Ph.D. thesis (pdf) - dirac

8.2. The origin of the excess modes 153
10
8
ω [meV]
6
4
2
0
0 1 2 3 4 5 6 7
Q [nm −1 ]
Figure 8.7: The dispersion of longitudinal sound modes measured by IXS. Squares
are atmospheric pressure, circles 300 MPa. The full lines show the linear dispersion
corresponding to the low Q sound speed measured by light scattering. The dashed
lines indicates the position of the boson peak at the same pressures (higher energy
higher pressure). The dashed-dotted line shows the estimated πΓ (see text).
Ioffe-Regel limit
It is often suggested that the mean free path of the sound speed reaches the order
of magnitude of the wavelength, the Ioffe-Regel limit, at the frequency of the boson
peak position (e.g. references [Quitmann and Soltwisch, 1998; Schroeder et al.,
2004]). Such a general connection was most recently proposed by Ruffle et al. [2006]
(and contested by Scopigno et al. [2006]), who define the Ioffe-Regel limit by ω l = πΓ
where ω l is the frequency of the sound mode. In figure 8.5 we indicate the value of
πΓ based on the Γ-values estimated from on the IXS data. The sound attenuation
was found to be pressure independent, which is why it is only indicated by one line
(see section 6.2 for details).
The position of the boson peak at atmospheric pressure and at 300 MPa (interpolated
from the data in figure 8.5) are indicated by horizontal lines in figure 8.7. This shows
good agreement between the boson peak position and the Ioffe-Regel limit at both
pressures.