Modern Polymer Spect..

108 3 Vibrational Spectra as a Probe of Structurtil Order
K
DIAMOND r-x
Figure 3-6. Example of lattice dyiiamical calculations on 0-bonded tridimenional crystals with
short range interactions. Dispersion curves for cubic diamond along the r + (K) i X symmetry
direction. Experimental points from neutron-scattering experiments; dispersion curves from least
squares frequency fitting of a six parameters short range valence force field (from [60]). The Raman
active phonon is the triply- degenerate state indicated with r;, near 1300 cm-'. Notice that at k # 0
the degeneracy at is removed because of the lowering of the symmetry throughout the whole BZ.
Notice also the three acoustic branches for which 1' - 0 at k i
r.
techniques (e.g., refs. [16-19]). Our aim is to present here methods for extracting
from the experimental data the maximum amount of information on structure and
properties of these relevant materials.
The next step in our analysis is to define the experimental observables predicted
by lattice dynamics. The spectroscopic selection rules are very restrictive and, of the
very many phonon frequencies calculated, very few can be directly observed experimentally
[ 16- 191 in the optical vibrational spectra.
First, only phonons with k = 0 can interact with the electromagnetic wave; thus,
only the fundamental frequencies at the centre of the Brillouin zone in k space are
potentially infrared or Raman active. Second, further restrictions on the spectroscopic
activity are introduced by the symmetry of the polymer chain. Once the