Theory of X-ray reflection broadening for textures with double-axis averaging: from semicrystalline polymers exhibiting twisted lamellar growth to discotic liquid crystals

It is shown that textures with double-axis averaging similar to the a-texture, or Keller-Machin Type I texture, are not specific to semicrystalline polymers exhibiting twisted lamellar growth. In this work, such texture is observed in extruded fibers of a typical discotic molecule, trans-diC₆₀-Zn porphyrin. Experimentally, these textures can be detected from the characteristic `comma'-like azimuthal profiles of the non-equatorial diffraction peaks in two-dimensional X-ray patterns. Analytical expressions for the azimuthal intensity distribution are developed, which are in good agreement with the experiment. In the proposed generalized coordinates, the diffraction peak shape becomes universal. This provides a simple means of checking the closeness of the sample morphology to the a-texture from just one two-dimensional pattern, without constructing the whole X-ray pole figure.