim

Porod region: for large Q

222 ),()()( RQFVNQI V

3)()cos()sin(3),(

QRQRQRQRRQF

)3/exp()0()( 220 QRIQI

20

20

)(lnlim3Qd

QIdRQ

)()( rr

Scattering Intensity: Fluctuations of electron density:

Scattering Amplitude of a sphere of radius R:

Guinier region: for Q 0

Ro: radius of gyration SV: interphase surface area

16

A B


Guinier approximation

0.00 0.02 0.04 0.06 0.08 0.10-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

qg

qmin

ln[I

(q)]

q2

)3/exp()0()( 22gRqIqI

rdr

rdrrR

V

Vg

)(

)(

1;0 ggqRqApproximation at small q

Guinier plot

22 )3/()0(ln)(ln qRIqI g

17

A


Porod approximation

Approximation at large q

4/)( qKqI P 3/~)( qKqI P

SKP2)(2

Bn

P IqKqI /)(

Porod plot

q

0.01 0.1 11E-5

1E-4

1E-3

0.01

0.1

1

Data Porod Approximation Guinier Approximation

I(q)

[Arb

.]

q [nm-1] n

BPn qIKqqI )(

Kp – proportional to the interphase surface area

18

0 2 4 6 8 10 12 14 160.000

0.002

0.004

0.006

0.008

0.010

IB=0I(q)

q4

q4

B


Contrast:Δη = ηparticle - ηmatrix

Particle shape factor

Inter-particle interference

Size distribution

I(Q) = Np {Vp(R) F(QR)}2 S(QRhc) N(R) dR

QmaxQmin

slope: Sv

shape: distribution

RR

lg(I)

lg(Q)

, N , w

, N , w

Small‐Angle Scattering

19


The scattering contrast: ()2

r

Electron density: (r)

Electron density : (r)

r

()2 > 0

()2 0

= particle – matrix

particle matrix

20

electron density: ∑ general:

Scattering length density


Case 1: Monodisperse spherical particles in a solution (matrix)

),()()( 222 RqFRVNqI PP

Number of particles

Scattering contrast

Particle volume

Formfactor

3)()cos()sin(3),(

QRQRQRQRRQF

21

Scattering amplitude of a homogeneous

sphere:



0.01 0.1 1 1010-2

10-1

100

101

102

103

104

105

106

107

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

5nm Kugel-Teilchen

q-4

22


0.01 0.1 1 1010-2

10-1

100

101

102

103

104

105

106

107

108

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

10 nm Kugel-Teilchen 5 nm Kugel-Teilchen


q-4

23


Case 2: Polydisperse spherical particles in a solution (matrix) (diluted system)

RdRqFRVRPNqI PP~)~,()~()~()( 222

Scattering contrast

Particle volume

Formfactor

Particle number

Size distribution

R2 4 6 8 10 12 14

0.2

0.4

0.6

P(R)

5.2±0.3 nm

7.5±2.3 nm

24



0.01 0.1 1 1010-2

10-1

100

101

102

103

104

105

106

107

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

5nm Kugel-Teilchen (polydisperse 10%) 5nm Kugel-Teilchen (monodisperse)

25



0.01 0.1 1 1010-2

10-1

100

101

102

103

104

105

106

107

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

5nm Kugel-Teilchen (polydisperse 20%) 5nm Kugel-Teilchen (monodisperse)

26


Case 3: Polydisperse spherical particles in a solution (matrix) (dense system)

0.01 0.1 1 1010-1

100

101

102

103

104

105

106

107

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

5nm Kugel-Teilchen (dichtes System) 5nm Kugel-Teilchen (verdüntes System)

Interferences between the scattering of single particles

27


Case 4: Sum of two sort of particles with different size distributions

0.01 0.1 1 10101

102

103

104

105

106

107

108

109

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

10nm Kugel-Teilchen 2nm Kugel-Teilchen resultierende Streukurve: +

polydisperse = 20%

28

Lecture: Introduction to Small‐Angle Scattering: FHI Berlin WS 2014‐2015 29

One example of small angle scattering instrumentation


The ASAXS‐Instrument at the Synchrotron BESSY II

sd [m]3.8 0.8

sample

30

1.4 1.35


The ASAXS‐Instrument from top


Some sample environments for SAXS

32

Sample chamber under vacuum

Sample changer on air

furnaces (293K – 1450K)


ASAXS‐Instrument at BESSY II: collection of sample holders

33

standardsamples

catalysts Scotch tapeX-Ray

sheet

sample

Powder samples

Liquid samples

optimal sample thickness:

