Soft modes and central peak in orientationally disordered crystals

The coupled dynamics of translations and rotations is studied with respect to mixed molecular crystals. At high temperatures the dynamic scattering law exhibits a Brillouin doublet which softens with decreasing temperature (fast orientational relaxation regime). In diluted molecular crystals of type ${\left(\mathrm{KCN}\right)}_c{\left(\mathrm{K}X\right)}_{1-c}$, $X=\mathrm{Cl}\mathrm{or}\mathrm{Br}$, the structural phase transition is suppressed and one reaches the slow orientational relaxation regime at low temperatures. Then the Brillouin doublet frequency passes through a minimum and increases again with decreasing temperature. At the same time a well-defined central resonance rises in the spectrum as a consequence of slowing-down orientational relaxation. The theory describes recent neutron-scattering experiments in mixtures by Rowe and Rush and recent Brillouin-scattering results by Satija and Wang.