An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
An Introduction to Neutron Scattering - Spallation Neutron Source
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Instrumental Resolution for SANS<br />
Traditionally, neutron scatterers tend <strong>to</strong> think in terms of Q and E resolution<br />
4π<br />
Q =<br />
sin θ<br />
λ<br />
For SANS, ( δλ/<br />
λ)<br />
For equal source - sample & sample - detec<strong>to</strong>r distances<br />
apertures at source and sample of h, δθ<br />
The smallest v alue of θ<br />
At this<br />
δQ<br />
rms<br />
~ ( δθ<br />
The largest<br />
value of θ , angular<br />
rms<br />
⇒<br />
/ θ<br />
min<br />
δQ<br />
rms<br />
Q<br />
)Q<br />
observable<br />
is<br />
~ δθ<br />
This is equal <strong>to</strong> the transvers e coherence length for the neutron and achieves<br />
a maximum of about 5 μm<br />
at the ILL 40 m SANS instrument using 15 Å neutrons.<br />
Note that at the largest va lues of θ , set by the detec<strong>to</strong>r size and distance from the<br />
sample, wavelengt h resolution<br />
2<br />
2<br />
~ 5% andθ<br />
is small,<br />
min<br />
=<br />
δλ<br />
λ<br />
2<br />
determined<br />
resolution<br />
rms<br />
2<br />
+<br />
cos<br />
rms<br />
4π<br />
/ λ ~ ( 2π<br />
/ λ)<br />
h / L<br />
object is ~ 2π/<br />
δQ<br />
sin<br />
dominates.<br />
2<br />
θ.<br />
δθ<br />
so<br />
by the direct<br />
dominates<br />
rms<br />
=<br />
2<br />
θ<br />
2<br />
δQ<br />
2<br />
Q<br />
2<br />
5/<br />
12h/L.<br />
and<br />
~ λh<br />
/ L .<br />
=<br />
0.<br />
0025<br />
of<br />
L<br />
+<br />
and<br />
beam size : θ<br />
δθ<br />
θ<br />
equal<br />
min<br />
2<br />
2<br />
~ 1.<br />
5h<br />
/ L
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