= ~ 0.36


Introduction to contrast variation

How:1. Combined use of X-ray and Neutron Small Angle Scattering

2. Isotope substitution in case of neutronslack: set of different samples to be prepared

3. Magnetic contrast variation in case of neutrons (polarised N.)

4. Anomalous Small Angle Scattering (ASAXS) in case of X-rays

Why: more complex systems, mixture of different phases

decide between different structural model solutions

34


X-rays

Neutrons

cizi / Mi

ci: composition : density

zi: electron number

Mi: mass number

nuclear: magnetic:

ci bi ci Mi

bi: scattering Mi : magnetization

length -radii of the circles are proportional to the scattering length

-negative values are indicated by cross-hatched shading

Scattering length densities, : X‐rays and Neutrons

35


Anomalous Small Angle X‐ray Scattering (ASAXS)

• ASAXS: Energy dependency of the atomic scattering amplitudes

3)()cos()()sin(3)R,F(q,

qRqRqRqREE

• Sc. Amplitude for a homogenous sphere of radius R:

Scattering Intensity effective electron density

drrqSErqFrVrNEqI p

0

22 ,,,,

Size distributionVolume

Form factorStructure factor

C

iiiA

M

EfcDNE

Electron

density

Matrix

Particle

Size

matrixparticleE

Contrast:

36


10 12 14 16 18 20 22 2456

25

30

35

40

45

Carbon

Selenium

Ruthenium

Ele

ktro

nend

icht

e

(E)

Energie [keV]

effective “electron density” becomes energy dependent.

Se

Ru

C

0.01 0.1 1 10101

102

103

104

105

106

107

108

109

Energie E1

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

E1

37




10 12 14 16 18 20 22 2456

25

30

35

40

45

Carbon

Selenium

Ruthenium

Ele

ktro

nend

icht

e

(E)

Energie [keV]

Se

Ru

C

E1 E2

0.01 0.1 1 10101

102

103

104

105

106

107

108

109

Energie E1 Energie E2 E1 - E2

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

38




10 12 14 16 18 20 22 2456

25

30

35

40

45

Carbon

Selenium

Ruthenium

Ele

ktro

nend

icht

e

(E)

Energie [keV]

Se

Ru

C

E1

0.01 0.1 1 10101

102

103

104

105

106

107

108

109

Energie E1 Energie E3 E1 - E3

scat

terin

g cr

oss

sect

ion

(cm

-1)

q (nm-1)

E3

39



ASAXS Movie: Al89Ni6La5 around Ni‐K edge

measured: 8000eV – 8450eV E = 2.25eV 201 energy steps constant q-range

on 2D gas detector

2D gas detector:

corrected by deadtime, monitor, transmission, detector sensitivity, solid angle distorsion,projection of detector surface on a sphere, and background subtraction

Instrument: SAXS @ BESSY


scattering curves are extracted from the corrected 2-dim. detector pictures

ASAXS Movie: Al89Ni6La5 around Ni‐K edge


Example 1: RuSe Nanoparticle for fuel cell applications

Example 2: In situ study of the degradation of PtNi3 alloys

42


Catalysts for polymer electrolyte membran fuel cells

CathodeAnodeH2

H+

e-H+ O2

Membrane

e-

e- H2O

O2

H2 -> 2H+ + 2e- ½ O2 + 2H+ + 2e- -> H2O

Oxygen ReductionHydrogen Oxidation

ASAXS

Ru‐Se Catalyst for fuel cells

43

Slow electrode kinetics,

Cost of catalyst,

Catalyst degradation…

…are the most critical issues in fuel cell

research

Lecture: Introduction to Small‐Angle Scattering: FHI Berlin WS 2014‐201524 March 2009 44

Anomalous Small Angle X‐Ray Scattering (ASAXS)

11.8 12.0 12.2 12.4 12.6

24

26

28

30

324244

|f 0+f'(

E)+i

f''(E)

| /

ele

ctro

ns

1222

0eV

1252

4eV

1261

4eV

1264

3eV

1265

3eV

Selenium

Ruthenium

energy / keV

21.00 21.25 21.50 21.75 22.00

34

36

38

40

42

2167

5eV

2184

0eV

2203

4eV

2209

1eV

2210

9eV

Selenium

Ruthenium

|f 0+f'(

E)+i

f''(E)

| /

ele

ctro

ns

energy / keV

Ru K edge- 442 eV- 277 eV- 83 eV- 26 eV- 8 eV

Se K edge- 438 eV- 134 eV- 44 eV- 15 eV- 5 eV

Atomic scattering amplitudes

10 12 14 16 18 20 22 2456

25

30

35

40

45

Carbon

Selenium

Ruthenium

|f 0+f'(

E)+i

f''(E)

| /

ele

ctro

ns

energy / keV

Sample preparation

Scotch tapeX-ray

sheet

sample

Lecture: Introduction to Small‐Angle Scattering: FHI Berlin WS 2014‐201524 March 2009 45

