Dynamic properties and layer displacement-layer displacement correlation functions of the smectic-A films on a substrate are investigated. The eigenfrequencies spectrum and eigenmotions of the film are calculated within the framework of a discrete model. It was found that the static as well as dynamic properties of freely standing and solid supported smectic-A films differ significantly. In particular, the acoustic mode is absent in the films on a substrate and the surface tension is not essential for the film dynamics. The correlation length of the spatial layer displacement correlation functions is finite for films on a substrate in contrast to the free standing films. An effect of thermal fluctuations on the specular and diffuse x-ray scattering was analyzed.

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A theoretical description of free surface motion is presented for a semi-infinite unbounded smectic-A (Sm-A) liquid crystal. The characteristic equation is analyzed in a wide range of frequencies and wave numbers. It is shown that at low frequencies the surface eigenmotion is a wave of the second sound type. The wave velocity is twice that of the maximum second sound velocity in the bulk phase. This Rayleigh mode may be excited and detected as surface transverse waves. At high frequencies the surface eigenmotion is a damping viscous mode. The spectral intensities of the surface displacement fluctuations are presented in rather simple form for separate areas of wave numbers and frequencies. These results may be used to describe light scattering experiments. It is shown that the surface tension is negligible when describing Sm-A surface eigenmotions, in contrast to ordinary liquids. At the same time the surface tension is sufficient for surface displacement fluctuations at low frequencies.

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Specular reflectivity measurements of artificial multilayers often exhibit a broadening of high order Bragg peaks and an intensity drop off that is slower than expected from the q −4 Fresnel dependence modified with a static Debye-Waller factor accounting for the interfacial roughness. This behaviour is described on the basis of a model that takes into account the finite size of the detector slit, which determines the instrumental resolution. The amplitude of the interface roughness as well as the in-and out-of-plane correlation lengths strongly affect the shape of the specular x-ray spectra. Information about in-plane and out-of-plane correlated roughness can be obtained, therefore, not only from diffuse scattering data but also from the quasi-specular reflectivity by relaxing the instrumental resolution. Moreover, for systems with short correlation lengths, quasi-specular reflectivity scans are more informative than rocking curves across Bragg reflections. The model is applied to the interpretation of x-ray scattering results on two multilayer systems: MgO(0 0 1)/[Fe(2 ML)/V(16 ML)] 30 and Si/SiO 2 /[CoFeB(3 nm)/MgO(1.5 nm)] 15 . The simulation of the experimental reflectivity scans properly describes the broadening of the higher order Bragg peaks, the damping of Kiessig fringes, and the increased intensity at higher scattering vectors as compared with the purely specular reflectivity.