Ph.D. thesis (pdf) - dirac

7.2. Elastic intensity and mean square displacement 125
1.4
1.2
1
Q=1.96 A −1
Int / Int (T=0K)
0.8
0.6
0.4
0.2
0
0 50 100 150 200 250 300 350
T / [K]
Figure 7.2: The incoherent intermediate scattering function of DBP as a function of
temperature at atmospheric pressure (full line) and at 500 MPa (diamonds).
and 〈u 2 〉 can hence be found from the slope in a plot with ln(I) versus Q 2 . Figure 7.3
illustrates the Q and the temperature dependence of the measured elastic signal. It
is seen that there is a small systematic deviation from the Q 2 behavior, with a peaklike
feature around Q = 1 Å −1 . This could be due to the coherent contribution of
the scattering. In order to cancel this contribution, we assume that the mean square
displacement is zero when the temperature is zero, and normalize the Q-dependent
intensities at all temperatures to the low temperature limit of the Q-dependence.
Apart from this small systematic deviation it is seen that the Q 2 dependence is
followed even at temperatures in the range 1.2 T g . However, this is not true at
even higher temperatures, which means that the Gaussian approximation becomes
inadequate.
7.2.2 The mean square displacements
Figure 7.4 shows the mean square displacement of DBP at atmospheric pressure and
at 500 MPa. The mean square displacement increases linearly with temperature
at low temperatures. The slope gradually increases at higher temperatures. The
departure from linear is smooth and starts well below T g (P) both at atmospheric
pressure and at elevated pressure.
The mean square displacement of cumene at atmospheric pressure and 500 MPa is
displayed in figure 7.5. A linear increase with temperature is seen almost up to T g
and an increase in slope in the vicinity of T g .