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.