Determination of structural chirality of berlinite and quartz using resonant x-ray diffraction with circularly polarized x-rays

Abstract

Many proteins, sugars, and pharmaceuticals crystallize into two forms that are mirror images of each other ͑enantiomers͒ such as our right and left hands ͑chiral͒. Berlinite ͑AlPO 4 ͒ and low quartz ͑SiO 2 ͒ have enantiomers belonging to a space-group pair, P3 1 21 ͑right-handed screw͒ and P3 2 21 ͑left-handed screw͒. We use circularly polarized resonant x-ray diffraction to study structural chirality. Our results demonstrate that positive and negative circularly polarized x-rays at the resonant energy of berlinite ͑Al 1s edge͒ and low quartz ͑Si 1s edge͒ can distinguish the absolute structure ͑right or left-handed screw͒ of an enantiomer. The advantage of our method is that the measurement of only one space-group forbidden reflection is enough to determine the chirality. This method is applicable to chiral motifs that occur in biomolecules, liquid crystals, ferroelectrics and antiferroelectrics, multiferroics, etc.

Overview of Low-Temperature Heat Capacity Data for Zn2(C8H4O4)2.C6H12N2 and the Salam Hypothesis

“…In the model system [Zn 2 DABCO] 4+ , the R-form is most favorable due to the PVED [29,30], but it is currently unclear which symmetry of the chains built of {Zn 2 DABCO} units corresponds to the most energetically favorable state. The method of resonant X-ray diffraction with circularly polarized X-rays [33] or optical methods seem to be most preferable for use at low and extra-low temperatures.…”

Preferred Orientation of Quartz in Metamorphic Rocks from the Bergell Alps

“…According to an extensive comparative study of a large number of quartz single crystals by Frondel [45], both enantiomorphic modifications are equally abundant in nature, though local dominance of one enantiomorph may occur. Enantiomorphs cannot be resolved with diffraction techniques unless an exeptional experimental setup is used [46], and have not been taken into account in quartz fabric studies. Consequently, we attributed all investigated quartz to the right-handed spacegroup P3 1 21 (#152) while the left-handed spacegroup is P3 2 21(#154).…”

Structural chirality of β -Mn

“…Higher-order harmonic generation and Kikuchi diffraction in electron scattering have recently been added to the list of techniques for the determination of chiral structures [8,9]. Likewise, resonant x-ray Bragg diffraction is a proven technique by which to label chiral structures, and it is the central topic of the present study [10][11][12][13][14][15]. The technique is more selective than optical activity, which is allowed in 15 crystal classes, four of which are not enantiomeric.…”

“…The β-Mn form contains 20 ions per unit cell in cubic enantiomorphs P4 1 32 and P4 3 32. The attendant crystallographic complexity sets it aside from low quartz, tellurium, and berlinite (AlPO 4 ) with enantiomorphs that belong to trigonal P3 1 21 (right-handed screw) and P3 2 21 (left-handed screw), and resonant ions occupy sites with multiplicity three [8,[10][11][12][13][14]. Diffraction patterns and azimuthal angle scans (rotation of the diffracting crystal about the axis of the reflection vector) were measured with the energy of primary x rays tuned to K edges (1s) of Si and Al, for example.…”