Ph.D. thesis (pdf) - dirac

144 Boson Peak
the Qout
Q in
factor (see equation 4.3.17 ). INX is moreover used for correcting for the
different detector efficiency by normalizing to the signal of a vanadium sample, it
performs corrections for sample absorption, and subtracts a measured background
signal.
Subtraction of the empty cell
The signal of the aluminum cell is negligible as compared to the signal of the hydrogenated
sample. The procedure used for subtraction is therefore without significance
for the final result. The pressure cell on the other hand, gives a significant signal
(see also the discussion in 7.1.2). In figure 8.1 we illustrate the raw signal of sample
plus pressure cell along with the signal of the pressure cell 1 .
We are mostly interested in the energy region 1 meV - 10 meV. The cell signal in this
region is a flat background with considerable lower intensity than the signal of the
sample. The intensity of the cell signal becomes comparable in order of magnitude
at energies somewhere around 15 meV. We therefore conclude that the result after
subtraction of the cell is reliable up to ∼ 15 meV, while we exclude higher energies
from the analysis. The elastic signal is also shown in figure 8.1. Here we see,
consistent with the backscattering data, that the high pressure cell contributes with
about half of the measured intensity.
8.1.3 Determining S(ω) and g(ω)
The discussion of the time of flight data in this chapter is based on S(ω) obtained by
normalizing to the elastic intensity and summing over all measured angles. In the
following section we justify this procedure by showing that it gives less scattered data
than interpolating to constant Q before summing, while the results are equivalent.
The data are interpolated from the measured I(θ, ω) to the I(Q, ω) using the program
IDA. We neglect coherent scattering which means that the measured intensity
is proportional to the incoherent dynamical structure factor:
I(Q, ω) = N σ inc
4π S inc(Q, ω) (8.1.1)
where N is the number of scatterers and σ inc is the incoherent scattering cross
section (see equation 4.3.17 and recall that the Qout
Q in
factor was corrected by INX).
1 The presence of the sample gives a “shadow” and hence less scatter (∼ 10%) from the cell, in
the cell+sample situation as compared to the empty cell alone. The cell signal shown in figure 8.1
has been corrected to take this effect into account.