Ph.D. thesis (pdf) - dirac

8.2. The origin of the excess modes 149
this as a linear function of Q 2 , at fixed ω, will in the ideal case give ln(g(ω)) at the
origin and − 〈u2 〉
3
as slope. However, the Q 2 -dependence is only found in the data at
high Q, moreover, the 〈u 2 〉 found at different energies is not the same. The result of
this procedure is therefore sensitive to the Q-range used. When only high Q’s are
used then it gives the same result as the constant Q or summing over angles, which
we discussed in the previous section.
A last method is to extract the DWF and the Q-independent intensity factors,
exp(−〈u 2 〉Q 2 ), from the elastic intensity and determine g(ω) as the slope of the Q 2
dependence of the left hand side of the below:
S inc (Q, ω)ω
exp(−〈u 2 〉Q 2 )n(ω) = Q2 g(ω). (8.1.6)
It is not possible to obtain any reasonable result from this procedure. This is a
natural consequence of the “incorrect” Q dependence in figure 8.3.
The deviation between the actual Q-dependence and the theoretical expected result
could be related to an error in the subtraction of the high pressure cell signal. A
relatively small error, which will not affect the measured inelastic signal will still
effect the elastic signal and therefore the Debye Waller factor determined from the
latter. However, we have similar problems with the data measured in aluminum
cells. A more likely explanation is that the Q-dependence is distorted due to multiple
scattering and multi-phonon scattering. It is also possible that the coherent
contribution plays a role.
8.2 The origin of the excess modes
In this section we present and analyze the pressure dependence of the boson peak
in PIB3850 at T = 140 K which is well below the glass transition temperature
(T g ≈ 195 K) at atmospheric pressure. We also include the pressure dependence
of Brillouin light scattering data from Begen et al. [2006 b]. This combination
of data obtained by three different experimental techniques allows us to make a
comparison of the pressure dependence of the sound modes and the boson peak
position in an organic system, including sound modes in the boson peak energy
region as well as both shear and longitudinal modes. The neutron data allow us
to analyze the influence of pressure on the shape and intensity of the boson peak
without the uncertainty from the unknown frequency dependence of the light to
vibration coupling factor which influences the Raman spectra. Combining this data
with literature data on the density of the sample we are moreover able to make the