Neutron Scattering

n, = 1- 8, + i(3, (6.19)
The effect of the absorption is shown in Fig . 6 .9 . It basically smoothes the sharp features of the
intensity close the critical angle and also restricts the penetration depth of the neutrons to finite
values .
The diffuse scattering is also modified in the regime of the total external reflection [8,9] .
In good approximation one gets
I,i (Qx>Qz)- tf(0)IzQzzexp ( -QZ6i ) sii(Qx)tf(0 , (6.20)
)z
for a single rough surface. For layer systems this expression becomes much more complicate.
Eq . (6 .20) shows, that the transmission functions of the incoming and the outgoing beam have
to be taken into account. The transmission function tf exhibits a maximum at the critical angle
(or the critical Qz, respectively, see Fig . 6 .9) because for incident angles 0 = 0, an evanescent
wave appears which runs parallel to the surface (0' = 0) [10] . Therefore, the diffuse scattering
also bas maxima called Yoneda wings at the positions 0=0, and 0'=0, (sec Fig .6 .10) .
4
Figure 6 .10 : Diffuse scattering
scan at fixed Qz . The symbols
correspond to the Born
approximation (dashed line in
Fig. 6.8) . The solid line displays
0
the better approximation
2
including the scattering effects
due to the total external reflection
C
o,
at 0=0, and 0'=0, . They are
0 1
visible as the Yoneda-maxima at
IQXI=0.0032 .E- ' .
The peak at the center is the
0 -4 -2 0 2 4 specular reflected intensity (0=0') .
Qx [0 .001Ä - ']
In summary, the optical properties of the sample affect the scattering only if the incident
or the exit angle is comparable or smaller than the critical angle which is usually smaller than
6 . 14