ИСТИНА

The majority of known crystals are chiral and may exist in the right or left configurations related by inversion. For many applications one should know the absolute atomic structure of chiral crystals. X-Ray methods used to distinguish right and left configurations are based on anomalous x-ray diffraction on heavy metals nuclei [1, 2]. But if a crystal consists of light atoms or all atoms in a crystal are the same, we need a new way. We propose a new method to determine the absolute configuration of any crystals, based on the azimuthal asymmetry of multiple scattering. In the X-ray scattering the intensity of each reflection is composed of intensities of the main two-wave reflection and a variety of three-wave (renninger's) contributions. The main contribution is not sensitive to the chirality and does not change when the crystal rotates around the azimuthal axis because of Friedel law: |F(hkl)|= |F(-h-k-l)|. But three-wave contributions are sensitive to chirality and do not rely on the imaginary parts of atomic scattering factors, and the azimuthal dependence of their intensity is different for the right and left configurations. Thus, in order to distinguish right and left crystal configurations, it is necessary to measure the three-wave azimuthal dependence and compare it with the theoretical calculations, which are all reliable and model independent. Measurements with circular polarized X-ray radiation are available now at the modern synchrotrons and can be realized at the “forbidden” Bragg reflections which do not contain strong two-wave contributions. The efficiency of this method was checked during the experiment on the ESRF's ID12 beamline. We have studied the right-handed and left-handed samples of SiO2 (quartz, space groups P3121 and P3221) and measured the azimuthal Renninger plots for the forbidden 001 reflection with the right and left circular polarizations of incident radiation. So we obtain the chiral asymmetry ratio (Ileft-Iright)/ (Ileft+Iright) as function of azimuthal angle. To exclude resonant contributions, we have choosed the beam energy 4.5 KeV (far from the absorption edges of Si and O). The measured azimuthal dependence of the asymmetry ratio is different for the right-handed and left-handed quartz in consistence with theoretical prediction and allows to find out the absolute atomic configuration of each sample. [1] J.M. Bijvoet, A.F. Peerdeman, A.J. Van Bommel, Nature 168 (4268): 271-273 (1951).
[2] H. D. Flack, Acta Crys., A39: 876 881 (1983).