A smectic-A liquid crystal in three dimensions has been predicted to exhibit algebraic decay of the layer correlations rather than true long-range order. As a consequence, the smectic Bragg peaks are expected to be power-law singularities of the form q∥-2+η and q⊥-4+2η, where ∥(⊥) is along (perpendicular to) the smectic density wave vector direction, rather than δ function peaks. Observation of these phenomena requires very high instrumental resolution together with a resolution function with wings which drop off much more rapidly than q∥-2(q⊥-4). We show that these requirements may be met by using a three crystal x-ray spectrometer with multiple-reflection channel cut crystals as monochromator and analyzer. We find that the smectic-A Bragg peaks observed in the liquid-crystal octyloxy-cyanobiphenyl are indeed consistent with the predicted power-law singularity form. Furthermore, the explicit values of η required to describe the measured profiles are in accordance with calculations of η using the harmonic approximation with empirically determined splay and layer compressibility elastic constants. ©1980 The American Physical Society
Bibliographical noteCopyright (1980) by the American Physical Society.
Als-Nielsen, J. A., Litster, J. D., Birgeneau, R. J., Kaplan, M., Safinya, C. R., Lindegaard-Andersen, A., & Mathiesen, S. (1980). Observation of Algebraic Decay of Positional Order in a Smectic Liquid Crystal. Physical Review B, 22(1), 312-320. https://doi.org/10.1103/PhysRevB.22.312