ИСТИНА

The resonant X-ray diffraction in various quartz phases is studied theoretically and compared with available experimental data. From the symmetry analysis all non-zero components of the scattering tensors have been found. Then they are calculated either with FDMNES program or with the full-potential ab initio XANES calculations (Taillefumier et al., Phys. Rev. B 66, 195107, 2002) which are extended to the resonant diffraction at Si K-edge. We consider both chiral (low-silica and high-silica and non-chiral (cristobalite and stishovite) phases. Calculations are performed on supercells including the core-hole on the absorbing atom. All the tensor components of the silicon atomic scattering factor are found as functions of x-ray energy E and then the structure factors of reflections are obtained using conventional crystallographic formulas. It is shown that the main term is dipole-dipole whereas dipole-quadrupole and quadrupole-quadrupole terms are at least two orders of magnitude smaller. The dipole-dipole anisotropy of the atomic factor is significant only up to 30 eV above the edge. The “forbidden” reflections in low-quartz and high-quartz (screw-axes 31, 32 and 62, 64) are found to be chiral even for the dipole-dipole scattering (Dmitrienko, Acta Cryst A 39, 29, 1983): their intensity and polarisation properties depend on the sign of the screw-axis. Our calculations show that superposition of chiral and non-chiral terms in the structure factor is very important for low-quartz. Our findings agree well both with available XANES data and with recent spectra of “forbidden” reflections in low-quartz (Tanaka et al., Phys. Rev. Lett. 100, 145502, 2008). Non-spiral phases of silica (cristobalite and stishovite) are also studied in details. In stishovite, the forbidden reflection 100 is the only accessible reflection at the Si K-edge. Therefore it is possible to observe it even in powder samples.