Coherent x-ray scattering and dynamics of fluctuations in smectic-A and crystal-B films: continuous model

We present a theoretical study of the dynamic displacement-displacement and intensity-intensity (for coherent soft x-ray scattering) correlations in Sm-A as well as Cr-B free-standing films. The work is based on a continuous hydrodynamic model that allows one to calculate efficiently the dynamic correlation functions and considerably simplifies earlier analyses of finite-size and surface effects in Sm-A films. The model is extended to Cr-B films. We show that despite the crystalline order, the Cr-B film is a strongly fluctuating system, which is due to an abnormally small shear elastic constant. An easy-shear approximation is developed to describe the fluctuations in the Cr-B phase. We predict nonmonotonic behavior of the intensity-intensity correlation function in both Sm-A and Cr-B films. The analysis can be applied to either coherent x-ray or conventional laser dynamic light scattering experiments.

Complex dynamic behavior of fluctuating smectic- A films as studied by scattering with coherent X-rays

Coherent dynamic x-ray scattering has been used to study the thermally excited layer fluctuations in freely suspended smectic films of the compound 4O.8. Using 8-keV x rays and films with a thickness around 0.3 &mgr;m we resolve relaxation times down to a few &mgr;s. A combination of damped and oscillatory behavior is observed for the layer undulations, which can be attributed to inertial effects. These are due to the surface contribution to the free energy which cannot be disregarded for thin films.