Neutron Scattering

Figure 10 Schematic picture of a displacive phase transition occuring at the zone tenter and the
corresponding dispersion curve .
metry high temperature phase the black ion in the middle occupies a site with inversion
symmetry .
'This symmetry is broken at the phase transition due to the displacement of
the black ion .
The right part of figure 10 shows the corresponding dispersion curve, here
the polarization pattern of the F-mode corresponds to the static distortion belo-,v
the
transition temperature, T, .
The phonon frequency of this mode softens upon approaching
the phase transition and is, therefore, called a "loft-mode" .T'he structural instability,
however, tan be also seen in the dispersion quite above T, :
the frequency of the relevant
mode at P is lower than those of modes with q-values in the Brillouin-zone .
In addition to the phonon softening one expects a broadening of the line width in
frequency ; finally the width of the phonon mode may surpass its frequency . Such overdamped
modes may no longer be described in the harmonie approximation .
The best studied example for a zone-tenter phase transition may be found in the
ferroelectric transition in perovskites, for example Pb'T'i0 3 see figure 11 . In the low
temperature phase the anions are deplaced against the cations, Pb, Ti, the corresponding
phonon frequency vanishes almost completely.
This polarization pattern has a strong
polar character and is connected to the dielectric constant through the LST-relation . 'The
softening of the 'TO mode induces a divergence in the dielectric constant, which explains
the interest of the phenomena for technical applications .
A structural phase transition may also lead to an enlargement of the unit tell .
Here,
the equivalent atoms in neighboring tells are not displaced identically ;
a schematic picture
is given in figure 12, where neighboring black ions are shifting in opposite direction .
The
phonon mode associated with such a displacement pattern necessarily has a finite wave-
13-17