Neutron Scattering

Tau
Figure 5
Scattering triangle corresponding to the observation of a phonon mode with wave vector q
at the reciprocallattice vector T.
d2a - (27)s
(dQdE' ) - ( ~) 2vo
1 G j (q, Q) 1 2 (13 .10 .a)
~~~(s)
(13 .10 .b)
.(,rt,(wj«1) +1/2 +1/2) (13 .10 .c)
(13 .10 .(1),
with vo the volume of the reciprocal unit cell . Equation (13 .10) describing the intensity
of a one-phonon measurement at specific Q closely resembles the elastic structure factor
of the Bragg reflection intensity, a part of expression (13 .10) is called dynamic structure
factor . 'The intensity is given by the sum over all reciprocal lattice and all wave vectors ;
however only the combination q+? = Q may contribute due to the 6-function in (13 .10 .4) .
The second b-fonction in (13 .10 .4) reflects the law of energy conservation, however, one
has to take into account that the scattering processes may lead to a creation as well as
to an annihilation of a single phonon, corresponding to the upper and the lower signs
respectively. There are two more general factors determining the intensity of the phonon
observation by neutron scattering . The term (13 .10b) indicates, independently of all
other terms, that the intensity is inversely proportional to the frequency of the mode .
High energy modes are always more difflcult to observe than the low lying ones . Since
neutron experiments suffer front the low flux of the existing sources, this effect frequently
prohibits the study of the high energy part of the phonon dispersion . 'T'he term (13 .10 .b)
13-7