Neutron Scattering

(15 .3)
T ß ( E)=T ô exp
E
k,T
- (E )21
g ( E) - exp - EO (15 .4)
due to the disorder in the material the activation energies E are distributed around an average
value Eo . For the distribution function in general a Gaussian is assumed .
Empirically it is found that the width a(T) decreases with increasing temperature . Though
such processes have been investigated well by spectroscopic techniques, their molecular
origin is still unclear . Here QENS with its ability to provide space time resolution on the
proper scales contributes to a further exploration of the molecular mechanisms behind these
relaxations .
15 .2 .1 Dynamic structure factors
We commence with the derivation of the dynamic structure factor for the ß-process which we
consider as a hopping process between two adjacent sites . For such a process the self
conelation function has been derived in the lecture on quasielastic scattering, it is given by a
sum of two contributions .
sm (Qd)
1+
Qd
+ 2
Cl
s
QQd)J
expC
T2E)J
(15 .5)
Sel
Sine?
Here d is the distance between the two sites and T(E) is the jump time conesponding to an
activation energy E . The complete scattering function is obtained in averaging Eq .[15 .5] with
the barrier distribution function g(E) obtained e .g . by dielectric spectroscopy. The Q-
dependence of the two contributions to Eq .[15 .5] is displayed in Fig .15 .2 as a function of
Q(d = 1.5A) . From the oscillation of bottr contributions with Q the jump distance may be
obtained . The associated time scale may be found from the time decay ofthe inelastic part .
15-4