Neutron Scattering

dynamics of ionic compounds with the long range Coulomb-interaction, tan only be poorly
described by such a model .
Even rohen parameterizing the Coulomb-potential V (r)
x ~ by the charges,
Zd, Zd,, in order to deduce the respective force constants, the problem of the long range
persists . It is not possible to tut the rum at a certain distance, rince the rums (Io not
converge . The satisfying solution of this problem consists in the Ewald-method [1] .
The Coulomb-potentials in an ionic crystal yields an attractive potential, which har
to be compensated by a repulsive one .
If the electron clouds of two ions of opposite
charge Start to overlap upon decrease of their distance, this repulsive potential will increase
rapidly. One may describe this interaction by a Born-Mayer-potential V(r) =
B-exp(-rlro ), inducing only two parameters for one type of ionic pair, B and r o . Amongst
the varions extensions of this type of model, called "rigid ion", we mention only the Shell
model, rohere the polarizability of the ions is described by a Separation between an electron
cloud (the Shell) and the tores .
'There are many different ways to couple the tores
and the clouds by force constants .
In order to prepare an inelastic neutron scattering study on the lattice dynamics of
a complex material, even a simple and un-adapted model may be helpful, as long as the
crystal structure and, therefore, the symmetry is correctly entered . By symmetry, degenerations
are fixed for certain points or even for unes in reciprocal space, and frequently the
structure factors follow some inelastic extinction rules .
In principle these predictions may
also be found by a careful analysis through group theory ; however, the use of a simple
model which does not need to describe the frequencies well is much less time demanding .
Some of these aspects have already been illustrated for the example of the NaCI structure
.
Concerning the dynamic structure factors one may add, that one will observe the
optical modes close to P best at the odd reciprocal lattice vectors (for example (333) )
independently of the forces involved .
13 .2 .3 Structural phase transitions and soft mode behavior
Structural phase transitions form still a topic of actual interest, where information
about the underlying microscopie mechanism may frequently be achieved only by inelastic
neutron scattering .
In figure 10 one finds the representation of a fictive structural phase transition in a
two-dimensional crystal structure with two atoms in the primitive tell .
In the high sym-
13- 16