Stanford Synchrotron Radiation Laboratory

X-ray ScatteringMike Toney

Stanford Synchrotron Radiation Laboratory

(00Qz) (20Qz)(-10Qz)

• J Als-Nielsen & D McMorrow, “Elements of Modern X-ray Physics”, Wiley (2001).

• M. Tolan, “X-ray Scattering from Soft-Matter: Materials Science and Basic Research”, Springer, 1998.

• RL Snyder, K. Fiala &HJ Bunge, Eds., “Defect and Microstructure Analysis by Diffraction”, Oxford (1999).

• G Renaud, “Oxide Surfaces and Metal/Oxide Interfaces Studied by Grazing Incidence Diffraction”, Surf Sci Repts 32, 1 (1998)

Bibliography

1. Peak Widths & Defects• Nanoparticles

2. Monoatomic Layers – Pentacene again3. Surface Diffraction

• Oxide Surfaces• Interfacial Water

4. Small Angle X-ray Scattering (SAXS)

Outline

Diffraction vs Scattering

0 20 40 60 80

1000

2000

3000

4000

5000

6000

7000

21 24 27

2000

4000

6000

Inte

nsity

2θInte

nsity

2θ

diffraction: Bragg peaks

scattering: the rest

Peak Widths

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

37.4 37.6 37.8 38 38.2 38.4 38.6 38.8 39 39.2

2 Theta

Inte

nsity

(111)

• Widths depend on particle size (D):∆2θ = 0.9 λ / D cos θ∆Q = π/D

∆2θ = 0.15deg => D = 50 nm

Nanoparticles

Kevin Stevens (MPT Solutions, NZ)Bridget Ingham (Imperial College, UK)Simon Brown (U Canterbury, NZ)

Cu particles nanoscaleparticles, formed by inert gas aggregation, are deposited from a molecular

Peak Widths

Cu particles: a = 3.6159 +/- 0.0005 Å(c.f. bulk 3.6149 Å)D = 12 nm compared to 30-60 nm from SEM

Cu2O (cuprite): ca 5% by volume

Monolayer Scattering

(00Qz) (20Qz)(-10Qz)

monoatomic layer of atoms

monoatomic layer of molecules

1 1.2 1.4 1.6 1.8 2 2.2 2.4

qxy (Å-1)

Inte

nsity

(a.u

.)

(11)

(02)(12)

(20) (21)

0.05 0.1 0.15 0.2 0.25 0.3 0.35

qz (Å-1)

Inte

nsity

(a.u

.)

peak (11)peak (12)peak (02)

Pentacene Monolayer

2θα

β

Transport in ab plane of crystal structureTransport in first few layers

Fritz et al., unpublished

• Monolayer: herringbone motif with molecules untilted

• lattice parameters (monolayer)a = 5.911 (3) Åb = 7.566 (3) Åγ = 90.0 (1)o

• Thin film:a = 5.933 (3) Åb = 7.540 (3) Åγ = 90 deg

5µm

a

bγ

Fritz et al., unpublished

Pentacene Monolayer

Pentacene revisited

0.007 Å-1

width

Fritz et al., unpublished

5 µm 1.5 nm - one layer

30 nm – ca 15 layers

5 µm

5 µm=> Grain size of > 30 nm

Surface ScatteringRECIPROCAL

SPACEREAL

SPACE

Infinite lattice results in pointsin reciprocal space.

A single plane of atoms resultsin lines of intensity.

Surface is combination.

Surface Scattering

CTR: crystal truncation rod

IK Robinson PRB 33, 3830 (1986).

A. Munkholm, S. Brennan & E.C. Carr, J. Appl. Phys. 82, 2944 (1997).

sum over all Bragg peaksnearest Bragg peak only

202 CTR

Hydrated Oxide Surface StructureSurface XRD to probe

Eng et el., Science 288, 1029 (2000)

α-Al2O3 (0001)

(00Qz) (20Qz)(-10Qz)

Hydrated Oxide Surface Structure

Some hydrated surface structures

Eng et el., Science 288, 1029 (2000)Trainor et el., Surf Sci 496, 238 (2002)Trainor et el., Surf Sci (2004)

