Neutron Scattering

For specular reflectivity measurements the condition 0=0' holds which is usually not true
for diffuse scattering experiments . The mean value of the wave vector transfer is given by
JQj= -sin (2)
(6 .3)
with the de Broglie wavelength of the neutrons k=hl(2mE) 1/2 . As it was mentioned before for a
small angle scattering experiment IQI has to be much smaller than the typical reciprocal
distance of the atours in the Sample. Therefore, ~ also bas to be Small. Depending on the
chosen wavelength the angle ~ is almost never larger than a few degees . For a surface
sensitive experiment, which is performed in reflection and not in transmission (sec Fig. 6.4),
this means that 0 and 0' are also small and positive .
Fig . 6 .4 : Sketch of the wave
vectors for a surface sensitive
experiment. The parameters of
the transmitted beam are
labeled with the index t. The
potential of air is denoted by
Vo that one of the Substrate
with V I .
From simple geometrical considerations the components of the wave vector transfer can be
deduced. They are defined by
2n
Qx =-(cos0'-cos0)
Q v = 0
2n
-(sin0'+sin0) (6 .4)
and can be used to estimate the accessible Q-range of surface sensitive experiments . At a
typical wavelength of the neutrons of about 0.2nm=2Â and angles not larger than 1 .0 degree
QZ would always be less than 0.1Â-1 . JQxj would even be restricted to 5 .10-4Â-1 . For
comparison: A simple cubic crystal with 3Â lattice spacing has a smallest reciprocal lattice
vector of 2.1Â-1 .
6 .5