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Small-Angle Neutron Scattering - Kfki

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Example: core-shell particles<br />

ρ 1<br />

, R 1<br />

ρ<br />

I ( q)<br />

= n[(<br />

ρ ρs ρ ρ Φ qR<br />

2<br />

1<br />

− ) V1Φ(<br />

qR1<br />

) − (<br />

1<br />

−<br />

0)<br />

V0<br />

(<br />

0)]<br />

Φ( x)<br />

= 3(sin x − x cos x) / x<br />

n is the particle number density<br />

3<br />

V<br />

i<br />

=<br />

3<br />

( 4 / 3) πRi<br />

ρ 0<br />

, R 0<br />

ρ s<br />

ρ =<br />

V<br />

V<br />

V<br />

( ρ<br />

0 0<br />

ρ0<br />

+ 1−<br />

)<br />

1<br />

V1<br />

1<br />

∆ρ<br />

=<br />

ρ −<br />

ρ s<br />

Mitglied in der Helmholtz-Gemeinschaft<br />

I( q) = nV ( ρ − ρ ) [ Φ( qR ) − Φ ( qR )] +<br />

2 2 2<br />

0 1 0 1 0<br />

+ 2 nVV ( ρ − ρ ) Φ( qR )[ Φ( qR ) − Φ( qR )]( ∆ ρ)<br />

+<br />

1 0 1 0 1 1 0<br />

+ nV Φ ( qR )( ∆ρ)<br />

2 2 2<br />

1 1<br />

Is<br />

Ics<br />

( q)<br />

( q)<br />

I ( ) c<br />

q

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