Chirality, birefringence, and polarization effects inα-quartzstudied by resonant elastic x-ray scattering

Abstract

We show that enantiomers are extremely sensitive to the quality of the light polarization in resonant elastic x-ray scattering experiments. In α-quartz, the (001) reflection shows a very strong sensitivity to a small fraction of linear component included in nominally circularly polarized light. This fraction induces an important phase difference between the angular dependence of the recorded intensity from each enantiomer. We are thus able to model all aspects of the resonant scattering and determine the dominant physics, extract the crystal chirality, and obtain very precise values for the Stokes polarization parameters. Effects of birefringence and of higher-order electric transitions are also quantified and it is shown that in comparison they are negligible.

Structural chirality of β -Mn

“…154 with l = 1. These findings are consistent with experiments, to a very good approximation, and they illustrate the direct correlation between crystal chirality and the intensity of space-group forbidden Bragg spots picked out by circular polarization in the primary beam [12]. In addition, dependence of ϒ(0, 0, l) on the azimuthal angle faithfully mirrors the threefold rotation symmetry.…”

“…Their content is trivial in the present case, however, since multipoles are evaluated for the Mn K edge.) Alternatively, multipoles can be estimated from a tried and tested simulation program of electronic structure [12]. Henceforth, we adopt a shorthand (μη) for the scattering amplitude F μη .…”

“…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.…”

Quadrupole moments in chiral materialDyFe3(BO3)4observed by resonant x-ray diffraction

“…5, and depend on the x-ray energy differently to each other. 26,27 Here we introduce two parameters ν = ±1 and λ = ±1. The parameter ν denotes the crystal handedness, namely ν = +1 for the right-handed space group #152, and ν = −1…”