Quantitative analysis of the x-ray diffraction intensities of undulated smectic phases in bent-core liquid crystals

X-ray diffraction diagrams of undulated smectic phases in bent-core liquid crystals have been theoretically studied. The intensities of the reflections have been obtained for different layer modulations, and a general expression has been deduced for orthogonal cells in terms of the different harmonics of the distortion. The case of sinusoidal modulation is especially simple and has been studied also in oblique cells. High-quality x-ray measurements of three compounds reported in the literature have been analyzed as examples. In all cases it has been deduced that the modulation is sinusoidal and its amplitude has been easily obtained by fitting the experimental intensities. Equatorial (h0) reflections have been also considered to obtain information about the structure of defects at the maxima and minima of the undulation.