Ph.D. thesis (pdf) - dirac

7.2. Elastic intensity and mean square displacement 123
0.2 mm giving a transmission of about 80%. This value is lower than one would
prefer for this type of experiment. However, the signal was weak already under
these conditions (see below), and it was impossible to get a reasonable signal with
a reduced sample thickness.
Along with the data from IN10 we include non-published data on glycerol obtained
prior to this work on IN16 [Frick and Alba-Simionesco, 2003]. IN16 is also a backscattering
instrument with almost the same energy resolution as IN10. However, IN16
has a larger flux and finer grid in Q because of a larger number of detectors. Another
advantage of this experiment is that it was performed using a niobium pressure cell.
This cell only goes up to ≈ 3 kbar, but has a much lower background signal.
7.1.2 Corrections
The raw data are total measured elastic intensities at 7 different Q values. The
preliminary treatment of the data was performed using the standard ILL software
sqwel. sqwel takes care of correcting for the different detector efficiency by normalizing
to the signal of a vanadium sample. sqwel moreover performs corrections for
sample self absorption and can subtract a measured background signal.
The aluminum cell gives a very small signal, and the subtraction of the empty cell
therefore has almost no effect on the final result. The situation for the pressure
cell, however, is quite different. The pressure cell gives as much elastic intensity as
the sample itself, and the cell subtraction procedure can lead to large errors in the
final result. We therefore subtracted the cell in an explicit procedure after using
sqwel. This allowed us to verify that the subtracted cell signal corresponded to the
total measured intensity at high temperatures where the sample liquid has no elastic
scattering. The high pressure data carries a low signal to noise ratio, due to the
relatively high intensity of the subtracted cell. The measured intensity of the sample
in the high pressure cell is moreover lower, because the sample exploits a smaller
part of the beam. Figure 7.1 illustrates the raw data (treated in sqwel, but with
no cell subtraction) from an atmospheric pressure and a high pressure experiment
respectively.
7.2 Elastic intensity and mean square displacement
The measured quantity, the elastic intensity, corresponds to the intermediate scattering
function at a given timescale as explained in section 4.3.10. The characteristic
timescale of the experiment is 1/δω ∼ 1 ns. The scattering is dominated by the