Scattering Experiments. Structural coherence length found for small regions from TEM images SAXS: Structural L coh average SANS: Structural and Magnetic.

Sample

Detector

k

k'

Beam

q = 4 π sin θλ

k'

k

qθ

X-rays: Scattering ~ Z

Neutrons: Scattering ~ μnuclear, Mperpendicular

H

Scattering Experiments

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I(x) = I0 exp(−x /Lcoh )

Structural coherence length found for small regions from TEM images

SAXS: Structural Lcoh average

SANS: Structural and Magnetic Lcoh averages

Coherence Length

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λ =2dhkl sinθhkl

Observe diffraction from planes of particles at small angles

Both the lattice symmetry and the shape of diffracting object contribute to the intensity I(q

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I(q)∝ Slattice(q)Pshape (q,R)

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qhkl =4π sinθhkl

λBragg’s Law

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Psphere (q,R) =3(sin(qR) −qRcos(qR))[ ]

2

qR( )6

Ignore scattering by the surfactant coating

the radius R = Rcore

Small Angle X-ray Scattering

140

120

100

80

60

40

20

0

I (a.u.)

4.03.53.02.52.01.51.0

2θ

10

-8

10

-6

10

-4

10

-2

10

0

( )log P qr

0.50

0.50fcc

hcp

(100)

(002)

(101)

(110)

(103)

(112), (201)

(111)

(200)

(311), (222)

Both hcp and fcc arrays observed

Shape factor, d=8.5 nm

d=8.5 nm

x=10.3 nm

ShcpθP(θ)

ShcpθP(θ)

0

-2

-4

-6

-8

3D Arrays Structures from SAXS

d=8.5 nm

x=9.6 nm

2θ ( )Degree0.00.51.01.52.02.53.03.5 ( . .)Intensity a u05001000150020002500(002)(101)

( )a( )bSpots due to 3 hcp supercrystals- Large Lcoh

Interparticle spacing slightly reduced

(a) Average intensity

(b) Sharpest peak

3D Arrays Made Over 4 Weeks

Nanoparticle Crystals vs Disordered Assemblies

SAXS patterns of 8.5 nm Fe nanoparticle FCC nanoparticle crystals and rapidly quenched assemblies

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