1 10

1024

1025

1026

1027

1028

Ru K edge: EK = 22117eV

scat

terin

g in

tens

ity /

a.u

.

q / nm-1

EK - 8eV EK - 26eV EK - 83eV EK - 277eV EK - 442eV Black Pearls

1

*1026

6.0

5.01.1

q / nm-1

ASAXS curves obtained at the:

1 10

1024

1025

1026

1027

1028


scat

terin

g in

tens

ity /

a.u

.

q / nm-1


1

*1026

4.0

3.01.1

q / nm-1

Ru on Black Pearls

Ru-K-edge (22117eV)

RuSex on Black Pearls

clear anomalous effect

0.1 1 10

1023

1024

1025

1026

1027

1028

EK - 5eV EK - 14eV EK - 44eV EK - 134eV EK - 438eV

scat

terin

g in

tens

ity

/ a.

u.

Se K edge: EK = 12658eV

q / nm-1

Black Pearls

RuSex on Black Pearls

Se-K-edge (12658eV)

no anomalous effect


ASAXS: RuSex/C

0 5 10 15 200.00

0.25

0.50

0.75

1.00

Black Pearls

Ru-particle

Se-particle

N(R

)*R

3 / a

.u.

radius / nm

0.0 0.5 1.0 1.50.00

0.25

0.50

0.75

1.00

N(R

)*R3 /

a.u

.

radius / nm

Volume weighted size distribution

1 10

1024

1025

1026

1027

1028


sc

atte

ring

inte

nsity

/ a

.u.

q / nm-1


1

*1026

6.0

5.01.1

q / nm-1

46


Structural model for the Ru‐Se based catalyst

5nm

Carbon-support

Ru-particle

G. Zehl, G. Schmithals, A. Hoell, S. Haas, C. Hartnig, I. Dorbandt, P. Bogdanoff, and S. Fiechter, Angew. Chem. Int. Ed. 2007, 46, 7311 –7314

47

TEM


Example 1: RuSe Nanoparticle for fuel cell applications

Example 2: In situ study of the degradation of PtNi3 alloys

48


Reference electrode

Counter electrode

Reference samplesfor ASAXS

Working electrode

Catalyst ink droplet

Experimental setup for in situ ASAXS at BESSY II


SAXS is capable to distinguish the mechanism of particle surface area loss

50

3. Coalescence

5. Mechanical detachment fromconductive support

2. Ostwald Ripening

1. Dissolution

4. Oxidation/PoisoningH2O

Atomic‐Scale Structural Dynamics in Monometallic Ensembles


8.0 8.1 8.2 8.3 8.4-10

-8

-6

-4

-2

0

2

4

E1E2

E4

f' f''

scat

terin

g fa

ctor

s

E / keV

E3

11.2 11.3 11.4 11.5 11.6-20

-16

-12

-8

-4

0

4

8

E1E2

E4

f' f''

scat

terin

g fa

ctor

s

E / keV

E3

For Ni-resonant scattering For Pt-resonant scattering

The protocol was kept the same as for the electrochemical characterization.

ASAXS was monitored during a chronoamperometry at 0.5 V after a certain number of stress cycles (0.5 – 1.1 V)

ASAXS: Selected Energies at Ni‐K and Pt‐L3 edges


ASAXS results HE-XRD: PDF-analysisPristine particles: partially chemically ordered PtNi3single phase.

Stressed particles: predominant PtNi3 phase and Ni phases.

Tuaev, X.; Rudi S.; Petkov V.; Hoell A.; Strasser, P. ACS Nano, 2013, 7(7), 5666-5674.

PtNi3, in‐situ ASAXS and SAXS

partially de-alloying takes place


Popularity of Small‐Angle Scattering / Publications

1990 1995 2000 2005 20100

200

400

600

800

1000

1200

1400

Num

ber o

f pub

licat

ions

Publication Year

Small Angle X-ray Scattering Small Angle Neutron Scattering Anomalous Small Angle X-ray Scattering Ultra Small Angle X-ray Scattering Grazing Incidence Small Angle X-ray Scattering

Next international Conference on Small-Angle Scattering:13. – 18. September 2015, TU Berlin (about 500 participants expected)

Year of an international SAS conference


Thank You!

Introduction toSmall Angle Scattering - FHI toSmall ... XRD Optical microscopy Electron microscopy...

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