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

Figure 7

Fourier spectra ⟨𝐶^𝑛_𝑞1,𝑞2⟩_𝑀 calculated as a function of 𝑞₂ (𝑞₁=1.71Å⁻¹) for 1≤𝑛≤9, for a flat (a), (c), (e) and curved (b), (d), (f) Ewald sphere. (a), (b) Amplitudes |⟨𝐶^𝑛_𝑞1,𝑞2⟩_𝑀| calculated in dilute limit approximation of scattering (see (13)) from 𝑁=10 clusters, averaged over 𝑀=10⁴ diffraction patterns. (c), (d) Amplitudes |⟨𝐶^𝑛_𝑞1,𝑞2⟩_𝑀| calculated for the case of coherent scattering (see (12)) from a cubic sample of 800nm in size consisting of 𝑁=400 clusters, averaged over 𝑀=10⁶ diffraction patterns. (e), (f) Difference spectra ⟨𝐶^𝑛_𝑞1,𝑞2⟩^diff_𝑀 show the difference (e) between the spectra in (c) and (a), and (f) between (d) and (b). The insets in (e) and (f) show full size of the peaks attributed to the inter-particle contribution.

(a)

(b)

(c)

(d)

(e)

(f)