Neutron Scattering

site with possible neighbour sites . If all sites are equivalent there is a unique characteristic
residence time 7 = 7k . P(r, t,) represents directly the correlation function Gs (r, t) . With the
initial condition
P(r, 0) = d(r) (17.16)
the infinite system of coupled differential equations (17.15) is solved by Fourier transformation
. FT of with respect to space leads to the intermediate scattering function
The initial conditions I(Q, 0) = 1 means that the proton exists somewhere in the sample . We
make the exponential ansatz
with
~tI (Q, I) = zT ~
( CXP(-iQSk)I
(Q, t) - 1(Q, t))
k=1
I(Q t) = exp(-f (Q) )
f (Q) = Z
~(1 - e~cp(-zQSk))
FT in time yields as scattering function a pure Lorentzian
1 f(a)
9T W2 + (
T
) .
(17.20)
The lack of an elastic term means, that the proton never returns to its starting point .
Figure 17 .4 : Q-dependence of the quasielastic linewidth in a PdH,, single crystal in (100) und
(110) direction . The data confirm a diffusion on octahedral interstitial sites .
17- 7