Ph.D. thesis (pdf) - dirac

6.2. Sound speed and attenuation 103
way up to 4 nm −1 , and bends after this (figure 6.2.2). Though this is difficult to
determine precisely with the relatively scarce number of Q-values.
12
10
8
ω [meV]
6
4
2
0
0 2 4 6 8
Q [nm −1 ]
Figure 6.9: The dispersion of cumene at T=160 K at ambient pressure and at 300
MPa. The dashed lines are guides to the eye. A few of the spectra are shown in
figure 6.10.
Int [arb. units]
120
100
80
60
40
20
0
−15 −10 −5 0 5 10 15
ω [meV]
Int [arb. units]
120
100
80
60
40
20
0
−15 −10 −5 0 5 10 15
ω [meV]
Figure 6.10: S coh (Q, ω) of cumene at Q =4 nm −1 at T=160 K and ambient pressure
(left) and 300 MPa (right). The full blue line illustrates the fit to equation 6.1.2. The
red curve shows the inelastic signal before convolution with the resolution function
(second term of equation 6.1.1) .
In figure 6.11 we show the sound speed, calculated as ω/Q at Q=2 nm −1 and
Q=4 nm −1 respectively, as a function of temperature and at ambient pressure as
well as at 300 MPa. The figure confirms that the dispersion is close to linear almost
up to Q=4 nm −1 . The speed seen at Q=4 nm −1 is systematically slightly lower, the
beginning of the deviation from linear dispersion, but the sound speed determined
from the two Q-values is the same within error-bars 1 .
The sound speed decreases with increasing temperature in the melt at atmospheric
pressure, while the sound speed at 300 MPa essentially is temperature independent
over the entire temperature range (figure 6.11). It is moreover striking that the
1 The fit for cumene at 2 nm −1 T =142 K and atmospheric pressure appears to be unreliable. It
is an outlier and the result is not robust to a change of fitting program.