X-Ray Cross-Correlation Analysis of Disordered Ensembles of Particles: Potentials and Limitations

Figure 6

Fourier spectra ⟨𝐶^𝑛_𝑞⟩_𝑀 calculated as a function of 𝑞 for 1≤𝑛≤9, for a flat (a), (c) and curved (b), (d) Ewald sphere. (a), (b) Amplitudes |⟨𝐶^𝑛_𝑞⟩_𝑀| calculated in dilute limit approximation of scattering (see (13)) from 𝑁=10 clusters, averaged over 𝑀=10⁴ diffraction patterns. (c), (d) Difference spectra ⟨𝐶^𝑛_𝑞⟩^diff_𝑀 calculated in the dilute limit approximation for a distorted oxygen pentamer for 𝑁=10, and 𝑀=10⁴ (see text for details). All atoms in each pentamer cluster in the sample were randomly displaced by 5% of the O-O distance from the positions of a regular pentamer. The scattered intensities used for calculation of the spectra shown in Figures 6 and 7 are expressed in the units of classical electron radius squared, and the spectra were normalized by the number of particles 𝑁 in the system.

(a)

(b)

(c)

(d)