Neutron Scattering

energy transfers (gains) structures in the spectra are visible that stem from molecular and
lattice vibrations . Note the second left scale in combination with the dashed fine that
illustrates the strongly nonlinear relation between energy and time-of-flight . For energy
gains AE » 1BT the scattering energy dies out due to the exponentiel Boltzmann factor .
At ambient temperature 1BT is equivalent to 25meV . Well above that energy gain the
unavoidable virtually constant background due to "frame overlap" may be determined .
2 4 6 0 0 .002 0 .004 0 .006
Flugzeit/ms
Flugzeit/s
Figure 10 .5 : Left : TOF-spectra from liquid water at ambient temperature for different
scattering angles between 30° and 140° . Parameters : A o = 0 .onm, AT = 18ps, L = 3 .05m,
N = 512 . Right : TOF-spectrum from imidazole (C 4H4NH) as crystalline solid at 300K
(the dashed fines displays the saine data scaled by x0 .1) and as melt at 403K at a
scattering angle of 95° .
Technically a TOF spectrum is accumulated at a fixed scattering angle for each detector .
That corresponds to the situation of the scattering triangle as depicted in fig . 10 .1 . A
glimpse on this figure makes clear that different momentum transfers Q and Q (depending
Le -
on energy transfer) for elastic and inelastic scattering have to be assigned to the different
time channels of the histogram from one specific detector .
modulus Q as for the direction of Q .
That applies as well for the
The sequence of curves in the left figure 10 .5 shows
the values of Q as function of scattering angle (different curves) and time channel .
property that the values become very similar for large energy gains -also expressed by
10- 8
The