X-Ray Fluctuation Correlation Analysis: Single-Particle Structure And Short-Range Orientational Order

Spatial correlations of X-ray scattering intensity have been applied in determining (1) the structure of single particles, and (2) local orientational order in disordered systems. While the mathematical treatment of diffraction data is almost identical in both cases, vastly different theories have been used to interpret the results in the two regimes. In (1), theories presented by Kam, Kirian, Saldin, and co-workers begin with the assumption that interference effects can be neglected in dilute systems. Interference effects at finite densities were not studied. On the other hand, in (2), the theory presented by Wochner, Altarelli, Kurta, and coworkers explicitly accounts for interference effects in dense systems. However, in this theory, physical interpretation of the data is difficult, and has progressed only slightly beyond phenomenological descriptions. We have developed an overarching 2D theory for intensity correlation analysis, merging ideas from theories in both (1) and (2), with mathematical simplicity close to Kirian's theory. A book-keeping device has also been developed, in which intensity correlations are represented by a graph expansion. Ensembleaveraging rules have been laid down to enable the calculation and interpretation of individual contributions to signal and noise. Key results on the effects of interference in single-particle structure determination have been verified in simulations. Through our new theory, we have also performed a preliminary assessment of the feasibility of studying orientational order in ambient water