Interfacial Water Structure

positively charged surface

negatively charged surface

oxygen

hydrogen• microscopic picture of the arrangement of water at oxide-aqueous interfaces

Surface X-ray Diffraction or Crystal Truncation Rods (CTRs)

Interfacial Water Structure

Toney et al., Nature 368, 444 (1994)

-ve of pzc

Ag(111)

+ve of pzc

(00Qz) (20Qz)(-10Qz)

Interfacial Water Structure

-(ve) charged surface

+(ve) charged surface

Small Angle Scattering

|Q| = (4π/λ)sin (θ/2)Kin

KoutQ = Kout - Kin

θKin

incident scattered

Measure I(Q) with Q ∼ 0.0001 – 1 Å-1

Scattering from density inhomogeneitiesof size 0.5 – 1000 nm

Small X-ray Angle Scattering Intensity

ρ1(2) = electron densityin phase 1(2)

pores = particles

23riQ rd e)r(

V1I(Q) •∫= ρ ρ(r) = electron density

S(Q)F(Q))(VNI(Q) 22

12 ρρ −=

single particleSAXS

inter particlescattering

∫ •

1V

3riQ rd e

Small Angle ScatteringIsolated pores or particles with diameter D

• Experimental Q range gives range of accessible diameters• Need 1/D Q 10/D<~ <~

π/D

Q-4

Inter-pore Interference: S(QR)

S(QR) = interference function using local mono-disperse approximation (positions correlated with size)JS Pederson, J Appl. Cryst. 27, 595 (1994)

SAXS from nearby pores interfere

Sample

2D Area Detector

• Sample to detector distance defines Q range (for a given λ)

• Q = (4π/λ) sin(θ/2)• Two or three detector distances

(0.1m to 3m) & incident beam sizes

• Gives large Q range• Performed in transmission• Window-less environment

θ

Incident X-Ray BeamMonochromate to E=7.66 keV,Slits: 100 x 100 or 200 x 200 µm

80 µm Si substrate transmission~25%

SAXS Setup

Spin coat MSSQ/Porogensolution

Heat to 450°C, at5°C/min under argon

Cool to room temperature

1.

2.

3.Thermally

Labile Polymer

Methyl Silsesquioxane(MSSQ), CH3SiO1.5

SiO

O

CH3

O

O Si

CH3

SiCH3

Si

CH3

O

O

O

O

∆ Argon

Porogens: copolymer poly(methyl methacrylate-co-dimethylaminoethyl methacrylate) or P(MMA-co-DMAEMA) & poly(ε-caprolactone) or PCL (6-armed star)

Matrix

Components Processing

Spin Coat

MSSQ crosslinks at 200°CPoragen fully degrades at 400°C

Nanoporous Films

Porogen

Small Angle X-ray Scattering

• MSSQ matrix• P(MMA-co-DMAEMA) porogen• Loading = weight percent in initial

material• Porosity is about 90% of loading• Fits with local monodisperse

model and log-normal distribution

Huang et al, Appl. Phys. Lett. 81, 2232 (2002)

Pore Size DistributionApproximations:

treat pores as spheres (ignore shape)local mono-disperse approximation for inter-pore scattering

5.45.340%

4.54.530%

3.12.715%

2.62.110%

D/2 (nm)

<R> (nm)

loading

σ ≈ 0.37

Nanoporous Films

Reconstruction of Pore Morphology

Allows determination of transition from closed pores to open pores to bicontinuous microstructure

Hedstrom et al, Langmuir20, 1535 (2004)

Nanoporous Films

=> transition to bicontinuous occurs between 15 & 25 %

closed and interconnected:number ∼ length3

bicontinuous:number ∼ length2

Grazing Incidence SAXS

2θ

incident scattered

• Use grazing incidence to limit penetration depth• Measure I(Q) with Q ∼ 0.01 – 1 Å-1

• Scattering from density inhomogeneities of size 50 – 100 Å

Applications:• Nanoparticles imbedded in

thin films• Nanoparticles on surfaces

k

k’

= (4π/λ) sin θQ = k’ – k

Summary

1. Peak Widths & Defects• Nanoparticles

2. Monoatomic Layers – Pentacene again3. Surface Diffraction

• Oxide Surfaces• Interfacial Water

4. SAXS applications to porous and particulate materials