Interpretation of a Specific Point in the Relationship between Zero-Angle Intensity and Contrast Observed by X-ray Small-Angle Scattering

The iso-zero-angle-intensity point (abbreviated as isoZAI point) is a specific point at which X-ray zero-angle intensities of samples with different structures take a constant value. The isoZAI point was first observed in X-ray contrast-variation studies of a homologous series of micelles. The condition for appearance of the isoZAI point has been theoretically derived by consideration of samples with inhomogeneous internal structure. The condition is given by

where ν_ij and ρ_ij are the volume and electron density of jth internal domain of the ith sample (1 ≤ i ≤ N, 1 ≤ j ≤ M), respectively. ρ₀^* denotes the position of the isoZAI point on the electron-density scale. The isoZAI point was found to give useful information for analysis of X-ray or neutron small-angle scattering data measured by the contrast-variation method.