Neutron Scattering

The scattering function of a polycrystal is obtained by averaging over all crystal orientations
S(Q, w) - 1 P
~rüw 2 +112
For small momentum transfers Qs k « 1 one eau expand f (Q) and obtains
The second relation allows an interpretation
dependence of the linewidth P - T .
.S2
P = 2Q2 6-F = 2Q 2 D (17 .22)
of the macroscopic diffusion coefficient D of
(17 .5) by the microscopie jump rate . While for small Q the macroscopic behaviour with the
Q2 dependence of the linewidth is observed the data at large Q show the elementary step of a
diffusion process . The fig . 17 .4 shows results for H in Pd .
Transport jumps are thermally activated and follow an Arrhenius law
E
7 = 7oexp(-,) (17 .23)
kBT
From this relation the barrier height between neighbour sites is obtained from the temperature
17 .2.4 More complex cases
More than one sublattice
For bec metals (fig . 17 .3), intermetallic compounds or metallic glasses one finds non equivalent
hydrogen sites with different coordination numbers and jump rates . In case of bec lattices
protons may occupy octahedral or different types of tetrahedral sites . The scattering function
requires the Integration over the many possible different starting configurations . S(Q, w) consists
now of a number ofLorentzians with different widths and partly rate dependent intensities
[3] . The formalisme is more complex but basically identical .
Blocking
With increasing hydrogen concentration the diffusion changes since somejump directions may
be blocked by a hydrogen neighbour . "Blocking" leads also to an increased probability ofback
jumps, since the starting site is with certainty empty after thejump .
Phonon-assisted Ibnnelling
In some cases like NbHo .o2 the temperature dependence of the diffusion coefficient deviates
from classical behaviour. The observation of an increasedjump rate at low temperature lead to
the idea of "phonon-assisted tunnelling" : phonons of suited symmetry can increase temporarily
the distance between the atours of the kost lattice which determine the jump barrier . The
17- 8