Direct reconstruction of the two-dimensional pair distribution function in systems with angular correlations
I. A. Zaluzhnyy, R. P. Kurta, A. P. Menushenkov, B. I. Ostrovskii, and, I. A. Vartanyants
TL;DR
This paper introduces a novel x-ray scattering method for directly reconstructing the 2D pair distribution function in systems with angular correlations, enabling detailed analysis of positional and bond-orientational order.
Contribution
It derives new relations between structure factor and PDF for quantitative real-space analysis of order in 2D systems, demonstrated on liquid crystal phase transitions.
Findings
Quantitative analysis of positional and bond-orientational order.
Real-space positional correlation lengths in different directions.
Application to liquid crystal phase transition study.
Abstract
An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of positional and bond-orientational (BO) order in real space. We apply this approach in the x-ray study of a liquid crystal (LC) film undergoing the smectic-hexatic phase transition, to analyze the interplay between the positional and BO order during the temperature evolution of the LC film. We analyze the positional correlation length in different directions in real space.
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