RESUMO
A method to calculate the location of all Bragg diffraction peaks from nanostructured thin films for arbitrary angles of incidence from just above the critical angle to transmission perpendicular to the film is reported. At grazing angles, the positions are calculated using the distorted wave Born approximation (DWBA), whereas for larger angles where the diffracted beams are transmitted though the substrate, the Born approximation (BA) is used. This method has been incorporated into simulation code (called NANOCELL) and may be used to overlay simulated spot patterns directly onto two-dimensional (2D) grazing angle of incidence small-angle X-ray scattering (GISAXS) patterns and 2D SAXS patterns. The GISAXS simulations are limited to the case where the angle of incidence is greater than the critical angle (alpha(i) > alpha(c)) and the diffraction occurs above the critical angle (alpha(f) > alpha(c)). For cases of surfactant self-assembled films, the limitations are not restrictive because, typically, the critical angle is around 0.2 degrees but the largest d spacings occur around 0.8 degrees 2theta. For these materials, one finds that the DWBA predicts that the spot positions from the transmitted main beam deviate only slightly from the BA and only for diffraction peaks close the critical angle. Additional diffraction peaks from the reflected main beam are observed in GISAXS geometry but are much less intense. Using these simulations, 2D spot patterns may be used to identify space group, identify the orientation, and quantitatively fit the lattice constants for SAXS data from any angle of incidence. Characteristic patterns for 2D GISAXS and 2D low-angle transmission SAXS patterns are generated for the most common thin film structures, and as a result, GISAXS and SAXS patterns that were previously difficult to interpret are now relatively straightforward. The simulation code (NANOCELL) is written in Mathematica and is available from the author upon request.
RESUMO
Grazing-angle of incidence small-angle X-ray scattering (GISAXS) and high-resolution field emission scanning electron microscopy have been used to characterize the mesophase symmetry, orientation, and long-range order in PEO20-PPO70-PEO20 (Pluronic P123) templated mesoporous silica thin films on conducting gold substrates as a function of silica-to-ethylene oxide (Si/EO) block ratio and relative humidity (RH). The films are formed by dip-coating followed by evaporation-induced self-assembly under tightly controlled RH. The general evolution of the mesophase follows the trends that are expected based on shape factors due to swelling of the PEO block. However, changes in orientation of the nanostructure relative to the substrate and the degree of long-range order are found to depend on Si/EO ratio. These effects are likely due to the dynamics of evaporation and self-assembly. Generally, at Si/EO ratios lower than 3.29, the films contained regions where the nanostructure was not oriented relative to the plane of the substrate. However, for Si/EO ratios greater than 3.62, conditions were found where the nanostructure of the film was highly oriented relative to the plane of the substrate. This is true over the range of RH studied, independent of the nanostructure symmetry. For low Si/EO ratios at the highest RH levels, the films were composed of a mixture of spherical and cylindrical pores. At high Si/EO ratios and high RH levels, the films had a highly oriented R-3m nanostructure but displayed streaking perpendicular to the substrate in the Bragg spots on GISAXS patterns. This streaking is interpreted as faulting along planes parallel to the substrate.
