The sequential derivation of an expression that describes an X-ray natural circular dichroism (XNCD) signal in the most general case is performed. The obtained expression is used as a basis to consider XNCD signals and their structural origins in copper metaborate CuB2O4 crystals at an incident radiation energy near the K absorption edge of copper and lanthanum–gallium silicate La$_3$Ga$_5$SiO$_{14}$ crystals at an incident radiation energy near the K absorption edge of gallium. It has been demonstrated that the measurements of circularly polarized X-ray absorption spectra in combination with corresponding first-principle calculations provide an efficient method for studying the contributions of crystallographically non-equivalent atoms to the X-ray optical activity of crystals.
78.20.Ek Optical activity
78.70.Dm X-ray absorption spectra
$^1$Department of Solid State Physics, Faculty of physics, Lomonosov Moscow State University, chair of Condensed Matter Physics.\
$^2$FSRC “Crystallography and Photonics” of RAS