Neutron Scattering

Figure 7 The plane in reciprocal space spaxmed by the (100) and (011) vectors for a fcc-lattice ; the
scattering triangle indicates the observation of A-modes .
[111]-direction which is a three-fold axis of the lattice .
'T'his behavior is a simple example
of the general relation between crystal symmetry and the phonon dispersion .
The crystal
symmetry yields constraints for the phonon modes which may be necessarily degenerate
at certain points or - like in the Ne-structure - along a direction . In the case of more
complex structures it is essential to profit from the predictions of the symmetry analysis .
The [110]-direction represents only a two-fold axis since [1-10] and [001] are not identical,
as consequence the corresponding transverse acoustic branches are not equivalent .
In addition figure 6 shows that at X=(100)=(011) A and E-branches are coinciding,
which may be explained due to the chape of the Brollouin-zone .
Figure 7 presents the
plane of the reciprocal space spanned by (100) and (011) ;
one recognizes that starting
at the zone-center, F, in the figure (133), in the [100]-direction one will reach the zoneboundary
at (233)-(100)=X . Similar, one will reach this point when starting at the
neighboring point (222) in [011]-direction .
However, in this path one finds the border of
the Brillouin-zone earlier and continues the last part on the zone boundary .
(100) and
(011) are equivalent points in reciprocal space ; they are connected by a reciprocal lattice
vector, (-1 1 1) .
For the phonon branches we conclude that 0- and E-branches have to
coincide . 'T'he symmetry further determines which branches coincide : for example the
longitudinal E-brauch with the transversal A-brauch .
Again, similar considerations in
more complex systems may decisively contribute to the identification of the branches .
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